Finite Group Databasebeta

← #11904505

Subgroups — #11904505

Order 1152.

3381 conjugacy classes of subgroups.

The subgroup lattice has 828 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#64367C211yesmaximal, characteristic, complemented
2C22×D3×Dic6C211yesmaximal, characteristic, complemented
3C3×#5828C211yesmaximal, characteristic, complemented
4C3×#5825C211yesmaximal, characteristic, complemented
5#10595361C214yesmaximal, complemented
6#10595271C214yesmaximal, complemented
7#10595161C214yesmaximal, complemented
8#10595160C214yesmaximal, complemented
9#10595023C211yesmaximal, characteristic, complemented
10#10594916C214yesmaximal, complemented
11#10594915C214yesmaximal, complemented
12#10594866C211yesmaximal, characteristic, complemented
13#10594828C211yesmaximal, characteristic, complemented
14#86355—31nomaximal
15#86022—31nomaximal
16C2×C32×#41C2211yescharacteristic
17#64367—28no—
18C2×Q8×C3⋊D3C2212yescomplemented
19C2×#3830C2214yes—
20C2×#3830C2212yescomplemented
21C2×#3828C2211yescharacteristic
22C2×#3828C2212yescomplemented
23C22×#634C2211yescharacteristic
24C22×#634C2212yescomplemented
25C22×C3×C4×D3C2211yescharacteristic
26C22×C3×Dic6C2211yescharacteristic
27C22×#627C2212yes—
28C22×D3×Dic3C2212yes—
29C2×D3×Dic6—28no—
30C2×D3×Dic6C2214yes—
31C2×D3×Dic6C2214yes—
32C3×#946C2212yes—
33C3×#944C2212yescomplemented
34C3×#938C2212yes—
35C3×#937C2212yes—
36C3×#936C2212yescomplemented
37C3×#935C2214yes—
38C3×#935C2212yes—
39C3×C4×#67C2214yes—
40C3×#926C2211yescharacteristic
41C3×#926C2211yescharacteristic
42C3×#924C2214yescomplemented
43#63982C2218yescomplemented
44#63977C2212yes—
45#67⋊Dic3C2218yes—
46#63971C2218yes—
47#63966C2214yes—
48#63966C2212yes—
49#63957C2214yes—
50#63953C2218yescomplemented
51#63909C2212yes—
52C4×#626C2214yes—
53#63896C2218yes—
54#63881C2218yes—
55#63871C2214yescomplemented
56#63866C2212yescomplemented
57#63865C2218yescomplemented
58#63864C2212yescomplemented
59#63857C2212yes—
60#63844C2214yescomplemented
61#63844C2214yescomplemented
62#63840C2218yescomplemented
63C2×#1010—31no—
64C2×#1010—31no—
65C2×#1010—61no—
66C22×D3×Q8—31no—
67C23×Dic6—31no—
68C3×#536—31no—
69C3×#525—31no—
70#5828D311yescharacteristic, complemented
71#5825D311yescharacteristic, complemented
72#5816—31no—
73#5791—31no—
74#5727—34no—
75#5677—34no—
76#5656—34no—
77#5648—34no—
78#5648—34no—
79#5633—34no—
80#5632—34no—
81#5632—34no—
82#5598—34no—
83#5586—34no—
84#5552—34no—
85D4×Dic6—34no—
86#5526—31no—
87#5524—31no—
88#5516—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×#638C2312yes—
98C2×#638C2314yes—
99C22×C3⋊Dic3C2314yes—
100C22×C3⋊Dic3C2312yes—
101Q8×C3⋊D3—28no—
102#3830—216no—
103#3830—28no—
104#3828—24no—
105#3828—28no—
106C2×C4⋊(C3⋊D3)C2311yescharacteristic
107C2×C4×C3⋊D3C2312yes—
108C2×C4×C3⋊D3C2314yes—
109C2×#634—28no—
110C2×#634D418yescomplemented
111C2×#634C2314yes—
112C2×#634C2311yescharacteristic
113C2×#634C2312yes—
114C2×#634C2312yes—
115C2×C3×#67C2314yes—
116C22×C3×Dic3C2312yes—
117C22×C3×Dic3C2311yescharacteristic
118C2×C3×C4×D3—24no—
119C2×C3×C4×D3C2312yes—
120C2×C3×C4×D3C2312yes—
121C2×C3×Dic6—24no—
122C2×C3×Dic6C2312yes—
123C2×C3×Dic6C2312yes—
124C2×#627—28no—
125C2×#627C2318yes—
126C2×#626C2314yes—
127C2×D3×Dic3—28no—
128C2×D3×Dic3C2318yes—
129D3×Dic6—216no—
130D3×Dic6—216no—
131C3×#217C2318yes—
132C3×#217C2312yes—
133C3×#217C2312yes—
134C3×#217C2314yes—
135C3×(C2×D3)⋊C4C2314yes—
136C3×C4⋊Dic3C2312yes—
137C3×C4⋊Dic3C2312yes—
138C3×Dic3⋊C4C2318yes—
139C3×Dic3⋊C4C2314yes—
140C3×C4×Dic3C2312yes—
141C3×C4×Dic3C2312yes—
142#3724C2318yes—
143Dic3⋊Dic3C2314yes—
144Dic3⋊Dic3C2318yes—
145#3722C2318yes—
146#3722C2314yes—
147(C2×D3)⋊Dic3C2314yes—
148Dic32C2318yes—
149#3486—91noSylow
150C2×C3×#41—21no—
151C2×C3×#41C2×D311yescharacteristic
152C2×C3×#41C2×D311yescharacteristic
153C22×C3×Q8—31no—
154C23×C3×C4—31no—
155C23×Dic3—32no—
156#1010—68no—
157#1010—68no—
158#1010—616no—
159C2×D3×Q8—32no—
160C2×D3×Q8—32no—
161C2×D3×Q8—34no—
162C2×D3×Q8—34no—
163C2×D3×Q8—62no—
164C2×D3×Q8—68no—
165C2×#237—34no—
166C2×#237—34no—
167C2×#237—32no—
168C2×#237—32no—
169C2×#237—64no—
170C2×#237—62no—
171C2×#235—32no—
172C2×#235—31no—
173C2×#235—31no—
174C2×#235—32no—
175C2×#235—61no—
176C2×#235—62no—
177C22×C4×D3—32no—
178C22×C4×D3C2×D311yescharacteristic
179C22×Dic6—31no—
180C22×Dic6—31no—
181C22×Dic6—32no—
182C22×Dic6—32no—
183C22×Dic6—32no—
184C22×Dic6—32no—
185C22×Dic6—34no—
186C22×Dic6—34no—
187C22×Dic6—61no—
188C22×Dic6—62no—
189C22×Dic6—68no—
190C22×Dic6C2×D311yescharacteristic
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×D312yes—
206#944—32no—
207#944C2×D312yescomplemented
208#939—38no—
209#938C2×D312yes—
210#937C2×D312yes—
211#936C2×D312yescomplemented
212#935C2×D312yes—
213#935C2×D314yes—
214D4×Dic3—38no—
215#930—32no—
216#929—32no—
217#929—34no—
218C4×#67—34no—
219C4×#67C2×D314yes—
220#926C2×D311yescharacteristic
221#926C2×D311yescharacteristic
222#924—32no—
223#924C2×D314yescomplemented
224#897—32no—
225#897—34no—
226#896—38no—
227#896—38no—
228#896—38no—
229#895—32no—
230#893—38no—
231#888—38no—
232#888—38no—
233#887—34no—
234#887—34no—
235#886—32no—
236#886—34no—
237#885—38no—
238#885—38no—
239#884—38no—
240#882—32no—
241#67⋊C4—38no—
242#67⋊C4—38no—
243#878—38no—
244#878—38no—
245#878—38no—
246#877—34no—
247#877—34no—
248#875—32no—
249C4×D12—34no—
250#869—32no—
251C4×Dic6—34no—
252C4×Dic6—34no—
253C23×C32C2412yes—
254C23×C32C2411yescharacteristic
255C22×C3⋊D3C2412yes—
256C22×C3×D3—22no—
257C22×C3×D3—24no—
258C22×C3×D3C2412yes—
259C32×Q8—22no—
260C32×D4—24no—
261C32×D4—22no—
262C2×C32×C4—24no—
263C2×C32×C4C2×D414yes—
264C2×C32×C4C2412yes—
265C2×C32×C4C2411yescharacteristic
266C2×C32×C4C2411yescharacteristic
267#638—24no—
268#638—28no—
269C2×C3⋊Dic3—28no—
270C2×C3⋊Dic3C2×D418yes—
271C2×C3⋊Dic3C2412yes—
272C2×C3⋊Dic3C2414yes—
273C4⋊(C3⋊D3)—22no—
274C4×C3⋊D3—24no—
275C4×C3⋊D3—28no—
276#634—22no—
277#634—28no—
278#634C2×D418yes—
279#634C2×D418yes—
280C3×#67—28no—
281C2×C3×Dic3—24no—
282C2×C3×Dic3—22no—
283C2×C3×Dic3C2414yes—
284C2×C3×Dic3C2414yes—
285C2×C3×Dic3C2414yes—
286C2×C3×Dic3C2412yes—
287C3×C4×D3—24no—
288C3×C4×D3—24no—
289C3×Dic6—24no—
290C3×Dic6—24no—
291#627—216no—
292#626—28no—
293D3×Dic3—216no—
294C2×2−1+4—91no—
295C23×Q8—91no—
296D4×Q8—94no—
297D4×Q8—94no—
298#548—94no—
299#548—94no—
300#536—31no—
301#536—91no—
302#536—94no—
303#525—31no—
304#525—91no—
305#525—94no—
306#519—91no—
307C24×C3—31no—
308C23×D3C22×D311yescharacteristic
309C3×#41—28no—
310C3×#41—24no—
311C3×#41—24no—
312C2×C3×Q8—21no—
313C2×C3×Q8—32no—
314C2×C3×Q8—32no—
315C2×C3×Q8—64no—
316C2×C3×Q8C22×D311yescharacteristic
317C2×C3×Q8C22×D311yescharacteristic
318C2×C3×D4—22no—
319C2×C3×D4—21no—
320C2×C3×D4—34no—
321C2×C3×D4C22×D312yes—
322C2×C3×D4C22×D312yes—
323C2×C3×D4C22×D311yescharacteristic
324C2×C3×D4C22×D311yescharacteristic
325C22×C3×C4—22no—
326C22×C3×C4—21no—
327C22×C3×C4—31no—
328C22×C3×C4—32no—
329C22×C3×C4—32no—
330C22×C3×C4—32no—
331C22×C3×C4—64no—
332C22×C3×C4C22×D312yes—
333C22×C3×C4C22×D312yes—
334C22×C3×C4C22×D311yescharacteristic
335C22×C3×C4C22×D311yescharacteristic
336C2×#67—32no—
337C2×#67—34no—
338C2×#67—34no—
339C2×#67—32no—
340C2×#67—34no—
341C2×#67—62no—
342C2×#67—64no—
343C2×#67C22×D314yes—
344C22×Dic3—32no—
345C22×Dic3—32no—
346C22×Dic3—34no—
347C22×Dic3—34no—
348C22×Dic3—38no—
349C22×Dic3—62no—
350C22×Dic3—64no—
351C22×Dic3—68no—
352C22×Dic3C22×D311yescharacteristic
353C22×Dic3C22×D312yes—
354D3×Q8—616no—
355D3×Q8—616no—
356D3×Q8—68no—
357D3×Q8—68no—
358D3×Q8—616no—
359#237—68no—
360#237—68no—
361#237—616no—
362#237—616no—
363#237—632no—
364#237—616no—
365#235—68no—
366#235—68no—
367#235—616no—
368#235—68no—
369#235—64no—
370#235—64no—
371C2×D12—34no—
372C2×D12—31no—
373C2×D12—31no—
374C2×D12—61no—
375C2×C4×D3—24no—
376C2×C4×D3—38no—
377C2×C4×D3—32no—
378C2×C4×D3—34no—
379C2×C4×D3—34no—
380C2×C4×D3—32no—
381C2×C4×D3—62no—
382C2×C4×D3—64no—
383C2×C4×D3—68no—
384C2×C4×D3C22×D312yes—
385C2×C4×D3C22×D312yes—
386C2×Dic6—24no—
387C2×Dic6—38no—
388C2×Dic6—38no—
389C2×Dic6—32no—
390C2×Dic6—32no—
391C2×Dic6—32no—
392C2×Dic6—32no—
393C2×Dic6—31no—
394C2×Dic6—34no—
395C2×Dic6—34no—
396C2×Dic6—31no—
397C2×Dic6—38no—
398C2×Dic6—38no—
399C2×Dic6—62no—
400C2×Dic6—61no—
401C2×Dic6—62no—
402C2×Dic6—64no—
403C2×Dic6—68no—
404C2×Dic6—616no—
405C2×Dic6—616no—
406C2×Dic6—68no—
407C2×Dic6—68no—
408C2×Dic6—68no—
409C2×Dic6—68no—
410C2×Dic6—616no—
411C2×Dic6C22×D312yes—
412C2×Dic6C22×D312yes—
413C3×C4⋊C4—32no—
414C3×C4⋊C4—32no—
415C3×C4⋊C4—34no—
416C3×C4⋊C4—38no—
417C3×C22⋊C4—32no—
418C3×C22⋊C4—32no—
419C3×C22⋊C4—34no—
420C3×C22⋊C4—38no—
421C3×C22⋊C4—34no—
422C3×C42—32no—
423C3×C42—32no—
424#217—34no—
425#217C22×D312yes—
426#217C22×D312yes—
427#217C22×D314yes—
428#217C22×D318yes—
429(C2×D3)⋊C4—34no—
430(C2×D3)⋊C4—34no—
431(C2×D3)⋊C4—38no—
432(C2×D3)⋊C4—38no—
433(C2×D3)⋊C4—34no—
434(C2×D3)⋊C4C22×D314yes—
435C4⋊Dic3—38no—
436C4⋊Dic3—34no—
437C4⋊Dic3C22×D312yes—
438C4⋊Dic3C22×D312yes—
439Dic3⋊C4—38no—
440Dic3⋊C4—38no—
441Dic3⋊C4—34no—
442Dic3⋊C4—38no—
443Dic3⋊C4C22×D318yes—
444Dic3⋊C4C22×D314yes—
445C4×Dic3—38no—
446C4×Dic3—38no—
447C4×Dic3C22×D312yes—
448C4×Dic3C22×D312yes—
449C22×C32—22no—
450C22×C32—22no—
451C22×C32—24no—
452C22×C32C22×D412yes—
453C22×C32C2511yescharacteristic
454C2×C3⋊D3—22no—
455C2×C3⋊D3—24no—
456C2×C3×D3—28no—
457C2×C3×D3—22no—
458C2×C3×D3—22no—
459C2×C3×D32−1+414yescomplemented
460C32×C4—22no—
461C32×C4C22×D412yes—
462C32×C4C22×D412yes—
463C3⋊Dic3—22no—
464C3⋊Dic3C22×D418yes—
465C3×Dic3—24no—
466C3×Dic3—22no—
467C3×Dic3—24no—
468C3×Dic3—24no—
4692−1+4—188no—
470C2×#41—94no—
471C2×#41—92no—
472C2×#41—91no—
473C2×#41—92no—
474C2×#41D3211yescharacteristic
475C22×Q8—31no—
476C22×Q8—92no—
477C22×Q8—94no—
478C22×Q8—94no—
479C22×Q8—92no—
480C22×Q8—91no—
481C22×Q8—92no—
482C22×Q8—188no—
483C23×C4—31no—
484C23×C4—92no—
485C4⋊Q8—32no—
486C4⋊Q8—92no—
487C4⋊Q8—98no—
488#124—32no—
489#124—92no—
490#124—98no—
491#123—32no—
492#123—34no—
493#123—94no—
494#123—92no—
495C22⋊Q8—32no—
496C22⋊Q8—34no—
497C22⋊Q8—98no—
498C22⋊Q8—98no—
499C22⋊Q8—98no—
500C22⋊Q8—92no—
501C22⋊Q8—94no—
502#121—32no—
503#121—98no—
504#121—92no—
505#120—32no—
506#120—92no—
507C4×Q8—94no—
508C4×Q8—94no—
509C4×D4—34no—
510C4×D4—94no—
511C4×D4—98no—
512C4×D4—98no—
513#117—31no—
514#117—31no—
515#117—94no—
516C23×C3—22no—
517C23×C3—21no—
518C23×C3—32no—
519C23×C3—64no—
520C23×C3—62no—
521C23×C3C23×D312yes—
522C23×C3C23×D312yes—
523C23×C3C23×D311yescharacteristic
524C23×C3C23×D311yescharacteristic
525C22×D3—22no—
526C22×D3—24no—
527C22×D3—32no—
528C22×D3—32no—
529C22×D3—62no—
530C22×D3C23×D312yes—
531C3×Q8—24no—
532C3×Q8—22no—
533C3×Q8—22no—
534C3×Q8—64no—
535C3×Q8—64no—
536C3×D4—28no—
537C3×D4—24no—
538C3×D4—24no—
539C3×D4—24no—
540C3×D4—22no—
541C3×D4—22no—
542C3×D4—68no—
543C2×C3×C4—28no—
544C2×C3×C4—24no—
545C2×C3×C4—24no—
546C2×C3×C4—21no—
547C2×C3×C4—22no—
548C2×C3×C4—21no—
549C2×C3×C4—24no—
550C2×C3×C4—34no—
551C2×C3×C4—34no—
552C2×C3×C4—32no—
553C2×C3×C4—34no—
554C2×C3×C4—62no—
555C2×C3×C4—64no—
556C2×C3×C4—64no—
557C2×C3×C4—64no—
558C2×C3×C4D3×D414yes—
559C2×C3×C4D3×D414yes—
560C2×C3×C4C23×D312yes—
561C2×C3×C4C23×D312yes—
562C2×C3×C4C23×D311yescharacteristic
563C2×C3×C4C23×D311yescharacteristic
564C2×C3×C4C23×D311yescharacteristic
565C2×C3×C4C23×D311yescharacteristic
566#67—28no—
567#67—68no—
568#67—68no—
569#67—68no—
570#67—616no—
571#67—68no—
572#67—64no—
573#67—64no—
574C2×Dic3—24no—
575C2×Dic3—22no—
576C2×Dic3—38no—
577C2×Dic3—38no—
578C2×Dic3—34no—
579C2×Dic3—34no—
580C2×Dic3—32no—
581C2×Dic3—32no—
582C2×Dic3—68no—
583C2×Dic3—64no—
584C2×Dic3—62no—
585C2×Dic3—616no—
586C2×Dic3—68no—
587C2×Dic3—68no—
588C2×Dic3—616no—
589C2×Dic3C23×D314yes—
590C2×Dic3C23×D314yes—
591C2×Dic3C23×D312yes—
592C2×Dic3C23×D314yes—
593D12—64no—
594D12—68no—
595D12—62no—
596D12—62no—
597C4×D3—24no—
598C4×D3—24no—
599C4×D3—68no—
600C4×D3—68no—
601C4×D3—616no—
602C4×D3—616no—
603C4×D3—68no—
604C4×D3—64no—
605C4×D3—64no—
606Dic6—24no—
607Dic6—24no—
608Dic6—38no—
609Dic6—38no—
610Dic6—38no—
611Dic6—38no—
612Dic6—68no—
613Dic6—68no—
614Dic6—616no—
615Dic6—616no—
616Dic6—68no—
617Dic6—68no—
618Dic6—64no—
619Dic6—616no—
620Dic6—62no—
621Dic6—62no—
622C2×C32—22no—
623C2×C32—42no—
624C2×C32C23×D411yescharacteristic
625C2×C32C2×2−1+412yes—
626C3⋊D3—42no—
627C3×D3—24no—
628C24—31no—
629#41—24no—
630#41—188no—
631#41—1816no—
632#41—188no—
633#41—184no—
634C2×Q8—32no—
635C2×Q8—32no—
636C2×Q8—64no—
637C2×Q8—98no—
638C2×Q8—92no—
639C2×Q8—92no—
640C2×Q8—94no—
641C2×Q8—91no—
642C2×Q8—98no—
643C2×Q8—188no—
644C2×Q8—188no—
645C2×Q8—1816no—
646C2×Q8—1816no—
647C2×Q8—188no—
648C2×Q8C2×D3211yescharacteristic
649C2×D4—34no—
650C2×D4—94no—
651C2×D4—92no—
652C2×D4—94no—
653C2×D4—91no—
654C2×D4C2×D3212yes—
655C2×D4C2×D3211yescharacteristic
656C22×C4—31no—
657C22×C4—32no—
658C22×C4—32no—
659C22×C4—32no—
660C22×C4—64no—
661C22×C4—98no—
662C22×C4—92no—
663C22×C4—94no—
664C22×C4—94no—
665C22×C4—92no—
666C22×C4—188no—
667C22×C4C2×D3212yes—
668C22×C4C2×D3211yescharacteristic
669C4⋊C4—32no—
670C4⋊C4—32no—
671C4⋊C4—34no—
672C4⋊C4—38no—
673C4⋊C4—98no—
674C4⋊C4—94no—
675C4⋊C4—98no—
676C22⋊C4—32no—
677C22⋊C4—32no—
678C22⋊C4—34no—
679C22⋊C4—38no—
680C22⋊C4—34no—
681C22⋊C4—94no—
682C22⋊C4—98no—
683C22⋊C4—94no—
684C42—32no—
685C42—32no—
686C42—98no—
687C22×C3—22no—
688C22×C3—22no—
689C22×C3—24no—
690C22×C3—22no—
691C22×C3—22no—
692C22×C3—24no—
693C22×C3—24no—
694C22×C3—22no—
695C22×C3—21no—
696C22×C3—34no—
697C22×C3—42no—
698C22×C3—44no—
699C22×C3—68no—
700C22×C3—62no—
701C22×C3—62no—
702C22×C3C2×D3×D412yes—
703C22×C3C2×D3×D412yes—
704C22×C3C24×D311yescharacteristic
705C22×C3C24×D311yescharacteristic
706C2×D3—28no—
707C2×D3—22no—
708C2×D3—22no—
709C2×D3—64no—
710C2×D3—62no—
711C2×D3—62no—
712C2×D3—64no—
713C2×D3—64no—
714C2×D3—124no—
715C2×D3#101014yescomplemented
716C3×C4—24no—
717C3×C4—22no—
718C3×C4—22no—
719C3×C4—22no—
720C3×C4—22no—
721C3×C4—62no—
722C3×C4—64no—
723C3×C4—64no—
724C3×C4—64no—
725C3×C4C2×D3×D412yes—
726C3×C4C2×D3×D412yes—
727C3×C4C2×D3×D412yes—
728C3×C4C2×D3×D412yes—
729Dic3—24no—
730Dic3—22no—
731Dic3—24no—
732Dic3—24no—
733Dic3—38no—
734Dic3—38no—
735Dic3—68no—
736Dic3—64no—
737Dic3—62no—
738Dic3—62no—
739C32#348611yescharacteristic, complemented, Sylow
740C23—32no—
741C23—64no—
742C23—62no—
743C23—92no—
744C23C22×D3212yes—
745C23C22×D3211yescharacteristic
746Q8—22no—
747Q8—64no—
748Q8—64no—
749Q8—98no—
750Q8—98no—
751Q8—188no—
752Q8—1816no—
753Q8—182no—
754D4—24no—
755D4—22no—
756D4—68no—
757D4—188no—
758D4—188no—
759D4—184no—
760D4—182no—
761C2×C4—24no—
762C2×C4—34no—
763C2×C4—34no—
764C2×C4—32no—
765C2×C4—34no—
766C2×C4—62no—
767C2×C4—64no—
768C2×C4—64no—
769C2×C4—64no—
770C2×C4—98no—
771C2×C4—94no—
772C2×C4—92no—
773C2×C4—188no—
774C2×C4—1816no—
775C2×C4—188no—
776C2×C4—184no—
777C2×C4#381114yes—
778C2×C4C22×D3212yes—
779C2×C4C22×D3211yescharacteristic
780C2×C4C22×D3211yescharacteristic
781C2×C3—22no—
782C2×C3—22no—
783C2×C3—22no—
784C2×C3—21no—
785C2×C3—42no—
786C2×C3—44no—
787C2×C3—42no—
788C2×C3—42no—
789C2×C3—64no—
790C2×C3C22×D3×D411yescharacteristic
791C2×C3C22×D3×D411yescharacteristic
792C2×C3C2×#101012yes—
793C2×C3D3×2−1+412yes—
794D3—24no—
795D3—124no—
796D3—122no—
797D3—122no—
798C22—22no—
799C22—24no—
800C22—22no—
801C22—34no—
802C22—68no—
803C22—62no—
804C22—62no—
805C22—184no—
806C22—182no—
807C22C2×#381112yes—
808C22C23×D3211yescharacteristic
809C4—22no—
810C4—64no—
811C4—64no—
812C4—62no—
813C4—64no—
814C4—98no—
815C4—182no—
816C4C2×#381112yes—
817C4C2×#381112yes—
818C3—21no—
819C3#8602211yescharacteristic, complemented
820C3#8635511yescharacteristic, complemented
821C2—22no—
822C2—42no—
823C2—64no—
824C2—362no—
825C2D3×#101012yes—
826C2C22×#381111yescharacteristic
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×#64367C2semidirect
2. C22×D3×Dic6C2semidirect
3. C3×#5828C2semidirect
4. C3×#5825C2semidirect
5. #10595361C2semidirect
6. #10595271C2semidirect
7. #10595161C2semidirect
8. #10595160C2semidirect
9. #10595023C2semidirect
10. #10594916C2semidirect
11. #10594915C2semidirect
12. #10594866C2semidirect
13. #10594828C2semidirect
18. C2×Q8×C3⋊D3C22semidirect
20. C2×#3830C22semidirect
22. C2×#3828C22semidirect
24. C22×#634C22semidirect
33. C3×#944C22semidirect
36. C3×#936C22semidirect
42. C3×#924C22semidirect
43. #63982C22semidirect
50. #63953C22semidirect
55. #63871C22semidirect
56. #63866C22semidirect
57. #63865C22semidirect
58. #63864C22semidirect
60. #63844C22semidirect
61. #63844C22semidirect
62. #63840C22semidirect
70. #5828D3semidirect
71. #5825D3semidirect
110. C2×#634D4semidirect
207. #944C2×D3semidirect
211. #936C2×D3semidirect
223. #924C2×D3semidirect
459. C2×C3×D32−1+4semidirect
715. C2×D3#1010semidirect
739. C32#3486semidirect
819. C3#86022semidirect
820. C3#86355semidirect

Maximal subgroups

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

subgroupindex
C2×#643672
C22×D3×Dic62
C3×#58282
C3×#58252
#105953612
#105952712
#105951612
#105951602
#105950232
#105949162
#105949152
#105948662
#105948282
#863553
#860223