Finite Group Databasebeta

← C2×#86926 #11703516

Subgroups — C2×#86926 #11703516

Order 768.

7478 conjugacy classes of subgroups.

The subgroup lattice has 864 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#554C211yesmaximal, characteristic, complemented
2#86926C2132yesmaximal, direct product factor
3C2×D3×C4⋊Q8C211yesmaximal, characteristic, complemented
4C2×#5722C211yesmaximal, characteristic, complemented
5C2×#5689C212yesmaximal, complemented
6C2×#5685C212yesmaximal, complemented
7C2×#5635C212yesmaximal, complemented
8C2×#5632C214yesmaximal, complemented
9C2×#5623C214yesmaximal, complemented
10C2×#5622C212yesmaximal, complemented
11C2×#5578C211yesmaximal, characteristic, complemented
12C2×Q8×Dic6C211yesmaximal, characteristic, complemented
13C2×#5543C211yesmaximal, characteristic, complemented
14C2×D4×Dic6C212yesmaximal, complemented
15C2×#5546C212yesmaximal
16C2×C4×#237C211yesmaximal, characteristic
17C2×#5511C212yesmaximal, complemented
18C22×#888C212yesmaximal, complemented
19C2×#3503—31nomaximal, Sylow
20C22×D3×Q8C2212yes—
21C22×#237C2211yescharacteristic
22C23×Dic6C2214yes—
23C3×#554C22116yescomplemented
24C2×C3×C4⋊Q8C2211yescharacteristic
25C2×C3×#125C2212yes—
26C2×C3×C22⋊Q8C2212yes—
27C2×C3×C22⋊Q8C2214yes—
28C2×C3×C4×Q8C2211yescharacteristic
29C2×C3×C4×D4C2211yescharacteristic
30C2×C3×C4×D4C2212yes—
31C22×C3×C4⋊C4C2212yes—
32C2×#946C2211yescharacteristic
33C2×Q8×Dic3C2212yes—
34C2×#944C2211yescharacteristic
35C2×#944C2214yes—
36C2×#944C2212yes—
37C2×D4×Dic3C2212yes—
38C2×D4×Dic3C2211yescharacteristic
39C2×C4×#67C2214yes—
40C2×C4×#67C2212yes—
41C22×C4⋊Dic3C2212yes—
42C2×#924C2212yes—
43C2×#924C2214yes—
44C22×Dic3⋊C4C2214yes—
45C22×C4×Dic3C2212yes—
46D3×C4⋊Q8C22116yescomplemented
47#5722C22116yescomplemented
48#5689C22132yescomplemented
49#5685C22132yescomplemented
50#5635C22132yescomplemented
51#5632C22164yescomplemented
52#5623C22164yescomplemented
53#5622C22132yescomplemented
54#5578C22116yescomplemented
55Q8×Dic6C22116yescomplemented
56#5546C22132yes—
57#5543C22116yescomplemented
58D4×Dic6C22132yescomplemented
59C4×#237C22116yes—
60#5511C22132yescomplemented
61C2×#897C2211yescharacteristic
62C2×#897C2214yes—
63C2×#896C2212yes—
64C2×#896C2214yes—
65C2×#892C2211yescharacteristic
66C2×D3×C4⋊C4C2212yes—
67C2×D3×C4⋊C4C2212yes—
68C2×#890C2212yes—
69C2×#889C2212yes—
70C2×#889C2214yes—
71C2×#889C2214yes—
72C2×#889C2214yes—
73C2×#888C2212yes—
74C2×#888C2214yes—
75C2×#888C2211yescharacteristic
76C2×#888C2212yes—
77C2×#888C2214yes—
78C2×#888C2212yes—
79C2×#888C2214yes—
80C2×#888C2212yes—
81C2×#888C2212yes—
82C2×#888C22132yescomplemented
83C2×#887C2211yescharacteristic
84C2×#887C2212yes—
85C2×#887C2214yes—
86C2×#887C2212yes—
87C2×#67⋊C4C2212yes—
88C2×#67⋊C4C2214yes—
89C2×#878C2214yes—
90C2×#878C2214yes—
91C2×#878C2214yes—
92C2×#877C2214yes—
93C2×#877C2212yes—
94C2×#872C2212yes—
95C2×C42×D3C2211yescharacteristic
96C2×#869C2211yescharacteristic
97C2×#869C2212yes—
98C2×C4×Dic6C2211yescharacteristic
99C2×C4×Dic6C2212yes—
100C2×C4×Dic6C2211yescharacteristic
101C2×C4×Dic6C2212yes—
102#3503—332no—
103C2×Q82—31no—
104C2×Q82—31no—
105C2×#557—32no—
106C2×#554—32no—
107C2×#554—31no—
108C2×#554—32no—
109C2×#554D311yescharacteristic, complemented
110C2×D4×Q8—34no—
111C2×D4×Q8—32no—
112C2×#544—32no—
113C2×#544—34no—
114C2×#533—32no—
115C2×#533—31no—
116C22×C4⋊Q8—31no—
117C22×C4⋊Q8—32no—
118C2×#520—32no—
119C2×C4×#41—31no—
120C22×C3×Q8C2311yescharacteristic
121C22×C3×Q8C2312yes—
122C22×C3×D4C2311yescharacteristic
123C23×C3×C4C2312yes—
124C23×C3×C4C2314yes—
125C22×#67C2312yes—
126C23×Dic3C2312yes—
127C23×Dic3C2314yes—
128C23×Dic3C2312yes—
129C2×D3×Q8—48no—
130C2×D3×Q8C23116yes—
131C2×#237Q8116yescomplemented
132C2×#237C2318yes—
133C22×C4×D3C2311yescharacteristic
134C22×C4×D3C2311yescharacteristic
135C22×C4×D3C2314yes—
136C22×C4×D3C2311yescharacteristic
137C22×Dic6—416no—
138C22×Dic6C2312yes—
139C22×Dic6C2314yes—
140C22×Dic6C2311yescharacteristic
141C22×Dic6C23132yes—
142C22×Dic6C2314yes—
143C22×Dic6C2314yes—
144C22×Dic6C2312yes—
145C22×Dic6C2311yescharacteristic
146C3×C4⋊Q8C2318yes—
147C3×#125C23116yes—
148C3×C22⋊Q8C23132yes—
149C3×C22⋊Q8C23116yes—
150C3×C4×Q8C2318yes—
151C3×C4×D4C2318yes—
152C3×C4×D4C23116yes—
153C2×C3×C4⋊C4C2312yes—
154C2×C3×C4⋊C4C2312yes—
155C2×C3×C4⋊C4C2314yes—
156C2×C3×C4⋊C4C2311yescharacteristic
157C2×C3×C4⋊C4C2311yescharacteristic
158C2×C3×C4⋊C4C2314yes—
159C2×C3×C4⋊C4C2312yes—
160C2×C3×C4⋊C4C23116yes—
161C2×C3×C22⋊C4C2314yes—
162C2×C3×C22⋊C4C2312yes—
163C2×C3×C42C2311yescharacteristic
164C2×C3×C42C2312yes—
165C2×#217C2314yes—
166C2×#217C2312yes—
167#946C2318yes—
168Q8×Dic3C23116yes—
169#944C23132yes—
170#944C23116yes—
171#944C2318yes—
172D4×Dic3C2318yes—
173D4×Dic3C23116yes—
174C4×#67C23132yes—
175C4×#67C23116yes—
176C2×(C2×D3)⋊C4C2312yes—
177C2×(C2×D3)⋊C4C2312yes—
178C2×(C2×D3)⋊C4C2312yes—
179C2×C4⋊Dic3C23116yes—
180C2×C4⋊Dic3C2311yescharacteristic
181C2×C4⋊Dic3C2312yes—
182C2×C4⋊Dic3C2311yescharacteristic
183C2×C4⋊Dic3C2312yes—
184C2×C4⋊Dic3C2314yes—
185C2×C4⋊Dic3C2312yes—
186C2×C4⋊Dic3C2314yes—
187#924C23132yes—
188#924C23116yes—
189C2×Dic3⋊C4C2312yes—
190C2×Dic3⋊C4C2312yes—
191C2×Dic3⋊C4C2312yes—
192C2×Dic3⋊C4C2312yes—
193C2×Dic3⋊C4C2314yes—
194C2×Dic3⋊C4C2312yes—
195C2×Dic3⋊C4C2312yes—
196C2×Dic3⋊C4C2312yes—
197C2×Dic3⋊C4C2314yes—
198C2×Dic3⋊C4C2314yes—
199C2×Dic3⋊C4C2314yes—
200C2×Dic3⋊C4C2314yes—
201C2×Dic3⋊C4C2314yes—
202C2×Dic3⋊C4C23132yes—
203C2×C4×Dic3C2311yescharacteristic
204C2×C4×Dic3C2312yes—
205C2×C4×Dic3C2314yes—
206C2×C4×Dic3C2312yes—
207C2×C4×Dic3C2311yescharacteristic
208C2×C4×Dic3C2311yescharacteristic
209C2×C4×Dic3C2314yes—
210C2×C4×Dic3C2312yes—
211C2×C4×Dic3C2312yes—
212C2×C4×Dic3C23116yes—
213#897C23132yes—
214#897C2318yes—
215#896C23116yes—
216#896C23132yes—
217#892C2318yes—
218D3×C4⋊C4C23116yes—
219D3×C4⋊C4C23116yes—
220#890C23116yes—
221#889C23132yes—
222#889C23132yes—
223#889C23132yes—
224#889C23116yes—
225#888C23132yes—
226#888C23132yes—
227#888C23116yes—
228#888C23116yes—
229#888C23116yes—
230#888C23132yes—
231#888C23116yes—
232#888C2318yes—
233#888C23116yes—
234#887C23132yes—
235#887C2318yes—
236#887C23116yes—
237#887C23116yes—
238#67⋊C4C23116yes—
239#67⋊C4C23132yes—
240#878C23132yes—
241#878C23132yes—
242#878C23132yes—
243#877C23116yes—
244#877C23132yes—
245#872C23116yes—
246C42×D3C2318yes—
247#869C23116yes—
248#869C2318yes—
249C4×Dic6C23116yes—
250C4×Dic6C23116yes—
251C4×Dic6C2318yes—
252C4×Dic6C2318yes—
253C22×#41—31no—
254C23×Q8—32no—
255C23×Q8—34no—
256Q82—316no—
257Q82—316no—
258#557—332no—
259#554—332no—
260#554—316no—
261#554—332no—
262#554C2×D3116yescomplemented
263D4×Q8—364no—
264D4×Q8—332no—
265#544—332no—
266#544—364no—
267#533—332no—
268#533—316no—
269C2×C4⋊Q8—32no—
270C2×C4⋊Q8—31no—
271C2×C4⋊Q8—34no—
272C2×C4⋊Q8—316no—
273C2×C4⋊Q8—32no—
274C2×C4⋊Q8—31no—
275C2×C4⋊Q8—34no—
276C2×C4⋊Q8—34no—
277C2×C4⋊Q8—32no—
278C2×C4⋊Q8—32no—
279C2×C4⋊Q8—32no—
280C2×C4⋊Q8—332no—
281C2×C4⋊Q8—34no—
282C2×C4⋊Q8—32no—
283C2×C4⋊Q8—31no—
284C2×C4⋊Q8—32no—
285C2×C4⋊Q8C2×D311yescharacteristic
286C2×#125—32no—
287C2×#125—34no—
288C2×#125—34no—
289C2×#125—34no—
290C2×#125—32no—
291C2×#125C2×D312yes—
292C2×C22⋊Q8—31no—
293C2×C22⋊Q8—32no—
294C2×C22⋊Q8—34no—
295C2×C22⋊Q8—32no—
296C2×C22⋊Q8—31no—
297C2×C22⋊Q8—34no—
298C2×C22⋊Q8—34no—
299C2×C22⋊Q8—34no—
300C2×C22⋊Q8—34no—
301C2×C22⋊Q8—34no—
302C2×C22⋊Q8C2×D312yes—
303C2×C22⋊Q8C2×D314yes—
304#520—332no—
305C4×#41—316no—
306C2×C4×Q8—32no—
307C2×C4×Q8—31no—
308C2×C4×Q8—32no—
309C2×C4×Q8—34no—
310C2×C4×Q8—32no—
311C2×C4×Q8—31no—
312C2×C4×Q8—32no—
313C2×C4×Q8—32no—
314C2×C4×Q8—31no—
315C2×C4×Q8C2×D311yescharacteristic
316C2×C4×D4—31no—
317C2×C4×D4—32no—
318C2×C4×D4—32no—
319C2×C4×D4—34no—
320C2×C4×D4—32no—
321C2×C4×D4—34no—
322C2×C4×D4C2×D311yescharacteristic
323C2×C4×D4C2×D312yes—
324C2×#117—31no—
325C2×#117—32no—
326C2×#117—34no—
327C2×#117—32no—
328C22×C4⋊C4—34no—
329C22×C4⋊C4—32no—
330C22×C4⋊C4—32no—
331C22×C4⋊C4—32no—
332C22×C4⋊C4C2×D312yes—
333C22×C42—32no—
334C22×C42—31no—
335C24×C3C2412yes—
336C23×D3C2411yescharacteristic
337C2×C3×Q8—24no—
338C2×C3×Q8—44no—
339C2×C3×Q8C2414yes—
340C2×C3×Q8C2418yes—
341C2×C3×D4C2×Q818yescomplemented
342C2×C3×D4C2414yes—
343C22×C3×C4—28no—
344C22×C3×C4—48no—
345C22×C3×C4C2412yes—
346C22×C3×C4C2412yes—
347C22×C3×C4C2418yes—
348C22×C3×C4C2411yescharacteristic
349C22×C3×C4C2414yes—
350C22×C3×C4C2412yes—
351C22×C3×C4C24116yes—
352C22×C3×C4C2411yescharacteristic
353C22×C3×C4C2411yescharacteristic
354C2×#67C2×Q8116yescomplemented
355C2×#67C2418yes—
356C22×Dic3—28no—
357C22×Dic3—48no—
358C22×Dic3C2×Q8116yescomplemented
359C22×Dic3C2418yes—
360C22×Dic3C2412yes—
361C22×Dic3C2411yescharacteristic
362C22×Dic3C2412yes—
363C22×Dic3C2412yes—
364C22×Dic3C2414yes—
365C22×Dic3C24116yes—
366C22×Dic3C2412yes—
367C22×Dic3C2411yescharacteristic
368C22×Dic3C2418yes—
369C22×Dic3C2411yescharacteristic
370D3×Q8—432no—
371#237C2×Q8164yescomplemented
372C2×C4×D3—24no—
373C2×C4×D3—24no—
374C2×C4×D3—48no—
375C2×C4×D3C2×Q818yescomplemented
376C2×C4×D3C2414yes—
377C2×C4×D3C2414yes—
378C2×C4×D3C24116yes—
379C2×C4×D3C2414yes—
380C2×Dic6—24no—
381C2×Dic6—28no—
382C2×Dic6—216no—
383C2×Dic6—464no—
384C2×Dic6—48no—
385C2×Dic6—48no—
386C2×Dic6—44no—
387C2×Dic6C2×Q818yescomplemented
388C2×Dic6C2414yes—
389C2×Dic6C2418yes—
390C2×Dic6C24116yes—
391C2×Dic6C2418yes—
392C2×Dic6C24116yes—
393C2×Dic6C24116yes—
394C2×Dic6C2414yes—
395C3×C4⋊C4C2418yes—
396C3×C4⋊C4C2418yes—
397C3×C4⋊C4C24116yes—
398C3×C4⋊C4C2414yes—
399C3×C4⋊C4C2414yes—
400C3×C4⋊C4C24116yes—
401C3×C4⋊C4C2418yes—
402C3×C22⋊C4C24116yes—
403C3×C22⋊C4C2418yes—
404C3×C42C2414yes—
405C3×C42C2418yes—
406#217C24116yes—
407#217C2418yes—
408(C2×D3)⋊C4C2418yes—
409(C2×D3)⋊C4C2418yes—
410(C2×D3)⋊C4C2418yes—
411C4⋊Dic3C2414yes—
412C4⋊Dic3C2418yes—
413C4⋊Dic3C2414yes—
414C4⋊Dic3C2418yes—
415C4⋊Dic3C24116yes—
416C4⋊Dic3C2418yes—
417C4⋊Dic3C24116yes—
418Dic3⋊C4C2418yes—
419Dic3⋊C4C2418yes—
420Dic3⋊C4C2418yes—
421Dic3⋊C4C2418yes—
422Dic3⋊C4C24116yes—
423Dic3⋊C4C2418yes—
424Dic3⋊C4C2418yes—
425Dic3⋊C4C2418yes—
426Dic3⋊C4C24116yes—
427Dic3⋊C4C24116yes—
428Dic3⋊C4C24116yes—
429Dic3⋊C4C24116yes—
430Dic3⋊C4C24116yes—
431C4×Dic3C2414yes—
432C4×Dic3C2418yes—
433C4×Dic3C24116yes—
434C4×Dic3C2418yes—
435C4×Dic3C2414yes—
436C4×Dic3C2414yes—
437C4×Dic3C24116yes—
438C4×Dic3C2418yes—
439C4×Dic3C2418yes—
440C2×#41—316no—
441C2×#41—38no—
442C22×Q8—316no—
443C22×Q8—31no—
444C22×Q8—31no—
445C22×Q8—34no—
446C22×Q8—32no—
447C22×Q8—34no—
448C22×Q8—34no—
449C22×Q8—32no—
450C22×Q8—332no—
451C22×Q8—1216no—
452C22×Q8—128no—
453C22×Q8C22×D311yescharacteristic
454C22×Q8C22×D312yes—
455C22×D4—32no—
456C22×D4C22×D311yescharacteristic
457C23×C4—32no—
458C23×C4—31no—
459C23×C4—32no—
460C23×C4—34no—
461C23×C4—31no—
462C23×C4—31no—
463C23×C4—34no—
464C23×C4C22×D312yes—
465C23×C4C22×D314yes—
466C4⋊Q8—316no—
467C4⋊Q8—38no—
468C4⋊Q8—332no—
469C4⋊Q8—316no—
470C4⋊Q8—38no—
471C4⋊Q8—332no—
472C4⋊Q8—332no—
473C4⋊Q8—316no—
474C4⋊Q8—316no—
475C4⋊Q8—316no—
476C4⋊Q8—332no—
477C4⋊Q8—316no—
478C4⋊Q8—38no—
479C4⋊Q8—316no—
480C4⋊Q8C22×D318yes—
481#125—316no—
482#125—332no—
483#125—332no—
484#125—332no—
485#125—316no—
486#125C22×D3116yes—
487C22⋊Q8—38no—
488C22⋊Q8—316no—
489C22⋊Q8—332no—
490C22⋊Q8—316no—
491C22⋊Q8—38no—
492C22⋊Q8—332no—
493C22⋊Q8—332no—
494C22⋊Q8—332no—
495C22⋊Q8—332no—
496C22⋊Q8—332no—
497C22⋊Q8C22×D3116yes—
498C22⋊Q8C22×D3132yes—
499C4×Q8—316no—
500C4×Q8—38no—
501C4×Q8—316no—
502C4×Q8—332no—
503C4×Q8—316no—
504C4×Q8—38no—
505C4×Q8—316no—
506C4×Q8—316no—
507C4×Q8—38no—
508C4×Q8C22×D318yes—
509C4×D4—38no—
510C4×D4—316no—
511C4×D4—316no—
512C4×D4—332no—
513C4×D4—316no—
514C4×D4—332no—
515C4×D4C22×D318yes—
516C4×D4C22×D3116yes—
517#117—38no—
518#117—316no—
519#117—332no—
520#117—316no—
521C2×C4⋊C4—34no—
522C2×C4⋊C4—32no—
523C2×C4⋊C4—31no—
524C2×C4⋊C4—32no—
525C2×C4⋊C4—34no—
526C2×C4⋊C4—34no—
527C2×C4⋊C4—32no—
528C2×C4⋊C4—332no—
529C2×C4⋊C4—34no—
530C2×C4⋊C4—34no—
531C2×C4⋊C4—316no—
532C2×C4⋊C4—32no—
533C2×C4⋊C4—32no—
534C2×C4⋊C4—32no—
535C2×C4⋊C4—31no—
536C2×C4⋊C4—32no—
537C2×C4⋊C4—34no—
538C2×C4⋊C4—32no—
539C2×C4⋊C4—32no—
540C2×C4⋊C4—34no—
541C2×C4⋊C4—32no—
542C2×C4⋊C4—34no—
543C2×C4⋊C4—316no—
544C2×C4⋊C4—316no—
545C2×C4⋊C4C22×D312yes—
546C2×C4⋊C4C22×D312yes—
547C2×C4⋊C4C22×D311yescharacteristic
548C2×C4⋊C4C22×D314yes—
549C2×C4⋊C4C22×D3116yes—
550C2×C4⋊C4C22×D311yescharacteristic
551C2×C4⋊C4C22×D314yes—
552C2×C4⋊C4C22×D312yes—
553C2×C22⋊C4—34no—
554C2×C22⋊C4—32no—
555C2×C22⋊C4—32no—
556C2×C22⋊C4—32no—
557C2×C22⋊C4—32no—
558C2×C22⋊C4C22×D314yes—
559C2×C22⋊C4C22×D312yes—
560C2×C42—31no—
561C2×C42—32no—
562C2×C42—34no—
563C2×C42—34no—
564C2×C42—32no—
565C2×C42—32no—
566C2×C42—32no—
567C2×C42—31no—
568C2×C42—316no—
569C2×C42—31no—
570C2×C42—38no—
571C2×C42C22×D312yes—
572C2×C42C22×D311yescharacteristic
573C23×C3—24no—
574C23×C3—24no—
575C23×C3C22×Q818yes—
576C23×C3C2514yes—
577C23×C3C2511yescharacteristic
578C22×D3—22no—
579C22×D3—22no—
580C22×D3C22×Q814yes—
581C22×D3C2512yes—
582C3×Q8—28no—
583C3×Q8—48no—
584C3×D4C22×Q8116yescomplemented
585C2×C3×C4—24no—
586C2×C3×C4—28no—
587C2×C3×C4—22no—
588C2×C3×C4—24no—
589C2×C3×C4—24no—
590C2×C3×C4—216no—
591C2×C3×C4—416no—
592C2×C3×C4C22×Q814yes—
593C2×C3×C42−1+414yes—
594C2×C3×C4C2514yes—
595C2×C3×C4C2514yes—
596C2×C3×C4C2512yes—
597C2×C3×C4C2518yes—
598C2×C3×C4C2514yes—
599C2×C3×C4C2512yes—
600C2×C3×C4C2512yes—
601#67C22×Q8132yescomplemented
602C2×Dic3—28no—
603C2×Dic3—24no—
604C2×Dic3—24no—
605C2×Dic3—24no—
606C2×Dic3—22no—
607C2×Dic3—216no—
608C2×Dic3—416no—
609C2×Dic3C22×Q818yes—
610C2×Dic3C22×Q814yes—
611C2×Dic3C22×Q8132yescomplemented
612C2×Dic3H(5,𝔽2)14yes—
613C2×Dic3C2514yes—
614C2×Dic3C2512yes—
615C2×Dic3C2514yes—
616C2×Dic3C2514yes—
617C2×Dic3C2518yes—
618C2×Dic3C2514yes—
619C2×Dic3C2512yes—
620C2×Dic3C2512yes—
621C4×D3—28no—
622C4×D3—28no—
623C4×D3—416no—
624C4×D3C22×Q8116yescomplemented
625Dic6—28no—
626Dic6—216no—
627Dic6—232no—
628Dic6—416no—
629Dic6—416no—
630Dic6—48no—
631Dic6C22×Q8116yescomplemented
632C24—31no—
633C24C23×D312yes—
634#41—364no—
635C2×Q8—24no—
636C2×Q8—38no—
637C2×Q8—34no—
638C2×Q8—34no—
639C2×Q8—316no—
640C2×Q8—38no—
641C2×Q8—316no—
642C2×Q8—316no—
643C2×Q8—38no—
644C2×Q8—44no—
645C2×Q8—68no—
646C2×Q8—616no—
647C2×Q8—64no—
648C2×Q8—128no—
649C2×Q8—128no—
650C2×Q8—124no—
651C2×Q8—1264no—
652C2×Q8—1232no—
653C2×Q8C23×D314yes—
654C2×Q8C23×D318yes—
655C2×D4—316no—
656C2×D4—38no—
657C2×D4D3×Q818yescomplemented
658C2×D4C23×D314yes—
659C22×C4—28no—
660C22×C4—316no—
661C22×C4—38no—
662C22×C4—32no—
663C22×C4—31no—
664C22×C4—31no—
665C22×C4—38no—
666C22×C4—34no—
667C22×C4—38no—
668C22×C4—32no—
669C22×C4—31no—
670C22×C4—32no—
671C22×C4—34no—
672C22×C4—32no—
673C22×C4—316no—
674C22×C4—34no—
675C22×C4—34no—
676C22×C4—316no—
677C22×C4—48no—
678C22×C4—64no—
679C22×C4—68no—
680C22×C4—64no—
681C22×C4—128no—
682C22×C4—128no—
683C22×C4C23×D318yes—
684C22×C4C23×D312yes—
685C22×C4C23×D312yes—
686C22×C4C23×D311yescharacteristic
687C22×C4C23×D314yes—
688C22×C4C23×D312yes—
689C22×C4C23×D3116yes—
690C22×C4C23×D311yescharacteristic
691C22×C4C23×D311yescharacteristic
692C4⋊C4—316no—
693C4⋊C4—38no—
694C4⋊C4—34no—
695C4⋊C4—38no—
696C4⋊C4—316no—
697C4⋊C4—316no—
698C4⋊C4—38no—
699C4⋊C4—316no—
700C4⋊C4—316no—
701C4⋊C4—38no—
702C4⋊C4—38no—
703C4⋊C4—38no—
704C4⋊C4—34no—
705C4⋊C4—38no—
706C4⋊C4—316no—
707C4⋊C4—38no—
708C4⋊C4—38no—
709C4⋊C4—316no—
710C4⋊C4—38no—
711C4⋊C4—316no—
712C4⋊C4C23×D318yes—
713C4⋊C4C23×D318yes—
714C4⋊C4C23×D314yes—
715C4⋊C4C23×D3116yes—
716C4⋊C4C23×D314yes—
717C4⋊C4C23×D3116yes—
718C4⋊C4C23×D318yes—
719C22⋊C4—316no—
720C22⋊C4—38no—
721C22⋊C4—38no—
722C22⋊C4—38no—
723C22⋊C4—38no—
724C22⋊C4C23×D3116yes—
725C22⋊C4C23×D318yes—
726C42—34no—
727C42—34no—
728C42—38no—
729C42—38no—
730C42—38no—
731C42—34no—
732C42—316no—
733C42—316no—
734C42—38no—
735C42C23×D314yes—
736C42C23×D318yes—
737C22×C3—24no—
738C22×C3—24no—
739C22×C3—216no—
740C22×C3C23×Q818yes—
741C22×C3C23×Q812yes—
742C22×C3C2×H(5,𝔽2)12yes—
743C22×C3C2×2−1+412yes—
744C22×C3C2611yescharacteristic
745C2×D3—22no—
746C2×D3—22no—
747C2×D3—28no—
748C2×D3C23×Q814yes—
749C3×C4—24no—
750C3×C4—28no—
751C3×C4—22no—
752C3×C4—24no—
753C3×C4—24no—
754C3×C4C23×Q814yes—
755C3×C4C2×2−1+414yes—
756Dic3—28no—
757Dic3—24no—
758Dic3—24no—
759Dic3—24no—
760Dic3—22no—
761Dic3C23×Q818yes—
762Dic3C23×Q814yes—
763Dic3C2×H(5,𝔽2)14yes—
764C23—24no—
765C23—24no—
766C23—34no—
767C23—32no—
768C23—62no—
769C23—62no—
770C23C2×D3×Q818yes—
771C23C24×D314yes—
772C23C24×D311yescharacteristic
773Q8—28no—
774Q8—316no—
775Q8—48no—
776Q8—616no—
777Q8—632no—
778Q8—68no—
779Q8—1216no—
780Q8—1216no—
781Q8—128no—
782D4—332no—
783D4C2×D3×Q8116yescomplemented
784C2×C4—24no—
785C2×C4—24no—
786C2×C4—24no—
787C2×C4—28no—
788C2×C4—22no—
789C2×C4—216no—
790C2×C4—34no—
791C2×C4—38no—
792C2×C4—332no—
793C2×C4—34no—
794C2×C4—34no—
795C2×C4—32no—
796C2×C4—32no—
797C2×C4—316no—
798C2×C4—34no—
799C2×C4—32no—
800C2×C4—34no—
801C2×C4—38no—
802C2×C4—34no—
803C2×C4—416no—
804C2×C4—68no—
805C2×C4—616no—
806C2×C4—62no—
807C2×C4—64no—
808C2×C4—64no—
809C2×C4—68no—
810C2×C4—64no—
811C2×C4—68no—
812C2×C4—1216no—
813C2×C4—1216no—
814C2×C4C2×D3×Q814yes—
815C2×C4#101014yes—
816C2×C4C24×D314yes—
817C2×C4C24×D314yes—
818C2×C4C24×D312yes—
819C2×C4C24×D318yes—
820C2×C4C24×D314yes—
821C2×C4C24×D312yes—
822C2×C4C24×D312yes—
823C2×C3—28no—
824C2×C3#350314yescomplemented
825C2×C3C24×Q811yescharacteristic
826C2×C3C22×H(5,𝔽2)11yescharacteristic
827C2×C3C22×2−1+411yescharacteristic
828D3—24no—
829C22—24no—
830C22—24no—
831C22—216no—
832C22—34no—
833C22—62no—
834C22—62no—
835C22—68no—
836C22C22×D3×Q818yes—
837C22C22×D3×Q812yes—
838C22C2×#101012yes—
839C22D3×H(5,𝔽2)12yes—
840C22C25×D311yescharacteristic
841C4—24no—
842C4—24no—
843C4—24no—
844C4—28no—
845C4—22no—
846C4—34no—
847C4—38no—
848C4—34no—
849C4—62no—
850C4—64no—
851C4—64no—
852C4—68no—
853C4—64no—
854C4C22×D3×Q814yes—
855C4C2×#101014yes—
856C3C2×#350311yescharacteristic, complemented, Sylow
857C2—28no—
858C2—64no—
859C2#8692614yesdirect product factor
860C2C23×D3×Q811yescharacteristic
861C2C22×#101011yescharacteristic
862C2C2×D3×H(5,𝔽2)11yescharacteristic
subgroupG/H
centerC23C24×D3
commutator, cosocleC22×C3C26
FrattiniC22C25×D3
FittingC2×C3×#554C2
socleC23×C3C25
prime radicalC22×#237C22
hypercenterC2×#554D3
hypocenterC3C2×#3503
LCSG ▷ C22×C3 ▷ C3
UCSC1 ◁ C23 ◁ C2×#554

Complements

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

NH ≅ G/Ntype
1. C2×C3×#554C2semidirect
2. #86926C2direct (N × H)
3. C2×D3×C4⋊Q8C2semidirect
4. C2×#5722C2semidirect
5. C2×#5689C2semidirect
6. C2×#5685C2semidirect
7. C2×#5635C2semidirect
8. C2×#5632C2semidirect
9. C2×#5623C2semidirect
10. C2×#5622C2semidirect
11. C2×#5578C2semidirect
12. C2×Q8×Dic6C2semidirect
13. C2×#5543C2semidirect
14. C2×D4×Dic6C2semidirect
17. C2×#5511C2semidirect
18. C22×#888C2semidirect
23. C3×#554C22semidirect
46. D3×C4⋊Q8C22semidirect
47. #5722C22semidirect
48. #5689C22semidirect
49. #5685C22semidirect
50. #5635C22semidirect
51. #5632C22semidirect
52. #5623C22semidirect
53. #5622C22semidirect
54. #5578C22semidirect
55. Q8×Dic6C22semidirect
57. #5543C22semidirect
58. D4×Dic6C22semidirect
60. #5511C22semidirect
82. C2×#888C22semidirect
109. C2×#554D3semidirect
131. C2×#237Q8semidirect
262. #554C2×D3semidirect
341. C2×C3×D4C2×Q8semidirect
354. C2×#67C2×Q8semidirect
358. C22×Dic3C2×Q8semidirect
371. #237C2×Q8semidirect
375. C2×C4×D3C2×Q8semidirect
387. C2×Dic6C2×Q8semidirect
584. C3×D4C22×Q8semidirect
601. #67C22×Q8semidirect
611. C2×Dic3C22×Q8semidirect
624. C4×D3C22×Q8semidirect
631. Dic6C22×Q8semidirect
657. C2×D4D3×Q8semidirect
783. D4C2×D3×Q8semidirect
824. C2×C3#3503semidirect
856. C3C2×#3503semidirect
859. C2#86926direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C3×#5542
#869262
C2×D3×C4⋊Q82
C2×#57222
C2×#56892
C2×#56852
C2×#56352
C2×#56322
C2×#56232
C2×#56222
C2×#55782
C2×Q8×Dic62
C2×#55432
C2×D4×Dic62
C2×#55462
C2×C4×#2372
C2×#55112
C22×#8882
C2×#35033