Finite Group Databasebeta

← C2×#85823 #11702013

Subgroups — C2×#85823 #11702013

Order 768.

7130 conjugacy classes of subgroups.

The subgroup lattice has 880 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×C4×#41C211yesmaximal, characteristic, complemented
2C2×#5833C211yesmaximal, characteristic
3C2×#5825C211yesmaximal, characteristic, complemented
4#85823C2132yesmaximal, direct product factor
5C2×#5583C212yesmaximal, complemented
6C2×#5578C212yesmaximal, complemented
7C2×#5561C212yesmaximal, complemented
8C2×#5557C212yesmaximal, complemented
9C2×#5564C214yesmaximal, complemented
10C2×#5538C214yesmaximal, complemented
11C2×#5534C212yesmaximal, complemented
12C2×#5519C211yesmaximal, characteristic, complemented
13C2×#5518C212yesmaximal, complemented
14C2×#5526C211yesmaximal, characteristic, complemented
15C2×#5479C212yesmaximal, complemented
16C2×#5470C212yesmaximal, complemented
17C2×C4×#235C211yesmaximal, characteristic, complemented
18C22×C4×Dic6C211yesmaximal, characteristic, complemented
19C2×#3461—31nomaximal, Sylow
20C22×C3×#41C2211yescharacteristic
21C22×#235C2211yescharacteristic
22C23×Dic6C2211yescharacteristic
23C3×C4×#41C22116yescomplemented
24C2×C3×C4×Q8C2211yescharacteristic
25C2×C3×C4×Q8C2211yescharacteristic
26C2×C3×C4×D4C2211yescharacteristic
27C2×C3×C4×D4C2211yescharacteristic
28C2×C3×C4×D4C2212yes—
29C2×C3×C4×D4C2212yes—
30C2×C3×#117C2211yescharacteristic
31C2×C3×#117C2212yes—
32C22×C3×C42C2211yescharacteristic
33C22×C3×C42C2212yes—
34#5833C22116yes—
35#5825C22116yescomplemented
36C2×#946C2212yes—
37C2×#944C2212yes—
38C2×#939C2214yes—
39C2×#938C2212yes—
40C2×#936C2212yes—
41C2×#935C2214yes—
42C2×#930C2212yes—
43C2×#929C2214yes—
44C2×C4×#67C2214yes—
45C2×C4×#67C2212yes—
46C2×C4×#67C2212yes—
47C2×#926C2214yes—
48C2×#926C2211yescharacteristic
49C22×C4⋊Dic3C2211yescharacteristic
50C2×#924C2214yes—
51C2×#924C2212yes—
52C2×#924C2212yes—
53C2×#924C2212yes—
54C22×Dic3⋊C4C2212yes—
55C22×C4×Dic3C2212yes—
56#5583C22132yescomplemented
57#5578C22132yescomplemented
58#5564C22164yescomplemented
59#5561C22132yescomplemented
60#5557C22132yescomplemented
61#5538C22164yescomplemented
62#5534C22132yescomplemented
63#5526C22116yescomplemented
64#5519C22116yescomplemented
65#5518C22132yescomplemented
66C2×#898C2214yes—
67C2×#897C2212yes—
68C2×#897C2212yes—
69C2×#896C2214yes—
70C2×#890C2212yes—
71C2×#889C2214yes—
72C2×#889C2214yes—
73C2×#888C2212yes—
74C2×#886C2214yes—
75C2×#885C2214yes—
76C2×#883C2214yes—
77C2×#879C2214yes—
78C2×#879C2214yes—
79C2×#878C2214yes—
80#5479C22132yescomplemented
81C2×#876C2214yes—
82C2×#875C2212yes—
83C4×#235C22116yescomplemented
84C2×C4×D12C2211yescharacteristic
85C2×C4×D12C2211yescharacteristic
86C2×#872C2212yes—
87C2×#872C2214yes—
88C2×C42×D3C2212yes—
89#5470C22132yescomplemented
90C2×#870C2214yes—
91C2×#870C2212yes—
92C2×#869C2212yes—
93C2×#869C2212yes—
94C2×C4×Dic6C2212yes—
95C2×C4×Dic6C2212yes—
96C2×C4×Dic6C2214yes—
97C2×C4×Dic6C2212yes—
98C2×C4×Dic6C2212yes—
99C2×C4×Dic6C2211yescharacteristic
100C2×C4×Dic6C2211yescharacteristic
101C2×C4×Dic6C22116yescomplemented
102#3461—332no—
103C2×#544—31no—
104C2×#542—32no—
105C2×#542—32no—
106C2×#541—32no—
107C2×#541—32no—
108C2×#539—34no—
109C2×#537—31no—
110C2×#536—31no—
111C2×#536—31no—
112C2×#533—32no—
113C2×#533—32no—
114C2×#529—32no—
115C2×#529—32no—
116C2×#529—34no—
117C2×C4×#41—31no—
118C2×C4×#41D311yescharacteristic, complemented
119C22×C4×Q8—31no—
120C2×C3×#41—28no—
121C2×C3×#41C2318yes—
122C22×C3×Q8C2311yescharacteristic
123C22×C3×D4C2312yes—
124C22×C3×D4C2311yescharacteristic
125C23×C3×C4C2312yes—
126C23×C3×C4C2311yescharacteristic
127C23×C3×C4C2312yes—
128C23×C3×C4C2311yescharacteristic
129C23×C3×C4C2312yes—
130C23×C3×C4C2311yescharacteristic
131C22×#67C2312yes—
132C22×#67C2314yes—
133C23×Dic3C2312yes—
134C23×Dic3C2312yes—
135C2×#235—28no—
136C2×#235C2318yes—
137C22×D12C2311yescharacteristic
138C22×C4×D3C2312yes—
139C22×C4×D3C2312yes—
140C22×C4×D3C2312yes—
141C22×Dic6—28no—
142C22×Dic6C2312yes—
143C22×Dic6C2312yes—
144C22×Dic6C2318yes—
145C22×Dic6C2311yescharacteristic
146C22×Dic6C2314yes—
147C3×C4×Q8C2318yes—
148C3×C4×Q8C2318yes—
149C3×C4×D4C23116yes—
150C3×C4×D4C2318yes—
151C3×C4×D4C2318yes—
152C3×C4×D4C23116yes—
153C3×#117C23116yes—
154C3×#117C2318yes—
155C2×C3×C4⋊C4C2311yescharacteristic
156C2×C3×C4⋊C4C2312yes—
157C2×C3×C4⋊C4C2312yes—
158C2×C3×C4⋊C4C2311yescharacteristic
159C2×C3×C22⋊C4C2312yes—
160C2×C3×C22⋊C4C2312yes—
161C2×C3×C22⋊C4C2312yes—
162C2×C3×C42C2311yescharacteristic
163C2×C3×C42C2311yescharacteristic
164C2×C3×C42C2311yescharacteristic
165C2×C3×C42C2311yescharacteristic
166C2×C3×C42C2312yes—
167C2×C3×C42C2318yes—
168C2×C3×C42C2312yes—
169C2×C3×C42C2312yes—
170C2×C3×C42C23116yes—
171C2×#217C2312yes—
172C2×#217C2314yes—
173C2×#217C2314yes—
174C2×#217C2314yes—
175#946C23116yes—
176#944C23116yes—
177#939C23132yes—
178#938C23116yes—
179#936C23116yes—
180#935C23132yes—
181#930C23116yes—
182#929C23132yes—
183C4×#67C23116yes—
184C4×#67C23116yes—
185C4×#67C23132yes—
186C2×(C2×D3)⋊C4C2312yes—
187C2×(C2×D3)⋊C4C2312yes—
188C2×(C2×D3)⋊C4C2314yes—
189C2×(C2×D3)⋊C4C2314yes—
190C2×(C2×D3)⋊C4C2314yes—
191#926C23132yes—
192#926C2318yes—
193C2×C4⋊Dic3C2312yes—
194C2×C4⋊Dic3C2312yes—
195C2×C4⋊Dic3C2311yescharacteristic
196C2×C4⋊Dic3C2314yes—
197C2×C4⋊Dic3C2311yescharacteristic
198C2×C4⋊Dic3C2318yes—
199C2×C4⋊Dic3C2314yes—
200C2×C4⋊Dic3C2314yes—
201#924C23116yes—
202#924C23116yes—
203#924C23132yes—
204#924C23116yes—
205C2×Dic3⋊C4C2314yes—
206C2×Dic3⋊C4C2314yes—
207C2×Dic3⋊C4C2312yes—
208C2×Dic3⋊C4C2314yes—
209C2×Dic3⋊C4C2314yes—
210C2×Dic3⋊C4C2312yes—
211C2×Dic3⋊C4C23116yes—
212C2×Dic3⋊C4C2314yes—
213C2×Dic3⋊C4C2314yes—
214C2×Dic3⋊C4C2314yes—
215C2×C4×Dic3C2312yes—
216C2×C4×Dic3C2314yes—
217C2×C4×Dic3C2314yes—
218C2×C4×Dic3C2312yes—
219C2×C4×Dic3C23116yes—
220C2×C4×Dic3C2312yes—
221#898C23132yes—
222#897C23116yes—
223#897C23116yes—
224#896C23132yes—
225#890C23116yes—
226#889C23132yes—
227#889C23132yes—
228#888C23116yes—
229#886C23132yes—
230#885C23132yes—
231#883C23132yes—
232#879C23132yes—
233#879C23132yes—
234#878C23132yes—
235#876C23132yes—
236#875C23116yes—
237C4×D12C2318yes—
238C4×D12C2318yes—
239#872C23116yes—
240#872C23132yes—
241C42×D3C23116yes—
242#870C23132yes—
243#870C23116yes—
244#869C23116yes—
245#869C23116yes—
246C4×Dic6C23116yes—
247C4×Dic6C23116yes—
248C4×Dic6C23116yes—
249C4×Dic6C23116yes—
250C4×Dic6C2318yes—
251C4×Dic6C23132yes—
252C4×Dic6C2318yes—
253C22×#41—31no—
254C22×#41C2×D311yescharacteristic
255C23×Q8—31no—
256#544—316no—
257#542—332no—
258#542—332no—
259#541—332no—
260#541—332no—
261#539—364no—
262#537—316no—
263#536—316no—
264#536—316no—
265#533—332no—
266#533—332no—
267C2×C4⋊Q8—32no—
268C2×C4⋊Q8—32no—
269C2×C4⋊Q8—32no—
270C2×C4⋊Q8—32no—
271#529—364no—
272#529—332no—
273#529—332no—
274C2×#126—34no—
275C2×#126—34no—
276C2×#126—34no—
277C2×#126—34no—
278C2×#125—34no—
279C2×#125—32no—
280C2×#125—34no—
281C2×#125—32no—
282C2×#125—34no—
283C2×#124—32no—
284C2×#124—34no—
285C2×#124—32no—
286C2×#123—34no—
287C2×#123—34no—
288C2×#123—34no—
289C2×#123—34no—
290C2×C22⋊Q8—32no—
291C2×C22⋊Q8—32no—
292C2×C22⋊Q8—32no—
293C2×C22⋊Q8—32no—
294C2×C22⋊Q8—34no—
295C2×C22⋊Q8—32no—
296C2×C22⋊Q8—32no—
297C2×C22⋊Q8—34no—
298C2×C22⋊Q8—34no—
299C2×#121—34no—
300C2×#121—32no—
301C2×#121—32no—
302C4×#41—316no—
303C4×#41C2×D3116yescomplemented
304C2×C4×Q8—32no—
305C2×C4×Q8—32no—
306C2×C4×Q8—32no—
307C2×C4×Q8—32no—
308C2×C4×Q8—31no—
309C2×C4×Q8—31no—
310C2×C4×Q8—34no—
311C2×C4×Q8—316no—
312C2×C4×Q8C2×D311yescharacteristic
313C2×C4×Q8C2×D311yescharacteristic
314C2×C4×D4—32no—
315C2×C4×D4—32no—
316C2×C4×D4—34no—
317C2×C4×D4—31no—
318C2×C4×D4—31no—
319C2×C4×D4C2×D312yes—
320C2×C4×D4C2×D311yescharacteristic
321C2×C4×D4C2×D312yes—
322C2×C4×D4C2×D311yescharacteristic
323C2×#117—31no—
324C2×#117—34no—
325C2×#117—32no—
326C2×#117—34no—
327C2×#117C2×D311yescharacteristic
328C2×#117C2×D312yes—
329C22×C4⋊C4—31no—
330C22×C4⋊C4—32no—
331C22×C42—32no—
332C22×C42—32no—
333C22×C42C2×D311yescharacteristic
334C22×C42C2×D312yes—
335C24×C3C2412yes—
336C24×C3C2411yescharacteristic
337C23×D3C2412yes—
338C3×#41—232no—
339C2×C3×Q8—24no—
340C2×C3×Q8C2414yes—
341C2×C3×D4—28no—
342C2×C3×D4—24no—
343C2×C3×D4C2418yes—
344C2×C3×D4C2414yes—
345C22×C3×C4—28no—
346C22×C3×C4—24no—
347C22×C3×C4—28no—
348C22×C3×C4—44no—
349C22×C3×C4—42no—
350C22×C3×C4#4118yes—
351C22×C3×C4C2411yescharacteristic
352C22×C3×C4C2414yes—
353C22×C3×C4C2411yescharacteristic
354C22×C3×C4C2411yescharacteristic
355C22×C3×C4C2412yes—
356C22×C3×C4C2412yes—
357C22×C3×C4C2412yes—
358C22×C3×C4C2418yes—
359C22×C3×C4C2418yes—
360C22×C3×C4C2414yes—
361C22×C3×C4C2418yes—
362C22×C3×C4C2411yescharacteristic
363C22×C3×C4C2411yescharacteristic
364C22×C3×C4C2414yes—
365C22×C3×C4C2411yescharacteristic
366C2×#67—28no—
367C2×#67—48no—
368C2×#67C2418yes—
369C2×#67C24116yes—
370C22×Dic3—28no—
371C22×Dic3—44no—
372C22×Dic3C2418yes—
373C22×Dic3C2412yes—
374C22×Dic3C2414yes—
375C22×Dic3C2412yes—
376C22×Dic3C2414yes—
377C22×Dic3C2412yes—
378C22×Dic3C2418yes—
379#235—232no—
380C2×D12—24no—
381C2×D12C2414yes—
382C2×C4×D3—28no—
383C2×C4×D3—28no—
384C2×C4×D3—44no—
385C2×C4×D3C2418yes—
386C2×C4×D3C2418yes—
387C2×C4×D3C2418yes—
388C2×Dic6—28no—
389C2×Dic6—28no—
390C2×Dic6—232no—
391C2×Dic6—24no—
392C2×Dic6—48no—
393C2×Dic6C2414yes—
394C2×Dic6C2418yes—
395C2×Dic6C2418yes—
396C2×Dic6C24116yes—
397C3×C4⋊C4C2414yes—
398C3×C4⋊C4C2418yes—
399C3×C4⋊C4C2418yes—
400C3×C4⋊C4C2414yes—
401C3×C22⋊C4C2418yes—
402C3×C22⋊C4C2418yes—
403C3×C22⋊C4C2418yes—
404C3×C42C2414yes—
405C3×C42C2414yes—
406C3×C42C2414yes—
407C3×C42C2414yes—
408C3×C42C2418yes—
409C3×C42C2418yes—
410C3×C42C2418yes—
411#217C2418yes—
412#217C24116yes—
413#217C24116yes—
414#217C24116yes—
415(C2×D3)⋊C4C2418yes—
416(C2×D3)⋊C4C2418yes—
417(C2×D3)⋊C4C24116yes—
418(C2×D3)⋊C4C24116yes—
419(C2×D3)⋊C4C24116yes—
420C4⋊Dic3C2418yes—
421C4⋊Dic3C2418yes—
422C4⋊Dic3C2414yes—
423C4⋊Dic3C24116yes—
424C4⋊Dic3C2414yes—
425C4⋊Dic3C24116yes—
426C4⋊Dic3C24116yes—
427Dic3⋊C4C24116yes—
428Dic3⋊C4C24116yes—
429Dic3⋊C4C2418yes—
430Dic3⋊C4C24116yes—
431Dic3⋊C4C24116yes—
432Dic3⋊C4C2418yes—
433Dic3⋊C4C24116yes—
434Dic3⋊C4C24116yes—
435Dic3⋊C4C24116yes—
436C4×Dic3C2418yes—
437C4×Dic3C24116yes—
438C4×Dic3C24116yes—
439C4×Dic3C2418yes—
440C4×Dic3C2418yes—
441C2×#41—28no—
442C2×#41—38no—
443C2×#41—68no—
444C2×#41C22×D318yes—
445C22×Q8—32no—
446C22×Q8—32no—
447C22×Q8—31no—
448C22×Q8—38no—
449C22×Q8—34no—
450C22×Q8—68no—
451C22×Q8C22×D311yescharacteristic
452C22×D4—32no—
453C22×D4—34no—
454C22×D4—31no—
455C22×D4C22×D312yes—
456C22×D4C22×D311yescharacteristic
457C23×C4—32no—
458C23×C4—32no—
459C23×C4—32no—
460C23×C4—32no—
461C23×C4—32no—
462C23×C4C22×D312yes—
463C23×C4C22×D312yes—
464C23×C4C22×D311yescharacteristic
465C23×C4C22×D311yescharacteristic
466C23×C4C22×D312yes—
467C23×C4C22×D311yescharacteristic
468C4⋊Q8—316no—
469C4⋊Q8—316no—
470C4⋊Q8—316no—
471C4⋊Q8—316no—
472#126—332no—
473#126—332no—
474#126—332no—
475#126—332no—
476#125—332no—
477#125—316no—
478#125—332no—
479#125—316no—
480#125—332no—
481#124—316no—
482#124—332no—
483#124—316no—
484#123—332no—
485#123—332no—
486#123—332no—
487#123—332no—
488C22⋊Q8—316no—
489C22⋊Q8—316no—
490C22⋊Q8—316no—
491C22⋊Q8—316no—
492C22⋊Q8—332no—
493C22⋊Q8—316no—
494C22⋊Q8—316no—
495C22⋊Q8—332no—
496C22⋊Q8—332no—
497#121—332no—
498#121—316no—
499#121—316no—
500C4×Q8—316no—
501C4×Q8—316no—
502C4×Q8—316no—
503C4×Q8—316no—
504C4×Q8—38no—
505C4×Q8—38no—
506C4×Q8—332no—
507C4×Q8C22×D318yes—
508C4×Q8C22×D318yes—
509C4×D4—316no—
510C4×D4—316no—
511C4×D4—332no—
512C4×D4—38no—
513C4×D4—38no—
514C4×D4C22×D318yes—
515C4×D4C22×D3116yes—
516C4×D4C22×D3116yes—
517C4×D4C22×D318yes—
518#117—38no—
519#117—332no—
520#117—316no—
521#117—332no—
522#117C22×D318yes—
523#117C22×D3116yes—
524C2×C4⋊C4—32no—
525C2×C4⋊C4—32no—
526C2×C4⋊C4—34no—
527C2×C4⋊C4—34no—
528C2×C4⋊C4—38no—
529C2×C4⋊C4—316no—
530C2×C4⋊C4—32no—
531C2×C4⋊C4—31no—
532C2×C4⋊C4—31no—
533C2×C4⋊C4—32no—
534C2×C4⋊C4—34no—
535C2×C4⋊C4—34no—
536C2×C4⋊C4—34no—
537C2×C4⋊C4—34no—
538C2×C4⋊C4—34no—
539C2×C4⋊C4—34no—
540C2×C4⋊C4—34no—
541C2×C4⋊C4—34no—
542C2×C4⋊C4C22×D312yes—
543C2×C4⋊C4C22×D311yescharacteristic
544C2×C4⋊C4C22×D311yescharacteristic
545C2×C4⋊C4C22×D312yes—
546C2×C22⋊C4—32no—
547C2×C22⋊C4—34no—
548C2×C22⋊C4—34no—
549C2×C22⋊C4—34no—
550C2×C22⋊C4—32no—
551C2×C22⋊C4—32no—
552C2×C22⋊C4—34no—
553C2×C22⋊C4—34no—
554C2×C22⋊C4—34no—
555C2×C22⋊C4C22×D312yes—
556C2×C22⋊C4C22×D312yes—
557C2×C22⋊C4C22×D312yes—
558C2×C42—32no—
559C2×C42—32no—
560C2×C42—34no—
561C2×C42—316no—
562C2×C42—32no—
563C2×C42—34no—
564C2×C42—316no—
565C2×C42C22×D311yescharacteristic
566C2×C42C22×D311yescharacteristic
567C2×C42C22×D312yes—
568C2×C42C22×D312yes—
569C2×C42C22×D318yes—
570C2×C42C22×D3116yes—
571C2×C42C22×D312yes—
572C2×C42C22×D311yescharacteristic
573C2×C42C22×D311yescharacteristic
574C23×C3—22no—
575C23×C3—22no—
576C23×C3—24no—
577C23×C3—24no—
578C23×C3—24no—
579C23×C3C2×#4114yes—
580C23×C3C2514yes—
581C23×C3C2512yes—
582C23×C3C2511yescharacteristic
583C22×D3—24no—
584C22×D3—24no—
585C22×D3—24no—
586C22×D3C2514yes—
587C3×Q8—28no—
588C3×D4—216no—
589C3×D4—28no—
590C2×C3×C4—24no—
591C2×C3×C4—22no—
592C2×C3×C4—24no—
593C2×C3×C4—24no—
594C2×C3×C4—22no—
595C2×C3×C4—22no—
596C2×C3×C4—216no—
597C2×C3×C4—28no—
598C2×C3×C4—216no—
599C2×C3×C4—48no—
600C2×C3×C4—44no—
601C2×C3×C4C2×#4114yes—
602C2×C3×C4C2×#4114yes—
603C2×C3×C4C2×#41116yes—
604C2×C3×C42−1+414yes—
605C2×C3×C4C2512yes—
606C2×C3×C4C2512yes—
607C2×C3×C4C2512yes—
608C2×C3×C4C2514yes—
609C2×C3×C4C2514yes—
610C2×C3×C4C2514yes—
611C2×C3×C4C2512yes—
612C2×C3×C4C2512yes—
613C2×C3×C4C2512yes—
614#67—216no—
615#67—416no—
616C2×Dic3—216no—
617C2×Dic3—28no—
618C2×Dic3—24no—
619C2×Dic3—24no—
620C2×Dic3—24no—
621C2×Dic3—28no—
622C2×Dic3—48no—
623C2×Dic3C2514yes—
624C2×Dic3C2518yes—
625C2×Dic3C2514yes—
626C2×Dic3C2518yes—
627C2×Dic3C2514yes—
628D12—28no—
629C4×D3—216no—
630C4×D3—216no—
631C4×D3—48no—
632Dic6—216no—
633Dic6—216no—
634Dic6—28no—
635Dic6—416no—
636C24—32no—
637C24C23×D312yes—
638C24C23×D311yescharacteristic
639#41—232no—
640#41—632no—
641C2×Q8—24no—
642C2×Q8—38no—
643C2×Q8—38no—
644C2×Q8—34no—
645C2×Q8—316no—
646C2×Q8—68no—
647C2×Q8—68no—
648C2×Q8—632no—
649C2×Q8—64no—
650C2×Q8—128no—
651C2×Q8C23×D314yes—
652C2×D4—28no—
653C2×D4—24no—
654C2×D4—38no—
655C2×D4—316no—
656C2×D4—34no—
657C2×D4—68no—
658C2×D4—64no—
659C2×D4—128no—
660C2×D4C23×D318yes—
661C2×D4C23×D314yes—
662C22×C4—28no—
663C22×C4—24no—
664C22×C4—28no—
665C22×C4—32no—
666C22×C4—34no—
667C22×C4—32no—
668C22×C4—32no—
669C22×C4—34no—
670C22×C4—38no—
671C22×C4—38no—
672C22×C4—38no—
673C22×C4—38no—
674C22×C4—38no—
675C22×C4—42no—
676C22×C4—44no—
677C22×C4—68no—
678C22×C4—68no—
679C22×C4—68no—
680C22×C4—124no—
681C22×C4—124no—
682C22×C4#23518yes—
683C22×C4C23×D311yescharacteristic
684C22×C4C23×D314yes—
685C22×C4C23×D311yescharacteristic
686C22×C4C23×D311yescharacteristic
687C22×C4C23×D312yes—
688C22×C4C23×D312yes—
689C22×C4C23×D312yes—
690C22×C4C23×D318yes—
691C22×C4C23×D318yes—
692C22×C4C23×D314yes—
693C22×C4C23×D318yes—
694C22×C4C23×D311yescharacteristic
695C22×C4C23×D311yescharacteristic
696C22×C4C23×D314yes—
697C22×C4C23×D311yescharacteristic
698C4⋊C4—38no—
699C4⋊C4—38no—
700C4⋊C4—316no—
701C4⋊C4—316no—
702C4⋊C4—38no—
703C4⋊C4—34no—
704C4⋊C4—34no—
705C4⋊C4—38no—
706C4⋊C4—316no—
707C4⋊C4—316no—
708C4⋊C4—316no—
709C4⋊C4—316no—
710C4⋊C4—316no—
711C4⋊C4—316no—
712C4⋊C4—316no—
713C4⋊C4—316no—
714C4⋊C4C23×D318yes—
715C4⋊C4C23×D314yes—
716C4⋊C4C23×D314yes—
717C4⋊C4C23×D318yes—
718C22⋊C4—38no—
719C22⋊C4—316no—
720C22⋊C4—316no—
721C22⋊C4—316no—
722C22⋊C4—38no—
723C22⋊C4—38no—
724C22⋊C4—316no—
725C22⋊C4—316no—
726C22⋊C4—316no—
727C22⋊C4C23×D318yes—
728C22⋊C4C23×D318yes—
729C22⋊C4C23×D318yes—
730C42—316no—
731C42—38no—
732C42—38no—
733C42—38no—
734C42—316no—
735C42C23×D314yes—
736C42C23×D314yes—
737C42C23×D314yes—
738C42C23×D318yes—
739C42C23×D314yes—
740C42C23×D318yes—
741C42C23×D318yes—
742C22×C3—22no—
743C22×C3—22no—
744C22×C3—28no—
745C22×C3—24no—
746C22×C3—24no—
747C22×C3—24no—
748C22×C3—48no—
749C22×C3C22×#4114yes—
750C22×C3C22×#4112yes—
751C22×C3C2×2−1+412yes—
752C22×C3#58512yes—
753C22×C3C2611yescharacteristic
754C2×D3—24no—
755C2×D3—24no—
756C2×D3—24no—
757C2×D3—48no—
758C3×C4—24no—
759C3×C4—22no—
760C3×C4—24no—
761C3×C4—24no—
762C3×C4—22no—
763C3×C4—22no—
764C3×C4C22×#4114yes—
765C3×C4C22×#4114yes—
766C3×C4C2×2−1+414yes—
767Dic3—28no—
768Dic3—24no—
769Dic3—24no—
770Dic3—24no—
771Dic3—28no—
772C23—22no—
773C23—22no—
774C23—24no—
775C23—24no—
776C23—24no—
777C23—34no—
778C23—64no—
779C23—64no—
780C23—64no—
781C23C2×#23514yes—
782C23C24×D314yes—
783C23C24×D312yes—
784C23C24×D311yescharacteristic
785Q8—28no—
786Q8—616no—
787Q8—616no—
788Q8—68no—
789Q8—1216no—
790D4—216no—
791D4—28no—
792D4—616no—
793D4—68no—
794D4—1216no—
795C2×C4—24no—
796C2×C4—22no—
797C2×C4—24no—
798C2×C4—22no—
799C2×C4—22no—
800C2×C4—24no—
801C2×C4—216no—
802C2×C4—28no—
803C2×C4—216no—
804C2×C4—34no—
805C2×C4—38no—
806C2×C4—34no—
807C2×C4—34no—
808C2×C4—38no—
809C2×C4—44no—
810C2×C4—48no—
811C2×C4—64no—
812C2×C4—616no—
813C2×C4—68no—
814C2×C4—64no—
815C2×C4—68no—
816C2×C4—64no—
817C2×C4—616no—
818C2×C4—616no—
819C2×C4—128no—
820C2×C4—128no—
821C2×C4C2×#23514yes—
822C2×C4C2×#23514yes—
823C2×C4C2×#235116yes—
824C2×C4#101014yes—
825C2×C4C24×D312yes—
826C2×C4C24×D312yes—
827C2×C4C24×D312yes—
828C2×C4C24×D314yes—
829C2×C4C24×D314yes—
830C2×C4C24×D314yes—
831C2×C4C24×D312yes—
832C2×C4C24×D312yes—
833C2×C4C24×D312yes—
834C2×C3—24no—
835C2×C3—44no—
836C2×C3#346114yescomplemented
837C2×C3C23×#4111yescharacteristic
838C2×C3C22×2−1+411yescharacteristic
839C2×C3C2×#58511yescharacteristic
840D3—44no—
841C22—22no—
842C22—22no—
843C22—28no—
844C22—24no—
845C22—24no—
846C22—24no—
847C22—48no—
848C22—64no—
849C22—64no—
850C22—64no—
851C22—128no—
852C22C22×#23514yes—
853C22C22×#23512yes—
854C22C2×#101012yes—
855C22#596412yes—
856C22C25×D311yescharacteristic
857C4—24no—
858C4—22no—
859C4—24no—
860C4—22no—
861C4—22no—
862C4—24no—
863C4—64no—
864C4—68no—
865C4—64no—
866C4—68no—
867C4—64no—
868C4C22×#23514yes—
869C4C22×#23514yes—
870C4C2×#101014yes—
871C3C2×#346111yescharacteristic, complemented, Sylow
872C2—24no—
873C2—44no—
874C2—124no—
875C2#8582314yesdirect product factor
876C2C23×#23511yescharacteristic
877C2C22×#101011yescharacteristic
878C2C2×#596411yescharacteristic
subgroupG/H
centerC22×C4C23×D3
commutator, cosocleC22×C3C26
FrattiniC22C25×D3
FittingC2×C3×C4×#41C2
socleC23×C3C25
prime radicalC2×#5833C2
hypercenterC2×C4×#41D3
hypocenterC3C2×#3461
LCSG ▷ C22×C3 ▷ C3
UCSC1 ◁ C22×C4 ◁ C2×C4×#41

Complements

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

NH ≅ G/Ntype
1. C2×C3×C4×#41C2semidirect
3. C2×#5825C2semidirect
4. #85823C2direct (N × H)
5. C2×#5583C2semidirect
6. C2×#5578C2semidirect
7. C2×#5561C2semidirect
8. C2×#5557C2semidirect
9. C2×#5564C2semidirect
10. C2×#5538C2semidirect
11. C2×#5534C2semidirect
12. C2×#5519C2semidirect
13. C2×#5518C2semidirect
14. C2×#5526C2semidirect
15. C2×#5479C2semidirect
16. C2×#5470C2semidirect
17. C2×C4×#235C2semidirect
18. C22×C4×Dic6C2semidirect
23. C3×C4×#41C22semidirect
35. #5825C22semidirect
56. #5583C22semidirect
57. #5578C22semidirect
58. #5564C22semidirect
59. #5561C22semidirect
60. #5557C22semidirect
61. #5538C22semidirect
62. #5534C22semidirect
63. #5526C22semidirect
64. #5519C22semidirect
65. #5518C22semidirect
80. #5479C22semidirect
83. C4×#235C22semidirect
89. #5470C22semidirect
101. C2×C4×Dic6C22semidirect
118. C2×C4×#41D3semidirect
303. C4×#41C2×D3semidirect
836. C2×C3#3461semidirect
871. C3C2×#3461semidirect
875. C2#85823direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C3×C4×#412
C2×#58332
C2×#58252
#858232
C2×#55832
C2×#55782
C2×#55612
C2×#55572
C2×#55642
C2×#55382
C2×#55342
C2×#55192
C2×#55182
C2×#55262
C2×#54792
C2×#54702
C2×C4×#2352
C22×C4×Dic62
C2×#34613