Finite Group Databasebeta

← C2×#10594919 #11902722

Subgroups — C2×#10594919 #11902722

Order 1152.

3917 conjugacy classes of subgroups.

The subgroup lattice has 786 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#3828C211yesmaximal, characteristic, complemented
2C22×#3795C211yesmaximal, characteristic, complemented
3C2×C3×#930C211yesmaximal, characteristic, complemented
4C2×C3×C4×#67C211yesmaximal, characteristic, complemented
5C2×#63979C212yesmaximal, complemented
6C2×#63971C212yesmaximal, complemented
7C2×#63912C212yesmaximal, complemented
8C2×#63911C211yesmaximal, characteristic, complemented
9C2×#63909C211yesmaximal, characteristic, complemented
10#10594919C2116yesmaximal, direct product factor
11C2×#63881C212yesmaximal, complemented
12C2×#63844C211yesmaximal, characteristic, complemented
13C2×#5599—31nomaximal
14C2×#5553—31nomaximal
15C23×C32×C4C2211yescharacteristic
16C22×#638C2212yes—
17C2×#3828—28no—
18C2×#3828C2218yescomplemented
19C22×C4⋊(C3⋊D3)C2211yescharacteristic
20C22×C4×C3⋊D3C2212yes—
21C22×#634C2211yescharacteristic
22C22×C3×#67C2211yescharacteristic
23C22×C3×#67C2212yes—
24C22×C3×D12C2211yescharacteristic
25C22×C3×C4×D3C2211yescharacteristic
26C22×#626C2212yes—
27C22×#626C2212yes—
28C22×#626C2212yes—
29C22×#625C2212yes—
30C22×D3×Dic3C2212yes—
31C2×#3795—28no—
32C2×#3795C2218yescomplemented
33C2×C3×#217C2211yescharacteristic
34C3×#930C2218yescomplemented
35C3×C4×#67C2218yescomplemented
36C2×C3×(C2×D3)⋊C4C2211yescharacteristic
37C2×C3×(C2×D3)⋊C4C2212yes—
38C2×C3×C4⋊Dic3C2211yescharacteristic
39C2×C3×Dic3⋊C4C2211yescharacteristic
40C2×C3×C4×Dic3C2211yescharacteristic
41#63979C22116yescomplemented
42#63971C22116yescomplemented
43C2×#3724C2212yes—
44C2×#3722C2212yes—
45C2×Dic32C2212yes—
46#63912C22116yescomplemented
47#63911C2218yescomplemented
48#63909C2218yescomplemented
49#63881C22116yescomplemented
50#63844C2218yescomplemented
51C22×#237—31no—
52C22×#235—31no—
53C22×#235—31no—
54C22×#235—31no—
55C22×#235—61no—
56C2×C3×#121—31no—
57C2×C3×C4×D4—31no—
58C2×#940—32no—
59C2×#940—32no—
60C2×#940—31no—
61C2×#939—32no—
62C2×#930—31no—
63C2×#930D311yescharacteristic, complemented
64C2×C4×#67D311yescharacteristic, complemented
65#5599—316no—
66#5553—316no—
67C2×#895—31no—
68C2×#893—32no—
69C2×#887—31no—
70C2×#884—32no—
71C2×#884—32no—
72C2×#884—32no—
73C2×#67⋊C4—32no—
74C2×#874—31no—
75C2×C4×Dic6—31no—
76C24×C32C2311yescharacteristic
77C23×C3⋊D3C2312yes—
78C23×C3×D3C2312yes—
79C23×C3×D3C2311yescharacteristic
80C22×C32×C4—24no—
81C22×C32×C4C2311yescharacteristic
82C22×C32×C4C2314yes—
83C22×C32×C4C2311yescharacteristic
84C2×#638—28no—
85C2×#638C2318yes—
86C22×C3⋊Dic3C2312yes—
87#3828—232no—
88C2×C4⋊(C3⋊D3)—24no—
89C2×C4⋊(C3⋊D3)C2314yes—
90C2×C4×C3⋊D3—28no—
91C2×C4×C3⋊D3C2318yes—
92C2×#634D418yescomplemented
93C2×#634C2314yes—
94C2×C3×#67—24no—
95C2×C3×#67—44no—
96C2×C3×#67C2314yes—
97C2×C3×#67C2318yes—
98C22×C3×Dic3C2311yescharacteristic
99C22×C3×Dic3C2311yescharacteristic
100C22×C3×Dic3C2312yes—
101C22×C3×Dic3C2311yescharacteristic
102C2×C3×D12—24no—
103C2×C3×D12C2314yes—
104C2×C3×C4×D3—24no—
105C2×C3×C4×D3C2314yes—
106C2×#626—28no—
107C2×#626—44no—
108C2×#626—44no—
109C2×#626C2318yes—
110C2×#626C2318yes—
111C2×#626C2318yes—
112C2×#625—28no—
113C2×#625C2318yes—
114C2×D3×Dic3—28no—
115C2×D3×Dic3C2318yes—
116#3795—232no—
117C3×#217C2314yes—
118C3×(C2×D3)⋊C4C2314yes—
119C3×(C2×D3)⋊C4C2318yes—
120C3×C4⋊Dic3C2314yes—
121C3×Dic3⋊C4C2314yes—
122C3×C4×Dic3C2314yes—
123#3724C2318yes—
124#3722C2318yes—
125Dic32C2318yes—
126C2×#550—91noSylow
127C22×C3×D4—31no—
128C22×C3×D4—32no—
129C22×C3×D4—31no—
130C23×C3×C4—21no—
131C23×C3×C4—31no—
132C23×C3×C4C2×D311yescharacteristic
133C23×C3×C4C2×D311yescharacteristic
134C22×#67—32no—
135C22×#67—32no—
136C22×#67—32no—
137C22×#67—32no—
138C22×#67—32no—
139C22×#67—32no—
140C22×#67—32no—
141C22×#67—62no—
142C22×#67C2×D311yescharacteristic
143C22×#67C2×D312yes—
144C23×Dic3—32no—
145C2×#237—38no—
146C2×#237—68no—
147C2×#235—38no—
148C2×#235—38no—
149C2×#235—38no—
150C2×#235—68no—
151C2×#235—68no—
152C2×#235—68no—
153C2×#235—68no—
154C2×#235—616no—
155C22×D12—32no—
156C22×D12—31no—
157C22×D12—31no—
158C22×D12—32no—
159C22×D12—32no—
160C22×D12—61no—
161C22×D12C2×D311yescharacteristic
162C22×C4×D3—32no—
163C22×C4×D3—32no—
164C22×C4×D3—32no—
165C22×C4×D3—62no—
166C22×C4×D3C2×D311yescharacteristic
167C22×Dic6—31no—
168C22×Dic6—31no—
169C22×Dic6—61no—
170C3×#121—38no—
171C3×C4×D4—38no—
172C2×C3×C4⋊C4—31no—
173C2×C3×C4⋊C4—31no—
174C2×C3×C22⋊C4—31no—
175C2×C3×C22⋊C4—32no—
176C2×C3×C22⋊C4—31no—
177C2×C3×C42—31no—
178C2×#217C2×D311yescharacteristic
179#940—316no—
180#940—316no—
181#940—38no—
182#939—316no—
183#930—38no—
184#930C2×D318yescomplemented
185C4×#67C2×D318yescomplemented
186C2×(C2×D3)⋊C4—32no—
187C2×(C2×D3)⋊C4—32no—
188C2×(C2×D3)⋊C4C2×D311yescharacteristic
189C2×(C2×D3)⋊C4C2×D312yes—
190C2×C4⋊Dic3C2×D311yescharacteristic
191C2×Dic3⋊C4—32no—
192C2×Dic3⋊C4—32no—
193C2×Dic3⋊C4C2×D311yescharacteristic
194C2×C4×Dic3—32no—
195C2×C4×Dic3—32no—
196C2×C4×Dic3C2×D311yescharacteristic
197#895—38no—
198#893—316no—
199#887—38no—
200#884—316no—
201#884—316no—
202#884—316no—
203#67⋊C4—316no—
204#874—38no—
205C4×Dic6—38no—
206C23×C32—22no—
207C23×C32—22no—
208C23×C32—22no—
209C23×C32C2412yes—
210C23×C32C2411yescharacteristic
211C22×C3⋊D3—24no—
212C22×C3⋊D3—24no—
213C22×C3⋊D3—24no—
214C22×C3⋊D3C2414yes—
215C22×C3×D3—24no—
216C22×C3×D3—22no—
217C22×C3×D3—24no—
218C22×C3×D3—22no—
219C22×C3×D3—22no—
220C22×C3×D3—24no—
221C22×C3×D3C2414yes—
222C22×C3×D3C2412yes—
223C2×C32×C4—22no—
224C2×C32×C4—28no—
225C2×C32×C4C2×D414yes—
226C2×C32×C4C2412yes—
227C2×C32×C4C2412yes—
228#638—216no—
229C2×C3⋊Dic3C2×D418yes—
230C2×C3⋊Dic3C2414yes—
231C4⋊(C3⋊D3)—28no—
232C4×C3⋊D3—216no—
233#634C2×D4116yescomplemented
234C3×#67—28no—
235C3×#67—48no—
236C2×C3×Dic3—22no—
237C2×C3×Dic3—22no—
238C2×C3×Dic3—24no—
239C2×C3×Dic3#4114yescomplemented
240C2×C3×Dic3C2414yes—
241C2×C3×Dic3C2412yes—
242C2×C3×Dic3C2412yes—
243C2×C3×Dic3C2412yes—
244C3×D12—28no—
245C3×C4×D3—28no—
246#626—216no—
247#626—48no—
248#626—48no—
249#625—216no—
250D3×Dic3—216no—
251C22×#41—91no—
252C22×#41—91no—
253#550—916no—
254C2×#127—91no—
255C2×#127—92no—
256C2×#121—31no—
257C2×#121—92no—
258C2×#121—92no—
259C2×#121—91no—
260C2×C4×Q8—91no—
261C2×C4×D4—31no—
262C2×C4×D4—92no—
263C24×C3—21no—
264C24×C3—32no—
265C24×C3—31no—
266C24×C3C22×D311yescharacteristic
267C24×C3C22×D311yescharacteristic
268C23×D3—32no—
269C23×D3—32no—
270C23×D3—62no—
271C23×D3C22×D312yes—
272C23×D3C22×D311yescharacteristic
273C2×C3×D4—34no—
274C2×C3×D4—38no—
275C2×C3×D4—34no—
276C2×C3×D4—64no—
277C2×C3×D4—64no—
278C2×C3×D4—124no—
279C22×C3×C4—28no—
280C22×C3×C4—24no—
281C22×C3×C4—24no—
282C22×C3×C4—21no—
283C22×C3×C4—21no—
284C22×C3×C4—24no—
285C22×C3×C4—31no—
286C22×C3×C4—32no—
287C22×C3×C4—31no—
288C22×C3×C4—31no—
289C22×C3×C4—34no—
290C22×C3×C4—64no—
291C22×C3×C4C22×D311yescharacteristic
292C22×C3×C4C22×D311yescharacteristic
293C22×C3×C4C22×D314yes—
294C22×C3×C4C22×D314yes—
295C22×C3×C4C22×D311yescharacteristic
296C22×C3×C4C22×D311yescharacteristic
297C2×#67—24no—
298C2×#67—38no—
299C2×#67—38no—
300C2×#67—38no—
301C2×#67—38no—
302C2×#67—38no—
303C2×#67—38no—
304C2×#67—38no—
305C2×#67—44no—
306C2×#67—68no—
307C2×#67—68no—
308C2×#67—68no—
309C2×#67—68no—
310C2×#67—68no—
311C2×#67—616no—
312C2×#67—68no—
313C2×#67—124no—
314C2×#67—124no—
315C2×#67C22×D314yes—
316C2×#67C22×D318yes—
317C22×Dic3—32no—
318C22×Dic3—32no—
319C22×Dic3—38no—
320C22×Dic3—62no—
321C22×Dic3—68no—
322C22×Dic3C22×D312yes—
323C22×Dic3C22×D311yescharacteristic
324C22×Dic3C22×D311yescharacteristic
325C22×Dic3C22×D311yescharacteristic
326#237—632no—
327#235—632no—
328#235—632no—
329#235—632no—
330#235—664no—
331C2×D12—24no—
332C2×D12—38no—
333C2×D12—34no—
334C2×D12—34no—
335C2×D12—38no—
336C2×D12—38no—
337C2×D12—64no—
338C2×D12—68no—
339C2×D12—68no—
340C2×D12—64no—
341C2×D12—64no—
342C2×D12—124no—
343C2×D12—124no—
344C2×D12C22×D314yes—
345C2×C4×D3—24no—
346C2×C4×D3—38no—
347C2×C4×D3—38no—
348C2×C4×D3—38no—
349C2×C4×D3—68no—
350C2×C4×D3—68no—
351C2×C4×D3—68no—
352C2×C4×D3—68no—
353C2×C4×D3—616no—
354C2×C4×D3C22×D314yes—
355C2×Dic6—38no—
356C2×Dic6—38no—
357C2×Dic6—34no—
358C2×Dic6—34no—
359C2×Dic6—68no—
360C2×Dic6—64no—
361C3×C4⋊C4—34no—
362C3×C4⋊C4—34no—
363C3×C22⋊C4—34no—
364C3×C22⋊C4—38no—
365C3×C22⋊C4—34no—
366C3×C42—34no—
367#217C22×D314yes—
368(C2×D3)⋊C4—38no—
369(C2×D3)⋊C4—38no—
370(C2×D3)⋊C4C22×D314yes—
371(C2×D3)⋊C4C22×D318yes—
372C4⋊Dic3C22×D314yes—
373Dic3⋊C4—38no—
374Dic3⋊C4—38no—
375Dic3⋊C4C22×D314yes—
376C4×Dic3—38no—
377C4×Dic3—38no—
378C4×Dic3C22×D314yes—
379C22×C32—22no—
380C22×C32—22no—
381C22×C32—22no—
382C22×C32—44no—
383C22×C32C22×D412yes—
384C22×C32C2×#4112yes—
385C22×C32H(5,𝔽2)12yes—
386C22×C32C2511yescharacteristic
387C2×C3⋊D3—24no—
388C2×C3⋊D3—24no—
389C2×C3⋊D3—24no—
390C2×C3⋊D3—48no—
391C2×C3×D3—24no—
392C2×C3×D3—22no—
393C2×C3×D3—24no—
394C2×C3×D3—22no—
395C2×C3×D3—22no—
396C2×C3×D3—24no—
397C2×C3×D3—44no—
398C2×C3×D3—48no—
399C32×C4—22no—
400C32×C4C22×D414yes—
401C3⋊Dic3C22×D418yes—
402C3×Dic3—22no—
403C3×Dic3—22no—
404C3×Dic3—24no—
405C3×Dic3C2×#4114yescomplemented
406C2×#41—98no—
407C2×#41—98no—
408C2×#41—188no—
409C2×#41—188no—
410C22×Q8—91no—
411C22×D4—31no—
412C22×D4—32no—
413C22×D4—31no—
414C22×D4—92no—
415C22×D4—92no—
416C22×D4—92no—
417C22×D4—92no—
418C22×D4—92no—
419C22×D4—91no—
420C23×C4—31no—
421C23×C4—92no—
422C23×C4—92no—
423C23×C4D3211yescharacteristic
424#127—98no—
425#127—916no—
426#121—38no—
427#121—916no—
428#121—916no—
429#121—98no—
430C4×Q8—98no—
431C4×D4—38no—
432C4×D4—916no—
433C2×C4⋊C4—31no—
434C2×C4⋊C4—31no—
435C2×C4⋊C4—92no—
436C2×C22⋊C4—31no—
437C2×C22⋊C4—31no—
438C2×C22⋊C4—32no—
439C2×C22⋊C4—92no—
440C2×C42—31no—
441C2×C42—92no—
442C23×C3—24no—
443C23×C3—22no—
444C23×C3—22no—
445C23×C3—22no—
446C23×C3—22no—
447C23×C3—22no—
448C23×C3—22no—
449C23×C3—22no—
450C23×C3—21no—
451C23×C3—34no—
452C23×C3—32no—
453C23×C3—42no—
454C23×C3—42no—
455C23×C3—64no—
456C23×C3—64no—
457C23×C3—62no—
458C23×C3—62no—
459C23×C3—62no—
460C23×C3—64no—
461C23×C3C23×D312yes—
462C23×C3C23×D312yes—
463C23×C3C23×D311yescharacteristic
464C23×C3C23×D311yescharacteristic
465C22×D3—22no—
466C22×D3—22no—
467C22×D3—24no—
468C22×D3—24no—
469C22×D3—24no—
470C22×D3—22no—
471C22×D3—34no—
472C22×D3—34no—
473C22×D3—64no—
474C22×D3—68no—
475C22×D3—64no—
476C22×D3—64no—
477C22×D3—64no—
478C22×D3—64no—
479C22×D3—64no—
480C22×D3—64no—
481C22×D3—124no—
482C22×D3—124no—
483C22×D3C23×D314yes—
484C22×D3C23×D312yes—
485C3×D4—68no—
486C3×D4—68no—
487C3×D4—128no—
488C2×C3×C4—24no—
489C2×C3×C4—216no—
490C2×C3×C4—22no—
491C2×C3×C4—22no—
492C2×C3×C4—28no—
493C2×C3×C4—28no—
494C2×C3×C4—22no—
495C2×C3×C4—22no—
496C2×C3×C4—24no—
497C2×C3×C4—34no—
498C2×C3×C4—32no—
499C2×C3×C4—34no—
500C2×C3×C4—32no—
501C2×C3×C4—32no—
502C2×C3×C4—62no—
503C2×C3×C4—62no—
504C2×C3×C4—64no—
505C2×C3×C4—68no—
506C2×C3×C4D3×D414yes—
507C2×C3×C4D3×D414yes—
508C2×C3×C4C23×D312yes—
509C2×C3×C4C23×D312yes—
510C2×C3×C4C23×D312yes—
511C2×C3×C4C23×D312yes—
512#67—28no—
513#67—48no—
514#67—616no—
515#67—616no—
516#67—616no—
517#67—616no—
518#67—632no—
519#67—616no—
520#67—128no—
521#67—128no—
522C2×Dic3—22no—
523C2×Dic3—24no—
524C2×Dic3—22no—
525C2×Dic3—38no—
526C2×Dic3—38no—
527C2×Dic3—34no—
528C2×Dic3—34no—
529C2×Dic3—68no—
530C2×Dic3—64no—
531C2×Dic3—616no—
532C2×Dic3#23514yescomplemented
533C2×Dic3C23×D314yes—
534C2×Dic3C23×D312yes—
535C2×Dic3C23×D312yes—
536C2×Dic3C23×D312yes—
537D12—28no—
538D12—616no—
539D12—616no—
540D12—68no—
541D12—68no—
542D12—128no—
543D12—128no—
544C4×D3—28no—
545C4×D3—616no—
546C4×D3—616no—
547C4×D3—616no—
548C4×D3—632no—
549Dic6—316no—
550Dic6—316no—
551Dic6—616no—
552C2×C32—42no—
553C2×C32#55014yescomplemented
554C2×C32C23×D411yescharacteristic
555C2×C32C22×#4111yescharacteristic
556C2×C32C2×H(5,𝔽2)11yescharacteristic
557C3⋊D3—44no—
558C3×D3—44no—
559C3×D3—42no—
560C24—31no—
561C24—32no—
562C24—92no—
563C24C2×D3211yescharacteristic
564#41—1832no—
565#41—1832no—
566C2×Q8—94no—
567C2×Q8—98no—
568C2×D4—34no—
569C2×D4—38no—
570C2×D4—34no—
571C2×D4—64no—
572C2×D4—64no—
573C2×D4—98no—
574C2×D4—98no—
575C2×D4—98no—
576C2×D4—98no—
577C2×D4—98no—
578C2×D4—94no—
579C2×D4—124no—
580C2×D4—188no—
581C2×D4—188no—
582C2×D4—188no—
583C2×D4—184no—
584C2×D4—364no—
585C2×D4—364no—
586C22×C4—24no—
587C22×C4—31no—
588C22×C4—31no—
589C22×C4—32no—
590C22×C4—31no—
591C22×C4—34no—
592C22×C4—64no—
593C22×C4—98no—
594C22×C4—92no—
595C22×C4—98no—
596C22×C4—188no—
597C22×C4—188no—
598C22×C4C2×D3214yes—
599C22×C4C2×D3211yescharacteristic
600C22×C4C2×D3211yescharacteristic
601C4⋊C4—34no—
602C4⋊C4—34no—
603C4⋊C4—98no—
604C22⋊C4—34no—
605C22⋊C4—34no—
606C22⋊C4—38no—
607C22⋊C4—98no—
608C42—34no—
609C42—98no—
610C22×C3—24no—
611C22×C3—22no—
612C22×C3—22no—
613C22×C3—22no—
614C22×C3—22no—
615C22×C3—22no—
616C22×C3—22no—
617C22×C3—22no—
618C22×C3—22no—
619C22×C3—22no—
620C22×C3—21no—
621C22×C3—42no—
622C22×C3—42no—
623C22×C3—48no—
624C22×C3—44no—
625C22×C3—44no—
626C22×C3—64no—
627C22×C3—64no—
628C22×C3—62no—
629C22×C3—62no—
630C22×C3—62no—
631C22×C3—64no—
632C22×C3—128no—
633C22×C3—124no—
634C22×C3C2×#23512yes—
635C22×C3C2×D3×D412yes—
636C22×C3C2×D3×D412yes—
637C22×C3#100412yes—
638C22×C3D3×#4112yes—
639C22×C3#100912yes—
640C22×C3C24×D311yescharacteristic
641C22×C3C24×D311yescharacteristic
642C2×D3—22no—
643C2×D3—22no—
644C2×D3—24no—
645C2×D3—24no—
646C2×D3—24no—
647C2×D3—22no—
648C2×D3—44no—
649C2×D3—48no—
650C2×D3—68no—
651C2×D3—64no—
652C2×D3—64no—
653C2×D3—64no—
654C2×D3—64no—
655C2×D3—64no—
656C2×D3—64no—
657C2×D3—124no—
658C2×D3—124no—
659C2×D3—1216no—
660C2×D3—128no—
661C2×D3—128no—
662C3×C4—24no—
663C3×C4—22no—
664C3×C4—22no—
665C3×C4—24no—
666C3×C4—34no—
667C3×C4—62no—
668C3×C4—62no—
669C3×C4—64no—
670C3×C4C2×D3×D414yes—
671C3×C4C2×D3×D414yes—
672Dic3—22no—
673Dic3—24no—
674Dic3—22no—
675Dic3—38no—
676Dic3—38no—
677Dic3—68no—
678Dic3C2×#23514yescomplemented
679C32C2×#55011yescharacteristic, complemented, Sylow
680C23—22no—
681C23—22no—
682C23—22no—
683C23—32no—
684C23—34no—
685C23—62no—
686C23—64no—
687C23—64no—
688C23—62no—
689C23—62no—
690C23—64no—
691C23—94no—
692C23—184no—
693C23—184no—
694C23—184no—
695C23C22×D3212yes—
696C23C22×D3211yescharacteristic
697Q8—916no—
698D4—68no—
699D4—68no—
700D4—128no—
701D4—1816no—
702D4—1816no—
703D4—1816no—
704D4—188no—
705D4—368no—
706D4—368no—
707C2×C4—22no—
708C2×C4—28no—
709C2×C4—34no—
710C2×C4—32no—
711C2×C4—32no—
712C2×C4—34no—
713C2×C4—32no—
714C2×C4—64no—
715C2×C4—62no—
716C2×C4—62no—
717C2×C4—68no—
718C2×C4—98no—
719C2×C4—94no—
720C2×C4—1816no—
721C2×C4—1816no—
722C2×C4#381114yes—
723C2×C4C22×D3212yes—
724C2×C4C22×D3212yes—
725C2×C3—21no—
726C2×C3—21no—
727C2×C3—21no—
728C2×C3—24no—
729C2×C3—44no—
730C2×C3—42no—
731C2×C3—42no—
732C2×C3—122no—
733C2×C3—124no—
734C2×C3#555314yescomplemented
735C2×C3#559914yescomplemented
736C2×C3C22×#23511yescharacteristic
737C2×C3C22×D3×D411yescharacteristic
738C2×C3C22×D3×D411yescharacteristic
739C2×C3C2×#100411yescharacteristic
740C2×C3C2×D3×#4111yescharacteristic
741C2×C3C2×#100911yescharacteristic
742D3—44no—
743D3—42no—
744D3—128no—
745D3—124no—
746D3—124no—
747C22—22no—
748C22—22no—
749C22—22no—
750C22—44no—
751C22—62no—
752C22—64no—
753C22—64no—
754C22—62no—
755C22—62no—
756C22—64no—
757C22—124no—
758C22—128no—
759C22—184no—
760C22—184no—
761C22—184no—
762C22—368no—
763C22D3×#23512yes—
764C22#6430712yes—
765C22C2×#381112yes—
766C22C23×D3211yescharacteristic
767C4—22no—
768C4—34no—
769C4—64no—
770C4—62no—
771C4—62no—
772C4—98no—
773C4C2×#381114yes—
774C3—21no—
775C3C2×#555311yescharacteristic, complemented
776C3C2×#559911yescharacteristic, complemented
777C2—42no—
778C2—122no—
779C2—124no—
780C2—364no—
781C2#1059491914yesdirect product factor
782C2C2×D3×#23511yescharacteristic
783C2C2×#6430711yescharacteristic
784C2C22×#381111yescharacteristic
subgroupG/H
centerC23C22×D32
commutator, cosocleC22×C32C25
FrattiniC22C23×D32
FittingC23×C32×C4C22
socleC23×C32C24
hypercenterC23×C4D32
hypocenterC32C2×#550
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C23 ◁ C23×C4

Complements

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

NH ≅ G/Ntype
1. C22×#3828C2semidirect
2. C22×#3795C2semidirect
3. C2×C3×#930C2semidirect
4. C2×C3×C4×#67C2semidirect
5. C2×#63979C2semidirect
6. C2×#63971C2semidirect
7. C2×#63912C2semidirect
8. C2×#63911C2semidirect
9. C2×#63909C2semidirect
10. #10594919C2direct (N × H)
11. C2×#63881C2semidirect
12. C2×#63844C2semidirect
18. C2×#3828C22semidirect
32. C2×#3795C22semidirect
34. C3×#930C22semidirect
35. C3×C4×#67C22semidirect
41. #63979C22semidirect
42. #63971C22semidirect
46. #63912C22semidirect
47. #63911C22semidirect
48. #63909C22semidirect
49. #63881C22semidirect
50. #63844C22semidirect
63. C2×#930D3semidirect
64. C2×C4×#67D3semidirect
92. C2×#634D4semidirect
184. #930C2×D3semidirect
185. C4×#67C2×D3semidirect
233. #634C2×D4semidirect
239. C2×C3×Dic3#41semidirect
405. C3×Dic3C2×#41semidirect
532. C2×Dic3#235semidirect
553. C2×C32#550semidirect
678. Dic3C2×#235semidirect
679. C32C2×#550semidirect
734. C2×C3#5553semidirect
735. C2×C3#5599semidirect
775. C3C2×#5553semidirect
776. C3C2×#5599semidirect
781. C2#10594919direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#38282
C22×#37952
C2×C3×#9302
C2×C3×C4×#672
C2×#639792
C2×#639712
C2×#639122
C2×#639112
C2×#639092
#105949192
C2×#638812
C2×#638442
C2×#55993
C2×#55533