Finite Group Databasebeta

← C2×#86587 #11703667

Subgroups — C2×#86587 #11703667

Order 768.

6958 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×#544C211yesmaximal, characteristic, complemented
2#86587C2132yesmaximal, direct product factor
3C2×#5730C212yesmaximal, complemented
4C2×#5729C212yesmaximal, complemented
5C2×#5721C212yesmaximal, complemented
6C2×#5728C212yesmaximal, complemented
7C2×#5689C212yesmaximal, complemented
8C2×D3×#125C212yesmaximal, complemented
9C2×#5685C212yesmaximal, complemented
10C2×#5690C212yesmaximal, complemented
11C2×#5636C214yesmaximal, complemented
12C2×#5635C214yesmaximal, complemented
13C2×#5523C211yesmaximal, characteristic
14C2×#5519C211yesmaximal, characteristic, complemented
15C2×#5517C211yesmaximal, characteristic, complemented
16C2×#5522C211yesmaximal, characteristic
17C2×#5504C211yesmaximal, characteristic
18C22×#890C211yesmaximal, characteristic, complemented
19C2×#3504—31nomaximal, Sylow
20C22×#235C2211yescharacteristic
21C3×#544C22116yescomplemented
22C2×C3×C4⋊Q8C2212yes—
23C2×C3×C4⋊Q8C2212yes—
24C2×C3×#125C2212yes—
25C2×C3×#125C2212yes—
26C2×C3×C22⋊Q8C2214yes—
27C2×C3×#117C2211yescharacteristic
28C2×C3×#117C2211yescharacteristic
29C22×C3×C4⋊C4C2211yescharacteristic
30C2×#946C2214yes—
31C2×#946C2214yes—
32C2×Q8×Dic3C2214yes—
33C2×#944C2214yes—
34C2×C4×#67C2214yes—
35C2×#926C2211yescharacteristic
36C22×C4⋊Dic3C2212yes—
37C22×C4⋊Dic3C2211yescharacteristic
38C22×Dic3⋊C4C2212yes—
39C22×C4×Dic3C2211yescharacteristic
40#5730C22132yescomplemented
41#5729C22132yescomplemented
42#5728C22132yescomplemented
43#5721C22132yescomplemented
44#5690C22132yescomplemented
45#5689C22132yescomplemented
46D3×#125C22132yescomplemented
47#5685C22132yescomplemented
48#5636C22164yescomplemented
49#5635C22164yescomplemented
50#5523C22116yes—
51#5522C22116yes—
52#5519C22116yescomplemented
53#5517C22116yescomplemented
54C2×#897C2214yes—
55C2×#897C2214yes—
56C2×#896C2214yes—
57C2×#896C2214yes—
58#5504C22116yes—
59C2×#893C2211yescharacteristic
60C2×#893C2212yes—
61C2×#893C2211yescharacteristic
62C2×#892C2212yes—
63C2×#892C2212yes—
64C2×D3×C4⋊C4C2214yes—
65C2×D3×C4⋊C4C2212yes—
66C2×D3×C4⋊C4C2212yes—
67C2×D3×C4⋊C4C2214yes—
68C2×#890C2212yes—
69C2×#890C2212yes—
70C2×#890C2211yescharacteristic
71C2×#890C2212yes—
72C2×#890C2212yes—
73C2×#890C2211yescharacteristic
74C2×#890C2212yes—
75C2×#890C22116yescomplemented
76C2×#889C2214yes—
77C2×#889C2214yes—
78C2×#889C2214yes—
79C2×#889C2214yes—
80C2×#888C2212yes—
81C2×#888C2214yes—
82C2×#888C2211yescharacteristic
83C2×#888C2211yescharacteristic
84C2×#887C2211yescharacteristic
85C2×#887C2214yes—
86C2×#887C2212yes—
87C2×#887C2211yescharacteristic
88C2×#67⋊C4C2212yes—
89C2×#67⋊C4C2214yes—
90C2×#67⋊C4C2212yes—
91C2×#878C2212yes—
92C2×#878C2214yes—
93C2×#878C2212yes—
94C2×C4×D12C2212yes—
95C2×#872C2212yes—
96C2×C42×D3C2212yes—
97C2×#870C2212yes—
98C2×#869C2212yes—
99C2×C4×Dic6C2212yes—
100C2×C4×Dic6C2212yes—
101C2×C4×Dic6C2212yes—
102#3504—332no—
103C2×#557—32no—
104C2×#557—32no—
105C2×#554—32no—
106C2×#554—32no—
107C2×#554—34no—
108C2×#554—34no—
109C2×#544—32no—
110C2×#544—32no—
111C2×#544—31no—
112C2×#544D311yescharacteristic, complemented
113C2×#533—32no—
114C2×#533—31no—
115C22×#125—32no—
116C22×#125—31no—
117C2×#520—31no—
118C2×#520—31no—
119C2×C4×#41—31no—
120C22×C3×Q8C2314yes—
121C23×C3×C4C2312yes—
122C23×C3×C4C2311yescharacteristic
123C22×#67C2312yes—
124C23×Dic3C2311yescharacteristic
125C23×Dic3C2311yescharacteristic
126C23×Dic3C2312yes—
127C2×#235Q8116yescomplemented
128C2×#235C2318yes—
129C22×D12C2311yescharacteristic
130C22×C4×D3C2312yes—
131C22×C4×D3C2312yes—
132C22×C4×D3C2314yes—
133C22×C4×D3C2314yes—
134C22×C4×D3C2312yes—
135C22×Dic6C2312yes—
136C22×Dic6C2312yes—
137C22×Dic6C2314yes—
138C22×Dic6C2311yescharacteristic
139C3×C4⋊Q8C23116yes—
140C3×C4⋊Q8C23116yes—
141C3×#125C23116yes—
142C3×#125C23116yes—
143C3×C22⋊Q8C23132yes—
144C3×#117C2318yes—
145C3×#117C2318yes—
146C2×C3×C4⋊C4C2311yescharacteristic
147C2×C3×C4⋊C4C2314yes—
148C2×C3×C4⋊C4C2312yes—
149C2×C3×C4⋊C4C2311yescharacteristic
150C2×C3×C4⋊C4C2314yes—
151C2×C3×C4⋊C4C2311yescharacteristic
152C2×C3×C4⋊C4C2311yescharacteristic
153C2×C3×C4⋊C4C2314yes—
154C2×C3×C4⋊C4C2312yes—
155C2×C3×C4⋊C4C2318yes—
156C2×C3×C22⋊C4C2312yes—
157C2×C3×C22⋊C4C2312yes—
158C2×C3×C42C2312yes—
159C2×C3×C42C2312yes—
160C2×#217C2312yes—
161#946C23132yes—
162#946C23132yes—
163Q8×Dic3C23132yes—
164#944C23132yes—
165C4×#67C23132yes—
166C2×(C2×D3)⋊C4C2312yes—
167C2×(C2×D3)⋊C4C2312yes—
168C2×(C2×D3)⋊C4C2314yes—
169C2×(C2×D3)⋊C4C2314yes—
170#926C2318yes—
171C2×C4⋊Dic3C23116yes—
172C2×C4⋊Dic3C2312yes—
173C2×C4⋊Dic3C2312yes—
174C2×C4⋊Dic3C2312yes—
175C2×C4⋊Dic3C2311yescharacteristic
176C2×C4⋊Dic3C2312yes—
177C2×C4⋊Dic3C2314yes—
178C2×C4⋊Dic3C2311yescharacteristic
179C2×C4⋊Dic3C2314yes—
180C2×C4⋊Dic3C2314yes—
181C2×C4⋊Dic3C2318yes—
182C2×Dic3⋊C4C23116yes—
183C2×Dic3⋊C4C2312yes—
184C2×Dic3⋊C4C2312yes—
185C2×Dic3⋊C4C2312yes—
186C2×Dic3⋊C4C2312yes—
187C2×Dic3⋊C4C2314yes—
188C2×Dic3⋊C4C2314yes—
189C2×Dic3⋊C4C2314yes—
190C2×Dic3⋊C4C2312yes—
191C2×Dic3⋊C4C2312yes—
192C2×Dic3⋊C4C2314yes—
193C2×Dic3⋊C4C2314yes—
194C2×Dic3⋊C4C2314yes—
195C2×C4×Dic3C2312yes—
196C2×C4×Dic3C2311yescharacteristic
197C2×C4×Dic3C2311yescharacteristic
198C2×C4×Dic3C2314yes—
199C2×C4×Dic3C2311yescharacteristic
200C2×C4×Dic3C2312yes—
201C2×C4×Dic3C2312yes—
202C2×C4×Dic3C2311yescharacteristic
203C2×C4×Dic3C2314yes—
204C2×C4×Dic3C2318yes—
205#897C23132yes—
206#897C23132yes—
207#896C23132yes—
208#896C23132yes—
209#893C2318yes—
210#893C23116yes—
211#893C2318yes—
212#892C23116yes—
213#892C23116yes—
214D3×C4⋊C4C23132yes—
215D3×C4⋊C4C23132yes—
216D3×C4⋊C4C23116yes—
217D3×C4⋊C4C23116yes—
218#890C23116yes—
219#890C2318yes—
220#890C23116yes—
221#890C23116yes—
222#890C23116yes—
223#890C23116yes—
224#890C2318yes—
225#889C23132yes—
226#889C23132yes—
227#889C23132yes—
228#889C23132yes—
229#888C23132yes—
230#888C23116yes—
231#888C2318yes—
232#888C2318yes—
233#887C23132yes—
234#887C2318yes—
235#887C23116yes—
236#887C2318yes—
237#67⋊C4C23116yes—
238#67⋊C4C23132yes—
239#67⋊C4C23116yes—
240#878C23116yes—
241#878C23132yes—
242#878C23116yes—
243C4×D12C23116yes—
244#872C23116yes—
245C42×D3C23116yes—
246#870C23116yes—
247#869C23116yes—
248C4×Dic6C23116yes—
249C4×Dic6C23116yes—
250C4×Dic6C23116yes—
251C22×#41—31no—
252#557—332no—
253#557—332no—
254#554—332no—
255#554—332no—
256#554—364no—
257#554—364no—
258#544—332no—
259#544—332no—
260#544—316no—
261#544C2×D3116yescomplemented
262#533—332no—
263#533—316no—
264C2×C4⋊Q8—34no—
265C2×C4⋊Q8—31no—
266C2×C4⋊Q8—31no—
267C2×C4⋊Q8—34no—
268C2×C4⋊Q8—32no—
269C2×C4⋊Q8—32no—
270C2×C4⋊Q8C2×D312yes—
271C2×C4⋊Q8C2×D312yes—
272C2×#125—332no—
273C2×#125—31no—
274C2×#125—32no—
275C2×#125—34no—
276C2×#125—34no—
277C2×#125—32no—
278C2×#125—32no—
279C2×#125—32no—
280C2×#125—316no—
281C2×#125—31no—
282C2×#125—34no—
283C2×#125—34no—
284C2×#125—32no—
285C2×#125—32no—
286C2×#125C2×D312yes—
287C2×#125C2×D312yes—
288C2×C22⋊Q8—34no—
289C2×C22⋊Q8—34no—
290C2×C22⋊Q8—34no—
291C2×C22⋊Q8—34no—
292C2×C22⋊Q8—34no—
293C2×C22⋊Q8—34no—
294C2×C22⋊Q8—32no—
295C2×C22⋊Q8—32no—
296C2×C22⋊Q8—34no—
297C2×C22⋊Q8C2×D314yes—
298#520—316no—
299#520—316no—
300C4×#41—316no—
301C2×C4×Q8—34no—
302C2×C4×Q8—31no—
303C2×C4×Q8—31no—
304C2×C4×Q8—32no—
305C2×C4×Q8—34no—
306C2×C4×Q8—32no—
307C2×C4×Q8—32no—
308C2×C4×Q8—32no—
309C2×C4×D4—34no—
310C2×C4×D4—31no—
311C2×C4×D4—31no—
312C2×C4×D4—32no—
313C2×C4×D4—32no—
314C2×C4×D4—32no—
315C2×C4×D4—34no—
316C2×C4×D4—32no—
317C2×#117—31no—
318C2×#117—32no—
319C2×#117—32no—
320C2×#117—32no—
321C2×#117C2×D311yescharacteristic
322C2×#117C2×D311yescharacteristic
323C22×C4⋊C4—31no—
324C22×C4⋊C4—32no—
325C22×C4⋊C4—32no—
326C22×C4⋊C4—32no—
327C22×C4⋊C4—32no—
328C22×C4⋊C4—34no—
329C22×C4⋊C4—34no—
330C22×C4⋊C4C2×D311yescharacteristic
331C22×C42—31no—
332C22×C42—32no—
333C24×C3C2411yescharacteristic
334C23×D3C2412yes—
335C2×C3×Q8—48no—
336C2×C3×Q8C24116yes—
337C22×C3×C4—44no—
338C22×C3×C4C2×Q818yes—
339C22×C3×C4C2412yes—
340C22×C3×C4C2412yes—
341C22×C3×C4C2414yes—
342C22×C3×C4C2412yes—
343C22×C3×C4C2412yes—
344C22×C3×C4C2418yes—
345C22×C3×C4C2411yescharacteristic
346C22×C3×C4C2411yescharacteristic
347C22×C3×C4C2414yes—
348C2×#67C2×Q8116yes—
349C2×#67C2418yes—
350C22×Dic3—42no—
351C22×Dic3—42no—
352C22×Dic3—44no—
353C22×Dic3C2411yescharacteristic
354C22×Dic3C2411yescharacteristic
355C22×Dic3C2412yes—
356C22×Dic3C2411yescharacteristic
357C22×Dic3C2411yescharacteristic
358C22×Dic3C2412yes—
359C22×Dic3C2414yes—
360C22×Dic3C2414yes—
361C22×Dic3C2414yes—
362C22×Dic3C2418yes—
363C22×Dic3C2412yes—
364#235C2×Q8164yescomplemented
365C2×D12C2×Q818yes—
366C2×D12C2414yes—
367C2×C4×D3—48no—
368C2×C4×D3—48no—
369C2×C4×D3—44no—
370C2×C4×D3—44no—
371C2×C4×D3C2×Q8116yes—
372C2×C4×D3C2418yes—
373C2×C4×D3C2418yes—
374C2×C4×D3C24116yes—
375C2×C4×D3C24116yes—
376C2×C4×D3C2418yes—
377C2×Dic6—44no—
378C2×Dic6—48no—
379C2×Dic6—44no—
380C2×Dic6C2×Q818yes—
381C2×Dic6C2418yes—
382C2×Dic6C2418yes—
383C2×Dic6C24116yes—
384C2×Dic6C2414yes—
385C3×C4⋊C4C2414yes—
386C3×C4⋊C4C24116yes—
387C3×C4⋊C4C2418yes—
388C3×C4⋊C4C2414yes—
389C3×C4⋊C4C24116yes—
390C3×C4⋊C4C2414yes—
391C3×C4⋊C4C2414yes—
392C3×C4⋊C4C24116yes—
393C3×C4⋊C4C2418yes—
394C3×C22⋊C4C2418yes—
395C3×C22⋊C4C2418yes—
396C3×C42C2418yes—
397C3×C42C2418yes—
398#217C2418yes—
399(C2×D3)⋊C4C2418yes—
400(C2×D3)⋊C4C2418yes—
401(C2×D3)⋊C4C24116yes—
402(C2×D3)⋊C4C24116yes—
403C4⋊Dic3C2418yes—
404C4⋊Dic3C2418yes—
405C4⋊Dic3C2418yes—
406C4⋊Dic3C2414yes—
407C4⋊Dic3C2418yes—
408C4⋊Dic3C24116yes—
409C4⋊Dic3C2414yes—
410C4⋊Dic3C24116yes—
411C4⋊Dic3C24116yes—
412Dic3⋊C4C2418yes—
413Dic3⋊C4C2418yes—
414Dic3⋊C4C2418yes—
415Dic3⋊C4C2418yes—
416Dic3⋊C4C24116yes—
417Dic3⋊C4C24116yes—
418Dic3⋊C4C24116yes—
419Dic3⋊C4C2418yes—
420Dic3⋊C4C2418yes—
421Dic3⋊C4C24116yes—
422Dic3⋊C4C24116yes—
423Dic3⋊C4C24116yes—
424C4×Dic3C2418yes—
425C4×Dic3C2414yes—
426C4×Dic3C2414yes—
427C4×Dic3C24116yes—
428C4×Dic3C2414yes—
429C4×Dic3C2418yes—
430C4×Dic3C2418yes—
431C4×Dic3C2414yes—
432C4×Dic3C24116yes—
433C2×#41—316no—
434C2×#41—38no—
435C22×Q8—31no—
436C22×Q8—32no—
437C22×Q8—34no—
438C22×Q8—32no—
439C22×Q8C22×D314yes—
440C22×D4—32no—
441C22×D4—31no—
442C23×C4—32no—
443C23×C4—32no—
444C23×C4—31no—
445C23×C4—31no—
446C23×C4—34no—
447C23×C4—34no—
448C23×C4—32no—
449C23×C4—32no—
450C23×C4C22×D312yes—
451C23×C4C22×D311yescharacteristic
452C4⋊Q8—332no—
453C4⋊Q8—38no—
454C4⋊Q8—38no—
455C4⋊Q8—332no—
456C4⋊Q8—316no—
457C4⋊Q8—316no—
458C4⋊Q8C22×D3116yes—
459C4⋊Q8C22×D3116yes—
460#125—38no—
461#125—316no—
462#125—316no—
463#125—332no—
464#125—332no—
465#125—316no—
466#125—316no—
467#125—38no—
468#125—332no—
469#125—332no—
470#125—316no—
471#125—316no—
472#125C22×D3116yes—
473#125C22×D3116yes—
474C22⋊Q8—332no—
475C22⋊Q8—332no—
476C22⋊Q8—332no—
477C22⋊Q8—332no—
478C22⋊Q8—332no—
479C22⋊Q8—332no—
480C22⋊Q8—316no—
481C22⋊Q8—316no—
482C22⋊Q8—332no—
483C22⋊Q8C22×D3132yes—
484C4×Q8—332no—
485C4×Q8—38no—
486C4×Q8—38no—
487C4×Q8—316no—
488C4×Q8—332no—
489C4×Q8—316no—
490C4×Q8—316no—
491C4×Q8—316no—
492C4×D4—332no—
493C4×D4—38no—
494C4×D4—38no—
495C4×D4—316no—
496C4×D4—316no—
497C4×D4—316no—
498C4×D4—332no—
499C4×D4—316no—
500#117—38no—
501#117—316no—
502#117—316no—
503#117—316no—
504#117C22×D318yes—
505#117C22×D318yes—
506C2×C4⋊C4—32no—
507C2×C4⋊C4—31no—
508C2×C4⋊C4—34no—
509C2×C4⋊C4—32no—
510C2×C4⋊C4—34no—
511C2×C4⋊C4—32no—
512C2×C4⋊C4—34no—
513C2×C4⋊C4—34no—
514C2×C4⋊C4—32no—
515C2×C4⋊C4—38no—
516C2×C4⋊C4—34no—
517C2×C4⋊C4—34no—
518C2×C4⋊C4—34no—
519C2×C4⋊C4—34no—
520C2×C4⋊C4—316no—
521C2×C4⋊C4—316no—
522C2×C4⋊C4—31no—
523C2×C4⋊C4—32no—
524C2×C4⋊C4—32no—
525C2×C4⋊C4—32no—
526C2×C4⋊C4—32no—
527C2×C4⋊C4—32no—
528C2×C4⋊C4—32no—
529C2×C4⋊C4—34no—
530C2×C4⋊C4—316no—
531C2×C4⋊C4—316no—
532C2×C4⋊C4—332no—
533C2×C4⋊C4—332no—
534C2×C4⋊C4C22×D311yescharacteristic
535C2×C4⋊C4C22×D312yes—
536C2×C4⋊C4C22×D314yes—
537C2×C4⋊C4C22×D314yes—
538C2×C4⋊C4C22×D312yes—
539C2×C4⋊C4C22×D318yes—
540C2×C4⋊C4C22×D311yescharacteristic
541C2×C4⋊C4C22×D311yescharacteristic
542C2×C4⋊C4C22×D311yescharacteristic
543C2×C4⋊C4C22×D314yes—
544C2×C22⋊C4—32no—
545C2×C22⋊C4—34no—
546C2×C22⋊C4—32no—
547C2×C22⋊C4—32no—
548C2×C22⋊C4—34no—
549C2×C22⋊C4C22×D312yes—
550C2×C22⋊C4C22×D312yes—
551C2×C42—31no—
552C2×C42—34no—
553C2×C42—34no—
554C2×C42—32no—
555C2×C42—32no—
556C2×C42—32no—
557C2×C42—31no—
558C2×C42—31no—
559C2×C42—38no—
560C2×C42—31no—
561C2×C42—316no—
562C2×C42C22×D312yes—
563C2×C42C22×D312yes—
564C23×C3—22no—
565C23×C3—22no—
566C23×C3C22×Q814yes—
567C23×C3C2512yes—
568C23×C3C2511yescharacteristic
569C22×D3—24no—
570C22×D3—24no—
571C22×D3C22×Q818yes—
572C22×D3C2514yes—
573C3×Q8—416no—
574C2×C3×C4—24no—
575C2×C3×C4—24no—
576C2×C3×C4—24no—
577C2×C3×C4—28no—
578C2×C3×C4—24no—
579C2×C3×C4—48no—
580C2×C3×C4C22×Q814yes—
581C2×C3×C4C22×Q814yes—
582C2×C3×C4C22×Q8116yes—
583C2×C3×C4C2514yes—
584C2×C3×C4C2514yes—
585C2×C3×C4C2518yes—
586C2×C3×C4C2514yes—
587C2×C3×C4C2514yes—
588C2×C3×C4C2512yes—
589C2×C3×C4C2512yes—
590#67C22×Q8132yes—
591C2×Dic3—24no—
592C2×Dic3—22no—
593C2×Dic3—22no—
594C2×Dic3—24no—
595C2×Dic3—28no—
596C2×Dic3—22no—
597C2×Dic3—22no—
598C2×Dic3—44no—
599C2×Dic3—44no—
600C2×Dic3—48no—
601C2×Dic3C22×Q818yes—
602C2×Dic3C2512yes—
603C2×Dic3C2512yes—
604C2×Dic3C2514yes—
605C2×Dic3C2512yes—
606C2×Dic3C2512yes—
607C2×Dic3C2514yes—
608C2×Dic3C2518yes—
609C2×Dic3C2514yes—
610D12C22×Q8116yes—
611C4×D3—416no—
612C4×D3—416no—
613C4×D3—48no—
614C4×D3—48no—
615C4×D3C22×Q8132yes—
616Dic6—48no—
617Dic6—416no—
618Dic6—48no—
619Dic6C22×Q8116yes—
620C24—32no—
621C24C23×D311yescharacteristic
622#41—364no—
623C2×Q8—38no—
624C2×Q8—34no—
625C2×Q8—38no—
626C2×Q8—316no—
627C2×Q8—38no—
628C2×Q8—48no—
629C2×Q8—124no—
630C2×Q8—124no—
631C2×Q8—128no—
632C2×Q8C23×D3116yes—
633C2×D4—316no—
634C2×D4—38no—
635C2×D4—38no—
636C2×D4—34no—
637C22×C4—32no—
638C22×C4—316no—
639C22×C4—38no—
640C22×C4—31no—
641C22×C4—31no—
642C22×C4—32no—
643C22×C4—31no—
644C22×C4—31no—
645C22×C4—32no—
646C22×C4—34no—
647C22×C4—34no—
648C22×C4—34no—
649C22×C4—38no—
650C22×C4—38no—
651C22×C4—38no—
652C22×C4—316no—
653C22×C4—316no—
654C22×C4—44no—
655C22×C4—128no—
656C22×C4—124no—
657C22×C4—128no—
658C22×C4—124no—
659C22×C4—122no—
660C22×C4—122no—
661C22×C4—124no—
662C22×C4D3×Q818yes—
663C22×C4C23×D312yes—
664C22×C4C23×D312yes—
665C22×C4C23×D312yes—
666C22×C4C23×D314yes—
667C22×C4C23×D312yes—
668C22×C4C23×D318yes—
669C22×C4C23×D314yes—
670C22×C4C23×D311yescharacteristic
671C22×C4C23×D311yescharacteristic
672C4⋊C4—38no—
673C4⋊C4—34no—
674C4⋊C4—316no—
675C4⋊C4—38no—
676C4⋊C4—316no—
677C4⋊C4—38no—
678C4⋊C4—316no—
679C4⋊C4—316no—
680C4⋊C4—38no—
681C4⋊C4—316no—
682C4⋊C4—316no—
683C4⋊C4—316no—
684C4⋊C4—316no—
685C4⋊C4—34no—
686C4⋊C4—38no—
687C4⋊C4—38no—
688C4⋊C4—38no—
689C4⋊C4—38no—
690C4⋊C4—38no—
691C4⋊C4—38no—
692C4⋊C4—316no—
693C4⋊C4C23×D314yes—
694C4⋊C4C23×D318yes—
695C4⋊C4C23×D3116yes—
696C4⋊C4C23×D3116yes—
697C4⋊C4C23×D318yes—
698C4⋊C4C23×D314yes—
699C4⋊C4C23×D314yes—
700C4⋊C4C23×D314yes—
701C4⋊C4C23×D3116yes—
702C22⋊C4—38no—
703C22⋊C4—316no—
704C22⋊C4—38no—
705C22⋊C4—38no—
706C22⋊C4—316no—
707C22⋊C4C23×D318yes—
708C22⋊C4C23×D318yes—
709C42—34no—
710C42—34no—
711C42—38no—
712C42—38no—
713C42—34no—
714C42—34no—
715C42—316no—
716C42—316no—
717C42—38no—
718C42C23×D318yes—
719C42C23×D318yes—
720C22×C3—22no—
721C22×C3—22no—
722C22×C3—28no—
723C22×C3C23×Q814yes—
724C22×C3C23×Q812yes—
725C22×C3#58512yes—
726C22×C3#58512yes—
727C22×C3C2611yescharacteristic
728C2×D3—24no—
729C2×D3—24no—
730C2×D3—216no—
731C2×D3C23×Q818yes—
732C3×C4—24no—
733C3×C4—24no—
734C3×C4—24no—
735C3×C4—28no—
736C3×C4—24no—
737C3×C4C23×Q814yes—
738C3×C4C23×Q814yes—
739Dic3—24no—
740Dic3—22no—
741Dic3—22no—
742Dic3—24no—
743Dic3—28no—
744Dic3—22no—
745Dic3—22no—
746Dic3C23×Q818yes—
747C23—22no—
748C23—22no—
749C23—38no—
750C23—34no—
751C23—64no—
752C23—64no—
753C23C2×D3×Q814yes—
754C23C24×D312yes—
755C23C24×D311yescharacteristic
756Q8—316no—
757Q8—416no—
758Q8—128no—
759Q8—128no—
760Q8—1216no—
761D4—332no—
762D4—316no—
763C2×C4—28no—
764C2×C4—24no—
765C2×C4—24no—
766C2×C4—24no—
767C2×C4—24no—
768C2×C4—38no—
769C2×C4—34no—
770C2×C4—332no—
771C2×C4—32no—
772C2×C4—32no—
773C2×C4—34no—
774C2×C4—32no—
775C2×C4—32no—
776C2×C4—34no—
777C2×C4—38no—
778C2×C4—48no—
779C2×C4—62no—
780C2×C4—64no—
781C2×C4—62no—
782C2×C4—62no—
783C2×C4—68no—
784C2×C4—62no—
785C2×C4—64no—
786C2×C4—1216no—
787C2×C4—128no—
788C2×C4—1216no—
789C2×C4—128no—
790C2×C4—124no—
791C2×C4—124no—
792C2×C4—128no—
793C2×C4C2×D3×Q814yes—
794C2×C4C2×D3×Q814yes—
795C2×C4C2×D3×Q8116yes—
796C2×C4C24×D314yes—
797C2×C4C24×D314yes—
798C2×C4C24×D314yes—
799C2×C4C24×D318yes—
800C2×C4C24×D314yes—
801C2×C4C24×D312yes—
802C2×C4C24×D312yes—
803C2×C3—24no—
804C2×C3#350414yescomplemented
805C2×C3C24×Q811yescharacteristic
806C2×C3C2×#58511yescharacteristic
807C2×C3C2×#58511yescharacteristic
808D3—28no—
809C22—22no—
810C22—22no—
811C22—28no—
812C22—38no—
813C22—64no—
814C22—64no—
815C22—616no—
816C22C22×D3×Q814yes—
817C22C22×D3×Q812yes—
818C22#596612yes—
819C22#596812yes—
820C22C25×D311yescharacteristic
821C4—28no—
822C4—24no—
823C4—24no—
824C4—24no—
825C4—24no—
826C4—38no—
827C4—62no—
828C4—64no—
829C4—62no—
830C4—62no—
831C4—68no—
832C4—62no—
833C4—64no—
834C4C22×D3×Q814yes—
835C4C22×D3×Q814yes—
836C3C2×#350411yescharacteristic, complemented, Sylow
837C2—24no—
838C2—68no—
839C2#8658714yesdirect product factor
840C2C23×D3×Q811yescharacteristic
841C2C2×#596611yescharacteristic
842C2C2×#596811yescharacteristic
subgroupG/H
centerC23C24×D3
commutator, cosocleC22×C3C26
FrattiniC22C25×D3
FittingC2×C3×#544C2
socleC23×C3C25
prime radicalC22×#235C22
hypercenterC2×#544D3
hypocenterC3C2×#3504
LCSG ▷ C22×C3 ▷ C3
UCSC1 ◁ C23 ◁ C2×#544

Complements

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

NH ≅ G/Ntype
1. C2×C3×#544C2semidirect
2. #86587C2direct (N × H)
3. C2×#5730C2semidirect
4. C2×#5729C2semidirect
5. C2×#5721C2semidirect
6. C2×#5728C2semidirect
7. C2×#5689C2semidirect
8. C2×D3×#125C2semidirect
9. C2×#5685C2semidirect
10. C2×#5690C2semidirect
11. C2×#5636C2semidirect
12. C2×#5635C2semidirect
14. C2×#5519C2semidirect
15. C2×#5517C2semidirect
18. C22×#890C2semidirect
21. C3×#544C22semidirect
40. #5730C22semidirect
41. #5729C22semidirect
42. #5728C22semidirect
43. #5721C22semidirect
44. #5690C22semidirect
45. #5689C22semidirect
46. D3×#125C22semidirect
47. #5685C22semidirect
48. #5636C22semidirect
49. #5635C22semidirect
52. #5519C22semidirect
53. #5517C22semidirect
75. C2×#890C22semidirect
112. C2×#544D3semidirect
127. C2×#235Q8semidirect
261. #544C2×D3semidirect
364. #235C2×Q8semidirect
804. C2×C3#3504semidirect
836. C3C2×#3504semidirect
839. C2#86587direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C3×#5442
#865872
C2×#57302
C2×#57292
C2×#57212
C2×#57282
C2×#56892
C2×D3×#1252
C2×#56852
C2×#56902
C2×#56362
C2×#56352
C2×#55232
C2×#55192
C2×#55172
C2×#55222
C2×#55042
C22×#8902
C2×#35043