Finite Group Databasebeta

← #11904509

Subgroups — #11904509

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×#64297C211yesmaximal, characteristic, complemented
2C22×D3×Dic6C211yesmaximal, characteristic, complemented
3#10595997C211yesmaximal, characteristic, complemented
4C3×#5524C211yesmaximal, characteristic, complemented
5C3×#5516C211yesmaximal, characteristic, complemented
6#10595023C211yesmaximal, characteristic, complemented
7#10594856C211yesmaximal, characteristic, complemented
8#10594383C214yesmaximal, complemented
9#10594382C214yesmaximal, complemented
10#10594081C214yesmaximal, complemented
11#10594078C214yesmaximal, complemented
12#10593899C214yesmaximal, complemented
13Dic6×D12C214yesmaximal, complemented
14#86022—31nomaximal
15#85881—31nomaximal
16C2×#3828C2211yescharacteristic
17C22×#634C2211yescharacteristic
18C2×C3×#235C2211yescharacteristic
19C22×C3×C4×D3C2211yescharacteristic
20C22×C3×Dic6C2211yescharacteristic
21C22×#627C2212yes—
22C2×#3804C2214yes—
23C22×D3×Dic3C2212yes—
24C2×#3799C2212yescomplemented
25C2×#3797C2212yescomplemented
26#64297—28no—
27C2×#3796C2212yescomplemented
28C2×D3×Dic6—28no—
29C2×D3×Dic6C2214yes—
30C2×D3×Dic6C2214yes—
31C2×D3×Dic6C2212yescomplemented
32C32×#117C2211yescharacteristic
33#64106C2214yescomplemented
34#64095C2214yes—
35#64084C2212yescomplemented
36#64078C2212yescomplemented
37C3×#926C2211yescharacteristic
38C3×#897C2212yes—
39C3×#895C2212yes—
40C3×#887C2214yescomplemented
41C3×#886C2212yes—
42C3×#882C2212yes—
43C3×#877C2214yes—
44C3×C4×D12C2214yes—
45C3×C4×Dic6C2214yescomplemented
46#63977C2212yes—
47#63966C2212yes—
48#63962C2214yes—
49#63918C2218yescomplemented
50#63909C2212yes—
51C4×#626C2214yes—
52#63895C2218yescomplemented
53#63893C2218yes—
54#63893C2218yescomplemented
55Dic3×D12C2218yes—
56#63886C2218yes—
57#63880C2218yes—
58#63866C2212yescomplemented
59#63860C2212yescomplemented
60#63857C2212yes—
61#63857C2214yescomplemented
62#63852C2218yescomplemented
63C2×#1010—31no—
64C2×#1007—31no—
65C22×D3×Q8—31no—
66C23×Dic6—31no—
67C3×#525—31no—
68C3×#519—31no—
69#5825—31no—
70#5791—31no—
71#5648—34no—
72#5632—34no—
73#5598—34no—
74#5586—34no—
75#5576—34no—
76#5576—34no—
77Q8×D12—34no—
78Q8×D12—34no—
79#5552—34no—
80D4×Dic6—34no—
81#5526—31no—
82#5526—31no—
83#5526—31no—
84#5526—34no—
85#5526—61no—
86#5524—31no—
87#5524—34no—
88#5524D311yescharacteristic, complemented
89#5516D311yescharacteristic, complemented
90C23×C3×D3C2311yescharacteristic
91C22×C32×C4C2311yescharacteristic
92C2×#638C2312yes—
93C22×C3⋊Dic3C2312yes—
94#3828—24no—
95C2×C4⋊(C3⋊D3)C2311yescharacteristic
96C2×C4×C3⋊D3C2312yes—
97C2×#634—24no—
98C2×#634C2312yes—
99C2×#634C2312yes—
100C2×#634C2311yescharacteristic
101C2×C3×#67C2312yes—
102C22×C3×Dic3C2311yescharacteristic
103C22×C3×Dic3C2312yes—
104C3×#235—24no—
105C2×C3×D12C2314yes—
106C2×C3×D12C2311yescharacteristic
107C2×C3×C4×D3—24no—
108C2×C3×C4×D3C2312yes—
109C2×C3×C4×D3C2312yes—
110C2×C3×C4×D3C2312yes—
111C2×C3×Dic6D418yescomplemented
112C2×C3×Dic6C2311yescharacteristic
113C2×C3×Dic6C2312yes—
114C2×C3×Dic6C2312yes—
115C2×#627—28no—
116C2×#627C2318yes—
117C2×#627C2314yes—
118C2×#626C2314yes—
119C2×#626C2314yes—
120C2×#624C2314yes—
121#3804—216no—
122C2×D3×Dic3—28no—
123C2×D3×Dic3C2318yes—
124C2×D3×Dic3C2314yes—
125#3799—28no—
126#3797—28no—
127#3796—28no—
128D3×Dic6—216no—
129D3×Dic6—216no—
130D3×Dic6—28no—
131C32×C4⋊C4C2312yes—
132C32×C22⋊C4C2312yes—
133C32×C42C2312yes—
134#3752C2318yes—
135C4⋊(C3⋊Dic3)C2318yes—
136C3×#217C2312yes—
137C3×(C2×D3)⋊C4C2314yes—
138C3×(C2×D3)⋊C4C2314yes—
139C3×C4⋊Dic3C2314yes—
140C3×C4⋊Dic3C2312yes—
141C3×Dic3⋊C4C2318yes—
142C3×C4×Dic3C2318yes—
143C3×C4×Dic3C2312yes—
144Dic3⋊Dic3C2314yes—
145Dic3⋊Dic3C2318yes—
146#3722C2314yes—
147(C2×D3)⋊Dic3C2318yes—
148(C2×D3)⋊Dic3C2314yes—
149#3486—91noSylow
150C2×C3×#41—31no—
151C22×C3×Q8—31no—
152C23×C3×C4—31no—
153C23×Dic3—32no—
154#1010—68no—
155#1007—68no—
156C2×#239—32no—
157C2×#239—32no—
158C2×D3×Q8—34no—
159C2×D3×Q8—34no—
160C2×D3×Q8—32no—
161C2×D3×Q8—32no—
162C2×D3×Q8—32no—
163C2×D3×Q8—68no—
164C2×#237—34no—
165C2×#237—32no—
166C2×#235—31no—
167C2×#235—31no—
168C2×#235—34no—
169C2×#235—32no—
170C2×#235—61no—
171C2×#235C2×D311yescharacteristic
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—32no—
181C22×Dic6—61no—
182C22×Dic6—68no—
183C22×Dic6C2×D311yescharacteristic
184C3×#123—32no—
185C3×C22⋊Q8—32no—
186C3×#121—32no—
187C3×#120—32no—
188C3×C4×Q8—34no—
189C3×C4×Q8—34no—
190C3×C4×D4—34no—
191C3×#117—21no—
192C3×#117—31no—
193C3×#117—34no—
194C3×#117C2×D311yescharacteristic
195C3×#117C2×D311yescharacteristic
196#953—32no—
197#944—32no—
198#939—38no—
199#936—32no—
200#935—34no—
201D4×Dic3—38no—
202#930—32no—
203#929—32no—
204C4×#67—34no—
205#926C2×D311yescharacteristic
206#924—32no—
207#924—34no—
208#897—32no—
209#897—34no—
210#897—34no—
211#897—34no—
212#897—38no—
213#897—38no—
214#897—38no—
215#897—64no—
216#897C2×D312yes—
217#896—38no—
218#895—38no—
219#895—32no—
220#895C2×D312yes—
221#888—38no—
222#887C2×D314yescomplemented
223#886—34no—
224#886—32no—
225#886—34no—
226#886—34no—
227#886—64no—
228#886C2×D312yes—
229#885—38no—
230#882—32no—
231#882C2×D312yes—
232#67⋊C4—38no—
233#878—38no—
234#878—38no—
235#877C2×D314yes—
236#875—32no—
237#875—32no—
238#875—32no—
239#875—38no—
240#875—62no—
241C4×D12—38no—
242C4×D12—34no—
243C4×D12—38no—
244C4×D12C2×D314yes—
245#869—32no—
246#869—32no—
247#869—32no—
248#869—38no—
249#869—62no—
250C4×Dic6C2×D314yescomplemented
251C23×C32C2411yescharacteristic
252C22×C3⋊D3C2412yes—
253C22×C3×D3—22no—
254C22×C3×D3—24no—
255C22×C3×D3C2412yes—
256C22×C3×D3C2412yes—
257C2×C32×C4C2×D414yes—
258C2×C32×C4C2414yes—
259C2×C32×C4C2411yescharacteristic
260C2×C32×C4C2411yescharacteristic
261#638—24no—
262C2×C3⋊Dic3—24no—
263C2×C3⋊Dic3C2412yes—
264C2×C3⋊Dic3C2414yes—
265C4⋊(C3⋊D3)—22no—
266C4×C3⋊D3—24no—
267#634—24no—
268#634—24no—
269#634—22no—
270C3×#67—24no—
271C2×C3×Dic3—22no—
272C2×C3×Dic3C2×D418yes—
273C2×C3×Dic3C2414yes—
274C2×C3×Dic3C2412yes—
275C2×C3×Dic3C2412yes—
276C2×C3×Dic3C2414yes—
277C3×D12—28no—
278C3×D12—22no—
279C3×C4×D3—24no—
280C3×C4×D3—24no—
281C3×C4×D3—24no—
282C3×Dic6—22no—
283C3×Dic6C2×D418yes—
284C3×Dic6C2×D418yes—
285#627—216no—
286#627—28no—
287#626—28no—
288#626—28no—
289#624—28no—
290D3×Dic3—216no—
291D3×Dic3—28no—
292C2×2−1+4—91no—
293C23×Q8—91no—
294D4×Q8—94no—
295D4×Q8—94no—
296#548—94no—
297#548—94no—
298#536—94no—
299#536—91no—
300#536—91no—
301#525—31no—
302#525—94no—
303#525—91no—
304#519—31no—
305C24×C3—31no—
306C23×D3C22×D311yescharacteristic
307C3×#41—64no—
308C2×C3×Q8—38no—
309C2×C3×Q8—32no—
310C2×C3×Q8—32no—
311C2×C3×Q8—31no—
312C2×C3×D4—32no—
313C2×C3×D4—34no—
314C2×C3×D4—31no—
315C22×C3×C4—21no—
316C22×C3×C4—32no—
317C22×C3×C4—31no—
318C22×C3×C4—32no—
319C22×C3×C4—32no—
320C22×C3×C4—32no—
321C22×C3×C4—64no—
322C22×C3×C4C22×D311yescharacteristic
323C22×C3×C4C22×D311yescharacteristic
324C2×#67—32no—
325C2×#67—32no—
326C2×#67—34no—
327C2×#67—34no—
328C2×#67—62no—
329C2×#67C22×D312yes—
330C22×Dic3—32no—
331C22×Dic3—32no—
332C22×Dic3—34no—
333C22×Dic3—38no—
334C22×Dic3—62no—
335C22×Dic3—68no—
336C22×Dic3C22×D311yescharacteristic
337C22×Dic3C22×D312yes—
338#239—68no—
339#239—68no—
340D3×Q8—68no—
341D3×Q8—616no—
342D3×Q8—616no—
343D3×Q8—68no—
344D3×Q8—68no—
345#237—616no—
346#237—68no—
347#235—24no—
348#235—616no—
349#235—64no—
350#235—64no—
351#235—68no—
352#235—124no—
353C2×D12—34no—
354C2×D12—34no—
355C2×D12—31no—
356C2×D12—31no—
357C2×D12—61no—
358C2×D12C22×D314yes—
359C2×D12C22×D311yescharacteristic
360C2×C4×D3—24no—
361C2×C4×D3—38no—
362C2×C4×D3—34no—
363C2×C4×D3—32no—
364C2×C4×D3—32no—
365C2×C4×D3—34no—
366C2×C4×D3—34no—
367C2×C4×D3—62no—
368C2×C4×D3—68no—
369C2×C4×D3C22×D312yes—
370C2×C4×D3C22×D312yes—
371C2×C4×D3C22×D312yes—
372C2×Dic6—31no—
373C2×Dic6—31no—
374C2×Dic6—32no—
375C2×Dic6—32no—
376C2×Dic6—32no—
377C2×Dic6—32no—
378C2×Dic6—34no—
379C2×Dic6—38no—
380C2×Dic6—34no—
381C2×Dic6—38no—
382C2×Dic6—61no—
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—68no—
392C2×Dic6—124no—
393C2×Dic6D1218yescomplemented
394C2×Dic6C22×D311yescharacteristic
395C2×Dic6C22×D312yes—
396C2×Dic6C22×D312yes—
397C3×C4⋊C4—22no—
398C3×C4⋊C4—34no—
399C3×C4⋊C4—38no—
400C3×C4⋊C4—32no—
401C3×C4⋊C4C22×D312yes—
402C3×C4⋊C4C22×D312yes—
403C3×C22⋊C4—22no—
404C3×C22⋊C4—32no—
405C3×C22⋊C4—34no—
406C3×C22⋊C4—34no—
407C3×C22⋊C4C22×D312yes—
408C3×C22⋊C4C22×D312yes—
409C3×C42—22no—
410C3×C42—38no—
411C3×C42—32no—
412C3×C42C22×D312yes—
413C3×C42C22×D312yes—
414#217—34no—
415#217—38no—
416#217C22×D312yes—
417(C2×D3)⋊C4—34no—
418(C2×D3)⋊C4—38no—
419(C2×D3)⋊C4—38no—
420(C2×D3)⋊C4—38no—
421(C2×D3)⋊C4—34no—
422(C2×D3)⋊C4—34no—
423(C2×D3)⋊C4—68no—
424(C2×D3)⋊C4C22×D314yes—
425(C2×D3)⋊C4C22×D314yes—
426C4⋊Dic3—38no—
427C4⋊Dic3—38no—
428C4⋊Dic3—34no—
429C4⋊Dic3—38no—
430C4⋊Dic3—68no—
431C4⋊Dic3C22×D312yes—
432C4⋊Dic3C22×D314yes—
433Dic3⋊C4—34no—
434Dic3⋊C4—38no—
435Dic3⋊C4C22×D318yes—
436C4×Dic3C22×D318yes—
437C4×Dic3C22×D312yes—
438C22×C32—22no—
439C22×C32C22×D412yes—
440C22×C32C2511yescharacteristic
441C2×C3⋊D3—22no—
442C2×C3⋊D3—24no—
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—24no—
450C32×C4C22×D412yes—
451C32×C4C22×D412yes—
452C3⋊Dic3—24no—
453C3⋊Dic3—22no—
454C3×Dic3—22no—
455C3×Dic3—22no—
456C3×Dic3—24no—
457C3×Dic3C22×D418yes—
4582−1+4—188no—
459C2×#41—31no—
460C2×#41—94no—
461C2×#41—92no—
462C2×#41—92no—
463C2×#41—91no—
464C22×Q8—31no—
465C22×Q8—92no—
466C22×Q8—94no—
467C22×Q8—94no—
468C22×Q8—92no—
469C22×Q8—92no—
470C22×Q8—91no—
471C22×Q8—188no—
472C23×C4—31no—
473C23×C4—92no—
474C4⋊Q8—98no—
475C4⋊Q8—92no—
476C4⋊Q8—92no—
477#124—98no—
478#124—92no—
479#124—92no—
480#123—32no—
481#123—92no—
482#123—94no—
483#123—94no—
484C22⋊Q8—32no—
485C22⋊Q8—98no—
486C22⋊Q8—98no—
487C22⋊Q8—98no—
488C22⋊Q8—92no—
489C22⋊Q8—94no—
490C22⋊Q8—94no—
491#121—32no—
492#121—92no—
493#121—98no—
494#120—32no—
495#120—92no—
496C4×Q8—34no—
497C4×Q8—34no—
498C4×D4—34no—
499C4×D4—98no—
500C4×D4—94no—
501C4×D4—98no—
502#117—31no—
503#117—34no—
504#117D3211yescharacteristic
505C23×C3—21no—
506C23×C3—32no—
507C23×C3—32no—
508C23×C3—64no—
509C23×C3—62no—
510C23×C3C23×D311yescharacteristic
511C23×C3C23×D311yescharacteristic
512C22×D3—22no—
513C22×D3—24no—
514C22×D3—32no—
515C22×D3—32no—
516C22×D3—62no—
517C22×D3C23×D312yes—
518C22×D3C23×D312yes—
519C3×Q8—38no—
520C3×Q8—38no—
521C3×Q8—62no—
522C3×D4—68no—
523C3×D4—64no—
524C3×D4—62no—
525C2×C3×C4—21no—
526C2×C3×C4—21no—
527C2×C3×C4—24no—
528C2×C3×C4—24no—
529C2×C3×C4—38no—
530C2×C3×C4—34no—
531C2×C3×C4—32no—
532C2×C3×C4—32no—
533C2×C3×C4—34no—
534C2×C3×C4—62no—
535C2×C3×C4—64no—
536C2×C3×C4—64no—
537C2×C3×C4—64no—
538C2×C3×C4C2×D1214yes—
539C2×C3×C4D3×D414yes—
540C2×C3×C4C23×D314yes—
541C2×C3×C4C23×D314yes—
542C2×C3×C4C23×D311yescharacteristic
543C2×C3×C4C23×D311yescharacteristic
544C2×C3×C4C23×D311yescharacteristic
545C2×C3×C4C23×D311yescharacteristic
546#67—24no—
547#67—68no—
548#67—64no—
549#67—64no—
550#67—68no—
551#67—124no—
552C2×Dic3—22no—
553C2×Dic3—32no—
554C2×Dic3—34no—
555C2×Dic3—32no—
556C2×Dic3—34no—
557C2×Dic3—62no—
558C2×Dic3—64no—
559C2×Dic3—64no—
560C2×Dic3—64no—
561C2×Dic3—616no—
562C2×Dic3—68no—
563C2×Dic3—124no—
564C2×Dic3C2×D1218yes—
565C2×Dic3C23×D314yes—
566C2×Dic3C23×D312yes—
567C2×Dic3C23×D312yes—
568C2×Dic3C23×D314yes—
569D12—28no—
570D12—22no—
571D12—68no—
572D12—68no—
573D12—62no—
574D12—62no—
575D12—122no—
576C4×D3—24no—
577C4×D3—24no—
578C4×D3—24no—
579C4×D3—68no—
580C4×D3—616no—
581C4×D3—68no—
582C4×D3—64no—
583C4×D3—64no—
584C4×D3—68no—
585C4×D3—124no—
586Dic6—22no—
587Dic6—616no—
588Dic6—68no—
589Dic6—64no—
590Dic6—64no—
591Dic6—62no—
592Dic6—64no—
593Dic6—64no—
594Dic6—62no—
595Dic6—616no—
596Dic6—68no—
597Dic6—124no—
598Dic6—124no—
599Dic6—122no—
600Dic6C2×D1218yes—
601Dic6C2×D1218yes—
602C2×C32—22no—
603C2×C32C23×D411yescharacteristic
604C2×C32C2×2−1+412yes—
605C3⋊D3—42no—
606C3×D3—24no—
607C3×D3—42no—
608C24—31no—
609#41—64no—
610#41—1816no—
611#41—188no—
612#41—188no—
613#41—184no—
614C2×Q8—32no—
615C2×Q8—32no—
616C2×Q8—31no—
617C2×Q8—38no—
618C2×Q8—98no—
619C2×Q8—94no—
620C2×Q8—92no—
621C2×Q8—92no—
622C2×Q8—91no—
623C2×Q8—188no—
624C2×Q8—1816no—
625C2×Q8—1816no—
626C2×Q8—188no—
627C2×Q8—188no—
628C2×Q8—184no—
629C2×D4—32no—
630C2×D4—34no—
631C2×D4—31no—
632C2×D4—94no—
633C2×D4—94no—
634C2×D4—92no—
635C2×D4—91no—
636C22×C4—32no—
637C22×C4—31no—
638C22×C4—32no—
639C22×C4—32no—
640C22×C4—32no—
641C22×C4—64no—
642C22×C4—94no—
643C22×C4—98no—
644C22×C4—94no—
645C22×C4—92no—
646C22×C4—92no—
647C22×C4—188no—
648C22×C4C2×D3211yescharacteristic
649C4⋊C4—38no—
650C4⋊C4—32no—
651C4⋊C4—34no—
652C4⋊C4—94no—
653C4⋊C4—98no—
654C4⋊C4—98no—
655C4⋊C4C2×D3212yes—
656C22⋊C4—32no—
657C22⋊C4—34no—
658C22⋊C4—34no—
659C22⋊C4—94no—
660C22⋊C4—94no—
661C22⋊C4—98no—
662C22⋊C4—98no—
663C22⋊C4C2×D3212yes—
664C42—38no—
665C42—32no—
666C42C2×D3212yes—
667C22×C3—22no—
668C22×C3—22no—
669C22×C3—22no—
670C22×C3—21no—
671C22×C3—34no—
672C22×C3—42no—
673C22×C3—68no—
674C22×C3—62no—
675C22×C3—62no—
676C22×C3—62no—
677C22×C3—64no—
678C22×C3C22×D1212yes—
679C22×C3C2×D3×D412yes—
680C22×C3C24×D311yescharacteristic
681C22×C3C24×D311yescharacteristic
682C2×D3—28no—
683C2×D3—22no—
684C2×D3—22no—
685C2×D3—22no—
686C2×D3—24no—
687C2×D3—62no—
688C2×D3—62no—
689C2×D3—64no—
690C2×D3—64no—
691C2×D3—122no—
692C2×D3—124no—
693C2×D3#101014yescomplemented
694C3×C4—24no—
695C3×C4—24no—
696C3×C4—22no—
697C3×C4—22no—
698C3×C4—38no—
699C3×C4—44no—
700C3×C4—62no—
701C3×C4—62no—
702C3×C4—64no—
703C3×C4C22×D1212yes—
704C3×C4C22×D1212yes—
705C3×C4C2×D3×D412yes—
706C3×C4C2×D3×D412yes—
707Dic3—22no—
708Dic3—22no—
709Dic3—24no—
710Dic3—64no—
711Dic3—62no—
712Dic3—64no—
713Dic3—62no—
714Dic3—124no—
715Dic3—122no—
716Dic3C22×D1218yes—
717C32#348611yescharacteristic, complemented, Sylow
718C23—32no—
719C23—32no—
720C23—64no—
721C23—62no—
722C23—92no—
723C23C22×D3211yescharacteristic
724Q8—38no—
725Q8—38no—
726Q8—62no—
727Q8—1816no—
728Q8—188no—
729Q8—184no—
730Q8—184no—
731Q8—182no—
732D4—68no—
733D4—64no—
734D4—62no—
735D4—188no—
736D4—188no—
737D4—184no—
738D4—182no—
739C2×C4—38no—
740C2×C4—34no—
741C2×C4—34no—
742C2×C4—32no—
743C2×C4—32no—
744C2×C4—62no—
745C2×C4—64no—
746C2×C4—64no—
747C2×C4—64no—
748C2×C4—94no—
749C2×C4—92no—
750C2×C4—188no—
751C2×C4—1816no—
752C2×C4—188no—
753C2×C4—184no—
754C2×C4—184no—
755C2×C4D3×D1214yes—
756C2×C4C22×D3214yes—
757C2×C4C22×D3211yescharacteristic
758C2×C4C22×D3211yescharacteristic
759C2×C3—22no—
760C2×C3—22no—
761C2×C3—21no—
762C2×C3—22no—
763C2×C3—42no—
764C2×C3—64no—
765C2×C3—122no—
766C2×C3C23×D1211yescharacteristic
767C2×C3C22×D3×D411yescharacteristic
768C2×C3C2×#101012yes—
769C2×C3D3×2−1+412yes—
770D3—24no—
771D3—42no—
772D3—122no—
773D3—122no—
774D3—242no—
775C22—22no—
776C22—34no—
777C22—68no—
778C22—62no—
779C22—62no—
780C22—62no—
781C22—64no—
782C22—182no—
783C22—184no—
784C22C2×D3×D1212yes—
785C22C23×D3211yescharacteristic
786C4—24no—
787C4—38no—
788C4—62no—
789C4—62no—
790C4—64no—
791C4—182no—
792C4—184no—
793C4C2×D3×D1212yes—
794C4C2×D3×D1212yes—
795C3—21no—
796C3#8588111yescharacteristic, complemented
797C3#8602211yescharacteristic, complemented
798C2—22no—
799C2—64no—
800C2—122no—
801C2—362no—
802C2C22×D3×D1211yescharacteristic
803C2D3×#101012yes—
subgroupG/H
center, FrattiniC22C23×D32
commutator, socle, cosocleC22×C32C25
FittingC32×#117C22
hypercenter#117D32
hypocenterC32#3486
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C22 ◁ #117

Complements

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

NH ≅ G/Ntype
1. C2×#64297C2semidirect
2. C22×D3×Dic6C2semidirect
3. #10595997C2semidirect
4. C3×#5524C2semidirect
5. C3×#5516C2semidirect
6. #10595023C2semidirect
7. #10594856C2semidirect
8. #10594383C2semidirect
9. #10594382C2semidirect
10. #10594081C2semidirect
11. #10594078C2semidirect
12. #10593899C2semidirect
13. Dic6×D12C2semidirect
24. C2×#3799C22semidirect
25. C2×#3797C22semidirect
27. C2×#3796C22semidirect
31. C2×D3×Dic6C22semidirect
33. #64106C22semidirect
35. #64084C22semidirect
36. #64078C22semidirect
40. C3×#887C22semidirect
45. C3×C4×Dic6C22semidirect
49. #63918C22semidirect
52. #63895C22semidirect
54. #63893C22semidirect
58. #63866C22semidirect
59. #63860C22semidirect
61. #63857C22semidirect
62. #63852C22semidirect
88. #5524D3semidirect
89. #5516D3semidirect
111. C2×C3×Dic6D4semidirect
222. #887C2×D3semidirect
250. C4×Dic6C2×D3semidirect
393. C2×Dic6D12semidirect
448. C2×C3×D32−1+4semidirect
693. C2×D3#1010semidirect
717. C32#3486semidirect
796. C3#85881semidirect
797. C3#86022semidirect

Maximal subgroups

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

subgroupindex
C2×#642972
C22×D3×Dic62
#105959972
C3×#55242
C3×#55162
#105950232
#105948562
#105943832
#105943822
#105940812
#105940782
#105938992
Dic6×D122
#860223
#858813