Finite Group Databasebeta

← C2×#86129 #11703404

Subgroups — C2×#86129 #11703404

Order 768.

7022 conjugacy classes of subgroups.

The subgroup lattice has 844 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#529C211yesmaximal, characteristic
2#86129C2132yesmaximal, direct product factor
3C2×#5701C214yesmaximal, complemented
4C2×#5685C212yesmaximal, complemented
5C2×#5671C212yesmaximal, complemented
6C2×#5650C214yesmaximal, complemented
7C2×#5622C212yesmaximal, complemented
8C2×#5600C212yesmaximal
9C2×#5567C211yesmaximal, characteristic, complemented
10C2×#5570C211yesmaximal, characteristic, complemented
11C2×#5542C211yesmaximal, characteristic, complemented
12C2×#5541C212yesmaximal, complemented
13C2×D4×Dic6C212yesmaximal, complemented
14C2×D4×Dic6C211yesmaximal, characteristic, complemented
15C2×#5518C212yesmaximal, complemented
16C2×#5516C212yesmaximal, complemented
17C2×#5470C211yesmaximal, characteristic, complemented
18C22×C4×Dic6C211yesmaximal, characteristic, complemented
19C2×#3523—31nomaximal, Sylow
20C23×Dic6C2211yescharacteristic
21C23×Dic6C2212yes—
22C3×#529C22116yes—
23C2×C3×#126C2212yes—
24C2×C3×#125C2211yescharacteristic
25C2×C3×#124C2211yescharacteristic
26C2×C3×#123C2212yes—
27C2×C3×C22⋊Q8C2211yescharacteristic
28C2×C3×#121C2211yescharacteristic
29C2×C3×C4×Q8C2211yescharacteristic
30C2×C3×C4×D4C2211yescharacteristic
31C2×C3×C4×D4C2212yes—
32C2×C3×#117C2212yes—
33C22×C3×C42C2211yescharacteristic
34C2×Q8×Dic3C2212yes—
35C2×#944C2212yes—
36C2×#936C2212yes—
37C2×#935C2214yes—
38C2×D4×Dic3C2212yes—
39C2×D4×Dic3C2214yes—
40C2×#926C2212yes—
41C2×#926C2212yes—
42C22×C4⋊Dic3C2211yescharacteristic
43C2×#924C2212yes—
44C2×#924C2212yes—
45C2×#924C2212yes—
46C2×#924C2212yes—
47C22×Dic3⋊C4C2212yes—
48C22×C4×Dic3C2212yes—
49#5701C22164yescomplemented
50#5685C22132yescomplemented
51#5671C22132yescomplemented
52#5650C22164yescomplemented
53#5622C22132yescomplemented
54#5600C22132yes—
55#5570C22116yescomplemented
56#5567C22116yescomplemented
57#5542C22116yescomplemented
58#5541C22132yescomplemented
59D4×Dic6C22116yescomplemented
60D4×Dic6C22132yescomplemented
61#5518C22132yescomplemented
62#5516C22132yescomplemented
63C2×#890C2212yes—
64C2×#890C2214yes—
65C2×#889C2214yes—
66C2×#889C2214yes—
67C2×#889C2214yes—
68C2×#889C2214yes—
69C2×#888C2214yes—
70C2×#888C2212yes—
71C2×#887C2212yes—
72C2×#887C2212yes—
73C2×#887C2214yes—
74C2×#887C2214yes—
75C2×#879C2214yes—
76C2×#879C2214yes—
77C2×#879C2214yes—
78C2×#879C2214yes—
79C2×#878C2214yes—
80C2×#878C2214yes—
81C2×#878C2214yes—
82C2×#877C2214yes—
83C2×#877C2214yes—
84C2×#877C2214yes—
85#5470C22116yescomplemented
86C2×#870C2212yes—
87C2×#870C2212yes—
88C2×#869C2211yescharacteristic
89C2×#869C2211yescharacteristic
90C2×#869C2212yes—
91C2×C4×Dic6C2211yescharacteristic
92C2×C4×Dic6C2212yes—
93C2×C4×Dic6C2211yescharacteristic
94C2×C4×Dic6C2212yes—
95C2×C4×Dic6C2212yes—
96C2×C4×Dic6C2212yes—
97C2×C4×Dic6C2212yes—
98C2×C4×Dic6C2211yescharacteristic
99C2×C4×Dic6C2211yescharacteristic
100C2×C4×Dic6C2212yes—
101C2×C4×Dic6C22116yescomplemented
102#3523—332no—
103C2×#557—32no—
104C2×#557—31no—
105C2×#557—31no—
106C2×#556—32no—
107C2×#556—31no—
108C2×#552—34no—
109C2×#552—32no—
110C2×D4×Q8—32no—
111C2×D4×Q8—31no—
112C2×#541—34no—
113C2×#541—32no—
114C2×#533—31no—
115C2×#533—32no—
116C2×#529—32no—
117C2×#529D311yescharacteristic
118C2×#519—32no—
119C22×C4×Q8—31no—
120C22×C3×Q8C2311yescharacteristic
121C22×C3×D4C2312yes—
122C22×C3×D4C2311yescharacteristic
123C23×C3×C4C2311yescharacteristic
124C23×C3×C4C2312yes—
125C23×C3×C4C2311yescharacteristic
126C23×C3×C4C2311yescharacteristic
127C23×Dic3C2314yes—
128C23×Dic3C2312yes—
129C23×Dic3C2312yes—
130C22×Dic6—28no—
131C22×Dic6—216no—
132C22×Dic6C2311yescharacteristic
133C22×Dic6C2312yes—
134C22×Dic6C2312yes—
135C22×Dic6C2318yes—
136C22×Dic6C2314yes—
137C22×Dic6C23116yes—
138C22×Dic6C2312yes—
139C22×Dic6C2311yescharacteristic
140C3×#126C23116yes—
141C3×#125C2318yes—
142C3×#124C2318yes—
143C3×#123C23116yes—
144C3×C22⋊Q8C2318yes—
145C3×#121C2318yes—
146C3×C4×Q8C2318yes—
147C3×C4×D4C23116yes—
148C3×C4×D4C2318yes—
149C3×#117C23116yes—
150C2×C3×C4⋊C4C2311yescharacteristic
151C2×C3×C4⋊C4C2312yes—
152C2×C3×C4⋊C4C2312yes—
153C2×C3×C4⋊C4C2311yescharacteristic
154C2×C3×C4⋊C4C2312yes—
155C2×C3×C4⋊C4C2312yes—
156C2×C3×C22⋊C4C2312yes—
157C2×C3×C22⋊C4C2312yes—
158C2×C3×C22⋊C4C2312yes—
159C2×C3×C22⋊C4C2312yes—
160C2×C3×C22⋊C4C2312yes—
161C2×C3×C42C2311yescharacteristic
162C2×C3×C42C2311yescharacteristic
163C2×C3×C42C2311yescharacteristic
164C2×C3×C42C2312yes—
165C2×C3×C42C2311yescharacteristic
166C2×C3×C42C2318yes—
167C2×#217C2314yes—
168C2×#217C2314yes—
169C2×#217C2314yes—
170C2×#217C2314yes—
171Q8×Dic3C23116yes—
172#944C23116yes—
173#936C23116yes—
174#935C23132yes—
175D4×Dic3C23132yes—
176D4×Dic3C23116yes—
177#926C23116yes—
178#926C23116yes—
179C2×C4⋊Dic3C2311yescharacteristic
180C2×C4⋊Dic3C2312yes—
181C2×C4⋊Dic3C2311yescharacteristic
182C2×C4⋊Dic3C2312yes—
183C2×C4⋊Dic3C2312yes—
184C2×C4⋊Dic3C2318yes—
185C2×C4⋊Dic3C2312yes—
186C2×C4⋊Dic3C2312yes—
187C2×C4⋊Dic3C2314yes—
188C2×C4⋊Dic3C2314yes—
189#924C23116yes—
190#924C23116yes—
191#924C23116yes—
192#924C23116yes—
193C2×Dic3⋊C4C23116yes—
194C2×Dic3⋊C4C2312yes—
195C2×Dic3⋊C4C2312yes—
196C2×Dic3⋊C4C2312yes—
197C2×Dic3⋊C4C2312yes—
198C2×Dic3⋊C4C2314yes—
199C2×Dic3⋊C4C2314yes—
200C2×Dic3⋊C4C2314yes—
201C2×Dic3⋊C4C2314yes—
202C2×Dic3⋊C4C2314yes—
203C2×Dic3⋊C4C2314yes—
204C2×Dic3⋊C4C2314yes—
205C2×Dic3⋊C4C2314yes—
206C2×C4×Dic3C2312yes—
207C2×C4×Dic3C2314yes—
208C2×C4×Dic3C2312yes—
209C2×C4×Dic3C2312yes—
210C2×C4×Dic3C2312yes—
211C2×C4×Dic3C2314yes—
212C2×C4×Dic3C2314yes—
213C2×C4×Dic3C23116yes—
214C2×C4×Dic3C2314yes—
215#890C23132yes—
216#890C23116yes—
217#889C23132yes—
218#889C23132yes—
219#889C23132yes—
220#889C23132yes—
221#888C23132yes—
222#888C23116yes—
223#887C23132yes—
224#887C23116yes—
225#887C23116yes—
226#887C23132yes—
227#879C23132yes—
228#879C23132yes—
229#879C23132yes—
230#879C23132yes—
231#878C23132yes—
232#878C23132yes—
233#878C23132yes—
234#877C23132yes—
235#877C23132yes—
236#877C23132yes—
237#870C23116yes—
238#870C23116yes—
239#869C2318yes—
240#869C2318yes—
241#869C23116yes—
242C4×Dic6C23116yes—
243C4×Dic6C23116yes—
244C4×Dic6C23116yes—
245C4×Dic6C2318yes—
246C4×Dic6C2318yes—
247C4×Dic6C2318yes—
248C4×Dic6C2318yes—
249C4×Dic6C23116yes—
250C4×Dic6C23116yes—
251C4×Dic6C23116yes—
252C23×Q8—31no—
253C23×Q8—32no—
254#557—332no—
255#557—316no—
256#557—316no—
257#556—332no—
258#556—316no—
259#552—364no—
260#552—332no—
261D4×Q8—332no—
262D4×Q8—316no—
263#541—364no—
264#541—332no—
265#533—332no—
266#533—316no—
267C2×C4⋊Q8—32no—
268C2×C4⋊Q8—32no—
269C2×C4⋊Q8—34no—
270C2×C4⋊Q8—31no—
271C2×C4⋊Q8—31no—
272C2×C4⋊Q8—32no—
273#529—332no—
274#529C2×D3116yes—
275C2×#126—34no—
276C2×#126—34no—
277C2×#126—34no—
278C2×#126—34no—
279C2×#126C2×D312yes—
280C2×#125—32no—
281C2×#125—34no—
282C2×#125—34no—
283C2×#125—34no—
284C2×#125—34no—
285C2×#125—34no—
286C2×#125—32no—
287C2×#125—32no—
288C2×#125C2×D311yescharacteristic
289C2×#124—32no—
290C2×#124C2×D311yescharacteristic
291C2×#123—34no—
292C2×#123C2×D312yes—
293C2×C22⋊Q8—32no—
294C2×C22⋊Q8—32no—
295C2×C22⋊Q8—32no—
296C2×C22⋊Q8—32no—
297C2×C22⋊Q8—34no—
298C2×C22⋊Q8—34no—
299C2×C22⋊Q8—34no—
300C2×C22⋊Q8C2×D311yescharacteristic
301C2×#121C2×D311yescharacteristic
302#519—332no—
303C2×C4×Q8—32no—
304C2×C4×Q8—34no—
305C2×C4×Q8—34no—
306C2×C4×Q8—32no—
307C2×C4×Q8—32no—
308C2×C4×Q8—31no—
309C2×C4×Q8—32no—
310C2×C4×Q8—31no—
311C2×C4×Q8—31no—
312C2×C4×Q8—32no—
313C2×C4×Q8—31no—
314C2×C4×Q8—32no—
315C2×C4×Q8—32no—
316C2×C4×Q8—32no—
317C2×C4×Q8—32no—
318C2×C4×Q8—316no—
319C2×C4×Q8C2×D311yescharacteristic
320C2×C4×D4—34no—
321C2×C4×D4—32no—
322C2×C4×D4C2×D312yes—
323C2×C4×D4C2×D311yescharacteristic
324C2×#117—32no—
325C2×#117—32no—
326C2×#117—34no—
327C2×#117—34no—
328C2×#117—34no—
329C2×#117C2×D312yes—
330C22×C4⋊C4—32no—
331C22×C4⋊C4—31no—
332C22×C42—32no—
333C22×C42C2×D311yescharacteristic
334C24×C3C2412yes—
335C24×C3C2411yescharacteristic
336C2×C3×Q8—24no—
337C2×C3×Q8C2414yes—
338C2×C3×D4—28no—
339C2×C3×D4—24no—
340C2×C3×D4C2418yes—
341C2×C3×D4C2414yes—
342C22×C3×C4—24no—
343C22×C3×C4—24no—
344C22×C3×C4—28no—
345C22×C3×C4—24no—
346C22×C3×C4C2411yescharacteristic
347C22×C3×C4C2411yescharacteristic
348C22×C3×C4C2414yes—
349C22×C3×C4C2412yes—
350C22×C3×C4C2412yes—
351C22×C3×C4C2412yes—
352C22×C3×C4C2411yescharacteristic
353C22×C3×C4C2411yescharacteristic
354C22×C3×C4C2414yes—
355C22×C3×C4C2414yes—
356C22×C3×C4C2418yes—
357C22×C3×C4C2411yescharacteristic
358C22×C3×C4C2411yescharacteristic
359C22×Dic3—28no—
360C22×Dic3—28no—
361C22×Dic3—216no—
362C22×Dic3C24116yes—
363C22×Dic3C2418yes—
364C22×Dic3C2418yes—
365C22×Dic3C2412yes—
366C22×Dic3C2414yes—
367C22×Dic3C2412yes—
368C22×Dic3C2414yes—
369C22×Dic3C2412yes—
370C22×Dic3C2412yes—
371C2×Dic6—24no—
372C2×Dic6—28no—
373C2×Dic6—28no—
374C2×Dic6—28no—
375C2×Dic6—216no—
376C2×Dic6—232no—
377C2×Dic6—264no—
378C2×Dic6#4118yes—
379C2×Dic6C2414yes—
380C2×Dic6C2418yes—
381C2×Dic6C2418yes—
382C2×Dic6C2418yes—
383C2×Dic6C24116yes—
384C2×Dic6C2414yes—
385C3×C4⋊C4C2414yes—
386C3×C4⋊C4C2418yes—
387C3×C4⋊C4C2418yes—
388C3×C4⋊C4C2414yes—
389C3×C4⋊C4C2418yes—
390C3×C4⋊C4C2418yes—
391C3×C22⋊C4C2418yes—
392C3×C22⋊C4C2418yes—
393C3×C22⋊C4C2418yes—
394C3×C22⋊C4C2418yes—
395C3×C22⋊C4C2418yes—
396C3×C42C2414yes—
397C3×C42C2414yes—
398C3×C42C2414yes—
399C3×C42C2418yes—
400C3×C42C2414yes—
401#217C24116yes—
402#217C24116yes—
403#217C24116yes—
404#217C24116yes—
405C4⋊Dic3C2414yes—
406C4⋊Dic3C2418yes—
407C4⋊Dic3C2414yes—
408C4⋊Dic3C2418yes—
409C4⋊Dic3C2418yes—
410C4⋊Dic3C2418yes—
411C4⋊Dic3C2418yes—
412C4⋊Dic3C24116yes—
413C4⋊Dic3C24116yes—
414Dic3⋊C4C2418yes—
415Dic3⋊C4C2418yes—
416Dic3⋊C4C2418yes—
417Dic3⋊C4C2418yes—
418Dic3⋊C4C24116yes—
419Dic3⋊C4C24116yes—
420Dic3⋊C4C24116yes—
421Dic3⋊C4C24116yes—
422Dic3⋊C4C24116yes—
423Dic3⋊C4C24116yes—
424Dic3⋊C4C24116yes—
425Dic3⋊C4C24116yes—
426C4×Dic3C2418yes—
427C4×Dic3C24116yes—
428C4×Dic3C2418yes—
429C4×Dic3C2418yes—
430C4×Dic3C2418yes—
431C4×Dic3C24116yes—
432C4×Dic3C24116yes—
433C4×Dic3C24116yes—
434C22×Q8—31no—
435C22×Q8—32no—
436C22×Q8—34no—
437C22×Q8—32no—
438C22×Q8—31no—
439C22×Q8—32no—
440C22×Q8—38no—
441C22×Q8—316no—
442C22×Q8—68no—
443C22×Q8—616no—
444C22×Q8C22×D311yescharacteristic
445C22×D4C22×D312yes—
446C22×D4C22×D311yescharacteristic
447C23×C4—32no—
448C23×C4—32no—
449C23×C4—34no—
450C23×C4C22×D311yescharacteristic
451C23×C4C22×D311yescharacteristic
452C23×C4C22×D312yes—
453C23×C4C22×D311yescharacteristic
454C4⋊Q8—316no—
455C4⋊Q8—316no—
456C4⋊Q8—332no—
457C4⋊Q8—38no—
458C4⋊Q8—38no—
459C4⋊Q8—316no—
460#126—332no—
461#126—332no—
462#126—332no—
463#126—332no—
464#126C22×D3116yes—
465#125—316no—
466#125—332no—
467#125—332no—
468#125—332no—
469#125—332no—
470#125—332no—
471#125—316no—
472#125—316no—
473#125C22×D318yes—
474#124—316no—
475#124C22×D318yes—
476#123—332no—
477#123C22×D3116yes—
478C22⋊Q8—316no—
479C22⋊Q8—316no—
480C22⋊Q8—316no—
481C22⋊Q8—316no—
482C22⋊Q8—332no—
483C22⋊Q8—332no—
484C22⋊Q8—332no—
485C22⋊Q8C22×D318yes—
486#121C22×D318yes—
487C4×Q8—316no—
488C4×Q8—332no—
489C4×Q8—332no—
490C4×Q8—316no—
491C4×Q8—316no—
492C4×Q8—38no—
493C4×Q8—316no—
494C4×Q8—38no—
495C4×Q8—38no—
496C4×Q8—316no—
497C4×Q8—38no—
498C4×Q8—316no—
499C4×Q8—316no—
500C4×Q8—316no—
501C4×Q8—316no—
502C4×Q8C22×D318yes—
503C4×D4—332no—
504C4×D4—316no—
505C4×D4C22×D3116yes—
506C4×D4C22×D318yes—
507#117—316no—
508#117—316no—
509#117—332no—
510#117—332no—
511#117—332no—
512#117C22×D3116yes—
513C2×C4⋊C4—32no—
514C2×C4⋊C4—31no—
515C2×C4⋊C4—32no—
516C2×C4⋊C4—31no—
517C2×C4⋊C4—32no—
518C2×C4⋊C4—32no—
519C2×C4⋊C4—32no—
520C2×C4⋊C4—316no—
521C2×C4⋊C4—38no—
522C2×C4⋊C4—34no—
523C2×C4⋊C4—32no—
524C2×C4⋊C4—34no—
525C2×C4⋊C4—34no—
526C2×C4⋊C4—34no—
527C2×C4⋊C4—32no—
528C2×C4⋊C4—34no—
529C2×C4⋊C4—32no—
530C2×C4⋊C4—32no—
531C2×C4⋊C4—34no—
532C2×C4⋊C4—34no—
533C2×C4⋊C4—34no—
534C2×C4⋊C4—34no—
535C2×C4⋊C4—34no—
536C2×C4⋊C4C22×D312yes—
537C2×C4⋊C4C22×D312yes—
538C2×C4⋊C4C22×D311yescharacteristic
539C2×C4⋊C4C22×D312yes—
540C2×C4⋊C4C22×D311yescharacteristic
541C2×C4⋊C4C22×D312yes—
542C2×C22⋊C4—34no—
543C2×C22⋊C4—34no—
544C2×C22⋊C4—34no—
545C2×C22⋊C4—34no—
546C2×C22⋊C4C22×D312yes—
547C2×C22⋊C4C22×D312yes—
548C2×C22⋊C4C22×D312yes—
549C2×C22⋊C4C22×D312yes—
550C2×C22⋊C4C22×D312yes—
551C2×C42—32no—
552C2×C42—34no—
553C2×C42—34no—
554C2×C42—34no—
555C2×C42—34no—
556C2×C42—32no—
557C2×C42—32no—
558C2×C42—32no—
559C2×C42—316no—
560C2×C42C22×D311yescharacteristic
561C2×C42C22×D312yes—
562C2×C42C22×D311yescharacteristic
563C2×C42C22×D311yescharacteristic
564C2×C42C22×D311yescharacteristic
565C2×C42C22×D318yes—
566C23×C3—22no—
567C23×C3—22no—
568C23×C3—24no—
569C23×C3—24no—
570C23×C3—24no—
571C23×C32−1+414yes—
572C23×C3C2514yes—
573C23×C3C2512yes—
574C23×C3C2511yescharacteristic
575C3×Q8—28no—
576C3×D4—216no—
577C3×D4—28no—
578C2×C3×C4—24no—
579C2×C3×C4—22no—
580C2×C3×C4—28no—
581C2×C3×C4—22no—
582C2×C3×C4—22no—
583C2×C3×C4—22no—
584C2×C3×C4—24no—
585C2×C3×C4—24no—
586C2×C3×C4—28no—
587C2×C3×C4—216no—
588C2×C3×C4—28no—
589C2×C3×C4C2×#4114yes—
590C2×C3×C42−1+414yes—
591C2×C3×C4C2512yes—
592C2×C3×C4C2512yes—
593C2×C3×C4C2514yes—
594C2×C3×C4C2514yes—
595C2×C3×C4C2514yes—
596C2×C3×C4C2512yes—
597C2×C3×C4C2512yes—
598C2×C3×C4C2512yes—
599C2×C3×C4C2512yes—
600C2×Dic3—24no—
601C2×Dic3—28no—
602C2×Dic3—28no—
603C2×Dic3—216no—
604C2×Dic3—24no—
605C2×Dic3—24no—
606C2×Dic3—216no—
607C2×Dic3—232no—
608C2×Dic3C2×#4118yes—
609C2×Dic3C2514yes—
610C2×Dic3C2518yes—
611C2×Dic3C2514yes—
612C2×Dic3C2518yes—
613C2×Dic3C2514yes—
614C2×Dic3C2514yes—
615Dic6—28no—
616Dic6—216no—
617Dic6—216no—
618Dic6—216no—
619Dic6—232no—
620Dic6C2×#41116yes—
621C24C23×D312yes—
622C24C23×D311yescharacteristic
623C2×Q8—24no—
624C2×Q8—38no—
625C2×Q8—34no—
626C2×Q8—38no—
627C2×Q8—316no—
628C2×Q8—38no—
629C2×Q8—34no—
630C2×Q8—38no—
631C2×Q8—616no—
632C2×Q8—68no—
633C2×Q8—632no—
634C2×Q8—664no—
635C2×Q8—64no—
636C2×Q8—68no—
637C2×Q8—68no—
638C2×Q8C23×D314yes—
639C2×D4—28no—
640C2×D4—24no—
641C2×D4C23×D318yes—
642C2×D4C23×D314yes—
643C22×C4—24no—
644C22×C4—24no—
645C22×C4—28no—
646C22×C4—24no—
647C22×C4—32no—
648C22×C4—38no—
649C22×C4—38no—
650C22×C4—316no—
651C22×C4—32no—
652C22×C4—34no—
653C22×C4—32no—
654C22×C4—34no—
655C22×C4—32no—
656C22×C4—68no—
657C22×C4—616no—
658C22×C4—68no—
659C22×C4C23×D314yes—
660C22×C4C23×D314yes—
661C22×C4C23×D314yes—
662C22×C4C23×D318yes—
663C22×C4C23×D311yescharacteristic
664C22×C4C23×D311yescharacteristic
665C22×C4C23×D312yes—
666C22×C4C23×D312yes—
667C22×C4C23×D312yes—
668C22×C4C23×D311yescharacteristic
669C22×C4C23×D311yescharacteristic
670C22×C4C23×D311yescharacteristic
671C22×C4C23×D311yescharacteristic
672C4⋊C4—38no—
673C4⋊C4—34no—
674C4⋊C4—38no—
675C4⋊C4—34no—
676C4⋊C4—38no—
677C4⋊C4—38no—
678C4⋊C4—38no—
679C4⋊C4—316no—
680C4⋊C4—38no—
681C4⋊C4—316no—
682C4⋊C4—316no—
683C4⋊C4—316no—
684C4⋊C4—38no—
685C4⋊C4—316no—
686C4⋊C4—38no—
687C4⋊C4—38no—
688C4⋊C4—316no—
689C4⋊C4—316no—
690C4⋊C4—316no—
691C4⋊C4—316no—
692C4⋊C4—316no—
693C4⋊C4C23×D318yes—
694C4⋊C4C23×D318yes—
695C4⋊C4C23×D314yes—
696C4⋊C4C23×D318yes—
697C4⋊C4C23×D314yes—
698C4⋊C4C23×D318yes—
699C22⋊C4—316no—
700C22⋊C4—316no—
701C22⋊C4—316no—
702C22⋊C4—316no—
703C22⋊C4C23×D318yes—
704C22⋊C4C23×D318yes—
705C22⋊C4C23×D318yes—
706C22⋊C4C23×D318yes—
707C22⋊C4C23×D318yes—
708C42—38no—
709C42—38no—
710C42—38no—
711C42—38no—
712C42—316no—
713C42—316no—
714C42—316no—
715C42—316no—
716C42C23×D314yes—
717C42C23×D314yes—
718C42C23×D314yes—
719C42C23×D314yes—
720C42C23×D318yes—
721C22×C3—22no—
722C22×C3—22no—
723C22×C3—28no—
724C22×C3—24no—
725C22×C3—24no—
726C22×C3—24no—
727C22×C3—48no—
728C22×C3C22×#4112yes—
729C22×C3C2×2−1+414yes—
730C22×C3C2×2−1+412yes—
731C22×C3C2×2−1+412yes—
732C22×C3C2611yescharacteristic
733C3×C4—24no—
734C3×C4—22no—
735C3×C4—22no—
736C3×C4—22no—
737C3×C4—22no—
738C3×C4—24no—
739C3×C4—24no—
740C3×C4C22×#4114yes—
741C3×C4C2×2−1+414yes—
742Dic3—24no—
743Dic3—28no—
744Dic3—28no—
745Dic3—24no—
746Dic3—24no—
747Dic3C22×#4118yes—
748C23—22no—
749C23—22no—
750C23—24no—
751C23—24no—
752C23—24no—
753C23#101014yes—
754C23C24×D314yes—
755C23C24×D312yes—
756C23C24×D311yescharacteristic
757Q8—28no—
758Q8—316no—
759Q8—632no—
760Q8—616no—
761Q8—68no—
762Q8—616no—
763Q8—616no—
764D4—216no—
765D4—28no—
766C2×C4—24no—
767C2×C4—22no—
768C2×C4—28no—
769C2×C4—22no—
770C2×C4—22no—
771C2×C4—22no—
772C2×C4—24no—
773C2×C4—24no—
774C2×C4—28no—
775C2×C4—216no—
776C2×C4—28no—
777C2×C4—38no—
778C2×C4—34no—
779C2×C4—34no—
780C2×C4—38no—
781C2×C4—34no—
782C2×C4—34no—
783C2×C4—38no—
784C2×C4—616no—
785C2×C4—632no—
786C2×C4—68no—
787C2×C4—64no—
788C2×C4—616no—
789C2×C4—64no—
790C2×C4—64no—
791C2×C4—68no—
792C2×C4D3×#4114yes—
793C2×C4#101014yes—
794C2×C4C24×D312yes—
795C2×C4C24×D312yes—
796C2×C4C24×D314yes—
797C2×C4C24×D314yes—
798C2×C4C24×D314yes—
799C2×C4C24×D312yes—
800C2×C4C24×D312yes—
801C2×C4C24×D312yes—
802C2×C4C24×D312yes—
803C2×C3—24no—
804C2×C3—44no—
805C2×C3#352314yescomplemented
806C2×C3C23×#4111yescharacteristic
807C2×C3C22×2−1+411yescharacteristic
808C2×C3C22×2−1+411yescharacteristic
809C22—22no—
810C22—22no—
811C22—28no—
812C22—24no—
813C22—24no—
814C22—24no—
815C22—48no—
816C22C2×D3×#4112yes—
817C22C2×#101014yes—
818C22C2×#101012yes—
819C22C2×#101012yes—
820C22C25×D311yescharacteristic
821C4—22no—
822C4—22no—
823C4—22no—
824C4—24no—
825C4—24no—
826C4—24no—
827C4—22no—
828C4—38no—
829C4—64no—
830C4—64no—
831C4—68no—
832C4—64no—
833C4—68no—
834C4C2×D3×#4114yes—
835C4C2×#101014yes—
836C3C2×#352311yescharacteristic, complemented, Sylow
837C2—24no—
838C2—44no—
839C2#8612914yesdirect product factor
840C2C22×#101011yescharacteristic
841C2C22×#101011yescharacteristic
842C2C22×D3×#4111yescharacteristic
subgroupG/H
centerC23C24×D3
commutator, cosocleC22×C3C26
FrattiniC22C25×D3
FittingC2×C3×#529C2
socleC23×C3C25
prime radicalC2×C3×#121C22
hypercenterC2×#529D3
hypocenterC3C2×#3523
LCSG ▷ C22×C3 ▷ C3
UCSC1 ◁ C23 ◁ C2×#529

Complements

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

NH ≅ G/Ntype
2. #86129C2direct (N × H)
3. C2×#5701C2semidirect
4. C2×#5685C2semidirect
5. C2×#5671C2semidirect
6. C2×#5650C2semidirect
7. C2×#5622C2semidirect
9. C2×#5567C2semidirect
10. C2×#5570C2semidirect
11. C2×#5542C2semidirect
12. C2×#5541C2semidirect
13. C2×D4×Dic6C2semidirect
14. C2×D4×Dic6C2semidirect
15. C2×#5518C2semidirect
16. C2×#5516C2semidirect
17. C2×#5470C2semidirect
18. C22×C4×Dic6C2semidirect
49. #5701C22semidirect
50. #5685C22semidirect
51. #5671C22semidirect
52. #5650C22semidirect
53. #5622C22semidirect
55. #5570C22semidirect
56. #5567C22semidirect
57. #5542C22semidirect
58. #5541C22semidirect
59. D4×Dic6C22semidirect
60. D4×Dic6C22semidirect
61. #5518C22semidirect
62. #5516C22semidirect
85. #5470C22semidirect
101. C2×C4×Dic6C22semidirect
805. C2×C3#3523semidirect
836. C3C2×#3523semidirect
839. C2#86129direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C3×#5292
#861292
C2×#57012
C2×#56852
C2×#56712
C2×#56502
C2×#56222
C2×#56002
C2×#55672
C2×#55702
C2×#55422
C2×#55412
C2×D4×Dic62
C2×#55182
C2×#55162
C2×#54702
C22×C4×Dic62
C2×#35233