Finite Group Databasebeta

← #11910394

Subgroups — #11910394

Order 1152.

2281 conjugacy classes of subgroups.

The subgroup lattice has 1186 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10596057C211yesmaximal, characteristic, complemented
2C3×#5595C212yesmaximal, complemented
3#10595529C211yesmaximal, characteristic, complemented
4#10595505C211yesmaximal, characteristic, complemented
5#10595501C212yesmaximal, complemented
6#10595313C212yesmaximal, complemented
7#10595306C211yesmaximal, characteristic, complemented
8#10595263C212yesmaximal, complemented
9#10595260C212yesmaximal, complemented
10#10595202C212yesmaximal, complemented
11#10595165C211yesmaximal, characteristic, complemented
12#10595133C212yesmaximal, complemented
13#10594310C211yesmaximal, characteristic, complemented
14#10594267C212yesmaximal, complemented
15#10594239C212yesmaximal, complemented
16#10594130C212yesmaximal, complemented
17#10594112C212yesmaximal, complemented
18#10594044C212yesmaximal, complemented
19#10594036C211yesmaximal, characteristic, complemented
20#87070—32nomaximal
21C23×C3⋊Dic3C2211yescharacteristic, complemented
22C2×#3830C2211yescharacteristic
23C2×#3805C2212yes—
24C2×#3805C2211yescharacteristic, complemented
25C2×C4×D32C2211yescharacteristic, complemented
26C32×#120C2211yescharacteristic, complemented
27#64162C2211yescharacteristic
28#64148C2212yes—
29#64144C2211yescharacteristic, complemented
30D4×C3⋊Dic3C2212yescomplemented
31#64095C2211yescharacteristic
32#64090C2212yes—
33#64087C2212yescomplemented
34#64086C2211yescharacteristic, complemented
35C3×#953C2212yes—
36C3×#953C2212yescomplemented
37C3×#940C2212yes—
38C3×#939C2212yes—
39C3×#939C2212yescomplemented
40C3×#938C2212yes—
41C3×#938C2212yescomplemented
42C3×#935C2212yescomplemented
43C3×#884C2212yes—
44C3×#884C2212yes—
45C3×#883C2212yes—
46C3×#883C2212yescomplemented
47C3×#879C2212yescomplemented
48C3×#879C2212yescomplemented
49#63983C2211yescharacteristic
50#63983C2212yes—
51#63983C2211yescharacteristic, complemented
52#63982C2212yescomplemented
53#63982C2212yescomplemented
54#63980C2212yes—
55#63980C2212yes—
56#63979C2211yescharacteristic
57#63978C2212yescomplemented
58#63975C2211yescharacteristic
59#63975C2211yescharacteristic, complemented
60#67⋊Dic3C2212yes—
61#67⋊Dic3C2212yes—
62#67⋊Dic3C2212yescomplemented
63#67⋊Dic3C2212yescomplemented
64#67⋊Dic3C2212yescomplemented
65#63971C2212yes—
66#63970C2212yescomplemented
67#63970C2212yescomplemented
68#63969C2212yescomplemented
69#63964C2212yescomplemented
70#63962C2212yes—
71#63962C2212yescomplemented
72#63961C2212yescomplemented
73#63959C2212yes—
74#63959C2212yes—
75#63959C2212yes—
76#63959C2212yescomplemented
77#63958C2212yes—
78#63957C2212yescomplemented
79#63956C2212yescomplemented
80C2×Dic32C2211yescharacteristic, complemented
81#63953C2212yes—
82#63953C2211yescharacteristic
83#63922C2212yescomplemented
84#63918C2212yescomplemented
85#63913C2211yescharacteristic, complemented
86#63908C2212yescomplemented
87#63905C2212yescomplemented
88#63899C2212yescomplemented
89#63898C2212yescomplemented
90#63895C2212yescomplemented
91#63884C2212yescomplemented
92#63881C2212yescomplemented
93#63878C2212yescomplemented
94C4×D3×Dic3C2212yescomplemented
95#63868C2212yescomplemented
96#63861C2212yescomplemented
97#63859C2212yescomplemented
98#63857C2212yescomplemented
99#63851C2212yescomplemented
100#63851C2212yescomplemented
101#63850C2212yescomplemented
102#63849C2211yescharacteristic, complemented
103#63847C2212yescomplemented
104#63846C2212yescomplemented
105#63845C2212yescomplemented
106#63840C2211yescharacteristic, complemented
107#63838C2212yescomplemented
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#5620—32no—
127#5606—32no—
128#5606—32no—
129#5600—32no—
130#5600—32no—
131#5596—32no—
132#5596—32no—
133#5595—32no—
134#5595D312yescomplemented
135#5594—32no—
136#5586—32no—
137#5586—32no—
138#5586—32no—
139#5586—61no—
140C24×C32C2311yescharacteristic
141C22×D32C2311yescharacteristic
142C2×C32×D4C2312yes—
143C2×C32×D4C2311yescharacteristic
144C2×#638C2312yes—
145C2×#638C2311yescharacteristic
146C2×#638C2311yescharacteristic
147C22×C3⋊Dic3—42no—
148C22×C3⋊Dic3C2312yes—
149C22×C3⋊Dic3C2311yescharacteristic
150C22×C3⋊Dic3C2311yescharacteristic
151C22×C3⋊Dic3C2312yes—
152C22×C3⋊Dic3C2311yescharacteristic
153#3830—42no—
154C2×C4×C3⋊D3C2311yescharacteristic
155C2×#634C2311yescharacteristic
156C2×C3×#67C2312yes—
157C2×C3×#67C2312yes—
158C2×C3×#67C2312yes—
159C2×C3×#67C2312yes—
160C2×C3×#67C2312yes—
161C2×C3×#67C2312yes—
162C2×C3×#67C2312yes—
163C2×C3×#67C2312yes—
164C22×C3×Dic3C2312yes—
165C2×C3×D12C2312yes—
166C2×C3×C4×D3C2312yes—
167C2×C3×C4×D3C2312yes—
168C2×#627C2312yes—
169C2×#627C2311yescharacteristic
170C2×#627C2312yes—
171C2×#626C2312yes—
172C2×#625C2312yes—
173C2×#625C2311yescharacteristic
174C2×#624C2311yescharacteristic
175#3805—44no—
176#3805—42no—
177C2×D3×Dic3C2312yes—
178C2×D3×Dic3C2312yes—
179C2×D3×Dic3C2312yes—
180C4×D32—42no—
181C32×C22⋊C4C2311yescharacteristic
182C32×C22⋊C4C2312yes—
183#3757C2311yescharacteristic
184#3757C2312yes—
185#3757C2312yes—
186#3752C2312yes—
187C4⋊(C3⋊Dic3)C2312yes—
188#3750C2312yes—
189#3750C2312yes—
190C4×C3⋊Dic3C2312yes—
191C3×#217C2312yes—
192C3×#217C2312yes—
193C3×#217C2312yes—
194C3×#217C2312yes—
195C3×#217C2312yes—
196C3×#217C2312yes—
197C3×#217C2312yes—
198C3×(C2×D3)⋊C4C2312yes—
199C3×(C2×D3)⋊C4C2312yes—
200C3×C4⋊Dic3C2312yes—
201C3×C4⋊Dic3C2312yes—
202C3×Dic3⋊C4C2312yes—
203C3×Dic3⋊C4C2312yes—
204C3×Dic3⋊C4C2312yes—
205C3×Dic3⋊C4C2312yes—
206C3×C4×Dic3C2312yes—
207#3724C2312yes—
208#3724C2312yes—
209#3724C2312yes—
210Dic3⋊Dic3C2312yes—
211Dic3⋊Dic3C2312yes—
212Dic3⋊Dic3C2312yes—
213Dic3⋊Dic3C2312yes—
214Dic3⋊Dic3C2312yes—
215Dic3⋊Dic3C2312yes—
216#3722C2311yescharacteristic
217#3722C2311yescharacteristic
218#3722C2312yes—
219(C2×D3)⋊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—
227Dic32C2312yes—
228Dic32C2312yes—
229Dic32C2311yescharacteristic
230Dic32C2311yescharacteristic
231Dic32C2312yes—
232#3529—91noSylow
233C23×Dic3—32no—
234C23×Dic3—61no—
235C2×#237—32no—
236C2×#237—32no—
237C2×#237—32no—
238C2×#237—32no—
239C2×#237—61no—
240C22×C4×D3—32no—
241C3×#127—32no—
242C3×#126—32no—
243C3×#126—32no—
244C3×#123—32no—
245C3×#123—32no—
246C3×#123—32no—
247C3×#121—32no—
248C3×#121—32no—
249C3×#121—32no—
250C3×#121—32no—
251C3×#121—32no—
252C3×#121—32no—
253C3×#120—21no—
254C3×#120—32no—
255C3×#120—32no—
256C3×#120C2×D312yescomplemented
257#953—32no—
258#953—61no—
259#953C2×D312yes—
260#953C2×D312yescomplemented
261#940—32no—
262#940C2×D312yes—
263#939—32no—
264#939—32no—
265#939—32no—
266#939—32no—
267#939—32no—
268#939—32no—
269#939—32no—
270#939—32no—
271#939—32no—
272#939—32no—
273#939—62no—
274#939C2×D312yes—
275#939C2×D312yescomplemented
276#938—32no—
277#938—32no—
278#938—32no—
279#938—32no—
280#938C2×D312yes—
281#938C2×D312yescomplemented
282#937—32no—
283#937—32no—
284#937—32no—
285#937—32no—
286#937—32no—
287#936—32no—
288#936—32no—
289#936—32no—
290#936—32no—
291#935—32no—
292#935—32no—
293#935—32no—
294#935—32no—
295#935—32no—
296#935—32no—
297#935—61no—
298#935C2×D312yescomplemented
299D4×Dic3—32no—
300D4×Dic3—32no—
301D4×Dic3—32no—
302D4×Dic3—32no—
303D4×Dic3—32no—
304D4×Dic3—32no—
305D4×Dic3—32no—
306D4×Dic3—32no—
307D4×Dic3—62no—
308#930—32no—
309#930—32no—
310#929—32no—
311#929—32no—
312#929—32no—
313#924—32no—
314#924—32no—
315#924—32no—
316#924—32no—
317C2×C4×Dic3—32no—
318C2×C4×Dic3—32no—
319#898—32no—
320#898—32no—
321#897—32no—
322#897—32no—
323#896—32no—
324#896—32no—
325#896—32no—
326#896—32no—
327#894—32no—
328#894—32no—
329#893—32no—
330#893—32no—
331#892—32no—
332#892—32no—
333#890—32no—
334#890—32no—
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#886—32no—
344#886—32no—
345#886—32no—
346#886—61no—
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#884C2×D312yes—
358#884C2×D312yes—
359#883—32no—
360#883—32no—
361#883—32no—
362#883—32no—
363#883C2×D312yes—
364#883C2×D312yescomplemented
365#882—32no—
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#67⋊C4—62no—
375#879—32no—
376#879—32no—
377#879—32no—
378#879—32no—
379#879C2×D312yescomplemented
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#878—62no—
390#877—32no—
391#877—32no—
392#877—32no—
393#877—32no—
394#877—61no—
395#876—32no—
396#876—32no—
397C42×D3—32no—
398#869—32no—
399C23×C32—42no—
400C23×C32—41no—
401C23×C32C2411yescharacteristic
402C23×C32C2412yes—
403C23×C32C2411yescharacteristic
404C22×C3⋊D3C2411yescharacteristic
405C22×C3×D3C2412yes—
406C22×C3×D3C2412yes—
407C2×D32—42no—
408C2×D32—41no—
409C32×D4—41no—
410C32×D4—42no—
411C2×C32×C4C2412yes—
412C2×C32×C4C2411yescharacteristic
413#638—41no—
414#638—41no—
415#638—42no—
416C2×C3⋊Dic3—22no—
417C2×C3⋊Dic3—22no—
418C2×C3⋊Dic3—24no—
419C2×C3⋊Dic3—42no—
420C2×C3⋊Dic3—41no—
421C2×C3⋊Dic3C2411yescharacteristic
422C2×C3⋊Dic3C2412yes—
423C2×C3⋊Dic3C2411yescharacteristic
424C2×C3⋊Dic3C2412yes—
425C2×C3⋊Dic3C2411yescharacteristic
426C4×C3⋊D3—22no—
427#634—41no—
428C3×#67—42no—
429C3×#67—42no—
430C3×#67—42no—
431C3×#67—42no—
432C3×#67—42no—
433C3×#67—42no—
434C3×#67—42no—
435C3×#67—42no—
436C2×C3×Dic3—42no—
437C2×C3×Dic3C2412yes—
438C2×C3×Dic3C2412yes—
439C2×C3×Dic3C2412yes—
440C2×C3×Dic3C2412yes—
441C2×C3×Dic3C2412yes—
442C2×C3×Dic3C2412yes—
443C3×D12—42no—
444C3×C4×D3—42no—
445C3×C4×D3—42no—
446#627—42no—
447#627—41no—
448#627—42no—
449#626—42no—
450#625—41no—
451#625—42no—
452#624—41no—
453D3×Dic3—24no—
454D3×Dic3—24no—
455D3×Dic3—42no—
456#563—92no—
457#563—91no—
458#562—92no—
459#562—92no—
460#562—92no—
461H(3,𝔽4)—91no—
462#560—32no—
463#560—91no—
464#560—91no—
465#560—92no—
466#532—91no—
467#532—92no—
468#529—92no—
469#529—92no—
470#529—92no—
471#525—92no—
472#525—91no—
473#525—92no—
474#525—91no—
475C24×C3—21no—
476C24×C3C22×D312yes—
477C23×D3—32no—
478C2×C3×D4—22no—
479C2×C3×D4—21no—
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×D4—32no—
487C2×C3×D4—32no—
488C2×C3×D4—32no—
489C2×C3×D4C22×D312yes—
490C2×C3×D4C22×D312yes—
491C2×C3×D4C22×D312yes—
492C22×C3×C4—32no—
493C22×C3×C4—32no—
494C22×C3×C4—32no—
495C2×#67—32no—
496C2×#67—32no—
497C2×#67—32no—
498C2×#67—32no—
499C2×#67—32no—
500C2×#67—32no—
501C2×#67—32no—
502C2×#67—32no—
503C2×#67—62no—
504C2×#67—61no—
505C2×#67—61no—
506C2×#67C22×D312yes—
507C2×#67C22×D312yes—
508C2×#67C22×D312yes—
509C2×#67C22×D312yes—
510C2×#67C22×D312yes—
511C2×#67C22×D312yes—
512C2×#67C22×D312yes—
513C2×#67C22×D312yes—
514C22×Dic3—32no—
515C22×Dic3—32no—
516C22×Dic3—32no—
517C22×Dic3—32no—
518C22×Dic3—32no—
519C22×Dic3—32no—
520C22×Dic3—32no—
521C22×Dic3—32no—
522C22×Dic3—32no—
523C22×Dic3—32no—
524C22×Dic3—61no—
525C22×Dic3—62no—
526C22×Dic3—62no—
527C22×Dic3—61no—
528C22×Dic3—61no—
529C22×Dic3—124no—
530C22×Dic3—124no—
531C22×Dic3C22×D312yes—
532#237—124no—
533#237—124no—
534#237—124no—
535#237—124no—
536#237—124no—
537C2×D12—32no—
538C2×D12C22×D312yes—
539C2×C4×D3—32no—
540C2×C4×D3—32no—
541C2×C4×D3—32no—
542C2×C4×D3—32no—
543C2×C4×D3—32no—
544C2×C4×D3—61no—
545C2×C4×D3—124no—
546C2×C4×D3C22×D312yes—
547C2×C4×D3C22×D312yes—
548C2×Dic6—32no—
549C2×Dic6—32no—
550C2×Dic6—32no—
551C2×Dic6—32no—
552C2×Dic6—32no—
553C2×Dic6—32no—
554C2×Dic6—61no—
555C3×C4⋊C4—32no—
556C3×C4⋊C4—32no—
557C3×C4⋊C4—32no—
558C3×C4⋊C4—32no—
559C3×C4⋊C4—32no—
560C3×C4⋊C4—32no—
561C3×C22⋊C4—21no—
562C3×C22⋊C4—22no—
563C3×C22⋊C4—32no—
564C3×C22⋊C4—32no—
565C3×C22⋊C4—32no—
566C3×C22⋊C4—32no—
567C3×C22⋊C4—32no—
568C3×C22⋊C4—32no—
569C3×C22⋊C4—32no—
570C3×C22⋊C4—32no—
571C3×C22⋊C4—32no—
572C3×C22⋊C4C22×D312yes—
573C3×C22⋊C4C22×D312yes—
574C3×C22⋊C4C22×D312yes—
575C3×C42—32no—
576#217—32no—
577#217—32no—
578#217—32no—
579#217—32no—
580#217—32no—
581#217—32no—
582#217—32no—
583#217—32no—
584#217—32no—
585#217—32no—
586#217—32no—
587#217—32no—
588#217—32no—
589#217—61no—
590#217—62no—
591#217—62no—
592#217C22×D312yes—
593#217C22×D312yes—
594#217C22×D312yes—
595#217C22×D312yes—
596#217C22×D312yes—
597#217C22×D312yes—
598#217C22×D312yes—
599(C2×D3)⋊C4—32no—
600(C2×D3)⋊C4—32no—
601(C2×D3)⋊C4—32no—
602(C2×D3)⋊C4—32no—
603(C2×D3)⋊C4—32no—
604(C2×D3)⋊C4—32no—
605(C2×D3)⋊C4—32no—
606(C2×D3)⋊C4—32no—
607(C2×D3)⋊C4—32no—
608(C2×D3)⋊C4—32no—
609(C2×D3)⋊C4—32no—
610(C2×D3)⋊C4—32no—
611(C2×D3)⋊C4—32no—
612(C2×D3)⋊C4—32no—
613(C2×D3)⋊C4—62no—
614(C2×D3)⋊C4C22×D312yes—
615(C2×D3)⋊C4C22×D312yes—
616C4⋊Dic3—32no—
617C4⋊Dic3—32no—
618C4⋊Dic3—32no—
619C4⋊Dic3—32no—
620C4⋊Dic3—32no—
621C4⋊Dic3—32no—
622C4⋊Dic3—32no—
623C4⋊Dic3—32no—
624C4⋊Dic3—62no—
625C4⋊Dic3C22×D312yes—
626C4⋊Dic3C22×D312yes—
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—32no—
636Dic3⋊C4—32no—
637Dic3⋊C4—32no—
638Dic3⋊C4—32no—
639Dic3⋊C4—32no—
640Dic3⋊C4—32no—
641Dic3⋊C4—32no—
642Dic3⋊C4—32no—
643Dic3⋊C4—62no—
644Dic3⋊C4—62no—
645Dic3⋊C4C22×D312yes—
646Dic3⋊C4C22×D312yes—
647Dic3⋊C4C22×D312yes—
648Dic3⋊C4C22×D312yes—
649C4×Dic3—32no—
650C4×Dic3—32no—
651C4×Dic3—32no—
652C4×Dic3—32no—
653C4×Dic3—32no—
654C4×Dic3—32no—
655C4×Dic3—32no—
656C4×Dic3—32no—
657C4×Dic3—32no—
658C4×Dic3—32no—
659C4×Dic3—62no—
660C4×Dic3C22×D312yes—
661C22×C32—21no—
662C22×C32—22no—
663C22×C32—22no—
664C22×C32—21no—
665C22×C32—22no—
666C22×C32—22no—
667C22×C32—22no—
668C22×C32—44no—
669C22×C32C2511yescharacteristic
670C2×C3⋊D3—21no—
671C2×C3⋊D3—22no—
672C2×C3×D3—22no—
673C2×C3×D3—22no—
674C2×C3×D3—22no—
675C2×C3×D3—22no—
676C2×C3×D3—22no—
677C2×C3×D3—22no—
678D32—44no—
679C32×C4—21no—
680C32×C4—22no—
681C3⋊Dic3—21no—
682C3⋊Dic3—21no—
683C3⋊Dic3—22no—
684C3⋊Dic3—22no—
685C3⋊Dic3H(5,𝔽2)12yes—
686C3×Dic3—22no—
687C3×Dic3—22no—
688C3×Dic3—22no—
689C3×Dic3—22no—
690C3×Dic3—22no—
691C3×Dic3—22no—
692C2×#41—92no—
693C2×#41—91no—
694C2×#41—91no—
695C23×C4—91no—
696C23×C4—91no—
697C4⋊Q8—92no—
698C4⋊Q8—91no—
699#127—32no—
700#127—91no—
701#126—32no—
702#126—32no—
703#126—92no—
704#126—92no—
705#126—92no—
706#126—92no—
707#125—92no—
708#125—92no—
709#125—92no—
710#124—92no—
711#124—91no—
712#124—91no—
713#124—92no—
714#124—92no—
715#124—92no—
716#124—92no—
717#123—32no—
718#123—32no—
719#123—32no—
720#123—91no—
721#123—91no—
722#123—92no—
723#123—92no—
724#123—92no—
725#123—92no—
726#123—92no—
727#123—92no—
728#123—92no—
729#123—91no—
730#123—91no—
731C22⋊Q8—92no—
732C22⋊Q8—92no—
733C22⋊Q8—92no—
734C22⋊Q8—92no—
735C22⋊Q8—92no—
736C22⋊Q8—92no—
737C22⋊Q8—92no—
738C22⋊Q8—92no—
739C22⋊Q8—92no—
740#121—32no—
741#121—32no—
742#121—32no—
743#121—32no—
744#121—32no—
745#121—32no—
746#121—92no—
747#121—92no—
748#121—92no—
749#121—92no—
750#121—92no—
751#121—92no—
752#121—92no—
753#121—92no—
754#121—92no—
755#120—32no—
756#120—32no—
757#120—92no—
758#120—91no—
759#120—91no—
760#120—92no—
761#120—91no—
762#120D3211yescharacteristic, complemented
763C4×Q8—92no—
764C4×D4—92no—
765C4×D4—92no—
766C4×D4—92no—
767C4×D4—92no—
768C4×D4—92no—
769C4×D4—92no—
770C4×D4—92no—
771C4×D4—92no—
772C4×D4—92no—
773#117—92no—
774#117—92no—
775#117—91no—
776#117—91no—
777C2×C42—92no—
778C2×C42—91no—
779C23×C3—21no—
780C23×C3—22no—
781C23×C3—21no—
782C23×C3—32no—
783C23×C3—32no—
784C23×C3—42no—
785C23×C3—42no—
786C23×C3—42no—
787C23×C3—42no—
788C23×C3—44no—
789C23×C3C23×D312yes—
790C23×C3C23×D312yes—
791C23×C3C23×D312yes—
792C23×C3C23×D312yes—
793C22×D3—32no—
794C22×D3—61no—
795C22×D3—122no—
796C22×D3—122no—
797C22×D3—122no—
798C22×D3C23×D312yes—
799C22×D3C23×D312yes—
800C3×D4—42no—
801C3×D4—42no—
802C3×D4—42no—
803C3×D4—42no—
804C3×D4—44no—
805C3×D4—122no—
806C3×D4—122no—
807C3×D4—122no—
808C3×D4—122no—
809C3×D4—122no—
810C3×D4—122no—
811C3×D4—122no—
812C3×D4—122no—
813C3×D4—122no—
814C2×C3×C4—22no—
815C2×C3×C4—21no—
816C2×C3×C4—32no—
817C2×C3×C4—32no—
818C2×C3×C4—32no—
819C2×C3×C4—32no—
820C2×C3×C4—32no—
821C2×C3×C4—32no—
822C2×C3×C4—122no—
823C2×C3×C4—122no—
824C2×C3×C4—122no—
825C2×C3×C4C23×D312yes—
826C2×C3×C4C23×D312yes—
827C2×C3×C4C23×D312yes—
828#67—42no—
829#67—42no—
830#67—42no—
831#67—42no—
832#67—42no—
833#67—42no—
834#67—42no—
835#67—42no—
836#67—122no—
837#67—122no—
838#67—122no—
839#67—122no—
840#67—122no—
841#67—122no—
842#67—122no—
843#67—122no—
844#67—122no—
845#67—122no—
846#67—124no—
847C2×Dic3—32no—
848C2×Dic3—32no—
849C2×Dic3—32no—
850C2×Dic3—32no—
851C2×Dic3—32no—
852C2×Dic3—32no—
853C2×Dic3—32no—
854C2×Dic3—42no—
855C2×Dic3—61no—
856C2×Dic3—61no—
857C2×Dic3—62no—
858C2×Dic3—62no—
859C2×Dic3—61no—
860C2×Dic3—64no—
861C2×Dic3—64no—
862C2×Dic3—64no—
863C2×Dic3—64no—
864C2×Dic3—64no—
865C2×Dic3—64no—
866C2×Dic3—64no—
867C2×Dic3—122no—
868C2×Dic3—124no—
869C2×Dic3—122no—
870C2×Dic3—122no—
871C2×Dic3—122no—
872C2×Dic3—122no—
873C2×Dic3—124no—
874C2×Dic3—122no—
875C2×Dic3C23×D312yes—
876C2×Dic3C23×D312yes—
877C2×Dic3C23×D312yes—
878C2×Dic3C23×D312yes—
879C2×Dic3C23×D312yes—
880C2×Dic3C23×D312yes—
881D12—42no—
882D12—122no—
883C4×D3—42no—
884C4×D3—42no—
885C4×D3—64no—
886C4×D3—64no—
887C4×D3—64no—
888C4×D3—122no—
889C4×D3—122no—
890C4×D3—122no—
891Dic6—122no—
892Dic6—122no—
893Dic6—122no—
894Dic6—122no—
895Dic6—122no—
896Dic6—122no—
897Dic6—122no—
898C2×C32—41no—
899C2×C32—42no—
900C2×C32—41no—
901C2×C32C2×H(5,𝔽2)11yescharacteristic
902C2×C32#58512yes—
903C3⋊D3—41no—
904C3×D3—42no—
905C3×D3—42no—
906C24—91no—
907C24C2×D3211yescharacteristic
908#41—362no—
909#41—364no—
910#41—362no—
911C2×Q8—92no—
912C2×Q8—92no—
913C2×Q8—91no—
914C2×Q8—91no—
915C2×D4—32no—
916C2×D4—32no—
917C2×D4—32no—
918C2×D4—32no—
919C2×D4—32no—
920C2×D4—32no—
921C2×D4—32no—
922C2×D4—32no—
923C2×D4—32no—
924C2×D4—92no—
925C2×D4—92no—
926C2×D4—91no—
927C2×D4—92no—
928C2×D4—91no—
929C2×D4—91no—
930C2×D4C2×D3212yes—
931C2×D4C2×D3211yescharacteristic
932C22×C4—32no—
933C22×C4—32no—
934C22×C4—32no—
935C22×C4—91no—
936C22×C4—92no—
937C22×C4—92no—
938C22×C4—92no—
939C22×C4—91no—
940C22×C4—91no—
941C22×C4—92no—
942C22×C4—91no—
943C22×C4—92no—
944C22×C4—91no—
945C22×C4—362no—
946C22×C4—362no—
947C4⋊C4—32no—
948C4⋊C4—32no—
949C4⋊C4—32no—
950C4⋊C4—32no—
951C4⋊C4—32no—
952C4⋊C4—32no—
953C4⋊C4—92no—
954C4⋊C4—92no—
955C4⋊C4—92no—
956C4⋊C4—92no—
957C4⋊C4—92no—
958C4⋊C4—92no—
959C4⋊C4—92no—
960C4⋊C4—92no—
961C4⋊C4—92no—
962C4⋊C4—92no—
963C4⋊C4—92no—
964C4⋊C4—92no—
965C22⋊C4—32no—
966C22⋊C4—32no—
967C22⋊C4—32no—
968C22⋊C4—32no—
969C22⋊C4—32no—
970C22⋊C4—32no—
971C22⋊C4—32no—
972C22⋊C4—32no—
973C22⋊C4—32no—
974C22⋊C4—91no—
975C22⋊C4—91no—
976C22⋊C4—92no—
977C22⋊C4—92no—
978C22⋊C4—92no—
979C22⋊C4—92no—
980C22⋊C4—92no—
981C22⋊C4—92no—
982C22⋊C4—92no—
983C22⋊C4—92no—
984C22⋊C4—92no—
985C22⋊C4—91no—
986C22⋊C4—92no—
987C22⋊C4—92no—
988C22⋊C4—92no—
989C22⋊C4C2×D3211yescharacteristic
990C22⋊C4C2×D3212yes—
991C42—32no—
992C42—92no—
993C42—92no—
994C42—92no—
995C42—91no—
996C42—91no—
997C42—92no—
998C22×C3—22no—
999C22×C3—24no—
1000C22×C3—22no—
1001C22×C3—22no—
1002C22×C3—22no—
1003C22×C3—22no—
1004C22×C3—22no—
1005C22×C3—22no—
1006C22×C3—22no—
1007C22×C3—22no—
1008C22×C3—22no—
1009C22×C3—22no—
1010C22×C3—22no—
1011C22×C3—22no—
1012C22×C3—21no—
1013C22×C3—42no—
1014C22×C3—42no—
1015C22×C3—42no—
1016C22×C3—41no—
1017C22×C3—42no—
1018C22×C3—48no—
1019C22×C3—48no—
1020C22×C3—62no—
1021C22×C3—62no—
1022C22×C3—62no—
1023C22×C3—62no—
1024C22×C3—62no—
1025C22×C3—62no—
1026C22×C3C24×D312yes—
1027C2×D3—22no—
1028C2×D3—22no—
1029C2×D3—22no—
1030C2×D3—22no—
1031C2×D3—22no—
1032C2×D3—22no—
1033C2×D3—62no—
1034C2×D3—62no—
1035C2×D3—62no—
1036C2×D3—121no—
1037C2×D3—122no—
1038C2×D3—128no—
1039C3×C4—22no—
1040C3×C4—22no—
1041C3×C4—22no—
1042C3×C4—41no—
1043C3×C4—42no—
1044C3×C4—62no—
1045C3×C4—62no—
1046C3×C4—62no—
1047C3×C4—62no—
1048C3×C4—62no—
1049C3×C4—62no—
1050Dic3—22no—
1051Dic3—22no—
1052Dic3—22no—
1053Dic3—22no—
1054Dic3—22no—
1055Dic3—22no—
1056Dic3—34no—
1057Dic3—62no—
1058Dic3—62no—
1059Dic3—62no—
1060Dic3—62no—
1061Dic3—62no—
1062Dic3—62no—
1063Dic3—62no—
1064Dic3—62no—
1065Dic3—121no—
1066Dic3—122no—
1067Dic3—122no—
1068C32#352911yescharacteristic, complemented, Sylow
1069C23—32no—
1070C23—32no—
1071C23—41no—
1072C23—42no—
1073C23—91no—
1074C23—361no—
1075C23—362no—
1076C23C22×D3211yescharacteristic
1077C23C22×D3212yes—
1078C23C22×D3211yescharacteristic
1079Q8—361no—
1080Q8—362no—
1081Q8—361no—
1082Q8—362no—
1083D4—41no—
1084D4—42no—
1085D4—122no—
1086D4—122no—
1087D4—122no—
1088D4—122no—
1089D4—122no—
1090D4—122no—
1091D4—122no—
1092D4—122no—
1093D4—122no—
1094D4—362no—
1095D4—361no—
1096D4—361no—
1097D4—362no—
1098D4—362no—
1099D4—361no—
1100C2×C4—32no—
1101C2×C4—32no—
1102C2×C4—32no—
1103C2×C4—32no—
1104C2×C4—32no—
1105C2×C4—32no—
1106C2×C4—91no—
1107C2×C4—92no—
1108C2×C4—91no—
1109C2×C4—91no—
1110C2×C4—92no—
1111C2×C4—122no—
1112C2×C4—122no—
1113C2×C4—122no—
1114C2×C4—182no—
1115C2×C4—184no—
1116C2×C4—184no—
1117C2×C4—182no—
1118C2×C4—184no—
1119C2×C4—182no—
1120C2×C4—361no—
1121C2×C4—362no—
1122C2×C4—362no—
1123C2×C4—361no—
1124C2×C4C22×D3212yes—
1125C2×C4C22×D3211yescharacteristic
1126C2×C3—21no—
1127C2×C3—22no—
1128C2×C3—42no—
1129C2×C3—44no—
1130C2×C3—42no—
1131C2×C3—42no—
1132C2×C3—42no—
1133C2×C3—42no—
1134C2×C3—81no—
1135C2×C3—122no—
1136C2×C3—122no—
1137C2×C3D3×H(5,𝔽2)12yes—
1138C2×C3#596612yes—
1139C2×C3#596612yes—
1140D3—42no—
1141D3—42no—
1142D3—122no—
1143D3—241no—
1144C22—21no—
1145C22—22no—
1146C22—21no—
1147C22—22no—
1148C22—22no—
1149C22—22no—
1150C22—22no—
1151C22—44no—
1152C22—62no—
1153C22—62no—
1154C22—62no—
1155C22—62no—
1156C22—62no—
1157C22—62no—
1158C22—181no—
1159C22—182no—
1160C22—364no—
1161C22C23×D3211yescharacteristic
1162C4—21no—
1163C4—22no—
1164C4—62no—
1165C4—62no—
1166C4—62no—
1167C4—62no—
1168C4—62no—
1169C4—62no—
1170C4—92no—
1171C4—181no—
1172C4—182no—
1173C4—181no—
1174C4—182no—
1175C3—21no—
1176C3#8707012yescomplemented
1177C2—41no—
1178C2—42no—
1179C2—41no—
1180C2—122no—
1181C2—122no—
1182C2—361no—
1183C2#1059667511yescharacteristic
1184C2#1059667912yes—
subgroupG/H
center, FrattiniC22C23×D32
commutator, socle, cosocleC22×C32C25
FittingC32×#120C22
hypercenter#120D32
hypocenterC32#3529
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C22 ◁ #120

Complements

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

NH ≅ G/Ntype
1. #10596057C2semidirect
2. C3×#5595C2semidirect
3. #10595529C2semidirect
4. #10595505C2semidirect
5. #10595501C2semidirect
6. #10595313C2semidirect
7. #10595306C2semidirect
8. #10595263C2semidirect
9. #10595260C2semidirect
10. #10595202C2semidirect
11. #10595165C2semidirect
12. #10595133C2semidirect
13. #10594310C2semidirect
14. #10594267C2semidirect
15. #10594239C2semidirect
16. #10594130C2semidirect
17. #10594112C2semidirect
18. #10594044C2semidirect
19. #10594036C2semidirect
21. C23×C3⋊Dic3C22semidirect
24. C2×#3805C22semidirect
25. C2×C4×D32C22semidirect
26. C32×#120C22semidirect
29. #64144C22semidirect
30. D4×C3⋊Dic3C22semidirect
33. #64087C22semidirect
34. #64086C22semidirect
36. C3×#953C22semidirect
39. C3×#939C22semidirect
41. C3×#938C22semidirect
42. C3×#935C22semidirect
46. C3×#883C22semidirect
47. C3×#879C22semidirect
48. C3×#879C22semidirect
51. #63983C22semidirect
52. #63982C22semidirect
53. #63982C22semidirect
57. #63978C22semidirect
59. #63975C22semidirect
62. #67⋊Dic3C22semidirect
63. #67⋊Dic3C22semidirect
64. #67⋊Dic3C22semidirect
66. #63970C22semidirect
67. #63970C22semidirect
68. #63969C22semidirect
69. #63964C22semidirect
71. #63962C22semidirect
72. #63961C22semidirect
76. #63959C22semidirect
78. #63957C22semidirect
79. #63956C22semidirect
80. C2×Dic32C22semidirect
83. #63922C22semidirect
84. #63918C22semidirect
85. #63913C22semidirect
86. #63908C22semidirect
87. #63905C22semidirect
88. #63899C22semidirect
89. #63898C22semidirect
90. #63895C22semidirect
91. #63884C22semidirect
92. #63881C22semidirect
93. #63878C22semidirect
94. C4×D3×Dic3C22semidirect
95. #63868C22semidirect
96. #63861C22semidirect
97. #63859C22semidirect
98. #63857C22semidirect
99. #63851C22semidirect
100. #63851C22semidirect
101. #63850C22semidirect
102. #63849C22semidirect
103. #63847C22semidirect
104. #63846C22semidirect
105. #63845C22semidirect
106. #63840C22semidirect
107. #63838C22semidirect
134. #5595D3semidirect
256. C3×#120C2×D3semidirect
260. #953C2×D3semidirect
275. #939C2×D3semidirect
281. #938C2×D3semidirect
298. #935C2×D3semidirect
364. #883C2×D3semidirect
379. #879C2×D3semidirect
380. #879C2×D3semidirect
762. #120D32semidirect
1068. C32#3529semidirect
1176. C3#87070semidirect

Maximal subgroups

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

subgroupindex
#105960572
C3×#55952
#105955292
#105955052
#105955012
#105953132
#105953062
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