Finite Group Databasebeta

← C109×#15501 #42133495

Subgroups — C109×#15501 #42133495

Order 27904.

2154 conjugacy classes of subgroups.

The subgroup lattice has 1318 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#397×C109C211yesmaximal, characteristic, complemented
2C2×#394×C109C211yesmaximal, characteristic, complemented
3C2×#392×C109C211yesmaximal, characteristic
4C2×#390×C109C211yesmaximal, characteristic, complemented
5C2×#386×C109C211yesmaximal, characteristic, complemented
6C2×#386×C109C211yesmaximal, characteristic, complemented
7C109×#1441C211yesmaximal, characteristic, complemented
8C109×#1440C211yesmaximal, characteristic, complemented
9C109×#1440C211yesmaximal, characteristic, complemented
10C109×#1439C211yesmaximal, characteristic, complemented
11C109×#1438C211yesmaximal, characteristic, complemented
12C109×#1438C211yesmaximal, characteristic, complemented
13C109×#1437C211yesmaximal, characteristic, complemented
14C109×#1434C211yesmaximal, characteristic, complemented
15C109×C22⋊#95C211yesmaximal, characteristic, complemented
16C23×D4×C109C2211yescharacteristic
17C23×D4×C109C2211yescharacteristic
18C23×D4×C109C2211yescharacteristic
19C24×C4×C109C2211yescharacteristic
20C22×C4⋊C4×C109C2211yescharacteristic
21C22×C4⋊C4×C109C2211yescharacteristic
22C22×C22⋊C4×C109C2211yescharacteristic
23C22×C22⋊C4×C109C2211yescharacteristic
24C22×C22⋊C4×C109C2211yescharacteristic
25C22×C22⋊C4×C109C2211yescharacteristic
26C22×C22⋊C4×C109C2211yescharacteristic
27C22×C22⋊C4×C109C2211yescharacteristic
28C22×C22⋊C4×C109C2211yescharacteristic
29C22×C22⋊C4×C109C2211yescharacteristic
30C22×C22⋊C4×C109C2211yescharacteristic
31C22×C22⋊C4×C109C2211yescharacteristic
32C22×C22⋊C4×C109C2211yescharacteristic
33C22×C22⋊C4×C109C2211yescharacteristic
34C22×C22⋊C4×C109C2211yescharacteristic
35C22×C22⋊C4×C109C2211yescharacteristic
36C22×C42×C109C2211yescharacteristic
37#397×C109—24no—
38#394×C109—24no—
39#392×C109—24no—
40#390×C109—24no—
41#386×C109—24no—
42#386×C109—24no—
43C2×#95×C109C2211yescharacteristic
44C2×#95×C109C2211yescharacteristic
45C2×#95×C109C2211yescharacteristic
46C2×#95×C109C2211yescharacteristic
47C2×#95×C109C2211yescharacteristic
48C2×#95×C109C2211yescharacteristic
49C2×#95×C109C2211yescharacteristic
50C2×#95×C109C2211yescharacteristic
51C2×#95×C109C2211yescharacteristic
52C2×#95×C109C2211yescharacteristic
53C2×#95×C109C2211yescharacteristic
54C2×#95×C109C2211yescharacteristic
55C2×#95×C109C2211yescharacteristic
56C2×#95×C109C2211yescharacteristic
57C25×C109C2311yescharacteristic
58C25×C109C2311yescharacteristic
59C25×C109C2311yescharacteristic
60C22×D4×C109—22no—
61C22×D4×C109—22no—
62C22×D4×C109—22no—
63C22×D4×C109—22no—
64C22×D4×C109—22no—
65C22×D4×C109—22no—
66C22×D4×C109—22no—
67C22×D4×C109—22no—
68C22×D4×C109—22no—
69C22×D4×C109—22no—
70C22×D4×C109—22no—
71C22×D4×C109—22no—
72C22×D4×C109—41no—
73C22×D4×C109—41no—
74C22×D4×C109—41no—
75C22×D4×C109—41no—
76C22×D4×C109—41no—
77C22×D4×C109—41no—
78C22×D4×C109—41no—
79C22×D4×C109—41no—
80C22×D4×C109D414yes—
81C23×C4×C109—22no—
82C23×C4×C109—22no—
83C23×C4×C109—22no—
84C23×C4×C109—41no—
85C23×C4×C109—41no—
86C23×C4×C109—41no—
87C23×C4×C109—41no—
88C23×C4×C109C2311yescharacteristic
89C23×C4×C109C2311yescharacteristic
90C23×C4×C109C2311yescharacteristic
91C23×C4×C109C2311yescharacteristic
92C23×C4×C109C2311yescharacteristic
93C23×C4×C109C2311yescharacteristic
94C23×C4×C109C2311yescharacteristic
95C23×C4×C109C2311yescharacteristic
96C23×C4×C109C2311yescharacteristic
97C23×C4×C109C2311yescharacteristic
98C23×C4×C109C2311yescharacteristic
99C23×C4×C109C2311yescharacteristic
100C2×C4⋊C4×C109—22no—
101C2×C4⋊C4×C109—22no—
102C2×C4⋊C4×C109—22no—
103C2×C4⋊C4×C109—22no—
104C2×C4⋊C4×C109—41no—
105C2×C4⋊C4×C109—41no—
106C2×C22⋊C4×C109—22no—
107C2×C22⋊C4×C109—22no—
108C2×C22⋊C4×C109—22no—
109C2×C22⋊C4×C109—22no—
110C2×C22⋊C4×C109—22no—
111C2×C22⋊C4×C109—22no—
112C2×C22⋊C4×C109—22no—
113C2×C22⋊C4×C109—22no—
114C2×C22⋊C4×C109—22no—
115C2×C22⋊C4×C109—22no—
116C2×C22⋊C4×C109—22no—
117C2×C22⋊C4×C109—22no—
118C2×C22⋊C4×C109—22no—
119C2×C22⋊C4×C109—22no—
120C2×C22⋊C4×C109—22no—
121C2×C22⋊C4×C109—22no—
122C2×C22⋊C4×C109—22no—
123C2×C22⋊C4×C109—22no—
124C2×C22⋊C4×C109—22no—
125C2×C22⋊C4×C109—22no—
126C2×C22⋊C4×C109—22no—
127C2×C22⋊C4×C109—22no—
128C2×C22⋊C4×C109—22no—
129C2×C22⋊C4×C109—22no—
130C2×C22⋊C4×C109—22no—
131C2×C22⋊C4×C109—41no—
132C2×C22⋊C4×C109—41no—
133C2×C22⋊C4×C109—41no—
134C2×C22⋊C4×C109—41no—
135C2×C22⋊C4×C109—41no—
136C2×C22⋊C4×C109—41no—
137C2×C22⋊C4×C109—41no—
138C2×C22⋊C4×C109—41no—
139C2×C22⋊C4×C109—41no—
140C2×C22⋊C4×C109—41no—
141C2×C22⋊C4×C109—41no—
142C2×C22⋊C4×C109—41no—
143C2×C22⋊C4×C109—41no—
144C2×C22⋊C4×C109—41no—
145C2×C22⋊C4×C109—41no—
146C2×C22⋊C4×C109—41no—
147C2×C22⋊C4×C109D414yescomplemented
148C2×C42×C109—22no—
149C2×C42×C109—22no—
150C2×C42×C109—41no—
151#95×C109—22no—
152#95×C109—22no—
153#95×C109—22no—
154#95×C109—22no—
155#95×C109—22no—
156#95×C109—22no—
157#95×C109—22no—
158#95×C109—22no—
159#95×C109—41no—
160#95×C109—41no—
161#95×C109—41no—
162#95×C109—41no—
163#95×C109—41no—
164#95×C109D414yescomplemented
165C24×C109—21no—
166C24×C109—21no—
167C24×C109—21no—
168C24×C109—21no—
169C24×C109—21no—
170C24×C109—21no—
171C24×C109—21no—
172C24×C109—21no—
173C24×C109—21no—
174C24×C109—21no—
175C24×C109—21no—
176C24×C109—21no—
177C24×C109—21no—
178C24×C109—21no—
179C24×C109—21no—
180C24×C109—21no—
181C24×C109—21no—
182C24×C109—21no—
183C24×C109—21no—
184C24×C109—21no—
185C24×C109—21no—
186C24×C109—21no—
187C24×C109—21no—
188C24×C109—21no—
189C24×C109—21no—
190C24×C109—21no—
191C24×C109—21no—
192C24×C109—21no—
193C24×C109—21no—
194C24×C109—21no—
195C24×C109—21no—
196C24×C109—21no—
197C24×C109—21no—
198C24×C109—21no—
199C24×C109—21no—
200C24×C109—21no—
201C24×C109—21no—
202C24×C109—21no—
203C24×C109—21no—
204C24×C109—21no—
205C24×C109C2×D412yes—
206C24×C109C2×D412yes—
207C24×C109C2×D412yes—
208C24×C109#4112yes—
209C24×C109#4112yes—
210C24×C109C2411yescharacteristic
211C2×D4×C109—28no—
212C2×D4×C109—28no—
213C2×D4×C109—28no—
214C2×D4×C109—44no—
215C2×D4×C109—44no—
216C2×D4×C109—44no—
217C2×D4×C109—44no—
218C2×D4×C109—44no—
219C2×D4×C109—44no—
220C2×D4×C109—44no—
221C2×D4×C109—44no—
222C2×D4×C109—44no—
223C2×D4×C109—44no—
224C2×D4×C109—44no—
225C2×D4×C109—44no—
226C2×D4×C109—44no—
227C2×D4×C109—44no—
228C2×D4×C109—44no—
229C2×D4×C109—44no—
230C2×D4×C109—44no—
231C2×D4×C109—44no—
232C22×C4×C109—21no—
233C22×C4×C109—21no—
234C22×C4×C109—21no—
235C22×C4×C109—21no—
236C22×C4×C109—21no—
237C22×C4×C109—21no—
238C22×C4×C109—21no—
239C22×C4×C109—21no—
240C22×C4×C109—21no—
241C22×C4×C109—21no—
242C22×C4×C109—21no—
243C22×C4×C109—21no—
244C22×C4×C109—21no—
245C22×C4×C109—21no—
246C22×C4×C109—21no—
247C22×C4×C109—21no—
248C22×C4×C109—21no—
249C22×C4×C109—21no—
250C22×C4×C109—21no—
251C22×C4×C109—21no—
252C22×C4×C109—21no—
253C22×C4×C109—21no—
254C22×C4×C109—21no—
255C22×C4×C109—21no—
256C22×C4×C109—21no—
257C22×C4×C109—21no—
258C22×C4×C109—21no—
259C22×C4×C109—21no—
260C22×C4×C109—21no—
261C22×C4×C109—21no—
262C22×C4×C109—21no—
263C22×C4×C109—21no—
264C22×C4×C109—21no—
265C22×C4×C109—21no—
266C22×C4×C109—21no—
267C22×C4×C109—21no—
268C22×C4×C109—21no—
269C22×C4×C109—21no—
270C22×C4×C109—21no—
271C22×C4×C109—21no—
272C22×C4×C109—21no—
273C22×C4×C109—21no—
274C22×C4×C109—21no—
275C22×C4×C109—21no—
276C22×C4×C109—21no—
277C22×C4×C109—21no—
278C22×C4×C109—21no—
279C22×C4×C109—21no—
280C22×C4×C109—21no—
281C22×C4×C109—21no—
282C22×C4×C109—21no—
283C22×C4×C109—21no—
284C22×C4×C109—21no—
285C22×C4×C109—21no—
286C22×C4×C109—21no—
287C22×C4×C109—21no—
288C22×C4×C109—21no—
289C22×C4×C109—21no—
290C22×C4×C109—21no—
291C22×C4×C109—21no—
292C22×C4×C109—21no—
293C22×C4×C109—21no—
294C22×C4×C109—21no—
295C22×C4×C109—21no—
296C22×C4×C109—21no—
297C22×C4×C109—21no—
298C22×C4×C109—21no—
299C22×C4×C109—21no—
300C22×C4×C109—21no—
301C22×C4×C109—21no—
302C22×C4×C109—21no—
303C22×C4×C109—21no—
304C22×C4×C109—21no—
305C22×C4×C109—21no—
306C22×C4×C109—44no—
307C22×C4×C109—44no—
308C22×C4×C109—44no—
309C22×C4×C109—44no—
310C22×C4×C109—44no—
311C22×C4×C109—44no—
312C22×C4×C109—44no—
313C22×C4×C109C2×D412yes—
314C22×C4×C109C2×D412yes—
315C22×C4×C109C2×D412yes—
316C22×C4×C109C2×D412yes—
317C22×C4×C109C2×D412yes—
318C22×C4×C109C2×D412yes—
319C22×C4×C109#4112yes—
320C22×C4×C109#4112yes—
321C22×C4×C109#4112yes—
322C22×C4×C109#4112yes—
323C4⋊C4×C109—44no—
324C4⋊C4×C109—44no—
325C22⋊C4×C109—44no—
326C22⋊C4×C109—44no—
327C22⋊C4×C109—44no—
328C22⋊C4×C109—44no—
329C22⋊C4×C109—44no—
330C22⋊C4×C109—44no—
331C22⋊C4×C109—44no—
332C22⋊C4×C109—44no—
333C22⋊C4×C109—44no—
334C22⋊C4×C109—44no—
335C22⋊C4×C109—44no—
336C22⋊C4×C109—44no—
337C22⋊C4×C109—44no—
338C22⋊C4×C109—44no—
339C42×C109—44no—
340C23×C109—22no—
341C23×C109—22no—
342C23×C109—22no—
343C23×C109—22no—
344C23×C109—22no—
345C23×C109—22no—
346C23×C109—22no—
347C23×C109—22no—
348C23×C109—22no—
349C23×C109—22no—
350C23×C109—22no—
351C23×C109—22no—
352C23×C109—22no—
353C23×C109—22no—
354C23×C109—22no—
355C23×C109—22no—
356C23×C109—22no—
357C23×C109—22no—
358C23×C109—22no—
359C23×C109—22no—
360C23×C109—22no—
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—41no—
373C23×C109—41no—
374C23×C109—41no—
375C23×C109—41no—
376C23×C109—41no—
377C23×C109—41no—
378C23×C109—41no—
379C23×C109—41no—
380C23×C109—41no—
381C23×C109—41no—
382C23×C109—41no—
383C23×C109—41no—
384C23×C109—41no—
385C23×C109—41no—
386C23×C109—41no—
387C23×C109—41no—
388C23×C109—41no—
389C23×C109—41no—
390C23×C109—41no—
391C23×C109—41no—
392C23×C109—41no—
393C23×C109—41no—
394C23×C109—41no—
395C23×C109—41no—
396C23×C109—41no—
397C23×C109—41no—
398C23×C109—41no—
399C23×C109—41no—
400C23×C109—41no—
401C23×C109—41no—
402C23×C109—41no—
403C23×C109—41no—
404C23×C109—41no—
405C23×C109—41no—
406C23×C109—41no—
407C23×C109—41no—
408C23×C109—41no—
409C23×C109—41no—
410C23×C109—41no—
411C23×C109—41no—
412C23×C109—41no—
413C23×C109—41no—
414C23×C109—41no—
415C23×C109—41no—
416C23×C109—41no—
417C23×C109—41no—
418C23×C109—41no—
419C23×C109—41no—
420C23×C109—41no—
421C23×C109—41no—
422C23×C109—41no—
423C23×C109—41no—
424C23×C109—41no—
425C23×C109—41no—
426C23×C109—41no—
427C23×C109—41no—
428C23×C109—41no—
429C23×C109—41no—
430C23×C109—41no—
431C23×C109—41no—
432C23×C109—41no—
433C23×C109—41no—
434C23×C109—41no—
435C23×C109—41no—
436C23×C109—41no—
437C23×C109—41no—
438C23×C109—41no—
439C23×C109—41no—
440C23×C109—41no—
441C23×C109—41no—
442C23×C109—41no—
443C23×C109—41no—
444C23×C109#12114yes—
445C23×C109C22×D411yescharacteristic
446C23×C109C22×D411yescharacteristic
447C23×C109C22×D411yescharacteristic
448C23×C109C2×#4111yescharacteristic
449C23×C109C2×#4111yescharacteristic
450C23×C109C2×#4111yescharacteristic
451C23×C109C2×#4111yescharacteristic
452C23×C109C2×#4111yescharacteristic
453C23×C109C2×#4111yescharacteristic
454C23×C109H(5,𝔽2)11yescharacteristic
455C23×C109H(5,𝔽2)11yescharacteristic
456C23×C109H(5,𝔽2)11yescharacteristic
457C23×C109H(5,𝔽2)11yescharacteristic
458C23×C109H(5,𝔽2)11yescharacteristic
459C23×C109H(5,𝔽2)11yescharacteristic
460D4×C109—416no—
461D4×C109—416no—
462D4×C109—416no—
463C2×C4×C109—22no—
464C2×C4×C109—22no—
465C2×C4×C109—22no—
466C2×C4×C109—22no—
467C2×C4×C109—22no—
468C2×C4×C109—22no—
469C2×C4×C109—22no—
470C2×C4×C109—22no—
471C2×C4×C109—22no—
472C2×C4×C109—22no—
473C2×C4×C109—22no—
474C2×C4×C109—22no—
475C2×C4×C109—22no—
476C2×C4×C109—22no—
477C2×C4×C109—22no—
478C2×C4×C109—22no—
479C2×C4×C109—22no—
480C2×C4×C109—22no—
481C2×C4×C109—22no—
482C2×C4×C109—22no—
483C2×C4×C109—22no—
484C2×C4×C109—22no—
485C2×C4×C109—22no—
486C2×C4×C109—22no—
487C2×C4×C109—22no—
488C2×C4×C109—22no—
489C2×C4×C109—22no—
490C2×C4×C109—416no—
491C2×C4×C109—41no—
492C2×C4×C109—41no—
493C2×C4×C109—41no—
494C2×C4×C109—41no—
495C2×C4×C109—41no—
496C2×C4×C109—41no—
497C2×C4×C109—41no—
498C2×C4×C109—41no—
499C2×C4×C109—41no—
500C2×C4×C109—41no—
501C2×C4×C109—41no—
502C2×C4×C109—41no—
503C2×C4×C109—41no—
504C2×C4×C109—41no—
505C2×C4×C109—41no—
506C2×C4×C109—41no—
507C2×C4×C109—41no—
508C2×C4×C109—41no—
509C2×C4×C109—41no—
510C2×C4×C109—41no—
511C2×C4×C109—41no—
512C2×C4×C109—41no—
513C2×C4×C109—41no—
514C2×C4×C109—41no—
515C2×C4×C109—41no—
516C2×C4×C109—41no—
517C2×C4×C109—41no—
518C2×C4×C109—41no—
519C2×C4×C109—41no—
520C2×C4×C109—41no—
521C2×C4×C109—41no—
522C2×C4×C109—41no—
523C2×C4×C109—41no—
524C2×C4×C109—41no—
525C2×C4×C109—41no—
526C2×C4×C109—41no—
527C2×C4×C109—41no—
528C2×C4×C109—41no—
529C2×C4×C109—41no—
530C2×C4×C109—41no—
531C2×C4×C109—41no—
532C2×C4×C109—41no—
533C2×C4×C109—41no—
534C2×C4×C109—41no—
535C2×C4×C109—41no—
536C2×C4×C109—41no—
537C2×C4×C109—41no—
538C2×C4×C109—41no—
539C2×C4×C109—41no—
540C2×C4×C109—41no—
541C2×C4×C109—41no—
542C2×C4×C109—41no—
543C2×C4×C109—41no—
544C2×C4×C109—41no—
545C2×C4×C109—41no—
546C2×C4×C109—41no—
547C2×C4×C109#12314yes—
548C22×C109—24no—
549C22×C109—24no—
550C22×C109—24no—
551C22×C109—42no—
552C22×C109—42no—
553C22×C109—42no—
554C22×C109—42no—
555C22×C109—42no—
556C22×C109—42no—
557C22×C109—42no—
558C22×C109—42no—
559C22×C109—42no—
560C22×C109—42no—
561C22×C109—42no—
562C22×C109—42no—
563C22×C109—42no—
564C22×C109—42no—
565C22×C109—42no—
566C22×C109—42no—
567C22×C109—42no—
568C22×C109—42no—
569C22×C109—42no—
570C22×C109—42no—
571C22×C109—42no—
572C22×C109—42no—
573C22×C109—42no—
574C22×C109—42no—
575C22×C109—42no—
576C22×C109—42no—
577C22×C109—81no—
578C22×C109—81no—
579C22×C109—81no—
580C22×C109—81no—
581C22×C109—81no—
582C22×C109—81no—
583C22×C109—81no—
584C22×C109—81no—
585C22×C109—81no—
586C22×C109—81no—
587C22×C109—81no—
588C22×C109—81no—
589C22×C109—81no—
590C22×C109—81no—
591C22×C109—81no—
592C22×C109—81no—
593C22×C109C2×#12111yescharacteristic
594C22×C109C2×#12311yescharacteristic
595C22×C109#52511yescharacteristic
596C22×C109#52911yescharacteristic
597C22×C109#53211yescharacteristic
598C22×C109#53211yescharacteristic
599C22×C109#53411yescharacteristic
600C22×C109#53411yescharacteristic
601C22×C109#53511yescharacteristic
602C22×C109#53811yescharacteristic
603C22×C109#53811yescharacteristic
604C22×C109#53811yescharacteristic
605C22×C109#53811yescharacteristic
606C22×C109#54011yescharacteristic
607C22×C109#54011yescharacteristic
608C22×C109D4211yescharacteristic
609C22×C109D4211yescharacteristic
610C22×C109#54611yescharacteristic
611C22×C109#54611yescharacteristic
612C22×C109#54611yescharacteristic
613C22×C109#54611yescharacteristic
614C22×C109#54611yescharacteristic
615C22×C109#54611yescharacteristic
616C22×C109#54611yescharacteristic
617C22×C109#55011yescharacteristic
618C22×C109#55111yescharacteristic
619C22×C109#55111yescharacteristic
620C22×C109#55111yescharacteristic
621C22×C109#55311yescharacteristic
622C22×C109#55311yescharacteristic
623C22×C109#55311yescharacteristic
624C22×C109#55511yescharacteristic
625C22×C109#55911yescharacteristic
626C22×C109#56011yescharacteristic
627C22×C109#56011yescharacteristic
628C4×C109—24no—
629C4×C109—42no—
630C4×C109—42no—
631C4×C109—42no—
632C4×C109—42no—
633C4×C109—42no—
634C4×C109—42no—
635C4×C109—42no—
636C4×C109—81no—
637C4×C109—81no—
638C4×C109—81no—
639C4×C109—81no—
640#15501C10911yesmaximal, characteristic, direct product factor, Sylow
641C2×C109—44no—
642C2×C109—82no—
643C2×C109—82no—
644C2×C109#241211yescharacteristic
645C2×C109#242011yescharacteristic
646C2×C109#242411yescharacteristic
647C2×C109#244511yescharacteristic
648C2×C109#246711yescharacteristic
649C2×C109#254311yescharacteristic
650C2×C109#255511yescharacteristic
651C2×C109#255711yescharacteristic
652C2×C109#260311yescharacteristic
653C2×C109#267311yescharacteristic
654C2×C109#267811yescharacteristic
655C2×C109#268811yescharacteristic
656C2×C109#269711yescharacteristic
657C2×C109#275611yescharacteristic
658C2×C109#279711yescharacteristic
659C2×#397C2×C10911yescharacteristic, complemented
660C2×#394C2×C10911yescharacteristic, complemented
661C2×#392C2×C10911yescharacteristic
662C2×#390C2×C10911yescharacteristic, complemented
663C2×#386C2×C10911yescharacteristic, complemented
664C2×#386C2×C10911yescharacteristic, complemented
665#1441C2×C10911yescharacteristic, complemented
666#1440C2×C10911yescharacteristic, complemented
667#1440C2×C10911yescharacteristic, complemented
668#1439C2×C10911yescharacteristic, complemented
669#1438C2×C10911yescharacteristic, complemented
670#1438C2×C10911yescharacteristic, complemented
671#1437C2×C10911yescharacteristic, complemented
672#1434C2×C10911yescharacteristic, complemented
673C22⋊#95C2×C10911yescharacteristic, complemented
674C109#1550111yescharacteristic, direct product factor, Sylow
675C23×D4C22×C10911yescharacteristic
676C23×D4C22×C10911yescharacteristic
677C23×D4C22×C10911yescharacteristic
678C24×C4C22×C10911yescharacteristic
679C22×C4⋊C4C22×C10911yescharacteristic
680C22×C4⋊C4C22×C10911yescharacteristic
681C22×C22⋊C4C22×C10911yescharacteristic
682C22×C22⋊C4C22×C10911yescharacteristic
683C22×C22⋊C4C22×C10911yescharacteristic
684C22×C22⋊C4C22×C10911yescharacteristic
685C22×C22⋊C4C22×C10911yescharacteristic
686C22×C22⋊C4C22×C10911yescharacteristic
687C22×C22⋊C4C22×C10911yescharacteristic
688C22×C22⋊C4C22×C10911yescharacteristic
689C22×C22⋊C4C22×C10911yescharacteristic
690C22×C22⋊C4C22×C10911yescharacteristic
691C22×C22⋊C4C22×C10911yescharacteristic
692C22×C22⋊C4C22×C10911yescharacteristic
693C22×C22⋊C4C22×C10911yescharacteristic
694C22×C22⋊C4C22×C10911yescharacteristic
695C22×C42C22×C10911yescharacteristic
696#397—24no—
697#394—24no—
698#392—24no—
699#390—24no—
700#386—24no—
701#386—24no—
702C2×#95C22×C10911yescharacteristic
703C2×#95C22×C10911yescharacteristic
704C2×#95C22×C10911yescharacteristic
705C2×#95C22×C10911yescharacteristic
706C2×#95C22×C10911yescharacteristic
707C2×#95C22×C10911yescharacteristic
708C2×#95C22×C10911yescharacteristic
709C2×#95C22×C10911yescharacteristic
710C2×#95C22×C10911yescharacteristic
711C2×#95C22×C10911yescharacteristic
712C2×#95C22×C10911yescharacteristic
713C2×#95C22×C10911yescharacteristic
714C2×#95C22×C10911yescharacteristic
715C2×#95C22×C10911yescharacteristic
716C25C23×C10911yescharacteristic
717C25C23×C10911yescharacteristic
718C25C23×C10911yescharacteristic
719C22×D4—22no—
720C22×D4—22no—
721C22×D4—22no—
722C22×D4—22no—
723C22×D4—22no—
724C22×D4—22no—
725C22×D4—22no—
726C22×D4—22no—
727C22×D4—22no—
728C22×D4—22no—
729C22×D4—22no—
730C22×D4—22no—
731C22×D4—41no—
732C22×D4—41no—
733C22×D4—41no—
734C22×D4—41no—
735C22×D4—41no—
736C22×D4—41no—
737C22×D4—41no—
738C22×D4—41no—
739C22×D4D4×C10914yes—
740C23×C4—22no—
741C23×C4—22no—
742C23×C4—22no—
743C23×C4—41no—
744C23×C4—41no—
745C23×C4—41no—
746C23×C4—41no—
747C23×C4C23×C10911yescharacteristic
748C23×C4C23×C10911yescharacteristic
749C23×C4C23×C10911yescharacteristic
750C23×C4C23×C10911yescharacteristic
751C23×C4C23×C10911yescharacteristic
752C23×C4C23×C10911yescharacteristic
753C23×C4C23×C10911yescharacteristic
754C23×C4C23×C10911yescharacteristic
755C23×C4C23×C10911yescharacteristic
756C23×C4C23×C10911yescharacteristic
757C23×C4C23×C10911yescharacteristic
758C23×C4C23×C10911yescharacteristic
759C2×C4⋊C4—22no—
760C2×C4⋊C4—22no—
761C2×C4⋊C4—22no—
762C2×C4⋊C4—22no—
763C2×C4⋊C4—41no—
764C2×C4⋊C4—41no—
765C2×C22⋊C4—22no—
766C2×C22⋊C4—22no—
767C2×C22⋊C4—22no—
768C2×C22⋊C4—22no—
769C2×C22⋊C4—22no—
770C2×C22⋊C4—22no—
771C2×C22⋊C4—22no—
772C2×C22⋊C4—22no—
773C2×C22⋊C4—22no—
774C2×C22⋊C4—22no—
775C2×C22⋊C4—22no—
776C2×C22⋊C4—22no—
777C2×C22⋊C4—22no—
778C2×C22⋊C4—22no—
779C2×C22⋊C4—22no—
780C2×C22⋊C4—22no—
781C2×C22⋊C4—22no—
782C2×C22⋊C4—22no—
783C2×C22⋊C4—22no—
784C2×C22⋊C4—22no—
785C2×C22⋊C4—22no—
786C2×C22⋊C4—22no—
787C2×C22⋊C4—22no—
788C2×C22⋊C4—22no—
789C2×C22⋊C4—22no—
790C2×C22⋊C4—41no—
791C2×C22⋊C4—41no—
792C2×C22⋊C4—41no—
793C2×C22⋊C4—41no—
794C2×C22⋊C4—41no—
795C2×C22⋊C4—41no—
796C2×C22⋊C4—41no—
797C2×C22⋊C4—41no—
798C2×C22⋊C4—41no—
799C2×C22⋊C4—41no—
800C2×C22⋊C4—41no—
801C2×C22⋊C4—41no—
802C2×C22⋊C4—41no—
803C2×C22⋊C4—41no—
804C2×C22⋊C4—41no—
805C2×C22⋊C4—41no—
806C2×C22⋊C4D4×C10914yescomplemented
807C2×C42—22no—
808C2×C42—22no—
809C2×C42—41no—
810#95—22no—
811#95—22no—
812#95—22no—
813#95—22no—
814#95—22no—
815#95—22no—
816#95—22no—
817#95—22no—
818#95—41no—
819#95—41no—
820#95—41no—
821#95—41no—
822#95—41no—
823#95D4×C10914yescomplemented
824C24—21no—
825C24—21no—
826C24—21no—
827C24—21no—
828C24—21no—
829C24—21no—
830C24—21no—
831C24—21no—
832C24—21no—
833C24—21no—
834C24—21no—
835C24—21no—
836C24—21no—
837C24—21no—
838C24—21no—
839C24—21no—
840C24—21no—
841C24—21no—
842C24—21no—
843C24—21no—
844C24—21no—
845C24—21no—
846C24—21no—
847C24—21no—
848C24—21no—
849C24—21no—
850C24—21no—
851C24—21no—
852C24—21no—
853C24—21no—
854C24—21no—
855C24—21no—
856C24—21no—
857C24—21no—
858C24—21no—
859C24—21no—
860C24—21no—
861C24—21no—
862C24—21no—
863C24—21no—
864C24C2×D4×C10912yes—
865C24C2×D4×C10912yes—
866C24C2×D4×C10912yes—
867C24#41×C10912yes—
868C24#41×C10912yes—
869C24C24×C10911yescharacteristic
870C2×D4—28no—
871C2×D4—28no—
872C2×D4—28no—
873C2×D4—44no—
874C2×D4—44no—
875C2×D4—44no—
876C2×D4—44no—
877C2×D4—44no—
878C2×D4—44no—
879C2×D4—44no—
880C2×D4—44no—
881C2×D4—44no—
882C2×D4—44no—
883C2×D4—44no—
884C2×D4—44no—
885C2×D4—44no—
886C2×D4—44no—
887C2×D4—44no—
888C2×D4—44no—
889C2×D4—44no—
890C2×D4—44no—
891C22×C4—21no—
892C22×C4—21no—
893C22×C4—21no—
894C22×C4—21no—
895C22×C4—21no—
896C22×C4—21no—
897C22×C4—21no—
898C22×C4—21no—
899C22×C4—21no—
900C22×C4—21no—
901C22×C4—21no—
902C22×C4—21no—
903C22×C4—21no—
904C22×C4—21no—
905C22×C4—21no—
906C22×C4—21no—
907C22×C4—21no—
908C22×C4—21no—
909C22×C4—21no—
910C22×C4—21no—
911C22×C4—21no—
912C22×C4—21no—
913C22×C4—21no—
914C22×C4—21no—
915C22×C4—21no—
916C22×C4—21no—
917C22×C4—21no—
918C22×C4—21no—
919C22×C4—21no—
920C22×C4—21no—
921C22×C4—21no—
922C22×C4—21no—
923C22×C4—21no—
924C22×C4—21no—
925C22×C4—21no—
926C22×C4—21no—
927C22×C4—21no—
928C22×C4—21no—
929C22×C4—21no—
930C22×C4—21no—
931C22×C4—21no—
932C22×C4—21no—
933C22×C4—21no—
934C22×C4—21no—
935C22×C4—21no—
936C22×C4—21no—
937C22×C4—21no—
938C22×C4—21no—
939C22×C4—21no—
940C22×C4—21no—
941C22×C4—21no—
942C22×C4—21no—
943C22×C4—21no—
944C22×C4—21no—
945C22×C4—21no—
946C22×C4—21no—
947C22×C4—21no—
948C22×C4—21no—
949C22×C4—21no—
950C22×C4—21no—
951C22×C4—21no—
952C22×C4—21no—
953C22×C4—21no—
954C22×C4—21no—
955C22×C4—21no—
956C22×C4—21no—
957C22×C4—21no—
958C22×C4—21no—
959C22×C4—21no—
960C22×C4—21no—
961C22×C4—21no—
962C22×C4—21no—
963C22×C4—21no—
964C22×C4—21no—
965C22×C4—44no—
966C22×C4—44no—
967C22×C4—44no—
968C22×C4—44no—
969C22×C4—44no—
970C22×C4—44no—
971C22×C4—44no—
972C22×C4C2×D4×C10912yes—
973C22×C4C2×D4×C10912yes—
974C22×C4C2×D4×C10912yes—
975C22×C4C2×D4×C10912yes—
976C22×C4C2×D4×C10912yes—
977C22×C4C2×D4×C10912yes—
978C22×C4#41×C10912yes—
979C22×C4#41×C10912yes—
980C22×C4#41×C10912yes—
981C22×C4#41×C10912yes—
982C4⋊C4—44no—
983C4⋊C4—44no—
984C22⋊C4—44no—
985C22⋊C4—44no—
986C22⋊C4—44no—
987C22⋊C4—44no—
988C22⋊C4—44no—
989C22⋊C4—44no—
990C22⋊C4—44no—
991C22⋊C4—44no—
992C22⋊C4—44no—
993C22⋊C4—44no—
994C22⋊C4—44no—
995C22⋊C4—44no—
996C22⋊C4—44no—
997C22⋊C4—44no—
998C42—44no—
999C23—22no—
1000C23—22no—
1001C23—22no—
1002C23—22no—
1003C23—22no—
1004C23—22no—
1005C23—22no—
1006C23—22no—
1007C23—22no—
1008C23—22no—
1009C23—22no—
1010C23—22no—
1011C23—22no—
1012C23—22no—
1013C23—22no—
1014C23—22no—
1015C23—22no—
1016C23—22no—
1017C23—22no—
1018C23—22no—
1019C23—22no—
1020C23—22no—
1021C23—22no—
1022C23—22no—
1023C23—22no—
1024C23—22no—
1025C23—22no—
1026C23—22no—
1027C23—22no—
1028C23—22no—
1029C23—22no—
1030C23—22no—
1031C23—41no—
1032C23—41no—
1033C23—41no—
1034C23—41no—
1035C23—41no—
1036C23—41no—
1037C23—41no—
1038C23—41no—
1039C23—41no—
1040C23—41no—
1041C23—41no—
1042C23—41no—
1043C23—41no—
1044C23—41no—
1045C23—41no—
1046C23—41no—
1047C23—41no—
1048C23—41no—
1049C23—41no—
1050C23—41no—
1051C23—41no—
1052C23—41no—
1053C23—41no—
1054C23—41no—
1055C23—41no—
1056C23—41no—
1057C23—41no—
1058C23—41no—
1059C23—41no—
1060C23—41no—
1061C23—41no—
1062C23—41no—
1063C23—41no—
1064C23—41no—
1065C23—41no—
1066C23—41no—
1067C23—41no—
1068C23—41no—
1069C23—41no—
1070C23—41no—
1071C23—41no—
1072C23—41no—
1073C23—41no—
1074C23—41no—
1075C23—41no—
1076C23—41no—
1077C23—41no—
1078C23—41no—
1079C23—41no—
1080C23—41no—
1081C23—41no—
1082C23—41no—
1083C23—41no—
1084C23—41no—
1085C23—41no—
1086C23—41no—
1087C23—41no—
1088C23—41no—
1089C23—41no—
1090C23—41no—
1091C23—41no—
1092C23—41no—
1093C23—41no—
1094C23—41no—
1095C23—41no—
1096C23—41no—
1097C23—41no—
1098C23—41no—
1099C23—41no—
1100C23—41no—
1101C23—41no—
1102C23—41no—
1103C23#121×C10914yes—
1104C23C22×D4×C10911yescharacteristic
1105C23C22×D4×C10911yescharacteristic
1106C23C22×D4×C10911yescharacteristic
1107C23C2×#41×C10911yescharacteristic
1108C23C2×#41×C10911yescharacteristic
1109C23C2×#41×C10911yescharacteristic
1110C23C2×#41×C10911yescharacteristic
1111C23C2×#41×C10911yescharacteristic
1112C23C2×#41×C10911yescharacteristic
1113C23H(5,𝔽2)×C10911yescharacteristic
1114C23H(5,𝔽2)×C10911yescharacteristic
1115C23H(5,𝔽2)×C10911yescharacteristic
1116C23H(5,𝔽2)×C10911yescharacteristic
1117C23H(5,𝔽2)×C10911yescharacteristic
1118C23H(5,𝔽2)×C10911yescharacteristic
1119D4—416no—
1120D4—416no—
1121D4—416no—
1122C2×C4—22no—
1123C2×C4—22no—
1124C2×C4—22no—
1125C2×C4—22no—
1126C2×C4—22no—
1127C2×C4—22no—
1128C2×C4—22no—
1129C2×C4—22no—
1130C2×C4—22no—
1131C2×C4—22no—
1132C2×C4—22no—
1133C2×C4—22no—
1134C2×C4—22no—
1135C2×C4—22no—
1136C2×C4—22no—
1137C2×C4—22no—
1138C2×C4—22no—
1139C2×C4—22no—
1140C2×C4—22no—
1141C2×C4—22no—
1142C2×C4—22no—
1143C2×C4—22no—
1144C2×C4—22no—
1145C2×C4—22no—
1146C2×C4—22no—
1147C2×C4—22no—
1148C2×C4—22no—
1149C2×C4—416no—
1150C2×C4—41no—
1151C2×C4—41no—
1152C2×C4—41no—
1153C2×C4—41no—
1154C2×C4—41no—
1155C2×C4—41no—
1156C2×C4—41no—
1157C2×C4—41no—
1158C2×C4—41no—
1159C2×C4—41no—
1160C2×C4—41no—
1161C2×C4—41no—
1162C2×C4—41no—
1163C2×C4—41no—
1164C2×C4—41no—
1165C2×C4—41no—
1166C2×C4—41no—
1167C2×C4—41no—
1168C2×C4—41no—
1169C2×C4—41no—
1170C2×C4—41no—
1171C2×C4—41no—
1172C2×C4—41no—
1173C2×C4—41no—
1174C2×C4—41no—
1175C2×C4—41no—
1176C2×C4—41no—
1177C2×C4—41no—
1178C2×C4—41no—
1179C2×C4—41no—
1180C2×C4—41no—
1181C2×C4—41no—
1182C2×C4—41no—
1183C2×C4—41no—
1184C2×C4—41no—
1185C2×C4—41no—
1186C2×C4—41no—
1187C2×C4—41no—
1188C2×C4—41no—
1189C2×C4—41no—
1190C2×C4—41no—
1191C2×C4—41no—
1192C2×C4—41no—
1193C2×C4—41no—
1194C2×C4—41no—
1195C2×C4—41no—
1196C2×C4—41no—
1197C2×C4—41no—
1198C2×C4—41no—
1199C2×C4—41no—
1200C2×C4—41no—
1201C2×C4—41no—
1202C2×C4—41no—
1203C2×C4—41no—
1204C2×C4—41no—
1205C2×C4—41no—
1206C2×C4#123×C10914yes—
1207C22—24no—
1208C22—24no—
1209C22—24no—
1210C22—42no—
1211C22—42no—
1212C22—42no—
1213C22—42no—
1214C22—42no—
1215C22—42no—
1216C22—42no—
1217C22—42no—
1218C22—42no—
1219C22—42no—
1220C22—42no—
1221C22—42no—
1222C22—42no—
1223C22—42no—
1224C22—42no—
1225C22—42no—
1226C22—42no—
1227C22—42no—
1228C22—42no—
1229C22—42no—
1230C22—42no—
1231C22—42no—
1232C22—42no—
1233C22—42no—
1234C22—42no—
1235C22—42no—
1236C22—81no—
1237C22—81no—
1238C22—81no—
1239C22—81no—
1240C22—81no—
1241C22—81no—
1242C22—81no—
1243C22—81no—
1244C22—81no—
1245C22—81no—
1246C22—81no—
1247C22—81no—
1248C22—81no—
1249C22—81no—
1250C22—81no—
1251C22—81no—
1252C22C2×#121×C10911yescharacteristic
1253C22C2×#123×C10911yescharacteristic
1254C22#525×C10911yescharacteristic
1255C22#529×C10911yescharacteristic
1256C22#532×C10911yescharacteristic
1257C22#532×C10911yescharacteristic
1258C22#534×C10911yescharacteristic
1259C22#534×C10911yescharacteristic
1260C22#535×C10911yescharacteristic
1261C22#538×C10911yescharacteristic
1262C22#538×C10911yescharacteristic
1263C22#538×C10911yescharacteristic
1264C22#538×C10911yescharacteristic
1265C22#540×C10911yescharacteristic
1266C22#540×C10911yescharacteristic
1267C22D42×C10911yescharacteristic
1268C22D42×C10911yescharacteristic
1269C22#546×C10911yescharacteristic
1270C22#546×C10911yescharacteristic
1271C22#546×C10911yescharacteristic
1272C22#546×C10911yescharacteristic
1273C22#546×C10911yescharacteristic
1274C22#546×C10911yescharacteristic
1275C22#546×C10911yescharacteristic
1276C22#550×C10911yescharacteristic
1277C22#551×C10911yescharacteristic
1278C22#551×C10911yescharacteristic
1279C22#551×C10911yescharacteristic
1280C22#553×C10911yescharacteristic
1281C22#553×C10911yescharacteristic
1282C22#553×C10911yescharacteristic
1283C22#555×C10911yescharacteristic
1284C22#559×C10911yescharacteristic
1285C22#560×C10911yescharacteristic
1286C22#560×C10911yescharacteristic
1287C4—24no—
1288C4—42no—
1289C4—42no—
1290C4—42no—
1291C4—42no—
1292C4—42no—
1293C4—42no—
1294C4—42no—
1295C4—81no—
1296C4—81no—
1297C4—81no—
1298C4—81no—
1299C2—44no—
1300C2—82no—
1301C2—82no—
1302C2C109×#241211yescharacteristic
1303C2C109×#242011yescharacteristic
1304C2C109×#242411yescharacteristic
1305C2C109×#244511yescharacteristic
1306C2C109×#246711yescharacteristic
1307C2C109×#254311yescharacteristic
1308C2C109×#255511yescharacteristic
1309C2C109×#255711yescharacteristic
1310C2C109×#260311yescharacteristic
1311C2C109×#267311yescharacteristic
1312C2C109×#267811yescharacteristic
1313C2C109×#268811yescharacteristic
1314C2C109×#269711yescharacteristic
1315C2C109×#275611yescharacteristic
1316C2C109×#279711yescharacteristic
subgroupG/H
center, socleC24×C109C24
commutator, Frattini, cosocleC24C24×C109
prime radicalC2×#392×C109C2
LCSG ▷ C24 ▷ C1
UCSC1 ◁ C24×C109 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×#397×C109C2semidirect
2. C2×#394×C109C2semidirect
4. C2×#390×C109C2semidirect
5. C2×#386×C109C2semidirect
6. C2×#386×C109C2semidirect
7. C109×#1441C2semidirect
8. C109×#1440C2semidirect
9. C109×#1440C2semidirect
10. C109×#1439C2semidirect
11. C109×#1438C2semidirect
12. C109×#1438C2semidirect
13. C109×#1437C2semidirect
14. C109×#1434C2semidirect
15. C109×C22⋊#95C2semidirect
147. C2×C22⋊C4×C109D4semidirect
164. #95×C109D4semidirect
640. #15501C109direct (N × H)
659. C2×#397C2×C109semidirect
660. C2×#394C2×C109semidirect
662. C2×#390C2×C109semidirect
663. C2×#386C2×C109semidirect
664. C2×#386C2×C109semidirect
665. #1441C2×C109semidirect
666. #1440C2×C109semidirect
667. #1440C2×C109semidirect
668. #1439C2×C109semidirect
669. #1438C2×C109semidirect
670. #1438C2×C109semidirect
671. #1437C2×C109semidirect
672. #1434C2×C109semidirect
673. C22⋊#95C2×C109semidirect
674. C109#15501direct (N × H)
806. C2×C22⋊C4D4×C109semidirect
823. #95D4×C109semidirect

Maximal subgroups

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

subgroupindex
C2×#397×C1092
C2×#394×C1092
C2×#392×C1092
C2×#390×C1092
C2×#386×C1092
C109×#14412
C109×#14402
C109×#14392
C109×#14382
C109×#14372
C109×#14342
C109×C22⋊#952
#15501109