Finite Group Databasebeta

← #11904506

Subgroups — #11904506

Order 1152.

3119 conjugacy classes of subgroups.

The subgroup lattice has 805 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#1010C211yesmaximal, characteristic, complemented
2C22×D3×Dic6C211yesmaximal, characteristic, complemented
3#10596296C211yesmaximal, characteristic, complemented
4C3×#5828C211yesmaximal, characteristic, complemented
5#10595400C214yesmaximal, complemented
6#10595270C214yesmaximal, complemented
7#10595157C214yesmaximal, complemented
8#10595154C214yesmaximal, complemented
9#10595022C211yesmaximal, characteristic, complemented
10#10594899C214yesmaximal, complemented
11Dic6×#67C214yesmaximal, complemented
12#10594856C211yesmaximal, characteristic, complemented
13#10594818C211yesmaximal, characteristic, complemented
14#87294—31nomaximal
15#86022—31nomaximal
16C2×C32×#41C2211yescharacteristic
17C22×#634C2211yescharacteristic
18C3×#1010—28no—
19C2×C3×D3×Q8C2212yescomplemented
20C2×C3×#237C2214yes—
21C2×C3×#237C2212yescomplemented
22C2×C3×#235C2211yescharacteristic
23C2×C3×#235C2212yescomplemented
24C22×C3×C4×D3C2211yescharacteristic
25C22×C3×Dic6C2211yescharacteristic
26C22×C3×Dic6C2212yescomplemented
27C22×#627C2212yes—
28C22×D3×Dic3C2212yes—
29C2×D3×Dic6—28no—
30C2×D3×Dic6C2214yes—
31C2×D3×Dic6C2214yes—
32#64153C2212yescomplemented
33#64145C2212yescomplemented
34#64144C2214yes—
35#64135C2211yescharacteristic
36#64133C2214yescomplemented
37C3×#946C2212yes—
38C3×#938C2212yes—
39C3×#937C2212yes—
40C3×#935C2212yes—
41C3×C4×#67C2214yes—
42C3×#926C2211yescharacteristic
43#63976C2212yes—
44Dic3×#67C2218yes—
45#63970C2218yes—
46#63964C2218yescomplemented
47#63962C2214yes—
48#63961C2212yes—
49#63959C2218yescomplemented
50#63955C2214yes—
51#63908C2212yes—
52C4×#625C2214yes—
53#63887C2218yes—
54#63879C2218yes—
55#63866C2212yescomplemented
56#63860C2212yescomplemented
57#63857C2214yescomplemented
58#63856C2212yes—
59#63851C2218yescomplemented
60#63843C2214yescomplemented
61Dic3×Dic6C2214yescomplemented
62#63839C2218yescomplemented
63C2×C3×2−1+4—31no—
64C2×#1010D311yescharacteristic, complemented
65C22×D3×Q8—31no—
66C23×Dic6—31no—
67C3×#525—31no—
68#5831—34no—
69#5831—34no—
70#5828—31no—
71#5828—34no—
72#5828D311yescharacteristic, complemented
73#5825—31no—
74#5825—31no—
75#5825—34no—
76#5825—31no—
77#5825—61no—
78Q8×#67—34no—
79Q8×#67—34no—
80#5812—31no—
81#5791—31no—
82#5648—34no—
83#5632—34no—
84#5598—34no—
85#5586—34no—
86#5552—34no—
87D4×Dic6—34no—
88#5526—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
97C22×C3⋊Dic3C2312yes—
98C2×#634—24no—
99C2×#634C2312yes—
100C2×#634C2312yes—
101C2×C3×#67C2314yes—
102C2×C3×#67C2312yes—
103C2×C3×#67C2314yes—
104C22×C3×Dic3C2311yescharacteristic
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×D3—24no—
114C2×C3×C4×D3C2312yes—
115C2×C3×C4×D3C2312yes—
116C2×C3×C4×D3C2312yes—
117C2×C3×C4×D3C2314yes—
118C2×C3×Dic6—28no—
119C2×C3×Dic6D418yescomplemented
120C2×C3×Dic6C2311yescharacteristic
121C2×C3×Dic6C2314yes—
122C2×C3×Dic6C2312yes—
123C2×C3×Dic6C2312yes—
124C2×#627—28no—
125C2×#627C2318yes—
126C2×#625C2314yes—
127C2×D3×Dic3—28no—
128C2×D3×Dic3C2318yes—
129D3×Dic6—216no—
130D3×Dic6—216no—
131#3757C2318yes—
132#3757C2312yes—
133C4⋊(C3⋊Dic3)C2312yes—
134#3750C2318yes—
135C4×C3⋊Dic3C2312yes—
136C3×#217C2312yes—
137C3×#217C2314yes—
138C3×(C2×D3)⋊C4C2314yes—
139C3×C4⋊Dic3C2312yes—
140C3×Dic3⋊C4C2314yes—
141C3×C4×Dic3C2312yes—
142#3724C2314yes—
143Dic3⋊Dic3C2318yes—
144Dic3⋊Dic3C2318yes—
145(C2×D3)⋊Dic3C2314yes—
146(C2×D3)⋊Dic3C2318yes—
147(C2×D3)⋊Dic3C2314yes—
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—32no—
161C23×C3×C4—31no—
162C23×Dic3—32no—
163#1010—28no—
164C2×D3×Q8—34no—
165C2×D3×Q8—34no—
166C2×D3×Q8—68no—
167C2×D3×Q8C2×D312yescomplemented
168C2×#237C2×D314yes—
169C2×#237C2×D312yescomplemented
170C2×#235C2×D311yescharacteristic
171C2×#235C2×D312yescomplemented
172C22×C4×D3—32no—
173C22×C4×D3C2×D311yescharacteristic
174C22×Dic6—31no—
175C22×Dic6—31no—
176C22×Dic6—32no—
177C22×Dic6—32no—
178C22×Dic6—34no—
179C22×Dic6—34no—
180C22×Dic6—61no—
181C22×Dic6—68no—
182C22×Dic6C2×D311yescharacteristic
183C22×Dic6C2×D312yescomplemented
184C3×#123—32no—
185C3×C22⋊Q8—32no—
186C3×#121—32no—
187C3×#120—32no—
188C3×C4×D4—34no—
189C3×#117—31no—
190#953—32no—
191#946—32no—
192#946—38no—
193#946C2×D312yes—
194Q8×Dic3—34no—
195Q8×Dic3—34no—
196#944—32no—
197#944—32no—
198#944—38no—
199#944—32no—
200#944—62no—
201#939—38no—
202#938—38no—
203#938—32no—
204#938C2×D312yes—
205#937—32no—
206#937C2×D312yes—
207#936—32no—
208#936—32no—
209#936—38no—
210#936—32no—
211#936—62no—
212#935—34no—
213#935—34no—
214#935—32no—
215#935—34no—
216#935—64no—
217#935C2×D312yes—
218D4×Dic3—38no—
219#930—32no—
220#929—32no—
221C4×#67—38no—
222C4×#67—34no—
223C4×#67—34no—
224C4×#67—38no—
225C4×#67C2×D314yes—
226#926—31no—
227#926—31no—
228#926—34no—
229#926—61no—
230#926C2×D311yescharacteristic
231#924—34no—
232#924—34no—
233#924—32no—
234#924—38no—
235#924—34no—
236#924—38no—
237#924—64no—
238#897—34no—
239#896—38no—
240#888—38no—
241#887—34no—
242#886—34no—
243#885—38no—
244#67⋊C4—38no—
245#878—38no—
246#878—38no—
247#877—34no—
248#875—32no—
249#869—32no—
250C4×Dic6—34no—
251C23×C32C2412yes—
252C23×C32C2411yescharacteristic
253C22×C3×D3—22no—
254C22×C3×D3—24no—
255C22×C3×D3C2412yes—
256C22×C3×D3C2412yes—
257C32×Q8—22no—
258C32×D4—24no—
259C32×D4—22no—
260C2×C32×C4—24no—
261C2×C32×C4C2×D414yes—
262C2×C32×C4C2412yes—
263C2×C32×C4C2411yescharacteristic
264C2×C32×C4C2411yescharacteristic
265C2×C3⋊Dic3—24no—
266C2×C3⋊Dic3C2414yes—
267C2×C3⋊Dic3C2414yes—
268#634—24no—
269#634—24no—
270C3×#67—24no—
271C3×#67—28no—
272C3×#67—28no—
273C2×C3×Dic3—22no—
274C2×C3×Dic3—28no—
275C2×C3×Dic3C2×D418yes—
276C2×C3×Dic3C2414yes—
277C2×C3×Dic3C2412yes—
278C2×C3×Dic3C2412yes—
279C2×C3×Dic3C2414yes—
280C3×D12—22no—
281C3×C4×D3—24no—
282C3×C4×D3—24no—
283C3×C4×D3—24no—
284C3×C4×D3—28no—
285C3×Dic6—22no—
286C3×Dic6—28no—
287C3×Dic6C2×D418yes—
288C3×Dic6C2×D418yes—
289#627—216no—
290#625—28no—
291D3×Dic3—216no—
292C2×2−1+4—31no—
293C23×Q8—91no—
294D4×Q8—94no—
295D4×Q8—94no—
296#548—94no—
297#548—94no—
298#536—91no—
299#536—94no—
300#536—91no—
301#525—31no—
302#525—94no—
303#525—91no—
304#519—91no—
305C24×C3—31no—
306C23×D3C22×D311yescharacteristic
307C3×#41—24no—
308C3×#41—24no—
309C3×#41—44no—
310C3×#41—68no—
311C3×#41—616no—
312C3×#41—68no—
313C3×#41—64no—
314C2×C3×Q8—21no—
315C2×C3×Q8—38no—
316C2×C3×Q8—32no—
317C2×C3×Q8—32no—
318C2×C3×Q8—34no—
319C2×C3×Q8—31no—
320C2×C3×Q8—68no—
321C2×C3×Q8—68no—
322C2×C3×Q8C22×D311yescharacteristic
323C2×C3×Q8C22×D311yescharacteristic
324C2×C3×D4—22no—
325C2×C3×D4—21no—
326C2×C3×D4—34no—
327C2×C3×D4—32no—
328C2×C3×D4—34no—
329C2×C3×D4—31no—
330C2×C3×D4C22×D312yes—
331C2×C3×D4C22×D312yes—
332C2×C3×D4C22×D311yescharacteristic
333C2×C3×D4C22×D311yescharacteristic
334C22×C3×C4—21no—
335C22×C3×C4—22no—
336C22×C3×C4—32no—
337C22×C3×C4—34no—
338C22×C3×C4—31no—
339C22×C3×C4—34no—
340C22×C3×C4—32no—
341C22×C3×C4—32no—
342C22×C3×C4—32no—
343C22×C3×C4—64no—
344C22×C3×C4C22×D312yes—
345C22×C3×C4C22×D312yes—
346C22×C3×C4C22×D311yescharacteristic
347C22×C3×C4C22×D311yescharacteristic
348C2×#67—34no—
349C2×#67—34no—
350C2×#67C22×D314yes—
351C2×#67C22×D312yes—
352C2×#67C22×D314yes—
353C22×Dic3—32no—
354C22×Dic3—32no—
355C22×Dic3—38no—
356C22×Dic3—62no—
357C22×Dic3—68no—
358C22×Dic3C22×D314yes—
359C22×Dic3C22×D311yescharacteristic
360C22×Dic3C22×D312yes—
361D3×Q8—28no—
362D3×Q8—616no—
363D3×Q8—616no—
364#237—216no—
365#237—28no—
366#235—24no—
367#235—28no—
368C2×D12C22×D311yescharacteristic
369C2×C4×D3—24no—
370C2×C4×D3—38no—
371C2×C4×D3—68no—
372C2×C4×D3C22×D314yes—
373C2×C4×D3C22×D312yes—
374C2×C4×D3C22×D312yes—
375C2×C4×D3C22×D312yes—
376C2×Dic6—28no—
377C2×Dic6—32no—
378C2×Dic6—32no—
379C2×Dic6—32no—
380C2×Dic6—32no—
381C2×Dic6—38no—
382C2×Dic6—38no—
383C2×Dic6—62no—
384C2×Dic6—62no—
385C2×Dic6—68no—
386C2×Dic6—64no—
387C2×Dic6—64no—
388C2×Dic6—68no—
389C2×Dic6—616no—
390C2×Dic6—616no—
391C2×Dic6—124no—
392C2×Dic6#6718yescomplemented
393C2×Dic6C22×D311yescharacteristic
394C2×Dic6C22×D314yes—
395C2×Dic6C22×D312yes—
396C2×Dic6C22×D312yes—
397C3×C4⋊C4—32no—
398C3×C4⋊C4—34no—
399C3×C22⋊C4—32no—
400C3×C22⋊C4—34no—
401C3×C22⋊C4—34no—
402C3×C42—32no—
403#217—32no—
404#217—38no—
405#217—38no—
406#217—32no—
407#217—34no—
408#217—34no—
409#217—38no—
410#217—68no—
411#217—62no—
412#217C22×D314yes—
413#217C22×D312yes—
414(C2×D3)⋊C4—38no—
415(C2×D3)⋊C4—34no—
416(C2×D3)⋊C4—34no—
417(C2×D3)⋊C4C22×D314yes—
418C4⋊Dic3—32no—
419C4⋊Dic3—32no—
420C4⋊Dic3—38no—
421C4⋊Dic3—38no—
422C4⋊Dic3—62no—
423C4⋊Dic3C22×D312yes—
424Dic3⋊C4—38no—
425Dic3⋊C4—38no—
426Dic3⋊C4—38no—
427Dic3⋊C4—34no—
428Dic3⋊C4—38no—
429Dic3⋊C4—34no—
430Dic3⋊C4—68no—
431Dic3⋊C4C22×D314yes—
432C4×Dic3—32no—
433C4×Dic3—32no—
434C4×Dic3—38no—
435C4×Dic3—38no—
436C4×Dic3—62no—
437C4×Dic3C22×D312yes—
438C22×C32—22no—
439C22×C32—22no—
440C22×C32—24no—
441C22×C32C22×D412yes—
442C22×C32C2511yescharacteristic
443C2×C3×D3—28no—
444C2×C3×D3—22no—
445C2×C3×D3—22no—
446C2×C3×D3—22no—
447C2×C3×D3—24no—
448C2×C3×D32−1+414yescomplemented
449C32×C4—22no—
450C32×C4C22×D412yes—
451C32×C4C22×D412yes—
452C3⋊Dic3—24no—
453C3⋊Dic3—24no—
454C3×Dic3—22no—
455C3×Dic3—22no—
456C3×Dic3—24no—
457C3×Dic3C22×D418yes—
4582−1+4—68no—
459C2×#41—34no—
460C2×#41—32no—
461C2×#41—31no—
462C2×#41—32no—
463C2×#41D3211yescharacteristic
464C22×Q8—32no—
465C22×Q8—31no—
466C22×Q8—32no—
467C22×Q8—92no—
468C22×Q8—94no—
469C22×Q8—94no—
470C22×Q8—91no—
471C22×Q8—188no—
472C23×C4—31no—
473C23×C4—92no—
474C4⋊Q8—92no—
475C4⋊Q8—98no—
476C4⋊Q8—92no—
477#124—92no—
478#124—98no—
479#124—92no—
480#123—32no—
481#123—94no—
482#123—92no—
483#123—94no—
484C22⋊Q8—32no—
485C22⋊Q8—98no—
486C22⋊Q8—98no—
487C22⋊Q8—98no—
488C22⋊Q8—94no—
489C22⋊Q8—92no—
490C22⋊Q8—94no—
491#121—32no—
492#121—92no—
493#121—98no—
494#120—32no—
495#120—92no—
496C4×Q8—94no—
497C4×Q8—94no—
498C4×D4—34no—
499C4×D4—98no—
500C4×D4—94no—
501C4×D4—98no—
502#117—31no—
503#117—94no—
504#117—91no—
505C23×C3—21no—
506C23×C3—22no—
507C23×C3—32no—
508C23×C3—32no—
509C23×C3—64no—
510C23×C3—62no—
511C23×C3C23×D312yes—
512C23×C3C23×D312yes—
513C23×C3C23×D311yescharacteristic
514C23×C3C23×D311yescharacteristic
515C22×D3—22no—
516C22×D3—24no—
517C22×D3C23×D312yes—
518C22×D3C23×D312yes—
519C3×Q8—22no—
520C3×Q8—22no—
521C3×Q8—38no—
522C3×Q8—38no—
523C3×Q8—42no—
524C3×Q8—68no—
525C3×Q8—62no—
526C3×D4—24no—
527C3×D4—24no—
528C3×D4—22no—
529C3×D4—22no—
530C3×D4—42no—
531C3×D4—44no—
532C3×D4—68no—
533C3×D4—68no—
534C3×D4—64no—
535C3×D4—62no—
536C2×C3×C4—24no—
537C2×C3×C4—24no—
538C2×C3×C4—21no—
539C2×C3×C4—21no—
540C2×C3×C4—22no—
541C2×C3×C4—24no—
542C2×C3×C4—38no—
543C2×C3×C4—34no—
544C2×C3×C4—34no—
545C2×C3×C4—32no—
546C2×C3×C4—32no—
547C2×C3×C4—44no—
548C2×C3×C4—68no—
549C2×C3×C4—68no—
550C2×C3×C4—62no—
551C2×C3×C4—64no—
552C2×C3×C4—64no—
553C2×C3×C4—64no—
554C2×C3×C4D3×D414yes—
555C2×C3×C4C2×#6714yes—
556C2×C3×C4C23×D312yes—
557C2×C3×C4C23×D312yes—
558C2×C3×C4C23×D311yescharacteristic
559C2×C3×C4C23×D311yescharacteristic
560C2×C3×C4C23×D311yescharacteristic
561C2×C3×C4C23×D311yescharacteristic
562#67—24no—
563#67—28no—
564#67—28no—
565#67—68no—
566#67—68no—
567C2×Dic3—22no—
568C2×Dic3—28no—
569C2×Dic3—34no—
570C2×Dic3—34no—
571C2×Dic3—34no—
572C2×Dic3—34no—
573C2×Dic3—64no—
574C2×Dic3—64no—
575C2×Dic3—64no—
576C2×Dic3—64no—
577C2×Dic3—616no—
578C2×Dic3—124no—
579C2×Dic3C2×#6718yes—
580C2×Dic3C23×D314yes—
581C2×Dic3C23×D312yes—
582C2×Dic3C23×D312yes—
583C2×Dic3C23×D314yes—
584D12—22no—
585C4×D3—24no—
586C4×D3—24no—
587C4×D3—24no—
588C4×D3—28no—
589C4×D3—616no—
590Dic6—22no—
591Dic6—28no—
592Dic6—616no—
593Dic6—64no—
594Dic6—64no—
595Dic6—64no—
596Dic6—64no—
597Dic6—616no—
598Dic6—124no—
599Dic6—124no—
600Dic6C2×#6718yes—
601Dic6C2×#6718yes—
602C2×C32—22no—
603C2×C32—42no—
604C2×C32C23×D411yescharacteristic
605C2×C32C2×2−1+412yes—
606C3×D3—24no—
607C3×D3—42no—
608C24—31no—
609#41—24no—
610#41—68no—
611#41—616no—
612#41—68no—
613#41—64no—
614C2×Q8—32no—
615C2×Q8—32no—
616C2×Q8—34no—
617C2×Q8—31no—
618C2×Q8—38no—
619C2×Q8—68no—
620C2×Q8—68no—
621C2×Q8—98no—
622C2×Q8—92no—
623C2×Q8—92no—
624C2×Q8—188no—
625C2×Q8—1816no—
626C2×Q8—1816no—
627C2×Q8—184no—
628C2×Q8C2×D3211yescharacteristic
629C2×D4—34no—
630C2×D4—32no—
631C2×D4—34no—
632C2×D4—31no—
633C2×D4—94no—
634C2×D4C2×D3212yes—
635C2×D4C2×D3211yescharacteristic
636C22×C4—32no—
637C22×C4—34no—
638C22×C4—31no—
639C22×C4—32no—
640C22×C4—32no—
641C22×C4—34no—
642C22×C4—32no—
643C22×C4—64no—
644C22×C4—98no—
645C22×C4—92no—
646C22×C4—188no—
647C22×C4C2×D3212yes—
648C22×C4C2×D3211yescharacteristic
649C4⋊C4—32no—
650C4⋊C4—34no—
651C4⋊C4—98no—
652C4⋊C4—94no—
653C4⋊C4—98no—
654C4⋊C4—92no—
655C4⋊C4—98no—
656C22⋊C4—32no—
657C22⋊C4—34no—
658C22⋊C4—34no—
659C22⋊C4—94no—
660C22⋊C4—98no—
661C22⋊C4—94no—
662C22⋊C4—92no—
663C22⋊C4—98no—
664C42—32no—
665C42—98no—
666C42—92no—
667C22×C3—22no—
668C22×C3—22no—
669C22×C3—22no—
670C22×C3—24no—
671C22×C3—24no—
672C22×C3—22no—
673C22×C3—22no—
674C22×C3—21no—
675C22×C3—34no—
676C22×C3—42no—
677C22×C3—42no—
678C22×C3—44no—
679C22×C3—68no—
680C22×C3—62no—
681C22×C3—62no—
682C22×C3—62no—
683C22×C3—64no—
684C22×C3C2×D3×D412yes—
685C22×C3C22×#6712yes—
686C22×C3C24×D311yescharacteristic
687C22×C3C24×D311yescharacteristic
688C2×D3—28no—
689C2×D3—22no—
690C2×D3—22no—
691C2×D3—24no—
692C2×D3—22no—
693C2×D3#101014yescomplemented
694C3×C4—22no—
695C3×C4—22no—
696C3×C4—22no—
697C3×C4—22no—
698C3×C4—38no—
699C3×C4—42no—
700C3×C4—62no—
701C3×C4—64no—
702C3×C4—62no—
703C3×C4C2×D3×D412yes—
704C3×C4C2×D3×D412yes—
705C3×C4C22×#6712yes—
706C3×C4C22×#6712yes—
707Dic3—22no—
708Dic3—24no—
709Dic3—22no—
710Dic3—64no—
711Dic3—64no—
712Dic3—64no—
713Dic3—64no—
714Dic3—124no—
715Dic3—124no—
716Dic3C22×#6718yes—
717C32#348611yescharacteristic, complemented, Sylow
718C23—32no—
719C23—32no—
720C23—64no—
721C23—62no—
722C23C22×D3212yes—
723C23C22×D3211yescharacteristic
724Q8—22no—
725Q8—38no—
726Q8—38no—
727Q8—68no—
728Q8—62no—
729Q8—1816no—
730Q8—184no—
731Q8—184no—
732D4—24no—
733D4—22no—
734D4—68no—
735D4—68no—
736D4—64no—
737D4—62no—
738D4—188no—
739C2×C4—24no—
740C2×C4—38no—
741C2×C4—34no—
742C2×C4—34no—
743C2×C4—32no—
744C2×C4—32no—
745C2×C4—68no—
746C2×C4—68no—
747C2×C4—62no—
748C2×C4—64no—
749C2×C4—64no—
750C2×C4—64no—
751C2×C4—94no—
752C2×C4—94no—
753C2×C4—1816no—
754C2×C4—184no—
755C2×C4D3×#6714yes—
756C2×C4C22×D3212yes—
757C2×C4C22×D3211yescharacteristic
758C2×C4C22×D3211yescharacteristic
759C2×C3—22no—
760C2×C3—22no—
761C2×C3—22no—
762C2×C3—21no—
763C2×C3—42no—
764C2×C3—42no—
765C2×C3—42no—
766C2×C3—64no—
767C2×C3—82no—
768C2×C3—122no—
769C2×C3C22×D3×D411yescharacteristic
770C2×C3C2×#101012yes—
771C2×C3D3×2−1+412yes—
772C2×C3C23×#6711yescharacteristic
773D3—24no—
774D3—42no—
775C22—22no—
776C22—24no—
777C22—22no—
778C22—34no—
779C22—68no—
780C22—62no—
781C22—62no—
782C22—64no—
783C22—62no—
784C22C2×D3×#6712yes—
785C22C23×D3211yescharacteristic
786C4—22no—
787C4—38no—
788C4—64no—
789C4—62no—
790C4—62no—
791C4—184no—
792C4—184no—
793C4C2×D3×#6712yes—
794C4C2×D3×#6712yes—
795C3—21no—
796C3#8602211yescharacteristic, complemented
797C3#8729411yescharacteristic, complemented
798C2—22no—
799C2—42no—
800C2—64no—
801C2—122no—
802C2D3×#101012yes—
803C2C22×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×D3×Dic6C2semidirect
3. #10596296C2semidirect
4. C3×#5828C2semidirect
5. #10595400C2semidirect
6. #10595270C2semidirect
7. #10595157C2semidirect
8. #10595154C2semidirect
9. #10595022C2semidirect
10. #10594899C2semidirect
11. Dic6×#67C2semidirect
12. #10594856C2semidirect
13. #10594818C2semidirect
19. C2×C3×D3×Q8C22semidirect
21. C2×C3×#237C22semidirect
23. C2×C3×#235C22semidirect
26. C22×C3×Dic6C22semidirect
32. #64153C22semidirect
33. #64145C22semidirect
36. #64133C22semidirect
46. #63964C22semidirect
49. #63959C22semidirect
55. #63866C22semidirect
56. #63860C22semidirect
57. #63857C22semidirect
59. #63851C22semidirect
60. #63843C22semidirect
61. Dic3×Dic6C22semidirect
62. #63839C22semidirect
64. C2×#1010D3semidirect
72. #5828D3semidirect
119. C2×C3×Dic6D4semidirect
167. C2×D3×Q8C2×D3semidirect
169. C2×#237C2×D3semidirect
171. C2×#235C2×D3semidirect
183. C22×Dic6C2×D3semidirect
392. C2×Dic6#67semidirect
448. C2×C3×D32−1+4semidirect
693. C2×D3#1010semidirect
717. C32#3486semidirect
796. C3#86022semidirect
797. 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×D3×Dic62
#105962962
C3×#58282
#105954002
#105952702
#105951572
#105951542
#105950222
#105948992
Dic6×#672
#105948562
#105948182
#872943
#860223