Finite Group Databasebeta

← #11909793

Subgroups — #11909793

Order 1152.

2326 conjugacy classes of subgroups.

The subgroup lattice has 951 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10596184C211yesmaximal, characteristic, complemented
2C3×#5718C211yesmaximal, characteristic, complemented
3C3×#5716C211yesmaximal, characteristic, complemented
4#10595272C212yesmaximal, complemented
5#10595222C212yesmaximal, complemented
6#10595201C214yesmaximal, complemented
7#10595198C212yesmaximal, complemented
8#10595172C212yesmaximal, complemented
9#10595157C212yesmaximal, complemented
10#10595151C214yesmaximal, complemented
11#10595134C212yesmaximal, complemented
12#10595133C212yesmaximal, complemented
13#10595124C212yesmaximal, complemented
14#10593974C211yesmaximal, characteristic, complemented
15#10593956C211yesmaximal, characteristic, complemented
16C4×D3×Dic6C211yesmaximal, characteristic, complemented
17#10593856C211yesmaximal, characteristic, complemented
18#86776—31nomaximal
19#86229—31nomaximal
20C2×C3×#237C2212yes—
21C2×C3×#237C2212yes—
22C2×#3805C2214yes—
23C2×D3×Dic6C2211yescharacteristic
24C32×#127C2211yescharacteristic
25#64145C2212yes—
26#64145C2212yes—
27#64144C2214yes—
28D4×C3⋊Dic3C2212yes—
29D4×C3⋊Dic3C2212yes—
30C4×#634C2211yescharacteristic
31C4×#634C2211yescharacteristic
32C3×#940C2212yes—
33C3×#939C2214yes—
34C3×#938C2212yes—
35C3×#938C2212yes—
36C3×#938C2212yes—
37C3×#936C2212yes—
38C3×D4×Dic3C2212yes—
39C3×D4×Dic3C2212yes—
40C3×D4×Dic3C2212yes—
41C3×C4×D12C2211yescharacteristic
42C3×C42×D3C2211yescharacteristic
43C3×#869C2211yescharacteristic
44C3×C4×Dic6C2211yescharacteristic
45#63982C2214yes—
46#67⋊Dic3C2214yes—
47Dic3×#67C2214yes—
48Dic3×#67C2214yes—
49#63970C2214yes—
50#63969C2214yes—
51#63969C2214yes—
52C2×Dic3⋊Dic3C2214yes—
53#63964C2214yes—
54#63964C2214yes—
55#63961C2214yes—
56#63959C2214yes—
57#63959C2214yes—
58#63956C2214yes—
59#63955C2214yes—
60#63919C2212yes—
61#63918C2212yes—
62C4×#627C2212yes—
63#63908C2211yescharacteristic
64#63905C2212yes—
65C4×#625C2212yes—
66#63898C2212yes—
67D3×C4⋊Dic3C2211yescharacteristic
68D3×C4⋊Dic3C2212yes—
69#63887C2214yes—
70D3×Dic3⋊C4C2212yes—
71C4×D3×Dic3C2212yes—
72#63872C2212yes—
73#63869C2211yescharacteristic
74#63860C2211yescharacteristic
75#63859C2212yes—
76#63857C2212yes—
77#63857C2211yescharacteristic
78#63855C2212yes—
79#63844C2211yescharacteristic
80#63844C2212yes—
81#63843C2212yes—
82Dic3×Dic6C2211yescharacteristic
83#63839C2214yes—
84#63837C2212yes—
85C3×#550—31no—
86C3×#532—31no—
87#5831—32no—
88#5827—32no—
89#5824—34no—
90#5730—31no—
91#5722—31no—
92#5718D311yescharacteristic, complemented
93#5716—32no—
94#5716D311yescharacteristic, complemented
95#5713—31no—
96#5713—31no—
97#5713—32no—
98#5713—61no—
99#5669—34no—
100#5611—34no—
101#5611—32no—
102#5611—32no—
103#5603—34no—
104#5603—32no—
105#5600—32no—
106#5598—32no—
107#5596—32no—
108C4×D3×Q8—31no—
109Q8×Dic6—31no—
110#5561—32no—
111#5559—32no—
112#5557—32no—
113#5557—31no—
114#5546—32no—
115#5543—32no—
116#5543—31no—
117#5539—32no—
118#5479—31no—
119C2×C4×Dic6—31no—
120C2×C32×D4C2312yes—
121C2×C32×D4C2312yes—
122C2×C32×D4C2312yes—
123C22×C3⋊Dic3C2314yes—
124C2×#634C2311yescharacteristic
125C2×#634C2311yescharacteristic
126C2×C3×#67C2314yes—
127C2×C3×#67C2314yes—
128C2×C3×#67C2314yes—
129C22×C3×Dic3C2314yes—
130C22×C3×Dic3C2314yes—
131C3×#237—28no—
132C3×#237—44no—
133C2×C3×D12C2311yescharacteristic
134C2×C3×C4×D3C2311yescharacteristic
135C2×C3×C4×D3C2311yescharacteristic
136C2×C3×C4×D3C2312yes—
137C2×C3×C4×D3C2311yescharacteristic
138C2×C3×Dic6C2312yes—
139C2×C3×Dic6C2311yescharacteristic
140C2×#627C2312yes—
141C2×#627C2314yes—
142C2×#625C2312yes—
143#3805—48no—
144C2×D3×Dic3C2312yes—
145C2×D3×Dic3C2312yes—
146C2×D3×Dic3C2314yes—
147D3×Dic6—24no—
148C32×C42C2311yescharacteristic
149#3757C2314yes—
150#3757C2314yes—
151#3757C2314yes—
152C4⋊(C3⋊Dic3)C2311yescharacteristic
153C4⋊(C3⋊Dic3)C2311yescharacteristic
154#3750C2312yes—
155#3750C2312yes—
156C4×C3⋊Dic3C2312yes—
157C4×C3⋊Dic3C2312yes—
158C3×#217C2314yes—
159C3×#217C2314yes—
160C3×#217C2314yes—
161C3×(C2×D3)⋊C4C2312yes—
162C3×C4⋊Dic3C2311yescharacteristic
163C3×C4⋊Dic3C2312yes—
164C3×C4⋊Dic3C2312yes—
165C3×C4⋊Dic3C2311yescharacteristic
166C3×Dic3⋊C4C2312yes—
167C3×C4×Dic3C2311yescharacteristic
168C3×C4×Dic3C2311yescharacteristic
169C3×C4×Dic3C2312yes—
170C3×C4×Dic3C2311yescharacteristic
171#3724C2314yes—
172#3724C2312yes—
173#3724C2312yes—
174Dic3⋊Dic3C2312yes—
175Dic3⋊Dic3C2314yes—
176Dic3⋊Dic3C2312yes—
177Dic3⋊Dic3C2312yes—
178Dic3⋊Dic3C2312yes—
179Dic3⋊Dic3C2314yes—
180Dic3⋊Dic3C2314yes—
181(C2×D3)⋊Dic3C2312yes—
182(C2×D3)⋊Dic3C2312yes—
183(C2×D3)⋊Dic3C2314yes—
184(C2×D3)⋊Dic3C2312yes—
185(C2×D3)⋊Dic3C2312yes—
186Dic32C2312yes—
187Dic32C2312yes—
188Dic32C2314yes—
189#3522—91noSylow
190C2×C3×#41—32no—
191C2×C3×#41—32no—
192C2×D3×Q8—31no—
193C2×#237—34no—
194C2×#237—34no—
195C2×#237C2×D312yes—
196C2×#237C2×D312yes—
197C22×Dic6—31no—
198C3×C4⋊Q8—31no—
199C3×#127—21no—
200C3×#127—32no—
201C3×#127C2×D311yescharacteristic
202C3×#127C2×D311yescharacteristic
203C3×#124—32no—
204C3×#121—32no—
205C3×#121—32no—
206C3×#121—32no—
207C3×#121—34no—
208C3×C4×Q8—31no—
209C3×C4×D4—32no—
210C3×C4×D4—32no—
211C3×C4×D4—32no—
212C3×C4×D4—31no—
213C2×C3×C42—31no—
214#946—34no—
215Q8×Dic3—32no—
216Q8×Dic3—31no—
217#944—34no—
218#940C2×D312yes—
219#939—34no—
220#939C2×D314yes—
221#938—34no—
222#938—31no—
223#938C2×D312yes—
224#938C2×D312yes—
225#938C2×D312yes—
226#936—32no—
227#936—32no—
228#936—32no—
229#936—32no—
230#936—34no—
231#936—34no—
232#936—31no—
233#936—62no—
234#936—62no—
235#936C2×D312yes—
236#935—34no—
237#935—34no—
238#935—34no—
239#935—34no—
240#935—34no—
241#935—64no—
242D4×Dic3—32no—
243D4×Dic3—32no—
244D4×Dic3—32no—
245D4×Dic3—32no—
246D4×Dic3—34no—
247D4×Dic3—34no—
248D4×Dic3—34no—
249D4×Dic3—32no—
250D4×Dic3—62no—
251D4×Dic3—62no—
252D4×Dic3C2×D312yes—
253D4×Dic3C2×D312yes—
254D4×Dic3C2×D312yes—
255#930—31no—
256#929—34no—
257#929—32no—
258C4×#67—34no—
259C4×#67—34no—
260C4×#67—32no—
261C4×#67—32no—
262#926—34no—
263#926—32no—
264C2×C4⋊Dic3—34no—
265C2×C4⋊Dic3—31no—
266C2×C4⋊Dic3—32no—
267#924—34no—
268#924—34no—
269#924—31no—
270#924—32no—
271C2×Dic3⋊C4—34no—
272C2×Dic3⋊C4—32no—
273C2×C4×Dic3—32no—
274#897—32no—
275#897—31no—
276#893—32no—
277D3×C4⋊C4—32no—
278D3×C4⋊C4—32no—
279D3×C4⋊C4—31no—
280#890—32no—
281#890—32no—
282#890—31no—
283#888—34no—
284#888—32no—
285#888—32no—
286#888—32no—
287#887—32no—
288#887—32no—
289#887—32no—
290#887—31no—
291#885—34no—
292#885—34no—
293#883—34no—
294#883—34no—
295#883—32no—
296#67⋊C4—34no—
297#879—34no—
298#879—34no—
299#879—32no—
300#878—34no—
301#878—34no—
302#878—34no—
303#878—34no—
304#878—34no—
305#877—34no—
306#876—32no—
307#875—31no—
308C4×D12C2×D311yescharacteristic
309#872—32no—
310C42×D3—32no—
311C42×D3C2×D311yescharacteristic
312#870—31no—
313#869—32no—
314#869C2×D311yescharacteristic
315C4×Dic6—31no—
316C4×Dic6—31no—
317C4×Dic6—31no—
318C4×Dic6—31no—
319C4×Dic6—31no—
320C4×Dic6—32no—
321C4×Dic6—31no—
322C4×Dic6—32no—
323C4×Dic6—32no—
324C4×Dic6—32no—
325C4×Dic6—61no—
326C4×Dic6—61no—
327C4×Dic6C2×D311yescharacteristic
328C23×C32C2414yes—
329C22×C3×D3C2412yes—
330C22×C3×D3C2411yescharacteristic
331C32×D4—24no—
332C32×D4—24no—
333C32×D4—42no—
334C2×C32×C4C2411yescharacteristic
335C2×C32×C4C2411yescharacteristic
336C2×C32×C4C2411yescharacteristic
337C2×C3⋊Dic3—44no—
338C2×C3⋊Dic3C2412yes—
339C2×C3⋊Dic3C2412yes—
340C2×C3⋊Dic3C2412yes—
341C2×C3⋊Dic3C2412yes—
342#634—22no—
343#634—22no—
344C3×#67—28no—
345C3×#67—28no—
346C3×#67—44no—
347C2×C3×Dic3—28no—
348C2×C3×Dic3—44no—
349C2×C3×Dic3C2411yescharacteristic
350C2×C3×Dic3C2414yes—
351C2×C3×Dic3C2412yes—
352C2×C3×Dic3C2411yescharacteristic
353C2×C3×Dic3C2411yescharacteristic
354C2×C3×Dic3C2412yes—
355C2×C3×Dic3C2412yes—
356C3×D12—22no—
357C3×C4×D3—22no—
358C3×C4×D3—22no—
359C3×C4×D3—24no—
360C3×C4×D3—22no—
361C3×Dic6—42no—
362C3×Dic6#4114yescomplemented
363#627—24no—
364#627—44no—
365#625—24no—
366D3×Dic3—24no—
367D3×Dic3—24no—
368D3×Dic3—44no—
369#559—92no—
370#559—91no—
371Q82—91no—
372#554—92no—
373#554—91no—
374#550—31no—
375#548—92no—
376#547—92no—
377#547—94no—
378#542—92no—
379#542—94no—
380#532—31no—
381#532—92no—
382#529—91no—
383#529—92no—
384#520—92no—
385C2×C4×Q8—91no—
386C3×#41—68no—
387C3×#41—124no—
388C2×C3×Q8—31no—
389C2×C3×Q8—32no—
390C2×C3×D4—22no—
391C2×C3×D4—22no—
392C2×C3×D4—22no—
393C2×C3×D4—34no—
394C2×C3×D4—34no—
395C2×C3×D4—34no—
396C2×C3×D4—31no—
397C2×C3×D4C22×D312yes—
398C2×C3×D4C22×D312yes—
399C2×C3×D4C22×D312yes—
400C2×C3×D4C22×D312yes—
401C2×C3×D4C22×D312yes—
402C2×C3×D4C22×D312yes—
403C22×C3×C4—34no—
404C22×C3×C4—34no—
405C22×C3×C4—31no—
406C22×C3×C4—31no—
407C22×C3×C4—32no—
408C22×C3×C4—31no—
409C2×#67—32no—
410C2×#67—32no—
411C2×#67C22×D314yes—
412C2×#67C22×D314yes—
413C2×#67C22×D314yes—
414C22×Dic3—34no—
415C22×Dic3—34no—
416C22×Dic3—32no—
417C22×Dic3—32no—
418C22×Dic3—34no—
419C22×Dic3—64no—
420C22×Dic3C22×D314yes—
421C22×Dic3C22×D314yes—
422D3×Q8—64no—
423#237—28no—
424#237—44no—
425#237—128no—
426#237—128no—
427C2×D12C22×D311yescharacteristic
428C2×C4×D3—32no—
429C2×C4×D3—32no—
430C2×C4×D3—34no—
431C2×C4×D3C22×D311yescharacteristic
432C2×C4×D3C22×D311yescharacteristic
433C2×C4×D3C22×D311yescharacteristic
434C2×C4×D3C22×D312yes—
435C2×Dic6—31no—
436C2×Dic6—31no—
437C2×Dic6—31no—
438C2×Dic6—31no—
439C2×Dic6—32no—
440C2×Dic6—32no—
441C2×Dic6—34no—
442C2×Dic6—34no—
443C2×Dic6—61no—
444C2×Dic6—61no—
445C2×Dic6—64no—
446C2×Dic6C22×D312yes—
447C2×Dic6C22×D311yescharacteristic
448C3×C4⋊C4—32no—
449C3×C4⋊C4—31no—
450C3×C4⋊C4—32no—
451C3×C4⋊C4—32no—
452C3×C4⋊C4—31no—
453C3×C22⋊C4—34no—
454C3×C22⋊C4—34no—
455C3×C22⋊C4—34no—
456C3×C22⋊C4—32no—
457C3×C42—21no—
458C3×C42—32no—
459C3×C42—31no—
460C3×C42—31no—
461C3×C42—31no—
462C3×C42C22×D311yescharacteristic
463C3×C42C22×D311yescharacteristic
464#217—34no—
465#217—34no—
466#217—34no—
467#217—34no—
468#217—34no—
469#217—34no—
470#217—34no—
471#217—32no—
472#217—32no—
473#217—32no—
474#217—32no—
475#217—64no—
476#217—64no—
477#217—64no—
478#217C22×D314yes—
479#217C22×D314yes—
480#217C22×D314yes—
481(C2×D3)⋊C4—32no—
482(C2×D3)⋊C4—32no—
483(C2×D3)⋊C4—32no—
484(C2×D3)⋊C4—32no—
485(C2×D3)⋊C4—34no—
486(C2×D3)⋊C4C22×D312yes—
487C4⋊Dic3—31no—
488C4⋊Dic3—31no—
489C4⋊Dic3—31no—
490C4⋊Dic3—31no—
491C4⋊Dic3—32no—
492C4⋊Dic3—32no—
493C4⋊Dic3—34no—
494C4⋊Dic3—34no—
495C4⋊Dic3—32no—
496C4⋊Dic3—34no—
497C4⋊Dic3—32no—
498C4⋊Dic3—61no—
499C4⋊Dic3—61no—
500C4⋊Dic3C22×D311yescharacteristic
501C4⋊Dic3C22×D312yes—
502C4⋊Dic3C22×D312yes—
503C4⋊Dic3C22×D311yescharacteristic
504Dic3⋊C4—32no—
505Dic3⋊C4—32no—
506Dic3⋊C4—32no—
507Dic3⋊C4—32no—
508Dic3⋊C4—32no—
509Dic3⋊C4—32no—
510Dic3⋊C4—32no—
511Dic3⋊C4—32no—
512Dic3⋊C4—34no—
513Dic3⋊C4—32no—
514Dic3⋊C4—32no—
515Dic3⋊C4—32no—
516Dic3⋊C4—34no—
517Dic3⋊C4—34no—
518Dic3⋊C4—32no—
519Dic3⋊C4—34no—
520Dic3⋊C4—34no—
521Dic3⋊C4—62no—
522Dic3⋊C4—62no—
523Dic3⋊C4C22×D312yes—
524C4×Dic3—32no—
525C4×Dic3—32no—
526C4×Dic3—32no—
527C4×Dic3—32no—
528C4×Dic3—32no—
529C4×Dic3—32no—
530C4×Dic3—34no—
531C4×Dic3—32no—
532C4×Dic3—32no—
533C4×Dic3—34no—
534C4×Dic3—62no—
535C4×Dic3—62no—
536C4×Dic3C22×D311yescharacteristic
537C4×Dic3C22×D312yes—
538C4×Dic3C22×D311yescharacteristic
539C4×Dic3C22×D311yescharacteristic
540C22×C32—24no—
541C22×C32—24no—
542C22×C32—24no—
543C22×C32C2511yescharacteristic
544C2×C3×D3—21no—
545C2×C3×D3—21no—
546C2×C3×D3—22no—
547C2×C3×D3—22no—
548C2×C3×D3—22no—
549C2×C3×D3H(5,𝔽2)12yes—
550C32×C4—21no—
551C32×C4C2×#4112yes—
552C32×C42−1+412yes—
553C3⋊Dic3—22no—
554C3⋊Dic3—22no—
555C3⋊Dic3—22no—
556C3⋊Dic3—22no—
557C3×Dic3—21no—
558C3×Dic3—22no—
559C3×Dic3—22no—
560C3×Dic3—24no—
561C3×Dic3—21no—
562C3×Dic3—21no—
563C3×Dic3C2×#4114yes—
564C2×#41—32no—
565C2×#41—32no—
566C2×#41—94no—
567C22×Q8—91no—
568C4⋊Q8—31no—
569C4⋊Q8—92no—
570C4⋊Q8—92no—
571C4⋊Q8—94no—
572#127—32no—
573#127D3211yescharacteristic
574#126—92no—
575#126—94no—
576#125—91no—
577#125—92no—
578#124—32no—
579#124—91no—
580#124—94no—
581#124—94no—
582#124—92no—
583#124—92no—
584#123—92no—
585#123—94no—
586#123—94no—
587#123—94no—
588#123—94no—
589C22⋊Q8—94no—
590C22⋊Q8—94no—
591C22⋊Q8—94no—
592C22⋊Q8—94no—
593C22⋊Q8—91no—
594C22⋊Q8—92no—
595#121—32no—
596#121—32no—
597#121—32no—
598#121—34no—
599#121—91no—
600#121—94no—
601C4×Q8—31no—
602C4×Q8—92no—
603C4×Q8—91no—
604C4×Q8—92no—
605C4×Q8—92no—
606C4×Q8—91no—
607C4×Q8—92no—
608C4×Q8—91no—
609C4×Q8—91no—
610C4×D4—32no—
611C4×D4—32no—
612C4×D4—32no—
613C4×D4—31no—
614C4×D4—94no—
615C4×D4—92no—
616C4×D4—92no—
617C4×D4—94no—
618C4×D4—94no—
619C4×D4—92no—
620C4×D4—92no—
621#117—92no—
622#117—94no—
623C2×C4⋊C4—92no—
624C2×C4⋊C4—91no—
625C2×C4⋊C4—92no—
626C2×C4⋊C4—94no—
627C2×C42—31no—
628C2×C42—92no—
629C23×C3—24no—
630C23×C3—31no—
631C23×C3—32no—
632C23×C3C23×D314yes—
633C23×C3C23×D314yes—
634C22×D3C23×D312yes—
635C22×D3C23×D311yescharacteristic
636C3×Q8—34no—
637C3×Q8—122no—
638C3×D4—24no—
639C3×D4—24no—
640C3×D4—24no—
641C3×D4—24no—
642C3×D4—44no—
643C3×D4—44no—
644C3×D4—42no—
645C3×D4—42no—
646C3×D4—68no—
647C3×D4—68no—
648C3×D4—62no—
649C3×D4—82no—
650C3×D4—124no—
651C2×C3×C4—21no—
652C2×C3×C4—21no—
653C2×C3×C4—21no—
654C2×C3×C4—32no—
655C2×C3×C4—31no—
656C2×C3×C4—32no—
657C2×C3×C4—34no—
658C2×C3×C4—31no—
659C2×C3×C4—32no—
660C2×C3×C4—31no—
661C2×C3×C4—62no—
662C2×C3×C4—68no—
663C2×C3×C4—62no—
664C2×C3×C4—64no—
665C2×C3×C4—62no—
666C2×C3×C4—124no—
667C2×C3×C4C23×D311yescharacteristic
668C2×C3×C4C23×D311yescharacteristic
669C2×C3×C4C23×D311yescharacteristic
670C2×C3×C4C23×D311yescharacteristic
671C2×C3×C4C23×D311yescharacteristic
672C2×C3×C4C23×D311yescharacteristic
673#67—28no—
674#67—28no—
675#67—44no—
676#67—64no—
677#67—64no—
678C2×Dic3—28no—
679C2×Dic3—32no—
680C2×Dic3—32no—
681C2×Dic3—32no—
682C2×Dic3—32no—
683C2×Dic3—32no—
684C2×Dic3—32no—
685C2×Dic3—32no—
686C2×Dic3—32no—
687C2×Dic3—44no—
688C2×Dic3—62no—
689C2×Dic3—62no—
690C2×Dic3—62no—
691C2×Dic3—62no—
692C2×Dic3—64no—
693C2×Dic3—64no—
694C2×Dic3—124no—
695C2×Dic3—124no—
696C2×Dic3—124no—
697C2×Dic3—244no—
698C2×Dic3C23×D311yescharacteristic
699C2×Dic3C23×D312yes—
700C2×Dic3C23×D314yes—
701C2×Dic3C23×D311yescharacteristic
702C2×Dic3C23×D311yescharacteristic
703C2×Dic3C23×D312yes—
704C2×Dic3C23×D312yes—
705D12—22no—
706C4×D3—22no—
707C4×D3—24no—
708C4×D3—22no—
709C4×D3—22no—
710C4×D3—64no—
711C4×D3—64no—
712C4×D3—124no—
713Dic6—42no—
714Dic6—64no—
715Dic6—62no—
716Dic6—62no—
717Dic6—62no—
718Dic6—62no—
719Dic6—64no—
720Dic6—122no—
721Dic6—122no—
722Dic6—124no—
723Dic6—124no—
724Dic6#23714yescomplemented
725C2×C32—44no—
726C2×C32C22×#4111yescharacteristic
727C2×C32C2×H(5,𝔽2)11yescharacteristic
728C2×C32C2×2−1+411yescharacteristic
729C3×D3—22no—
730C3×D3—42no—
731#41—68no—
732#41—124no—
733#41—368no—
734C2×Q8—31no—
735C2×Q8—32no—
736C2×Q8—92no—
737C2×Q8—94no—
738C2×Q8—91no—
739C2×Q8—91no—
740C2×Q8—184no—
741C2×D4—34no—
742C2×D4—34no—
743C2×D4—34no—
744C2×D4—31no—
745C2×D4—92no—
746C2×D4C2×D3212yes—
747C2×D4C2×D3212yes—
748C2×D4C2×D3212yes—
749C22×C4—34no—
750C22×C4—34no—
751C22×C4—31no—
752C22×C4—31no—
753C22×C4—31no—
754C22×C4—32no—
755C22×C4—92no—
756C22×C4—92no—
757C22×C4—94no—
758C22×C4—94no—
759C4⋊C4—32no—
760C4⋊C4—32no—
761C4⋊C4—31no—
762C4⋊C4—31no—
763C4⋊C4—32no—
764C4⋊C4—92no—
765C4⋊C4—92no—
766C4⋊C4—94no—
767C4⋊C4—94no—
768C4⋊C4—92no—
769C4⋊C4—92no—
770C4⋊C4—92no—
771C4⋊C4—92no—
772C4⋊C4—94no—
773C4⋊C4—94no—
774C4⋊C4—91no—
775C4⋊C4—92no—
776C4⋊C4—91no—
777C4⋊C4—92no—
778C22⋊C4—34no—
779C22⋊C4—34no—
780C22⋊C4—34no—
781C22⋊C4—32no—
782C22⋊C4—92no—
783C22⋊C4—92no—
784C22⋊C4—92no—
785C22⋊C4—94no—
786C22⋊C4—92no—
787C22⋊C4—94no—
788C22⋊C4—94no—
789C22⋊C4—94no—
790C42—31no—
791C42—31no—
792C42—31no—
793C42—32no—
794C42—92no—
795C42—92no—
796C42—94no—
797C42—92no—
798C42—92no—
799C42C2×D3211yescharacteristic
800C22×C3—24no—
801C22×C3—24no—
802C22×C3—24no—
803C22×C3—24no—
804C22×C3—24no—
805C22×C3—24no—
806C22×C3—21no—
807C22×C3—32no—
808C22×C3—44no—
809C22×C3—44no—
810C22×C3—44no—
811C22×C3—61no—
812C22×C3—61no—
813C22×C3—62no—
814C22×C3—62no—
815C22×C3—62no—
816C22×C3C24×D311yescharacteristic
817C22×C3C24×D311yescharacteristic
818C2×D3—21no—
819C2×D3—21no—
820C2×D3—22no—
821C2×D3—22no—
822C2×D3—22no—
823C2×D3#100412yes—
824C3×C4—21no—
825C3×C4—21no—
826C3×C4—22no—
827C3×C4—22no—
828C3×C4—34no—
829C3×C4—41no—
830C3×C4—61no—
831C3×C4—62no—
832C3×C4—62no—
833C3×C4—61no—
834C3×C4—64no—
835C3×C4—61no—
836C3×C4C2×#23712yes—
837C3×C4D3×#4112yes—
838C3×C4#101012yes—
839C3×C4#101012yes—
840Dic3—22no—
841Dic3—24no—
842Dic3—21no—
843Dic3—21no—
844Dic3—21no—
845Dic3—22no—
846Dic3—62no—
847Dic3—62no—
848Dic3—62no—
849Dic3—62no—
850Dic3—62no—
851Dic3—62no—
852Dic3—62no—
853Dic3—62no—
854Dic3—122no—
855Dic3—122no—
856Dic3—122no—
857Dic3—122no—
858Dic3C2×#23714yes—
859C32#352211yescharacteristic, complemented, Sylow
860C23—31no—
861C23—32no—
862C23C22×D3214yes—
863Q8—34no—
864Q8—122no—
865Q8—184no—
866Q8—182no—
867Q8—182no—
868Q8—364no—
869D4—24no—
870D4—24no—
871D4—42no—
872D4—68no—
873D4—68no—
874D4—62no—
875D4—124no—
876D4—184no—
877C2×C4—32no—
878C2×C4—31no—
879C2×C4—31no—
880C2×C4—31no—
881C2×C4—32no—
882C2×C4—34no—
883C2×C4—32no—
884C2×C4—62no—
885C2×C4—68no—
886C2×C4—62no—
887C2×C4—62no—
888C2×C4—64no—
889C2×C4—92no—
890C2×C4—92no—
891C2×C4—92no—
892C2×C4—92no—
893C2×C4—124no—
894C2×C4—184no—
895C2×C4—184no—
896C2×C4—364no—
897C2×C4—364no—
898C2×C4C22×D3211yescharacteristic
899C2×C4C22×D3211yescharacteristic
900C2×C4C22×D3211yescharacteristic
901C2×C3—21no—
902C2×C3—21no—
903C2×C3—21no—
904C2×C3—44no—
905C2×C3—44no—
906C2×C3—62no—
907C2×C3—84no—
908C2×C3—122no—
909C2×C3C22×#23711yescharacteristic
910C2×C3C2×#100411yescharacteristic
911C2×C3C2×D3×#4111yescharacteristic
912C2×C3C2×#101011yescharacteristic
913C2×C3C2×#101011yescharacteristic
914C2×C3D3×H(5,𝔽2)11yescharacteristic
915D3—22no—
916D3—42no—
917C22—24no—
918C22—24no—
919C22—24no—
920C22—32no—
921C22—61no—
922C22—61no—
923C22—62no—
924C22—62no—
925C22—62no—
926C22C23×D3211yescharacteristic
927C4—21no—
928C4—34no—
929C4—61no—
930C4—62no—
931C4—61no—
932C4—61no—
933C4—64no—
934C4—62no—
935C4—182no—
936C4—182no—
937C4—182no—
938C4—182no—
939C4#6430912yes—
940C4D3×#23712yes—
941C3—21no—
942C3#8622911yescharacteristic, complemented
943C3#8677611yescharacteristic, complemented
944C2—44no—
945C2—62no—
946C2—122no—
947C2C2×#6430911yescharacteristic
948C2C2×D3×#23711yescharacteristic
949C2D3×#100411yescharacteristic
subgroupG/H
center, FrattiniC22C23×D32
commutator, socle, cosocleC22×C32C25
FittingC32×#127C22
hypercenter#127D32
hypocenterC32#3522
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C22 ◁ #127

Complements

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

NH ≅ G/Ntype
1. #10596184C2semidirect
2. C3×#5718C2semidirect
3. C3×#5716C2semidirect
4. #10595272C2semidirect
5. #10595222C2semidirect
6. #10595201C2semidirect
7. #10595198C2semidirect
8. #10595172C2semidirect
9. #10595157C2semidirect
10. #10595151C2semidirect
11. #10595134C2semidirect
12. #10595133C2semidirect
13. #10595124C2semidirect
14. #10593974C2semidirect
15. #10593956C2semidirect
16. C4×D3×Dic6C2semidirect
17. #10593856C2semidirect
92. #5718D3semidirect
94. #5716D3semidirect
362. C3×Dic6#41semidirect
724. Dic6#237semidirect
859. C32#3522semidirect
942. C3#86229semidirect
943. C3#86776semidirect

Maximal subgroups

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

subgroupindex
#105961842
C3×#57182
C3×#57162
#105952722
#105952222
#105952012
#105951982
#105951722
#105951572
#105951512
#105951342
#105951332
#105951242
#105939742
#105939562
C4×D3×Dic62
#105938562
#867763
#862293