Finite Group Databasebeta

← C2×C109×#2418 #42152642

Subgroups — C2×C109×#2418 #42152642

Order 27904.

5054 conjugacy classes of subgroups.

The subgroup lattice has 1004 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#123×C109C211yesmaximal, characteristic, complemented
2C22×#120×C109C211yesmaximal, characteristic
3C22×C4×D4×C109C211yesmaximal, characteristic, complemented
4C23×C22⋊C4×C109C211yesmaximal, characteristic, complemented
5C109×#2418C2116yesmaximal, direct product factor
6C2×#399×C109C211yesmaximal, characteristic, complemented
7C2×#397×C109C211yesmaximal, characteristic, complemented
8C2×#394×C109C211yesmaximal, characteristic, complemented
9C2×#394×C109C211yesmaximal, characteristic, complemented
10C2×#388×C109C211yesmaximal, characteristic, complemented
11C2×#388×C109C211yesmaximal, characteristic, complemented
12C2×#386×C109C211yesmaximal, characteristic, complemented
13C2×#386×C109C211yesmaximal, characteristic, complemented
14C2×#385×C109C211yesmaximal, characteristic, complemented
15C2×#380×C109C211yesmaximal, characteristic, complemented
16C2×#379×C109C211yesmaximal, characteristic, complemented
17C26×C109C2211yescharacteristic
18C23×D4×C109C2211yescharacteristic
19C23×D4×C109C2211yescharacteristic
20C23×D4×C109C2211yescharacteristic
21C24×C4×C109C2211yescharacteristic
22C24×C4×C109C2211yescharacteristic
23C24×C4×C109C2211yescharacteristic, complemented
24C2×#123×C109—28no—
25C2×#123×C109C2218yescomplemented
26C2×#120×C109—28no—
27C2×#120×C109C2218yes—
28C2×C4×D4×C109—28no—
29C2×C4×D4×C109C2218yescomplemented
30C22×C4⋊C4×C109C2211yescharacteristic, complemented
31C22×C4⋊C4×C109C2211yescharacteristic, complemented
32C22×C4⋊C4×C109C2211yescharacteristic, complemented
33C22×C4⋊C4×C109C2211yescharacteristic, complemented
34C22×C4⋊C4×C109C2211yescharacteristic, complemented
35C22×C22⋊C4×C109—28no—
36C22×C22⋊C4×C109C2211yescharacteristic
37C22×C22⋊C4×C109C2211yescharacteristic
38C22×C22⋊C4×C109C2211yescharacteristic
39C22×C22⋊C4×C109C2211yescharacteristic
40C22×C22⋊C4×C109C2211yescharacteristic
41C22×C22⋊C4×C109C2211yescharacteristic
42C22×C22⋊C4×C109C2211yescharacteristic
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×C109C2218yescomplemented
50C22×C22⋊C4×C109C2211yescharacteristic, complemented
51C22×C22⋊C4×C109C2211yescharacteristic, complemented
52C22×C22⋊C4×C109C2211yescharacteristic, complemented
53C22×C42×C109C2211yescharacteristic, complemented
54#399×C109C2218yescomplemented
55#397×C109C2218yescomplemented
56#394×C109C2218yescomplemented
57#394×C109C2218yescomplemented
58#388×C109C2218yescomplemented
59#388×C109C2218yescomplemented
60#386×C109C2218yescomplemented
61#386×C109C2218yescomplemented
62#385×C109C2218yescomplemented
63#380×C109C2218yescomplemented
64#379×C109C2218yescomplemented
65C2×#95×C109C2211yescharacteristic, complemented
66C2×#95×C109C2211yescharacteristic, complemented
67C2×#95×C109C2211yescharacteristic, complemented
68C2×#95×C109C2211yescharacteristic, complemented
69C2×#95×C109C2211yescharacteristic, complemented
70C2×#95×C109C2211yescharacteristic, complemented
71C25×C109—24no—
72C25×C109—24no—
73C25×C109—24no—
74C25×C109—24no—
75C25×C109—24no—
76C25×C109—42no—
77C25×C109—42no—
78C25×C109C2311yescharacteristic
79C25×C109C2311yescharacteristic
80C25×C109C2311yescharacteristic
81C25×C109C2314yes—
82C25×C109C2311yescharacteristic
83C22×D4×C109—24no—
84C22×D4×C109—24no—
85C22×D4×C109—24no—
86C22×D4×C109—24no—
87C22×D4×C109—24no—
88C22×D4×C109—24no—
89C22×D4×C109—42no—
90C22×D4×C109—42no—
91C22×D4×C109D418yes—
92C22×D4×C109C2314yes—
93C22×D4×C109C2314yes—
94C22×D4×C109C2314yes—
95C23×C4×C109—24no—
96C23×C4×C109—24no—
97C23×C4×C109—24no—
98C23×C4×C109—24no—
99C23×C4×C109—24no—
100C23×C4×C109—24no—
101C23×C4×C109—42no—
102C23×C4×C109—42no—
103C23×C4×C109—42no—
104C23×C4×C109C2311yescharacteristic
105C23×C4×C109C2311yescharacteristic
106C23×C4×C109C2311yescharacteristic
107C23×C4×C109C2311yescharacteristic
108C23×C4×C109C2311yescharacteristic
109C23×C4×C109C2311yescharacteristic
110C23×C4×C109C2311yescharacteristic
111C23×C4×C109C2311yescharacteristic
112C23×C4×C109C2314yes—
113C23×C4×C109C2314yes—
114C23×C4×C109C2311yescharacteristic
115C23×C4×C109C2311yescharacteristic
116C23×C4×C109C2311yescharacteristic
117C23×C4×C109C2314yescomplemented
118#123×C109—232no—
119#120×C109—232no—
120C4×D4×C109—232no—
121C2×C4⋊C4×C109—24no—
122C2×C4⋊C4×C109—24no—
123C2×C4⋊C4×C109—24no—
124C2×C4⋊C4×C109—42no—
125C2×C4⋊C4×C109—42no—
126C2×C4⋊C4×C109C2314yescomplemented
127C2×C4⋊C4×C109C2314yescomplemented
128C2×C4⋊C4×C109C2314yescomplemented
129C2×C4⋊C4×C109C2314yescomplemented
130C2×C4⋊C4×C109C2314yescomplemented
131C2×C22⋊C4×C109—24no—
132C2×C22⋊C4×C109—24no—
133C2×C22⋊C4×C109—24no—
134C2×C22⋊C4×C109—24no—
135C2×C22⋊C4×C109—24no—
136C2×C22⋊C4×C109—24no—
137C2×C22⋊C4×C109—24no—
138C2×C22⋊C4×C109—24no—
139C2×C22⋊C4×C109—24no—
140C2×C22⋊C4×C109—24no—
141C2×C22⋊C4×C109—24no—
142C2×C22⋊C4×C109—24no—
143C2×C22⋊C4×C109—232no—
144C2×C22⋊C4×C109—42no—
145C2×C22⋊C4×C109—42no—
146C2×C22⋊C4×C109—42no—
147C2×C22⋊C4×C109D418yescomplemented
148C2×C22⋊C4×C109C2314yes—
149C2×C22⋊C4×C109C2314yes—
150C2×C22⋊C4×C109C2314yes—
151C2×C22⋊C4×C109C2314yes—
152C2×C22⋊C4×C109C2314yes—
153C2×C22⋊C4×C109C2314yes—
154C2×C22⋊C4×C109C2314yes—
155C2×C22⋊C4×C109C2314yes—
156C2×C22⋊C4×C109C2314yes—
157C2×C22⋊C4×C109C2314yes—
158C2×C22⋊C4×C109C2314yes—
159C2×C22⋊C4×C109C2314yes—
160C2×C22⋊C4×C109C2314yes—
161C2×C22⋊C4×C109C2314yescomplemented
162C2×C22⋊C4×C109C2314yescomplemented
163C2×C22⋊C4×C109C2314yescomplemented
164C2×C42×C109—24no—
165C2×C42×C109C2314yescomplemented
166#95×C109C2314yescomplemented
167#95×C109C2314yescomplemented
168#95×C109C2314yescomplemented
169#95×C109C2314yescomplemented
170#95×C109C2314yescomplemented
171#95×C109C2314yescomplemented
172C24×C109—22no—
173C24×C109—22no—
174C24×C109—22no—
175C24×C109—22no—
176C24×C109—232no—
177C24×C109—28no—
178C24×C109—22no—
179C24×C109—22no—
180C24×C109—22no—
181C24×C109—22no—
182C24×C109—22no—
183C24×C109—22no—
184C24×C109—22no—
185C24×C109—28no—
186C24×C109—28no—
187C24×C109—22no—
188C24×C109—22no—
189C24×C109—22no—
190C24×C109—22no—
191C24×C109—22no—
192C24×C109—22no—
193C24×C109—22no—
194C24×C109—22no—
195C24×C109—22no—
196C24×C109—22no—
197C24×C109—22no—
198C24×C109—28no—
199C24×C109—28no—
200C24×C109—44no—
201C24×C109—44no—
202C24×C109—416no—
203C24×C109—416no—
204C24×C109—416no—
205C24×C109—416no—
206C24×C109—416no—
207C24×C109—416no—
208C24×C109C2×D414yes—
209C24×C109C2×D414yes—
210C24×C109C2×D414yes—
211C24×C109#4114yes—
212C24×C109#4114yes—
213C24×C109#4114yes—
214C24×C109C2412yes—
215C24×C109C2412yes—
216C24×C109C2412yes—
217C24×C109C2412yes—
218C24×C109C2411yescharacteristic
219C2×D4×C109—232no—
220C2×D4×C109—28no—
221C2×D4×C109—28no—
222C2×D4×C109—28no—
223C2×D4×C109—28no—
224C2×D4×C109—28no—
225C2×D4×C109—28no—
226C2×D4×C109—44no—
227C2×D4×C109—44no—
228C2×D4×C109—416no—
229C2×D4×C109—416no—
230C2×D4×C109C2×D4116yes—
231C22×C4×C109—22no—
232C22×C4×C109—22no—
233C22×C4×C109—22no—
234C22×C4×C109—22no—
235C22×C4×C109—22no—
236C22×C4×C109—22no—
237C22×C4×C109—22no—
238C22×C4×C109—22no—
239C22×C4×C109—22no—
240C22×C4×C109—22no—
241C22×C4×C109—22no—
242C22×C4×C109—22no—
243C22×C4×C109—22no—
244C22×C4×C109—22no—
245C22×C4×C109—22no—
246C22×C4×C109—22no—
247C22×C4×C109—28no—
248C22×C4×C109—28no—
249C22×C4×C109—22no—
250C22×C4×C109—22no—
251C22×C4×C109—22no—
252C22×C4×C109—22no—
253C22×C4×C109—28no—
254C22×C4×C109—22no—
255C22×C4×C109—22no—
256C22×C4×C109—22no—
257C22×C4×C109—22no—
258C22×C4×C109—22no—
259C22×C4×C109—22no—
260C22×C4×C109—22no—
261C22×C4×C109—22no—
262C22×C4×C109—22no—
263C22×C4×C109—22no—
264C22×C4×C109—28no—
265C22×C4×C109—28no—
266C22×C4×C109—28no—
267C22×C4×C109—44no—
268C22×C4×C109—44no—
269C22×C4×C109—44no—
270C22×C4×C109—416no—
271C22×C4×C109—416no—
272C22×C4×C109—416no—
273C22×C4×C109C2×D414yes—
274C22×C4×C109C2×D414yes—
275C22×C4×C109C2×D414yes—
276C22×C4×C109C2412yes—
277C22×C4×C109C2412yes—
278C22×C4×C109C2412yes—
279C22×C4×C109C2412yes—
280C22×C4×C109C2412yes—
281C22×C4×C109C2412yes—
282C22×C4×C109C2412yes—
283C22×C4×C109C2412yes—
284C22×C4×C109C2412yes—
285C22×C4×C109C2412yes—
286C22×C4×C109C2412yes—
287C4⋊C4×C109—28no—
288C4⋊C4×C109—28no—
289C4⋊C4×C109—28no—
290C4⋊C4×C109—44no—
291C4⋊C4×C109—44no—
292C22⋊C4×C109—28no—
293C22⋊C4×C109—28no—
294C22⋊C4×C109—28no—
295C22⋊C4×C109—28no—
296C22⋊C4×C109—28no—
297C22⋊C4×C109—28no—
298C22⋊C4×C109—28no—
299C22⋊C4×C109—28no—
300C22⋊C4×C109—28no—
301C22⋊C4×C109—28no—
302C22⋊C4×C109—28no—
303C22⋊C4×C109—28no—
304C22⋊C4×C109—44no—
305C22⋊C4×C109—44no—
306C22⋊C4×C109—44no—
307C22⋊C4×C109C2×D4116yescomplemented
308C42×C109—28no—
309C23×C109—28no—
310C23×C109—28no—
311C23×C109—28no—
312C23×C109—28no—
313C23×C109—28no—
314C23×C109—28no—
315C23×C109—22no—
316C23×C109—22no—
317C23×C109—22no—
318C23×C109—22no—
319C23×C109—232no—
320C23×C109—28no—
321C23×C109—28no—
322C23×C109—28no—
323C23×C109—28no—
324C23×C109—28no—
325C23×C109—28no—
326C23×C109—28no—
327C23×C109—28no—
328C23×C109—28no—
329C23×C109—22no—
330C23×C109—22no—
331C23×C109—22no—
332C23×C109—22no—
333C23×C109—22no—
334C23×C109—22no—
335C23×C109—22no—
336C23×C109—22no—
337C23×C109—22no—
338C23×C109—22no—
339C23×C109—22no—
340C23×C109—22no—
341C23×C109—22no—
342C23×C109—22no—
343C23×C109—22no—
344C23×C109—22no—
345C23×C109—22no—
346C23×C109—22no—
347C23×C109—416no—
348C23×C109—416no—
349C23×C109—416no—
350C23×C109—416no—
351C23×C109—4128no—
352C23×C109—416no—
353C23×C109—44no—
354C23×C109—44no—
355C23×C109—416no—
356C23×C109—44no—
357C23×C109—44no—
358C23×C109—44no—
359C23×C109—44no—
360C23×C109—44no—
361C23×C109—44no—
362C23×C109—44no—
363C23×C109—44no—
364C23×C109—44no—
365C23×C109—44no—
366C23×C109#123116yescomplemented
367C23×C109C22×D414yes—
368C23×C109C22×D414yes—
369C23×C109C22×D414yes—
370C23×C109C22×D412yes—
371C23×C109C22×D412yes—
372C23×C109C2×#4114yes—
373C23×C109C2×#4114yes—
374C23×C109C2×#4114yes—
375C23×C109C2×#4112yes—
376C23×C109C2×#4112yes—
377C23×C109C2×#4112yes—
378C23×C109H(5,𝔽2)12yes—
379C23×C109H(5,𝔽2)12yes—
380C23×C109C2511yescharacteristic
381D4×C109—232no—
382D4×C109—416no—
383D4×C109—416no—
384C2×C4×C109—28no—
385C2×C4×C109—28no—
386C2×C4×C109—28no—
387C2×C4×C109—22no—
388C2×C4×C109—22no—
389C2×C4×C109—22no—
390C2×C4×C109—22no—
391C2×C4×C109—22no—
392C2×C4×C109—22no—
393C2×C4×C109—22no—
394C2×C4×C109—22no—
395C2×C4×C109—22no—
396C2×C4×C109—22no—
397C2×C4×C109—22no—
398C2×C4×C109—22no—
399C2×C4×C109—22no—
400C2×C4×C109—22no—
401C2×C4×C109—22no—
402C2×C4×C109—22no—
403C2×C4×C109—22no—
404C2×C4×C109—22no—
405C2×C4×C109—22no—
406C2×C4×C109—22no—
407C2×C4×C109—22no—
408C2×C4×C109—22no—
409C2×C4×C109—22no—
410C2×C4×C109—22no—
411C2×C4×C109—22no—
412C2×C4×C109—22no—
413C2×C4×C109—22no—
414C2×C4×C109—22no—
415C2×C4×C109—22no—
416C2×C4×C109—22no—
417C2×C4×C109—416no—
418C2×C4×C109—416no—
419C2×C4×C109—416no—
420C2×C4×C109—44no—
421C2×C4×C109—44no—
422C2×C4×C109—44no—
423C2×C4×C109—44no—
424C2×C4×C109—44no—
425C2×C4×C109—44no—
426C2×C4×C109—44no—
427C2×C4×C109—44no—
428C2×C4×C109C22×D414yes—
429C2×C4×C109C22×D414yes—
430C2×C4×C109C22×D414yes—
431C22×C109—24no—
432C22×C109—232no—
433C22×C109—24no—
434C22×C109—24no—
435C22×C109—24no—
436C22×C109—24no—
437C22×C109—24no—
438C22×C109—24no—
439C22×C109—24no—
440C22×C109—24no—
441C22×C109—24no—
442C22×C109—24no—
443C22×C109—24no—
444C22×C109—24no—
445C22×C109—24no—
446C22×C109—24no—
447C22×C109—464no—
448C22×C109—42no—
449C22×C109—42no—
450C22×C109—42no—
451C22×C109—416no—
452C22×C109—416no—
453C22×C109—416no—
454C22×C109—42no—
455C22×C109—42no—
456C22×C109—42no—
457C22×C109—42no—
458C22×C109—42no—
459C22×C109—42no—
460C22×C109—42no—
461C22×C109—42no—
462C22×C109—42no—
463C22×C109C2×#12314yes—
464C22×C109C2×#12318yescomplemented
465C22×C109#52514yes—
466C22×C109#53814yes—
467C22×C109D4214yes—
468C22×C109#54614yes—
469C22×C109#54614yes—
470C22×C109#55114yes—
471C22×C109C23×D411yescharacteristic
472C22×C109C23×D411yescharacteristic
473C22×C109C22×#4111yescharacteristic
474C22×C109C22×#4111yescharacteristic
475C22×C109C22×#4111yescharacteristic
476C22×C109C2×H(5,𝔽2)11yescharacteristic
477C22×C109C2×H(5,𝔽2)11yescharacteristic
478C4×C109—24no—
479C4×C109—24no—
480C4×C109—24no—
481C4×C109—42no—
482C4×C109—42no—
483C4×C109—42no—
484C4×C109—42no—
485C4×C109—42no—
486C4×C109—42no—
487C4×C109—42no—
488C4×C109—42no—
489C2×#2418C10911yesmaximal, characteristic, direct product factor, Sylow
490C2×C109—28no—
491C2×C109—44no—
492C2×C109—44no—
493C2×C109—44no—
494C2×C109#241818yesdirect product factor
495C2×C109C22×#12311yescharacteristic
496C2×C109C2×#52511yescharacteristic
497C2×C109C2×#53811yescharacteristic
498C2×C109C2×D4211yescharacteristic
499C2×C109C2×#54611yescharacteristic
500C2×C109C2×#54611yescharacteristic
501C2×C109C2×#55111yescharacteristic
502C22×#123C2×C10911yescharacteristic, complemented
503C22×#120C2×C10911yescharacteristic
504C22×C4×D4C2×C10911yescharacteristic, complemented
505C23×C22⋊C4C2×C10911yescharacteristic, complemented
506#2418C2×C109116yesdirect product factor
507C2×#399C2×C10911yescharacteristic, complemented
508C2×#397C2×C10911yescharacteristic, complemented
509C2×#394C2×C10911yescharacteristic, complemented
510C2×#394C2×C10911yescharacteristic, complemented
511C2×#388C2×C10911yescharacteristic, complemented
512C2×#388C2×C10911yescharacteristic, complemented
513C2×#386C2×C10911yescharacteristic, complemented
514C2×#386C2×C10911yescharacteristic, complemented
515C2×#385C2×C10911yescharacteristic, complemented
516C2×#380C2×C10911yescharacteristic, complemented
517C2×#379C2×C10911yescharacteristic, complemented
518C109C2×#241811yescharacteristic, direct product factor, Sylow
519C26C22×C10911yescharacteristic
520C23×D4C22×C10911yescharacteristic
521C23×D4C22×C10911yescharacteristic
522C23×D4C22×C10911yescharacteristic
523C24×C4C22×C10911yescharacteristic
524C24×C4C22×C10911yescharacteristic
525C24×C4C22×C10911yescharacteristic, complemented
526C2×#123—28no—
527C2×#123C22×C10918yescomplemented
528C2×#120—28no—
529C2×#120C22×C10918yes—
530C2×C4×D4—28no—
531C2×C4×D4C22×C10918yescomplemented
532C22×C4⋊C4C22×C10911yescharacteristic, complemented
533C22×C4⋊C4C22×C10911yescharacteristic, complemented
534C22×C4⋊C4C22×C10911yescharacteristic, complemented
535C22×C4⋊C4C22×C10911yescharacteristic, complemented
536C22×C4⋊C4C22×C10911yescharacteristic, complemented
537C22×C22⋊C4—28no—
538C22×C22⋊C4C22×C10911yescharacteristic
539C22×C22⋊C4C22×C10911yescharacteristic
540C22×C22⋊C4C22×C10911yescharacteristic
541C22×C22⋊C4C22×C10911yescharacteristic
542C22×C22⋊C4C22×C10911yescharacteristic
543C22×C22⋊C4C22×C10911yescharacteristic
544C22×C22⋊C4C22×C10911yescharacteristic
545C22×C22⋊C4C22×C10911yescharacteristic
546C22×C22⋊C4C22×C10911yescharacteristic
547C22×C22⋊C4C22×C10911yescharacteristic
548C22×C22⋊C4C22×C10911yescharacteristic
549C22×C22⋊C4C22×C10911yescharacteristic
550C22×C22⋊C4C22×C10911yescharacteristic
551C22×C22⋊C4C22×C10918yescomplemented
552C22×C22⋊C4C22×C10911yescharacteristic, complemented
553C22×C22⋊C4C22×C10911yescharacteristic, complemented
554C22×C22⋊C4C22×C10911yescharacteristic, complemented
555C22×C42C22×C10911yescharacteristic, complemented
556#399C22×C10918yescomplemented
557#397C22×C10918yescomplemented
558#394C22×C10918yescomplemented
559#394C22×C10918yescomplemented
560#388C22×C10918yescomplemented
561#388C22×C10918yescomplemented
562#386C22×C10918yescomplemented
563#386C22×C10918yescomplemented
564#385C22×C10918yescomplemented
565#380C22×C10918yescomplemented
566#379C22×C10918yescomplemented
567C2×#95C22×C10911yescharacteristic, complemented
568C2×#95C22×C10911yescharacteristic, complemented
569C2×#95C22×C10911yescharacteristic, complemented
570C2×#95C22×C10911yescharacteristic, complemented
571C2×#95C22×C10911yescharacteristic, complemented
572C2×#95C22×C10911yescharacteristic, complemented
573C25—24no—
574C25—24no—
575C25—24no—
576C25—24no—
577C25—24no—
578C25—42no—
579C25—42no—
580C25C23×C10911yescharacteristic
581C25C23×C10911yescharacteristic
582C25C23×C10911yescharacteristic
583C25C23×C10914yes—
584C25C23×C10911yescharacteristic
585C22×D4—24no—
586C22×D4—24no—
587C22×D4—24no—
588C22×D4—24no—
589C22×D4—24no—
590C22×D4—24no—
591C22×D4—42no—
592C22×D4—42no—
593C22×D4D4×C10918yes—
594C22×D4C23×C10914yes—
595C22×D4C23×C10914yes—
596C22×D4C23×C10914yes—
597C23×C4—24no—
598C23×C4—24no—
599C23×C4—24no—
600C23×C4—24no—
601C23×C4—24no—
602C23×C4—24no—
603C23×C4—42no—
604C23×C4—42no—
605C23×C4—42no—
606C23×C4C23×C10911yescharacteristic
607C23×C4C23×C10911yescharacteristic
608C23×C4C23×C10911yescharacteristic
609C23×C4C23×C10911yescharacteristic
610C23×C4C23×C10911yescharacteristic
611C23×C4C23×C10911yescharacteristic
612C23×C4C23×C10911yescharacteristic
613C23×C4C23×C10911yescharacteristic
614C23×C4C23×C10914yes—
615C23×C4C23×C10914yes—
616C23×C4C23×C10911yescharacteristic
617C23×C4C23×C10911yescharacteristic
618C23×C4C23×C10911yescharacteristic
619C23×C4C23×C10914yescomplemented
620#123—232no—
621#120—232no—
622C4×D4—232no—
623C2×C4⋊C4—24no—
624C2×C4⋊C4—24no—
625C2×C4⋊C4—24no—
626C2×C4⋊C4—42no—
627C2×C4⋊C4—42no—
628C2×C4⋊C4C23×C10914yescomplemented
629C2×C4⋊C4C23×C10914yescomplemented
630C2×C4⋊C4C23×C10914yescomplemented
631C2×C4⋊C4C23×C10914yescomplemented
632C2×C4⋊C4C23×C10914yescomplemented
633C2×C22⋊C4—24no—
634C2×C22⋊C4—24no—
635C2×C22⋊C4—24no—
636C2×C22⋊C4—24no—
637C2×C22⋊C4—24no—
638C2×C22⋊C4—24no—
639C2×C22⋊C4—24no—
640C2×C22⋊C4—24no—
641C2×C22⋊C4—24no—
642C2×C22⋊C4—24no—
643C2×C22⋊C4—24no—
644C2×C22⋊C4—24no—
645C2×C22⋊C4—232no—
646C2×C22⋊C4—42no—
647C2×C22⋊C4—42no—
648C2×C22⋊C4—42no—
649C2×C22⋊C4D4×C10918yescomplemented
650C2×C22⋊C4C23×C10914yes—
651C2×C22⋊C4C23×C10914yes—
652C2×C22⋊C4C23×C10914yes—
653C2×C22⋊C4C23×C10914yes—
654C2×C22⋊C4C23×C10914yes—
655C2×C22⋊C4C23×C10914yes—
656C2×C22⋊C4C23×C10914yes—
657C2×C22⋊C4C23×C10914yes—
658C2×C22⋊C4C23×C10914yes—
659C2×C22⋊C4C23×C10914yes—
660C2×C22⋊C4C23×C10914yes—
661C2×C22⋊C4C23×C10914yes—
662C2×C22⋊C4C23×C10914yes—
663C2×C22⋊C4C23×C10914yescomplemented
664C2×C22⋊C4C23×C10914yescomplemented
665C2×C22⋊C4C23×C10914yescomplemented
666C2×C42—24no—
667C2×C42C23×C10914yescomplemented
668#95C23×C10914yescomplemented
669#95C23×C10914yescomplemented
670#95C23×C10914yescomplemented
671#95C23×C10914yescomplemented
672#95C23×C10914yescomplemented
673#95C23×C10914yescomplemented
674C24—22no—
675C24—22no—
676C24—22no—
677C24—22no—
678C24—232no—
679C24—28no—
680C24—22no—
681C24—22no—
682C24—22no—
683C24—22no—
684C24—22no—
685C24—22no—
686C24—22no—
687C24—28no—
688C24—28no—
689C24—22no—
690C24—22no—
691C24—22no—
692C24—22no—
693C24—22no—
694C24—22no—
695C24—22no—
696C24—22no—
697C24—22no—
698C24—22no—
699C24—22no—
700C24—28no—
701C24—28no—
702C24—44no—
703C24—44no—
704C24—416no—
705C24—416no—
706C24—416no—
707C24—416no—
708C24—416no—
709C24—416no—
710C24C2×D4×C10914yes—
711C24C2×D4×C10914yes—
712C24C2×D4×C10914yes—
713C24#41×C10914yes—
714C24#41×C10914yes—
715C24#41×C10914yes—
716C24C24×C10912yes—
717C24C24×C10912yes—
718C24C24×C10912yes—
719C24C24×C10912yes—
720C24C24×C10911yescharacteristic
721C2×D4—232no—
722C2×D4—28no—
723C2×D4—28no—
724C2×D4—28no—
725C2×D4—28no—
726C2×D4—28no—
727C2×D4—28no—
728C2×D4—44no—
729C2×D4—44no—
730C2×D4—416no—
731C2×D4—416no—
732C2×D4C2×D4×C109116yes—
733C22×C4—22no—
734C22×C4—22no—
735C22×C4—22no—
736C22×C4—22no—
737C22×C4—22no—
738C22×C4—22no—
739C22×C4—22no—
740C22×C4—22no—
741C22×C4—22no—
742C22×C4—22no—
743C22×C4—22no—
744C22×C4—22no—
745C22×C4—22no—
746C22×C4—22no—
747C22×C4—22no—
748C22×C4—22no—
749C22×C4—28no—
750C22×C4—28no—
751C22×C4—22no—
752C22×C4—22no—
753C22×C4—22no—
754C22×C4—22no—
755C22×C4—28no—
756C22×C4—22no—
757C22×C4—22no—
758C22×C4—22no—
759C22×C4—22no—
760C22×C4—22no—
761C22×C4—22no—
762C22×C4—22no—
763C22×C4—22no—
764C22×C4—22no—
765C22×C4—22no—
766C22×C4—28no—
767C22×C4—28no—
768C22×C4—28no—
769C22×C4—44no—
770C22×C4—44no—
771C22×C4—44no—
772C22×C4—416no—
773C22×C4—416no—
774C22×C4—416no—
775C22×C4C2×D4×C10914yes—
776C22×C4C2×D4×C10914yes—
777C22×C4C2×D4×C10914yes—
778C22×C4C24×C10912yes—
779C22×C4C24×C10912yes—
780C22×C4C24×C10912yes—
781C22×C4C24×C10912yes—
782C22×C4C24×C10912yes—
783C22×C4C24×C10912yes—
784C22×C4C24×C10912yes—
785C22×C4C24×C10912yes—
786C22×C4C24×C10912yes—
787C22×C4C24×C10912yes—
788C22×C4C24×C10912yes—
789C4⋊C4—28no—
790C4⋊C4—28no—
791C4⋊C4—28no—
792C4⋊C4—44no—
793C4⋊C4—44no—
794C22⋊C4—28no—
795C22⋊C4—28no—
796C22⋊C4—28no—
797C22⋊C4—28no—
798C22⋊C4—28no—
799C22⋊C4—28no—
800C22⋊C4—28no—
801C22⋊C4—28no—
802C22⋊C4—28no—
803C22⋊C4—28no—
804C22⋊C4—28no—
805C22⋊C4—28no—
806C22⋊C4—44no—
807C22⋊C4—44no—
808C22⋊C4—44no—
809C22⋊C4C2×D4×C109116yescomplemented
810C42—28no—
811C23—28no—
812C23—28no—
813C23—28no—
814C23—28no—
815C23—28no—
816C23—28no—
817C23—22no—
818C23—22no—
819C23—22no—
820C23—22no—
821C23—232no—
822C23—28no—
823C23—28no—
824C23—28no—
825C23—28no—
826C23—28no—
827C23—28no—
828C23—28no—
829C23—28no—
830C23—28no—
831C23—22no—
832C23—22no—
833C23—22no—
834C23—22no—
835C23—22no—
836C23—22no—
837C23—22no—
838C23—22no—
839C23—22no—
840C23—22no—
841C23—22no—
842C23—22no—
843C23—22no—
844C23—22no—
845C23—22no—
846C23—22no—
847C23—22no—
848C23—22no—
849C23—416no—
850C23—416no—
851C23—416no—
852C23—416no—
853C23—416no—
854C23—4128no—
855C23—44no—
856C23—44no—
857C23—416no—
858C23—44no—
859C23—44no—
860C23—44no—
861C23—44no—
862C23—44no—
863C23—44no—
864C23—44no—
865C23—44no—
866C23—44no—
867C23—44no—
868C23#123×C109116yescomplemented
869C23C22×D4×C10914yes—
870C23C22×D4×C10914yes—
871C23C22×D4×C10914yes—
872C23C22×D4×C10912yes—
873C23C22×D4×C10912yes—
874C23C2×#41×C10914yes—
875C23C2×#41×C10914yes—
876C23C2×#41×C10914yes—
877C23C2×#41×C10912yes—
878C23C2×#41×C10912yes—
879C23C2×#41×C10912yes—
880C23H(5,𝔽2)×C10912yes—
881C23H(5,𝔽2)×C10912yes—
882C23C25×C10911yescharacteristic
883D4—232no—
884D4—416no—
885D4—416no—
886C2×C4—28no—
887C2×C4—28no—
888C2×C4—28no—
889C2×C4—22no—
890C2×C4—22no—
891C2×C4—22no—
892C2×C4—22no—
893C2×C4—22no—
894C2×C4—22no—
895C2×C4—22no—
896C2×C4—22no—
897C2×C4—22no—
898C2×C4—22no—
899C2×C4—22no—
900C2×C4—22no—
901C2×C4—22no—
902C2×C4—22no—
903C2×C4—22no—
904C2×C4—22no—
905C2×C4—22no—
906C2×C4—22no—
907C2×C4—22no—
908C2×C4—22no—
909C2×C4—22no—
910C2×C4—22no—
911C2×C4—22no—
912C2×C4—22no—
913C2×C4—22no—
914C2×C4—22no—
915C2×C4—22no—
916C2×C4—22no—
917C2×C4—22no—
918C2×C4—22no—
919C2×C4—416no—
920C2×C4—416no—
921C2×C4—416no—
922C2×C4—44no—
923C2×C4—44no—
924C2×C4—44no—
925C2×C4—44no—
926C2×C4—44no—
927C2×C4—44no—
928C2×C4—44no—
929C2×C4—44no—
930C2×C4C22×D4×C10914yes—
931C2×C4C22×D4×C10914yes—
932C2×C4C22×D4×C10914yes—
933C22—24no—
934C22—24no—
935C22—24no—
936C22—24no—
937C22—24no—
938C22—24no—
939C22—232no—
940C22—24no—
941C22—24no—
942C22—24no—
943C22—24no—
944C22—24no—
945C22—24no—
946C22—24no—
947C22—24no—
948C22—24no—
949C22—464no—
950C22—42no—
951C22—42no—
952C22—42no—
953C22—42no—
954C22—42no—
955C22—42no—
956C22—42no—
957C22—42no—
958C22—42no—
959C22—42no—
960C22—42no—
961C22—42no—
962C22—416no—
963C22—416no—
964C22—416no—
965C22C2×#123×C10914yes—
966C22C2×#123×C10918yescomplemented
967C22#525×C10914yes—
968C22#538×C10914yes—
969C22D42×C10914yes—
970C22#546×C10914yes—
971C22#546×C10914yes—
972C22#551×C10914yes—
973C22C23×D4×C10911yescharacteristic
974C22C23×D4×C10911yescharacteristic
975C22C22×#41×C10911yescharacteristic
976C22C22×#41×C10911yescharacteristic
977C22C22×#41×C10911yescharacteristic
978C22C2×H(5,𝔽2)×C10911yescharacteristic
979C22C2×H(5,𝔽2)×C10911yescharacteristic
980C4—24no—
981C4—24no—
982C4—24no—
983C4—42no—
984C4—42no—
985C4—42no—
986C4—42no—
987C4—42no—
988C4—42no—
989C4—42no—
990C4—42no—
991C2—28no—
992C2—44no—
993C2—44no—
994C2—44no—
995C2C109×#241818yesdirect product factor
996C2C22×#123×C10911yescharacteristic
997C2C2×#525×C10911yescharacteristic
998C2C2×#538×C10911yescharacteristic
999C2C2×D42×C10911yescharacteristic
1000C2C2×#546×C10911yescharacteristic
1001C2C2×#546×C10911yescharacteristic
1002C2C2×#551×C10911yescharacteristic
subgroupG/H
center, socleC24×C109C24
commutator, Frattini, cosocleC23C25×C109
prime radicalC22×#120×C109C2
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C24×C109 ◁ G

Complements

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

NH ≅ G/Ntype
1. C22×#123×C109C2semidirect
3. C22×C4×D4×C109C2semidirect
4. C23×C22⋊C4×C109C2semidirect
5. C109×#2418C2direct (N × H)
6. C2×#399×C109C2semidirect
7. C2×#397×C109C2semidirect
8. C2×#394×C109C2semidirect
9. C2×#394×C109C2semidirect
10. C2×#388×C109C2semidirect
11. C2×#388×C109C2semidirect
12. C2×#386×C109C2semidirect
13. C2×#386×C109C2semidirect
14. C2×#385×C109C2semidirect
15. C2×#380×C109C2semidirect
16. C2×#379×C109C2semidirect
23. C24×C4×C109C22semidirect
25. C2×#123×C109C22semidirect
29. C2×C4×D4×C109C22semidirect
30. C22×C4⋊C4×C109C22semidirect
31. C22×C4⋊C4×C109C22semidirect
32. C22×C4⋊C4×C109C22semidirect
33. C22×C4⋊C4×C109C22semidirect
34. C22×C4⋊C4×C109C22semidirect
49. C22×C22⋊C4×C109C22semidirect
50. C22×C22⋊C4×C109C22semidirect
51. C22×C22⋊C4×C109C22semidirect
52. C22×C22⋊C4×C109C22semidirect
53. C22×C42×C109C22semidirect
54. #399×C109C22semidirect
55. #397×C109C22semidirect
56. #394×C109C22semidirect
57. #394×C109C22semidirect
58. #388×C109C22semidirect
59. #388×C109C22semidirect
60. #386×C109C22semidirect
61. #386×C109C22semidirect
62. #385×C109C22semidirect
63. #380×C109C22semidirect
64. #379×C109C22semidirect
65. C2×#95×C109C22semidirect
66. C2×#95×C109C22semidirect
67. C2×#95×C109C22semidirect
68. C2×#95×C109C22semidirect
69. C2×#95×C109C22semidirect
70. C2×#95×C109C22semidirect
117. C23×C4×C109C23semidirect
126. C2×C4⋊C4×C109C23semidirect
127. C2×C4⋊C4×C109C23semidirect
128. C2×C4⋊C4×C109C23semidirect
129. C2×C4⋊C4×C109C23semidirect
130. C2×C4⋊C4×C109C23semidirect
147. C2×C22⋊C4×C109D4semidirect
161. C2×C22⋊C4×C109C23semidirect
162. C2×C22⋊C4×C109C23semidirect
163. C2×C22⋊C4×C109C23semidirect
165. C2×C42×C109C23semidirect
166. #95×C109C23semidirect
167. #95×C109C23semidirect
168. #95×C109C23semidirect
169. #95×C109C23semidirect
170. #95×C109C23semidirect
171. #95×C109C23semidirect
307. C22⋊C4×C109C2×D4semidirect
366. C23×C109#123semidirect
464. C22×C109C2×#123semidirect
489. C2×#2418C109direct (N × H)
494. C2×C109#2418direct (N × H)
502. C22×#123C2×C109semidirect
504. C22×C4×D4C2×C109semidirect
505. C23×C22⋊C4C2×C109semidirect
506. #2418C2×C109direct (N × H)
507. C2×#399C2×C109semidirect
508. C2×#397C2×C109semidirect
509. C2×#394C2×C109semidirect
510. C2×#394C2×C109semidirect
511. C2×#388C2×C109semidirect
512. C2×#388C2×C109semidirect
513. C2×#386C2×C109semidirect
514. C2×#386C2×C109semidirect
515. C2×#385C2×C109semidirect
516. C2×#380C2×C109semidirect
517. C2×#379C2×C109semidirect
518. C109C2×#2418direct (N × H)
525. C24×C4C22×C109semidirect
527. C2×#123C22×C109semidirect
531. C2×C4×D4C22×C109semidirect
532. C22×C4⋊C4C22×C109semidirect
533. C22×C4⋊C4C22×C109semidirect
534. C22×C4⋊C4C22×C109semidirect
535. C22×C4⋊C4C22×C109semidirect
536. C22×C4⋊C4C22×C109semidirect
551. C22×C22⋊C4C22×C109semidirect
552. C22×C22⋊C4C22×C109semidirect
553. C22×C22⋊C4C22×C109semidirect
554. C22×C22⋊C4C22×C109semidirect
555. C22×C42C22×C109semidirect
556. #399C22×C109semidirect
557. #397C22×C109semidirect
558. #394C22×C109semidirect
559. #394C22×C109semidirect
560. #388C22×C109semidirect
561. #388C22×C109semidirect
562. #386C22×C109semidirect
563. #386C22×C109semidirect
564. #385C22×C109semidirect
565. #380C22×C109semidirect
566. #379C22×C109semidirect
567. C2×#95C22×C109semidirect
568. C2×#95C22×C109semidirect
569. C2×#95C22×C109semidirect
570. C2×#95C22×C109semidirect
571. C2×#95C22×C109semidirect
572. C2×#95C22×C109semidirect
619. C23×C4C23×C109semidirect
628. C2×C4⋊C4C23×C109semidirect
629. C2×C4⋊C4C23×C109semidirect
630. C2×C4⋊C4C23×C109semidirect
631. C2×C4⋊C4C23×C109semidirect
632. C2×C4⋊C4C23×C109semidirect
649. C2×C22⋊C4D4×C109semidirect
663. C2×C22⋊C4C23×C109semidirect
664. C2×C22⋊C4C23×C109semidirect
665. C2×C22⋊C4C23×C109semidirect
667. C2×C42C23×C109semidirect
668. #95C23×C109semidirect
669. #95C23×C109semidirect
670. #95C23×C109semidirect
671. #95C23×C109semidirect
672. #95C23×C109semidirect
673. #95C23×C109semidirect
809. C22⋊C4C2×D4×C109semidirect
868. C23#123×C109semidirect
966. C22C2×#123×C109semidirect
995. C2C109×#2418direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#123×C1092
C22×#120×C1092
C22×C4×D4×C1092
C23×C22⋊C4×C1092
C109×#24182
C2×#399×C1092
C2×#397×C1092
C2×#394×C1092
C2×#388×C1092
C2×#386×C1092
C2×#385×C1092
C2×#380×C1092
C2×#379×C1092
C2×#2418109