Finite Group Databasebeta

← #11910386

Subgroups — #11910386

Order 1152.

2233 conjugacy classes of subgroups.

The subgroup lattice has 1170 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10596071C211yesmaximal, characteristic, complemented
2C3×#5620C212yesmaximal, complemented
3#10595260C212yesmaximal, complemented
4#10595259C212yesmaximal, complemented
5#10595256C211yesmaximal, characteristic, complemented
6#10595213C211yesmaximal, characteristic, complemented
7#10595133C212yesmaximal, complemented
8#10595130C212yesmaximal, complemented
9#10595130C212yesmaximal, complemented
10#10594975C212yesmaximal, complemented
11#10594963C211yesmaximal, characteristic, complemented
12#10594929C211yesmaximal, characteristic, complemented
13#10594507C211yesmaximal, characteristic, complemented
14#10594497C211yesmaximal, characteristic, complemented
15#10594435C212yesmaximal, complemented
16#10594234C212yesmaximal, complemented
17#10594169C212yesmaximal, complemented
18#10594112C212yesmaximal, complemented
19#10594082C212yesmaximal, complemented
20#87070—32nomaximal
21C2×#3805C2212yes—
22C2×#3805C2211yescharacteristic
23C2×#3805C2211yescharacteristic, complemented
24C22×D3×Dic3C2212yescomplemented
25C32×#121C2211yescharacteristic
26#64145C2211yescharacteristic
27#64144C2212yescomplemented
28D4×C3⋊Dic3C2211yescharacteristic
29D4×C3⋊Dic3C2212yescomplemented
30#64133C2211yescharacteristic, complemented
31C2×C4×C3⋊Dic3C2211yescharacteristic, complemented
32#64099C2211yescharacteristic, complemented
33#64096C2211yescharacteristic, complemented
34#64088C2212yescomplemented
35#64086C2212yescomplemented
36C3×#940C2212yes—
37C3×#939C2212yes—
38C3×#939C2212yes—
39C3×#938C2212yescomplemented
40C3×#937C2212yes—
41C3×#937C2212yescomplemented
42C3×#930C2212yescomplemented
43C3×#929C2212yescomplemented
44C3×#898C2212yescomplemented
45C3×#894C2212yescomplemented
46C3×#886C2212yes—
47C3×#884C2212yes—
48C3×#882C2212yescomplemented
49C3×#879C2212yescomplemented
50#63982C2211yescharacteristic, complemented
51#63980C2211yescharacteristic
52#63980C2212yescomplemented
53#63976C2212yes—
54#63976C2212yes—
55#63976C2212yescomplemented
56#67⋊Dic3C2212yes—
57#67⋊Dic3C2212yescomplemented
58#67⋊Dic3C2212yescomplemented
59#63970C2212yes—
60#63970C2212yes—
61#63970C2212yescomplemented
62#63970C2212yescomplemented
63#63969C2212yes—
64#63969C2212yescomplemented
65#63969C2212yescomplemented
66#63964C2212yescomplemented
67#63964C2212yescomplemented
68#63961C2212yescomplemented
69#63959C2212yes—
70#63959C2212yes—
71#63959C2212yescomplemented
72#63919C2211yescharacteristic, complemented
73#63918C2212yescomplemented
74#63915C2211yescharacteristic
75#63915C2211yescharacteristic
76#63915C2211yescharacteristic, complemented
77#63914C2211yescharacteristic
78#63913C2212yes—
79#63908C2212yescomplemented
80#63905C2212yescomplemented
81#63902C2211yescharacteristic
82#63902C2212yes—
83#63902C2212yescomplemented
84#63899C2212yescomplemented
85#63899C2212yescomplemented
86#63898C2212yescomplemented
87#63898C2212yescomplemented
88#63896C2212yescomplemented
89#63893C2212yescomplemented
90#63893C2212yescomplemented
91#63891C2212yes—
92#63891C2212yescomplemented
93#63885C2212yes—
94#63885C2212yes—
95#63885C2212yes—
96#63884C2212yescomplemented
97#63878C2212yescomplemented
98#63878C2212yescomplemented
99C4×D3×Dic3C2212yescomplemented
100#63870C2211yescharacteristic, complemented
101#63862C2212yescomplemented
102#63859C2212yescomplemented
103#63859C2212yescomplemented
104#63851C2212yescomplemented
105#63847C2212yescomplemented
106#63846C2212yescomplemented
107#63838C2211yescharacteristic, complemented
108C3×#560—32no—
109#5720—32no—
110#5716—32no—
111#5712—32no—
112#5712—32no—
113#5706—32no—
114#5706—32no—
115#5667—32no—
116#5667—32no—
117#5656—32no—
118#5651—32no—
119#5649—32no—
120#5649—32no—
121#5621—32no—
122#5621—32no—
123#5621—32no—
124#5621—32no—
125#5620—32no—
126#5620D312yescomplemented
127#5606—32no—
128#5606—32no—
129#5600—32no—
130#5600—32no—
131#5600—61no—
132#5596—32no—
133#5596—32no—
134#5595—32no—
135#5595—32no—
136#5594—32no—
137#5586—32no—
138#5586—32no—
139#5586—32no—
140C23×C3×D3C2312yes—
141C2×C32×D4C2311yescharacteristic
142C2×C32×D4C2312yes—
143C22×C32×C4C2311yescharacteristic
144C22×C3⋊Dic3C2312yes—
145C22×C3⋊Dic3C2311yescharacteristic
146C22×C3⋊Dic3C2311yescharacteristic
147C2×#634C2311yescharacteristic
148C2×C3×#67C2312yes—
149C2×C3×#67C2312yes—
150C2×C3×#67C2312yes—
151C2×C3×#67C2312yes—
152C2×C3×#67C2312yes—
153C2×C3×#67C2312yes—
154C2×C3×#67C2312yes—
155C22×C3×Dic3C2312yes—
156C2×C3×D12C2312yes—
157C2×C3×D12C2312yes—
158C2×C3×C4×D3C2312yes—
159C2×#627C2311yescharacteristic
160C2×#627C2312yes—
161C2×#627C2311yescharacteristic
162C2×#627C2311yescharacteristic
163C2×#625C2312yes—
164C2×#625C2311yescharacteristic
165C2×#625C2311yescharacteristic
166C2×#625C2312yes—
167C2×#625C2311yescharacteristic
168C2×#625C2312yes—
169#3805—42no—
170#3805—44no—
171#3805—42no—
172C2×D3×Dic3—44no—
173C2×D3×Dic3C2312yes—
174C2×D3×Dic3C2312yes—
175C2×D3×Dic3C2312yes—
176C2×D3×Dic3C2312yes—
177C2×D3×Dic3C2312yes—
178C2×D3×Dic3C2312yes—
179C32×C4⋊C4C2311yescharacteristic
180C32×C22⋊C4C2312yes—
181#3757C2312yes—
182#3757C2312yes—
183#3757C2312yes—
184#3757C2312yes—
185C4⋊(C3⋊Dic3)C2312yes—
186C4⋊(C3⋊Dic3)C2311yescharacteristic
187#3750C2312yes—
188#3750C2312yes—
189#3750C2312yes—
190C4×C3⋊Dic3C2311yescharacteristic
191C4×C3⋊Dic3C2312yes—
192C4×C3⋊Dic3C2311yescharacteristic
193C4×C3⋊Dic3C2311yescharacteristic
194C4×C3⋊Dic3C2311yescharacteristic
195C3×#217C2312yes—
196C3×#217C2312yes—
197C3×#217C2312yes—
198C3×(C2×D3)⋊C4C2312yes—
199C3×(C2×D3)⋊C4C2312yes—
200C3×(C2×D3)⋊C4C2312yes—
201C3×(C2×D3)⋊C4C2312yes—
202C3×(C2×D3)⋊C4C2312yes—
203C3×(C2×D3)⋊C4C2312yes—
204C3×(C2×D3)⋊C4C2312yes—
205C3×C4⋊Dic3C2312yes—
206C3×C4⋊Dic3C2312yes—
207C3×Dic3⋊C4C2312yes—
208C3×Dic3⋊C4C2312yes—
209C3×Dic3⋊C4C2312yes—
210C3×C4×Dic3C2312yes—
211#3724C2311yescharacteristic
212#3724C2312yes—
213#3724C2312yes—
214#3724C2311yescharacteristic
215Dic3⋊Dic3C2312yes—
216Dic3⋊Dic3C2312yes—
217Dic3⋊Dic3C2312yes—
218Dic3⋊Dic3C2312yes—
219Dic3⋊Dic3C2312yes—
220(C2×D3)⋊Dic3C2312yes—
221(C2×D3)⋊Dic3C2312yes—
222(C2×D3)⋊Dic3C2312yes—
223(C2×D3)⋊Dic3C2312yes—
224(C2×D3)⋊Dic3C2312yes—
225(C2×D3)⋊Dic3C2312yes—
226(C2×D3)⋊Dic3C2312yes—
227(C2×D3)⋊Dic3C2312yes—
228(C2×D3)⋊Dic3C2312yes—
229Dic32C2312yes—
230Dic32C2312yes—
231#3529—91noSylow
232C23×Dic3—32no—
233C2×#237—32no—
234C2×#237—32no—
235C2×#237—32no—
236C2×#237—32no—
237C22×C4×D3—32no—
238C3×#127—32no—
239C3×#126—32no—
240C3×#126—32no—
241C3×#123—32no—
242C3×#123—32no—
243C3×#123—32no—
244C3×#121—21no—
245C3×#121—32no—
246C3×#121—32no—
247C3×#121—32no—
248C3×#121—32no—
249C3×#121—32no—
250C3×#121C2×D312yes—
251C3×#120—32no—
252C3×#120—32no—
253C3×#120—32no—
254#953—32no—
255#953—32no—
256#953—32no—
257#940—32no—
258#940C2×D312yes—
259#939—32no—
260#939—32no—
261#939—32no—
262#939—32no—
263#939—32no—
264#939—32no—
265#939—32no—
266#939—32no—
267#939—32no—
268#939—32no—
269#939C2×D312yes—
270#939C2×D312yes—
271#938—32no—
272#938—32no—
273#938—32no—
274#938—32no—
275#938—32no—
276#938C2×D312yescomplemented
277#937—32no—
278#937—32no—
279#937—32no—
280#937C2×D312yes—
281#937C2×D312yescomplemented
282#936—32no—
283#936—32no—
284#936—32no—
285#936—32no—
286#936—61no—
287#935—32no—
288#935—32no—
289#935—32no—
290#935—32no—
291#935—32no—
292#935—32no—
293#935—32no—
294#935—62no—
295D4×Dic3—32no—
296D4×Dic3—32no—
297D4×Dic3—32no—
298D4×Dic3—32no—
299D4×Dic3—32no—
300D4×Dic3—32no—
301D4×Dic3—32no—
302D4×Dic3—32no—
303D4×Dic3—61no—
304D4×Dic3—62no—
305#930—32no—
306#930C2×D312yescomplemented
307#929—32no—
308#929—32no—
309#929C2×D312yescomplemented
310#924—32no—
311#924—32no—
312#924—32no—
313#924—32no—
314#924—61no—
315C2×C4×Dic3—32no—
316C2×C4×Dic3—32no—
317C2×C4×Dic3—61no—
318#898—32no—
319#898C2×D312yescomplemented
320#897—32no—
321#897—32no—
322#896—32no—
323#896—32no—
324#896—32no—
325#896—32no—
326#894—32no—
327#894C2×D312yescomplemented
328#893—32no—
329#893—32no—
330#892—32no—
331#892—32no—
332#890—32no—
333#890—32no—
334#890—61no—
335#889—32no—
336#889—32no—
337#889—32no—
338#889—32no—
339#888—32no—
340#888—32no—
341#887—32no—
342#887—32no—
343#887—61no—
344#886—32no—
345#886—32no—
346#886C2×D312yes—
347#885—32no—
348#885—32no—
349#885—32no—
350#885—32no—
351#885—32no—
352#885—32no—
353#885—32no—
354#885—32no—
355#884—32no—
356#884—32no—
357#884—32no—
358#884C2×D312yes—
359#883—32no—
360#883—32no—
361#883—32no—
362#883—32no—
363#883—32no—
364#883—32no—
365#882C2×D312yescomplemented
366#67⋊C4—32no—
367#67⋊C4—32no—
368#67⋊C4—32no—
369#67⋊C4—32no—
370#67⋊C4—32no—
371#67⋊C4—32no—
372#67⋊C4—32no—
373#67⋊C4—32no—
374#879—32no—
375#879—32no—
376#879—32no—
377#879—32no—
378#879—32no—
379#879—62no—
380#879C2×D312yescomplemented
381#878—32no—
382#878—32no—
383#878—32no—
384#878—32no—
385#878—32no—
386#878—32no—
387#878—32no—
388#878—32no—
389#877—32no—
390#877—32no—
391#877—32no—
392#877—32no—
393#877—62no—
394#876—32no—
395#876—32no—
396C42×D3—32no—
397#869—32no—
398C23×C32C2412yes—
399C23×C32C2411yescharacteristic
400C22×C3×D3—42no—
401C22×C3×D3—42no—
402C22×C3×D3—42no—
403C22×C3×D3C2412yes—
404C22×C3×D3C2412yes—
405C22×C3×D3C2412yes—
406C32×D4—41no—
407C32×D4—42no—
408C2×C32×C4—41no—
409C2×C32×C4C2412yes—
410C2×C32×C4C2411yescharacteristic
411C2×C32×C4C2411yescharacteristic
412C2×C3⋊Dic3—24no—
413C2×C3⋊Dic3—22no—
414C2×C3⋊Dic3—41no—
415C2×C3⋊Dic3C2412yes—
416C2×C3⋊Dic3C2411yescharacteristic
417C2×C3⋊Dic3C2411yescharacteristic
418C2×C3⋊Dic3C2411yescharacteristic
419C2×C3⋊Dic3C2412yes—
420C2×C3⋊Dic3C2411yescharacteristic
421#634—41no—
422C3×#67—42no—
423C3×#67—42no—
424C3×#67—42no—
425C3×#67—42no—
426C3×#67—42no—
427C3×#67—42no—
428C3×#67—42no—
429C2×C3×Dic3—42no—
430C2×C3×Dic3C2412yes—
431C2×C3×Dic3C2412yes—
432C2×C3×Dic3C2412yes—
433C2×C3×Dic3C2412yes—
434C2×C3×Dic3C2412yes—
435C3×D12—42no—
436C3×D12—42no—
437C3×C4×D3—42no—
438#627—41no—
439#627—42no—
440#627—41no—
441#627—41no—
442#625—42no—
443#625—41no—
444#625—41no—
445#625—42no—
446#625—42no—
447#625—41no—
448D3×Dic3—24no—
449D3×Dic3—24no—
450D3×Dic3—24no—
451D3×Dic3—42no—
452D3×Dic3—42no—
453D3×Dic3—42no—
454#563—92no—
455#563—91no—
456#562—91no—
457#562—92no—
458#562—92no—
459#562—91no—
460H(3,𝔽4)—91no—
461#560—32no—
462#560—92no—
463#560—92no—
464#532—91no—
465#532—92no—
466#529—92no—
467#529—91no—
468#529—92no—
469#529—91no—
470#525—92no—
471#525—92no—
472#525—92no—
473C24×C3—32no—
474C23×D3C22×D312yes—
475C2×C3×D4—22no—
476C2×C3×D4—21no—
477C2×C3×D4—32no—
478C2×C3×D4—32no—
479C2×C3×D4—32no—
480C2×C3×D4—32no—
481C2×C3×D4—32no—
482C2×C3×D4—32no—
483C2×C3×D4—32no—
484C2×C3×D4—32no—
485C2×C3×D4—32no—
486C2×C3×D4C22×D312yes—
487C2×C3×D4C22×D312yes—
488C2×C3×D4C22×D312yes—
489C22×C3×C4—21no—
490C22×C3×C4—32no—
491C22×C3×C4—32no—
492C22×C3×C4C22×D312yes—
493C2×#67—32no—
494C2×#67—32no—
495C2×#67—32no—
496C2×#67—32no—
497C2×#67—32no—
498C2×#67—32no—
499C2×#67—32no—
500C2×#67—32no—
501C2×#67—32no—
502C2×#67C22×D312yes—
503C2×#67C22×D312yes—
504C2×#67C22×D312yes—
505C2×#67C22×D312yes—
506C2×#67C22×D312yes—
507C2×#67C22×D312yes—
508C2×#67C22×D312yes—
509C22×Dic3—32no—
510C22×Dic3—32no—
511C22×Dic3—32no—
512C22×Dic3—32no—
513C22×Dic3—32no—
514C22×Dic3—32no—
515C22×Dic3—32no—
516C22×Dic3—32no—
517C22×Dic3—32no—
518C22×Dic3—32no—
519C22×Dic3—62no—
520C22×Dic3—61no—
521C22×Dic3—61no—
522C22×Dic3—124no—
523C22×Dic3C22×D312yes—
524#237—124no—
525#237—124no—
526#237—124no—
527#237—124no—
528C2×D12C22×D312yes—
529C2×D12C22×D312yes—
530C2×C4×D3—32no—
531C2×C4×D3—32no—
532C2×C4×D3—32no—
533C2×C4×D3—32no—
534C2×C4×D3—32no—
535C2×C4×D3—32no—
536C2×C4×D3—124no—
537C2×C4×D3C22×D312yes—
538C2×Dic6—32no—
539C2×Dic6—32no—
540C2×Dic6—32no—
541C2×Dic6—32no—
542C2×Dic6—32no—
543C2×Dic6—32no—
544C2×Dic6—61no—
545C3×C4⋊C4—21no—
546C3×C4⋊C4—32no—
547C3×C4⋊C4—32no—
548C3×C4⋊C4—32no—
549C3×C4⋊C4—32no—
550C3×C4⋊C4—32no—
551C3×C4⋊C4C22×D312yes—
552C3×C22⋊C4—22no—
553C3×C22⋊C4—32no—
554C3×C22⋊C4—32no—
555C3×C22⋊C4—32no—
556C3×C22⋊C4—32no—
557C3×C22⋊C4—32no—
558C3×C22⋊C4—32no—
559C3×C22⋊C4—32no—
560C3×C22⋊C4—32no—
561C3×C22⋊C4—32no—
562C3×C22⋊C4—32no—
563C3×C22⋊C4C22×D312yes—
564C3×C22⋊C4C22×D312yes—
565C3×C42—32no—
566#217—32no—
567#217—32no—
568#217—32no—
569#217—32no—
570#217—32no—
571#217—32no—
572#217—32no—
573#217—32no—
574#217—32no—
575#217—32no—
576#217—32no—
577#217—32no—
578#217—32no—
579#217—32no—
580#217—32no—
581#217—32no—
582#217—32no—
583#217—62no—
584#217—62no—
585#217—62no—
586#217—62no—
587#217C22×D312yes—
588#217C22×D312yes—
589#217C22×D312yes—
590(C2×D3)⋊C4—32no—
591(C2×D3)⋊C4—32no—
592(C2×D3)⋊C4—32no—
593(C2×D3)⋊C4—32no—
594(C2×D3)⋊C4—32no—
595(C2×D3)⋊C4—32no—
596(C2×D3)⋊C4—32no—
597(C2×D3)⋊C4—32no—
598(C2×D3)⋊C4—32no—
599(C2×D3)⋊C4C22×D312yes—
600(C2×D3)⋊C4C22×D312yes—
601(C2×D3)⋊C4C22×D312yes—
602(C2×D3)⋊C4C22×D312yes—
603(C2×D3)⋊C4C22×D312yes—
604(C2×D3)⋊C4C22×D312yes—
605(C2×D3)⋊C4C22×D312yes—
606C4⋊Dic3—32no—
607C4⋊Dic3—32no—
608C4⋊Dic3—32no—
609C4⋊Dic3—32no—
610C4⋊Dic3—32no—
611C4⋊Dic3—32no—
612C4⋊Dic3—32no—
613C4⋊Dic3—32no—
614C4⋊Dic3—62no—
615C4⋊Dic3—61no—
616C4⋊Dic3C22×D312yes—
617C4⋊Dic3C22×D312yes—
618Dic3⋊C4—32no—
619Dic3⋊C4—32no—
620Dic3⋊C4—32no—
621Dic3⋊C4—32no—
622Dic3⋊C4—32no—
623Dic3⋊C4—32no—
624Dic3⋊C4—32no—
625Dic3⋊C4—32no—
626Dic3⋊C4—32no—
627Dic3⋊C4—32no—
628Dic3⋊C4—32no—
629Dic3⋊C4—32no—
630Dic3⋊C4—32no—
631Dic3⋊C4—32no—
632Dic3⋊C4—32no—
633Dic3⋊C4—32no—
634Dic3⋊C4—32no—
635Dic3⋊C4—62no—
636Dic3⋊C4—62no—
637Dic3⋊C4—62no—
638Dic3⋊C4C22×D312yes—
639Dic3⋊C4C22×D312yes—
640Dic3⋊C4C22×D312yes—
641C4×Dic3—32no—
642C4×Dic3—32no—
643C4×Dic3—32no—
644C4×Dic3—32no—
645C4×Dic3—32no—
646C4×Dic3—32no—
647C4×Dic3—32no—
648C4×Dic3—32no—
649C4×Dic3—32no—
650C4×Dic3—32no—
651C4×Dic3—61no—
652C4×Dic3—62no—
653C4×Dic3—61no—
654C4×Dic3—61no—
655C4×Dic3—61no—
656C4×Dic3C22×D312yes—
657C22×C32—21no—
658C22×C32—22no—
659C22×C32—21no—
660C22×C32—21no—
661C22×C32—22no—
662C22×C32—22no—
663C22×C32C2511yescharacteristic
664C2×C3×D3—22no—
665C2×C3×D3—22no—
666C2×C3×D3—22no—
667C2×C3×D3—22no—
668C2×C3×D3—22no—
669C2×C3×D3—22no—
670C2×C3×D3—22no—
671C2×C3×D3—22no—
672C2×C3×D3—22no—
673C2×C3×D3—48no—
674C32×C4—21no—
675C32×C4—22no—
676C32×C4—21no—
677C3⋊Dic3—22no—
678C3⋊Dic3—21no—
679C3⋊Dic3—22no—
680C3⋊Dic3—21no—
681C3⋊Dic3—21no—
682C3⋊Dic3H(5,𝔽2)12yes—
683C3×Dic3—22no—
684C3×Dic3—22no—
685C3×Dic3—22no—
686C3×Dic3—22no—
687C3×Dic3—22no—
688C2×#41—92no—
689C2×#41—91no—
690C2×#41—91no—
691C23×C4—92no—
692C4⋊Q8—92no—
693C4⋊Q8—91no—
694#127—32no—
695#127—91no—
696#126—32no—
697#126—32no—
698#126—92no—
699#126—92no—
700#126—92no—
701#126—92no—
702#125—92no—
703#125—91no—
704#125—92no—
705#125—91no—
706#124—92no—
707#124—91no—
708#124—91no—
709#124—91no—
710#124—92no—
711#124—92no—
712#124—92no—
713#124—91no—
714#123—32no—
715#123—32no—
716#123—32no—
717#123—92no—
718#123—92no—
719#123—92no—
720#123—92no—
721#123—92no—
722#123—92no—
723#123—92no—
724#123—92no—
725#123—92no—
726C22⋊Q8—91no—
727C22⋊Q8—92no—
728C22⋊Q8—92no—
729C22⋊Q8—92no—
730C22⋊Q8—92no—
731C22⋊Q8—92no—
732C22⋊Q8—92no—
733C22⋊Q8—92no—
734C22⋊Q8—92no—
735C22⋊Q8—91no—
736#121—32no—
737#121—32no—
738#121—32no—
739#121—32no—
740#121—32no—
741#121—92no—
742#121—92no—
743#121—92no—
744#121—92no—
745#121—92no—
746#121—92no—
747#121—91no—
748#121—92no—
749#121—92no—
750#121—92no—
751#121D3211yescharacteristic
752#120—32no—
753#120—32no—
754#120—32no—
755#120—92no—
756#120—92no—
757#120—92no—
758C4×Q8—91no—
759C4×Q8—91no—
760C4×D4—92no—
761C4×D4—91no—
762C4×D4—92no—
763C4×D4—92no—
764C4×D4—92no—
765C4×D4—92no—
766C4×D4—92no—
767C4×D4—92no—
768C4×D4—91no—
769C4×D4—92no—
770#117—92no—
771#117—92no—
772#117—92no—
773C2×C42—92no—
774C2×C42—91no—
775C23×C3—21no—
776C23×C3—22no—
777C23×C3—32no—
778C23×C3—32no—
779C23×C3—32no—
780C23×C3—122no—
781C23×C3—122no—
782C23×C3—122no—
783C23×C3C23×D312yes—
784C23×C3C23×D312yes—
785C23×C3C23×D312yes—
786C22×D3—42no—
787C22×D3—42no—
788C22×D3—42no—
789C22×D3C23×D312yes—
790C22×D3C23×D312yes—
791C22×D3C23×D312yes—
792C3×D4—42no—
793C3×D4—42no—
794C3×D4—42no—
795C3×D4—42no—
796C3×D4—44no—
797C3×D4—122no—
798C3×D4—122no—
799C3×D4—122no—
800C3×D4—122no—
801C3×D4—122no—
802C3×D4—122no—
803C3×D4—122no—
804C3×D4—122no—
805C3×D4—122no—
806C2×C3×C4—21no—
807C2×C3×C4—21no—
808C2×C3×C4—22no—
809C2×C3×C4—32no—
810C2×C3×C4—32no—
811C2×C3×C4—32no—
812C2×C3×C4—32no—
813C2×C3×C4—32no—
814C2×C3×C4—42no—
815C2×C3×C4—42no—
816C2×C3×C4—122no—
817C2×C3×C4—122no—
818C2×C3×C4C23×D312yes—
819C2×C3×C4C23×D312yes—
820C2×C3×C4C23×D312yes—
821C2×C3×C4C23×D312yes—
822#67—42no—
823#67—42no—
824#67—42no—
825#67—42no—
826#67—42no—
827#67—42no—
828#67—42no—
829#67—122no—
830#67—122no—
831#67—122no—
832#67—122no—
833#67—122no—
834#67—122no—
835#67—122no—
836#67—122no—
837#67—122no—
838C2×Dic3—32no—
839C2×Dic3—32no—
840C2×Dic3—32no—
841C2×Dic3—32no—
842C2×Dic3—32no—
843C2×Dic3—32no—
844C2×Dic3—32no—
845C2×Dic3—32no—
846C2×Dic3—42no—
847C2×Dic3—61no—
848C2×Dic3—61no—
849C2×Dic3—61no—
850C2×Dic3—61no—
851C2×Dic3—62no—
852C2×Dic3—62no—
853C2×Dic3—64no—
854C2×Dic3—64no—
855C2×Dic3—64no—
856C2×Dic3—64no—
857C2×Dic3—64no—
858C2×Dic3—64no—
859C2×Dic3—124no—
860C2×Dic3—122no—
861C2×Dic3—122no—
862C2×Dic3—122no—
863C2×Dic3—122no—
864C2×Dic3—122no—
865C2×Dic3—122no—
866C2×Dic3C23×D312yes—
867C2×Dic3C23×D312yes—
868C2×Dic3C23×D312yes—
869C2×Dic3C23×D312yes—
870C2×Dic3C23×D312yes—
871D12—42no—
872D12—42no—
873C4×D3—42no—
874C4×D3—64no—
875C4×D3—64no—
876C4×D3—64no—
877C4×D3—122no—
878C4×D3—122no—
879C4×D3—122no—
880Dic6—122no—
881Dic6—122no—
882Dic6—122no—
883Dic6—122no—
884Dic6—122no—
885Dic6—122no—
886Dic6—122no—
887C2×C32—41no—
888C2×C32—42no—
889C2×C32C2×H(5,𝔽2)11yescharacteristic
890C2×C32#58511yescharacteristic
891C2×C32#58511yescharacteristic
892C3×D3—42no—
893C3×D3—42no—
894C3×D3—42no—
895C24—32no—
896#41—362no—
897#41—364no—
898#41—362no—
899C2×Q8—91no—
900C2×Q8—92no—
901C2×Q8—91no—
902C2×Q8—91no—
903C2×Q8—91no—
904C2×D4—32no—
905C2×D4—32no—
906C2×D4—32no—
907C2×D4—32no—
908C2×D4—32no—
909C2×D4—32no—
910C2×D4—32no—
911C2×D4—32no—
912C2×D4—32no—
913C2×D4—91no—
914C2×D4—92no—
915C2×D4—92no—
916C2×D4—91no—
917C2×D4—92no—
918C2×D4—91no—
919C2×D4C2×D3211yescharacteristic
920C2×D4C2×D3212yes—
921C22×C4—32no—
922C22×C4—32no—
923C22×C4—92no—
924C22×C4—92no—
925C22×C4—92no—
926C22×C4—92no—
927C22×C4—92no—
928C22×C4—92no—
929C22×C4—91no—
930C22×C4—92no—
931C22×C4—91no—
932C22×C4—364no—
933C22×C4C2×D3211yescharacteristic
934C4⋊C4—32no—
935C4⋊C4—32no—
936C4⋊C4—32no—
937C4⋊C4—32no—
938C4⋊C4—32no—
939C4⋊C4—92no—
940C4⋊C4—92no—
941C4⋊C4—92no—
942C4⋊C4—92no—
943C4⋊C4—92no—
944C4⋊C4—91no—
945C4⋊C4—92no—
946C4⋊C4—92no—
947C4⋊C4—91no—
948C4⋊C4—92no—
949C4⋊C4—92no—
950C4⋊C4—92no—
951C4⋊C4—91no—
952C4⋊C4—92no—
953C4⋊C4C2×D3211yescharacteristic
954C22⋊C4—32no—
955C22⋊C4—32no—
956C22⋊C4—32no—
957C22⋊C4—32no—
958C22⋊C4—32no—
959C22⋊C4—32no—
960C22⋊C4—32no—
961C22⋊C4—32no—
962C22⋊C4—32no—
963C22⋊C4—32no—
964C22⋊C4—92no—
965C22⋊C4—92no—
966C22⋊C4—92no—
967C22⋊C4—92no—
968C22⋊C4—92no—
969C22⋊C4—92no—
970C22⋊C4—92no—
971C22⋊C4—92no—
972C22⋊C4—92no—
973C22⋊C4—92no—
974C22⋊C4—92no—
975C22⋊C4—92no—
976C22⋊C4—92no—
977C22⋊C4C2×D3212yes—
978C42—32no—
979C42—92no—
980C42—92no—
981C42—92no—
982C42—91no—
983C42—91no—
984C42—91no—
985C42—91no—
986C22×C3—22no—
987C22×C3—22no—
988C22×C3—22no—
989C22×C3—22no—
990C22×C3—22no—
991C22×C3—22no—
992C22×C3—22no—
993C22×C3—22no—
994C22×C3—22no—
995C22×C3—22no—
996C22×C3—21no—
997C22×C3—41no—
998C22×C3—41no—
999C22×C3—42no—
1000C22×C3—42no—
1001C22×C3—42no—
1002C22×C3—62no—
1003C22×C3—62no—
1004C22×C3—62no—
1005C22×C3—62no—
1006C22×C3—62no—
1007C22×C3—62no—
1008C22×C3—62no—
1009C22×C3—62no—
1010C22×C3—62no—
1011C22×C3—128no—
1012C22×C3C24×D312yes—
1013C2×D3—22no—
1014C2×D3—22no—
1015C2×D3—22no—
1016C2×D3—22no—
1017C2×D3—22no—
1018C2×D3—22no—
1019C2×D3—22no—
1020C2×D3—22no—
1021C2×D3—22no—
1022C2×D3—48no—
1023C3×C4—22no—
1024C3×C4—22no—
1025C3×C4—22no—
1026C3×C4—22no—
1027C3×C4—22no—
1028C3×C4—41no—
1029C3×C4—42no—
1030C3×C4—62no—
1031C3×C4—62no—
1032C3×C4—62no—
1033C3×C4—62no—
1034C3×C4—62no—
1035Dic3—22no—
1036Dic3—22no—
1037Dic3—22no—
1038Dic3—22no—
1039Dic3—22no—
1040Dic3—34no—
1041Dic3—62no—
1042Dic3—62no—
1043Dic3—62no—
1044Dic3—62no—
1045Dic3—62no—
1046Dic3—62no—
1047Dic3—62no—
1048Dic3—62no—
1049Dic3—122no—
1050Dic3—121no—
1051Dic3—121no—
1052Dic3—122no—
1053Dic3—121no—
1054C32#352911yescharacteristic, complemented, Sylow
1055C23—32no—
1056C23—32no—
1057C23—32no—
1058C23—122no—
1059C23—122no—
1060C23—122no—
1061C23C22×D3212yes—
1062C23C22×D3211yescharacteristic
1063Q8—361no—
1064Q8—361no—
1065Q8—362no—
1066Q8—361no—
1067Q8—361no—
1068D4—41no—
1069D4—42no—
1070D4—122no—
1071D4—122no—
1072D4—122no—
1073D4—122no—
1074D4—122no—
1075D4—122no—
1076D4—122no—
1077D4—122no—
1078D4—122no—
1079D4—362no—
1080D4—361no—
1081D4—361no—
1082D4—362no—
1083D4—362no—
1084D4—361no—
1085C2×C4—32no—
1086C2×C4—32no—
1087C2×C4—32no—
1088C2×C4—32no—
1089C2×C4—32no—
1090C2×C4—41no—
1091C2×C4—91no—
1092C2×C4—92no—
1093C2×C4—91no—
1094C2×C4—91no—
1095C2×C4—91no—
1096C2×C4—92no—
1097C2×C4—122no—
1098C2×C4—122no—
1099C2×C4—184no—
1100C2×C4—184no—
1101C2×C4—184no—
1102C2×C4—184no—
1103C2×C4—182no—
1104C2×C4—362no—
1105C2×C4—362no—
1106C2×C4—362no—
1107C2×C4—361no—
1108C2×C4C22×D3212yes—
1109C2×C4C22×D3211yescharacteristic
1110C2×C4C22×D3211yescharacteristic
1111C2×C3—21no—
1112C2×C3—21no—
1113C2×C3—21no—
1114C2×C3—42no—
1115C2×C3—42no—
1116C2×C3—42no—
1117C2×C3—42no—
1118C2×C3—82no—
1119C2×C3—122no—
1120C2×C3—122no—
1121C2×C3—122no—
1122C2×C3D3×H(5,𝔽2)12yes—
1123C2×C3#596612yes—
1124C2×C3#596612yes—
1125D3—42no—
1126D3—42no—
1127D3—42no—
1128C22—21no—
1129C22—21no—
1130C22—22no—
1131C22—22no—
1132C22—22no—
1133C22—21no—
1134C22—62no—
1135C22—62no—
1136C22—62no—
1137C22—62no—
1138C22—62no—
1139C22—62no—
1140C22—62no—
1141C22—62no—
1142C22—62no—
1143C22—128no—
1144C22C23×D3211yescharacteristic
1145C4—21no—
1146C4—21no—
1147C4—22no—
1148C4—62no—
1149C4—62no—
1150C4—62no—
1151C4—62no—
1152C4—62no—
1153C4—92no—
1154C4—181no—
1155C4—182no—
1156C4—181no—
1157C4—182no—
1158C4—181no—
1159C3—21no—
1160C3#8707012yescomplemented
1161C2—42no—
1162C2—41no—
1163C2—122no—
1164C2—122no—
1165C2—122no—
1166C2#1059667911yescharacteristic
1167C2#1059667911yescharacteristic
1168C2#1059669211yescharacteristic
subgroupG/H
center, FrattiniC22C23×D32
commutator, socle, cosocleC22×C32C25
FittingC32×#121C22
hypercenter#121D32
hypocenterC32#3529
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C22 ◁ #121

Complements

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

NH ≅ G/Ntype
1. #10596071C2semidirect
2. C3×#5620C2semidirect
3. #10595260C2semidirect
4. #10595259C2semidirect
5. #10595256C2semidirect
6. #10595213C2semidirect
7. #10595133C2semidirect
8. #10595130C2semidirect
9. #10595130C2semidirect
10. #10594975C2semidirect
11. #10594963C2semidirect
12. #10594929C2semidirect
13. #10594507C2semidirect
14. #10594497C2semidirect
15. #10594435C2semidirect
16. #10594234C2semidirect
17. #10594169C2semidirect
18. #10594112C2semidirect
19. #10594082C2semidirect
23. C2×#3805C22semidirect
24. C22×D3×Dic3C22semidirect
27. #64144C22semidirect
29. D4×C3⋊Dic3C22semidirect
30. #64133C22semidirect
31. C2×C4×C3⋊Dic3C22semidirect
32. #64099C22semidirect
33. #64096C22semidirect
34. #64088C22semidirect
35. #64086C22semidirect
39. C3×#938C22semidirect
41. C3×#937C22semidirect
42. C3×#930C22semidirect
43. C3×#929C22semidirect
44. C3×#898C22semidirect
45. C3×#894C22semidirect
48. C3×#882C22semidirect
49. C3×#879C22semidirect
50. #63982C22semidirect
52. #63980C22semidirect
55. #63976C22semidirect
57. #67⋊Dic3C22semidirect
58. #67⋊Dic3C22semidirect
61. #63970C22semidirect
62. #63970C22semidirect
64. #63969C22semidirect
65. #63969C22semidirect
66. #63964C22semidirect
67. #63964C22semidirect
68. #63961C22semidirect
71. #63959C22semidirect
72. #63919C22semidirect
73. #63918C22semidirect
76. #63915C22semidirect
79. #63908C22semidirect
80. #63905C22semidirect
83. #63902C22semidirect
84. #63899C22semidirect
85. #63899C22semidirect
86. #63898C22semidirect
87. #63898C22semidirect
88. #63896C22semidirect
89. #63893C22semidirect
90. #63893C22semidirect
92. #63891C22semidirect
96. #63884C22semidirect
97. #63878C22semidirect
98. #63878C22semidirect
99. C4×D3×Dic3C22semidirect
100. #63870C22semidirect
101. #63862C22semidirect
102. #63859C22semidirect
103. #63859C22semidirect
104. #63851C22semidirect
105. #63847C22semidirect
106. #63846C22semidirect
107. #63838C22semidirect
126. #5620D3semidirect
276. #938C2×D3semidirect
281. #937C2×D3semidirect
306. #930C2×D3semidirect
309. #929C2×D3semidirect
319. #898C2×D3semidirect
327. #894C2×D3semidirect
365. #882C2×D3semidirect
380. #879C2×D3semidirect
1054. C32#3529semidirect
1160. C3#87070semidirect

Maximal subgroups

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

subgroupindex
#105960712
C3×#56202
#105952602
#105952592
#105952562
#105952132
#105951332
#105951302
#105949752
#105949632
#105949292
#105945072
#105944972
#105944352
#105942342
#105941692
#105941122
#105940822
#870703