Finite Group Databasebeta

← #11904504

Subgroups — #11904504

Order 1152.

3149 conjugacy classes of subgroups.

The subgroup lattice has 818 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#1010C211yesmaximal, characteristic, complemented
2C22×#3797C211yesmaximal, characteristic, complemented
3#10596299C211yesmaximal, characteristic, complemented
4C3×#5825C211yesmaximal, characteristic, complemented
5#10595403C214yesmaximal, complemented
6#10595270C214yesmaximal, complemented
7#10595237C214yesmaximal, complemented
8#10595159C214yesmaximal, complemented
9#10595034C211yesmaximal, characteristic, complemented
10#10594855C211yesmaximal, characteristic, complemented
11#10594830C214yesmaximal, complemented
12#10594818C211yesmaximal, characteristic, complemented
13#10594803C214yesmaximal, complemented
14#87294—31nomaximal
15#86355—31nomaximal
16C2×C32×#41C2211yescharacteristic
17C22×C4×C3⋊D3C2211yescharacteristic
18C3×#1010—28no—
19C2×C3×D3×Q8C2212yescomplemented
20C2×C3×#237C2214yes—
21C2×C3×#237C2212yescomplemented
22C2×C3×#235C2211yescharacteristic
23C2×C3×#235C2212yescomplemented
24C22×C3×Dic6C2211yescharacteristic
25C22×C3×Dic6C2211yescharacteristic
26C22×C3×Dic6C2212yescomplemented
27C22×#627C2212yes—
28C22×#624C2212yes—
29C2×#3797—28no—
30C2×#3797C2214yes—
31C2×#3797C2214yes—
32#64155C2212yes—
33#64147C2212yes—
34#64146C2212yes—
35#64144C2212yes—
36C4×#638C2214yes—
37#64135C2211yescharacteristic
38C3×#944C2212yescomplemented
39C3×#936C2212yescomplemented
40C3×#935C2214yes—
41C3×#926C2211yescharacteristic
42C3×#924C2214yescomplemented
43#63981C2212yes—
44#63964C2218yescomplemented
45#63962C2212yes—
46#63961C2214yes—
47#63959C2218yescomplemented
48#63958C2218yes—
49#63955C2214yes—
50#63952C2218yes—
51#63916C2212yes—
52#63904C2218yes—
53C4×#626C2214yes—
54#63888C2218yes—
55#63873C2212yescomplemented
56#63871C2212yes—
57#63863C2212yescomplemented
58#63856C2214yescomplemented
59#63851C2218yescomplemented
60#63843C2214yescomplemented
61Dic3×Dic6C2214yescomplemented
62#63839C2218yescomplemented
63C2×C3×2−1+4—31no—
64C2×#1010D311yescharacteristic, complemented
65C22×D3×Q8—31no—
66C22×D3×Q8—31no—
67C3×#536—31no—
68#5831—34no—
69#5831—34no—
70#5828—31no—
71#5828—31no—
72#5828—34no—
73#5828—31no—
74#5828—61no—
75#5825—31no—
76#5825—34no—
77#5825D311yescharacteristic, complemented
78#5816—31no—
79Q8×#67—34no—
80Q8×#67—34no—
81#5812—31no—
82#5727—34no—
83#5677—34no—
84#5656—34no—
85#5648—34no—
86#5633—34no—
87#5632—34no—
88#5524—31no—
89#5516—31no—
90C23×C3⋊D3C2311yescharacteristic
91C32×#41—24no—
92C2×C32×Q8C2311yescharacteristic
93C2×C32×D4C2312yes—
94C2×C32×D4C2311yescharacteristic
95C22×C32×C4C2312yes—
96C22×C32×C4C2311yescharacteristic
97C2×#638C2314yes—
98C22×C3⋊Dic3C2311yescharacteristic
99C2×C4×C3⋊D3—24no—
100C2×C4×C3⋊D3C2312yes—
101C2×C4×C3⋊D3C2312yes—
102C2×C3×#67C2312yes—
103C2×C3×#67C2314yes—
104C22×C3×Dic3C2312yes—
105C22×C3×Dic3C2314yes—
106C22×C3×Dic3C2312yes—
107C3×D3×Q8—28no—
108C3×#237—216no—
109C3×#237—28no—
110C3×#235—24no—
111C3×#235—28no—
112C2×C3×D12C2311yescharacteristic
113C2×C3×C4×D3C2312yes—
114C2×C3×C4×D3C2314yes—
115C2×C3×Dic6—24no—
116C2×C3×Dic6—28no—
117C2×C3×Dic6D418yescomplemented
118C2×C3×Dic6C2312yes—
119C2×C3×Dic6C2312yes—
120C2×C3×Dic6C2311yescharacteristic
121C2×C3×Dic6C2314yes—
122C2×C3×Dic6C2312yes—
123C2×C3×Dic6C2312yes—
124C2×#627—28no—
125C2×#627C2318yes—
126C2×#626C2314yes—
127C2×#624—28no—
128C2×#624C2318yes—
129#3797—216no—
130#3797—216no—
131#3757C2312yes—
132#3757C2314yes—
133#3752C2314yes—
134C4⋊(C3⋊Dic3)C2312yes—
135#3750C2314yes—
136C4×C3⋊Dic3C2312yes—
137C3×#217C2318yes—
138C3×#217C2312yes—
139C3×C4⋊Dic3C2312yes—
140C3×Dic3⋊C4C2318yes—
141C3×C4×Dic3C2312yes—
142#3724C2318yes—
143Dic3⋊Dic3C2314yes—
144Dic3⋊Dic3C2318yes—
145#3722C2314yes—
146(C2×D3)⋊Dic3C2314yes—
147(C2×D3)⋊Dic3C2318yes—
148Dic32C2318yes—
149#3486—91noSylow
150C3×2−1+4—68no—
151C2×C3×#41—21no—
152C2×C3×#41—34no—
153C2×C3×#41—32no—
154C2×C3×#41—31no—
155C2×C3×#41—32no—
156C2×C3×#41C2×D311yescharacteristic
157C2×C3×#41C2×D311yescharacteristic
158C22×C3×Q8—32no—
159C22×C3×Q8—31no—
160C22×C3×Q8—31no—
161C22×C3×Q8—32no—
162#1010—28no—
163C2×D3×Q8—34no—
164C2×D3×Q8—34no—
165C2×D3×Q8—34no—
166C2×D3×Q8—34no—
167C2×D3×Q8—68no—
168C2×D3×Q8—68no—
169C2×D3×Q8C2×D312yescomplemented
170C2×#237C2×D314yes—
171C2×#237C2×D312yescomplemented
172C2×#235C2×D311yescharacteristic
173C2×#235C2×D312yescomplemented
174C22×C4×D3—31no—
175C22×C4×D3—31no—
176C22×C4×D3—32no—
177C22×C4×D3—32no—
178C22×C4×D3—61no—
179C22×Dic6—32no—
180C22×Dic6—32no—
181C22×Dic6C2×D311yescharacteristic
182C22×Dic6C2×D311yescharacteristic
183C22×Dic6C2×D312yescomplemented
184C3×C4⋊Q8—32no—
185C3×#124—32no—
186C3×#123—34no—
187C3×C22⋊Q8—34no—
188C3×#117—31no—
189#947—32no—
190#946—32no—
191#946—32no—
192#946—34no—
193#946—32no—
194#946—38no—
195#946—62no—
196Q8×Dic3—34no—
197Q8×Dic3—34no—
198#944—32no—
199#944—32no—
200#944—38no—
201#944C2×D312yescomplemented
202#938—32no—
203#938—32no—
204#938—38no—
205#938—32no—
206#938—62no—
207#937—32no—
208#937—32no—
209#937—32no—
210#937—62no—
211#936—32no—
212#936—38no—
213#936C2×D312yescomplemented
214#935—32no—
215#935—32no—
216#935—34no—
217#935—32no—
218#935—62no—
219#935C2×D314yes—
220#929—34no—
221C4×#67—34no—
222C4×#67—34no—
223C4×#67—38no—
224C4×#67—38no—
225C4×#67—34no—
226C4×#67—64no—
227#926—31no—
228#926—31no—
229#926—34no—
230#926—61no—
231#926C2×D311yescharacteristic
232#924—34no—
233#924—38no—
234#924—38no—
235#924C2×D314yescomplemented
236#897—32no—
237#896—38no—
238#896—38no—
239#895—32no—
240#893—38no—
241#888—38no—
242#887—34no—
243#886—32no—
244#885—38no—
245#884—38no—
246#882—32no—
247#67⋊C4—38no—
248#878—38no—
249#877—34no—
250C4×D12—34no—
251C4×Dic6—34no—
252C23×C32C2412yes—
253C23×C32C2411yescharacteristic
254C22×C3⋊D3—22no—
255C22×C3⋊D3—24no—
256C22×C3⋊D3C2412yes—
257C22×C3×D3C2412yes—
258C32×Q8—22no—
259C32×D4—24no—
260C32×D4—22no—
261C2×C32×C4—24no—
262C2×C32×C4C2×D414yes—
263C2×C32×C4C2412yes—
264C2×C32×C4C2411yescharacteristic
265C2×C32×C4C2411yescharacteristic
266#638—28no—
267C2×C3⋊Dic3—22no—
268C2×C3⋊Dic3C2414yes—
269C2×C3⋊Dic3C2412yes—
270C4×C3⋊D3—24no—
271C4×C3⋊D3—24no—
272C3×#67—24no—
273C3×#67—28no—
274C2×C3×Dic3—24no—
275C2×C3×Dic3—28no—
276C2×C3×Dic3C2×D418yes—
277C2×C3×Dic3C2414yes—
278C2×C3×Dic3C2414yes—
279C2×C3×Dic3C2412yes—
280C2×C3×Dic3C2414yes—
281C3×D12—22no—
282C3×C4×D3—24no—
283C3×C4×D3—28no—
284C3×Dic6—24no—
285C3×Dic6—24no—
286C3×Dic6—22no—
287C3×Dic6—28no—
288C3×Dic6C2×D418yes—
289C3×Dic6C2×D418yes—
290#627—216no—
291#626—28no—
292#624—216no—
293C2×2−1+4—31no—
294C23×Q8—91no—
295D4×Q8—94no—
296D4×Q8—94no—
297#548—94no—
298#548—94no—
299#536—31no—
300#536—94no—
301#536—91no—
302#525—91no—
303#525—94no—
304#525—91no—
305#519—91no—
306C23×D3—31no—
307C23×D3—31no—
308C23×D3—61no—
309C3×#41—24no—
310C3×#41—24no—
311C3×#41—44no—
312C3×#41—68no—
313C3×#41—616no—
314C3×#41—68no—
315C3×#41—64no—
316C2×C3×Q8—21no—
317C2×C3×Q8—38no—
318C2×C3×Q8—32no—
319C2×C3×Q8—32no—
320C2×C3×Q8—34no—
321C2×C3×Q8—31no—
322C2×C3×Q8—32no—
323C2×C3×Q8—32no—
324C2×C3×Q8—68no—
325C2×C3×Q8—68no—
326C2×C3×Q8—64no—
327C2×C3×Q8C22×D311yescharacteristic
328C2×C3×Q8C22×D311yescharacteristic
329C2×C3×D4—22no—
330C2×C3×D4—21no—
331C2×C3×D4—32no—
332C2×C3×D4—34no—
333C2×C3×D4—31no—
334C2×C3×D4C22×D312yes—
335C2×C3×D4C22×D312yes—
336C2×C3×D4C22×D311yescharacteristic
337C2×C3×D4C22×D311yescharacteristic
338C22×C3×C4—21no—
339C22×C3×C4—22no—
340C22×C3×C4—32no—
341C22×C3×C4—34no—
342C22×C3×C4—32no—
343C22×C3×C4—34no—
344C22×C3×C4—32no—
345C22×C3×C4C22×D312yes—
346C22×C3×C4C22×D312yes—
347C22×C3×C4C22×D311yescharacteristic
348C22×C3×C4C22×D311yescharacteristic
349C2×#67—34no—
350C2×#67—34no—
351C2×#67—34no—
352C2×#67—64no—
353C2×#67C22×D312yes—
354C2×#67C22×D314yes—
355C22×Dic3—31no—
356C22×Dic3—31no—
357C22×Dic3—61no—
358C22×Dic3C22×D314yes—
359C22×Dic3C22×D312yes—
360C22×Dic3C22×D312yes—
361D3×Q8—28no—
362D3×Q8—616no—
363D3×Q8—616no—
364D3×Q8—616no—
365D3×Q8—616no—
366#237—216no—
367#237—28no—
368#235—24no—
369#235—28no—
370C2×D12—34no—
371C2×D12C22×D311yescharacteristic
372C2×C4×D3—32no—
373C2×C4×D3—32no—
374C2×C4×D3—32no—
375C2×C4×D3—32no—
376C2×C4×D3—38no—
377C2×C4×D3—38no—
378C2×C4×D3—62no—
379C2×C4×D3—62no—
380C2×C4×D3—68no—
381C2×C4×D3—64no—
382C2×C4×D3—64no—
383C2×C4×D3—68no—
384C2×C4×D3—124no—
385C2×C4×D3C22×D312yes—
386C2×C4×D3C22×D314yes—
387C2×Dic6—24no—
388C2×Dic6—28no—
389C2×Dic6—38no—
390C2×Dic6—38no—
391C2×Dic6—68no—
392C2×Dic6—68no—
393C2×Dic6#6718yescomplemented
394C2×Dic6C22×D314yes—
395C2×Dic6C22×D311yescharacteristic
396C2×Dic6C22×D312yes—
397C2×Dic6C22×D312yes—
398C2×Dic6C22×D312yes—
399C2×Dic6C22×D312yes—
400C3×C4⋊C4—32no—
401C3×C4⋊C4—38no—
402C3×C22⋊C4—32no—
403C3×C22⋊C4—38no—
404C3×C42—32no—
405#217—32no—
406#217—34no—
407#217—34no—
408#217—32no—
409#217—38no—
410#217—34no—
411#217—62no—
412#217—64no—
413#217C22×D318yes—
414#217C22×D312yes—
415(C2×D3)⋊C4—34no—
416(C2×D3)⋊C4—38no—
417(C2×D3)⋊C4—34no—
418(C2×D3)⋊C4—34no—
419(C2×D3)⋊C4—34no—
420(C2×D3)⋊C4—34no—
421(C2×D3)⋊C4—64no—
422C4⋊Dic3—32no—
423C4⋊Dic3—32no—
424C4⋊Dic3—34no—
425C4⋊Dic3—38no—
426C4⋊Dic3—62no—
427C4⋊Dic3C22×D312yes—
428Dic3⋊C4—34no—
429Dic3⋊C4—34no—
430Dic3⋊C4—38no—
431Dic3⋊C4—38no—
432Dic3⋊C4—34no—
433Dic3⋊C4—38no—
434Dic3⋊C4—64no—
435Dic3⋊C4C22×D318yes—
436C4×Dic3—32no—
437C4×Dic3—32no—
438C4×Dic3—38no—
439C4×Dic3—38no—
440C4×Dic3—62no—
441C4×Dic3C22×D312yes—
442C22×C32—22no—
443C22×C32—22no—
444C22×C32—24no—
445C22×C32C22×D412yes—
446C22×C32C2511yescharacteristic
447C2×C3⋊D3—28no—
448C2×C3⋊D3—22no—
449C2×C3⋊D3—22no—
450C2×C3⋊D32−1+414yescomplemented
451C2×C3×D3—22no—
452C2×C3×D3—24no—
453C32×C4—22no—
454C32×C4C22×D412yes—
455C32×C4C22×D412yes—
456C3⋊Dic3—22no—
457C3⋊Dic3—24no—
458C3×Dic3—24no—
459C3×Dic3—22no—
460C3×Dic3—24no—
461C3×Dic3C22×D418yes—
4622−1+4—68no—
463C2×#41—34no—
464C2×#41—32no—
465C2×#41—31no—
466C2×#41—32no—
467C2×#41D3211yescharacteristic
468C22×Q8—32no—
469C22×Q8—31no—
470C22×Q8—31no—
471C22×Q8—32no—
472C22×Q8—92no—
473C22×Q8—94no—
474C22×Q8—94no—
475C22×Q8—188no—
476C23×C4—92no—
477C23×C4—91no—
478C4⋊Q8—32no—
479C4⋊Q8—98no—
480C4⋊Q8—92no—
481#124—32no—
482#124—98no—
483#124—92no—
484#123—34no—
485#123—92no—
486#123—94no—
487#123—92no—
488C22⋊Q8—34no—
489C22⋊Q8—98no—
490C22⋊Q8—98no—
491C22⋊Q8—98no—
492C22⋊Q8—92no—
493C22⋊Q8—94no—
494C22⋊Q8—92no—
495#121—98no—
496#121—92no—
497#121—92no—
498#120—92no—
499#120—92no—
500C4×Q8—94no—
501C4×Q8—94no—
502C4×D4—94no—
503C4×D4—98no—
504C4×D4—98no—
505C4×D4—94no—
506#117—31no—
507#117—94no—
508#117—91no—
509C23×C3—21no—
510C23×C3—22no—
511C23×C3—32no—
512C23×C3C23×D312yes—
513C23×C3C23×D312yes—
514C23×C3C23×D311yescharacteristic
515C23×C3C23×D311yescharacteristic
516C22×D3—32no—
517C22×D3—32no—
518C22×D3—62no—
519C22×D3—64no—
520C22×D3—64no—
521C22×D3—62no—
522C22×D3—62no—
523C22×D3—124no—
524C22×D3—122no—
525C22×D3C23×D312yes—
526C3×Q8—22no—
527C3×Q8—22no—
528C3×Q8—38no—
529C3×Q8—38no—
530C3×Q8—42no—
531C3×Q8—68no—
532C3×Q8—62no—
533C3×Q8—64no—
534C3×Q8—64no—
535C3×D4—24no—
536C3×D4—24no—
537C3×D4—22no—
538C3×D4—22no—
539C3×D4—42no—
540C3×D4—44no—
541C3×D4—68no—
542C3×D4—64no—
543C3×D4—62no—
544C2×C3×C4—24no—
545C2×C3×C4—24no—
546C2×C3×C4—21no—
547C2×C3×C4—21no—
548C2×C3×C4—22no—
549C2×C3×C4—24no—
550C2×C3×C4—38no—
551C2×C3×C4—34no—
552C2×C3×C4—34no—
553C2×C3×C4—32no—
554C2×C3×C4—34no—
555C2×C3×C4—44no—
556C2×C3×C4—68no—
557C2×C3×C4—68no—
558C2×C3×C4—64no—
559C2×C3×C4—64no—
560C2×C3×C4D3×D414yes—
561C2×C3×C4C2×#6714yes—
562C2×C3×C4C23×D312yes—
563C2×C3×C4C23×D312yes—
564C2×C3×C4C23×D311yescharacteristic
565C2×C3×C4C23×D311yescharacteristic
566C2×C3×C4C23×D311yescharacteristic
567C2×C3×C4C23×D311yescharacteristic
568#67—24no—
569#67—28no—
570#67—68no—
571#67—68no—
572#67—68no—
573#67—128no—
574C2×Dic3—24no—
575C2×Dic3—28no—
576C2×Dic3—34no—
577C2×Dic3—34no—
578C2×Dic3—32no—
579C2×Dic3—32no—
580C2×Dic3—64no—
581C2×Dic3—62no—
582C2×Dic3—62no—
583C2×Dic3—62no—
584C2×Dic3—122no—
585C2×Dic3C2×#6718yes—
586C2×Dic3C23×D314yes—
587C2×Dic3C23×D312yes—
588C2×Dic3C23×D314yes—
589C2×Dic3C23×D314yes—
590D12—22no—
591D12—68no—
592C4×D3—24no—
593C4×D3—28no—
594C4×D3—616no—
595C4×D3—64no—
596C4×D3—64no—
597C4×D3—64no—
598C4×D3—64no—
599C4×D3—616no—
600C4×D3—124no—
601C4×D3—124no—
602Dic6—24no—
603Dic6—24no—
604Dic6—22no—
605Dic6—28no—
606Dic6—616no—
607Dic6—616no—
608Dic6C2×#6718yes—
609Dic6C2×#6718yes—
610C2×C32—22no—
611C2×C32—42no—
612C2×C32C23×D411yescharacteristic
613C2×C32C2×2−1+412yes—
614C3⋊D3—24no—
615C3×D3—42no—
616C24—91no—
617#41—24no—
618#41—68no—
619#41—616no—
620#41—68no—
621#41—64no—
622C2×Q8—32no—
623C2×Q8—32no—
624C2×Q8—32no—
625C2×Q8—32no—
626C2×Q8—34no—
627C2×Q8—31no—
628C2×Q8—38no—
629C2×Q8—68no—
630C2×Q8—68no—
631C2×Q8—64no—
632C2×Q8—98no—
633C2×Q8—188no—
634C2×Q8—1816no—
635C2×Q8—1816no—
636C2×Q8C2×D3211yescharacteristic
637C2×D4—32no—
638C2×D4—34no—
639C2×D4—31no—
640C2×D4—94no—
641C2×D4—94no—
642C2×D4C2×D3212yes—
643C2×D4C2×D3211yescharacteristic
644C22×C4—32no—
645C22×C4—34no—
646C22×C4—32no—
647C22×C4—34no—
648C22×C4—32no—
649C22×C4—98no—
650C22×C4—91no—
651C22×C4—92no—
652C22×C4—92no—
653C22×C4—188no—
654C22×C4—184no—
655C22×C4C2×D3212yes—
656C22×C4C2×D3211yescharacteristic
657C4⋊C4—32no—
658C4⋊C4—38no—
659C4⋊C4—98no—
660C4⋊C4—98no—
661C4⋊C4—94no—
662C4⋊C4—92no—
663C4⋊C4—94no—
664C22⋊C4—32no—
665C22⋊C4—38no—
666C22⋊C4—94no—
667C22⋊C4—94no—
668C22⋊C4—98no—
669C22⋊C4—92no—
670C22⋊C4—94no—
671C22⋊C4—94no—
672C42—32no—
673C42—98no—
674C42—92no—
675C22×C3—22no—
676C22×C3—22no—
677C22×C3—22no—
678C22×C3—24no—
679C22×C3—24no—
680C22×C3—22no—
681C22×C3—22no—
682C22×C3—21no—
683C22×C3—42no—
684C22×C3—44no—
685C22×C3—42no—
686C22×C3—62no—
687C22×C3—64no—
688C22×C3C2×D3×D412yes—
689C22×C3C22×#6712yes—
690C22×C3C24×D311yescharacteristic
691C22×C3C24×D311yescharacteristic
692C2×D3—24no—
693C2×D3—22no—
694C2×D3—34no—
695C2×D3—34no—
696C2×D3—64no—
697C2×D3—68no—
698C2×D3—68no—
699C2×D3—62no—
700C2×D3—62no—
701C2×D3—62no—
702C2×D3—62no—
703C2×D3—122no—
704C2×D3—122no—
705C2×D3—128no—
706C3×C4—22no—
707C3×C4—22no—
708C3×C4—22no—
709C3×C4—22no—
710C3×C4—38no—
711C3×C4—42no—
712C3×C4—62no—
713C3×C4—64no—
714C3×C4—64no—
715C3×C4C2×D3×D412yes—
716C3×C4C2×D3×D412yes—
717C3×C4C22×#6712yes—
718C3×C4C22×#6712yes—
719Dic3—24no—
720Dic3—24no—
721Dic3—22no—
722Dic3—62no—
723Dic3—64no—
724Dic3—64no—
725Dic3—62no—
726Dic3—122no—
727Dic3—124no—
728Dic3C22×#6718yes—
729C32#348611yescharacteristic, complemented, Sylow
730C23—32no—
731C23—92no—
732C23—184no—
733C23—182no—
734C23C22×D3212yes—
735C23C22×D3211yescharacteristic
736Q8—22no—
737Q8—38no—
738Q8—38no—
739Q8—68no—
740Q8—62no—
741Q8—64no—
742Q8—64no—
743Q8—1816no—
744D4—24no—
745D4—22no—
746D4—68no—
747D4—64no—
748D4—62no—
749D4—188no—
750D4—188no—
751C2×C4—24no—
752C2×C4—38no—
753C2×C4—34no—
754C2×C4—34no—
755C2×C4—34no—
756C2×C4—32no—
757C2×C4—68no—
758C2×C4—68no—
759C2×C4—64no—
760C2×C4—64no—
761C2×C4—94no—
762C2×C4—92no—
763C2×C4—1816no—
764C2×C4—182no—
765C2×C4—184no—
766C2×C4—184no—
767C2×C4D3×#6714yes—
768C2×C4C22×D3212yes—
769C2×C4C22×D3211yescharacteristic
770C2×C4C22×D3211yescharacteristic
771C2×C3—22no—
772C2×C3—22no—
773C2×C3—22no—
774C2×C3—21no—
775C2×C3—42no—
776C2×C3—42no—
777C2×C3—42no—
778C2×C3—82no—
779C2×C3—122no—
780C2×C3C22×D3×D411yescharacteristic
781C2×C3D3×2−1+412yes—
782C2×C3D3×2−1+412yes—
783C2×C3C23×#6711yescharacteristic
784D3—42no—
785D3—64no—
786D3—64no—
787D3—124no—
788C22—22no—
789C22—24no—
790C22—22no—
791C22—64no—
792C22—62no—
793C22—94no—
794C22—188no—
795C22—182no—
796C22—182no—
797C22C2×D3×#6712yes—
798C22C23×D3211yescharacteristic
799C4—22no—
800C4—38no—
801C4—64no—
802C4—62no—
803C4—64no—
804C4—184no—
805C4—182no—
806C4C2×D3×#6712yes—
807C4C2×D3×#6712yes—
808C3—21no—
809C3#8635511yescharacteristic, complemented
810C3#8729411yescharacteristic, complemented
811C2—22no—
812C2—42no—
813C2—122no—
814C2—184no—
815C2#1059669412yes—
816C2C22×D3×#6711yescharacteristic
subgroupG/H
center, FrattiniC22C23×D32
commutator, socle, cosocleC22×C32C25
FittingC2×C32×#41C22
hypercenterC2×#41D32
hypocenterC32#3486
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C22 ◁ C2×#41

Complements

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

NH ≅ G/Ntype
1. C2×C3×#1010C2semidirect
2. C22×#3797C2semidirect
3. #10596299C2semidirect
4. C3×#5825C2semidirect
5. #10595403C2semidirect
6. #10595270C2semidirect
7. #10595237C2semidirect
8. #10595159C2semidirect
9. #10595034C2semidirect
10. #10594855C2semidirect
11. #10594830C2semidirect
12. #10594818C2semidirect
13. #10594803C2semidirect
19. C2×C3×D3×Q8C22semidirect
21. C2×C3×#237C22semidirect
23. C2×C3×#235C22semidirect
26. C22×C3×Dic6C22semidirect
38. C3×#944C22semidirect
39. C3×#936C22semidirect
42. C3×#924C22semidirect
44. #63964C22semidirect
47. #63959C22semidirect
55. #63873C22semidirect
57. #63863C22semidirect
58. #63856C22semidirect
59. #63851C22semidirect
60. #63843C22semidirect
61. Dic3×Dic6C22semidirect
62. #63839C22semidirect
64. C2×#1010D3semidirect
77. #5825D3semidirect
117. C2×C3×Dic6D4semidirect
169. C2×D3×Q8C2×D3semidirect
171. C2×#237C2×D3semidirect
173. C2×#235C2×D3semidirect
183. C22×Dic6C2×D3semidirect
201. #944C2×D3semidirect
213. #936C2×D3semidirect
235. #924C2×D3semidirect
393. C2×Dic6#67semidirect
450. C2×C3⋊D32−1+4semidirect
729. C32#3486semidirect
809. C3#86355semidirect
810. C3#87294semidirect

Maximal subgroups

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

subgroupindex
C2×C3×#10102
C22×#37972
#105962992
C3×#58252
#105954032
#105952702
#105952372
#105951592
#105950342
#105948552
#105948302
#105948182
#105948032
#872943
#863553