Finite Group Databasebeta

← C2×#10594890 #11902544

Subgroups — C2×#10594890 #11902544

Order 1152.

3477 conjugacy classes of subgroups.

The subgroup lattice has 744 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C3×#235C211yesmaximal, characteristic, complemented
2C22×#3796C211yesmaximal, characteristic, complemented
3C2×C4×#638C211yesmaximal, characteristic, complemented
4C2×C3×#924C211yesmaximal, characteristic, complemented
5C2×#63971C212yesmaximal, complemented
6C2×#63969C212yesmaximal, complemented
7C2×#63898C211yesmaximal, characteristic, complemented
8#10594890C2116yesmaximal, direct product factor
9C2×D3×Dic3⋊C4C212yesmaximal, complemented
10C2×#63873C211yesmaximal, characteristic, complemented
11C2×#63871C211yesmaximal, characteristic, complemented
12C2×#63850C212yesmaximal, complemented
13C2×#5824—31nomaximal
14C2×#5631—31nomaximal
15C23×C32×C4C2211yescharacteristic
16C22×#638C2211yescharacteristic
17C22×C4×C3⋊D3C2211yescharacteristic
18C22×C3×#67C2212yes—
19C2×C3×#235—28no—
20C2×C3×#235C2218yescomplemented
21C22×C3×D12C2211yescharacteristic
22C22×C3×C4×D3C2212yes—
23C22×C3×Dic6C2211yescharacteristic
24C22×C3×Dic6C2211yescharacteristic
25C22×#626C2212yes—
26C22×D3×Dic3C2212yes—
27C22×D3×Dic3C2212yes—
28C2×#3796—28no—
29C2×#3796C2218yescomplemented
30C2×#3757C2211yescharacteristic
31C4×#638C2218yescomplemented
32C2×#3752C2211yescharacteristic
33C2×#3750C2211yescharacteristic
34C2×C4×C3⋊Dic3C2211yescharacteristic
35C2×C3×#217C2212yes—
36C2×C3×C4⋊Dic3C2211yescharacteristic
37C3×#924C2218yescomplemented
38C2×C3×Dic3⋊C4C2212yes—
39#63971C22116yescomplemented
40#63969C22116yescomplemented
41C2×#3724C2212yes—
42C2×#3724C2212yes—
43C2×Dic3⋊Dic3C2212yes—
44C2×#3722C2212yes—
45C2×(C2×D3)⋊Dic3C2212yes—
46#63898C2218yescomplemented
47D3×Dic3⋊C4C22116yescomplemented
48#63873C2218yescomplemented
49#63871C2218yescomplemented
50#63850C22116yescomplemented
51C22×C3×#41—31no—
52C22×#239—31no—
53C22×#237—31no—
54C22×#235D311yescharacteristic, complemented
55C2×C3×C22⋊Q8—31no—
56#5824—316no—
57C2×#946—31no—
58C2×#944—31no—
59C2×#944—31no—
60C2×#939—32no—
61C2×#935—32no—
62C2×D4×Dic3—31no—
63C2×#929—32no—
64C2×C4×#67—31no—
65C2×C4×#67—31no—
66C2×C4×#67—61no—
67C2×#924D311yescharacteristic, complemented
68C22×Dic3⋊C4—32no—
69#5631—316no—
70C2×#897—31no—
71C2×#894—32no—
72C2×#893—31no—
73C2×D3×C4⋊C4—32no—
74C2×#884—32no—
75C2×#883—32no—
76C24×C32C2311yescharacteristic
77C23×C3⋊D3C2311yescharacteristic
78C23×C3×D3C2312yes—
79C22×C32×C4—24no—
80C22×C32×C4C2311yescharacteristic
81C22×C32×C4C2314yes—
82C22×C32×C4C2311yescharacteristic
83C2×#638—24no—
84C2×#638C2314yes—
85C22×C3⋊Dic3C2311yescharacteristic
86C22×C3⋊Dic3C2311yescharacteristic
87C22×C3⋊Dic3C2311yescharacteristic
88C2×C4×C3⋊D3—24no—
89C2×C4×C3⋊D3C2314yes—
90C2×C3×#67—28no—
91C2×C3×#67C2318yes—
92C22×C3×Dic3C2312yes—
93C22×C3×Dic3C2312yes—
94C22×C3×Dic3C2312yes—
95C3×#235—232no—
96C2×C3×D12D418yescomplemented
97C2×C3×D12C2314yes—
98C2×C3×C4×D3—28no—
99C2×C3×C4×D3C2318yes—
100C2×C3×Dic6—24no—
101C2×C3×Dic6—24no—
102C2×C3×Dic6C2314yes—
103C2×C3×Dic6C2314yes—
104C2×#626—28no—
105C2×#626C2318yes—
106C2×D3×Dic3—28no—
107C2×D3×Dic3—28no—
108C2×D3×Dic3C2318yes—
109C2×D3×Dic3C2318yes—
110#3796—232no—
111#3757C2314yes—
112#3752C2314yes—
113#3750C2314yes—
114C4×C3⋊Dic3C2314yes—
115C3×#217C2318yes—
116C3×C4⋊Dic3C2314yes—
117C3×Dic3⋊C4C2318yes—
118#3724C2318yes—
119#3724C2318yes—
120Dic3⋊Dic3C2318yes—
121#3722C2318yes—
122(C2×D3)⋊Dic3C2318yes—
123C2×#547—91noSylow
124C2×C3×#41—38no—
125C2×C3×#41—68no—
126C22×C3×Q8—31no—
127C22×C3×Q8—31no—
128C22×C3×D4—32no—
129C22×C3×D4—31no—
130C23×C3×C4—21no—
131C23×C3×C4—32no—
132C23×C3×C4C2×D311yescharacteristic
133C23×C3×C4C2×D311yescharacteristic
134C22×#67—31no—
135C22×#67—31no—
136C22×#67—32no—
137C22×#67—61no—
138C22×#67C2×D312yes—
139C23×Dic3—32no—
140C23×Dic3—32no—
141C2×#239—38no—
142C2×#239—68no—
143C2×#237—38no—
144C2×#237—68no—
145C2×#235—28no—
146C2×#235C2×D318yescomplemented
147C22×D12—32no—
148C22×D12C2×D311yescharacteristic
149C22×C4×D3—32no—
150C22×C4×D3—32no—
151C22×C4×D3—31no—
152C22×C4×D3—31no—
153C22×C4×D3—61no—
154C22×C4×D3C2×D312yes—
155C22×Dic6C2×D311yescharacteristic
156C22×Dic6C2×D311yescharacteristic
157C3×C22⋊Q8—38no—
158C2×C3×C4⋊C4—32no—
159C2×C3×C4⋊C4—31no—
160C2×C3×C22⋊C4—32no—
161C2×#217—31no—
162C2×#217—31no—
163C2×#217—32no—
164C2×#217—61no—
165C2×#217C2×D312yes—
166#946—38no—
167#944—38no—
168#944—38no—
169#939—316no—
170#935—316no—
171D4×Dic3—38no—
172#929—316no—
173C4×#67—38no—
174C4×#67—38no—
175C4×#67—68no—
176C2×(C2×D3)⋊C4—32no—
177C2×(C2×D3)⋊C4—31no—
178C2×(C2×D3)⋊C4—31no—
179C2×(C2×D3)⋊C4—32no—
180C2×(C2×D3)⋊C4—32no—
181C2×(C2×D3)⋊C4—61no—
182C2×C4⋊Dic3—32no—
183C2×C4⋊Dic3C2×D311yescharacteristic
184#924C2×D318yescomplemented
185C2×Dic3⋊C4—31no—
186C2×Dic3⋊C4—31no—
187C2×Dic3⋊C4—32no—
188C2×Dic3⋊C4—32no—
189C2×Dic3⋊C4—32no—
190C2×Dic3⋊C4—32no—
191C2×Dic3⋊C4—32no—
192C2×Dic3⋊C4—316no—
193C2×Dic3⋊C4—61no—
194C2×Dic3⋊C4C2×D312yes—
195C2×C4×Dic3—31no—
196C2×C4×Dic3—31no—
197C2×C4×Dic3—61no—
198#897—38no—
199#894—316no—
200#893—38no—
201D3×C4⋊C4—316no—
202#884—316no—
203#883—316no—
204C23×C32—22no—
205C23×C32—22no—
206C23×C32—22no—
207C23×C32C2412yes—
208C23×C32C2411yescharacteristic
209C22×C3⋊D3—22no—
210C22×C3⋊D3—22no—
211C22×C3⋊D3—22no—
212C22×C3⋊D3C2412yes—
213C22×C3×D3—24no—
214C22×C3×D3—24no—
215C22×C3×D3C2×D418yes—
216C22×C3×D3C2414yes—
217C2×C32×C4—22no—
218C2×C32×C4—28no—
219C2×C32×C4C2×D414yes—
220C2×C32×C4C2412yes—
221C2×C32×C4C2412yes—
222#638—28no—
223C2×C3⋊Dic3—22no—
224C2×C3⋊Dic3—22no—
225C2×C3⋊Dic3#4114yescomplemented
226C2×C3⋊Dic3C2412yes—
227C2×C3⋊Dic3C2412yes—
228C2×C3⋊Dic3C2412yes—
229C4×C3⋊D3—28no—
230C3×#67—216no—
231C2×C3×Dic3—24no—
232C2×C3×Dic3—24no—
233C2×C3×Dic3—24no—
234C2×C3×Dic3C2414yes—
235C2×C3×Dic3C2414yes—
236C2×C3×Dic3C2414yes—
237C3×D12C2×D4116yescomplemented
238C3×C4×D3—216no—
239C3×Dic6—28no—
240C3×Dic6—28no—
241#626—216no—
242D3×Dic3—216no—
243D3×Dic3—216no—
244C22×#41—31no—
245C22×#41—91no—
246#547—916no—
247C2×C4⋊Q8—91no—
248C2×#123—92no—
249C2×#123—92no—
250C2×C22⋊Q8—31no—
251C2×C22⋊Q8—91no—
252C2×#121—92no—
253C2×C4×D4—91no—
254C2×C4×D4—91no—
255C22×C4⋊C4—92no—
256C24×C3—21no—
257C24×C3—32no—
258C24×C3C22×D311yescharacteristic
259C24×C3C22×D311yescharacteristic
260C23×D3—31no—
261C23×D3—31no—
262C23×D3—61no—
263C23×D3C22×D312yes—
264C3×#41—632no—
265C2×C3×Q8—34no—
266C2×C3×Q8—34no—
267C2×C3×Q8—64no—
268C2×C3×Q8—64no—
269C2×C3×D4—38no—
270C2×C3×D4—38no—
271C2×C3×D4—34no—
272C2×C3×D4—68no—
273C22×C3×C4—24no—
274C22×C3×C4—24no—
275C22×C3×C4—21no—
276C22×C3×C4—21no—
277C22×C3×C4—24no—
278C22×C3×C4—32no—
279C22×C3×C4—32no—
280C22×C3×C4—32no—
281C22×C3×C4—38no—
282C22×C3×C4—44no—
283C22×C3×C4—68no—
284C22×C3×C4C22×D311yescharacteristic
285C22×C3×C4C22×D311yescharacteristic
286C22×C3×C4C22×D314yes—
287C22×C3×C4C22×D314yes—
288C22×C3×C4C22×D311yescharacteristic
289C22×C3×C4C22×D311yescharacteristic
290C2×#67—28no—
291C2×#67—34no—
292C2×#67—34no—
293C2×#67—38no—
294C2×#67—64no—
295C2×#67—68no—
296C2×#67—64no—
297C2×#67—64no—
298C2×#67—68no—
299C2×#67C22×D318yes—
300C22×Dic3—31no—
301C22×Dic3—31no—
302C22×Dic3—31no—
303C22×Dic3—31no—
304C22×Dic3—31no—
305C22×Dic3—31no—
306C22×Dic3—38no—
307C22×Dic3—38no—
308C22×Dic3—61no—
309C22×Dic3—61no—
310C22×Dic3—61no—
311C22×Dic3—68no—
312C22×Dic3—68no—
313C22×Dic3C22×D312yes—
314C22×Dic3C22×D312yes—
315C22×Dic3C22×D312yes—
316#239—632no—
317#237—632no—
318#235—232no—
319C2×D12—38no—
320C2×D12—68no—
321C2×D12#6718yescomplemented
322C2×D12C22×D314yes—
323C2×C4×D3—28no—
324C2×C4×D3—38no—
325C2×C4×D3—38no—
326C2×C4×D3—34no—
327C2×C4×D3—34no—
328C2×C4×D3—64no—
329C2×C4×D3—68no—
330C2×C4×D3—68no—
331C2×C4×D3—64no—
332C2×C4×D3—64no—
333C2×C4×D3—124no—
334C2×C4×D3C22×D318yes—
335C2×Dic6—24no—
336C2×Dic6—24no—
337C2×Dic6C22×D314yes—
338C2×Dic6C22×D314yes—
339C3×C4⋊C4—38no—
340C3×C4⋊C4—34no—
341C3×C22⋊C4—38no—
342#217—34no—
343#217—34no—
344#217—38no—
345#217—64no—
346#217C22×D318yes—
347(C2×D3)⋊C4—38no—
348(C2×D3)⋊C4—34no—
349(C2×D3)⋊C4—34no—
350(C2×D3)⋊C4—38no—
351(C2×D3)⋊C4—38no—
352(C2×D3)⋊C4—64no—
353C4⋊Dic3—38no—
354C4⋊Dic3C22×D314yes—
355Dic3⋊C4—34no—
356Dic3⋊C4—34no—
357Dic3⋊C4—38no—
358Dic3⋊C4—38no—
359Dic3⋊C4—38no—
360Dic3⋊C4—38no—
361Dic3⋊C4—38no—
362Dic3⋊C4—64no—
363Dic3⋊C4C22×D318yes—
364C4×Dic3—34no—
365C4×Dic3—34no—
366C4×Dic3—64no—
367C22×C32—22no—
368C22×C32—22no—
369C22×C32—22no—
370C22×C32—44no—
371C22×C32C22×D412yes—
372C22×C32C2×#4112yes—
373C22×C322−1+412yes—
374C22×C32C2511yescharacteristic
375C2×C3⋊D3—22no—
376C2×C3⋊D3—22no—
377C2×C3⋊D3—22no—
378C2×C3⋊D3—44no—
379C2×C3×D3—216no—
380C2×C3×D3—24no—
381C2×C3×D3—24no—
382C2×C3×D3C22×D418yes—
383C32×C4—22no—
384C32×C4C22×D414yes—
385C3⋊Dic3—22no—
386C3⋊Dic3—22no—
387C3⋊Dic3C2×#4114yescomplemented
388C3×Dic3—24no—
389C3×Dic3—24no—
390C3×Dic3—24no—
391C2×#41—38no—
392C2×#41—68no—
393C2×#41—98no—
394C2×#41—188no—
395C22×Q8—31no—
396C22×Q8—31no—
397C22×D4—32no—
398C22×D4—31no—
399C22×D4—92no—
400C22×D4—91no—
401C23×C4—32no—
402C23×C4—92no—
403C23×C4—92no—
404C23×C4—91no—
405C23×C4D3211yescharacteristic
406C4⋊Q8—98no—
407#123—916no—
408#123—916no—
409C22⋊Q8—38no—
410C22⋊Q8—98no—
411#121—916no—
412C4×D4—98no—
413C4×D4—98no—
414C2×C4⋊C4—32no—
415C2×C4⋊C4—31no—
416C2×C4⋊C4—916no—
417C2×C4⋊C4—92no—
418C2×C4⋊C4—92no—
419C2×C4⋊C4—92no—
420C2×C4⋊C4—91no—
421C2×C22⋊C4—32no—
422C2×C22⋊C4—92no—
423C2×C22⋊C4—92no—
424C2×C22⋊C4—91no—
425C2×C22⋊C4—91no—
426C2×C42—91no—
427C23×C3—24no—
428C23×C3—22no—
429C23×C3—22no—
430C23×C3—22no—
431C23×C3—22no—
432C23×C3—22no—
433C23×C3—22no—
434C23×C3—22no—
435C23×C3—21no—
436C23×C3—38no—
437C23×C3—34no—
438C23×C3—42no—
439C23×C3—42no—
440C23×C3—64no—
441C23×C3—64no—
442C23×C3C23×D312yes—
443C23×C3C23×D312yes—
444C23×C3C23×D311yescharacteristic
445C23×C3C23×D311yescharacteristic
446C22×D3—24no—
447C22×D3—24no—
448C22×D3—32no—
449C22×D3—32no—
450C22×D3—62no—
451C22×D3—64no—
452C22×D3—62no—
453C22×D3—62no—
454C22×D3—62no—
455C22×D3—62no—
456C22×D3—62no—
457C22×D3—62no—
458C22×D3—122no—
459C22×D3—122no—
460C22×D3C2×#6718yes—
461C22×D3C23×D314yes—
462C3×Q8—68no—
463C3×Q8—68no—
464C3×D4—316no—
465C3×D4—616no—
466C2×C3×C4—22no—
467C2×C3×C4—22no—
468C2×C3×C4—28no—
469C2×C3×C4—28no—
470C2×C3×C4—22no—
471C2×C3×C4—22no—
472C2×C3×C4—24no—
473C2×C3×C4—34no—
474C2×C3×C4—34no—
475C2×C3×C4—34no—
476C2×C3×C4—48no—
477C2×C3×C4—42no—
478C2×C3×C4—616no—
479C2×C3×C4—64no—
480C2×C3×C4—64no—
481C2×C3×C4—64no—
482C2×C3×C4D3×D414yes—
483C2×C3×C4C2×#6714yes—
484C2×C3×C4C23×D312yes—
485C2×C3×C4C23×D312yes—
486C2×C3×C4C23×D312yes—
487C2×C3×C4C23×D312yes—
488#67—216no—
489#67—616no—
490#67—68no—
491#67—68no—
492#67—616no—
493C2×Dic3—24no—
494C2×Dic3—24no—
495C2×Dic3—24no—
496C2×Dic3—34no—
497C2×Dic3—34no—
498C2×Dic3—32no—
499C2×Dic3—32no—
500C2×Dic3—32no—
501C2×Dic3—32no—
502C2×Dic3—32no—
503C2×Dic3—32no—
504C2×Dic3—64no—
505C2×Dic3—62no—
506C2×Dic3—62no—
507C2×Dic3—62no—
508C2×Dic3—616no—
509C2×Dic3—616no—
510C2×Dic3—62no—
511C2×Dic3—62no—
512C2×Dic3—62no—
513C2×Dic3—62no—
514C2×Dic3—122no—
515C2×Dic3—122no—
516C2×Dic3C23×D314yes—
517C2×Dic3C23×D314yes—
518C2×Dic3C23×D314yes—
519D12—616no—
520D12C2×#67116yescomplemented
521C4×D3—216no—
522C4×D3—616no—
523C4×D3—616no—
524C4×D3—68no—
525C4×D3—68no—
526C4×D3—128no—
527Dic6—28no—
528Dic6—28no—
529C2×C32—42no—
530C2×C32#54714yescomplemented
531C2×C32C23×D411yescharacteristic
532C2×C32C22×#4111yescharacteristic
533C2×C32C2×2−1+411yescharacteristic
534C3⋊D3—42no—
535C3×D3—28no—
536C24—32no—
537C24—91no—
538C24C2×D3211yescharacteristic
539#41—632no—
540#41—1832no—
541C2×Q8—34no—
542C2×Q8—34no—
543C2×Q8—64no—
544C2×Q8—64no—
545C2×D4—38no—
546C2×D4—34no—
547C2×D4—38no—
548C2×D4—68no—
549C2×D4—98no—
550C2×D4—94no—
551C2×D4—188no—
552C2×D4—184no—
553C22×C4—24no—
554C22×C4—32no—
555C22×C4—32no—
556C22×C4—32no—
557C22×C4—38no—
558C22×C4—68no—
559C22×C4—98no—
560C22×C4—98no—
561C22×C4—91no—
562C22×C4—91no—
563C22×C4—91no—
564C22×C4—94no—
565C22×C4—188no—
566C22×C4—188no—
567C22×C4—184no—
568C22×C4C2×D3214yes—
569C22×C4C2×D3211yescharacteristic
570C22×C4C2×D3211yescharacteristic
571C4⋊C4—38no—
572C4⋊C4—34no—
573C4⋊C4—98no—
574C4⋊C4—98no—
575C4⋊C4—98no—
576C4⋊C4—94no—
577C22⋊C4—38no—
578C22⋊C4—98no—
579C22⋊C4—98no—
580C22⋊C4—94no—
581C22⋊C4—94no—
582C42—94no—
583C22×C3—24no—
584C22×C3—22no—
585C22×C3—22no—
586C22×C3—22no—
587C22×C3—22no—
588C22×C3—22no—
589C22×C3—22no—
590C22×C3—22no—
591C22×C3—22no—
592C22×C3—22no—
593C22×C3—21no—
594C22×C3—38no—
595C22×C3—42no—
596C22×C3—42no—
597C22×C3—48no—
598C22×C3—44no—
599C22×C3—44no—
600C22×C3—64no—
601C22×C3—64no—
602C22×C3—616no—
603C22×C3C2×D3×D412yes—
604C22×C3#100712yes—
605C22×C3D3×#4112yes—
606C22×C3D3×#4112yes—
607C22×C3#101012yes—
608C22×C3C22×#6712yes—
609C22×C3C24×D311yescharacteristic
610C22×C3C24×D311yescharacteristic
611C2×D3—24no—
612C2×D3—24no—
613C2×D3—216no—
614C2×D3—64no—
615C2×D3—62no—
616C2×D3—62no—
617C2×D3—62no—
618C2×D3—62no—
619C2×D3—62no—
620C2×D3—62no—
621C2×D3—122no—
622C2×D3—122no—
623C2×D3—128no—
624C2×D3—124no—
625C2×D3—124no—
626C2×D3C22×#6718yes—
627C3×C4—22no—
628C3×C4—22no—
629C3×C4—24no—
630C3×C4—42no—
631C3×C4—64no—
632C3×C4—64no—
633C3×C4—64no—
634C3×C4C2×D3×D414yes—
635C3×C4C22×#6714yes—
636Dic3—24no—
637Dic3—24no—
638Dic3—24no—
639Dic3—34no—
640Dic3—34no—
641Dic3—64no—
642Dic3—62no—
643Dic3—62no—
644Dic3—62no—
645Dic3—62no—
646Dic3—122no—
647Dic3—122no—
648C32C2×#54711yescharacteristic, complemented, Sylow
649C23—22no—
650C23—22no—
651C23—22no—
652C23—38no—
653C23—34no—
654C23—64no—
655C23—64no—
656C23—92no—
657C23—182no—
658C23—182no—
659C23—182no—
660C23C22×D3212yes—
661C23C22×D3211yescharacteristic
662Q8—68no—
663Q8—68no—
664D4—316no—
665D4—616no—
666D4—1816no—
667D4—188no—
668C2×C4—22no—
669C2×C4—28no—
670C2×C4—34no—
671C2×C4—34no—
672C2×C4—34no—
673C2×C4—616no—
674C2×C4—64no—
675C2×C4—64no—
676C2×C4—64no—
677C2×C4—94no—
678C2×C4—92no—
679C2×C4—92no—
680C2×C4—92no—
681C2×C4—1816no—
682C2×C4—1816no—
683C2×C4—182no—
684C2×C4—182no—
685C2×C4—188no—
686C2×C4D3×#6714yes—
687C2×C4C22×D3212yes—
688C2×C4C22×D3212yes—
689C2×C3—21no—
690C2×C3—21no—
691C2×C3—24no—
692C2×C3—21no—
693C2×C3—44no—
694C2×C3—42no—
695C2×C3—42no—
696C2×C3—68no—
697C2×C3#563114yescomplemented
698C2×C3#582414yescomplemented
699C2×C3C22×D3×D411yescharacteristic
700C2×C3C2×#100711yescharacteristic
701C2×C3C2×D3×#4111yescharacteristic
702C2×C3C2×D3×#4111yescharacteristic
703C2×C3C2×#101011yescharacteristic
704C2×C3C23×#6711yescharacteristic
705D3—28no—
706D3—124no—
707D3—122no—
708D3—122no—
709C22—22no—
710C22—22no—
711C22—22no—
712C22—38no—
713C22—44no—
714C22—64no—
715C22—64no—
716C22—616no—
717C22—182no—
718C22—182no—
719C22—182no—
720C22—364no—
721C22#6429712yes—
722C22#6430612yes—
723C22C2×D3×#6712yes—
724C22C23×D3211yescharacteristic
725C4—22no—
726C4—64no—
727C4—64no—
728C4—64no—
729C4—94no—
730C4—182no—
731C4—182no—
732C4C2×D3×#6714yes—
733C3—21no—
734C3C2×#563111yescharacteristic, complemented
735C3C2×#582411yescharacteristic, complemented
736C2—42no—
737C2—68no—
738C2—362no—
739C2#1059489014yesdirect product factor
740C2C2×#6429711yescharacteristic
741C2C2×#6430611yescharacteristic
742C2C22×D3×#6711yescharacteristic
subgroupG/H
centerC23C22×D32
commutator, cosocleC22×C32C25
FrattiniC22C23×D32
FittingC23×C32×C4C22
socleC23×C32C24
hypercenterC23×C4D32
hypocenterC32C2×#547
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C23 ◁ C23×C4

Complements

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

NH ≅ G/Ntype
1. C22×C3×#235C2semidirect
2. C22×#3796C2semidirect
3. C2×C4×#638C2semidirect
4. C2×C3×#924C2semidirect
5. C2×#63971C2semidirect
6. C2×#63969C2semidirect
7. C2×#63898C2semidirect
8. #10594890C2direct (N × H)
9. C2×D3×Dic3⋊C4C2semidirect
10. C2×#63873C2semidirect
11. C2×#63871C2semidirect
12. C2×#63850C2semidirect
20. C2×C3×#235C22semidirect
29. C2×#3796C22semidirect
31. C4×#638C22semidirect
37. C3×#924C22semidirect
39. #63971C22semidirect
40. #63969C22semidirect
46. #63898C22semidirect
47. D3×Dic3⋊C4C22semidirect
48. #63873C22semidirect
49. #63871C22semidirect
50. #63850C22semidirect
54. C22×#235D3semidirect
67. C2×#924D3semidirect
96. C2×C3×D12D4semidirect
146. C2×#235C2×D3semidirect
184. #924C2×D3semidirect
225. C2×C3⋊Dic3#41semidirect
237. C3×D12C2×D4semidirect
321. C2×D12#67semidirect
387. C3⋊Dic3C2×#41semidirect
520. D12C2×#67semidirect
530. C2×C32#547semidirect
648. C32C2×#547semidirect
697. C2×C3#5631semidirect
698. C2×C3#5824semidirect
734. C3C2×#5631semidirect
735. C3C2×#5824semidirect
739. C2#10594890direct (N × H)

Maximal subgroups

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

subgroupindex
C22×C3×#2352
C22×#37962
C2×C4×#6382
C2×C3×#9242
C2×#639712
C2×#639692
C2×#638982
#105948902
C2×D3×Dic3⋊C42
C2×#638732
C2×#638712
C2×#638502
C2×#58243
C2×#56313