Finite Group Databasebeta

← #11904511

Subgroups — #11904511

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
1C23×C3×Dic6C211yesmaximal, characteristic, complemented
2C2×#64297C211yesmaximal, characteristic, complemented
3#10596262C211yesmaximal, characteristic, complemented
4C3×#5791C211yesmaximal, characteristic, complemented
5#10595498C214yesmaximal, complemented
6#10594902C214yesmaximal, complemented
7#10594900C214yesmaximal, complemented
8Dic6×#67C214yesmaximal, complemented
9#10594897C214yesmaximal, complemented
10#10594866C211yesmaximal, characteristic, complemented
11#10594855C211yesmaximal, characteristic, complemented
12#10594818C211yesmaximal, characteristic, complemented
13#10594803C214yesmaximal, complemented
14#87251—31nomaximal
15#86022—31nomaximal
16C23×C32×C4C2211yescharacteristic
17C2×#3828C2211yescharacteristic
18C23×C3×Dic3C2212yes—
19C2×C3×#235C2211yescharacteristic
20C22×C3×Dic6—28no—
21C22×C3×Dic6C2211yescharacteristic
22C22×C3×Dic6C2212yes—
23C22×C3×Dic6C2214yes—
24C22×C3×Dic6C2214yes—
25C22×C3×Dic6C2211yescharacteristic
26C2×#3804C2214yes—
27C2×#3799C2212yescomplemented
28C2×#3797C2212yescomplemented
29#64297—28no—
30C2×#3796C2212yescomplemented
31C2×D3×Dic6C2212yescomplemented
32#64162C2212yes—
33#64139C2212yes—
34#64138C2212yes—
35C4×#638C2214yes—
36#64135C2211yescharacteristic
37#64133C2212yes—
38C3×#953C2212yes—
39C3×#930C2212yes—
40C3×#929C2212yes—
41C3×C4×#67C2214yes—
42C3×#926C2211yescharacteristic
43C3×#924C2212yes—
44#63978C2218yes—
45Dic3×#67C2218yes—
46#63966C2214yes—
47#63964C2218yes—
48#63961C2214yes—
49#63955C2214yes—
50#63952C2218yes—
51#63907C2218yescomplemented
52#63888C2218yescomplemented
53#63887C2218yescomplemented
54#63873C2212yescomplemented
55#63871C2214yescomplemented
56#63866C2212yescomplemented
57#63864C2212yescomplemented
58#63863C2212yescomplemented
59#63856C2214yescomplemented
60#63843C2214yescomplemented
61Dic3×Dic6C2214yescomplemented
62#63839C2218yescomplemented
63C23×C3×Q8—31no—
64C2×#1010—31no—
65C2×#1007—31no—
66C23×Dic6D311yescharacteristic, complemented
67C3×#525—31no—
68#5825—31no—
69#5817—34no—
70#5817—34no—
71#5816—31no—
72#5816—34no—
73#5816—31no—
74Q8×#67—34no—
75Q8×#67—34no—
76#5812—31no—
77#5791—31no—
78#5791—31no—
79#5791—34no—
80#5791—61no—
81#5791D311yescharacteristic, complemented
82#5648—34no—
83#5632—34no—
84#5598—34no—
85#5586—34no—
86#5552—34no—
87D4×Dic6—34no—
88#5526—31no—
89#5516—31no—
90C24×C32C2311yescharacteristic
91C22×C32×C4—24no—
92C22×C32×C4C2312yes—
93C22×C32×C4C2312yes—
94C22×C32×C4C2311yescharacteristic
95C22×C32×C4C2311yescharacteristic
96C2×#638C2312yes—
97C2×#638C2314yes—
98#3828—24no—
99C2×C4⋊(C3⋊D3)C2311yescharacteristic
100C2×C4×C3⋊D3C2312yes—
101C2×#634C2311yescharacteristic
102C2×C3×#67C2314yes—
103C2×C3×#67C2312yes—
104C22×C3×Dic3—28no—
105C22×C3×Dic3C2318yes—
106C22×C3×Dic3C2312yes—
107C22×C3×Dic3C2312yes—
108C3×#235—24no—
109C2×C3×D12C2311yescharacteristic
110C2×C3×C4×D3C2312yes—
111C2×C3×Dic6—24no—
112C2×C3×Dic6—28no—
113C2×C3×Dic6—216no—
114C2×C3×Dic6—216no—
115C2×C3×Dic6D418yescomplemented
116C2×C3×Dic6C2311yescharacteristic
117C2×C3×Dic6C2318yes—
118C2×C3×Dic6C2312yes—
119C2×C3×Dic6C2312yes—
120C2×C3×Dic6C2312yes—
121C2×C3×Dic6C2312yes—
122C2×#627C2314yes—
123C2×#626C2314yes—
124C2×#624C2314yes—
125#3804—216no—
126C2×D3×Dic3C2314yes—
127#3799—28no—
128#3797—28no—
129#3796—28no—
130D3×Dic6—28no—
131#3757C2314yes—
132#3757C2312yes—
133#3752C2314yes—
134C4⋊(C3⋊Dic3)C2312yes—
135#3750C2314yes—
136C4×C3⋊Dic3C2312yes—
137C3×#217C2314yes—
138C3×#217C2312yes—
139C3×(C2×D3)⋊C4C2314yes—
140C3×C4⋊Dic3C2312yes—
141C3×Dic3⋊C4C2314yes—
142C3×C4×Dic3C2312yes—
143#3724C2318yes—
144Dic3⋊Dic3C2318yes—
145Dic3⋊Dic3C2318yes—
146#3722C2318yes—
147(C2×D3)⋊Dic3C2318yes—
148Dic32C2318yes—
149#3486—91noSylow
150C2×C3×#41—31no—
151C22×C3×Q8—31no—
152C22×C3×Q8—34no—
153C22×C3×Q8—34no—
154C22×C3×Q8—32no—
155C22×C3×Q8—31no—
156C22×C3×Q8—68no—
157C23×C3×C4—21no—
158C23×C3×C4—32no—
159C23×C3×C4C2×D311yescharacteristic
160C23×C3×C4C2×D311yescharacteristic
161C23×Dic3C2×D312yes—
162#1010—68no—
163#1007—68no—
164C2×#239—32no—
165C2×#239—32no—
166C2×D3×Q8—32no—
167C2×D3×Q8—32no—
168C2×D3×Q8—32no—
169C2×#237—34no—
170C2×#237—32no—
171C2×#235—31no—
172C2×#235—31no—
173C2×#235—34no—
174C2×#235—32no—
175C2×#235—61no—
176C2×#235C2×D311yescharacteristic
177C22×Dic6—28no—
178C22×Dic6—32no—
179C22×Dic6C2×D314yes—
180C22×Dic6C2×D312yes—
181C22×Dic6C2×D311yescharacteristic
182C22×Dic6C2×D314yes—
183C22×Dic6C2×D311yescharacteristic
184C3×#123—32no—
185C3×C22⋊Q8—32no—
186C3×#121—32no—
187C3×#120—32no—
188C3×C4×D4—34no—
189C3×#117—31no—
190#953—32no—
191#953—32no—
192#953—62no—
193#953C2×D312yes—
194#947—32no—
195#947—38no—
196#947—32no—
197#946—34no—
198#946—38no—
199#946—34no—
200#946—38no—
201Q8×Dic3—34no—
202Q8×Dic3—34no—
203#944—32no—
204#944—32no—
205#944—38no—
206#944—32no—
207#939—38no—
208#936—32no—
209#935—34no—
210D4×Dic3—38no—
211#930—32no—
212#930—32no—
213#930—38no—
214#930—62no—
215#930C2×D312yes—
216#929—32no—
217#929—32no—
218#929—34no—
219#929—34no—
220#929—62no—
221#929C2×D312yes—
222C4×#67—34no—
223C4×#67—34no—
224C4×#67—38no—
225C4×#67—38no—
226C4×#67—64no—
227C4×#67C2×D314yes—
228#926—31no—
229#926—31no—
230#926—34no—
231#926—61no—
232#926C2×D311yescharacteristic
233#924—32no—
234#924—32no—
235#924—34no—
236#924—38no—
237#924—62no—
238#924C2×D312yes—
239#897—34no—
240#896—38no—
241#888—38no—
242#887—34no—
243#886—34no—
244#885—38no—
245#67⋊C4—38no—
246#878—38no—
247#878—38no—
248#877—34no—
249#875—32no—
250#869—32no—
251C4×Dic6—34no—
252C23×C32—22no—
253C23×C32—24no—
254C23×C32C2411yescharacteristic
255C23×C32C2412yes—
256C22×C3⋊D3C2412yes—
257C22×C3×D3C2412yes—
258C2×C32×C4—22no—
259C2×C32×C4—24no—
260C2×C32×C4—24no—
261C2×C32×C4C2×D414yes—
262C2×C32×C4C2412yes—
263C2×C32×C4C2411yescharacteristic
264C2×C32×C4C2411yescharacteristic
265#638—24no—
266#638—28no—
267C2×C3⋊Dic3C2414yes—
268C2×C3⋊Dic3C2412yes—
269C4⋊(C3⋊D3)—22no—
270C4×C3⋊D3—24no—
271#634—22no—
272C3×#67—24no—
273C3×#67—28no—
274C2×C3×Dic3—24no—
275C2×C3×Dic3—216no—
276C2×C3×Dic3C2×D418yes—
277C2×C3×Dic3C2414yes—
278C2×C3×Dic3C2414yes—
279C2×C3×Dic3C2412yes—
280C2×C3×Dic3C2414yes—
281C3×D12—22no—
282C3×C4×D3—24no—
283C3×Dic6—22no—
284C3×Dic6—24no—
285C3×Dic6—24no—
286C3×Dic6—216no—
287C3×Dic6C2×D418yes—
288C3×Dic6C2×D418yes—
289#627—28no—
290#626—28no—
291#624—28no—
292D3×Dic3—28no—
293C2×2−1+4—91no—
294C23×Q8—31no—
295D4×Q8—94no—
296D4×Q8—94no—
297#548—94no—
298#548—94no—
299#536—91no—
300#536—94no—
301#536—91no—
302#525—31no—
303#525—94no—
304#525—91no—
305#519—91no—
306C24×C3—21no—
307C24×C3C22×D311yescharacteristic
308C24×C3C22×D311yescharacteristic
309C3×#41—64no—
310C2×C3×Q8—38no—
311C2×C3×Q8—32no—
312C2×C3×Q8—32no—
313C2×C3×Q8—31no—
314C2×C3×Q8—38no—
315C2×C3×Q8—32no—
316C2×C3×Q8—32no—
317C2×C3×Q8—68no—
318C2×C3×Q8—616no—
319C2×C3×Q8—616no—
320C2×C3×Q8—64no—
321C2×C3×D4—34no—
322C2×C3×D4—32no—
323C2×C3×D4—31no—
324C22×C3×C4—24no—
325C22×C3×C4—24no—
326C22×C3×C4—21no—
327C22×C3×C4—22no—
328C22×C3×C4—22no—
329C22×C3×C4—21no—
330C22×C3×C4—32no—
331C22×C3×C4—38no—
332C22×C3×C4—32no—
333C22×C3×C4—32no—
334C22×C3×C4—44no—
335C22×C3×C4—68no—
336C22×C3×C4C22×D312yes—
337C22×C3×C4C22×D312yes—
338C22×C3×C4C22×D312yes—
339C22×C3×C4C22×D312yes—
340C22×C3×C4C22×D311yescharacteristic
341C22×C3×C4C22×D311yescharacteristic
342C22×C3×C4C22×D311yescharacteristic
343C22×C3×C4C22×D311yescharacteristic
344C2×#67—34no—
345C2×#67—32no—
346C2×#67—34no—
347C2×#67—32no—
348C2×#67—34no—
349C2×#67—64no—
350C2×#67—62no—
351C2×#67C22×D314yes—
352C2×#67C22×D312yes—
353C22×Dic3—28no—
354C22×Dic3—34no—
355C22×Dic3C22×D318yes—
356C22×Dic3C22×D312yes—
357C22×Dic3C22×D312yes—
358#239—68no—
359#239—68no—
360D3×Q8—68no—
361D3×Q8—68no—
362D3×Q8—68no—
363#237—616no—
364#237—68no—
365#235—24no—
366#235—616no—
367#235—64no—
368#235—64no—
369#235—68no—
370#235—124no—
371C2×D12—34no—
372C2×D12—31no—
373C2×D12—31no—
374C2×D12—61no—
375C2×D12C22×D311yescharacteristic
376C2×C4×D3—34no—
377C2×C4×D3—32no—
378C2×C4×D3—32no—
379C2×C4×D3—34no—
380C2×C4×D3—34no—
381C2×C4×D3—62no—
382C2×C4×D3C22×D312yes—
383C2×Dic6—24no—
384C2×Dic6—28no—
385C2×Dic6—216no—
386C2×Dic6—216no—
387C2×Dic6—31no—
388C2×Dic6—31no—
389C2×Dic6—34no—
390C2×Dic6—34no—
391C2×Dic6—61no—
392C2×Dic6—68no—
393C2×Dic6#6718yescomplemented
394C2×Dic6C22×D312yes—
395C2×Dic6C22×D318yes—
396C2×Dic6C22×D312yes—
397C2×Dic6C22×D311yescharacteristic
398C2×Dic6C22×D312yes—
399C2×Dic6C22×D312yes—
400C3×C4⋊C4—32no—
401C3×C4⋊C4—34no—
402C3×C22⋊C4—32no—
403C3×C22⋊C4—34no—
404C3×C22⋊C4—34no—
405C3×C42—32no—
406#217—32no—
407#217—34no—
408#217—34no—
409#217—32no—
410#217—38no—
411#217—64no—
412#217—62no—
413#217C22×D314yes—
414#217C22×D312yes—
415(C2×D3)⋊C4—38no—
416(C2×D3)⋊C4—34no—
417(C2×D3)⋊C4—34no—
418(C2×D3)⋊C4—38no—
419(C2×D3)⋊C4—38no—
420(C2×D3)⋊C4—64no—
421(C2×D3)⋊C4C22×D314yes—
422C4⋊Dic3—32no—
423C4⋊Dic3—32no—
424C4⋊Dic3—38no—
425C4⋊Dic3—38no—
426C4⋊Dic3—62no—
427C4⋊Dic3C22×D312yes—
428Dic3⋊C4—34no—
429Dic3⋊C4—34no—
430Dic3⋊C4—38no—
431Dic3⋊C4—38no—
432Dic3⋊C4—38no—
433Dic3⋊C4—38no—
434Dic3⋊C4—64no—
435Dic3⋊C4C22×D314yes—
436C4×Dic3—32no—
437C4×Dic3—32no—
438C4×Dic3—38no—
439C4×Dic3—38no—
440C4×Dic3—62no—
441C4×Dic3C22×D312yes—
442C22×C32—28no—
443C22×C32—22no—
444C22×C32—22no—
445C22×C32—22no—
446C22×C32C22×D412yes—
447C22×C322−1+414yescomplemented
448C22×C32C2511yescharacteristic
449C2×C3⋊D3—22no—
450C2×C3⋊D3—24no—
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—22no—
459C3×Dic3—24no—
460C3×Dic3—24no—
461C3×Dic3C22×D418yes—
4622−1+4—188no—
463C2×#41—31no—
464C2×#41—94no—
465C2×#41—92no—
466C2×#41—92no—
467C2×#41—91no—
468C22×Q8—31no—
469C22×Q8—32no—
470C22×Q8—31no—
471C22×Q8—34no—
472C22×Q8—34no—
473C22×Q8—68no—
474C22×Q8—92no—
475C22×Q8—92no—
476C23×C4—32no—
477C23×C4D3211yescharacteristic
478C4⋊Q8—92no—
479C4⋊Q8—98no—
480C4⋊Q8—92no—
481#124—92no—
482#124—98no—
483#124—92no—
484#123—32no—
485#123—94no—
486#123—94no—
487#123—92no—
488C22⋊Q8—32no—
489C22⋊Q8—98no—
490C22⋊Q8—98no—
491C22⋊Q8—98no—
492C22⋊Q8—94no—
493C22⋊Q8—94no—
494C22⋊Q8—92no—
495#121—32no—
496#121—98no—
497#121—92no—
498#120—32no—
499#120—92no—
500C4×Q8—94no—
501C4×Q8—94no—
502C4×D4—34no—
503C4×D4—98no—
504C4×D4—98no—
505C4×D4—94no—
506#117—31no—
507#117—94no—
508#117—91no—
509C23×C3—22no—
510C23×C3—24no—
511C23×C3—24no—
512C23×C3—22no—
513C23×C3—22no—
514C23×C3—21no—
515C23×C3—32no—
516C23×C3—42no—
517C23×C3—44no—
518C23×C3C23×D311yescharacteristic
519C23×C3C23×D312yes—
520C23×C3C23×D312yes—
521C23×C3C23×D311yescharacteristic
522C22×D3—32no—
523C22×D3—32no—
524C22×D3—62no—
525C22×D3C23×D312yes—
526C3×Q8—38no—
527C3×Q8—38no—
528C3×Q8—616no—
529C3×Q8—64no—
530C3×Q8—64no—
531C3×Q8—62no—
532C3×D4—68no—
533C3×D4—64no—
534C3×D4—62no—
535C2×C3×C4—22no—
536C2×C3×C4—22no—
537C2×C3×C4—24no—
538C2×C3×C4—24no—
539C2×C3×C4—24no—
540C2×C3×C4—24no—
541C2×C3×C4—21no—
542C2×C3×C4—21no—
543C2×C3×C4—22no—
544C2×C3×C4—24no—
545C2×C3×C4—38no—
546C2×C3×C4—34no—
547C2×C3×C4—34no—
548C2×C3×C4—34no—
549C2×C3×C4—32no—
550C2×C3×C4—44no—
551C2×C3×C4—44no—
552C2×C3×C4—42no—
553C2×C3×C4—616no—
554C2×C3×C4—64no—
555C2×C3×C4—64no—
556C2×C3×C4D3×D414yes—
557C2×C3×C4C2×#6714yes—
558C2×C3×C4C23×D312yes—
559C2×C3×C4C23×D312yes—
560C2×C3×C4C23×D311yescharacteristic
561C2×C3×C4C23×D311yescharacteristic
562C2×C3×C4C23×D311yescharacteristic
563C2×C3×C4C23×D311yescharacteristic
564#67—24no—
565#67—28no—
566#67—64no—
567#67—68no—
568#67—68no—
569#67—64no—
570#67—68no—
571#67—124no—
572#67—128no—
573C2×Dic3—24no—
574C2×Dic3—216no—
575C2×Dic3—34no—
576C2×Dic3—34no—
577C2×Dic3—32no—
578C2×Dic3—32no—
579C2×Dic3—64no—
580C2×Dic3—62no—
581C2×Dic3—68no—
582C2×Dic3C2×#6718yes—
583C2×Dic3C23×D314yes—
584C2×Dic3C23×D312yes—
585C2×Dic3C23×D314yes—
586C2×Dic3C23×D314yes—
587D12—22no—
588D12—68no—
589D12—62no—
590D12—62no—
591D12—122no—
592C4×D3—24no—
593C4×D3—68no—
594C4×D3—68no—
595C4×D3—64no—
596C4×D3—64no—
597C4×D3—68no—
598C4×D3—124no—
599Dic6—22no—
600Dic6—24no—
601Dic6—24no—
602Dic6—216no—
603Dic6—68no—
604Dic6—62no—
605Dic6—62no—
606Dic6—68no—
607Dic6—122no—
608Dic6C2×#6718yes—
609Dic6C2×#6718yes—
610C2×C32—22no—
611C2×C32—24no—
612C2×C32C23×D411yescharacteristic
613C2×C32C2×2−1+412yes—
614C3⋊D3—42no—
615C3×D3—42no—
616C24C2×D3211yescharacteristic
617#41—64no—
618#41—1816no—
619#41—188no—
620#41—188no—
621#41—184no—
622C2×Q8—32no—
623C2×Q8—32no—
624C2×Q8—31no—
625C2×Q8—38no—
626C2×Q8—32no—
627C2×Q8—32no—
628C2×Q8—38no—
629C2×Q8—68no—
630C2×Q8—616no—
631C2×Q8—616no—
632C2×Q8—64no—
633C2×Q8—94no—
634C2×Q8—91no—
635C2×Q8—188no—
636C2×Q8—188no—
637C2×D4—34no—
638C2×D4—32no—
639C2×D4—31no—
640C2×D4—94no—
641C2×D4—94no—
642C2×D4—92no—
643C2×D4—91no—
644C22×C4—24no—
645C22×C4—32no—
646C22×C4—38no—
647C22×C4—32no—
648C22×C4—32no—
649C22×C4—68no—
650C22×C4—94no—
651C22×C4—94no—
652C22×C4—92no—
653C22×C4C2×D3212yes—
654C22×C4C2×D3212yes—
655C22×C4C2×D3211yescharacteristic
656C22×C4C2×D3211yescharacteristic
657C4⋊C4—32no—
658C4⋊C4—34no—
659C4⋊C4—98no—
660C4⋊C4—98no—
661C4⋊C4—98no—
662C4⋊C4—92no—
663C4⋊C4—94no—
664C22⋊C4—32no—
665C22⋊C4—34no—
666C22⋊C4—34no—
667C22⋊C4—98no—
668C22⋊C4—98no—
669C22⋊C4—92no—
670C22⋊C4—94no—
671C22⋊C4—94no—
672C42—32no—
673C42—98no—
674C42—92no—
675C22×C3—28no—
676C22×C3—28no—
677C22×C3—22no—
678C22×C3—22no—
679C22×C3—22no—
680C22×C3—22no—
681C22×C3—22no—
682C22×C3—22no—
683C22×C3—24no—
684C22×C3—22no—
685C22×C3—21no—
686C22×C3—42no—
687C22×C3—42no—
688C22×C3—42no—
689C22×C3—48no—
690C22×C3—64no—
691C22×C3—62no—
692C22×C3C2×D3×D412yes—
693C22×C3#100714yescomplemented
694C22×C3#101014yescomplemented
695C22×C3C22×#6712yes—
696C22×C3C24×D311yescharacteristic
697C22×C3C24×D311yescharacteristic
698C2×D3—22no—
699C2×D3—24no—
700C2×D3—62no—
701C2×D3—64no—
702C2×D3—64no—
703C2×D3—62no—
704C2×D3—122no—
705C2×D3—124no—
706C3×C4—22no—
707C3×C4—22no—
708C3×C4—22no—
709C3×C4—22no—
710C3×C4—38no—
711C3×C4—42no—
712C3×C4—64no—
713C3×C4—64no—
714C3×C4—62no—
715C3×C4C2×D3×D412yes—
716C3×C4C2×D3×D412yes—
717C3×C4C22×#6712yes—
718C3×C4C22×#6712yes—
719Dic3—22no—
720Dic3—24no—
721Dic3—24no—
722Dic3—62no—
723Dic3—64no—
724Dic3—64no—
725Dic3—62no—
726Dic3—122no—
727Dic3—124no—
728Dic3C22×#6718yes—
729C32#348611yescharacteristic, complemented, Sylow
730C23—24no—
731C23—22no—
732C23—32no—
733C23—92no—
734C23C22×D3212yes—
735C23C22×D3211yescharacteristic
736Q8—38no—
737Q8—38no—
738Q8—616no—
739Q8—64no—
740Q8—64no—
741Q8—62no—
742Q8—188no—
743Q8—182no—
744D4—68no—
745D4—64no—
746D4—62no—
747D4—188no—
748D4—188no—
749D4—184no—
750D4—182no—
751C2×C4—22no—
752C2×C4—24no—
753C2×C4—24no—
754C2×C4—38no—
755C2×C4—34no—
756C2×C4—34no—
757C2×C4—32no—
758C2×C4—34no—
759C2×C4—616no—
760C2×C4—64no—
761C2×C4—64no—
762C2×C4—94no—
763C2×C4—92no—
764C2×C4—188no—
765C2×C4—188no—
766C2×C4—184no—
767C2×C4D3×#6714yes—
768C2×C4C22×D3212yes—
769C2×C4C22×D3211yescharacteristic
770C2×C4C22×D3211yescharacteristic
771C2×C3—22no—
772C2×C3—24no—
773C2×C3—24no—
774C2×C3—22no—
775C2×C3—22no—
776C2×C3—21no—
777C2×C3—44no—
778C2×C3—42no—
779C2×C3—122no—
780C2×C3C22×D3×D411yescharacteristic
781C2×C3C2×#100712yes—
782C2×C3C2×#101012yes—
783C2×C3C23×#6711yescharacteristic
784D3—42no—
785D3—122no—
786D3—122no—
787D3—242no—
788C22—28no—
789C22—22no—
790C22—22no—
791C22—22no—
792C22—64no—
793C22—62no—
794C22—184no—
795C22—182no—
796C22#6429714yescomplemented
797C22C2×D3×#6712yes—
798C22C23×D3211yescharacteristic
799C4—22no—
800C4—38no—
801C4—64no—
802C4—64no—
803C4—62no—
804C4—184no—
805C4—182no—
806C4C2×D3×#6712yes—
807C4C2×D3×#6712yes—
808C3—21no—
809C3#8602211yescharacteristic, complemented
810C3#8725111yescharacteristic, complemented
811C2—24no—
812C2—22no—
813C2—122no—
814C2—362no—
815C2C2×#6429712yes—
816C2C22×D3×#6711yescharacteristic
subgroupG/H
center, FrattiniC22C23×D32
commutator, socle, cosocleC22×C32C25
FittingC23×C32×C4C22
hypercenterC23×C4D32
hypocenterC32#3486
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C22 ◁ C23×C4

Complements

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

NH ≅ G/Ntype
1. C23×C3×Dic6C2semidirect
2. C2×#64297C2semidirect
3. #10596262C2semidirect
4. C3×#5791C2semidirect
5. #10595498C2semidirect
6. #10594902C2semidirect
7. #10594900C2semidirect
8. Dic6×#67C2semidirect
9. #10594897C2semidirect
10. #10594866C2semidirect
11. #10594855C2semidirect
12. #10594818C2semidirect
13. #10594803C2semidirect
27. C2×#3799C22semidirect
28. C2×#3797C22semidirect
30. C2×#3796C22semidirect
31. C2×D3×Dic6C22semidirect
51. #63907C22semidirect
52. #63888C22semidirect
53. #63887C22semidirect
54. #63873C22semidirect
55. #63871C22semidirect
56. #63866C22semidirect
57. #63864C22semidirect
58. #63863C22semidirect
59. #63856C22semidirect
60. #63843C22semidirect
61. Dic3×Dic6C22semidirect
62. #63839C22semidirect
66. C23×Dic6D3semidirect
81. #5791D3semidirect
115. C2×C3×Dic6D4semidirect
393. C2×Dic6#67semidirect
447. C22×C322−1+4semidirect
693. C22×C3#1007semidirect
694. C22×C3#1010semidirect
729. C32#3486semidirect
796. C22#64297semidirect
809. C3#86022semidirect
810. C3#87251semidirect

Maximal subgroups

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

subgroupindex
C23×C3×Dic62
C2×#642972
#105962622
C3×#57912
#105954982
#105949022
#105949002
Dic6×#672
#105948972
#105948662
#105948552
#105948182
#105948032
#872513
#860223