Finite Group Databasebeta

← C2×#10594916 #11902613

Subgroups — C2×#10594916 #11902613

Order 1152.

3685 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×#3828C211yesmaximal, characteristic, complemented
2C22×D3×Dic6C211yesmaximal, characteristic, complemented
3C2×C3×C4×#67C211yesmaximal, characteristic, complemented
4C2×C3×#924C211yesmaximal, characteristic, complemented
5C2×#63971C212yesmaximal, complemented
6C2×#63953C212yesmaximal, complemented
7C2×#63909C211yesmaximal, characteristic, complemented
8#10594916C2116yesmaximal, direct product factor
9C2×#63881C212yesmaximal, complemented
10C2×#63865C212yesmaximal, complemented
11C2×#63864C211yesmaximal, characteristic, complemented
12C2×#63844C211yesmaximal, characteristic, complemented
13C2×#5633—31nomaximal
14C2×#5552—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×C4×D3C2211yescharacteristic
24C22×C3×Dic6C2211yescharacteristic
25C22×#627C2212yes—
26C22×#626C2212yes—
27C22×D3×Dic3C2212yes—
28C2×D3×Dic6—28no—
29C2×D3×Dic6C2218yescomplemented
30C2×C3×#217C2212yes—
31C2×C3×#217C2211yescharacteristic
32C3×C4×#67C2218yescomplemented
33C2×C3×(C2×D3)⋊C4C2211yescharacteristic
34C2×C3×C4⋊Dic3C2211yescharacteristic
35C3×#924C2218yescomplemented
36C2×C3×Dic3⋊C4C2212yes—
37C2×C3×Dic3⋊C4C2211yescharacteristic
38C2×C3×C4×Dic3C2211yescharacteristic
39#63971C22116yescomplemented
40C2×#3724C2212yes—
41C2×#3722C2212yes—
42C2×#3722C2212yes—
43C2×#3722C2212yes—
44C2×Dic32C2212yes—
45#63953C22116yescomplemented
46#63909C2218yescomplemented
47#63881C22116yescomplemented
48#63865C22116yescomplemented
49#63864C2218yescomplemented
50#63844C2218yescomplemented
51C22×D3×Q8—31no—
52C22×#235—31no—
53C22×#235—31no—
54C22×#235—61no—
55C23×Dic6—31no—
56C2×C3×C22⋊Q8—31no—
57C2×C3×C4×D4—31no—
58C2×#947—31no—
59C2×#939—32no—
60C2×#930—31no—
61C2×C4×#67D311yescharacteristic, complemented
62C2×#924D311yescharacteristic, complemented
63#5633—316no—
64#5552—316no—
65C2×#896—32no—
66C2×#896—32no—
67C2×#895—31no—
68C2×#893—32no—
69C2×#887—31no—
70C2×#885—32no—
71C2×#885—32no—
72C2×#884—32no—
73C2×#67⋊C4—32no—
74C2×#875—31no—
75C2×C4×Dic6—31no—
76C24×C32C2311yescharacteristic
77C23×C3⋊D3C2312yes—
78C23×C3×D3C2311yescharacteristic
79C22×C32×C4—24no—
80C22×C32×C4C2311yescharacteristic
81C22×C32×C4C2314yes—
82C22×C32×C4C2311yescharacteristic
83C2×#638—28no—
84C2×#638C2318yes—
85C22×C3⋊Dic3C2312yes—
86#3828—232no—
87C2×C4⋊(C3⋊D3)—24no—
88C2×C4⋊(C3⋊D3)C2314yes—
89C2×C4×C3⋊D3—28no—
90C2×C4×C3⋊D3C2318yes—
91C2×#634D418yescomplemented
92C2×#634C2314yes—
93C2×C3×#67—24no—
94C2×C3×#67C2314yes—
95C22×C3×Dic3C2311yescharacteristic
96C22×C3×Dic3C2311yescharacteristic
97C22×C3×Dic3C2312yes—
98C22×C3×Dic3C2312yes—
99C22×C3×Dic3C2311yescharacteristic
100C2×C3×C4×D3—24no—
101C2×C3×C4×D3C2314yes—
102C2×C3×Dic6—24no—
103C2×C3×Dic6C2314yes—
104C2×#627—28no—
105C2×#627C2318yes—
106C2×#626—28no—
107C2×#626C2318yes—
108C2×D3×Dic3—28no—
109C2×D3×Dic3C2318yes—
110D3×Dic6—232no—
111C3×#217C2318yes—
112C3×#217C2314yes—
113C3×(C2×D3)⋊C4C2314yes—
114C3×C4⋊Dic3C2314yes—
115C3×Dic3⋊C4C2318yes—
116C3×Dic3⋊C4C2314yes—
117C3×C4×Dic3C2314yes—
118#3724C2318yes—
119#3722C2318yes—
120#3722C2318yes—
121#3722C2318yes—
122Dic32C2318yes—
123C2×#548—91noSylow
124C22×C3×Q8—31no—
125C22×C3×D4—31no—
126C23×C3×C4—21no—
127C23×C3×C4—31no—
128C23×C3×C4C2×D311yescharacteristic
129C23×C3×C4C2×D311yescharacteristic
130C22×#67—32no—
131C22×#67—32no—
132C22×#67—32no—
133C22×#67—62no—
134C22×#67C2×D311yescharacteristic
135C23×Dic3—32no—
136C2×D3×Q8—38no—
137C2×D3×Q8—68no—
138C2×#235—38no—
139C2×#235—38no—
140C2×#235—68no—
141C2×#235—68no—
142C2×#235—68no—
143C2×#235—616no—
144C22×D12—32no—
145C22×D12—31no—
146C22×D12—31no—
147C22×D12—61no—
148C22×C4×D3—32no—
149C22×C4×D3—32no—
150C22×C4×D3—32no—
151C22×C4×D3—62no—
152C22×C4×D3C2×D311yescharacteristic
153C22×Dic6—31no—
154C22×Dic6—31no—
155C22×Dic6—32no—
156C22×Dic6—32no—
157C22×Dic6—38no—
158C22×Dic6—61no—
159C22×Dic6—68no—
160C22×Dic6C2×D311yescharacteristic
161C3×C22⋊Q8—38no—
162C3×C4×D4—38no—
163C2×C3×C4⋊C4—32no—
164C2×C3×C4⋊C4—31no—
165C2×C3×C4⋊C4—31no—
166C2×C3×C22⋊C4—32no—
167C2×C3×C22⋊C4—31no—
168C2×C3×C22⋊C4—31no—
169C2×C3×C42—31no—
170C2×#217C2×D311yescharacteristic
171C2×#217C2×D312yes—
172#947—38no—
173#939—316no—
174#930—38no—
175C4×#67C2×D318yescomplemented
176C2×(C2×D3)⋊C4—32no—
177C2×(C2×D3)⋊C4—32no—
178C2×(C2×D3)⋊C4—32no—
179C2×(C2×D3)⋊C4—32no—
180C2×(C2×D3)⋊C4—32no—
181C2×(C2×D3)⋊C4—32no—
182C2×(C2×D3)⋊C4C2×D311yescharacteristic
183C2×C4⋊Dic3C2×D311yescharacteristic
184#924C2×D318yescomplemented
185C2×Dic3⋊C4—32no—
186C2×Dic3⋊C4—32no—
187C2×Dic3⋊C4C2×D312yes—
188C2×Dic3⋊C4C2×D311yescharacteristic
189C2×C4×Dic3—32no—
190C2×C4×Dic3—32no—
191C2×C4×Dic3C2×D311yescharacteristic
192#896—316no—
193#896—316no—
194#895—38no—
195#893—316no—
196#887—38no—
197#885—316no—
198#885—316no—
199#884—316no—
200#67⋊C4—316no—
201#875—38no—
202C4×Dic6—38no—
203C23×C32—22no—
204C23×C32—22no—
205C23×C32—22no—
206C23×C32C2412yes—
207C23×C32C2411yescharacteristic
208C22×C3⋊D3—24no—
209C22×C3⋊D3—24no—
210C22×C3⋊D3—24no—
211C22×C3⋊D3C2414yes—
212C22×C3×D3—22no—
213C22×C3×D3—22no—
214C22×C3×D3#4114yescomplemented
215C22×C3×D3C2412yes—
216C2×C32×C4—22no—
217C2×C32×C4—28no—
218C2×C32×C4C2×D414yes—
219C2×C32×C4C2412yes—
220C2×C32×C4C2412yes—
221#638—216no—
222C2×C3⋊Dic3C2×D418yes—
223C2×C3⋊Dic3C2414yes—
224C4⋊(C3⋊D3)—28no—
225C4×C3⋊D3—216no—
226#634C2×D4116yescomplemented
227C3×#67—28no—
228C2×C3×Dic3—24no—
229C2×C3×Dic3—22no—
230C2×C3×Dic3—24no—
231C2×C3×Dic3—22no—
232C2×C3×Dic3—22no—
233C2×C3×Dic3C2412yes—
234C2×C3×Dic3C2414yes—
235C2×C3×Dic3C2412yes—
236C2×C3×Dic3C2414yes—
237C2×C3×Dic3C2412yes—
238C3×C4×D3—28no—
239C3×Dic6—28no—
240#627—216no—
241#626—216no—
242D3×Dic3—216no—
243C22×#41—91no—
244C23×Q8—91no—
245#548—916no—
246C2×#124—91no—
247C2×#124—92no—
248C2×C22⋊Q8—31no—
249C2×C22⋊Q8—92no—
250C2×#121—92no—
251C2×#121—91no—
252C2×C4×Q8—91no—
253C2×C4×D4—31no—
254C2×C4×D4—92no—
255C24×C3—21no—
256C24×C3—31no—
257C24×C3C22×D311yescharacteristic
258C24×C3C22×D311yescharacteristic
259C23×D3—32no—
260C23×D3—32no—
261C23×D3—62no—
262C23×D3C22×D311yescharacteristic
263C2×C3×Q8—34no—
264C2×C3×Q8—64no—
265C2×C3×D4—34no—
266C2×C3×D4—64no—
267C22×C3×C4—28no—
268C22×C3×C4—24no—
269C22×C3×C4—24no—
270C22×C3×C4—21no—
271C22×C3×C4—21no—
272C22×C3×C4—24no—
273C22×C3×C4—31no—
274C22×C3×C4—32no—
275C22×C3×C4—31no—
276C22×C3×C4—31no—
277C22×C3×C4—32no—
278C22×C3×C4—34no—
279C22×C3×C4—64no—
280C22×C3×C4C22×D311yescharacteristic
281C22×C3×C4C22×D311yescharacteristic
282C22×C3×C4C22×D314yes—
283C22×C3×C4C22×D314yes—
284C22×C3×C4C22×D311yescharacteristic
285C22×C3×C4C22×D311yescharacteristic
286C2×#67—24no—
287C2×#67—38no—
288C2×#67—38no—
289C2×#67—38no—
290C2×#67—68no—
291C2×#67—68no—
292C2×#67—68no—
293C2×#67—68no—
294C2×#67—616no—
295C2×#67C22×D314yes—
296C22×Dic3—32no—
297C22×Dic3—32no—
298C22×Dic3—38no—
299C22×Dic3—62no—
300C22×Dic3—68no—
301C22×Dic3C22×D311yescharacteristic
302C22×Dic3C22×D312yes—
303C22×Dic3C22×D311yescharacteristic
304C22×Dic3C22×D311yescharacteristic
305C22×Dic3C22×D312yes—
306D3×Q8—632no—
307#235—632no—
308#235—632no—
309#235—664no—
310C2×D12—38no—
311C2×D12—34no—
312C2×D12—34no—
313C2×D12—64no—
314C2×D12—68no—
315C2×D12—68no—
316C2×D12—64no—
317C2×D12—64no—
318C2×C4×D3—24no—
319C2×C4×D3—38no—
320C2×C4×D3—38no—
321C2×C4×D3—38no—
322C2×C4×D3—68no—
323C2×C4×D3—68no—
324C2×C4×D3—68no—
325C2×C4×D3—68no—
326C2×C4×D3—616no—
327C2×C4×D3C22×D314yes—
328C2×Dic6—24no—
329C2×Dic6—38no—
330C2×Dic6—38no—
331C2×Dic6—34no—
332C2×Dic6—34no—
333C2×Dic6—38no—
334C2×Dic6—38no—
335C2×Dic6—68no—
336C2×Dic6—64no—
337C2×Dic6—632no—
338C2×Dic6—68no—
339C2×Dic6—68no—
340C2×Dic6C22×D314yes—
341C3×C4⋊C4—34no—
342C3×C4⋊C4—38no—
343C3×C4⋊C4—34no—
344C3×C22⋊C4—38no—
345C3×C22⋊C4—34no—
346C3×C22⋊C4—34no—
347C3×C42—34no—
348#217C22×D314yes—
349#217C22×D318yes—
350(C2×D3)⋊C4—38no—
351(C2×D3)⋊C4—38no—
352(C2×D3)⋊C4—38no—
353(C2×D3)⋊C4—38no—
354(C2×D3)⋊C4—38no—
355(C2×D3)⋊C4—38no—
356(C2×D3)⋊C4C22×D314yes—
357C4⋊Dic3C22×D314yes—
358Dic3⋊C4—38no—
359Dic3⋊C4—38no—
360Dic3⋊C4C22×D318yes—
361Dic3⋊C4C22×D314yes—
362C4×Dic3—38no—
363C4×Dic3—38no—
364C4×Dic3C22×D314yes—
365C22×C32—22no—
366C22×C32—22no—
367C22×C32—22no—
368C22×C32—44no—
369C22×C32C22×D412yes—
370C22×C32C2×#4112yes—
371C22×C322−1+412yes—
372C22×C32C2511yescharacteristic
373C2×C3⋊D3—24no—
374C2×C3⋊D3—24no—
375C2×C3⋊D3—24no—
376C2×C3⋊D3—48no—
377C2×C3×D3—28no—
378C2×C3×D3—22no—
379C2×C3×D3—22no—
380C2×C3×D3C2×#4114yescomplemented
381C32×C4—22no—
382C32×C4C22×D414yes—
383C3⋊Dic3C22×D418yes—
384C3×Dic3—24no—
385C3×Dic3—22no—
386C3×Dic3—24no—
387C3×Dic3—22no—
388C3×Dic3—22no—
389C2×#41—98no—
390C2×#41—188no—
391C22×Q8—31no—
392C22×Q8—92no—
393C22×Q8—98no—
394C22×Q8—91no—
395C22×Q8—188no—
396C22×D4—31no—
397C22×D4—92no—
398C22×D4—92no—
399C22×D4—91no—
400C23×C4—31no—
401C23×C4—92no—
402C23×C4—92no—
403C23×C4D3211yescharacteristic
404#124—98no—
405#124—916no—
406C22⋊Q8—38no—
407C22⋊Q8—916no—
408#121—916no—
409#121—98no—
410C4×Q8—98no—
411C4×D4—38no—
412C4×D4—916no—
413C2×C4⋊C4—31no—
414C2×C4⋊C4—32no—
415C2×C4⋊C4—31no—
416C2×C4⋊C4—92no—
417C2×C22⋊C4—31no—
418C2×C22⋊C4—32no—
419C2×C22⋊C4—31no—
420C2×C22⋊C4—92no—
421C2×C22⋊C4—92no—
422C2×C22⋊C4—92no—
423C2×C42—31no—
424C2×C42—92no—
425C23×C3—24no—
426C23×C3—22no—
427C23×C3—22no—
428C23×C3—22no—
429C23×C3—22no—
430C23×C3—22no—
431C23×C3—22no—
432C23×C3—22no—
433C23×C3—21no—
434C23×C3—34no—
435C23×C3—32no—
436C23×C3—42no—
437C23×C3—42no—
438C23×C3—62no—
439C23×C3—62no—
440C23×C3C23×D312yes—
441C23×C3C23×D312yes—
442C23×C3C23×D311yescharacteristic
443C23×C3C23×D311yescharacteristic
444C22×D3—22no—
445C22×D3—22no—
446C22×D3—34no—
447C22×D3—34no—
448C22×D3—64no—
449C22×D3—68no—
450C22×D3—64no—
451C22×D3—64no—
452C22×D3—64no—
453C22×D3—64no—
454C22×D3—64no—
455C22×D3—64no—
456C22×D3—124no—
457C22×D3—124no—
458C22×D3#23514yescomplemented
459C22×D3C23×D312yes—
460C3×Q8—68no—
461C3×D4—68no—
462C2×C3×C4—24no—
463C2×C3×C4—216no—
464C2×C3×C4—22no—
465C2×C3×C4—22no—
466C2×C3×C4—28no—
467C2×C3×C4—28no—
468C2×C3×C4—22no—
469C2×C3×C4—22no—
470C2×C3×C4—24no—
471C2×C3×C4—32no—
472C2×C3×C4—34no—
473C2×C3×C4—32no—
474C2×C3×C4—32no—
475C2×C3×C4—34no—
476C2×C3×C4—64no—
477C2×C3×C4—62no—
478C2×C3×C4—64no—
479C2×C3×C4—62no—
480C2×C3×C4—62no—
481C2×C3×C4—68no—
482C2×C3×C4D3×D414yes—
483C2×C3×C4D3×D414yes—
484C2×C3×C4C23×D312yes—
485C2×C3×C4C23×D312yes—
486C2×C3×C4C23×D312yes—
487C2×C3×C4C23×D312yes—
488#67—28no—
489#67—616no—
490#67—616no—
491#67—616no—
492#67—632no—
493C2×Dic3—22no—
494C2×Dic3—24no—
495C2×Dic3—22no—
496C2×Dic3—24no—
497C2×Dic3—22no—
498C2×Dic3—38no—
499C2×Dic3—38no—
500C2×Dic3—34no—
501C2×Dic3—34no—
502C2×Dic3—68no—
503C2×Dic3—64no—
504C2×Dic3—616no—
505C2×Dic3C23×D312yes—
506C2×Dic3C23×D314yes—
507C2×Dic3C23×D312yes—
508C2×Dic3C23×D312yes—
509C2×Dic3C23×D314yes—
510D12—616no—
511D12—616no—
512D12—68no—
513D12—68no—
514C4×D3—28no—
515C4×D3—616no—
516C4×D3—616no—
517C4×D3—616no—
518C4×D3—632no—
519Dic6—28no—
520Dic6—316no—
521Dic6—316no—
522Dic6—616no—
523Dic6—616no—
524Dic6—616no—
525C2×C32—42no—
526C2×C32#54814yescomplemented
527C2×C32C23×D411yescharacteristic
528C2×C32C22×#4111yescharacteristic
529C2×C32C2×2−1+411yescharacteristic
530C3⋊D3—44no—
531C3×D3—24no—
532C24—31no—
533C24—92no—
534C24C2×D3211yescharacteristic
535#41—1832no—
536C2×Q8—34no—
537C2×Q8—64no—
538C2×Q8—98no—
539C2×Q8—94no—
540C2×Q8—98no—
541C2×Q8—188no—
542C2×Q8—1832no—
543C2×D4—34no—
544C2×D4—64no—
545C2×D4—98no—
546C2×D4—98no—
547C2×D4—94no—
548C2×D4—188no—
549C2×D4—188no—
550C2×D4—184no—
551C22×C4—24no—
552C22×C4—31no—
553C22×C4—31no—
554C22×C4—32no—
555C22×C4—31no—
556C22×C4—32no—
557C22×C4—34no—
558C22×C4—64no—
559C22×C4—98no—
560C22×C4—92no—
561C22×C4—98no—
562C22×C4—188no—
563C22×C4—188no—
564C22×C4C2×D3214yes—
565C22×C4C2×D3211yescharacteristic
566C22×C4C2×D3211yescharacteristic
567C4⋊C4—34no—
568C4⋊C4—38no—
569C4⋊C4—34no—
570C4⋊C4—98no—
571C22⋊C4—34no—
572C22⋊C4—38no—
573C22⋊C4—34no—
574C22⋊C4—98no—
575C22⋊C4—98no—
576C22⋊C4—98no—
577C42—34no—
578C42—98no—
579C22×C3—24no—
580C22×C3—22no—
581C22×C3—22no—
582C22×C3—22no—
583C22×C3—22no—
584C22×C3—22no—
585C22×C3—22no—
586C22×C3—22no—
587C22×C3—22no—
588C22×C3—22no—
589C22×C3—21no—
590C22×C3—34no—
591C22×C3—42no—
592C22×C3—42no—
593C22×C3—48no—
594C22×C3—44no—
595C22×C3—44no—
596C22×C3—68no—
597C22×C3—62no—
598C22×C3—62no—
599C22×C3C2×#23512yes—
600C22×C3C2×D3×D412yes—
601C22×C3C2×D3×D412yes—
602C22×C3#100712yes—
603C22×C3D3×#4112yes—
604C22×C3#101012yes—
605C22×C3C24×D311yescharacteristic
606C22×C3C24×D311yescharacteristic
607C2×D3—22no—
608C2×D3—22no—
609C2×D3—28no—
610C2×D3—68no—
611C2×D3—64no—
612C2×D3—64no—
613C2×D3—64no—
614C2×D3—64no—
615C2×D3—64no—
616C2×D3—64no—
617C2×D3—124no—
618C2×D3—124no—
619C2×D3—1216no—
620C2×D3—128no—
621C2×D3—128no—
622C2×D3C2×#23514yescomplemented
623C3×C4—24no—
624C3×C4—22no—
625C3×C4—22no—
626C3×C4—24no—
627C3×C4—64no—
628C3×C4—62no—
629C3×C4—64no—
630C3×C4—62no—
631C3×C4—62no—
632C3×C4C2×D3×D414yes—
633C3×C4C2×D3×D414yes—
634Dic3—22no—
635Dic3—24no—
636Dic3—22no—
637Dic3—24no—
638Dic3—22no—
639Dic3—38no—
640Dic3—38no—
641Dic3—68no—
642C32C2×#54811yescharacteristic, complemented, Sylow
643C23—22no—
644C23—22no—
645C23—22no—
646C23—34no—
647C23—32no—
648C23—62no—
649C23—62no—
650C23—94no—
651C23—184no—
652C23—184no—
653C23—184no—
654C23C22×D3212yes—
655C23C22×D3211yescharacteristic
656Q8—68no—
657Q8—916no—
658Q8—1816no—
659D4—68no—
660D4—1816no—
661D4—1816no—
662D4—188no—
663C2×C4—22no—
664C2×C4—28no—
665C2×C4—32no—
666C2×C4—32no—
667C2×C4—34no—
668C2×C4—32no—
669C2×C4—34no—
670C2×C4—62no—
671C2×C4—62no—
672C2×C4—64no—
673C2×C4—62no—
674C2×C4—64no—
675C2×C4—68no—
676C2×C4—98no—
677C2×C4—94no—
678C2×C4—1816no—
679C2×C4—1816no—
680C2×C4#381114yes—
681C2×C4C22×D3212yes—
682C2×C4C22×D3212yes—
683C2×C3—21no—
684C2×C3—21no—
685C2×C3—21no—
686C2×C3—24no—
687C2×C3—44no—
688C2×C3—42no—
689C2×C3—42no—
690C2×C3—64no—
691C2×C3#555214yescomplemented
692C2×C3#563314yescomplemented
693C2×C3C22×#23511yescharacteristic
694C2×C3C22×D3×D411yescharacteristic
695C2×C3C22×D3×D411yescharacteristic
696C2×C3C2×#100711yescharacteristic
697C2×C3C2×D3×#4111yescharacteristic
698C2×C3C2×#101011yescharacteristic
699D3—24no—
700D3—128no—
701D3—124no—
702D3—124no—
703C22—22no—
704C22—22no—
705C22—22no—
706C22—34no—
707C22—44no—
708C22—62no—
709C22—62no—
710C22—68no—
711C22—184no—
712C22—184no—
713C22—184no—
714C22—368no—
715C22#6429712yes—
716C22D3×#23512yes—
717C22C2×#381112yes—
718C22C23×D3211yescharacteristic
719C4—22no—
720C4—62no—
721C4—62no—
722C4—64no—
723C4—62no—
724C4—64no—
725C4—98no—
726C4C2×#381114yes—
727C3—21no—
728C3C2×#555211yescharacteristic, complemented
729C3C2×#563311yescharacteristic, complemented
730C2—42no—
731C2—64no—
732C2—364no—
733C2#1059491614yesdirect product factor
734C2C2×#6429711yescharacteristic
735C2C2×D3×#23511yescharacteristic
736C2C22×#381111yescharacteristic
subgroupG/H
centerC23C22×D32
commutator, cosocleC22×C32C25
FrattiniC22C23×D32
FittingC23×C32×C4C22
socleC23×C32C24
hypercenterC23×C4D32
hypocenterC32C2×#548
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×D3×Dic6C2semidirect
3. C2×C3×C4×#67C2semidirect
4. C2×C3×#924C2semidirect
5. C2×#63971C2semidirect
6. C2×#63953C2semidirect
7. C2×#63909C2semidirect
8. #10594916C2direct (N × H)
9. C2×#63881C2semidirect
10. C2×#63865C2semidirect
11. C2×#63864C2semidirect
12. C2×#63844C2semidirect
18. C2×#3828C22semidirect
29. C2×D3×Dic6C22semidirect
32. C3×C4×#67C22semidirect
35. C3×#924C22semidirect
39. #63971C22semidirect
45. #63953C22semidirect
46. #63909C22semidirect
47. #63881C22semidirect
48. #63865C22semidirect
49. #63864C22semidirect
50. #63844C22semidirect
61. C2×C4×#67D3semidirect
62. C2×#924D3semidirect
91. C2×#634D4semidirect
175. C4×#67C2×D3semidirect
184. #924C2×D3semidirect
214. C22×C3×D3#41semidirect
226. #634C2×D4semidirect
380. C2×C3×D3C2×#41semidirect
458. C22×D3#235semidirect
526. C2×C32#548semidirect
622. C2×D3C2×#235semidirect
642. C32C2×#548semidirect
691. C2×C3#5552semidirect
692. C2×C3#5633semidirect
728. C3C2×#5552semidirect
729. C3C2×#5633semidirect
733. C2#10594916direct (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×D3×Dic62
C2×C3×C4×#672
C2×C3×#9242
C2×#639712
C2×#639532
C2×#639092
#105949162
C2×#638812
C2×#638652
C2×#638642
C2×#638442
C2×#56333
C2×#55523