Finite Group Databasebeta

← C2×#10595248 #11902545

Subgroups — C2×#10595248 #11902545

Order 1152.

3709 conjugacy classes of subgroups.

The subgroup lattice has 738 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#3830C211yesmaximal, characteristic, complemented
2C22×C3×#237C211yesmaximal, characteristic, complemented
3C2×C3×D4×Dic3C211yesmaximal, characteristic, complemented
4C2×#63978C212yesmaximal, complemented
5C2×#63966C212yesmaximal, complemented
6C22×Dic3⋊Dic3C212yesmaximal, complemented
7C2×#63962C212yesmaximal, complemented
8#10595248C2116yesmaximal, direct product factor
9C2×C4×#626C211yesmaximal, characteristic, complemented
10C2×#63871C211yesmaximal, characteristic, complemented
11C2×#63866C211yesmaximal, characteristic, complemented
12C2×#63857C211yesmaximal, characteristic, complemented
13C2×#5824—31nomaximal
14C2×#5555—31nomaximal
15C22×C32×D4C2211yescharacteristic
16C22×#638C2212yes—
17C23×C3⋊Dic3C2212yes—
18C2×#3830—28no—
19C2×#3830C2218yescomplemented
20C22×C4×C3⋊D3C2211yescharacteristic
21C22×#634C2211yescharacteristic
22C22×C3×#67C2212yes—
23C23×C3×Dic3C2212yes—
24C23×C3×Dic3C2212yes—
25C2×C3×#237—28no—
26C2×C3×#237C2218yescomplemented
27C22×C3×C4×D3C2211yescharacteristic
28C22×C3×Dic6C2211yescharacteristic
29C22×#626C2211yescharacteristic
30C2×C3×#217C2212yes—
31C3×D4×Dic3C2218yescomplemented
32C2×C3×C4⋊Dic3C2211yescharacteristic
33C2×C3×C4×Dic3C2211yescharacteristic
34#63978C22116yescomplemented
35#63966C22116yescomplemented
36C2×Dic3⋊Dic3C2212yes—
37C2×Dic3⋊Dic3C2212yes—
38C2×Dic3⋊Dic3C2212yes—
39C2×Dic3⋊Dic3C2212yes—
40C2×Dic3⋊Dic3C2211yescharacteristic
41C2×Dic3⋊Dic3C22116yescomplemented
42C2×#3722C2212yes—
43C2×#3722C2211yescharacteristic
44#63962C22116yescomplemented
45C2×(C2×D3)⋊Dic3C2212yes—
46C2×(C2×D3)⋊Dic3C2211yescharacteristic
47C4×#626C2218yescomplemented
48#63871C2218yescomplemented
49#63866C2218yescomplemented
50#63857C2218yescomplemented
51C22×C3×#41—31no—
52C22×#237—31no—
53C22×#237—31no—
54C22×#237—61no—
55C22×#237D311yescharacteristic, complemented
56C2×C3×C4×D4—31no—
57#5824—316no—
58C2×#946—31no—
59C2×#944—31no—
60C2×#939—32no—
61C2×#935—32no—
62C2×D4×Dic3D311yescharacteristic, complemented
63C2×#930—32no—
64C2×#929—32no—
65C2×C4×#67—31no—
66C22×C4⋊Dic3—32no—
67C2×#924—31no—
68C22×Dic3⋊C4—32no—
69#5555—316no—
70C2×#897—31no—
71C2×#897—31no—
72C2×#886—32no—
73C2×#886—32no—
74C2×C4×D12—31no—
75C2×#869—31no—
76C24×C32C2312yes—
77C23×C3⋊D3C2311yescharacteristic
78C23×C3×D3C2311yescharacteristic
79C2×C32×D4D418yescomplemented
80C2×C32×D4C2314yes—
81C22×C32×C4C2311yescharacteristic
82C2×#638—28no—
83C2×#638C2318yes—
84C22×C3⋊Dic3—28no—
85C22×C3⋊Dic3C2312yes—
86C22×C3⋊Dic3C2311yescharacteristic
87C22×C3⋊Dic3C2318yes—
88#3830—232no—
89C2×C4×C3⋊D3—24no—
90C2×C4×C3⋊D3C2314yes—
91C2×#634—24no—
92C2×#634C2314yes—
93C2×C3×#67—28no—
94C2×C3×#67C2318yes—
95C22×C3×Dic3—28no—
96C22×C3×Dic3—28no—
97C22×C3×Dic3C2311yescharacteristic
98C22×C3×Dic3C2312yes—
99C22×C3×Dic3C2318yes—
100C22×C3×Dic3C2312yes—
101C22×C3×Dic3C2311yescharacteristic
102C22×C3×Dic3C2318yes—
103C22×C3×Dic3C2311yescharacteristic
104C3×#237—232no—
105C2×C3×C4×D3—24no—
106C2×C3×C4×D3C2314yes—
107C2×C3×Dic6—24no—
108C2×C3×Dic6C2314yes—
109C2×#626—24no—
110C2×#626C2314yes—
111C3×#217C2318yes—
112C3×C4⋊Dic3C2314yes—
113C3×C4×Dic3C2314yes—
114Dic3⋊Dic3C2318yes—
115Dic3⋊Dic3C2318yes—
116Dic3⋊Dic3C2318yes—
117Dic3⋊Dic3C2318yes—
118Dic3⋊Dic3C2314yes—
119#3722C2318yes—
120#3722C2314yes—
121(C2×D3)⋊Dic3C2318yes—
122(C2×D3)⋊Dic3C2314yes—
123C2×#547—91noSylow
124C2×C3×#41—38no—
125C2×C3×#41—68no—
126C22×C3×Q8—31no—
127C22×C3×D4—21no—
128C22×C3×D4—32no—
129C22×C3×D4C2×D311yescharacteristic
130C22×C3×D4C2×D311yescharacteristic
131C23×C3×C4—32no—
132C23×C3×C4—32no—
133C23×C3×C4—31no—
134C22×#67—32no—
135C22×#67—32no—
136C22×#67—31no—
137C22×#67—62no—
138C22×#67C2×D312yes—
139C23×Dic3—32no—
140C23×Dic3—32no—
141C23×Dic3—62no—
142C23×Dic3C2×D312yes—
143C23×Dic3C2×D312yes—
144C2×#237—28no—
145C2×#237—38no—
146C2×#237—38no—
147C2×#237—68no—
148C2×#237—616no—
149C2×#237—68no—
150C2×#237—68no—
151C2×#237C2×D318yescomplemented
152C22×D12—31no—
153C22×C4×D3—31no—
154C22×C4×D3—31no—
155C22×C4×D3—61no—
156C22×C4×D3C2×D311yescharacteristic
157C22×Dic6—31no—
158C22×Dic6—31no—
159C22×Dic6—61no—
160C22×Dic6C2×D311yescharacteristic
161C3×C4×D4—38no—
162C2×C3×C4⋊C4—31no—
163C2×C3×C22⋊C4—32no—
164C2×C3×C42—31no—
165C2×#217—32no—
166C2×#217—31no—
167C2×#217C2×D312yes—
168#946—38no—
169#944—38no—
170#939—316no—
171#935—316no—
172D4×Dic3C2×D318yescomplemented
173#930—316no—
174#929—316no—
175C4×#67—38no—
176C2×(C2×D3)⋊C4—31no—
177C2×(C2×D3)⋊C4—32no—
178C2×(C2×D3)⋊C4—31no—
179C2×(C2×D3)⋊C4—32no—
180C2×(C2×D3)⋊C4—31no—
181C2×(C2×D3)⋊C4—32no—
182C2×C4⋊Dic3—32no—
183C2×C4⋊Dic3—32no—
184C2×C4⋊Dic3—31no—
185C2×C4⋊Dic3—32no—
186C2×C4⋊Dic3—32no—
187C2×C4⋊Dic3—316no—
188C2×C4⋊Dic3C2×D311yescharacteristic
189#924—38no—
190C2×Dic3⋊C4—31no—
191C2×Dic3⋊C4—32no—
192C2×Dic3⋊C4—32no—
193C2×Dic3⋊C4—32no—
194C2×Dic3⋊C4—316no—
195C2×Dic3⋊C4—32no—
196C2×C4×Dic3C2×D311yescharacteristic
197#897—38no—
198#897—38no—
199#886—316no—
200#886—316no—
201C4×D12—38no—
202#869—38no—
203C23×C32—24no—
204C23×C32—24no—
205C23×C32C2×D418yes—
206C23×C32C2414yes—
207C23×C32C2411yescharacteristic
208C22×C3⋊D3—22no—
209C22×C3⋊D3—22no—
210C22×C3⋊D3—22no—
211C22×C3⋊D3C2412yes—
212C22×C3×D3—22no—
213C22×C3×D3—22no—
214C22×C3×D3—22no—
215C22×C3×D3C2412yes—
216C32×D4C2×D4116yescomplemented
217C2×C32×C4C2×D414yes—
218C2×C32×C4C2412yes—
219#638—216no—
220C2×C3⋊Dic3—24no—
221C2×C3⋊Dic3—22no—
222C2×C3⋊Dic3—216no—
223C2×C3⋊Dic3C2414yes—
224C2×C3⋊Dic3C2412yes—
225C4×C3⋊D3—28no—
226#634—28no—
227C3×#67—216no—
228C2×C3×Dic3—24no—
229C2×C3×Dic3—22no—
230C2×C3×Dic3—216no—
231C2×C3×Dic3—24no—
232C2×C3×Dic3—22no—
233C2×C3×Dic3—216no—
234C2×C3×Dic3#4114yescomplemented
235C2×C3×Dic3C2412yes—
236C2×C3×Dic3C2414yes—
237C2×C3×Dic3C2414yes—
238C2×C3×Dic3C2412yes—
239C2×C3×Dic3C2412yes—
240C3×C4×D3—28no—
241C3×Dic6—28no—
242#626—28no—
243C22×#41—31no—
244C22×#41—91no—
245#547—916no—
246C2×C4⋊Q8—91no—
247C2×#123—92no—
248C2×#123—92no—
249C2×C22⋊Q8—91no—
250C2×C22⋊Q8—91no—
251C2×#121—92no—
252C2×C4×D4—31no—
253C2×C4×D4—91no—
254C22×C4⋊C4—92no—
255C24×C3—22no—
256C24×C3—31no—
257C24×C3C22×D312yes—
258C24×C3C22×D312yes—
259C23×D3—31no—
260C23×D3—31no—
261C23×D3—61no—
262C23×D3C22×D311yescharacteristic
263C3×#41—632no—
264C2×C3×Q8—34no—
265C2×C3×Q8—64no—
266C2×C3×D4—28no—
267C2×C3×D4—24no—
268C2×C3×D4—38no—
269C2×C3×D4—68no—
270C2×C3×D4D1218yescomplemented
271C2×C3×D4#6718yescomplemented
272C2×C3×D4C22×D314yes—
273C2×C3×D4C22×D314yes—
274C22×C3×C4—21no—
275C22×C3×C4—31no—
276C22×C3×C4—31no—
277C22×C3×C4—32no—
278C22×C3×C4—38no—
279C22×C3×C4—31no—
280C22×C3×C4—32no—
281C22×C3×C4—38no—
282C22×C3×C4—34no—
283C22×C3×C4—68no—
284C22×C3×C4—68no—
285C22×C3×C4—64no—
286C22×C3×C4C22×D311yescharacteristic
287C22×C3×C4C22×D311yescharacteristic
288C2×#67—28no—
289C2×#67—38no—
290C2×#67—38no—
291C2×#67—34no—
292C2×#67—68no—
293C2×#67—616no—
294C2×#67—68no—
295C2×#67—68no—
296C2×#67—64no—
297C2×#67C22×D318yes—
298C22×Dic3—28no—
299C22×Dic3—28no—
300C22×Dic3—38no—
301C22×Dic3—32no—
302C22×Dic3—31no—
303C22×Dic3—38no—
304C22×Dic3—32no—
305C22×Dic3—31no—
306C22×Dic3—62no—
307C22×Dic3—61no—
308C22×Dic3—68no—
309C22×Dic3—616no—
310C22×Dic3—68no—
311C22×Dic3—68no—
312C22×Dic3C22×D318yes—
313C22×Dic3C22×D311yescharacteristic
314C22×Dic3C22×D312yes—
315C22×Dic3C22×D318yes—
316C22×Dic3C22×D312yes—
317C22×Dic3C22×D311yescharacteristic
318C22×Dic3C22×D311yescharacteristic
319#237—232no—
320#237—664no—
321#237—632no—
322#237—632no—
323C2×D12—34no—
324C2×D12—64no—
325C2×C4×D3—24no—
326C2×C4×D3—34no—
327C2×C4×D3—34no—
328C2×C4×D3—64no—
329C2×C4×D3—68no—
330C2×C4×D3—64no—
331C2×C4×D3—64no—
332C2×C4×D3C22×D314yes—
333C2×Dic6—24no—
334C2×Dic6—34no—
335C2×Dic6—34no—
336C2×Dic6—64no—
337C2×Dic6—68no—
338C2×Dic6—64no—
339C2×Dic6—64no—
340C2×Dic6C22×D314yes—
341C3×C4⋊C4—34no—
342C3×C22⋊C4—38no—
343C3×C42—34no—
344#217—38no—
345#217—34no—
346#217C22×D318yes—
347(C2×D3)⋊C4—34no—
348(C2×D3)⋊C4—38no—
349(C2×D3)⋊C4—34no—
350(C2×D3)⋊C4—38no—
351(C2×D3)⋊C4—34no—
352(C2×D3)⋊C4—38no—
353C4⋊Dic3—38no—
354C4⋊Dic3—38no—
355C4⋊Dic3—34no—
356C4⋊Dic3—38no—
357C4⋊Dic3—38no—
358C4⋊Dic3C22×D314yes—
359Dic3⋊C4—34no—
360Dic3⋊C4—38no—
361Dic3⋊C4—38no—
362Dic3⋊C4—38no—
363Dic3⋊C4—38no—
364C4×Dic3C22×D314yes—
365C22×C32—216no—
366C22×C32—24no—
367C22×C32—24no—
368C22×C32C22×D418yes—
369C22×C32C22×D412yes—
370C22×C32C2×#4112yes—
371C22×C322−1+412yes—
372C22×C32C2511yescharacteristic
373C2×C3⋊D3—22no—
374C2×C3⋊D3—22no—
375C2×C3⋊D3—22no—
376C2×C3⋊D3—44no—
377C2×C3×D3—22no—
378C2×C3×D3—22no—
379C2×C3×D3—22no—
380C2×C3×D3—44no—
381C32×C4C22×D414yes—
382C3⋊Dic3—24no—
383C3⋊Dic3—22no—
384C3×Dic3—24no—
385C3×Dic3—22no—
386C3×Dic3—24no—
387C3×Dic3—22no—
388C3×Dic3C2×#4114yescomplemented
389C2×#41—38no—
390C2×#41—68no—
391C2×#41—98no—
392C2×#41—188no—
393C22×Q8—31no—
394C22×Q8—91no—
395C22×D4—32no—
396C22×D4—91no—
397C22×D4—92no—
398C22×D4D3211yescharacteristic
399C23×C4—32no—
400C23×C4—32no—
401C23×C4—31no—
402C23×C4—92no—
403C23×C4—91no—
404C4⋊Q8—98no—
405#123—916no—
406#123—916no—
407C22⋊Q8—98no—
408C22⋊Q8—98no—
409#121—916no—
410C4×D4—38no—
411C4×D4—98no—
412C2×C4⋊C4—31no—
413C2×C4⋊C4—91no—
414C2×C4⋊C4—92no—
415C2×C4⋊C4—92no—
416C2×C4⋊C4—92no—
417C2×C4⋊C4—916no—
418C2×C4⋊C4—92no—
419C2×C22⋊C4—32no—
420C2×C22⋊C4—91no—
421C2×C22⋊C4—92no—
422C2×C22⋊C4—91no—
423C2×C22⋊C4—92no—
424C2×C42—31no—
425C23×C3—24no—
426C23×C3—24no—
427C23×C3—24no—
428C23×C3—24no—
429C23×C3—24no—
430C23×C3—21no—
431C23×C3—28no—
432C23×C3—32no—
433C23×C3—44no—
434C23×C3—44no—
435C23×C3—62no—
436C23×C3—62no—
437C23×C3—62no—
438C23×C3C2×D1218yes—
439C23×C3C2×#6718yes—
440C23×C3C23×D314yes—
441C23×C3C23×D314yes—
442C23×C3C23×D311yescharacteristic
443C23×C3C23×D311yescharacteristic
444C22×D3—22no—
445C22×D3—22no—
446C22×D3—22no—
447C22×D3—32no—
448C22×D3—32no—
449C22×D3—62no—
450C22×D3—64no—
451C22×D3—62no—
452C22×D3—62no—
453C22×D3—62no—
454C22×D3—62no—
455C22×D3—62no—
456C22×D3—62no—
457C22×D3—122no—
458C22×D3—122no—
459C22×D3C23×D312yes—
460C3×Q8—68no—
461C3×D4—216no—
462C3×D4—616no—
463C3×D4C2×D12116yescomplemented
464C3×D4C2×#67116yescomplemented
465C2×C3×C4—22no—
466C2×C3×C4—24no—
467C2×C3×C4—34no—
468C2×C3×C4—32no—
469C2×C3×C4—32no—
470C2×C3×C4—34no—
471C2×C3×C4—32no—
472C2×C3×C4—34no—
473C2×C3×C4—616no—
474C2×C3×C4—62no—
475C2×C3×C4—64no—
476C2×C3×C4—616no—
477C2×C3×C4—64no—
478C2×C3×C4—62no—
479C2×C3×C4—68no—
480C2×C3×C4C2×D1214yes—
481C2×C3×C4C2×#6714yes—
482C2×C3×C4C23×D312yes—
483C2×C3×C4C23×D312yes—
484#67—216no—
485#67—632no—
486#67—616no—
487#67—616no—
488#67—68no—
489C2×Dic3—24no—
490C2×Dic3—22no—
491C2×Dic3—24no—
492C2×Dic3—22no—
493C2×Dic3—216no—
494C2×Dic3—216no—
495C2×Dic3—34no—
496C2×Dic3—32no—
497C2×Dic3—34no—
498C2×Dic3—32no—
499C2×Dic3—64no—
500C2×Dic3—62no—
501C2×Dic3—68no—
502C2×Dic3—64no—
503C2×Dic3—632no—
504C2×Dic3—64no—
505C2×Dic3—62no—
506C2×Dic3—616no—
507C2×Dic3—64no—
508C2×Dic3—62no—
509C2×Dic3—616no—
510C2×Dic3#23714yescomplemented
511C2×Dic3C23×D312yes—
512C2×Dic3C23×D314yes—
513C2×Dic3C23×D314yes—
514C2×Dic3C23×D312yes—
515C2×Dic3C23×D312yes—
516D12—68no—
517C4×D3—28no—
518C4×D3—616no—
519C4×D3—68no—
520C4×D3—68no—
521Dic6—28no—
522Dic6—616no—
523Dic6—68no—
524Dic6—68no—
525C2×C32—28no—
526C2×C32#54714yescomplemented
527C2×C32C23×D411yescharacteristic
528C2×C32C22×#4111yescharacteristic
529C2×C32C2×2−1+411yescharacteristic
530C3⋊D3—42no—
531C3×D3—42no—
532C24—31no—
533C24—91no—
534C24C2×D3212yes—
535#41—632no—
536#41—1832no—
537C2×Q8—34no—
538C2×Q8—64no—
539C2×Q8—94no—
540C2×Q8—184no—
541C2×D4—38no—
542C2×D4—68no—
543C2×D4—94no—
544C2×D4—98no—
545C2×D4—184no—
546C2×D4—188no—
547C2×D4#62618yescomplemented
548C2×D4C2×D3214yes—
549C22×C4—31no—
550C22×C4—38no—
551C22×C4—38no—
552C22×C4—31no—
553C22×C4—32no—
554C22×C4—31no—
555C22×C4—32no—
556C22×C4—34no—
557C22×C4—68no—
558C22×C4—68no—
559C22×C4—64no—
560C22×C4—98no—
561C22×C4—91no—
562C22×C4—92no—
563C22×C4—94no—
564C22×C4—188no—
565C22×C4—184no—
566C22×C4C2×D3211yescharacteristic
567C4⋊C4—34no—
568C4⋊C4—94no—
569C4⋊C4—98no—
570C4⋊C4—98no—
571C4⋊C4—98no—
572C4⋊C4—98no—
573C22⋊C4—38no—
574C22⋊C4—94no—
575C22⋊C4—98no—
576C22⋊C4—94no—
577C22⋊C4—98no—
578C42—34no—
579C22×C3—24no—
580C22×C3—24no—
581C22×C3—24no—
582C22×C3—24no—
583C22×C3—216no—
584C22×C3—216no—
585C22×C3—22no—
586C22×C3—22no—
587C22×C3—22no—
588C22×C3—28no—
589C22×C3—21no—
590C22×C3—44no—
591C22×C3—44no—
592C22×C3—416no—
593C22×C3—62no—
594C22×C3—62no—
595C22×C3—62no—
596C22×C3—124no—
597C22×C3C22×D1218yes—
598C22×C3C22×D1212yes—
599C22×C3C2×#23712yes—
600C22×C3D3×#4112yes—
601C22×C3#101012yes—
602C22×C3#101012yes—
603C22×C3C22×#6718yes—
604C22×C3C22×#6712yes—
605C22×C3C24×D311yescharacteristic
606C22×C3C24×D311yescharacteristic
607C2×D3—22no—
608C2×D3—22no—
609C2×D3—22no—
610C2×D3—44no—
611C2×D3—64no—
612C2×D3—62no—
613C2×D3—62no—
614C2×D3—62no—
615C2×D3—62no—
616C2×D3—62no—
617C2×D3—62no—
618C2×D3—122no—
619C2×D3—122no—
620C2×D3—128no—
621C2×D3—124no—
622C2×D3—124no—
623C3×C4—24no—
624C3×C4—34no—
625C3×C4—62no—
626C3×C4—64no—
627C3×C4—64no—
628C3×C4—62no—
629C3×C4C22×D1214yes—
630C3×C4C22×#6714yes—
631Dic3—24no—
632Dic3—22no—
633Dic3—24no—
634Dic3—22no—
635Dic3—68no—
636Dic3—64no—
637Dic3—64no—
638Dic3—62no—
639Dic3—64no—
640Dic3—62no—
641Dic3C2×#23714yescomplemented
642C32C2×#54711yescharacteristic, complemented, Sylow
643C23—24no—
644C23—24no—
645C23—32no—
646C23—62no—
647C23—62no—
648C23—62no—
649C23—92no—
650C23—182no—
651C23—182no—
652C23—182no—
653C23C2×#62618yes—
654C23C22×D3214yes—
655C23C22×D3211yescharacteristic
656Q8—68no—
657Q8—188no—
658D4—616no—
659D4—188no—
660D4—1816no—
661D4C2×#626116yescomplemented
662C2×C4—34no—
663C2×C4—32no—
664C2×C4—32no—
665C2×C4—34no—
666C2×C4—32no—
667C2×C4—34no—
668C2×C4—616no—
669C2×C4—62no—
670C2×C4—64no—
671C2×C4—62no—
672C2×C4—64no—
673C2×C4—616no—
674C2×C4—68no—
675C2×C4—92no—
676C2×C4—94no—
677C2×C4—182no—
678C2×C4—184no—
679C2×C4—1816no—
680C2×C4—188no—
681C2×C4C2×#62614yes—
682C2×C4C22×D3212yes—
683C2×C3—28no—
684C2×C3—28no—
685C2×C3—21no—
686C2×C3—21no—
687C2×C3—21no—
688C2×C3—24no—
689C2×C3—48no—
690C2×C3—122no—
691C2×C3#555514yescomplemented
692C2×C3#582414yescomplemented
693C2×C3C23×D1211yescharacteristic
694C2×C3C22×#23711yescharacteristic
695C2×C3C2×D3×#4111yescharacteristic
696C2×C3C2×#101011yescharacteristic
697C2×C3C2×#101011yescharacteristic
698C2×C3C23×#6711yescharacteristic
699D3—42no—
700D3—124no—
701D3—122no—
702D3—122no—
703C22—24no—
704C22—24no—
705C22—216no—
706C22—62no—
707C22—62no—
708C22—62no—
709C22—124no—
710C22—182no—
711C22—182no—
712C22—182no—
713C22—364no—
714C22#6430912yes—
715C22D3×#23712yes—
716C22C22×#62618yes—
717C22C22×#62612yes—
718C22C23×D3211yescharacteristic
719C4—34no—
720C4—62no—
721C4—64no—
722C4—62no—
723C4—64no—
724C4—182no—
725C4—184no—
726C4C22×#62614yes—
727C3—21no—
728C3C2×#555511yescharacteristic, complemented
729C3C2×#582411yescharacteristic, complemented
730C2—28no—
731C2—122no—
732C2—362no—
733C2#1059524814yesdirect product factor
734C2C2×#6430911yescharacteristic
735C2C2×D3×#23711yescharacteristic
736C2C23×#62611yescharacteristic
subgroupG/H
centerC23C22×D32
commutator, cosocleC22×C32C25
FrattiniC22C23×D32
FittingC22×C32×D4C22
socleC23×C32C24
hypercenterC22×D4D32
hypocenterC32C2×#547
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C23 ◁ C22×D4

Complements

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

NH ≅ G/Ntype
1. C22×#3830C2semidirect
2. C22×C3×#237C2semidirect
3. C2×C3×D4×Dic3C2semidirect
4. C2×#63978C2semidirect
5. C2×#63966C2semidirect
6. C22×Dic3⋊Dic3C2semidirect
7. C2×#63962C2semidirect
8. #10595248C2direct (N × H)
9. C2×C4×#626C2semidirect
10. C2×#63871C2semidirect
11. C2×#63866C2semidirect
12. C2×#63857C2semidirect
19. C2×#3830C22semidirect
26. C2×C3×#237C22semidirect
31. C3×D4×Dic3C22semidirect
34. #63978C22semidirect
35. #63966C22semidirect
41. C2×Dic3⋊Dic3C22semidirect
44. #63962C22semidirect
47. C4×#626C22semidirect
48. #63871C22semidirect
49. #63866C22semidirect
50. #63857C22semidirect
55. C22×#237D3semidirect
62. C2×D4×Dic3D3semidirect
79. C2×C32×D4D4semidirect
151. C2×#237C2×D3semidirect
172. D4×Dic3C2×D3semidirect
216. C32×D4C2×D4semidirect
234. C2×C3×Dic3#41semidirect
270. C2×C3×D4D12semidirect
271. C2×C3×D4#67semidirect
388. C3×Dic3C2×#41semidirect
463. C3×D4C2×D12semidirect
464. C3×D4C2×#67semidirect
510. C2×Dic3#237semidirect
526. C2×C32#547semidirect
547. C2×D4#626semidirect
641. Dic3C2×#237semidirect
642. C32C2×#547semidirect
661. D4C2×#626semidirect
691. C2×C3#5555semidirect
692. C2×C3#5824semidirect
728. C3C2×#5555semidirect
729. C3C2×#5824semidirect
733. C2#10595248direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#38302
C22×C3×#2372
C2×C3×D4×Dic32
C2×#639782
C2×#639662
C22×Dic3⋊Dic32
C2×#639622
#105952482
C2×C4×#6262
C2×#638712
C2×#638662
C2×#638572
C2×#58243
C2×#55553