Finite Group Databasebeta

← C109×#24140 #42142134

Subgroups — C109×#24140 #42142134

Order 27904.

1556 conjugacy classes of subgroups.

The subgroup lattice has 940 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C109×#3505C211yesmaximal, characteristic, complemented
2C109×#2848C211yesmaximal, characteristic, complemented
3C109×#2847C211yesmaximal, characteristic, complemented
4C4×#120×C109C211yesmaximal, characteristic, complemented
5C109×#2044C212yesmaximal, complemented
6C109×#2021C212yesmaximal, complemented
7C109×#1996C211yesmaximal, characteristic, complemented
8C109×#1964C211yesmaximal, characteristic, complemented
9C109×#1889C212yesmaximal, complemented
10C109×#1867C212yesmaximal, complemented
11C109×#1799C211yesmaximal, characteristic, complemented
12C24×C4×C109C2211yescharacteristic
13#553×C109—21no—
14#553×C109—22no—
15#552×C109—21no—
16#551×C109—22no—
17#548×C109—21no—
18#546×C109—21no—
19#539×C109—21no—
20#538×C109—21no—
21#534×C109C2212yes—
22#529×C109—21no—
23#525×C109—21no—
24C2×C22⋊Q8×C109—21no—
25C2×C22⋊Q8×C109C2211yescharacteristic
26C2×#121×C109—21no—
27C2×#121×C109C2211yescharacteristic
28C2×#120×C109C2211yescharacteristic
29C2×#120×C109C2212yes—
30#518×C109C2212yes—
31C2×C4×D4×C109—21no—
32C2×C4×D4×C109C2211yescharacteristic
33C2×#99×C109C2212yes—
34C2×#99×C109C2212yes—
35C2×#99×C109C2212yes—
36#386×C109—21no—
37#386×C109—22no—
38#386×C109C2211yescharacteristic
39#386×C109C2212yes—
40#385×C109—21no—
41#385×C109—22no—
42#385×C109C2211yescharacteristic
43#385×C109C2212yes—
44#380×C109—21no—
45#380×C109—21no—
46#380×C109C2211yescharacteristic
47#380×C109C2211yescharacteristic
48#379×C109C2212yes—
49#379×C109C2211yescharacteristic
50C4×C22⋊C4×C109—21no—
51C4×C22⋊C4×C109C2211yescharacteristic
52#342×C109C2212yes—
53#342×C109C2212yes—
54#342×C109C2212yes—
55C25×C109C2311yescharacteristic
56C2×#41×C109—21no—
57C22×Q8×C109D411yescharacteristic, complemented
58C22×D4×C109—21no—
59C22×D4×C109—22no—
60C22×D4×C109D411yescharacteristic, complemented
61C22×D4×C109C2311yescharacteristic
62C22×D4×C109C2312yes—
63C23×C4×C109—21no—
64C23×C4×C109—21no—
65C23×C4×C109—21no—
66C23×C4×C109—21no—
67C23×C4×C109—21no—
68C23×C4×C109—21no—
69C23×C4×C109—44no—
70C23×C4×C109D411yescharacteristic, complemented
71C23×C4×C109C2311yescharacteristic
72C23×C4×C109C2311yescharacteristic
73#126×C109—22no—
74#126×C109—22no—
75#126×C109—22no—
76#125×C109—21no—
77#125×C109—22no—
78#124×C109—21no—
79#124×C109—22no—
80#123×C109—22no—
81#123×C109—22no—
82#123×C109—22no—
83#123×C109—22no—
84#123×C109—22no—
85C22⋊Q8×C109—21no—
86C22⋊Q8×C109—22no—
87C22⋊Q8×C109—21no—
88C22⋊Q8×C109—21no—
89C22⋊Q8×C109—21no—
90C22⋊Q8×C109—21no—
91C22⋊Q8×C109—44no—
92#121×C109—21no—
93#121×C109—22no—
94#121×C109—21no—
95#121×C109—21no—
96#121×C109—21no—
97#121×C109—21no—
98#121×C109—22no—
99#121×C109—22no—
100#121×C109—44no—
101#120×C109—22no—
102#120×C109—22no—
103#120×C109—22no—
104#120×C109—22no—
105#120×C109—24no—
106#120×C109—42no—
107C4×Q8×C109—21no—
108C4×D4×C109—22no—
109C4×D4×C109—21no—
110C4×D4×C109—21no—
111C4×D4×C109—21no—
112C4×D4×C109—21no—
113C4×D4×C109—21no—
114C4×D4×C109—22no—
115C4×D4×C109—22no—
116C4×D4×C109—22no—
117C4×D4×C109—22no—
118C4×D4×C109—44no—
119#117×C109—21no—
120#117×C109—22no—
121#117×C109—22no—
122C2×C4⋊C4×C109—21no—
123C2×C4⋊C4×C109—21no—
124C2×C4⋊C4×C109—21no—
125C2×C4⋊C4×C109—22no—
126C2×C4⋊C4×C109D411yescharacteristic, complemented
127C2×C4⋊C4×C109D411yescharacteristic, complemented
128C2×C4⋊C4×C109D411yescharacteristic, complemented
129C2×C4⋊C4×C109D412yescomplemented
130C2×C22⋊C4×C109—22no—
131C2×C22⋊C4×C109—21no—
132C2×C22⋊C4×C109—21no—
133C2×C22⋊C4×C109—22no—
134C2×C22⋊C4×C109—21no—
135C2×C22⋊C4×C109—22no—
136C2×C22⋊C4×C109—22no—
137C2×C22⋊C4×C109—21no—
138C2×C22⋊C4×C109—22no—
139C2×C22⋊C4×C109D411yescharacteristic, complemented
140C2×C22⋊C4×C109D412yescomplemented
141C2×C22⋊C4×C109C2312yes—
142C2×C22⋊C4×C109C2311yescharacteristic
143C2×C22⋊C4×C109C2312yes—
144C2×C22⋊C4×C109C2311yescharacteristic
145C2×C22⋊C4×C109C2312yes—
146C2×C22⋊C4×C109C2311yescharacteristic
147C2×C42×C109—21no—
148C2×C42×C109D411yescharacteristic, complemented
149#99×C109—24no—
150#99×C109—42no—
151#99×C109—42no—
152#95×C109—21no—
153#95×C109—21no—
154#95×C109—21no—
155#95×C109—22no—
156#95×C109—22no—
157#95×C109—21no—
158#95×C109—21no—
159C24×C109—21no—
160C24×C109—21no—
161C24×C109—21no—
162C24×C109—21no—
163C24×C109—21no—
164C24×C109—21no—
165C24×C109—42no—
166C24×C109—42no—
167C24×C109C2×D412yes—
168C24×C109C2×D411yescharacteristic
169C24×C109#4112yescomplemented
170C24×C109C2411yescharacteristic
171#41×C109—82no—
172C2×Q8×C109—21no—
173C2×Q8×C109—21no—
174C2×Q8×C109—42no—
175C2×D4×C109—24no—
176C2×D4×C109—21no—
177C2×D4×C109—22no—
178C2×D4×C109—21no—
179C2×D4×C109—22no—
180C2×D4×C109—22no—
181C2×D4×C109—21no—
182C2×D4×C109—21no—
183C2×D4×C109—22no—
184C2×D4×C109—21no—
185C2×D4×C109—22no—
186C2×D4×C109—21no—
187C2×D4×C109—22no—
188C2×D4×C109—22no—
189C2×D4×C109—22no—
190C2×D4×C109—21no—
191C2×D4×C109—21no—
192C2×D4×C109—42no—
193C2×D4×C109—42no—
194C2×D4×C109—42no—
195C2×D4×C109—44no—
196C2×D4×C109—44no—
197C2×D4×C109—44no—
198C22×C4×C109—24no—
199C22×C4×C109—24no—
200C22×C4×C109—24no—
201C22×C4×C109—21no—
202C22×C4×C109—21no—
203C22×C4×C109—21no—
204C22×C4×C109—21no—
205C22×C4×C109—22no—
206C22×C4×C109—22no—
207C22×C4×C109—21no—
208C22×C4×C109—21no—
209C22×C4×C109—21no—
210C22×C4×C109—22no—
211C22×C4×C109—22no—
212C22×C4×C109—42no—
213C22×C4×C109—42no—
214C22×C4×C109—42no—
215C22×C4×C109—42no—
216C22×C4×C109—42no—
217C22×C4×C109—42no—
218C22×C4×C109—42no—
219C22×C4×C109—42no—
220C22×C4×C109—42no—
221C22×C4×C109—42no—
222C22×C4×C109—42no—
223C22×C4×C109—42no—
224C22×C4×C109—41no—
225C22×C4×C109—41no—
226C22×C4×C109—41no—
227C22×C4×C109—41no—
228C22×C4×C109C2×D411yescharacteristic
229C22×C4×C109C2×D412yes—
230C22×C4×C109C2×D411yescharacteristic
231C22×C4×C109C2×D411yescharacteristic
232C22×C4×C109C2×D411yescharacteristic
233C22×C4×C109C2×D411yescharacteristic
234C22×C4×C109C2×D412yes—
235C22×C4×C109C2×D411yescharacteristic
236C22×C4×C109C2×D412yes—
237C22×C4×C109C2×D411yescharacteristic
238C22×C4×C109C2×D411yescharacteristic
239C22×C4×C109C2×D411yescharacteristic
240C4⋊C4×C109—22no—
241C4⋊C4×C109—22no—
242C4⋊C4×C109—22no—
243C4⋊C4×C109—22no—
244C4⋊C4×C109—21no—
245C4⋊C4×C109—22no—
246C4⋊C4×C109—21no—
247C4⋊C4×C109—21no—
248C4⋊C4×C109—21no—
249C4⋊C4×C109—21no—
250C4⋊C4×C109—22no—
251C4⋊C4×C109—21no—
252C4⋊C4×C109—42no—
253C4⋊C4×C109—42no—
254C4⋊C4×C109—42no—
255C4⋊C4×C109—44no—
256C22⋊C4×C109—22no—
257C22⋊C4×C109—22no—
258C22⋊C4×C109—24no—
259C22⋊C4×C109—22no—
260C22⋊C4×C109—22no—
261C22⋊C4×C109—22no—
262C22⋊C4×C109—22no—
263C22⋊C4×C109—21no—
264C22⋊C4×C109—22no—
265C22⋊C4×C109—21no—
266C22⋊C4×C109—22no—
267C22⋊C4×C109—21no—
268C22⋊C4×C109—22no—
269C22⋊C4×C109—21no—
270C22⋊C4×C109—21no—
271C22⋊C4×C109—22no—
272C22⋊C4×C109—22no—
273C22⋊C4×C109—22no—
274C22⋊C4×C109—21no—
275C22⋊C4×C109—22no—
276C22⋊C4×C109—22no—
277C22⋊C4×C109—21no—
278C22⋊C4×C109—44no—
279C22⋊C4×C109—42no—
280C22⋊C4×C109—44no—
281C22⋊C4×C109—44no—
282C22⋊C4×C109—42no—
283C22⋊C4×C109—42no—
284C22⋊C4×C109—44no—
285C22⋊C4×C109#4112yescomplemented
286C42×C109—22no—
287C42×C109—22no—
288C42×C109—21no—
289C42×C109—21no—
290C42×C109—42no—
291C23×C109—22no—
292C23×C109—22no—
293C23×C109—22no—
294C23×C109—22no—
295C23×C109—22no—
296C23×C109—22no—
297C23×C109—22no—
298C23×C109—22no—
299C23×C109—22no—
300C23×C109—21no—
301C23×C109—22no—
302C23×C109—21no—
303C23×C109—21no—
304C23×C109—22no—
305C23×C109—22no—
306C23×C109—41no—
307C23×C109—44no—
308C23×C109—41no—
309C23×C109—41no—
310C23×C109—41no—
311C23×C109—41no—
312C23×C109—41no—
313C23×C109—41no—
314C23×C109—41no—
315C23×C109—44no—
316C23×C109—44no—
317C23×C109—44no—
318C23×C109—41no—
319C23×C109—41no—
320C23×C109—42no—
321C23×C109—42no—
322C23×C109—41no—
323C23×C109—41no—
324C23×C109—41no—
325C23×C109—41no—
326C23×C109C22×D411yescharacteristic
327C23×C109C22×D411yescharacteristic
328C23×C109C22×D411yescharacteristic
329C23×C109C2×#4111yescharacteristic
330C23×C109C2×#4111yescharacteristic
331C23×C109H(5,𝔽2)11yescharacteristic
332C23×C1092−1+411yescharacteristic
333Q8×C109—42no—
334Q8×C109—81no—
335D4×C109—48no—
336D4×C109—42no—
337D4×C109—42no—
338D4×C109—41no—
339D4×C109—41no—
340D4×C109—41no—
341D4×C109—42no—
342D4×C109—42no—
343D4×C109—41no—
344D4×C109—42no—
345D4×C109—81no—
346D4×C109—82no—
347D4×C109—82no—
348D4×C109—88no—
349C2×C4×C109—22no—
350C2×C4×C109—22no—
351C2×C4×C109—22no—
352C2×C4×C109—22no—
353C2×C4×C109—22no—
354C2×C4×C109—22no—
355C2×C4×C109—21no—
356C2×C4×C109—22no—
357C2×C4×C109—21no—
358C2×C4×C109—21no—
359C2×C4×C109—22no—
360C2×C4×C109—22no—
361C2×C4×C109—21no—
362C2×C4×C109—22no—
363C2×C4×C109—21no—
364C2×C4×C109—22no—
365C2×C4×C109—22no—
366C2×C4×C109—41no—
367C2×C4×C109—41no—
368C2×C4×C109—41no—
369C2×C4×C109—44no—
370C2×C4×C109—44no—
371C2×C4×C109—44no—
372C2×C4×C109—41no—
373C2×C4×C109—41no—
374C2×C4×C109—41no—
375C2×C4×C109—41no—
376C2×C4×C109—41no—
377C2×C4×C109—41no—
378C2×C4×C109—44no—
379C2×C4×C109—42no—
380C2×C4×C109—41no—
381C2×C4×C109—42no—
382C2×C4×C109—41no—
383C2×C4×C109—42no—
384C2×C4×C109—41no—
385C2×C4×C109—42no—
386C2×C4×C109—42no—
387C2×C4×C109—42no—
388C2×C4×C109—41no—
389C2×C4×C109—42no—
390C2×C4×C109—41no—
391C2×C4×C109—42no—
392C2×C4×C109—42no—
393C2×C4×C109—81no—
394C2×C4×C109—82no—
395C2×C4×C109—82no—
396C2×C4×C109#12011yescharacteristic
397C2×C4×C109#12011yescharacteristic
398C2×C4×C109#12011yescharacteristic
399C2×C4×C109#12011yescharacteristic
400C22×C109—21no—
401C22×C109—21no—
402C22×C109—21no—
403C22×C109—21no—
404C22×C109—21no—
405C22×C109—21no—
406C22×C109—24no—
407C22×C109—24no—
408C22×C109—24no—
409C22×C109—41no—
410C22×C109—41no—
411C22×C109—41no—
412C22×C109—41no—
413C22×C109—42no—
414C22×C109—42no—
415C22×C109—42no—
416C22×C109—42no—
417C22×C109—42no—
418C22×C109—42no—
419C22×C109—42no—
420C22×C109—42no—
421C22×C109—42no—
422C22×C109—42no—
423C22×C109—42no—
424C22×C109—42no—
425C22×C109—42no—
426C22×C109—41no—
427C22×C109—42no—
428C22×C109—41no—
429C22×C109—42no—
430C22×C109—42no—
431C22×C109—41no—
432C22×C109—82no—
433C22×C109—81no—
434C22×C109—82no—
435C22×C109C2×#12011yescharacteristic
436C22×C109#52511yescharacteristic
437C22×C109#53711yescharacteristic
438C22×C109#54611yescharacteristic
439C22×C109#54711yescharacteristic
440C22×C109#54811yescharacteristic
441C22×C109#55011yescharacteristic
442C4×C109—21no—
443C4×C109—21no—
444C4×C109—21no—
445C4×C109—42no—
446C4×C109—41no—
447C4×C109—42no—
448C4×C109—42no—
449C4×C109—41no—
450C4×C109—42no—
451C4×C109—41no—
452C4×C109—42no—
453C4×C109—82no—
454C4×C109—81no—
455C4×C109—82no—
456C4×C109B(4,𝔽2)12yes—
457#24140C10911yesmaximal, characteristic, direct product factor, Sylow
458C2×C109—21no—
459C2×C109—21no—
460C2×C109—21no—
461C2×C109—21no—
462C2×C109—21no—
463C2×C109—21no—
464C2×C109—44no—
465C2×C109—81no—
466C2×C109—82no—
467C2×C109#240711yescharacteristic
468C2×C109C2×B(4,𝔽2)11yescharacteristic
469C2×C109#302511yescharacteristic
470#3505C2×C10911yescharacteristic, complemented
471#2848C2×C10911yescharacteristic, complemented
472#2847C2×C10911yescharacteristic, complemented
473C4×#120C2×C10911yescharacteristic, complemented
474#2044C2×C10912yescomplemented
475#2021C2×C10912yescomplemented
476#1996C2×C10911yescharacteristic, complemented
477#1964C2×C10911yescharacteristic, complemented
478#1889C2×C10912yescomplemented
479#1867C2×C10912yescomplemented
480#1799C2×C10911yescharacteristic, complemented
481C109#2414011yescharacteristic, direct product factor, Sylow
482C24×C4C22×C10911yescharacteristic
483#553—21no—
484#553—22no—
485#552—21no—
486#551—22no—
487#548—21no—
488#546—21no—
489#539—21no—
490#538—21no—
491#534C22×C10912yes—
492#529—21no—
493#525—21no—
494C2×C22⋊Q8—21no—
495C2×C22⋊Q8C22×C10911yescharacteristic
496C2×#121—21no—
497C2×#121C22×C10911yescharacteristic
498C2×#120C22×C10911yescharacteristic
499C2×#120C22×C10912yes—
500#518C22×C10912yes—
501C2×C4×D4—21no—
502C2×C4×D4C22×C10911yescharacteristic
503C2×#99C22×C10912yes—
504C2×#99C22×C10912yes—
505C2×#99C22×C10912yes—
506#386—22no—
507#386—21no—
508#386C22×C10912yes—
509#386C22×C10911yescharacteristic
510#385—22no—
511#385—21no—
512#385C22×C10912yes—
513#385C22×C10911yescharacteristic
514#380—21no—
515#380—21no—
516#380C22×C10911yescharacteristic
517#380C22×C10911yescharacteristic
518#379C22×C10912yes—
519#379C22×C10911yescharacteristic
520C4×C22⋊C4—21no—
521C4×C22⋊C4C22×C10911yescharacteristic
522#342C22×C10912yes—
523#342C22×C10912yes—
524#342C22×C10912yes—
525C25C23×C10911yescharacteristic
526C2×#41—21no—
527C22×Q8D4×C10911yescharacteristic, complemented
528C22×D4—21no—
529C22×D4—22no—
530C22×D4D4×C10911yescharacteristic, complemented
531C22×D4C23×C10911yescharacteristic
532C22×D4C23×C10912yes—
533C23×C4—21no—
534C23×C4—21no—
535C23×C4—21no—
536C23×C4—21no—
537C23×C4—21no—
538C23×C4—21no—
539C23×C4—44no—
540C23×C4D4×C10911yescharacteristic, complemented
541C23×C4C23×C10911yescharacteristic
542C23×C4C23×C10911yescharacteristic
543#126—22no—
544#126—22no—
545#126—22no—
546#125—21no—
547#125—22no—
548#124—21no—
549#124—22no—
550#123—22no—
551#123—22no—
552#123—22no—
553#123—22no—
554#123—22no—
555C22⋊Q8—21no—
556C22⋊Q8—22no—
557C22⋊Q8—21no—
558C22⋊Q8—21no—
559C22⋊Q8—21no—
560C22⋊Q8—21no—
561C22⋊Q8—44no—
562#121—21no—
563#121—22no—
564#121—21no—
565#121—21no—
566#121—21no—
567#121—21no—
568#121—22no—
569#121—22no—
570#121—44no—
571#120—22no—
572#120—22no—
573#120—22no—
574#120—22no—
575#120—24no—
576#120—42no—
577C4×Q8—21no—
578C4×D4—22no—
579C4×D4—21no—
580C4×D4—21no—
581C4×D4—21no—
582C4×D4—21no—
583C4×D4—21no—
584C4×D4—22no—
585C4×D4—22no—
586C4×D4—22no—
587C4×D4—22no—
588C4×D4—44no—
589#117—21no—
590#117—22no—
591#117—22no—
592C2×C4⋊C4—21no—
593C2×C4⋊C4—21no—
594C2×C4⋊C4—21no—
595C2×C4⋊C4—22no—
596C2×C4⋊C4D4×C10911yescharacteristic, complemented
597C2×C4⋊C4D4×C10911yescharacteristic, complemented
598C2×C4⋊C4D4×C10911yescharacteristic, complemented
599C2×C4⋊C4D4×C10912yescomplemented
600C2×C22⋊C4—22no—
601C2×C22⋊C4—21no—
602C2×C22⋊C4—21no—
603C2×C22⋊C4—22no—
604C2×C22⋊C4—21no—
605C2×C22⋊C4—22no—
606C2×C22⋊C4—22no—
607C2×C22⋊C4—21no—
608C2×C22⋊C4—22no—
609C2×C22⋊C4D4×C10911yescharacteristic, complemented
610C2×C22⋊C4D4×C10912yescomplemented
611C2×C22⋊C4C23×C10912yes—
612C2×C22⋊C4C23×C10911yescharacteristic
613C2×C22⋊C4C23×C10912yes—
614C2×C22⋊C4C23×C10911yescharacteristic
615C2×C22⋊C4C23×C10912yes—
616C2×C22⋊C4C23×C10911yescharacteristic
617C2×C42—21no—
618C2×C42D4×C10911yescharacteristic, complemented
619#99—24no—
620#99—42no—
621#99—42no—
622#95—21no—
623#95—21no—
624#95—21no—
625#95—22no—
626#95—22no—
627#95—21no—
628#95—21no—
629C24—21no—
630C24—21no—
631C24—21no—
632C24—21no—
633C24—21no—
634C24—21no—
635C24—42no—
636C24—42no—
637C24C2×D4×C10912yes—
638C24C2×D4×C10911yescharacteristic
639C24#41×C10912yescomplemented
640C24C24×C10911yescharacteristic
641#41—82no—
642C2×Q8—21no—
643C2×Q8—21no—
644C2×Q8—42no—
645C2×D4—24no—
646C2×D4—21no—
647C2×D4—22no—
648C2×D4—21no—
649C2×D4—22no—
650C2×D4—22no—
651C2×D4—21no—
652C2×D4—21no—
653C2×D4—22no—
654C2×D4—21no—
655C2×D4—22no—
656C2×D4—21no—
657C2×D4—22no—
658C2×D4—22no—
659C2×D4—22no—
660C2×D4—21no—
661C2×D4—21no—
662C2×D4—42no—
663C2×D4—42no—
664C2×D4—42no—
665C2×D4—44no—
666C2×D4—44no—
667C2×D4—44no—
668C22×C4—24no—
669C22×C4—24no—
670C22×C4—24no—
671C22×C4—21no—
672C22×C4—21no—
673C22×C4—21no—
674C22×C4—21no—
675C22×C4—22no—
676C22×C4—22no—
677C22×C4—21no—
678C22×C4—21no—
679C22×C4—21no—
680C22×C4—22no—
681C22×C4—22no—
682C22×C4—42no—
683C22×C4—42no—
684C22×C4—42no—
685C22×C4—42no—
686C22×C4—42no—
687C22×C4—42no—
688C22×C4—42no—
689C22×C4—42no—
690C22×C4—42no—
691C22×C4—42no—
692C22×C4—42no—
693C22×C4—42no—
694C22×C4—41no—
695C22×C4—41no—
696C22×C4—41no—
697C22×C4—41no—
698C22×C4C2×D4×C10911yescharacteristic
699C22×C4C2×D4×C10912yes—
700C22×C4C2×D4×C10911yescharacteristic
701C22×C4C2×D4×C10911yescharacteristic
702C22×C4C2×D4×C10911yescharacteristic
703C22×C4C2×D4×C10911yescharacteristic
704C22×C4C2×D4×C10912yes—
705C22×C4C2×D4×C10911yescharacteristic
706C22×C4C2×D4×C10912yes—
707C22×C4C2×D4×C10911yescharacteristic
708C22×C4C2×D4×C10911yescharacteristic
709C22×C4C2×D4×C10911yescharacteristic
710C4⋊C4—22no—
711C4⋊C4—22no—
712C4⋊C4—22no—
713C4⋊C4—22no—
714C4⋊C4—21no—
715C4⋊C4—22no—
716C4⋊C4—21no—
717C4⋊C4—21no—
718C4⋊C4—21no—
719C4⋊C4—21no—
720C4⋊C4—22no—
721C4⋊C4—21no—
722C4⋊C4—42no—
723C4⋊C4—42no—
724C4⋊C4—42no—
725C4⋊C4—44no—
726C22⋊C4—22no—
727C22⋊C4—22no—
728C22⋊C4—24no—
729C22⋊C4—22no—
730C22⋊C4—22no—
731C22⋊C4—22no—
732C22⋊C4—22no—
733C22⋊C4—21no—
734C22⋊C4—22no—
735C22⋊C4—21no—
736C22⋊C4—22no—
737C22⋊C4—21no—
738C22⋊C4—22no—
739C22⋊C4—21no—
740C22⋊C4—21no—
741C22⋊C4—22no—
742C22⋊C4—22no—
743C22⋊C4—22no—
744C22⋊C4—21no—
745C22⋊C4—22no—
746C22⋊C4—22no—
747C22⋊C4—21no—
748C22⋊C4—44no—
749C22⋊C4—42no—
750C22⋊C4—44no—
751C22⋊C4—44no—
752C22⋊C4—42no—
753C22⋊C4—42no—
754C22⋊C4—44no—
755C22⋊C4#41×C10912yescomplemented
756C42—22no—
757C42—22no—
758C42—21no—
759C42—21no—
760C42—42no—
761C23—22no—
762C23—22no—
763C23—22no—
764C23—22no—
765C23—22no—
766C23—22no—
767C23—22no—
768C23—22no—
769C23—22no—
770C23—21no—
771C23—22no—
772C23—21no—
773C23—21no—
774C23—22no—
775C23—22no—
776C23—41no—
777C23—44no—
778C23—41no—
779C23—41no—
780C23—41no—
781C23—41no—
782C23—41no—
783C23—41no—
784C23—41no—
785C23—44no—
786C23—44no—
787C23—44no—
788C23—41no—
789C23—41no—
790C23—42no—
791C23—42no—
792C23—41no—
793C23—41no—
794C23—41no—
795C23—41no—
796C23C22×D4×C10911yescharacteristic
797C23C22×D4×C10911yescharacteristic
798C23C22×D4×C10911yescharacteristic
799C23C2×#41×C10911yescharacteristic
800C23C2×#41×C10911yescharacteristic
801C23H(5,𝔽2)×C10911yescharacteristic
802C232−1+4×C10911yescharacteristic
803Q8—42no—
804Q8—81no—
805D4—48no—
806D4—42no—
807D4—42no—
808D4—41no—
809D4—41no—
810D4—41no—
811D4—42no—
812D4—42no—
813D4—41no—
814D4—42no—
815D4—81no—
816D4—82no—
817D4—82no—
818D4—88no—
819C2×C4—22no—
820C2×C4—22no—
821C2×C4—22no—
822C2×C4—22no—
823C2×C4—22no—
824C2×C4—22no—
825C2×C4—21no—
826C2×C4—22no—
827C2×C4—21no—
828C2×C4—21no—
829C2×C4—22no—
830C2×C4—22no—
831C2×C4—21no—
832C2×C4—22no—
833C2×C4—21no—
834C2×C4—22no—
835C2×C4—22no—
836C2×C4—41no—
837C2×C4—41no—
838C2×C4—41no—
839C2×C4—44no—
840C2×C4—44no—
841C2×C4—44no—
842C2×C4—41no—
843C2×C4—41no—
844C2×C4—41no—
845C2×C4—41no—
846C2×C4—41no—
847C2×C4—41no—
848C2×C4—44no—
849C2×C4—42no—
850C2×C4—41no—
851C2×C4—42no—
852C2×C4—41no—
853C2×C4—42no—
854C2×C4—41no—
855C2×C4—42no—
856C2×C4—42no—
857C2×C4—42no—
858C2×C4—41no—
859C2×C4—42no—
860C2×C4—41no—
861C2×C4—42no—
862C2×C4—42no—
863C2×C4—81no—
864C2×C4—82no—
865C2×C4—82no—
866C2×C4#120×C10911yescharacteristic
867C2×C4#120×C10911yescharacteristic
868C2×C4#120×C10911yescharacteristic
869C2×C4#120×C10911yescharacteristic
870C22—21no—
871C22—21no—
872C22—21no—
873C22—21no—
874C22—21no—
875C22—21no—
876C22—24no—
877C22—24no—
878C22—24no—
879C22—41no—
880C22—41no—
881C22—41no—
882C22—41no—
883C22—42no—
884C22—42no—
885C22—42no—
886C22—42no—
887C22—42no—
888C22—42no—
889C22—42no—
890C22—42no—
891C22—42no—
892C22—42no—
893C22—42no—
894C22—42no—
895C22—42no—
896C22—41no—
897C22—42no—
898C22—42no—
899C22—41no—
900C22—41no—
901C22—42no—
902C22—82no—
903C22—81no—
904C22—82no—
905C22C2×#120×C10911yescharacteristic
906C22#525×C10911yescharacteristic
907C22#537×C10911yescharacteristic
908C22#546×C10911yescharacteristic
909C22#547×C10911yescharacteristic
910C22#548×C10911yescharacteristic
911C22#550×C10911yescharacteristic
912C4—21no—
913C4—21no—
914C4—21no—
915C4—42no—
916C4—42no—
917C4—41no—
918C4—42no—
919C4—41no—
920C4—42no—
921C4—41no—
922C4—42no—
923C4—82no—
924C4—82no—
925C4—81no—
926C4B(4,𝔽2)×C10912yes—
927C2—21no—
928C2—21no—
929C2—21no—
930C2—21no—
931C2—21no—
932C2—21no—
933C2—44no—
934C2—81no—
935C2—82no—
936C2C109×#240711yescharacteristic
937C2C2×B(4,𝔽2)×C10911yescharacteristic
938C2C109×#302511yescharacteristic
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×#2848C2semidirect
3. C109×#2847C2semidirect
4. C4×#120×C109C2semidirect
5. C109×#2044C2semidirect
6. C109×#2021C2semidirect
7. C109×#1996C2semidirect
8. C109×#1964C2semidirect
9. C109×#1889C2semidirect
10. C109×#1867C2semidirect
11. C109×#1799C2semidirect
57. C22×Q8×C109D4semidirect
60. C22×D4×C109D4semidirect
70. C23×C4×C109D4semidirect
126. C2×C4⋊C4×C109D4semidirect
127. C2×C4⋊C4×C109D4semidirect
128. C2×C4⋊C4×C109D4semidirect
129. C2×C4⋊C4×C109D4semidirect
139. C2×C22⋊C4×C109D4semidirect
140. C2×C22⋊C4×C109D4semidirect
148. C2×C42×C109D4semidirect
169. C24×C109#41semidirect
285. C22⋊C4×C109#41semidirect
457. #24140C109direct (N × H)
470. #3505C2×C109semidirect
471. #2848C2×C109semidirect
472. #2847C2×C109semidirect
473. C4×#120C2×C109semidirect
474. #2044C2×C109semidirect
475. #2021C2×C109semidirect
476. #1996C2×C109semidirect
477. #1964C2×C109semidirect
478. #1889C2×C109semidirect
479. #1867C2×C109semidirect
480. #1799C2×C109semidirect
481. C109#24140direct (N × H)
527. C22×Q8D4×C109semidirect
530. C22×D4D4×C109semidirect
540. C23×C4D4×C109semidirect
596. C2×C4⋊C4D4×C109semidirect
597. C2×C4⋊C4D4×C109semidirect
598. C2×C4⋊C4D4×C109semidirect
599. C2×C4⋊C4D4×C109semidirect
609. C2×C22⋊C4D4×C109semidirect
610. C2×C22⋊C4D4×C109semidirect
618. C2×C42D4×C109semidirect
639. C24#41×C109semidirect
755. 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×#28482
C109×#28472
C4×#120×C1092
C109×#20442
C109×#20212
C109×#19962
C109×#19642
C109×#18892
C109×#18672
C109×#17992
#24140109