Finite Group Databasebeta

← C2×C109×#2424 #42152644

Subgroups — C2×C109×#2424 #42152644

Order 27904.

5898 conjugacy classes of subgroups.

The subgroup lattice has 1112 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#121×C109C211yesmaximal, characteristic, complemented
2C22×#121×C109C211yesmaximal, characteristic, complemented
3C22×#120×C109C211yesmaximal, characteristic, complemented
4C22×#120×C109C211yesmaximal, characteristic, complemented
5C22×C4×D4×C109C211yesmaximal, characteristic, complemented
6C23×C22⋊C4×C109C211yesmaximal, characteristic, complemented
7C109×#2424C2116yesmaximal, direct product factor
8C2×#396×C109C211yesmaximal, characteristic, complemented
9C2×#394×C109C211yesmaximal, characteristic, complemented
10C2×#394×C109C211yesmaximal, characteristic, complemented
11C2×#392×C109C211yesmaximal, characteristic, complemented
12C2×#390×C109C211yesmaximal, characteristic, complemented
13C2×#388×C109C211yesmaximal, characteristic, complemented
14C2×#386×C109C211yesmaximal, characteristic, complemented
15C2×#386×C109C211yesmaximal, characteristic, complemented
16C2×#385×C109C211yesmaximal, characteristic, complemented
17C26×C109C2211yescharacteristic
18C23×D4×C109C2211yescharacteristic
19C23×D4×C109C2211yescharacteristic
20C23×D4×C109C2211yescharacteristic
21C23×D4×C109C2211yescharacteristic
22C23×D4×C109C2211yescharacteristic
23C23×D4×C109C2211yescharacteristic
24C23×D4×C109C2211yescharacteristic, complemented
25C24×C4×C109C2211yescharacteristic
26C24×C4×C109C2211yescharacteristic
27C24×C4×C109C2211yescharacteristic, complemented
28C2×#121×C109—28no—
29C2×#121×C109—28no—
30C2×#121×C109C2218yescomplemented
31C2×#121×C109C2218yescomplemented
32C2×#120×C109—28no—
33C2×#120×C109—28no—
34C2×#120×C109C2218yescomplemented
35C2×#120×C109C2218yescomplemented
36C2×C4×D4×C109—28no—
37C2×C4×D4×C109C2218yescomplemented
38C22×C4⋊C4×C109C2211yescharacteristic, complemented
39C22×C4⋊C4×C109C2211yescharacteristic, complemented
40C22×C4⋊C4×C109C2211yescharacteristic, complemented
41C22×C4⋊C4×C109C2211yescharacteristic, complemented
42C22×C22⋊C4×C109—28no—
43C22×C22⋊C4×C109C2211yescharacteristic
44C22×C22⋊C4×C109C2211yescharacteristic
45C22×C22⋊C4×C109C2211yescharacteristic
46C22×C22⋊C4×C109C2211yescharacteristic
47C22×C22⋊C4×C109C2211yescharacteristic
48C22×C22⋊C4×C109C2211yescharacteristic
49C22×C22⋊C4×C109C2211yescharacteristic
50C22×C22⋊C4×C109C2211yescharacteristic
51C22×C22⋊C4×C109C2211yescharacteristic
52C22×C22⋊C4×C109C2211yescharacteristic
53C22×C22⋊C4×C109C2218yescomplemented
54C22×C22⋊C4×C109C2211yescharacteristic, complemented
55C22×C22⋊C4×C109C2211yescharacteristic, complemented
56C22×C22⋊C4×C109C2211yescharacteristic, complemented
57C22×C22⋊C4×C109C2211yescharacteristic, complemented
58C22×C22⋊C4×C109C2211yescharacteristic, complemented
59C22×C42×C109C2211yescharacteristic, complemented
60#396×C109C2218yescomplemented
61#394×C109C2218yescomplemented
62#394×C109C2218yescomplemented
63#392×C109C2218yescomplemented
64#390×C109C2218yescomplemented
65#388×C109C2218yescomplemented
66#386×C109C2218yescomplemented
67#386×C109C2218yescomplemented
68#385×C109C2218yescomplemented
69C2×#95×C109C2211yescharacteristic, complemented
70C2×#95×C109C2211yescharacteristic, complemented
71C2×#95×C109C2211yescharacteristic, complemented
72C2×#95×C109C2211yescharacteristic, complemented
73C25×C109—24no—
74C25×C109—24no—
75C25×C109—24no—
76C25×C109—24no—
77C25×C109—24no—
78C25×C109—42no—
79C25×C109—42no—
80C25×C109C2311yescharacteristic
81C25×C109C2311yescharacteristic
82C25×C109C2311yescharacteristic
83C25×C109C2311yescharacteristic
84C25×C109C2314yes—
85C25×C109C2311yescharacteristic
86C22×D4×C109—24no—
87C22×D4×C109—24no—
88C22×D4×C109—24no—
89C22×D4×C109—24no—
90C22×D4×C109—24no—
91C22×D4×C109—24no—
92C22×D4×C109—24no—
93C22×D4×C109—24no—
94C22×D4×C109—24no—
95C22×D4×C109—24no—
96C22×D4×C109—24no—
97C22×D4×C109—24no—
98C22×D4×C109—24no—
99C22×D4×C109—24no—
100C22×D4×C109—24no—
101C22×D4×C109—42no—
102C22×D4×C109—42no—
103C22×D4×C109—42no—
104C22×D4×C109—42no—
105C22×D4×C109—42no—
106C22×D4×C109D418yescomplemented
107C22×D4×C109C2314yes—
108C22×D4×C109C2314yes—
109C22×D4×C109C2314yes—
110C22×D4×C109C2314yes—
111C22×D4×C109C2314yes—
112C22×D4×C109C2314yes—
113C22×D4×C109C2314yescomplemented
114C23×C4×C109—24no—
115C23×C4×C109—24no—
116C23×C4×C109—24no—
117C23×C4×C109—24no—
118C23×C4×C109—24no—
119C23×C4×C109—24no—
120C23×C4×C109—42no—
121C23×C4×C109—42no—
122C23×C4×C109—42no—
123C23×C4×C109C2311yescharacteristic
124C23×C4×C109C2311yescharacteristic
125C23×C4×C109C2311yescharacteristic
126C23×C4×C109C2311yescharacteristic
127C23×C4×C109C2311yescharacteristic
128C23×C4×C109C2314yes—
129C23×C4×C109C2314yes—
130C23×C4×C109C2311yescharacteristic
131C23×C4×C109C2311yescharacteristic
132C23×C4×C109C2311yescharacteristic
133C23×C4×C109C2311yescharacteristic
134C23×C4×C109C2311yescharacteristic
135C23×C4×C109C2314yescomplemented
136#121×C109—232no—
137#121×C109—232no—
138#120×C109—232no—
139#120×C109—232no—
140C4×D4×C109—232no—
141C2×C4⋊C4×C109—24no—
142C2×C4⋊C4×C109—24no—
143C2×C4⋊C4×C109—24no—
144C2×C4⋊C4×C109—42no—
145C2×C4⋊C4×C109C2314yescomplemented
146C2×C4⋊C4×C109C2314yescomplemented
147C2×C4⋊C4×C109C2314yescomplemented
148C2×C4⋊C4×C109C2314yescomplemented
149C2×C22⋊C4×C109—24no—
150C2×C22⋊C4×C109—24no—
151C2×C22⋊C4×C109—24no—
152C2×C22⋊C4×C109—24no—
153C2×C22⋊C4×C109—24no—
154C2×C22⋊C4×C109—24no—
155C2×C22⋊C4×C109—24no—
156C2×C22⋊C4×C109—24no—
157C2×C22⋊C4×C109—24no—
158C2×C22⋊C4×C109—24no—
159C2×C22⋊C4×C109—24no—
160C2×C22⋊C4×C109—24no—
161C2×C22⋊C4×C109—232no—
162C2×C22⋊C4×C109—42no—
163C2×C22⋊C4×C109D418yescomplemented
164C2×C22⋊C4×C109D418yescomplemented
165C2×C22⋊C4×C109C2314yes—
166C2×C22⋊C4×C109C2314yes—
167C2×C22⋊C4×C109C2314yes—
168C2×C22⋊C4×C109C2314yes—
169C2×C22⋊C4×C109C2314yes—
170C2×C22⋊C4×C109C2314yes—
171C2×C22⋊C4×C109C2314yes—
172C2×C22⋊C4×C109C2314yes—
173C2×C22⋊C4×C109C2314yes—
174C2×C22⋊C4×C109C2314yes—
175C2×C22⋊C4×C109C2314yescomplemented
176C2×C22⋊C4×C109C2314yescomplemented
177C2×C22⋊C4×C109C2314yescomplemented
178C2×C22⋊C4×C109C2314yescomplemented
179C2×C22⋊C4×C109C2314yescomplemented
180C2×C42×C109—24no—
181C2×C42×C109C2314yescomplemented
182#95×C109C2314yescomplemented
183#95×C109C2314yescomplemented
184#95×C109C2314yescomplemented
185#95×C109C2314yescomplemented
186C24×C109—22no—
187C24×C109—22no—
188C24×C109—22no—
189C24×C109—22no—
190C24×C109—232no—
191C24×C109—28no—
192C24×C109—22no—
193C24×C109—22no—
194C24×C109—22no—
195C24×C109—22no—
196C24×C109—22no—
197C24×C109—22no—
198C24×C109—22no—
199C24×C109—22no—
200C24×C109—22no—
201C24×C109—28no—
202C24×C109—28no—
203C24×C109—22no—
204C24×C109—22no—
205C24×C109—22no—
206C24×C109—22no—
207C24×C109—22no—
208C24×C109—22no—
209C24×C109—22no—
210C24×C109—22no—
211C24×C109—22no—
212C24×C109—22no—
213C24×C109—22no—
214C24×C109—28no—
215C24×C109—28no—
216C24×C109—22no—
217C24×C109—22no—
218C24×C109—22no—
219C24×C109—22no—
220C24×C109—22no—
221C24×C109—44no—
222C24×C109—44no—
223C24×C109—416no—
224C24×C109—416no—
225C24×C109—416no—
226C24×C109—416no—
227C24×C109—416no—
228C24×C109—416no—
229C24×C109C2×D414yes—
230C24×C109C2×D414yes—
231C24×C109C2×D414yes—
232C24×C109C2×D414yes—
233C24×C109#4114yes—
234C24×C109#4114yes—
235C24×C109C2412yes—
236C24×C109C2412yes—
237C24×C109C2412yes—
238C24×C109C2412yes—
239C24×C109C2412yes—
240C24×C109C2411yescharacteristic
241C2×D4×C109—232no—
242C2×D4×C109—28no—
243C2×D4×C109—28no—
244C2×D4×C109—28no—
245C2×D4×C109—28no—
246C2×D4×C109—28no—
247C2×D4×C109—28no—
248C2×D4×C109—28no—
249C2×D4×C109—28no—
250C2×D4×C109—28no—
251C2×D4×C109—28no—
252C2×D4×C109—28no—
253C2×D4×C109—28no—
254C2×D4×C109—28no—
255C2×D4×C109—28no—
256C2×D4×C109—28no—
257C2×D4×C109—44no—
258C2×D4×C109—44no—
259C2×D4×C109—44no—
260C2×D4×C109—44no—
261C2×D4×C109—44no—
262C2×D4×C109—416no—
263C2×D4×C109—416no—
264C2×D4×C109—416no—
265C2×D4×C109—416no—
266C2×D4×C109—416no—
267C2×D4×C109—416no—
268C2×D4×C109C2×D4116yescomplemented
269C22×C4×C109—22no—
270C22×C4×C109—22no—
271C22×C4×C109—22no—
272C22×C4×C109—22no—
273C22×C4×C109—22no—
274C22×C4×C109—22no—
275C22×C4×C109—22no—
276C22×C4×C109—22no—
277C22×C4×C109—22no—
278C22×C4×C109—22no—
279C22×C4×C109—22no—
280C22×C4×C109—22no—
281C22×C4×C109—22no—
282C22×C4×C109—22no—
283C22×C4×C109—22no—
284C22×C4×C109—22no—
285C22×C4×C109—22no—
286C22×C4×C109—22no—
287C22×C4×C109—22no—
288C22×C4×C109—28no—
289C22×C4×C109—28no—
290C22×C4×C109—22no—
291C22×C4×C109—22no—
292C22×C4×C109—22no—
293C22×C4×C109—22no—
294C22×C4×C109—22no—
295C22×C4×C109—22no—
296C22×C4×C109—28no—
297C22×C4×C109—28no—
298C22×C4×C109—28no—
299C22×C4×C109—28no—
300C22×C4×C109—44no—
301C22×C4×C109—44no—
302C22×C4×C109—44no—
303C22×C4×C109—416no—
304C22×C4×C109—416no—
305C22×C4×C109—416no—
306C22×C4×C109C2×D414yes—
307C22×C4×C109C2×D414yes—
308C22×C4×C109C2×D414yes—
309C22×C4×C109C2×D414yes—
310C22×C4×C109C2×D414yes—
311C22×C4×C109C2412yes—
312C22×C4×C109C2412yes—
313C22×C4×C109C2412yes—
314C22×C4×C109C2412yes—
315C22×C4×C109C2412yes—
316C22×C4×C109C2412yes—
317C22×C4×C109C2412yes—
318C22×C4×C109C2412yes—
319C22×C4×C109C2412yes—
320C22×C4×C109C2412yes—
321C4⋊C4×C109—28no—
322C4⋊C4×C109—28no—
323C4⋊C4×C109—28no—
324C4⋊C4×C109—44no—
325C22⋊C4×C109—28no—
326C22⋊C4×C109—28no—
327C22⋊C4×C109—28no—
328C22⋊C4×C109—28no—
329C22⋊C4×C109—28no—
330C22⋊C4×C109—28no—
331C22⋊C4×C109—28no—
332C22⋊C4×C109—28no—
333C22⋊C4×C109—28no—
334C22⋊C4×C109—28no—
335C22⋊C4×C109—28no—
336C22⋊C4×C109—28no—
337C22⋊C4×C109—44no—
338C22⋊C4×C109C2×D4116yescomplemented
339C22⋊C4×C109C2×D4116yescomplemented
340C42×C109—28no—
341C23×C109—28no—
342C23×C109—28no—
343C23×C109—28no—
344C23×C109—28no—
345C23×C109—28no—
346C23×C109—28no—
347C23×C109—22no—
348C23×C109—22no—
349C23×C109—22no—
350C23×C109—22no—
351C23×C109—232no—
352C23×C109—28no—
353C23×C109—28no—
354C23×C109—28no—
355C23×C109—28no—
356C23×C109—28no—
357C23×C109—28no—
358C23×C109—28no—
359C23×C109—28no—
360C23×C109—28no—
361C23×C109—22no—
362C23×C109—22no—
363C23×C109—22no—
364C23×C109—22no—
365C23×C109—22no—
366C23×C109—22no—
367C23×C109—22no—
368C23×C109—22no—
369C23×C109—22no—
370C23×C109—22no—
371C23×C109—22no—
372C23×C109—22no—
373C23×C109—22no—
374C23×C109—22no—
375C23×C109—22no—
376C23×C109—22no—
377C23×C109—22no—
378C23×C109—22no—
379C23×C109—22no—
380C23×C109—22no—
381C23×C109—22no—
382C23×C109—22no—
383C23×C109—22no—
384C23×C109—22no—
385C23×C109—22no—
386C23×C109—416no—
387C23×C109—416no—
388C23×C109—416no—
389C23×C109—416no—
390C23×C109—4128no—
391C23×C109—416no—
392C23×C109—44no—
393C23×C109—44no—
394C23×C109—416no—
395C23×C109—44no—
396C23×C109—44no—
397C23×C109—44no—
398C23×C109—44no—
399C23×C109—44no—
400C23×C109—44no—
401C23×C109—44no—
402C23×C109—44no—
403C23×C109—44no—
404C23×C109—44no—
405C23×C109—44no—
406C23×C109—44no—
407C23×C109—44no—
408C23×C109—44no—
409C23×C109—44no—
410C23×C109—44no—
411C23×C109—44no—
412C23×C109#121116yescomplemented
413C23×C109C22×D414yes—
414C23×C109C22×D414yes—
415C23×C109C22×D414yes—
416C23×C109C22×D414yes—
417C23×C109C22×D412yes—
418C23×C109C22×D412yes—
419C23×C109C22×D412yes—
420C23×C109C2×#4114yes—
421C23×C109C2×#4114yes—
422C23×C109C2×#4112yes—
423C23×C109C2×#4112yes—
424C23×C109H(5,𝔽2)12yes—
425C23×C109H(5,𝔽2)12yes—
426C23×C109C2511yescharacteristic
427D4×C109—232no—
428D4×C109—416no—
429D4×C109—416no—
430D4×C109—416no—
431D4×C109—416no—
432D4×C109—416no—
433D4×C109—416no—
434C2×C4×C109—28no—
435C2×C4×C109—28no—
436C2×C4×C109—28no—
437C2×C4×C109—28no—
438C2×C4×C109—28no—
439C2×C4×C109—22no—
440C2×C4×C109—22no—
441C2×C4×C109—22no—
442C2×C4×C109—22no—
443C2×C4×C109—22no—
444C2×C4×C109—22no—
445C2×C4×C109—22no—
446C2×C4×C109—22no—
447C2×C4×C109—22no—
448C2×C4×C109—22no—
449C2×C4×C109—22no—
450C2×C4×C109—22no—
451C2×C4×C109—22no—
452C2×C4×C109—22no—
453C2×C4×C109—22no—
454C2×C4×C109—22no—
455C2×C4×C109—22no—
456C2×C4×C109—22no—
457C2×C4×C109—22no—
458C2×C4×C109—22no—
459C2×C4×C109—22no—
460C2×C4×C109—22no—
461C2×C4×C109—22no—
462C2×C4×C109—22no—
463C2×C4×C109—22no—
464C2×C4×C109—416no—
465C2×C4×C109—416no—
466C2×C4×C109—416no—
467C2×C4×C109—44no—
468C2×C4×C109—44no—
469C2×C4×C109—44no—
470C2×C4×C109—44no—
471C2×C4×C109—44no—
472C2×C4×C109C22×D414yes—
473C2×C4×C109C22×D414yes—
474C2×C4×C109C22×D414yes—
475C2×C4×C109C22×D414yes—
476C2×C4×C109C22×D414yes—
477C22×C109—24no—
478C22×C109—232no—
479C22×C109—24no—
480C22×C109—24no—
481C22×C109—24no—
482C22×C109—24no—
483C22×C109—24no—
484C22×C109—24no—
485C22×C109—24no—
486C22×C109—24no—
487C22×C109—24no—
488C22×C109—24no—
489C22×C109—24no—
490C22×C109—24no—
491C22×C109—24no—
492C22×C109—24no—
493C22×C109—464no—
494C22×C109—42no—
495C22×C109—42no—
496C22×C109—42no—
497C22×C109—416no—
498C22×C109—416no—
499C22×C109—416no—
500C22×C109—42no—
501C22×C109—42no—
502C22×C109—42no—
503C22×C109—42no—
504C22×C109—42no—
505C22×C109—42no—
506C22×C109—42no—
507C22×C109—42no—
508C22×C109—42no—
509C22×C109—42no—
510C22×C109—42no—
511C22×C109—42no—
512C22×C109—42no—
513C22×C109—42no—
514C22×C109—42no—
515C22×C109—42no—
516C22×C109—88no—
517C22×C109C2×#12114yes—
518C22×C109C2×#12118yescomplemented
519C22×C109#52514yes—
520C22×C109#53814yes—
521C22×C109D4214yes—
522C22×C109D4214yes—
523C22×C109#54614yes—
524C22×C109#54614yes—
525C22×C109C23×D411yescharacteristic
526C22×C109C23×D411yescharacteristic
527C22×C109C23×D411yescharacteristic
528C22×C109C22×#4111yescharacteristic
529C22×C109C22×#4111yescharacteristic
530C22×C109C2×H(5,𝔽2)11yescharacteristic
531C22×C109C2×H(5,𝔽2)11yescharacteristic
532C4×C109—24no—
533C4×C109—24no—
534C4×C109—24no—
535C4×C109—24no—
536C4×C109—24no—
537C4×C109—42no—
538C4×C109—42no—
539C4×C109—42no—
540C4×C109—42no—
541C4×C109—42no—
542C2×#2424C10911yesmaximal, characteristic, direct product factor, Sylow
543C2×C109—28no—
544C2×C109—44no—
545C2×C109—44no—
546C2×C109—44no—
547C2×C109—82no—
548C2×C109#242418yesdirect product factor
549C2×C109C22×#12111yescharacteristic
550C2×C109C2×#52511yescharacteristic
551C2×C109C2×#53811yescharacteristic
552C2×C109C2×D4211yescharacteristic
553C2×C109C2×D4211yescharacteristic
554C2×C109C2×#54611yescharacteristic
555C2×C109C2×#54611yescharacteristic
556C22×#121C2×C10911yescharacteristic, complemented
557C22×#121C2×C10911yescharacteristic, complemented
558C22×#120C2×C10911yescharacteristic, complemented
559C22×#120C2×C10911yescharacteristic, complemented
560C22×C4×D4C2×C10911yescharacteristic, complemented
561C23×C22⋊C4C2×C10911yescharacteristic, complemented
562#2424C2×C109116yesdirect product factor
563C2×#396C2×C10911yescharacteristic, complemented
564C2×#394C2×C10911yescharacteristic, complemented
565C2×#394C2×C10911yescharacteristic, complemented
566C2×#392C2×C10911yescharacteristic, complemented
567C2×#390C2×C10911yescharacteristic, complemented
568C2×#388C2×C10911yescharacteristic, complemented
569C2×#386C2×C10911yescharacteristic, complemented
570C2×#386C2×C10911yescharacteristic, complemented
571C2×#385C2×C10911yescharacteristic, complemented
572C109C2×#242411yescharacteristic, direct product factor, Sylow
573C26C22×C10911yescharacteristic
574C23×D4C22×C10911yescharacteristic
575C23×D4C22×C10911yescharacteristic
576C23×D4C22×C10911yescharacteristic
577C23×D4C22×C10911yescharacteristic
578C23×D4C22×C10911yescharacteristic
579C23×D4C22×C10911yescharacteristic
580C23×D4C22×C10911yescharacteristic, complemented
581C24×C4C22×C10911yescharacteristic
582C24×C4C22×C10911yescharacteristic
583C24×C4C22×C10911yescharacteristic, complemented
584C2×#121—28no—
585C2×#121—28no—
586C2×#121C22×C10918yescomplemented
587C2×#121C22×C10918yescomplemented
588C2×#120—28no—
589C2×#120—28no—
590C2×#120C22×C10918yescomplemented
591C2×#120C22×C10918yescomplemented
592C2×C4×D4—28no—
593C2×C4×D4C22×C10918yescomplemented
594C22×C4⋊C4C22×C10911yescharacteristic, complemented
595C22×C4⋊C4C22×C10911yescharacteristic, complemented
596C22×C4⋊C4C22×C10911yescharacteristic, complemented
597C22×C4⋊C4C22×C10911yescharacteristic, complemented
598C22×C22⋊C4—28no—
599C22×C22⋊C4C22×C10911yescharacteristic
600C22×C22⋊C4C22×C10911yescharacteristic
601C22×C22⋊C4C22×C10911yescharacteristic
602C22×C22⋊C4C22×C10911yescharacteristic
603C22×C22⋊C4C22×C10911yescharacteristic
604C22×C22⋊C4C22×C10911yescharacteristic
605C22×C22⋊C4C22×C10911yescharacteristic
606C22×C22⋊C4C22×C10911yescharacteristic
607C22×C22⋊C4C22×C10911yescharacteristic
608C22×C22⋊C4C22×C10911yescharacteristic
609C22×C22⋊C4C22×C10918yescomplemented
610C22×C22⋊C4C22×C10911yescharacteristic, complemented
611C22×C22⋊C4C22×C10911yescharacteristic, complemented
612C22×C22⋊C4C22×C10911yescharacteristic, complemented
613C22×C22⋊C4C22×C10911yescharacteristic, complemented
614C22×C22⋊C4C22×C10911yescharacteristic, complemented
615C22×C42C22×C10911yescharacteristic, complemented
616#396C22×C10918yescomplemented
617#394C22×C10918yescomplemented
618#394C22×C10918yescomplemented
619#392C22×C10918yescomplemented
620#390C22×C10918yescomplemented
621#388C22×C10918yescomplemented
622#386C22×C10918yescomplemented
623#386C22×C10918yescomplemented
624#385C22×C10918yescomplemented
625C2×#95C22×C10911yescharacteristic, complemented
626C2×#95C22×C10911yescharacteristic, complemented
627C2×#95C22×C10911yescharacteristic, complemented
628C2×#95C22×C10911yescharacteristic, complemented
629C25—24no—
630C25—24no—
631C25—24no—
632C25—24no—
633C25—24no—
634C25—42no—
635C25—42no—
636C25C23×C10911yescharacteristic
637C25C23×C10911yescharacteristic
638C25C23×C10911yescharacteristic
639C25C23×C10911yescharacteristic
640C25C23×C10914yes—
641C25C23×C10911yescharacteristic
642C22×D4—24no—
643C22×D4—24no—
644C22×D4—24no—
645C22×D4—24no—
646C22×D4—24no—
647C22×D4—24no—
648C22×D4—24no—
649C22×D4—24no—
650C22×D4—24no—
651C22×D4—24no—
652C22×D4—24no—
653C22×D4—24no—
654C22×D4—24no—
655C22×D4—24no—
656C22×D4—24no—
657C22×D4—42no—
658C22×D4—42no—
659C22×D4—42no—
660C22×D4—42no—
661C22×D4—42no—
662C22×D4D4×C10918yescomplemented
663C22×D4C23×C10914yes—
664C22×D4C23×C10914yes—
665C22×D4C23×C10914yes—
666C22×D4C23×C10914yes—
667C22×D4C23×C10914yes—
668C22×D4C23×C10914yes—
669C22×D4C23×C10914yescomplemented
670C23×C4—24no—
671C23×C4—24no—
672C23×C4—24no—
673C23×C4—24no—
674C23×C4—24no—
675C23×C4—24no—
676C23×C4—42no—
677C23×C4—42no—
678C23×C4—42no—
679C23×C4C23×C10911yescharacteristic
680C23×C4C23×C10911yescharacteristic
681C23×C4C23×C10911yescharacteristic
682C23×C4C23×C10911yescharacteristic
683C23×C4C23×C10911yescharacteristic
684C23×C4C23×C10914yes—
685C23×C4C23×C10914yes—
686C23×C4C23×C10911yescharacteristic
687C23×C4C23×C10911yescharacteristic
688C23×C4C23×C10911yescharacteristic
689C23×C4C23×C10911yescharacteristic
690C23×C4C23×C10911yescharacteristic
691C23×C4C23×C10914yescomplemented
692#121—232no—
693#121—232no—
694#120—232no—
695#120—232no—
696C4×D4—232no—
697C2×C4⋊C4—24no—
698C2×C4⋊C4—24no—
699C2×C4⋊C4—24no—
700C2×C4⋊C4—42no—
701C2×C4⋊C4C23×C10914yescomplemented
702C2×C4⋊C4C23×C10914yescomplemented
703C2×C4⋊C4C23×C10914yescomplemented
704C2×C4⋊C4C23×C10914yescomplemented
705C2×C22⋊C4—24no—
706C2×C22⋊C4—24no—
707C2×C22⋊C4—24no—
708C2×C22⋊C4—24no—
709C2×C22⋊C4—24no—
710C2×C22⋊C4—24no—
711C2×C22⋊C4—24no—
712C2×C22⋊C4—24no—
713C2×C22⋊C4—24no—
714C2×C22⋊C4—24no—
715C2×C22⋊C4—24no—
716C2×C22⋊C4—24no—
717C2×C22⋊C4—232no—
718C2×C22⋊C4—42no—
719C2×C22⋊C4D4×C10918yescomplemented
720C2×C22⋊C4D4×C10918yescomplemented
721C2×C22⋊C4C23×C10914yes—
722C2×C22⋊C4C23×C10914yes—
723C2×C22⋊C4C23×C10914yes—
724C2×C22⋊C4C23×C10914yes—
725C2×C22⋊C4C23×C10914yes—
726C2×C22⋊C4C23×C10914yes—
727C2×C22⋊C4C23×C10914yes—
728C2×C22⋊C4C23×C10914yes—
729C2×C22⋊C4C23×C10914yes—
730C2×C22⋊C4C23×C10914yes—
731C2×C22⋊C4C23×C10914yescomplemented
732C2×C22⋊C4C23×C10914yescomplemented
733C2×C22⋊C4C23×C10914yescomplemented
734C2×C22⋊C4C23×C10914yescomplemented
735C2×C22⋊C4C23×C10914yescomplemented
736C2×C42—24no—
737C2×C42C23×C10914yescomplemented
738#95C23×C10914yescomplemented
739#95C23×C10914yescomplemented
740#95C23×C10914yescomplemented
741#95C23×C10914yescomplemented
742C24—22no—
743C24—22no—
744C24—22no—
745C24—22no—
746C24—232no—
747C24—28no—
748C24—22no—
749C24—22no—
750C24—22no—
751C24—22no—
752C24—22no—
753C24—22no—
754C24—22no—
755C24—22no—
756C24—22no—
757C24—28no—
758C24—28no—
759C24—22no—
760C24—22no—
761C24—22no—
762C24—22no—
763C24—22no—
764C24—22no—
765C24—22no—
766C24—22no—
767C24—22no—
768C24—22no—
769C24—22no—
770C24—28no—
771C24—28no—
772C24—22no—
773C24—22no—
774C24—22no—
775C24—22no—
776C24—22no—
777C24—44no—
778C24—44no—
779C24—416no—
780C24—416no—
781C24—416no—
782C24—416no—
783C24—416no—
784C24—416no—
785C24C2×D4×C10914yes—
786C24C2×D4×C10914yes—
787C24C2×D4×C10914yes—
788C24C2×D4×C10914yes—
789C24#41×C10914yes—
790C24#41×C10914yes—
791C24C24×C10912yes—
792C24C24×C10912yes—
793C24C24×C10912yes—
794C24C24×C10912yes—
795C24C24×C10912yes—
796C24C24×C10911yescharacteristic
797C2×D4—232no—
798C2×D4—28no—
799C2×D4—28no—
800C2×D4—28no—
801C2×D4—28no—
802C2×D4—28no—
803C2×D4—28no—
804C2×D4—28no—
805C2×D4—28no—
806C2×D4—28no—
807C2×D4—28no—
808C2×D4—28no—
809C2×D4—28no—
810C2×D4—28no—
811C2×D4—28no—
812C2×D4—28no—
813C2×D4—44no—
814C2×D4—44no—
815C2×D4—44no—
816C2×D4—44no—
817C2×D4—44no—
818C2×D4—416no—
819C2×D4—416no—
820C2×D4—416no—
821C2×D4—416no—
822C2×D4—416no—
823C2×D4—416no—
824C2×D4C2×D4×C109116yescomplemented
825C22×C4—22no—
826C22×C4—22no—
827C22×C4—22no—
828C22×C4—22no—
829C22×C4—22no—
830C22×C4—22no—
831C22×C4—22no—
832C22×C4—22no—
833C22×C4—22no—
834C22×C4—22no—
835C22×C4—22no—
836C22×C4—22no—
837C22×C4—22no—
838C22×C4—22no—
839C22×C4—22no—
840C22×C4—22no—
841C22×C4—22no—
842C22×C4—22no—
843C22×C4—22no—
844C22×C4—28no—
845C22×C4—28no—
846C22×C4—22no—
847C22×C4—22no—
848C22×C4—22no—
849C22×C4—22no—
850C22×C4—22no—
851C22×C4—22no—
852C22×C4—28no—
853C22×C4—28no—
854C22×C4—28no—
855C22×C4—28no—
856C22×C4—44no—
857C22×C4—44no—
858C22×C4—44no—
859C22×C4—416no—
860C22×C4—416no—
861C22×C4—416no—
862C22×C4C2×D4×C10914yes—
863C22×C4C2×D4×C10914yes—
864C22×C4C2×D4×C10914yes—
865C22×C4C2×D4×C10914yes—
866C22×C4C2×D4×C10914yes—
867C22×C4C24×C10912yes—
868C22×C4C24×C10912yes—
869C22×C4C24×C10912yes—
870C22×C4C24×C10912yes—
871C22×C4C24×C10912yes—
872C22×C4C24×C10912yes—
873C22×C4C24×C10912yes—
874C22×C4C24×C10912yes—
875C22×C4C24×C10912yes—
876C22×C4C24×C10912yes—
877C4⋊C4—28no—
878C4⋊C4—28no—
879C4⋊C4—28no—
880C4⋊C4—44no—
881C22⋊C4—28no—
882C22⋊C4—28no—
883C22⋊C4—28no—
884C22⋊C4—28no—
885C22⋊C4—28no—
886C22⋊C4—28no—
887C22⋊C4—28no—
888C22⋊C4—28no—
889C22⋊C4—28no—
890C22⋊C4—28no—
891C22⋊C4—28no—
892C22⋊C4—28no—
893C22⋊C4—44no—
894C22⋊C4C2×D4×C109116yescomplemented
895C22⋊C4C2×D4×C109116yescomplemented
896C42—28no—
897C23—28no—
898C23—28no—
899C23—28no—
900C23—28no—
901C23—28no—
902C23—28no—
903C23—22no—
904C23—22no—
905C23—22no—
906C23—22no—
907C23—232no—
908C23—28no—
909C23—28no—
910C23—28no—
911C23—28no—
912C23—28no—
913C23—28no—
914C23—28no—
915C23—28no—
916C23—28no—
917C23—22no—
918C23—22no—
919C23—22no—
920C23—22no—
921C23—22no—
922C23—22no—
923C23—22no—
924C23—22no—
925C23—22no—
926C23—22no—
927C23—22no—
928C23—22no—
929C23—22no—
930C23—22no—
931C23—22no—
932C23—22no—
933C23—22no—
934C23—22no—
935C23—22no—
936C23—22no—
937C23—22no—
938C23—22no—
939C23—22no—
940C23—22no—
941C23—22no—
942C23—416no—
943C23—416no—
944C23—416no—
945C23—416no—
946C23—416no—
947C23—4128no—
948C23—44no—
949C23—44no—
950C23—416no—
951C23—44no—
952C23—44no—
953C23—44no—
954C23—44no—
955C23—44no—
956C23—44no—
957C23—44no—
958C23—44no—
959C23—44no—
960C23—44no—
961C23—44no—
962C23—44no—
963C23—44no—
964C23—44no—
965C23—44no—
966C23—44no—
967C23—44no—
968C23#121×C109116yescomplemented
969C23C22×D4×C10914yes—
970C23C22×D4×C10914yes—
971C23C22×D4×C10914yes—
972C23C22×D4×C10914yes—
973C23C22×D4×C10912yes—
974C23C22×D4×C10912yes—
975C23C22×D4×C10912yes—
976C23C2×#41×C10914yes—
977C23C2×#41×C10914yes—
978C23C2×#41×C10912yes—
979C23C2×#41×C10912yes—
980C23H(5,𝔽2)×C10912yes—
981C23H(5,𝔽2)×C10912yes—
982C23C25×C10911yescharacteristic
983D4—232no—
984D4—416no—
985D4—416no—
986D4—416no—
987D4—416no—
988D4—416no—
989D4—416no—
990C2×C4—28no—
991C2×C4—28no—
992C2×C4—28no—
993C2×C4—28no—
994C2×C4—28no—
995C2×C4—22no—
996C2×C4—22no—
997C2×C4—22no—
998C2×C4—22no—
999C2×C4—22no—
1000C2×C4—22no—
1001C2×C4—22no—
1002C2×C4—22no—
1003C2×C4—22no—
1004C2×C4—22no—
1005C2×C4—22no—
1006C2×C4—22no—
1007C2×C4—22no—
1008C2×C4—22no—
1009C2×C4—22no—
1010C2×C4—22no—
1011C2×C4—22no—
1012C2×C4—22no—
1013C2×C4—22no—
1014C2×C4—22no—
1015C2×C4—22no—
1016C2×C4—22no—
1017C2×C4—22no—
1018C2×C4—22no—
1019C2×C4—22no—
1020C2×C4—416no—
1021C2×C4—416no—
1022C2×C4—416no—
1023C2×C4—44no—
1024C2×C4—44no—
1025C2×C4—44no—
1026C2×C4—44no—
1027C2×C4—44no—
1028C2×C4C22×D4×C10914yes—
1029C2×C4C22×D4×C10914yes—
1030C2×C4C22×D4×C10914yes—
1031C2×C4C22×D4×C10914yes—
1032C2×C4C22×D4×C10914yes—
1033C22—24no—
1034C22—24no—
1035C22—24no—
1036C22—24no—
1037C22—24no—
1038C22—24no—
1039C22—232no—
1040C22—24no—
1041C22—24no—
1042C22—24no—
1043C22—24no—
1044C22—24no—
1045C22—24no—
1046C22—24no—
1047C22—24no—
1048C22—24no—
1049C22—464no—
1050C22—42no—
1051C22—42no—
1052C22—42no—
1053C22—42no—
1054C22—42no—
1055C22—42no—
1056C22—42no—
1057C22—42no—
1058C22—42no—
1059C22—42no—
1060C22—42no—
1061C22—42no—
1062C22—416no—
1063C22—416no—
1064C22—416no—
1065C22—42no—
1066C22—42no—
1067C22—42no—
1068C22—42no—
1069C22—42no—
1070C22—42no—
1071C22—42no—
1072C22—88no—
1073C22C2×#121×C10914yes—
1074C22C2×#121×C10918yescomplemented
1075C22#525×C10914yes—
1076C22#538×C10914yes—
1077C22D42×C10914yes—
1078C22D42×C10914yes—
1079C22#546×C10914yes—
1080C22#546×C10914yes—
1081C22C23×D4×C10911yescharacteristic
1082C22C23×D4×C10911yescharacteristic
1083C22C23×D4×C10911yescharacteristic
1084C22C22×#41×C10911yescharacteristic
1085C22C22×#41×C10911yescharacteristic
1086C22C2×H(5,𝔽2)×C10911yescharacteristic
1087C22C2×H(5,𝔽2)×C10911yescharacteristic
1088C4—24no—
1089C4—24no—
1090C4—24no—
1091C4—24no—
1092C4—24no—
1093C4—42no—
1094C4—42no—
1095C4—42no—
1096C4—42no—
1097C4—42no—
1098C2—28no—
1099C2—44no—
1100C2—44no—
1101C2—44no—
1102C2—82no—
1103C2C109×#242418yesdirect product factor
1104C2C22×#121×C10911yescharacteristic
1105C2C2×#525×C10911yescharacteristic
1106C2C2×#538×C10911yescharacteristic
1107C2C2×D42×C10911yescharacteristic
1108C2C2×D42×C10911yescharacteristic
1109C2C2×#546×C10911yescharacteristic
1110C2C2×#546×C10911yescharacteristic
subgroupG/H
center, socleC24×C109C24
commutator, Frattini, cosocleC23C25×C109
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C24×C109 ◁ G

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
1. C22×#121×C109C2semidirect
2. C22×#121×C109C2semidirect
3. C22×#120×C109C2semidirect
4. C22×#120×C109C2semidirect
5. C22×C4×D4×C109C2semidirect
6. C23×C22⋊C4×C109C2semidirect
7. C109×#2424C2direct (N × H)
8. C2×#396×C109C2semidirect
9. C2×#394×C109C2semidirect
10. C2×#394×C109C2semidirect
11. C2×#392×C109C2semidirect
12. C2×#390×C109C2semidirect
13. C2×#388×C109C2semidirect
14. C2×#386×C109C2semidirect
15. C2×#386×C109C2semidirect
16. C2×#385×C109C2semidirect
24. C23×D4×C109C22semidirect
27. C24×C4×C109C22semidirect
30. C2×#121×C109C22semidirect
31. C2×#121×C109C22semidirect
34. C2×#120×C109C22semidirect
35. C2×#120×C109C22semidirect
37. C2×C4×D4×C109C22semidirect
38. C22×C4⋊C4×C109C22semidirect
39. C22×C4⋊C4×C109C22semidirect
40. C22×C4⋊C4×C109C22semidirect
41. C22×C4⋊C4×C109C22semidirect
53. C22×C22⋊C4×C109C22semidirect
54. C22×C22⋊C4×C109C22semidirect
55. C22×C22⋊C4×C109C22semidirect
56. C22×C22⋊C4×C109C22semidirect
57. C22×C22⋊C4×C109C22semidirect
58. C22×C22⋊C4×C109C22semidirect
59. C22×C42×C109C22semidirect
60. #396×C109C22semidirect
61. #394×C109C22semidirect
62. #394×C109C22semidirect
63. #392×C109C22semidirect
64. #390×C109C22semidirect
65. #388×C109C22semidirect
66. #386×C109C22semidirect
67. #386×C109C22semidirect
68. #385×C109C22semidirect
69. C2×#95×C109C22semidirect
70. C2×#95×C109C22semidirect
71. C2×#95×C109C22semidirect
72. C2×#95×C109C22semidirect
106. C22×D4×C109D4semidirect
113. C22×D4×C109C23semidirect
135. C23×C4×C109C23semidirect
145. C2×C4⋊C4×C109C23semidirect
146. C2×C4⋊C4×C109C23semidirect
147. C2×C4⋊C4×C109C23semidirect
148. C2×C4⋊C4×C109C23semidirect
163. C2×C22⋊C4×C109D4semidirect
164. C2×C22⋊C4×C109D4semidirect
175. C2×C22⋊C4×C109C23semidirect
176. C2×C22⋊C4×C109C23semidirect
177. C2×C22⋊C4×C109C23semidirect
178. C2×C22⋊C4×C109C23semidirect
179. C2×C22⋊C4×C109C23semidirect
181. C2×C42×C109C23semidirect
182. #95×C109C23semidirect
183. #95×C109C23semidirect
184. #95×C109C23semidirect
185. #95×C109C23semidirect
268. C2×D4×C109C2×D4semidirect
338. C22⋊C4×C109C2×D4semidirect
339. C22⋊C4×C109C2×D4semidirect
412. C23×C109#121semidirect
518. C22×C109C2×#121semidirect
542. C2×#2424C109direct (N × H)
548. C2×C109#2424direct (N × H)
556. C22×#121C2×C109semidirect
557. C22×#121C2×C109semidirect
558. C22×#120C2×C109semidirect
559. C22×#120C2×C109semidirect
560. C22×C4×D4C2×C109semidirect
561. C23×C22⋊C4C2×C109semidirect
562. #2424C2×C109direct (N × H)
563. C2×#396C2×C109semidirect
564. C2×#394C2×C109semidirect
565. C2×#394C2×C109semidirect
566. C2×#392C2×C109semidirect
567. C2×#390C2×C109semidirect
568. C2×#388C2×C109semidirect
569. C2×#386C2×C109semidirect
570. C2×#386C2×C109semidirect
571. C2×#385C2×C109semidirect
572. C109C2×#2424direct (N × H)
580. C23×D4C22×C109semidirect
583. C24×C4C22×C109semidirect
586. C2×#121C22×C109semidirect
587. C2×#121C22×C109semidirect
590. C2×#120C22×C109semidirect
591. C2×#120C22×C109semidirect
593. C2×C4×D4C22×C109semidirect
594. C22×C4⋊C4C22×C109semidirect
595. C22×C4⋊C4C22×C109semidirect
596. C22×C4⋊C4C22×C109semidirect
597. C22×C4⋊C4C22×C109semidirect
609. C22×C22⋊C4C22×C109semidirect
610. C22×C22⋊C4C22×C109semidirect
611. C22×C22⋊C4C22×C109semidirect
612. C22×C22⋊C4C22×C109semidirect
613. C22×C22⋊C4C22×C109semidirect
614. C22×C22⋊C4C22×C109semidirect
615. C22×C42C22×C109semidirect
616. #396C22×C109semidirect
617. #394C22×C109semidirect
618. #394C22×C109semidirect
619. #392C22×C109semidirect
620. #390C22×C109semidirect
621. #388C22×C109semidirect
622. #386C22×C109semidirect
623. #386C22×C109semidirect
624. #385C22×C109semidirect
625. C2×#95C22×C109semidirect
626. C2×#95C22×C109semidirect
627. C2×#95C22×C109semidirect
628. C2×#95C22×C109semidirect
662. C22×D4D4×C109semidirect
669. C22×D4C23×C109semidirect
691. C23×C4C23×C109semidirect
701. C2×C4⋊C4C23×C109semidirect
702. C2×C4⋊C4C23×C109semidirect
703. C2×C4⋊C4C23×C109semidirect
704. C2×C4⋊C4C23×C109semidirect
719. C2×C22⋊C4D4×C109semidirect
720. C2×C22⋊C4D4×C109semidirect
731. C2×C22⋊C4C23×C109semidirect
732. C2×C22⋊C4C23×C109semidirect
733. C2×C22⋊C4C23×C109semidirect
734. C2×C22⋊C4C23×C109semidirect
735. C2×C22⋊C4C23×C109semidirect
737. C2×C42C23×C109semidirect
738. #95C23×C109semidirect
739. #95C23×C109semidirect
740. #95C23×C109semidirect
741. #95C23×C109semidirect
824. C2×D4C2×D4×C109semidirect
894. C22⋊C4C2×D4×C109semidirect
895. C22⋊C4C2×D4×C109semidirect
968. C23#121×C109semidirect
1074. C22C2×#121×C109semidirect
1103. C2C109×#2424direct (N × H)

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
C22×#121×C1092
C22×#120×C1092
C22×C4×D4×C1092
C23×C22⋊C4×C1092
C109×#24242
C2×#396×C1092
C2×#394×C1092
C2×#392×C1092
C2×#390×C1092
C2×#388×C1092
C2×#386×C1092
C2×#385×C1092
C2×#2424109