Finite Group Databasebeta

← C109×#25585 #42143579

Subgroups — C109×#25585 #42143579

Order 27904.

1636 conjugacy classes of subgroups.

The subgroup lattice has 786 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C109×#3505C211yesmaximal, characteristic, complemented
2C109×#2435C211yesmaximal, characteristic, complemented
3C109×#2433C211yesmaximal, characteristic, complemented
4C109×#2408C211yesmaximal, characteristic, complemented
5C109×#2021C214yesmaximal, complemented
6C109×#1996C211yesmaximal, characteristic, complemented
7C109×#1964C211yesmaximal, characteristic, complemented
8C109×#1889C214yesmaximal, complemented
9C4×#99×C109C211yesmaximal, characteristic, complemented
10C23×D4×C109C2211yescharacteristic
11#553×C109—21no—
12#553×C109—22no—
13#552×C109—21no—
14#551×C109—22no—
15#548×C109—21no—
16#546×C109—21no—
17#539×C109—21no—
18#538×C109—21no—
19#534×C109C2212yes—
20C2×#127×C109—21no—
21#529×C109—21no—
22C2×#124×C109—21no—
23#525×C109—21no—
24C2×C22⋊Q8×C109C2211yescharacteristic
25C2×#121×C109—21no—
26C2×#121×C109C2211yescharacteristic
27C2×#120×C109C2214yes—
28C2×#120×C109C2212yes—
29#518×C109C2212yes—
30C2×C4×D4×C109C2211yescharacteristic
31C2×#99×C109C2212yes—
32C2×#99×C109C2214yes—
33#394×C109—22no—
34#394×C109—21no—
35#392×C109—22no—
36#392×C109—21no—
37#390×C109—21no—
38#390×C109—21no—
39#390×C109—21no—
40#380×C109C2211yescharacteristic
41#379×C109C2214yes—
42#379×C109C2212yes—
43C4×C22⋊C4×C109C2211yescharacteristic
44C4×C22⋊C4×C109C2211yescharacteristic
45#342×C109C2214yes—
46#342×C109C2212yes—
47C25×C109C2312yes—
48C2×#41×C109—21no—
49C22×Q8×C109D411yescharacteristic, complemented
50C22×D4×C109—22no—
51C22×D4×C109—24no—
52C22×D4×C109—21no—
53C22×D4×C109—21no—
54C22×D4×C109—21no—
55C22×D4×C109—21no—
56C22×D4×C109—21no—
57C22×D4×C109—21no—
58C22×D4×C109—44no—
59C22×D4×C109D411yescharacteristic, complemented
60C22×D4×C109C2311yescharacteristic
61C22×D4×C109C2312yes—
62C23×C4×C109D411yescharacteristic, complemented
63C23×C4×C109C2311yescharacteristic
64#127×C109—44no—
65#126×C109—22no—
66#126×C109—22no—
67#126×C109—22no—
68#125×C109—21no—
69#125×C109—22no—
70#124×C109—21no—
71#124×C109—22no—
72#124×C109—44no—
73#123×C109—22no—
74#123×C109—22no—
75#123×C109—22no—
76#123×C109—22no—
77#123×C109—22no—
78C22⋊Q8×C109—21no—
79C22⋊Q8×C109—22no—
80C22⋊Q8×C109—21no—
81C22⋊Q8×C109—21no—
82C22⋊Q8×C109—21no—
83C22⋊Q8×C109—21no—
84#121×C109—21no—
85#121×C109—22no—
86#121×C109—21no—
87#121×C109—21no—
88#121×C109—21no—
89#121×C109—21no—
90#121×C109—22no—
91#121×C109—22no—
92#121×C109—44no—
93#120×C109—22no—
94#120×C109—22no—
95#120×C109—28no—
96#120×C109—44no—
97#120×C109—44no—
98C4×Q8×C109—21no—
99C4×D4×C109—22no—
100C4×D4×C109—21no—
101C4×D4×C109—21no—
102C4×D4×C109—21no—
103C4×D4×C109—21no—
104C4×D4×C109—21no—
105C4×D4×C109—22no—
106C4×D4×C109—22no—
107C4×D4×C109—22no—
108C4×D4×C109—22no—
109#117×C109—21no—
110#117×C109—22no—
111#117×C109—22no—
112C2×C4⋊C4×C109—21no—
113C2×C4⋊C4×C109D411yescharacteristic, complemented
114C2×C4⋊C4×C109D411yescharacteristic, complemented
115C2×C4⋊C4×C109D411yescharacteristic, complemented
116C2×C4⋊C4×C109D412yescomplemented
117C2×C22⋊C4×C109—22no—
118C2×C22⋊C4×C109—24no—
119C2×C22⋊C4×C109—22no—
120C2×C22⋊C4×C109—22no—
121C2×C22⋊C4×C109—24no—
122C2×C22⋊C4×C109—22no—
123C2×C22⋊C4×C109—24no—
124C2×C22⋊C4×C109D411yescharacteristic, complemented
125C2×C22⋊C4×C109D412yescomplemented
126C2×C22⋊C4×C109C2312yes—
127C2×C22⋊C4×C109C2312yes—
128C2×C22⋊C4×C109C2311yescharacteristic
129C2×C22⋊C4×C109C2312yes—
130C2×C22⋊C4×C109C2312yes—
131C2×C42×C109—21no—
132C2×C42×C109—21no—
133C2×C42×C109D411yescharacteristic, complemented
134#99×C109—24no—
135#99×C109—44no—
136#95×C109—21no—
137#95×C109—21no—
138#95×C109—21no—
139C24×C109—22no—
140C24×C109—22no—
141C24×C109—22no—
142C24×C109—24no—
143C24×C109—24no—
144C24×C109—44no—
145C24×C109—82no—
146C24×C109C2×D412yes—
147C24×C109C2×D411yescharacteristic
148C24×C109C2411yescharacteristic
149#41×C109—82no—
150C2×Q8×C109—21no—
151C2×Q8×C109—21no—
152C2×Q8×C109—42no—
153C2×D4×C109—24no—
154C2×D4×C109—24no—
155C2×D4×C109—24no—
156C2×D4×C109—21no—
157C2×D4×C109—22no—
158C2×D4×C109—21no—
159C2×D4×C109—22no—
160C2×D4×C109—22no—
161C2×D4×C109—24no—
162C2×D4×C109—24no—
163C2×D4×C109—22no—
164C2×D4×C109—22no—
165C2×D4×C109—22no—
166C2×D4×C109—21no—
167C2×D4×C109—21no—
168C2×D4×C109—42no—
169C2×D4×C109—42no—
170C2×D4×C109—42no—
171C2×D4×C109—42no—
172C2×D4×C109—48no—
173C2×D4×C109—44no—
174C2×D4×C109—44no—
175C2×D4×C109—44no—
176C2×D4×C109—44no—
177C2×D4×C109—44no—
178C2×D4×C109—48no—
179C2×D4×C109—41no—
180C2×D4×C109—41no—
181C2×D4×C109—41no—
182C2×D4×C109—41no—
183C2×D4×C109—84no—
184C2×D4×C109—82no—
185C22×C4×C109—22no—
186C22×C4×C109—22no—
187C22×C4×C109—22no—
188C22×C4×C109—21no—
189C22×C4×C109—21no—
190C22×C4×C109—22no—
191C22×C4×C109—22no—
192C22×C4×C109—42no—
193C22×C4×C109—42no—
194C22×C4×C109C2×D411yescharacteristic
195C22×C4×C109C2×D412yes—
196C22×C4×C109C2×D411yescharacteristic
197C22×C4×C109C2×D411yescharacteristic
198C22×C4×C109C2×D411yescharacteristic
199C22×C4×C109C2×D411yescharacteristic
200C22×C4×C109C2×D412yes—
201C22×C4×C109C2×D411yescharacteristic
202C22×C4×C109C2×D412yes—
203C22×C4×C109C2×D411yescharacteristic
204C22×C4×C109C2×D411yescharacteristic
205C22×C4×C109C2×D411yescharacteristic
206C4⋊C4×C109—22no—
207C4⋊C4×C109—22no—
208C4⋊C4×C109—22no—
209C4⋊C4×C109—22no—
210C4⋊C4×C109—21no—
211C4⋊C4×C109—22no—
212C4⋊C4×C109—21no—
213C4⋊C4×C109—21no—
214C4⋊C4×C109—21no—
215C4⋊C4×C109—21no—
216C4⋊C4×C109—22no—
217C4⋊C4×C109—21no—
218C4⋊C4×C109—42no—
219C22⋊C4×C109—22no—
220C22⋊C4×C109—22no—
221C22⋊C4×C109—22no—
222C22⋊C4×C109—22no—
223C22⋊C4×C109—22no—
224C22⋊C4×C109—22no—
225C22⋊C4×C109—21no—
226C22⋊C4×C109—22no—
227C22⋊C4×C109—21no—
228C22⋊C4×C109—22no—
229C22⋊C4×C109—22no—
230C22⋊C4×C109—22no—
231C22⋊C4×C109—21no—
232C22⋊C4×C109—21no—
233C22⋊C4×C109—22no—
234C22⋊C4×C109—22no—
235C22⋊C4×C109—22no—
236C22⋊C4×C109—24no—
237C22⋊C4×C109—48no—
238C22⋊C4×C109—44no—
239C22⋊C4×C109—44no—
240C22⋊C4×C109—48no—
241C22⋊C4×C109—84no—
242C22⋊C4×C109—82no—
243C22⋊C4×C109#4114yescomplemented
244C42×C109—22no—
245C42×C109—22no—
246C42×C109—21no—
247C42×C109—21no—
248C42×C109—42no—
249C42×C109—42no—
250C23×C109—24no—
251C23×C109—24no—
252C23×C109—24no—
253C23×C109—21no—
254C23×C109—22no—
255C23×C109—21no—
256C23×C109—21no—
257C23×C109—24no—
258C23×C109—41no—
259C23×C109—41no—
260C23×C109—41no—
261C23×C109—41no—
262C23×C109—44no—
263C23×C109—42no—
264C23×C109—42no—
265C23×C109—42no—
266C23×C109—42no—
267C23×C109—42no—
268C23×C109—44no—
269C23×C109—42no—
270C23×C109—42no—
271C23×C109—42no—
272C23×C109—42no—
273C23×C109—42no—
274C23×C109—44no—
275C23×C109—44no—
276C23×C109—88no—
277C23×C109—88no—
278C23×C109C22×D411yescharacteristic
279C23×C109C22×D411yescharacteristic
280C23×C109C22×D411yescharacteristic
281C23×C109C2×#4112yes—
282C23×C109H(5,𝔽2)12yes—
283Q8×C109—42no—
284Q8×C109—81no—
285D4×C109—44no—
286D4×C109—44no—
287D4×C109—44no—
288D4×C109—42no—
289D4×C109—42no—
290D4×C109—42no—
291D4×C109—42no—
292D4×C109—44no—
293D4×C109—44no—
294D4×C109—42no—
295D4×C109—81no—
296D4×C109—82no—
297D4×C109—82no—
298D4×C109—816no—
299D4×C109—88no—
300C2×C4×C109—22no—
301C2×C4×C109—22no—
302C2×C4×C109—22no—
303C2×C4×C109—21no—
304C2×C4×C109—22no—
305C2×C4×C109—21no—
306C2×C4×C109—21no—
307C2×C4×C109—22no—
308C2×C4×C109—22no—
309C2×C4×C109—21no—
310C2×C4×C109—21no—
311C2×C4×C109—24no—
312C2×C4×C109—24no—
313C2×C4×C109—41no—
314C2×C4×C109—41no—
315C2×C4×C109—41no—
316C2×C4×C109—42no—
317C2×C4×C109—42no—
318C2×C4×C109—42no—
319C2×C4×C109—41no—
320C2×C4×C109—42no—
321C2×C4×C109—41no—
322C2×C4×C109—42no—
323C2×C4×C109—42no—
324C2×C4×C109—42no—
325C2×C4×C109—42no—
326C2×C4×C109—42no—
327C2×C4×C109—42no—
328C2×C4×C109—42no—
329C2×C4×C109—81no—
330C2×C4×C109—82no—
331C2×C4×C109—82no—
332C2×C4×C109#12011yescharacteristic
333C2×C4×C109#12011yescharacteristic
334C2×C4×C109#12011yescharacteristic
335C2×C4×C109#12011yescharacteristic
336C22×C109—21no—
337C22×C109—21no—
338C22×C109—21no—
339C22×C109—21no—
340C22×C109—21no—
341C22×C109—21no—
342C22×C109—42no—
343C22×C109—42no—
344C22×C109—42no—
345C22×C109—48no—
346C22×C109—44no—
347C22×C109—48no—
348C22×C109—44no—
349C22×C109—41no—
350C22×C109—42no—
351C22×C109—41no—
352C22×C109—42no—
353C22×C109—44no—
354C22×C109—42no—
355C22×C109—41no—
356C22×C109—84no—
357C22×C109—81no—
358C22×C109—84no—
359C22×C109—82no—
360C22×C109—84no—
361C22×C109—82no—
362C22×C109—82no—
363C22×C109—82no—
364C22×C109C2×#12011yescharacteristic
365C22×C109#53211yescharacteristic
366C22×C109#53511yescharacteristic
367C22×C109#54612yes—
368C22×C109#55012yes—
369C4×C109—21no—
370C4×C109—21no—
371C4×C109—21no—
372C4×C109—44no—
373C4×C109—41no—
374C4×C109—42no—
375C4×C109—41no—
376C4×C109—42no—
377C4×C109—41no—
378C4×C109—42no—
379C4×C109—82no—
380C4×C109—82no—
381C4×C109B(4,𝔽2)12yes—
382#25585C10911yesmaximal, characteristic, direct product factor, Sylow
383C2×C109—22no—
384C2×C109—21no—
385C2×C109—22no—
386C2×C109—21no—
387C2×C109—84no—
388C2×C109—81no—
389C2×C109—82no—
390C2×C109#243111yescharacteristic
391C2×C109C2×B(4,𝔽2)11yescharacteristic
392C2×C109#302711yescharacteristic
393#3505C2×C10911yescharacteristic, complemented
394#2435C2×C10911yescharacteristic, complemented
395#2433C2×C10911yescharacteristic, complemented
396#2408C2×C10911yescharacteristic, complemented
397#2021C2×C10914yescomplemented
398#1996C2×C10911yescharacteristic, complemented
399#1964C2×C10911yescharacteristic, complemented
400#1889C2×C10914yescomplemented
401C4×#99C2×C10911yescharacteristic, complemented
402C109#2558511yescharacteristic, direct product factor, Sylow
403C23×D4C22×C10911yescharacteristic
404#553—21no—
405#553—22no—
406#552—21no—
407#551—22no—
408#548—21no—
409#546—21no—
410#539—21no—
411#538—21no—
412#534C22×C10912yes—
413C2×#127—21no—
414#529—21no—
415C2×#124—21no—
416#525—21no—
417C2×C22⋊Q8C22×C10911yescharacteristic
418C2×#121—21no—
419C2×#121C22×C10911yescharacteristic
420C2×#120C22×C10914yes—
421C2×#120C22×C10912yes—
422#518C22×C10912yes—
423C2×C4×D4C22×C10911yescharacteristic
424C2×#99C22×C10912yes—
425C2×#99C22×C10914yes—
426#394—21no—
427#394—22no—
428#392—21no—
429#392—22no—
430#390—21no—
431#390—21no—
432#390—21no—
433#380C22×C10911yescharacteristic
434#379C22×C10912yes—
435#379C22×C10914yes—
436C4×C22⋊C4C22×C10911yescharacteristic
437C4×C22⋊C4C22×C10911yescharacteristic
438#342C22×C10912yes—
439#342C22×C10914yes—
440C25C23×C10912yes—
441C2×#41—21no—
442C22×Q8D4×C10911yescharacteristic, complemented
443C22×D4—22no—
444C22×D4—24no—
445C22×D4—21no—
446C22×D4—21no—
447C22×D4—21no—
448C22×D4—21no—
449C22×D4—21no—
450C22×D4—21no—
451C22×D4—44no—
452C22×D4D4×C10911yescharacteristic, complemented
453C22×D4C23×C10911yescharacteristic
454C22×D4C23×C10912yes—
455C23×C4D4×C10911yescharacteristic, complemented
456C23×C4C23×C10911yescharacteristic
457#127—44no—
458#126—22no—
459#126—22no—
460#126—22no—
461#125—21no—
462#125—22no—
463#124—21no—
464#124—22no—
465#124—44no—
466#123—22no—
467#123—22no—
468#123—22no—
469#123—22no—
470#123—22no—
471C22⋊Q8—21no—
472C22⋊Q8—22no—
473C22⋊Q8—21no—
474C22⋊Q8—21no—
475C22⋊Q8—21no—
476C22⋊Q8—21no—
477#121—21no—
478#121—22no—
479#121—21no—
480#121—21no—
481#121—21no—
482#121—21no—
483#121—22no—
484#121—22no—
485#121—44no—
486#120—22no—
487#120—22no—
488#120—28no—
489#120—44no—
490#120—44no—
491C4×Q8—21no—
492C4×D4—22no—
493C4×D4—21no—
494C4×D4—21no—
495C4×D4—21no—
496C4×D4—21no—
497C4×D4—21no—
498C4×D4—22no—
499C4×D4—22no—
500C4×D4—22no—
501C4×D4—22no—
502#117—21no—
503#117—22no—
504#117—22no—
505C2×C4⋊C4—21no—
506C2×C4⋊C4D4×C10911yescharacteristic, complemented
507C2×C4⋊C4D4×C10911yescharacteristic, complemented
508C2×C4⋊C4D4×C10911yescharacteristic, complemented
509C2×C4⋊C4D4×C10912yescomplemented
510C2×C22⋊C4—22no—
511C2×C22⋊C4—24no—
512C2×C22⋊C4—22no—
513C2×C22⋊C4—22no—
514C2×C22⋊C4—24no—
515C2×C22⋊C4—22no—
516C2×C22⋊C4—24no—
517C2×C22⋊C4D4×C10911yescharacteristic, complemented
518C2×C22⋊C4D4×C10912yescomplemented
519C2×C22⋊C4C23×C10912yes—
520C2×C22⋊C4C23×C10912yes—
521C2×C22⋊C4C23×C10911yescharacteristic
522C2×C22⋊C4C23×C10912yes—
523C2×C22⋊C4C23×C10912yes—
524C2×C42—21no—
525C2×C42—21no—
526C2×C42D4×C10911yescharacteristic, complemented
527#99—24no—
528#99—44no—
529#95—21no—
530#95—21no—
531#95—21no—
532C24—22no—
533C24—22no—
534C24—22no—
535C24—24no—
536C24—24no—
537C24—44no—
538C24—82no—
539C24C2×D4×C10912yes—
540C24C2×D4×C10911yescharacteristic
541C24C24×C10911yescharacteristic
542#41—82no—
543C2×Q8—21no—
544C2×Q8—21no—
545C2×Q8—42no—
546C2×D4—24no—
547C2×D4—24no—
548C2×D4—24no—
549C2×D4—21no—
550C2×D4—22no—
551C2×D4—21no—
552C2×D4—22no—
553C2×D4—22no—
554C2×D4—24no—
555C2×D4—24no—
556C2×D4—22no—
557C2×D4—22no—
558C2×D4—22no—
559C2×D4—21no—
560C2×D4—21no—
561C2×D4—42no—
562C2×D4—42no—
563C2×D4—42no—
564C2×D4—42no—
565C2×D4—48no—
566C2×D4—44no—
567C2×D4—44no—
568C2×D4—44no—
569C2×D4—44no—
570C2×D4—44no—
571C2×D4—48no—
572C2×D4—41no—
573C2×D4—41no—
574C2×D4—41no—
575C2×D4—41no—
576C2×D4—84no—
577C2×D4—82no—
578C22×C4—22no—
579C22×C4—22no—
580C22×C4—22no—
581C22×C4—21no—
582C22×C4—21no—
583C22×C4—22no—
584C22×C4—22no—
585C22×C4—42no—
586C22×C4—42no—
587C22×C4C2×D4×C10911yescharacteristic
588C22×C4C2×D4×C10912yes—
589C22×C4C2×D4×C10911yescharacteristic
590C22×C4C2×D4×C10911yescharacteristic
591C22×C4C2×D4×C10911yescharacteristic
592C22×C4C2×D4×C10911yescharacteristic
593C22×C4C2×D4×C10912yes—
594C22×C4C2×D4×C10911yescharacteristic
595C22×C4C2×D4×C10912yes—
596C22×C4C2×D4×C10911yescharacteristic
597C22×C4C2×D4×C10911yescharacteristic
598C22×C4C2×D4×C10911yescharacteristic
599C4⋊C4—22no—
600C4⋊C4—22no—
601C4⋊C4—22no—
602C4⋊C4—22no—
603C4⋊C4—21no—
604C4⋊C4—22no—
605C4⋊C4—21no—
606C4⋊C4—21no—
607C4⋊C4—21no—
608C4⋊C4—21no—
609C4⋊C4—22no—
610C4⋊C4—21no—
611C4⋊C4—42no—
612C22⋊C4—22no—
613C22⋊C4—22no—
614C22⋊C4—22no—
615C22⋊C4—22no—
616C22⋊C4—22no—
617C22⋊C4—22no—
618C22⋊C4—21no—
619C22⋊C4—22no—
620C22⋊C4—21no—
621C22⋊C4—22no—
622C22⋊C4—22no—
623C22⋊C4—22no—
624C22⋊C4—21no—
625C22⋊C4—21no—
626C22⋊C4—22no—
627C22⋊C4—22no—
628C22⋊C4—22no—
629C22⋊C4—24no—
630C22⋊C4—48no—
631C22⋊C4—44no—
632C22⋊C4—44no—
633C22⋊C4—48no—
634C22⋊C4—84no—
635C22⋊C4—82no—
636C22⋊C4#41×C10914yescomplemented
637C42—22no—
638C42—22no—
639C42—21no—
640C42—21no—
641C42—42no—
642C42—42no—
643C23—24no—
644C23—24no—
645C23—24no—
646C23—21no—
647C23—22no—
648C23—21no—
649C23—21no—
650C23—24no—
651C23—41no—
652C23—41no—
653C23—41no—
654C23—41no—
655C23—44no—
656C23—42no—
657C23—42no—
658C23—42no—
659C23—42no—
660C23—42no—
661C23—44no—
662C23—42no—
663C23—42no—
664C23—42no—
665C23—42no—
666C23—42no—
667C23—44no—
668C23—44no—
669C23—88no—
670C23—88no—
671C23C22×D4×C10911yescharacteristic
672C23C22×D4×C10911yescharacteristic
673C23C22×D4×C10911yescharacteristic
674C23C2×#41×C10912yes—
675C23H(5,𝔽2)×C10912yes—
676Q8—42no—
677Q8—81no—
678D4—44no—
679D4—44no—
680D4—44no—
681D4—42no—
682D4—42no—
683D4—42no—
684D4—42no—
685D4—44no—
686D4—44no—
687D4—42no—
688D4—81no—
689D4—82no—
690D4—82no—
691D4—816no—
692D4—88no—
693C2×C4—22no—
694C2×C4—22no—
695C2×C4—22no—
696C2×C4—21no—
697C2×C4—22no—
698C2×C4—21no—
699C2×C4—21no—
700C2×C4—22no—
701C2×C4—22no—
702C2×C4—21no—
703C2×C4—21no—
704C2×C4—24no—
705C2×C4—24no—
706C2×C4—41no—
707C2×C4—41no—
708C2×C4—41no—
709C2×C4—42no—
710C2×C4—42no—
711C2×C4—42no—
712C2×C4—41no—
713C2×C4—42no—
714C2×C4—41no—
715C2×C4—42no—
716C2×C4—42no—
717C2×C4—42no—
718C2×C4—42no—
719C2×C4—42no—
720C2×C4—42no—
721C2×C4—42no—
722C2×C4—81no—
723C2×C4—82no—
724C2×C4—82no—
725C2×C4#120×C10911yescharacteristic
726C2×C4#120×C10911yescharacteristic
727C2×C4#120×C10911yescharacteristic
728C2×C4#120×C10911yescharacteristic
729C22—21no—
730C22—21no—
731C22—21no—
732C22—21no—
733C22—21no—
734C22—21no—
735C22—42no—
736C22—42no—
737C22—42no—
738C22—48no—
739C22—44no—
740C22—48no—
741C22—44no—
742C22—41no—
743C22—42no—
744C22—41no—
745C22—42no—
746C22—44no—
747C22—42no—
748C22—41no—
749C22—84no—
750C22—81no—
751C22—84no—
752C22—82no—
753C22—84no—
754C22—82no—
755C22—82no—
756C22—82no—
757C22C2×#120×C10911yescharacteristic
758C22#532×C10911yescharacteristic
759C22#535×C10911yescharacteristic
760C22#546×C10912yes—
761C22#550×C10912yes—
762C4—21no—
763C4—21no—
764C4—21no—
765C4—44no—
766C4—41no—
767C4—42no—
768C4—41no—
769C4—42no—
770C4—41no—
771C4—42no—
772C4—82no—
773C4—82no—
774C4B(4,𝔽2)×C10912yes—
775C2—22no—
776C2—21no—
777C2—22no—
778C2—21no—
779C2—84no—
780C2—81no—
781C2—82no—
782C2C109×#243111yescharacteristic
783C2C2×B(4,𝔽2)×C10911yescharacteristic
784C2C109×#302711yescharacteristic
subgroupG/H
center, socleC22×C109C2×#120
commutator, Frattini, cosocleC24C24×C109
LCSG ▷ C24 ▷ C2 ▷ C1
UCSC1 ◁ C22×C109 ◁ C23×C4×C109 ◁ G

Complements

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

NH ≅ G/Ntype
1. C109×#3505C2semidirect
2. C109×#2435C2semidirect
3. C109×#2433C2semidirect
4. C109×#2408C2semidirect
5. C109×#2021C2semidirect
6. C109×#1996C2semidirect
7. C109×#1964C2semidirect
8. C109×#1889C2semidirect
9. C4×#99×C109C2semidirect
49. C22×Q8×C109D4semidirect
59. C22×D4×C109D4semidirect
62. C23×C4×C109D4semidirect
113. C2×C4⋊C4×C109D4semidirect
114. C2×C4⋊C4×C109D4semidirect
115. C2×C4⋊C4×C109D4semidirect
116. C2×C4⋊C4×C109D4semidirect
124. C2×C22⋊C4×C109D4semidirect
125. C2×C22⋊C4×C109D4semidirect
133. C2×C42×C109D4semidirect
243. C22⋊C4×C109#41semidirect
382. #25585C109direct (N × H)
393. #3505C2×C109semidirect
394. #2435C2×C109semidirect
395. #2433C2×C109semidirect
396. #2408C2×C109semidirect
397. #2021C2×C109semidirect
398. #1996C2×C109semidirect
399. #1964C2×C109semidirect
400. #1889C2×C109semidirect
401. C4×#99C2×C109semidirect
402. C109#25585direct (N × H)
442. C22×Q8D4×C109semidirect
452. C22×D4D4×C109semidirect
455. C23×C4D4×C109semidirect
506. C2×C4⋊C4D4×C109semidirect
507. C2×C4⋊C4D4×C109semidirect
508. C2×C4⋊C4D4×C109semidirect
509. C2×C4⋊C4D4×C109semidirect
517. C2×C22⋊C4D4×C109semidirect
518. C2×C22⋊C4D4×C109semidirect
526. C2×C42D4×C109semidirect
636. C22⋊C4#41×C109semidirect

Maximal subgroups

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

subgroupindex
C109×#35052
C109×#24352
C109×#24332
C109×#24082
C109×#20212
C109×#19962
C109×#19642
C109×#18892
C4×#99×C1092
#25585109