Finite Group Databasebeta

← C2×#87025 #11703405

Subgroups — C2×#87025 #11703405

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×#557C211yesmaximal, characteristic, complemented
2#87025C2132yesmaximal, direct product factor
3C2×#5727C212yesmaximal, complemented
4C2×#5727C211yesmaximal, characteristic, complemented
5C2×#5731C212yesmaximal, complemented
6C2×#5728C211yesmaximal, characteristic, complemented
7C2×#5693C214yesmaximal, complemented
8C2×#5685C212yesmaximal, complemented
9C2×#5696C214yesmaximal, complemented
10C2×#5691C212yesmaximal
11C2×#5581C212yesmaximal, complemented
12C2×#5578C212yesmaximal, complemented
13C2×#5580C211yesmaximal, characteristic
14C2×#5572C212yesmaximal, complemented
15C2×C4×D3×Q8C211yesmaximal, characteristic, complemented
16C2×#5567C211yesmaximal, characteristic, complemented
17C2×#5568C212yesmaximal, complemented
18C2×#5584C211yesmaximal, characteristic, complemented
19C2×#3523—31nomaximal, Sylow
20C22×D3×Q8C2211yescharacteristic
21C22×D3×Q8C2212yes—
22C3×#557C22116yescomplemented
23C2×C3×C4⋊Q8C2211yescharacteristic
24C2×C3×C4⋊Q8C2212yes—
25C2×C3×#125C2212yes—
26C2×C3×#125C2214yes—
27C2×C3×C4×Q8C2211yescharacteristic
28C2×C3×C4×Q8C2212yes—
29C2×C3×C4×Q8C2211yescharacteristic
30C2×C3×C4×Q8C2212yes—
31C2×#947C2211yescharacteristic
32C2×#946C2212yes—
33C2×#946C2211yescharacteristic
34C2×#946C2212yes—
35C2×#946C2212yes—
36C2×Q8×Dic3C2211yescharacteristic
37C2×Q8×Dic3C2212yes—
38C2×#944C2212yes—
39#5731C22132yescomplemented
40#5728C22116yescomplemented
41#5727C22116yescomplemented
42#5727C22132yescomplemented
43#5696C22164yescomplemented
44#5693C22164yescomplemented
45#5691C22132yes—
46#5685C22132yescomplemented
47#5584C22116yescomplemented
48#5581C22132yescomplemented
49#5580C22116yes—
50#5578C22132yescomplemented
51#5572C22132yescomplemented
52C4×D3×Q8C22116yescomplemented
53#5568C22132yescomplemented
54#5567C22116yescomplemented
55C2×#898C2214yes—
56C2×#898C2214yes—
57C2×#898C2212yes—
58C2×#898C2214yes—
59C2×#897C2212yes—
60C2×#896C2214yes—
61C2×#896C2214yes—
62C2×#896C2214yes—
63C2×#895C2211yescharacteristic
64C2×#894C2212yes—
65C2×#894C2214yes—
66C2×#893C2212yes—
67C2×#893C2214yes—
68C2×#892C2212yes—
69C2×#892C2214yes—
70C2×#892C2212yes—
71C2×D3×C4⋊C4C2211yescharacteristic
72C2×D3×C4⋊C4C2212yes—
73C2×#890C2211yescharacteristic
74C2×#890C2212yes—
75C2×#889C2214yes—
76C2×#889C2214yes—
77C2×#889C2214yes—
78C2×#889C2214yes—
79C2×#888C2212yes—
80C2×#888C2214yes—
81C2×#887C2212yes—
82C2×#887C2212yes—
83C2×#887C2211yescharacteristic
84C2×#887C2212yes—
85C2×#887C2214yes—
86C2×#876C2214yes—
87C2×#875C2212yes—
88C2×C4×D12C2211yescharacteristic
89C2×C4×D12C2212yes—
90C2×#872C2214yes—
91C2×#872C2212yes—
92C2×#872C2214yes—
93C2×C42×D3C2211yescharacteristic
94C2×C42×D3C2212yes—
95C2×#870C2212yes—
96C2×#869C2211yescharacteristic
97C2×C4×Dic6C2212yes—
98C2×C4×Dic6C2212yes—
99C2×C4×Dic6C2211yescharacteristic
100C2×C4×Dic6C2212yes—
101C2×C4×Dic6C2214yes—
102#3523—332no—
103C2×#557—32no—
104C2×#557—31no—
105C2×#557D311yescharacteristic, complemented
106C2×#556—31no—
107C2×#556—32no—
108C2×#552—34no—
109C2×#552—32no—
110C2×D4×Q8—32no—
111C2×D4×Q8—31no—
112C2×#541—32no—
113C2×#541—34no—
114C2×#533—31no—
115C2×#533—32no—
116C2×#529—32no—
117C2×#529—31no—
118C2×#519—32no—
119C22×C4×Q8—31no—
120C22×C3×Q8C2311yescharacteristic
121C22×C3×Q8C2312yes—
122C22×C3×Q8C2311yescharacteristic
123C2×D3×Q8—28no—
124C2×D3×Q8—216no—
125C2×D3×Q8C2318yes—
126C2×D3×Q8C23116yes—
127C22×D12C2311yescharacteristic
128C22×D12C2312yes—
129C22×C4×D3C2311yescharacteristic
130C22×C4×D3C2312yes—
131C22×C4×D3C2312yes—
132C22×C4×D3C2314yes—
133C22×C4×D3C2311yescharacteristic
134C22×C4×D3C2312yes—
135C22×C4×D3C2311yescharacteristic
136C22×Dic6C2312yes—
137C22×Dic6C2314yes—
138C22×Dic6C2312yes—
139C22×Dic6C2311yescharacteristic
140C3×C4⋊Q8C2318yes—
141C3×C4⋊Q8C23116yes—
142C3×#125C23116yes—
143C3×#125C23132yes—
144C3×C4×Q8C2318yes—
145C3×C4×Q8C23116yes—
146C3×C4×Q8C2318yes—
147C3×C4×Q8C23116yes—
148C2×C3×C4⋊C4C2311yescharacteristic
149C2×C3×C4⋊C4C2312yes—
150C2×C3×C4⋊C4C2314yes—
151C2×C3×C4⋊C4C2311yescharacteristic
152C2×C3×C4⋊C4C2312yes—
153C2×C3×C4⋊C4C2314yes—
154C2×C3×C4⋊C4C2312yes—
155C2×C3×C4⋊C4C2314yes—
156C2×C3×C4⋊C4C2312yes—
157C2×C3×C42C2312yes—
158C2×C3×C42C2311yescharacteristic
159C2×C3×C42C2312yes—
160C2×C3×C42C2314yes—
161#947C2318yes—
162#946C23116yes—
163#946C23116yes—
164#946C23116yes—
165#946C2318yes—
166Q8×Dic3C23116yes—
167Q8×Dic3C2318yes—
168#944C23116yes—
169C2×(C2×D3)⋊C4C2312yes—
170C2×(C2×D3)⋊C4C2312yes—
171C2×(C2×D3)⋊C4C2314yes—
172C2×(C2×D3)⋊C4C2312yes—
173C2×(C2×D3)⋊C4C2314yes—
174C2×(C2×D3)⋊C4C2312yes—
175C2×(C2×D3)⋊C4C2312yes—
176C2×(C2×D3)⋊C4C2314yes—
177C2×(C2×D3)⋊C4C2314yes—
178C2×C4⋊Dic3C2311yescharacteristic
179C2×C4⋊Dic3C2312yes—
180C2×C4⋊Dic3C2311yescharacteristic
181C2×C4⋊Dic3C2312yes—
182C2×C4⋊Dic3C2314yes—
183C2×C4⋊Dic3C2312yes—
184C2×C4⋊Dic3C2312yes—
185C2×Dic3⋊C4C2312yes—
186C2×Dic3⋊C4C2314yes—
187C2×Dic3⋊C4C2312yes—
188C2×Dic3⋊C4C2312yes—
189C2×Dic3⋊C4C2312yes—
190C2×Dic3⋊C4C2314yes—
191C2×Dic3⋊C4C2314yes—
192C2×Dic3⋊C4C2314yes—
193C2×Dic3⋊C4C2312yes—
194C2×Dic3⋊C4C2314yes—
195C2×Dic3⋊C4C2314yes—
196C2×C4×Dic3C2311yescharacteristic
197C2×C4×Dic3C2312yes—
198C2×C4×Dic3C2312yes—
199C2×C4×Dic3C2314yes—
200C2×C4×Dic3C2314yes—
201C2×C4×Dic3C2311yescharacteristic
202C2×C4×Dic3C2311yescharacteristic
203C2×C4×Dic3C2312yes—
204C2×C4×Dic3C2314yes—
205#898C23132yes—
206#898C23132yes—
207#898C23132yes—
208#898C23116yes—
209#897C23116yes—
210#896C23132yes—
211#896C23132yes—
212#896C23132yes—
213#895C2318yes—
214#894C23132yes—
215#894C23116yes—
216#893C23132yes—
217#893C23116yes—
218#892C23132yes—
219#892C23116yes—
220#892C23116yes—
221D3×C4⋊C4C23116yes—
222D3×C4⋊C4C2318yes—
223#890C2318yes—
224#890C23116yes—
225#889C23132yes—
226#889C23132yes—
227#889C23132yes—
228#889C23132yes—
229#888C23132yes—
230#888C23116yes—
231#887C23116yes—
232#887C23132yes—
233#887C23116yes—
234#887C23116yes—
235#887C2318yes—
236#876C23132yes—
237#875C23116yes—
238C4×D12C23116yes—
239C4×D12C2318yes—
240#872C23132yes—
241#872C23132yes—
242#872C23116yes—
243C42×D3C23116yes—
244C42×D3C2318yes—
245#870C23116yes—
246#869C2318yes—
247C4×Dic6C23116yes—
248C4×Dic6C23116yes—
249C4×Dic6C23132yes—
250C4×Dic6C2318yes—
251C4×Dic6C23116yes—
252C23×Q8—31no—
253C23×Q8—32no—
254#557—332no—
255#557—316no—
256#557C2×D3116yescomplemented
257#556—332no—
258#556—316no—
259#552—364no—
260#552—332no—
261D4×Q8—332no—
262D4×Q8—316no—
263#541—332no—
264#541—364no—
265#533—316no—
266#533—332no—
267C2×C4⋊Q8—32no—
268C2×C4⋊Q8—32no—
269C2×C4⋊Q8—34no—
270C2×C4⋊Q8—31no—
271C2×C4⋊Q8C2×D311yescharacteristic
272C2×C4⋊Q8C2×D312yes—
273#529—332no—
274#529—316no—
275C2×#126—32no—
276C2×#126—34no—
277C2×#126—34no—
278C2×#126—34no—
279C2×#126—34no—
280C2×#125—31no—
281C2×#125—34no—
282C2×#125—32no—
283C2×#125—34no—
284C2×#125—34no—
285C2×#125—34no—
286C2×#125—32no—
287C2×#125C2×D312yes—
288C2×#125C2×D314yes—
289C2×#124—31no—
290C2×#124—32no—
291C2×#123—32no—
292C2×#123—34no—
293C2×C22⋊Q8—31no—
294C2×C22⋊Q8—32no—
295C2×C22⋊Q8—32no—
296C2×C22⋊Q8—32no—
297C2×C22⋊Q8—32no—
298C2×C22⋊Q8—34no—
299C2×C22⋊Q8—34no—
300C2×C22⋊Q8—34no—
301C2×#121—31no—
302#519—332no—
303C2×C4×Q8—31no—
304C2×C4×Q8—32no—
305C2×C4×Q8—316no—
306C2×C4×Q8—31no—
307C2×C4×Q8—32no—
308C2×C4×Q8—34no—
309C2×C4×Q8—32no—
310C2×C4×Q8—32no—
311C2×C4×Q8—31no—
312C2×C4×Q8—32no—
313C2×C4×Q8—34no—
314C2×C4×Q8—32no—
315C2×C4×Q8—32no—
316C2×C4×Q8C2×D311yescharacteristic
317C2×C4×Q8C2×D312yes—
318C2×C4×Q8C2×D311yescharacteristic
319C2×C4×Q8C2×D312yes—
320C2×C4×D4—34no—
321C2×C4×D4—32no—
322C2×C4×D4—32no—
323C2×C4×D4—31no—
324C2×#117—34no—
325C2×#117—32no—
326C2×#117—32no—
327C2×#117—32no—
328C2×#117—34no—
329C2×#117—34no—
330C22×C4⋊C4—32no—
331C22×C4⋊C4—31no—
332C22×C42—32no—
333C22×C42—31no—
334C23×D3C2412yes—
335C23×D3C2411yescharacteristic
336C2×C3×Q8—24no—
337C2×C3×Q8—28no—
338C2×C3×Q8—24no—
339C2×C3×Q8C2414yes—
340C2×C3×Q8C2418yes—
341C2×C3×Q8C2414yes—
342C22×C3×C4C2412yes—
343C22×C3×C4C2412yes—
344C22×C3×C4C2411yescharacteristic
345C22×C3×C4C2412yes—
346C22×C3×C4C2414yes—
347C22×C3×C4C2412yes—
348C22×C3×C4C2411yescharacteristic
349C22×C3×C4C2411yescharacteristic
350C22×Dic3C2411yescharacteristic
351C22×Dic3C2411yescharacteristic
352C22×Dic3C2414yes—
353C22×Dic3C2412yes—
354C22×Dic3C2411yescharacteristic
355C22×Dic3C2412yes—
356C22×Dic3C2412yes—
357D3×Q8—232no—
358D3×Q8—264no—
359C2×D12—28no—
360C2×D12—24no—
361C2×D12C2414yes—
362C2×D12C2418yes—
363C2×C4×D3—28no—
364C2×C4×D3—24no—
365C2×C4×D3—24no—
366C2×C4×D3—28no—
367C2×C4×D3—24no—
368C2×C4×D3—28no—
369C2×C4×D3—216no—
370C2×C4×D3C2414yes—
371C2×C4×D3C2418yes—
372C2×C4×D3C2414yes—
373C2×C4×D3C2414yes—
374C2×C4×D3C2418yes—
375C2×C4×D3C2418yes—
376C2×C4×D3C24116yes—
377C2×Dic6—28no—
378C2×Dic6—28no—
379C2×Dic6—216no—
380C2×Dic6#4118yes—
381C2×Dic6C2418yes—
382C2×Dic6C2418yes—
383C2×Dic6C24116yes—
384C2×Dic6C2414yes—
385C3×C4⋊C4C2414yes—
386C3×C4⋊C4C2418yes—
387C3×C4⋊C4C24116yes—
388C3×C4⋊C4C2414yes—
389C3×C4⋊C4C2418yes—
390C3×C4⋊C4C24116yes—
391C3×C4⋊C4C2418yes—
392C3×C4⋊C4C24116yes—
393C3×C4⋊C4C2418yes—
394C3×C42C2418yes—
395C3×C42C2414yes—
396C3×C42C2418yes—
397C3×C42C24116yes—
398(C2×D3)⋊C4C2418yes—
399(C2×D3)⋊C4C2418yes—
400(C2×D3)⋊C4C24116yes—
401(C2×D3)⋊C4C2418yes—
402(C2×D3)⋊C4C24116yes—
403(C2×D3)⋊C4C2418yes—
404(C2×D3)⋊C4C2418yes—
405(C2×D3)⋊C4C24116yes—
406(C2×D3)⋊C4C24116yes—
407C4⋊Dic3C2414yes—
408C4⋊Dic3C2418yes—
409C4⋊Dic3C2414yes—
410C4⋊Dic3C2418yes—
411C4⋊Dic3C24116yes—
412C4⋊Dic3C2418yes—
413C4⋊Dic3C2418yes—
414Dic3⋊C4C2418yes—
415Dic3⋊C4C24116yes—
416Dic3⋊C4C2418yes—
417Dic3⋊C4C2418yes—
418Dic3⋊C4C2418yes—
419Dic3⋊C4C24116yes—
420Dic3⋊C4C24116yes—
421Dic3⋊C4C24116yes—
422Dic3⋊C4C2418yes—
423Dic3⋊C4C24116yes—
424Dic3⋊C4C24116yes—
425C4×Dic3C2414yes—
426C4×Dic3C2418yes—
427C4×Dic3C2418yes—
428C4×Dic3C24116yes—
429C4×Dic3C24116yes—
430C4×Dic3C2414yes—
431C4×Dic3C2414yes—
432C4×Dic3C2418yes—
433C4×Dic3C24116yes—
434C22×Q8—38no—
435C22×Q8—316no—
436C22×Q8—31no—
437C22×Q8—32no—
438C22×Q8—32no—
439C22×Q8—34no—
440C22×Q8—68no—
441C22×Q8—616no—
442C22×Q8C22×D311yescharacteristic
443C22×Q8C22×D312yes—
444C22×Q8C22×D311yescharacteristic
445C22×D4—32no—
446C22×D4—31no—
447C23×C4—31no—
448C23×C4—32no—
449C23×C4—32no—
450C23×C4—31no—
451C23×C4—34no—
452C23×C4—32no—
453C23×C4—31no—
454C4⋊Q8—316no—
455C4⋊Q8—316no—
456C4⋊Q8—332no—
457C4⋊Q8—38no—
458C4⋊Q8C22×D318yes—
459C4⋊Q8C22×D3116yes—
460#126—316no—
461#126—332no—
462#126—332no—
463#126—332no—
464#126—332no—
465#125—38no—
466#125—332no—
467#125—316no—
468#125—332no—
469#125—332no—
470#125—332no—
471#125—316no—
472#125C22×D3116yes—
473#125C22×D3132yes—
474#124—38no—
475#124—316no—
476#123—316no—
477#123—332no—
478C22⋊Q8—38no—
479C22⋊Q8—316no—
480C22⋊Q8—316no—
481C22⋊Q8—316no—
482C22⋊Q8—316no—
483C22⋊Q8—332no—
484C22⋊Q8—332no—
485C22⋊Q8—332no—
486#121—38no—
487C4×Q8—38no—
488C4×Q8—316no—
489C4×Q8—38no—
490C4×Q8—316no—
491C4×Q8—332no—
492C4×Q8—316no—
493C4×Q8—316no—
494C4×Q8—38no—
495C4×Q8—316no—
496C4×Q8—332no—
497C4×Q8—316no—
498C4×Q8—316no—
499C4×Q8C22×D318yes—
500C4×Q8C22×D3116yes—
501C4×Q8C22×D318yes—
502C4×Q8C22×D3116yes—
503C4×D4—332no—
504C4×D4—316no—
505C4×D4—316no—
506C4×D4—38no—
507#117—332no—
508#117—316no—
509#117—316no—
510#117—316no—
511#117—332no—
512#117—332no—
513C2×C4⋊C4—32no—
514C2×C4⋊C4—32no—
515C2×C4⋊C4—31no—
516C2×C4⋊C4—32no—
517C2×C4⋊C4—32no—
518C2×C4⋊C4—34no—
519C2×C4⋊C4—32no—
520C2×C4⋊C4—32no—
521C2×C4⋊C4—34no—
522C2×C4⋊C4—32no—
523C2×C4⋊C4—34no—
524C2×C4⋊C4—34no—
525C2×C4⋊C4—32no—
526C2×C4⋊C4—31no—
527C2×C4⋊C4—32no—
528C2×C4⋊C4—34no—
529C2×C4⋊C4—34no—
530C2×C4⋊C4—34no—
531C2×C4⋊C4—316no—
532C2×C4⋊C4—38no—
533C2×C4⋊C4C22×D311yescharacteristic
534C2×C4⋊C4C22×D312yes—
535C2×C4⋊C4C22×D314yes—
536C2×C4⋊C4C22×D312yes—
537C2×C4⋊C4C22×D312yes—
538C2×C4⋊C4C22×D314yes—
539C2×C4⋊C4C22×D311yescharacteristic
540C2×C4⋊C4C22×D314yes—
541C2×C4⋊C4C22×D312yes—
542C2×C22⋊C4—32no—
543C2×C22⋊C4—32no—
544C2×C22⋊C4—34no—
545C2×C22⋊C4—34no—
546C2×C22⋊C4—32no—
547C2×C22⋊C4—34no—
548C2×C22⋊C4—32no—
549C2×C22⋊C4—34no—
550C2×C22⋊C4—32no—
551C2×C42—32no—
552C2×C42—31no—
553C2×C42—34no—
554C2×C42—34no—
555C2×C42—34no—
556C2×C42—32no—
557C2×C42—31no—
558C2×C42—32no—
559C2×C42—31no—
560C2×C42—316no—
561C2×C42—38no—
562C2×C42C22×D314yes—
563C2×C42C22×D312yes—
564C2×C42C22×D311yescharacteristic
565C2×C42C22×D312yes—
566C23×C3C2511yescharacteristic
567C22×D3—22no—
568C22×D3—22no—
569C22×D3—24no—
570C22×D3—24no—
571C22×D3—24no—
572C22×D32−1+414yes—
573C22×D3C2514yes—
574C22×D3C2512yes—
575C3×Q8—28no—
576C3×Q8—216no—
577C3×Q8—28no—
578C2×C3×C4—24no—
579C2×C3×C4—28no—
580C2×C3×C4—24no—
581C2×C3×C4—22no—
582C2×C3×C4—24no—
583C2×C3×C4—24no—
584C2×C3×C4C2×#4114yes—
585C2×C3×C42−1+414yes—
586C2×C3×C4C2514yes—
587C2×C3×C4C2514yes—
588C2×C3×C4C2512yes—
589C2×C3×C4C2514yes—
590C2×C3×C4C2518yes—
591C2×C3×C4C2514yes—
592C2×C3×C4C2512yes—
593C2×C3×C4C2512yes—
594C2×Dic3—22no—
595C2×Dic3—24no—
596C2×Dic3—28no—
597C2×Dic3—22no—
598C2×Dic3—22no—
599C2×Dic3—24no—
600C2×Dic3C2×#4118yes—
601C2×Dic3C2512yes—
602C2×Dic3C2512yes—
603C2×Dic3C2518yes—
604C2×Dic3C2514yes—
605C2×Dic3C2512yes—
606C2×Dic3C2514yes—
607C2×Dic3C2514yes—
608D12—216no—
609D12—28no—
610C4×D3—216no—
611C4×D3—28no—
612C4×D3—28no—
613C4×D3—216no—
614C4×D3—28no—
615C4×D3—216no—
616C4×D3—232no—
617Dic6—216no—
618Dic6—216no—
619Dic6—232no—
620Dic6C2×#41116yes—
621C24—31no—
622C24—32no—
623C2×Q8—24no—
624C2×Q8—24no—
625C2×Q8—28no—
626C2×Q8—38no—
627C2×Q8—34no—
628C2×Q8—38no—
629C2×Q8—38no—
630C2×Q8—316no—
631C2×Q8—68no—
632C2×Q8—616no—
633C2×Q8—632no—
634C2×Q8—664no—
635C2×Q8—68no—
636C2×Q8C23×D314yes—
637C2×Q8C23×D318yes—
638C2×Q8C23×D314yes—
639C2×D4—38no—
640C2×D4—34no—
641C2×D4—68no—
642C2×D4—64no—
643C22×C4—32no—
644C22×C4—31no—
645C22×C4—31no—
646C22×C4—34no—
647C22×C4—32no—
648C22×C4—32no—
649C22×C4—31no—
650C22×C4—34no—
651C22×C4—34no—
652C22×C4—38no—
653C22×C4—38no—
654C22×C4—34no—
655C22×C4—316no—
656C22×C4—38no—
657C22×C4—68no—
658C22×C4—616no—
659C22×C4—68no—
660C22×C4—64no—
661C22×C4—64no—
662C22×C4—64no—
663C22×C4—68no—
664C22×C4C23×D312yes—
665C22×C4C23×D312yes—
666C22×C4C23×D311yescharacteristic
667C22×C4C23×D314yes—
668C22×C4C23×D312yes—
669C22×C4C23×D312yes—
670C22×C4C23×D311yescharacteristic
671C22×C4C23×D311yescharacteristic
672C4⋊C4—38no—
673C4⋊C4—38no—
674C4⋊C4—34no—
675C4⋊C4—38no—
676C4⋊C4—38no—
677C4⋊C4—316no—
678C4⋊C4—38no—
679C4⋊C4—38no—
680C4⋊C4—316no—
681C4⋊C4—38no—
682C4⋊C4—316no—
683C4⋊C4—316no—
684C4⋊C4—38no—
685C4⋊C4—34no—
686C4⋊C4—38no—
687C4⋊C4—316no—
688C4⋊C4—316no—
689C4⋊C4—316no—
690C4⋊C4C23×D314yes—
691C4⋊C4C23×D318yes—
692C4⋊C4C23×D3116yes—
693C4⋊C4C23×D318yes—
694C4⋊C4C23×D318yes—
695C4⋊C4C23×D3116yes—
696C4⋊C4C23×D314yes—
697C4⋊C4C23×D3116yes—
698C4⋊C4C23×D318yes—
699C22⋊C4—38no—
700C22⋊C4—38no—
701C22⋊C4—316no—
702C22⋊C4—316no—
703C22⋊C4—38no—
704C22⋊C4—316no—
705C22⋊C4—38no—
706C22⋊C4—316no—
707C22⋊C4—38no—
708C42—38no—
709C42—34no—
710C42—38no—
711C42—34no—
712C42—38no—
713C42—34no—
714C42—316no—
715C42—316no—
716C42—316no—
717C42C23×D314yes—
718C42C23×D318yes—
719C42C23×D3116yes—
720C42C23×D318yes—
721C22×C3C22×#4112yes—
722C22×C3C2×2−1+412yes—
723C22×C3C2×2−1+412yes—
724C22×C3C2611yescharacteristic
725C2×D3—22no—
726C2×D3—22no—
727C2×D3—28no—
728C2×D3—24no—
729C2×D3—24no—
730C2×D3—24no—
731C2×D3—48no—
732C2×D3C2×2−1+414yes—
733C3×C4—24no—
734C3×C4—28no—
735C3×C4—24no—
736C3×C4—22no—
737C3×C4—24no—
738C3×C4—24no—
739C3×C4C22×#4114yes—
740C3×C4C2×2−1+414yes—
741Dic3—22no—
742Dic3—24no—
743Dic3—28no—
744Dic3—22no—
745Dic3—22no—
746Dic3—24no—
747Dic3C22×#4118yes—
748C23—34no—
749C23—32no—
750C23—34no—
751C23—62no—
752C23—62no—
753C23—64no—
754C23—64no—
755C23—64no—
756C23C24×D311yescharacteristic
757Q8—28no—
758Q8—28no—
759Q8—216no—
760Q8—316no—
761Q8—616no—
762Q8—632no—
763Q8—616no—
764D4—616no—
765D4—68no—
766C2×C4—24no—
767C2×C4—24no—
768C2×C4—28no—
769C2×C4—24no—
770C2×C4—22no—
771C2×C4—24no—
772C2×C4—38no—
773C2×C4—34no—
774C2×C4—32no—
775C2×C4—32no—
776C2×C4—38no—
777C2×C4—34no—
778C2×C4—32no—
779C2×C4—34no—
780C2×C4—616no—
781C2×C4—632no—
782C2×C4—616no—
783C2×C4—68no—
784C2×C4—62no—
785C2×C4—68no—
786C2×C4—64no—
787C2×C4—62no—
788C2×C4—62no—
789C2×C4—64no—
790C2×C4—68no—
791C2×C4—68no—
792C2×C4—616no—
793C2×C4#100714yes—
794C2×C4D3×#4114yes—
795C2×C4C24×D314yes—
796C2×C4C24×D314yes—
797C2×C4C24×D312yes—
798C2×C4C24×D314yes—
799C2×C4C24×D318yes—
800C2×C4C24×D314yes—
801C2×C4C24×D312yes—
802C2×C4C24×D312yes—
803C2×C3#352314yescomplemented
804C2×C3C23×#4111yescharacteristic
805C2×C3C22×2−1+411yescharacteristic
806C2×C3C22×2−1+411yescharacteristic
807D3—24no—
808D3—44no—
809C22—34no—
810C22—62no—
811C22—62no—
812C22—68no—
813C22—64no—
814C22—64no—
815C22—64no—
816C22—128no—
817C22C2×#100712yes—
818C22C2×D3×#4112yes—
819C22D3×2−1+412yes—
820C22C25×D311yescharacteristic
821C4—24no—
822C4—24no—
823C4—28no—
824C4—24no—
825C4—22no—
826C4—24no—
827C4—38no—
828C4—62no—
829C4—68no—
830C4—62no—
831C4—64no—
832C4—62no—
833C4—64no—
834C4C2×#100714yes—
835C4C2×D3×#4114yes—
836C3C2×#352311yescharacteristic, complemented, Sylow
837C2—64no—
838C2—124no—
839C2#8702514yesdirect product factor
840C2C22×#100711yescharacteristic
841C2C22×D3×#4111yescharacteristic
842C2C2×D3×2−1+411yescharacteristic
subgroupG/H
centerC23C24×D3
commutator, cosocleC22×C3C26
FrattiniC22C25×D3
FittingC2×C3×#557C2
socleC23×C3C25
prime radicalC2×#895C22
hypercenterC2×#557D3
hypocenterC3C2×#3523
LCSG ▷ C22×C3 ▷ C3
UCSC1 ◁ C23 ◁ C2×#557

Complements

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

NH ≅ G/Ntype
1. C2×C3×#557C2semidirect
2. #87025C2direct (N × H)
3. C2×#5727C2semidirect
4. C2×#5727C2semidirect
5. C2×#5731C2semidirect
6. C2×#5728C2semidirect
7. C2×#5693C2semidirect
8. C2×#5685C2semidirect
9. C2×#5696C2semidirect
11. C2×#5581C2semidirect
12. C2×#5578C2semidirect
14. C2×#5572C2semidirect
15. C2×C4×D3×Q8C2semidirect
16. C2×#5567C2semidirect
17. C2×#5568C2semidirect
18. C2×#5584C2semidirect
22. C3×#557C22semidirect
39. #5731C22semidirect
40. #5728C22semidirect
41. #5727C22semidirect
42. #5727C22semidirect
43. #5696C22semidirect
44. #5693C22semidirect
46. #5685C22semidirect
47. #5584C22semidirect
48. #5581C22semidirect
50. #5578C22semidirect
51. #5572C22semidirect
52. C4×D3×Q8C22semidirect
53. #5568C22semidirect
54. #5567C22semidirect
105. C2×#557D3semidirect
256. #557C2×D3semidirect
803. C2×C3#3523semidirect
836. C3C2×#3523semidirect
839. C2#87025direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C3×#5572
#870252
C2×#57272
C2×#57312
C2×#57282
C2×#56932
C2×#56852
C2×#56962
C2×#56912
C2×#55812
C2×#55782
C2×#55802
C2×#55722
C2×C4×D3×Q82
C2×#55672
C2×#55682
C2×#55842
C2×#35233