Finite Group Databasebeta

← #11904346

Subgroups — #11904346

Order 1152.

3965 conjugacy classes of subgroups.

The subgroup lattice has 894 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#64307C211yesmaximal, characteristic, complemented
2C22×#3802C211yesmaximal, characteristic, complemented
3#10595995C211yesmaximal, characteristic, complemented
4C3×#5525C211yesmaximal, characteristic, complemented
5C3×#5521C211yesmaximal, characteristic, complemented
6#10595042C211yesmaximal, characteristic, complemented
7#10595034C211yesmaximal, characteristic, complemented
8#10594630C214yesmaximal, complemented
9#10594621C214yesmaximal, complemented
10#10594290C214yesmaximal, complemented
11D3×#882C214yesmaximal, complemented
12#10594005C214yesmaximal, complemented
13#10594004C214yesmaximal, complemented
14#86330—31nomaximal
15#85867—31nomaximal
16C23×D32C2212yescomplemented
17C2×#3828C2211yescharacteristic, complemented
18C22×C4×C3⋊D3C2211yescharacteristic, complemented
19C2×C3×#235C2211yescharacteristic, complemented
20C22×C3×D12C2211yescharacteristic
21C22×C3×D12C2211yescharacteristic, complemented
22C2×D3×#67C2214yescomplemented
23C22×#625C2212yescomplemented
24#64307—28no—
25C2×#3802—28no—
26C2×#3802C2214yescomplemented
27C2×#3802C2214yescomplemented
28C2×#3802C2212yescomplemented
29C2×D3×D12C2218yescomplemented
30C2×D3×D12C2212yescomplemented
31C2×#3796C2212yescomplemented
32C2×#3795C2212yescomplemented
33C32×#117C2211yescharacteristic, complemented
34#64106C2212yescomplemented
35#64104C2212yescomplemented
36#64095C2212yescomplemented
37#64091C2212yescomplemented
38C4×C4⋊(C3⋊D3)C2214yescomplemented
39C3×#926C2211yescharacteristic, complemented
40C3×#895C2214yescomplemented
41C3×#893C2214yescomplemented
42C3×#882C2214yescomplemented
43C3×D3×C22⋊C4C2214yescomplemented
44C3×#875C2212yescomplemented
45C3×#874C2212yescomplemented
46C3×C4×D12C2214yescomplemented
47#63981C2212yescomplemented
48#63977C2214yescomplemented
49#63962C2212yescomplemented
50#63923C2218yescomplemented
51#63922C2218yescomplemented
52#63922C2218yescomplemented
53D3×(C2×D3)⋊C4C2218yescomplemented
54#63916C2212yescomplemented
55#63916C2214yescomplemented
56#63911C2212yescomplemented
57#63908C2218yescomplemented
58#63906C2218yescomplemented
59C4×#626C2214yescomplemented
60#63891C2218yescomplemented
61#63871C2212yescomplemented
62#63860C2212yescomplemented
63C2×#1009—31no—
64C2×#1004—31no—
65C22×D3×D4—31no—
66C22×D3×D4—31no—
67C3×#535—31no—
68C3×#518—31no—
69#5828—31no—
70#5805—31no—
71#5717—34no—
72#5676—34no—
73#5612—34no—
74#5609—34no—
75#5589—34no—
76D3×#120—34no—
77#5554—34no—
78#5554—34no—
79D4×D12—34no—
80D4×D12—34no—
81#5525—31no—
82#5525D311yescharacteristic, complemented
83#5524—31no—
84#5524—31no—
85#5524—31no—
86#5524—61no—
87#5521D311yescharacteristic, complemented
88#5493—34no—
89C2×#882—34no—
90C23×C3⋊D3C2311yescharacteristic
91C23×C3×D3C2312yes—
92C23×C3×D3C2312yes—
93C22×D32—28no—
94C22×D32—48no—
95C22×D32C2318yes—
96C22×D32C2314yescomplemented
97C22×C32×C4C2311yescharacteristic
98C2×#638C2312yes—
99C22×C3⋊Dic3C2311yescharacteristic
100#3828—24no—
101C2×C4⋊(C3⋊D3)C2314yes—
102C2×C4⋊(C3⋊D3)C2311yescharacteristic, complemented
103C2×C4×C3⋊D3—24no—
104C2×C4×C3⋊D3C2312yes—
105C2×C4×C3⋊D3C2312yes—
106C2×C4×C3⋊D3C2312yescomplemented
107C2×#634C2311yescharacteristic, complemented
108C2×C3×#67C2312yes—
109C3×#235—24no—
110C2×C3×D12—24no—
111C2×C3×D12D418yescomplemented
112C2×C3×D12C2312yes—
113C2×C3×D12C2312yes—
114C2×C3×D12C2312yes—
115C2×C3×D12C2312yes—
116C2×C3×D12C2311yescharacteristic, complemented
117C2×C3×D12C2318yescomplemented
118C2×C3×C4×D3C2312yescomplemented
119C2×C3×C4×D3C2318yescomplemented
120C2×C3×Dic6C2311yescharacteristic, complemented
121D3×#67—216no—
122C2×#626C2314yes—
123C2×#626C2314yescomplemented
124C2×#626C2318yescomplemented
125C2×#625—28no—
126C2×#625C2318yes—
127C2×#625C2314yescomplemented
128C2×D3×Dic3C2314yescomplemented
129#3802—216no—
130#3802—216no—
131#3802—28no—
132D3×D12—28no—
133D3×D12—416no—
134#3796—28no—
135#3795—28no—
136C32×C4⋊C4C2312yescomplemented
137C32×C22⋊C4C2312yes—
138C32×C42C2312yescomplemented
139#3752C2314yes—
140#3752C2314yescomplemented
141C4⋊(C3⋊Dic3)C2314yescomplemented
142C3×#217C2312yes—
143C3×(C2×D3)⋊C4C2318yescomplemented
144C3×(C2×D3)⋊C4C2318yescomplemented
145C3×C4⋊Dic3C2312yescomplemented
146C3×C4×Dic3C2312yescomplemented
147Dic3⋊Dic3C2314yescomplemented
148#3722C2314yes—
149(C2×D3)⋊Dic3C2318yescomplemented
150(C2×D3)⋊Dic3C2314yescomplemented
151#3484—91noSylow
152C24×D3—32no—
153C24×D3—32no—
154C2×C3×#41—31no—
155C22×C3×D4—31no—
156C22×C3×D4—31no—
157C22×#67—32no—
158C22×#67—32no—
159C22×#67—34no—
160#1009—68no—
161C2×#239—32no—
162#1004—68no—
163C2×#237—32no—
164C2×#237—32no—
165C2×D3×D4—34no—
166C2×D3×D4—34no—
167C2×D3×D4—34no—
168C2×D3×D4—34no—
169C2×D3×D4—34no—
170C2×D3×D4—32no—
171C2×D3×D4—32no—
172C2×D3×D4—32no—
173C2×D3×D4—38no—
174C2×D3×D4—68no—
175C2×D3×D4—68no—
176C2×#235—31no—
177C2×#235—31no—
178C2×#235—32no—
179C2×#235—61no—
180C2×#235C2×D311yescharacteristic, complemented
181C22×D12—32no—
182C22×D12—38no—
183C22×D12C2×D311yescharacteristic
184C22×D12C2×D311yescharacteristic, complemented
185C22×C4×D3—31no—
186C22×C4×D3—31no—
187C22×C4×D3—61no—
188C3×#127—32no—
189C3×#124—32no—
190C3×#121—34no—
191C3×#120—34no—
192C3×C4×D4—34no—
193C3×C4×D4—34no—
194C3×#117—21no—
195C3×#117—31no—
196C3×#117C2×D311yescharacteristic, complemented
197C3×#117C2×D311yescharacteristic, complemented
198C2×C3×C22⋊C4—34no—
199#953—34no—
200#946—32no—
201#940—32no—
202#938—38no—
203#938—34no—
204#938—32no—
205#937—32no—
206#937—38no—
207#937—38no—
208#936—32no—
209#935—32no—
210#930—38no—
211#930—38no—
212C4×#67—34no—
213C2×(C2×D3)⋊C4—38no—
214#926C2×D311yescharacteristic, complemented
215#897—32no—
216#897—32no—
217#897—32no—
218#897—62no—
219#895—34no—
220#895—32no—
221#895—32no—
222#895—32no—
223#895—62no—
224#895C2×D314yescomplemented
225#893C2×D314yescomplemented
226#886—32no—
227#886—32no—
228#886—32no—
229#886—38no—
230#886—62no—
231#884—38no—
232#883—38no—
233#882—34no—
234#882—32no—
235#882—38no—
236#882—38no—
237#882—32no—
238#882—32no—
239#882—38no—
240#882—38no—
241#882—62no—
242#882C2×D314yescomplemented
243D3×C22⋊C4—38no—
244D3×C22⋊C4C2×D314yescomplemented
245#875—32no—
246#875C2×D312yescomplemented
247#874—32no—
248#874C2×D312yescomplemented
249C4×D12—34no—
250C4×D12—34no—
251C4×D12—34no—
252C4×D12—64no—
253C4×D12C2×D314yescomplemented
254C23×C32C2411yescharacteristic
255C22×C3⋊D3—22no—
256C22×C3⋊D3—24no—
257C22×C3⋊D3C2412yes—
258C22×C3⋊D3C2412yes—
259C22×C3×D3—24no—
260C22×C3×D3—44no—
261C22×C3×D3—44no—
262C22×C3×D3C2×D418yescomplemented
263C22×C3×D3C2414yes—
264C22×C3×D3C2412yes—
265C22×C3×D3C2414yes—
266C2×D32—216no—
267C2×D32—216no—
268C2×D32—28no—
269C2×D32—48no—
270C2×D32—432no—
271C2×D32—48no—
272C2×C32×C4C2×D414yescomplemented
273C2×C32×C4C2414yes—
274C2×C32×C4C2411yescharacteristic
275C2×C32×C4C2411yescharacteristic
276#638—24no—
277C2×C3⋊Dic3—22no—
278C2×C3⋊Dic3C2412yes—
279C2×C3⋊Dic3C2412yes—
280C4⋊(C3⋊D3)—28no—
281C4⋊(C3⋊D3)—22no—
282C4×C3⋊D3—24no—
283C4×C3⋊D3—24no—
284C4×C3⋊D3—24no—
285#634—22no—
286C3×#67—24no—
287C2×C3×Dic3C2414yes—
288C2×C3×Dic3C2412yes—
289C3×D12—24no—
290C3×D12—24no—
291C3×D12—22no—
292C3×D12—48no—
293C3×D12C2×D418yescomplemented
294C3×D12C2×D418yescomplemented
295C3×C4×D3—24no—
296C3×C4×D3—48no—
297C3×Dic6—22no—
298#626—28no—
299#626—28no—
300#626—48no—
301#625—28no—
302#625—216no—
303D3×Dic3—28no—
304C2×H(5,𝔽2)—91no—
305C23×D4—91no—
306#546—94no—
307#546—94no—
308D42—94no—
309D42—94no—
310#535—31no—
311#535—91no—
312#534—94no—
313#525—91no—
314#525—91no—
315C2×#120—94no—
316#518—31no—
317C24×C3—32no—
318C24×C3—32no—
319C23×D3—31no—
320C23×D3—31no—
321C23×D3—38no—
322C23×D3—38no—
323C23×D3—34no—
324C23×D3—34no—
325C23×D3—61no—
326C23×D3—68no—
327C23×D3—68no—
328C23×D3—128no—
329C23×D3—128no—
330C23×D3C22×D312yes—
331C23×D3C22×D312yes—
332C3×#41—64no—
333C2×C3×Q8—31no—
334C2×C3×D4—32no—
335C2×C3×D4—38no—
336C2×C3×D4—32no—
337C2×C3×D4—32no—
338C2×C3×D4—32no—
339C2×C3×D4—32no—
340C2×C3×D4—31no—
341C2×C3×D4—38no—
342C2×C3×D4—64no—
343C22×C3×C4—21no—
344C22×C3×C4—32no—
345C22×C3×C4—38no—
346C22×C3×C4C22×D311yescharacteristic
347C22×C3×C4C22×D311yescharacteristic
348C2×#67—32no—
349C2×#67—32no—
350C2×#67—34no—
351C2×#67—38no—
352C2×#67—38no—
353C2×#67—34no—
354C2×#67—34no—
355C2×#67—34no—
356C2×#67—38no—
357C2×#67—62no—
358C2×#67—616no—
359C2×#67—68no—
360C2×#67—68no—
361C2×#67C22×D312yes—
362C22×Dic3—31no—
363C22×Dic3—31no—
364C22×Dic3—34no—
365C22×Dic3—61no—
366#239—68no—
367#237—68no—
368#237—68no—
369D3×D4—68no—
370D3×D4—616no—
371D3×D4—616no—
372D3×D4—68no—
373D3×D4—616no—
374D3×D4—616no—
375D3×D4—616no—
376D3×D4—68no—
377D3×D4—1216no—
378#235—24no—
379#235—64no—
380#235—64no—
381#235—68no—
382#235—124no—
383C2×D12—24no—
384C2×D12—34no—
385C2×D12—34no—
386C2×D12—34no—
387C2×D12—34no—
388C2×D12—31no—
389C2×D12—31no—
390C2×D12—38no—
391C2×D12—64no—
392C2×D12—61no—
393C2×D12—68no—
394C2×D12—1216no—
395C2×D12D1218yescomplemented
396C2×D12C22×D312yes—
397C2×D12C22×D312yes—
398C2×D12C22×D312yes—
399C2×D12C22×D312yes—
400C2×D12C22×D311yescharacteristic, complemented
401C2×D12C22×D318yescomplemented
402C2×C4×D3—34no—
403C2×C4×D3—32no—
404C2×C4×D3—32no—
405C2×C4×D3—32no—
406C2×C4×D3—32no—
407C2×C4×D3—32no—
408C2×C4×D3—32no—
409C2×C4×D3—62no—
410C2×C4×D3—62no—
411C2×C4×D3—62no—
412C2×C4×D3—64no—
413C2×C4×D3—64no—
414C2×C4×D3—124no—
415C2×C4×D3C22×D312yescomplemented
416C2×C4×D3C22×D318yescomplemented
417C2×Dic6—31no—
418C2×Dic6—31no—
419C2×Dic6—61no—
420C2×Dic6C22×D311yescharacteristic, complemented
421C3×C4⋊C4—22no—
422C3×C4⋊C4—32no—
423C3×C4⋊C4C22×D312yescomplemented
424C3×C4⋊C4C22×D312yescomplemented
425C3×C22⋊C4—22no—
426C3×C22⋊C4—32no—
427C3×C22⋊C4—38no—
428C3×C22⋊C4—38no—
429C3×C22⋊C4C22×D312yes—
430C3×C22⋊C4C22×D312yes—
431C3×C42—22no—
432C3×C42—32no—
433C3×C42C22×D312yescomplemented
434C3×C42C22×D312yescomplemented
435#217—38no—
436#217—34no—
437#217C22×D312yes—
438(C2×D3)⋊C4—34no—
439(C2×D3)⋊C4—38no—
440(C2×D3)⋊C4—34no—
441(C2×D3)⋊C4—34no—
442(C2×D3)⋊C4—34no—
443(C2×D3)⋊C4—34no—
444(C2×D3)⋊C4—34no—
445(C2×D3)⋊C4—34no—
446(C2×D3)⋊C4—64no—
447(C2×D3)⋊C4—64no—
448(C2×D3)⋊C4C22×D318yescomplemented
449(C2×D3)⋊C4C22×D318yescomplemented
450C4⋊Dic3—34no—
451C4⋊Dic3—34no—
452C4⋊Dic3—34no—
453C4⋊Dic3—64no—
454C4⋊Dic3C22×D312yescomplemented
455Dic3⋊C4—34no—
456C4×Dic3C22×D312yescomplemented
457C22×C32—22no—
458C22×C32C22×D412yes—
459C22×C32C2511yescharacteristic
460C2×C3⋊D3—28no—
461C2×C3⋊D3—22no—
462C2×C3⋊D3—22no—
463C2×C3⋊D3—22no—
464C2×C3⋊D3—24no—
465C2×C3⋊D3H(5,𝔽2)14yescomplemented
466C2×C3×D3—28no—
467C2×C3×D3—22no—
468C2×C3×D3—24no—
469C2×C3×D3—24no—
470C2×C3×D3—28no—
471C2×C3×D3—48no—
472C2×C3×D3—48no—
473C2×C3×D3C22×D418yes—
474D32—432no—
475D32—88no—
476C32×C4—24no—
477C32×C4C22×D412yes—
478C32×C4C22×D412yes—
479C3⋊Dic3—22no—
480C3⋊Dic3—22no—
481C3×Dic3—22no—
482C3×Dic3—24no—
483C25—92no—
484H(5,𝔽2)—188no—
485C2×#41—31no—
486C2×#41—92no—
487C2×#41—92no—
488C2×#41—91no—
489C22×D4—31no—
490C22×D4—31no—
491C22×D4—92no—
492C22×D4—98no—
493C22×D4—92no—
494C22×D4—94no—
495C22×D4—94no—
496C22×D4—94no—
497C22×D4—92no—
498C22×D4—188no—
499C23×C4—91no—
500#127—32no—
501#127—92no—
502#124—32no—
503#124—92no—
504#123—98no—
505#123—92no—
506#123—92no—
507C22⋊Q8—92no—
508C22⋊Q8—92no—
509#121—34no—
510#121—98no—
511#121—92no—
512#121—94no—
513#121—98no—
514#121—92no—
515#120—34no—
516#120—98no—
517#120—92no—
518#120—98no—
519#120—98no—
520#120—94no—
521#120—92no—
522C4×D4—34no—
523C4×D4—34no—
524C4×D4—94no—
525C4×D4—94no—
526#117—31no—
527#117D3211yescharacteristic, complemented
528C2×C22⋊C4—34no—
529C2×C22⋊C4—98no—
530C23×C3—21no—
531C23×C3—34no—
532C23×C3—38no—
533C23×C3—34no—
534C23×C3—32no—
535C23×C3—64no—
536C23×C3—124no—
537C23×C3—124no—
538C23×C3C23×D311yescharacteristic
539C23×C3C23×D311yescharacteristic
540C22×D3—24no—
541C22×D3—32no—
542C22×D3—32no—
543C22×D3—32no—
544C22×D3—32no—
545C22×D3—44no—
546C22×D3—44no—
547C22×D3—62no—
548C22×D3—62no—
549C22×D3—616no—
550C22×D3—616no—
551C22×D3—616no—
552C22×D3—68no—
553C22×D3—64no—
554C22×D3—64no—
555C22×D3—62no—
556C22×D3—62no—
557C22×D3—616no—
558C22×D3—68no—
559C22×D3—124no—
560C22×D3—122no—
561C22×D3—128no—
562C22×D3—128no—
563C22×D3—128no—
564C22×D3—128no—
565C22×D3—1232no—
566C22×D3—1232no—
567C22×D3C2×D1218yescomplemented
568C22×D3C23×D314yes—
569C22×D3C23×D312yes—
570C22×D3C23×D314yes—
571C3×Q8—62no—
572C3×D4—38no—
573C3×D4—38no—
574C3×D4—64no—
575C3×D4—64no—
576C3×D4—64no—
577C3×D4—62no—
578C3×D4—128no—
579C2×C3×C4—21no—
580C2×C3×C4—21no—
581C2×C3×C4—24no—
582C2×C3×C4—24no—
583C2×C3×C4—32no—
584C2×C3×C4—34no—
585C2×C3×C4—64no—
586C2×C3×C4—128no—
587C2×C3×C4C2×D1214yescomplemented
588C2×C3×C4D3×D414yescomplemented
589C2×C3×C4C23×D314yes—
590C2×C3×C4C23×D314yes—
591C2×C3×C4C23×D311yescharacteristic
592C2×C3×C4C23×D311yescharacteristic
593C2×C3×C4C23×D311yescharacteristic
594C2×C3×C4C23×D311yescharacteristic
595#67—24no—
596#67—68no—
597#67—68no—
598#67—616no—
599#67—68no—
600#67—64no—
601#67—64no—
602#67—68no—
603#67—616no—
604#67—124no—
605#67—128no—
606C2×Dic3—32no—
607C2×Dic3—32no—
608C2×Dic3—32no—
609C2×Dic3—32no—
610C2×Dic3—62no—
611C2×Dic3—62no—
612C2×Dic3—68no—
613C2×Dic3—62no—
614C2×Dic3—62no—
615C2×Dic3—122no—
616C2×Dic3C23×D314yes—
617C2×Dic3C23×D312yes—
618D12—24no—
619D12—24no—
620D12—22no—
621D12—48no—
622D12—68no—
623D12—68no—
624D12—68no—
625D12—68no—
626D12—62no—
627D12—62no—
628D12—122no—
629D12—128no—
630D12—128no—
631D12C2×D1218yescomplemented
632D12C2×D1218yescomplemented
633C4×D3—24no—
634C4×D3—48no—
635C4×D3—68no—
636C4×D3—64no—
637C4×D3—64no—
638C4×D3—64no—
639C4×D3—64no—
640C4×D3—64no—
641C4×D3—64no—
642C4×D3—124no—
643C4×D3—124no—
644C4×D3—124no—
645Dic6—22no—
646Dic6—62no—
647Dic6—62no—
648Dic6—122no—
649C2×C32—22no—
650C2×C32C23×D411yescharacteristic
651C2×C32C2×H(5,𝔽2)12yes—
652C3⋊D3—24no—
653C3⋊D3—42no—
654C3×D3—28no—
655C3×D3—44no—
656C3×D3—42no—
657C24—32no—
658C24—32no—
659C24—98no—
660C24—94no—
661C24—91no—
662C24—188no—
663C24—368no—
664#41—64no—
665#41—188no—
666#41—188no—
667#41—184no—
668C2×Q8—31no—
669C2×Q8—91no—
670C2×D4—32no—
671C2×D4—32no—
672C2×D4—32no—
673C2×D4—32no—
674C2×D4—32no—
675C2×D4—31no—
676C2×D4—38no—
677C2×D4—38no—
678C2×D4—64no—
679C2×D4—94no—
680C2×D4—94no—
681C2×D4—98no—
682C2×D4—94no—
683C2×D4—98no—
684C2×D4—92no—
685C2×D4—94no—
686C2×D4—91no—
687C2×D4—188no—
688C2×D4—1816no—
689C2×D4—1816no—
690C2×D4—188no—
691C2×D4—1816no—
692C2×D4—188no—
693C2×D4—3616no—
694C22×C4—32no—
695C22×C4—38no—
696C22×C4—94no—
697C22×C4—91no—
698C22×C4—92no—
699C22×C4—92no—
700C22×C4—92no—
701C22×C4—184no—
702C22×C4C2×D3211yescharacteristic
703C4⋊C4—32no—
704C4⋊C4—94no—
705C4⋊C4—94no—
706C4⋊C4C2×D3212yescomplemented
707C22⋊C4—32no—
708C22⋊C4—38no—
709C22⋊C4—38no—
710C22⋊C4—94no—
711C22⋊C4—98no—
712C22⋊C4—94no—
713C22⋊C4—94no—
714C22⋊C4—94no—
715C22⋊C4C2×D3212yes—
716C42—32no—
717C42C2×D3212yescomplemented
718C22×C3—22no—
719C22×C3—22no—
720C22×C3—22no—
721C22×C3—21no—
722C22×C3—38no—
723C22×C3—42no—
724C22×C3—68no—
725C22×C3—62no—
726C22×C3—64no—
727C22×C3—64no—
728C22×C3—68no—
729C22×C3—128no—
730C22×C3—128no—
731C22×C3C22×D1212yes—
732C22×C3C2×D3×D412yes—
733C22×C3C24×D311yescharacteristic
734C22×C3C24×D311yescharacteristic
735C2×D3—28no—
736C2×D3—22no—
737C2×D3—24no—
738C2×D3—24no—
739C2×D3—28no—
740C2×D3—34no—
741C2×D3—34no—
742C2×D3—48no—
743C2×D3—48no—
744C2×D3—64no—
745C2×D3—68no—
746C2×D3—68no—
747C2×D3—62no—
748C2×D3—62no—
749C2×D3—62no—
750C2×D3—62no—
751C2×D3—62no—
752C2×D3—62no—
753C2×D3—64no—
754C2×D3—64no—
755C2×D3—122no—
756C2×D3—122no—
757C2×D3—128no—
758C2×D3—122no—
759C2×D3—124no—
760C2×D3—1232no—
761C2×D3—1232no—
762C2×D3—248no—
763C2×D3—248no—
764C2×D3C22×D1218yes—
765C3×C4—24no—
766C3×C4—24no—
767C3×C4—22no—
768C3×C4—22no—
769C3×C4—44no—
770C3×C4—62no—
771C3×C4—64no—
772C3×C4C22×D1212yes—
773C3×C4C22×D1212yes—
774C3×C4C2×D3×D412yes—
775C3×C4C2×D3×D412yes—
776Dic3—22no—
777Dic3—24no—
778Dic3—62no—
779Dic3—62no—
780Dic3—62no—
781Dic3—62no—
782Dic3—122no—
783Dic3—122no—
784C32#348411yescharacteristic, complemented, Sylow
785C23—34no—
786C23—38no—
787C23—34no—
788C23—32no—
789C23—64no—
790C23—92no—
791C23—92no—
792C23—124no—
793C23—124no—
794C23—184no—
795C23—1816no—
796C23—188no—
797C23—1816no—
798C23—182no—
799C23—368no—
800C23—368no—
801C23—3632no—
802C23C22×D3211yescharacteristic
803Q8—62no—
804Q8—182no—
805D4—38no—
806D4—38no—
807D4—64no—
808D4—64no—
809D4—64no—
810D4—62no—
811D4—128no—
812D4—188no—
813D4—188no—
814D4—188no—
815D4—1816no—
816D4—188no—
817D4—184no—
818D4—182no—
819D4—368no—
820C2×C4—34no—
821C2×C4—32no—
822C2×C4—64no—
823C2×C4—92no—
824C2×C4—92no—
825C2×C4—128no—
826C2×C4—188no—
827C2×C4—182no—
828C2×C4—184no—
829C2×C4—184no—
830C2×C4—184no—
831C2×C4D3×D1214yescomplemented
832C2×C4C22×D3214yes—
833C2×C4C22×D3211yescharacteristic
834C2×C4C22×D3211yescharacteristic
835C2×C3—22no—
836C2×C3—22no—
837C2×C3—21no—
838C2×C3—22no—
839C2×C3—42no—
840C2×C3—68no—
841C2×C3—124no—
842C2×C3—122no—
843C2×C3C23×D1211yescharacteristic
844C2×C3C22×D3×D411yescharacteristic
845C2×C3D3×H(5,𝔽2)12yes—
846C2×C3D3×H(5,𝔽2)12yes—
847D3—28no—
848D3—44no—
849D3—42no—
850D3—64no—
851D3—64no—
852D3—124no—
853D3—122no—
854D3—122no—
855D3—242no—
856C22—22no—
857C22—38no—
858C22—68no—
859C22—62no—
860C22—64no—
861C22—64no—
862C22—68no—
863C22—94no—
864C22—128no—
865C22—128no—
866C22—188no—
867C22—182no—
868C22—182no—
869C22—182no—
870C22—184no—
871C22—3632no—
872C22—728no—
873C22C2×D3×D1212yes—
874C22C23×D3211yescharacteristic
875C4—24no—
876C4—62no—
877C4—64no—
878C4—182no—
879C4—182no—
880C4C2×D3×D1212yes—
881C4C2×D3×D1212yes—
882C3—21no—
883C3#8586711yescharacteristic, complemented
884C3#8633011yescharacteristic, complemented
885C2—22no—
886C2—68no—
887C2—124no—
888C2—122no—
889C2—184no—
890C2—362no—
891C2C22×D3×D1211yescharacteristic
892C2#1059669212yes—
subgroupG/H
center, FrattiniC22C23×D32
commutator, socle, cosocleC22×C32C25
FittingC32×#117C22
hypercenter#117D32
hypocenterC32#3484
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C22 ◁ #117

Complements

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

NH ≅ G/Ntype
1. C2×#64307C2semidirect
2. C22×#3802C2semidirect
3. #10595995C2semidirect
4. C3×#5525C2semidirect
5. C3×#5521C2semidirect
6. #10595042C2semidirect
7. #10595034C2semidirect
8. #10594630C2semidirect
9. #10594621C2semidirect
10. #10594290C2semidirect
11. D3×#882C2semidirect
12. #10594005C2semidirect
13. #10594004C2semidirect
16. C23×D32C22semidirect
17. C2×#3828C22semidirect
18. C22×C4×C3⋊D3C22semidirect
19. C2×C3×#235C22semidirect
21. C22×C3×D12C22semidirect
22. C2×D3×#67C22semidirect
23. C22×#625C22semidirect
26. C2×#3802C22semidirect
27. C2×#3802C22semidirect
28. C2×#3802C22semidirect
29. C2×D3×D12C22semidirect
30. C2×D3×D12C22semidirect
31. C2×#3796C22semidirect
32. C2×#3795C22semidirect
33. C32×#117C22semidirect
34. #64106C22semidirect
35. #64104C22semidirect
36. #64095C22semidirect
37. #64091C22semidirect
38. C4×C4⋊(C3⋊D3)C22semidirect
39. C3×#926C22semidirect
40. C3×#895C22semidirect
41. C3×#893C22semidirect
42. C3×#882C22semidirect
43. C3×D3×C22⋊C4C22semidirect
44. C3×#875C22semidirect
45. C3×#874C22semidirect
46. C3×C4×D12C22semidirect
47. #63981C22semidirect
48. #63977C22semidirect
49. #63962C22semidirect
50. #63923C22semidirect
51. #63922C22semidirect
52. #63922C22semidirect
53. D3×(C2×D3)⋊C4C22semidirect
54. #63916C22semidirect
55. #63916C22semidirect
56. #63911C22semidirect
57. #63908C22semidirect
58. #63906C22semidirect
59. C4×#626C22semidirect
60. #63891C22semidirect
61. #63871C22semidirect
62. #63860C22semidirect
82. #5525D3semidirect
87. #5521D3semidirect
96. C22×D32C23semidirect
102. C2×C4⋊(C3⋊D3)C23semidirect
106. C2×C4×C3⋊D3C23semidirect
107. C2×#634C23semidirect
111. C2×C3×D12D4semidirect
116. C2×C3×D12C23semidirect
117. C2×C3×D12C23semidirect
118. C2×C3×C4×D3C23semidirect
119. C2×C3×C4×D3C23semidirect
120. C2×C3×Dic6C23semidirect
123. C2×#626C23semidirect
124. C2×#626C23semidirect
127. C2×#625C23semidirect
128. C2×D3×Dic3C23semidirect
136. C32×C4⋊C4C23semidirect
138. C32×C42C23semidirect
140. #3752C23semidirect
141. C4⋊(C3⋊Dic3)C23semidirect
143. C3×(C2×D3)⋊C4C23semidirect
144. C3×(C2×D3)⋊C4C23semidirect
145. C3×C4⋊Dic3C23semidirect
146. C3×C4×Dic3C23semidirect
147. Dic3⋊Dic3C23semidirect
149. (C2×D3)⋊Dic3C23semidirect
150. (C2×D3)⋊Dic3C23semidirect
180. C2×#235C2×D3semidirect
184. C22×D12C2×D3semidirect
196. C3×#117C2×D3semidirect
197. C3×#117C2×D3semidirect
214. #926C2×D3semidirect
224. #895C2×D3semidirect
225. #893C2×D3semidirect
242. #882C2×D3semidirect
244. D3×C22⋊C4C2×D3semidirect
246. #875C2×D3semidirect
248. #874C2×D3semidirect
253. C4×D12C2×D3semidirect
262. C22×C3×D3C2×D4semidirect
272. C2×C32×C4C2×D4semidirect
293. C3×D12C2×D4semidirect
294. C3×D12C2×D4semidirect
395. C2×D12D12semidirect
400. C2×D12C22×D3semidirect
401. C2×D12C22×D3semidirect
415. C2×C4×D3C22×D3semidirect
416. C2×C4×D3C22×D3semidirect
420. C2×Dic6C22×D3semidirect
423. C3×C4⋊C4C22×D3semidirect
424. C3×C4⋊C4C22×D3semidirect
433. C3×C42C22×D3semidirect
434. C3×C42C22×D3semidirect
448. (C2×D3)⋊C4C22×D3semidirect
449. (C2×D3)⋊C4C22×D3semidirect
454. C4⋊Dic3C22×D3semidirect
456. C4×Dic3C22×D3semidirect
465. C2×C3⋊D3H(5,𝔽2)semidirect
527. #117D32semidirect
567. C22×D3C2×D12semidirect
587. C2×C3×C4C2×D12semidirect
588. C2×C3×C4D3×D4semidirect
631. D12C2×D12semidirect
632. D12C2×D12semidirect
706. C4⋊C4C2×D32semidirect
717. C42C2×D32semidirect
784. C32#3484semidirect
831. C2×C4D3×D12semidirect
883. C3#85867semidirect
884. C3#86330semidirect

Maximal subgroups

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

subgroupindex
C2×#643072
C22×#38022
#105959952
C3×#55252
C3×#55212
#105950422
#105950342
#105946302
#105946212
#105942902
D3×#8822
#105940052
#105940042
#863303
#858673