Finite Group Databasebeta

← #11904440

Subgroups — #11904440

Order 1152.

3569 conjugacy classes of subgroups.

The subgroup lattice has 862 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#64366C211yesmaximal, characteristic, complemented
2C22×#3799C211yesmaximal, characteristic, complemented
3C3×#5828C211yesmaximal, characteristic, complemented
4C3×#5825C211yesmaximal, characteristic, complemented
5#10595341C214yesmaximal, complemented
6#10595243C214yesmaximal, complemented
7#10595242C214yesmaximal, complemented
8#10595169C214yesmaximal, complemented
9#10595023C211yesmaximal, characteristic, complemented
10#10595018C214yesmaximal, complemented
11#10594996C211yesmaximal, characteristic, complemented
12#10594866C211yesmaximal, characteristic, complemented
13#10594834C214yesmaximal, complemented
14#86354—31nomaximal
15#86040—31nomaximal
16C2×C32×#41C2211yescharacteristic
17#64366—28no—
18C2×#3832C2212yescomplemented
19C2×D4×C3⋊D3C2214yes—
20C2×D4×C3⋊D3C2212yescomplemented
21C2×#3828C2211yescharacteristic
22C2×#3828C2212yescomplemented
23C22×C4⋊(C3⋊D3)C2211yescharacteristic
24C22×C4⋊(C3⋊D3)C2212yescomplemented
25C22×C3×C4×D3C2211yescharacteristic, complemented
26C22×C3×Dic6C2211yescharacteristic, complemented
27C22×#626C2212yescomplemented
28C22×#624C2212yescomplemented
29C2×#3799—28no—
30C2×#3799C2214yescomplemented
31C2×#3799C2214yescomplemented
32C3×#946C2212yescomplemented
33C3×#944C2212yescomplemented
34C3×#938C2212yescomplemented
35C3×#937C2212yescomplemented
36C3×#936C2212yescomplemented
37C3×#935C2214yescomplemented
38C3×#935C2212yescomplemented
39C3×C4×#67C2214yescomplemented
40C3×#926C2211yescharacteristic, complemented
41C3×#926C2211yescharacteristic, complemented
42C3×#924C2214yescomplemented
43#63981C2218yescomplemented
44#63977C2212yescomplemented
45#63975C2218yescomplemented
46#63974C2214yescomplemented
47#63974C2218yescomplemented
48#63966C2214yescomplemented
49#63966C2212yescomplemented
50#63958C2218yescomplemented
51#63910C2218yescomplemented
52#63909C2212yescomplemented
53C4×#626C2214yescomplemented
54#63897C2218yescomplemented
55#63894C2214yescomplemented
56#63894C2214yescomplemented
57#63883C2218yescomplemented
58#63871C2214yescomplemented
59#63866C2212yescomplemented
60#63864C2212yescomplemented
61#63857C2212yescomplemented
62#63853C2218yescomplemented
63C2×#1009—31no—
64C2×#1009—31no—
65C2×#1009—61no—
66C22×#239—31no—
67C22×#235—31no—
68C3×#536—31no—
69C3×#525—31no—
70#5828D311yescharacteristic, complemented
71#5825D311yescharacteristic, complemented
72#5816—31no—
73#5791—31no—
74#5726—34no—
75#5676—34no—
76#5653—34no—
77D3×#123—34no—
78D3×#123—34no—
79#5631—34no—
80#5631—34no—
81#5630—34no—
82#5612—34no—
83#5589—34no—
84#5551—34no—
85#5550—34no—
86#5526—31no—
87#5524—31no—
88#5521—31no—
89#5521—31no—
90C23×C3⋊D3C2314yes—
91C23×C3⋊D3C2312yes—
92C23×C3×D3C2311yescharacteristic
93C32×#41—24no—
94C2×C32×Q8C2311yescharacteristic
95C2×C32×D4C2312yes—
96C2×C32×D4C2311yescharacteristic
97C22×C32×C4C2312yes—
98C22×C32×C4C2311yescharacteristic
99C2×#638C2312yes—
100C2×#638C2314yes—
101#3832—28no—
102D4×C3⋊D3—216no—
103D4×C3⋊D3—28no—
104#3828—24no—
105#3828—28no—
106C2×C4⋊(C3⋊D3)—28no—
107C2×C4⋊(C3⋊D3)D418yescomplemented
108C2×C4⋊(C3⋊D3)C2311yescharacteristic
109C2×C4⋊(C3⋊D3)C2314yes—
110C2×C4⋊(C3⋊D3)C2312yes—
111C2×C4⋊(C3⋊D3)C2312yes—
112C2×C4×C3⋊D3C2312yes—
113C2×C4×C3⋊D3C2314yes—
114C2×#634C2311yescharacteristic
115C2×C3×#67C2314yes—
116C22×C3×Dic3C2311yescharacteristic
117C22×C3×Dic3C2312yes—
118C2×C3×C4×D3—24no—
119C2×C3×C4×D3C2312yes—
120C2×C3×C4×D3C2312yes—
121C2×C3×Dic6—24no—
122C2×C3×Dic6C2312yes—
123C2×C3×Dic6C2312yes—
124C2×#626—28no—
125C2×#626C2318yes—
126C2×#626C2314yes—
127C2×#624—28no—
128C2×#624C2318yes—
129C2×#624C2318yes—
130#3799—216no—
131#3799—216no—
132C3×#217C2318yes—
133C3×#217C2312yes—
134C3×#217C2312yes—
135C3×#217C2314yes—
136C3×(C2×D3)⋊C4C2314yes—
137C3×C4⋊Dic3C2312yes—
138C3×C4⋊Dic3C2312yes—
139C3×Dic3⋊C4C2318yes—
140C3×Dic3⋊C4C2314yes—
141C3×C4×Dic3C2312yes—
142C3×C4×Dic3C2312yes—
143Dic3⋊Dic3C2318yes—
144Dic3⋊Dic3C2314yes—
145#3722C2318yes—
146#3722C2318yes—
147#3722C2314yes—
148(C2×D3)⋊Dic3C2314yes—
149#3485—91noSylow
150C2×C3×#41—21no—
151C2×C3×#41C2×D311yescharacteristic
152C2×C3×#41C2×D311yescharacteristic
153C22×C3×Q8—31no—
154C23×C3×C4—31no—
155C22×#67—32no—
156#1009—68no—
157#1009—68no—
158#1009—616no—
159C2×#239—32no—
160C2×#239—32no—
161C2×#239—34no—
162C2×#239—34no—
163C2×#239—62no—
164C2×#239—68no—
165C2×D3×D4—34no—
166C2×D3×D4—34no—
167C2×D3×D4—32no—
168C2×D3×D4—32no—
169C2×D3×D4—64no—
170C2×D3×D4—62no—
171C2×#235—31no—
172C2×#235—31no—
173C2×#235—32no—
174C2×#235—32no—
175C2×#235—34no—
176C2×#235—34no—
177C2×#235—61no—
178C2×#235—62no—
179C2×#235—68no—
180C22×D12—31no—
181C22×D12—31no—
182C22×D12—32no—
183C22×D12—32no—
184C22×D12—32no—
185C22×D12—61no—
186C22×D12—62no—
187C22×C4×D3—32no—
188C22×C4×D3—32no—
189C22×C4×D3C2×D311yescharacteristic, complemented
190C22×Dic6C2×D311yescharacteristic, complemented
191C3×C4⋊Q8—32no—
192C3×#124—32no—
193C3×#123—32no—
194C3×#123—34no—
195C3×C22⋊Q8—32no—
196C3×C22⋊Q8—34no—
197C3×#121—32no—
198C3×#120—32no—
199C3×C4×D4—34no—
200C3×#117—31no—
201C3×#117—31no—
202#953—32no—
203#947—32no—
204#946—34no—
205#946C2×D312yescomplemented
206#944—32no—
207#944C2×D312yescomplemented
208#938—38no—
209#938C2×D312yescomplemented
210#937—38no—
211#937C2×D312yescomplemented
212#936C2×D312yescomplemented
213#935C2×D312yescomplemented
214#935C2×D314yescomplemented
215#930—32no—
216#929—32no—
217#929—34no—
218C4×#67—34no—
219C4×#67C2×D314yescomplemented
220#926C2×D311yescharacteristic, complemented
221#926C2×D311yescharacteristic, complemented
222#924—32no—
223#924C2×D314yescomplemented
224#897—32no—
225#897—34no—
226#895—32no—
227#895—38no—
228#894—38no—
229#894—38no—
230#894—38no—
231#893—34no—
232#893—34no—
233D3×C4⋊C4—38no—
234D3×C4⋊C4—38no—
235#886—32no—
236#886—34no—
237#884—38no—
238#884—38no—
239#883—38no—
240#883—38no—
241#883—38no—
242#882—32no—
243#882—38no—
244D3×C22⋊C4—34no—
245D3×C22⋊C4—38no—
246D3×C22⋊C4—34no—
247D3×C22⋊C4—38no—
248#875—32no—
249C4×D12—34no—
250C4×D12—34no—
251C4×D12—34no—
252#869—32no—
253C23×C32C2412yes—
254C23×C32C2411yescharacteristic
255C22×C3⋊D3—28no—
256C22×C3⋊D3—44no—
257C22×C3⋊D3—48no—
258C22×C3⋊D3C2×D418yes—
259C22×C3⋊D3C2412yes—
260C22×C3⋊D3C2414yes—
261C22×C3×D3—22no—
262C22×C3×D3—42no—
263C22×C3×D3C2412yes—
264C32×Q8—22no—
265C32×D4—24no—
266C32×D4—22no—
267C2×C32×C4—24no—
268C2×C32×C4C2×D414yes—
269C2×C32×C4C2412yes—
270C2×C32×C4C2411yescharacteristic
271C2×C32×C4C2411yescharacteristic
272#638—24no—
273#638—28no—
274C2×C3⋊Dic3C2412yes—
275C4⋊(C3⋊D3)—28no—
276C4⋊(C3⋊D3)—22no—
277C4⋊(C3⋊D3)C2×D418yes—
278C4⋊(C3⋊D3)C2×D418yes—
279C4×C3⋊D3—28no—
280C4×C3⋊D3—24no—
281#634—22no—
282C3×#67—44no—
283C2×C3×Dic3—22no—
284C2×C3×Dic3—24no—
285C2×C3×Dic3C2414yes—
286C2×C3×Dic3C2414yes—
287C2×C3×Dic3C2412yes—
288C2×C3×Dic3C2414yes—
289C3×C4×D3—24no—
290C3×C4×D3—24no—
291C3×Dic6—24no—
292C3×Dic6—24no—
293#626—216no—
294#626—44no—
295#624—216no—
296#624—48no—
297C2×H(5,𝔽2)—91no—
298C22×#41—91no—
299#547—94no—
300#547—94no—
301#546—94no—
302#546—94no—
303#536—31no—
304#536—91no—
305#534—94no—
306#525—31no—
307#525—91no—
308C2×#123—94no—
309#518—91no—
310C24×C3—31no—
311C23×D3—32no—
312C23×D3—32no—
313C23×D3—34no—
314C23×D3—34no—
315C23×D3—62no—
316C23×D3—64no—
317C23×D3C22×D311yescharacteristic
318C3×#41—28no—
319C3×#41—24no—
320C3×#41—24no—
321C2×C3×Q8—21no—
322C2×C3×Q8—32no—
323C2×C3×Q8—32no—
324C2×C3×Q8—64no—
325C2×C3×Q8C22×D311yescharacteristic
326C2×C3×Q8C22×D311yescharacteristic
327C2×C3×D4—22no—
328C2×C3×D4—21no—
329C2×C3×D4—34no—
330C2×C3×D4C22×D312yes—
331C2×C3×D4C22×D312yes—
332C2×C3×D4C22×D311yescharacteristic
333C2×C3×D4C22×D311yescharacteristic
334C22×C3×C4—22no—
335C22×C3×C4—21no—
336C22×C3×C4—31no—
337C22×C3×C4—32no—
338C22×C3×C4—32no—
339C22×C3×C4—32no—
340C22×C3×C4—64no—
341C22×C3×C4C22×D312yes—
342C22×C3×C4C22×D312yes—
343C22×C3×C4C22×D311yescharacteristic
344C22×C3×C4C22×D311yescharacteristic
345C2×#67—32no—
346C2×#67—34no—
347C2×#67—34no—
348C2×#67—32no—
349C2×#67—38no—
350C2×#67—34no—
351C2×#67—62no—
352C2×#67—64no—
353C2×#67—68no—
354C2×#67C22×D314yes—
355C22×Dic3C22×D312yes—
356C22×Dic3C22×D311yescharacteristic
357#239—616no—
358#239—616no—
359#239—68no—
360#239—68no—
361#239—616no—
362D3×D4—68no—
363D3×D4—68no—
364D3×D4—616no—
365D3×D4—616no—
366D3×D4—616no—
367D3×D4—632no—
368#235—616no—
369#235—616no—
370#235—68no—
371#235—68no—
372#235—616no—
373#235—68no—
374#235—64no—
375#235—64no—
376C2×D12—38no—
377C2×D12—38no—
378C2×D12—32no—
379C2×D12—32no—
380C2×D12—32no—
381C2×D12—32no—
382C2×D12—38no—
383C2×D12—31no—
384C2×D12—34no—
385C2×D12—34no—
386C2×D12—31no—
387C2×D12—34no—
388C2×D12—62no—
389C2×D12—61no—
390C2×D12—62no—
391C2×D12—64no—
392C2×D12—68no—
393C2×D12—68no—
394C2×D12—68no—
395C2×D12—616no—
396C2×D12—68no—
397C2×C4×D3—24no—
398C2×C4×D3—32no—
399C2×C4×D3—34no—
400C2×C4×D3—34no—
401C2×C4×D3—32no—
402C2×C4×D3—38no—
403C2×C4×D3—38no—
404C2×C4×D3—38no—
405C2×C4×D3—38no—
406C2×C4×D3—64no—
407C2×C4×D3—62no—
408C2×C4×D3—68no—
409C2×C4×D3—68no—
410C2×C4×D3C22×D312yes—
411C2×C4×D3C22×D312yes—
412C2×Dic6—24no—
413C2×Dic6—31no—
414C2×Dic6—31no—
415C2×Dic6—61no—
416C2×Dic6C22×D312yes—
417C2×Dic6C22×D312yes—
418C3×C4⋊C4—34no—
419C3×C4⋊C4—38no—
420C3×C4⋊C4—32no—
421C3×C4⋊C4—32no—
422C3×C22⋊C4—32no—
423C3×C22⋊C4—34no—
424C3×C22⋊C4—32no—
425C3×C22⋊C4—38no—
426C3×C22⋊C4—34no—
427C3×C42—32no—
428C3×C42—32no—
429#217—34no—
430#217C22×D314yes—
431#217C22×D312yes—
432#217C22×D312yes—
433#217C22×D318yes—
434(C2×D3)⋊C4—34no—
435(C2×D3)⋊C4—34no—
436(C2×D3)⋊C4—38no—
437(C2×D3)⋊C4—38no—
438(C2×D3)⋊C4—38no—
439(C2×D3)⋊C4—34no—
440(C2×D3)⋊C4—38no—
441(C2×D3)⋊C4C22×D314yes—
442C4⋊Dic3—38no—
443C4⋊Dic3—34no—
444C4⋊Dic3C22×D312yes—
445C4⋊Dic3C22×D312yes—
446Dic3⋊C4—34no—
447Dic3⋊C4—38no—
448Dic3⋊C4C22×D318yes—
449Dic3⋊C4C22×D314yes—
450C4×Dic3C22×D312yes—
451C4×Dic3C22×D312yes—
452C22×C32—22no—
453C22×C32—22no—
454C22×C32—24no—
455C22×C32C22×D412yes—
456C22×C32C2511yescharacteristic
457C2×C3⋊D3—22no—
458C2×C3⋊D3—28no—
459C2×C3⋊D3—24no—
460C2×C3⋊D3—48no—
461C2×C3⋊D3—88no—
462C2×C3⋊D3C22×D418yes—
463C2×C3×D3—22no—
464C2×C3×D3—22no—
465C2×C3×D3—22no—
466C2×C3×D3—44no—
467C32×C4—22no—
468C32×C4C22×D412yes—
469C32×C4C22×D412yes—
470C3⋊Dic3—22no—
471C3×Dic3—22no—
472C3×Dic3—24no—
473C3×Dic3—24no—
474C3×Dic3—24no—
475H(5,𝔽2)—188no—
476C2×#41—94no—
477C2×#41—94no—
478C2×#41—92no—
479C2×#41—91no—
480C2×#41—92no—
481C2×#41—188no—
482C2×#41D3211yescharacteristic
483C22×Q8—31no—
484C22×D4—92no—
485C22×D4—94no—
486C22×D4—92no—
487C22×D4—91no—
488C22×D4—92no—
489C23×C4—31no—
490C23×C4—92no—
491C4⋊Q8—32no—
492C4⋊Q8—92no—
493#124—32no—
494#124—92no—
495#123—32no—
496#123—34no—
497#123—98no—
498#123—98no—
499#123—92no—
500#123—94no—
501#123—98no—
502C22⋊Q8—32no—
503C22⋊Q8—34no—
504C22⋊Q8—92no—
505C22⋊Q8—94no—
506#121—32no—
507#121—98no—
508#121—98no—
509#121—92no—
510#120—32no—
511#120—98no—
512#120—92no—
513C4×D4—34no—
514C4×D4—94no—
515C4×D4—94no—
516C4×D4—94no—
517#117—31no—
518#117—31no—
519C2×C4⋊C4—98no—
520C2×C22⋊C4—94no—
521C2×C22⋊C4—98no—
522C23×C3—22no—
523C23×C3—21no—
524C23×C3—32no—
525C23×C3—62no—
526C23×C3—122no—
527C23×C3C23×D312yes—
528C23×C3C23×D312yes—
529C23×C3C23×D311yescharacteristic
530C23×C3C23×D311yescharacteristic
531C22×D3—22no—
532C22×D3—34no—
533C22×D3—34no—
534C22×D3—38no—
535C22×D3—38no—
536C22×D3—32no—
537C22×D3—32no—
538C22×D3—42no—
539C22×D3—64no—
540C22×D3—62no—
541C22×D3—68no—
542C22×D3—68no—
543C22×D3—68no—
544C22×D3—616no—
545C22×D3—124no—
546C22×D3—124no—
547C22×D3—128no—
548C22×D3—128no—
549C22×D3—244no—
550C22×D3—248no—
551C22×D3C23×D312yes—
552C3×Q8—24no—
553C3×Q8—22no—
554C3×Q8—22no—
555C3×Q8—64no—
556C3×Q8—64no—
557C3×D4—28no—
558C3×D4—24no—
559C3×D4—24no—
560C3×D4—24no—
561C3×D4—22no—
562C3×D4—22no—
563C3×D4—124no—
564C2×C3×C4—28no—
565C2×C3×C4—24no—
566C2×C3×C4—24no—
567C2×C3×C4—21no—
568C2×C3×C4—22no—
569C2×C3×C4—21no—
570C2×C3×C4—24no—
571C2×C3×C4—32no—
572C2×C3×C4—34no—
573C2×C3×C4—34no—
574C2×C3×C4—34no—
575C2×C3×C4—62no—
576C2×C3×C4—64no—
577C2×C3×C4—64no—
578C2×C3×C4—64no—
579C2×C3×C4D3×D414yes—
580C2×C3×C4D3×D414yes—
581C2×C3×C4C23×D312yes—
582C2×C3×C4C23×D312yes—
583C2×C3×C4C23×D311yescharacteristic
584C2×C3×C4C23×D311yescharacteristic
585C2×C3×C4C23×D311yescharacteristic
586C2×C3×C4C23×D311yescharacteristic
587#67—44no—
588#67—616no—
589#67—68no—
590#67—68no—
591#67—616no—
592#67—68no—
593#67—64no—
594#67—64no—
595#67—124no—
596C2×Dic3—24no—
597C2×Dic3—22no—
598C2×Dic3—32no—
599C2×Dic3—32no—
600C2×Dic3—62no—
601C2×Dic3C23×D314yes—
602C2×Dic3C23×D314yes—
603C2×Dic3C23×D314yes—
604C2×Dic3C23×D312yes—
605D12—38no—
606D12—38no—
607D12—38no—
608D12—38no—
609D12—68no—
610D12—68no—
611D12—68no—
612D12—68no—
613D12—64no—
614D12—616no—
615D12—616no—
616D12—62no—
617D12—62no—
618D12—124no—
619C4×D3—24no—
620C4×D3—24no—
621C4×D3—616no—
622C4×D3—616no—
623C4×D3—68no—
624C4×D3—68no—
625C4×D3—616no—
626C4×D3—68no—
627C4×D3—64no—
628C4×D3—64no—
629C4×D3—128no—
630C4×D3—128no—
631Dic6—24no—
632Dic6—24no—
633Dic6—64no—
634Dic6—62no—
635Dic6—62no—
636C2×C32—22no—
637C2×C32—42no—
638C2×C32C23×D411yescharacteristic
639C2×C32#58512yes—
640C3⋊D3—28no—
641C3⋊D3—42no—
642C3×D3—42no—
643C24—31no—
644C24—92no—
645C24—94no—
646#41—24no—
647#41—188no—
648#41—1816no—
649#41—1816no—
650#41—188no—
651#41—184no—
652C2×Q8—32no—
653C2×Q8—32no—
654C2×Q8—64no—
655C2×Q8—91no—
656C2×Q8C2×D3211yescharacteristic
657C2×D4—34no—
658C2×D4—98no—
659C2×D4—94no—
660C2×D4—92no—
661C2×D4—94no—
662C2×D4—92no—
663C2×D4—92no—
664C2×D4—94no—
665C2×D4—91no—
666C2×D4—98no—
667C2×D4—188no—
668C2×D4—188no—
669C2×D4—188no—
670C2×D4—1816no—
671C2×D4C2×D3212yes—
672C2×D4C2×D3211yescharacteristic
673C22×C4—31no—
674C22×C4—32no—
675C22×C4—32no—
676C22×C4—32no—
677C22×C4—64no—
678C22×C4—98no—
679C22×C4—98no—
680C22×C4—94no—
681C22×C4—92no—
682C22×C4—188no—
683C22×C4C2×D3212yes—
684C22×C4C2×D3211yescharacteristic
685C4⋊C4—34no—
686C4⋊C4—38no—
687C4⋊C4—32no—
688C4⋊C4—32no—
689C4⋊C4—94no—
690C4⋊C4—98no—
691C22⋊C4—32no—
692C22⋊C4—32no—
693C22⋊C4—34no—
694C22⋊C4—38no—
695C22⋊C4—34no—
696C22⋊C4—94no—
697C22⋊C4—98no—
698C22⋊C4—98no—
699C22⋊C4—94no—
700C42—32no—
701C42—32no—
702C22×C3—22no—
703C22×C3—22no—
704C22×C3—24no—
705C22×C3—22no—
706C22×C3—22no—
707C22×C3—24no—
708C22×C3—24no—
709C22×C3—22no—
710C22×C3—21no—
711C22×C3—42no—
712C22×C3—44no—
713C22×C3—62no—
714C22×C3—62no—
715C22×C3—62no—
716C22×C3—124no—
717C22×C3C2×D3×D412yes—
718C22×C3C2×D3×D412yes—
719C22×C3C24×D311yescharacteristic
720C22×C3C24×D311yescharacteristic
721C2×D3—22no—
722C2×D3—22no—
723C2×D3—22no—
724C2×D3—38no—
725C2×D3—38no—
726C2×D3—44no—
727C2×D3—68no—
728C2×D3—68no—
729C2×D3—68no—
730C2×D3—64no—
731C2×D3—62no—
732C2×D3—62no—
733C2×D3—64no—
734C2×D3—64no—
735C2×D3—128no—
736C2×D3—124no—
737C2×D3—128no—
738C2×D3—128no—
739C2×D3—248no—
740C2×D3—248no—
741C2×D3—248no—
742C2×D3—2416no—
743C3×C4—24no—
744C3×C4—22no—
745C3×C4—22no—
746C3×C4—22no—
747C3×C4—22no—
748C3×C4—62no—
749C3×C4—64no—
750C3×C4—64no—
751C3×C4—64no—
752C3×C4C2×D3×D412yes—
753C3×C4C2×D3×D412yes—
754C3×C4C2×D3×D412yes—
755C3×C4C2×D3×D412yes—
756Dic3—24no—
757Dic3—22no—
758Dic3—24no—
759Dic3—24no—
760Dic3—64no—
761Dic3—62no—
762Dic3—62no—
763C32#348511yescharacteristic, complemented, Sylow
764C23—32no—
765C23—62no—
766C23—94no—
767C23—98no—
768C23—92no—
769C23—122no—
770C23—188no—
771C23—364no—
772C23—368no—
773C23C22×D3212yes—
774C23C22×D3211yescharacteristic
775Q8—22no—
776Q8—64no—
777Q8—64no—
778Q8—182no—
779D4—24no—
780D4—22no—
781D4—98no—
782D4—98no—
783D4—124no—
784D4—188no—
785D4—1816no—
786D4—188no—
787D4—184no—
788D4—182no—
789D4—364no—
790C2×C4—24no—
791C2×C4—34no—
792C2×C4—34no—
793C2×C4—32no—
794C2×C4—34no—
795C2×C4—62no—
796C2×C4—64no—
797C2×C4—64no—
798C2×C4—64no—
799C2×C4—92no—
800C2×C4—188no—
801C2×C4—1816no—
802C2×C4—184no—
803C2×C4—368no—
804C2×C4#381114yes—
805C2×C4C22×D3212yes—
806C2×C4C22×D3211yescharacteristic
807C2×C4C22×D3211yescharacteristic
808C2×C3—22no—
809C2×C3—22no—
810C2×C3—22no—
811C2×C3—21no—
812C2×C3—42no—
813C2×C3—44no—
814C2×C3—42no—
815C2×C3—42no—
816C2×C3—122no—
817C2×C3C22×D3×D411yescharacteristic
818C2×C3C22×D3×D411yescharacteristic
819C2×C3#596412yes—
820C2×C3#596812yes—
821D3—42no—
822D3—68no—
823D3—68no—
824D3—128no—
825D3—124no—
826D3—122no—
827D3—122no—
828C22—22no—
829C22—24no—
830C22—22no—
831C22—62no—
832C22—62no—
833C22—62no—
834C22—98no—
835C22—124no—
836C22—188no—
837C22—184no—
838C22—182no—
839C22—368no—
840C22—728no—
841C22C2×#381112yes—
842C22C23×D3211yescharacteristic
843C4—22no—
844C4—64no—
845C4—64no—
846C4—62no—
847C4—64no—
848C4—182no—
849C4C2×#381112yes—
850C4C2×#381112yes—
851C3—21no—
852C3#8604011yescharacteristic, complemented
853C3#8635411yescharacteristic, complemented
854C2—22no—
855C2—42no—
856C2—122no—
857C2—188no—
858C2—362no—
859C2#1059669712yes—
860C2C22×#381111yescharacteristic
subgroupG/H
center, FrattiniC22C23×D32
commutator, socle, cosocleC22×C32C25
FittingC2×C32×#41C22
hypercenterC2×#41D32
hypocenterC32#3485
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C22 ◁ C2×#41

Complements

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

NH ≅ G/Ntype
1. C2×#64366C2semidirect
2. C22×#3799C2semidirect
3. C3×#5828C2semidirect
4. C3×#5825C2semidirect
5. #10595341C2semidirect
6. #10595243C2semidirect
7. #10595242C2semidirect
8. #10595169C2semidirect
9. #10595023C2semidirect
10. #10595018C2semidirect
11. #10594996C2semidirect
12. #10594866C2semidirect
13. #10594834C2semidirect
18. C2×#3832C22semidirect
20. C2×D4×C3⋊D3C22semidirect
22. C2×#3828C22semidirect
24. C22×C4⋊(C3⋊D3)C22semidirect
25. C22×C3×C4×D3C22semidirect
26. C22×C3×Dic6C22semidirect
27. C22×#626C22semidirect
28. C22×#624C22semidirect
30. C2×#3799C22semidirect
31. C2×#3799C22semidirect
32. C3×#946C22semidirect
33. C3×#944C22semidirect
34. C3×#938C22semidirect
35. C3×#937C22semidirect
36. C3×#936C22semidirect
37. C3×#935C22semidirect
38. C3×#935C22semidirect
39. C3×C4×#67C22semidirect
40. C3×#926C22semidirect
41. C3×#926C22semidirect
42. C3×#924C22semidirect
43. #63981C22semidirect
44. #63977C22semidirect
45. #63975C22semidirect
46. #63974C22semidirect
47. #63974C22semidirect
48. #63966C22semidirect
49. #63966C22semidirect
50. #63958C22semidirect
51. #63910C22semidirect
52. #63909C22semidirect
53. C4×#626C22semidirect
54. #63897C22semidirect
55. #63894C22semidirect
56. #63894C22semidirect
57. #63883C22semidirect
58. #63871C22semidirect
59. #63866C22semidirect
60. #63864C22semidirect
61. #63857C22semidirect
62. #63853C22semidirect
70. #5828D3semidirect
71. #5825D3semidirect
107. C2×C4⋊(C3⋊D3)D4semidirect
189. C22×C4×D3C2×D3semidirect
190. C22×Dic6C2×D3semidirect
205. #946C2×D3semidirect
207. #944C2×D3semidirect
209. #938C2×D3semidirect
211. #937C2×D3semidirect
212. #936C2×D3semidirect
213. #935C2×D3semidirect
214. #935C2×D3semidirect
219. C4×#67C2×D3semidirect
220. #926C2×D3semidirect
221. #926C2×D3semidirect
223. #924C2×D3semidirect
763. C32#3485semidirect
852. C3#86040semidirect
853. C3#86354semidirect

Maximal subgroups

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

subgroupindex
C2×#643662
C22×#37992
C3×#58282
C3×#58252
#105953412
#105952432
#105952422
#105951692
#105950232
#105950182
#105949962
#105948662
#105948342
#863543
#860403