Finite Group Databasebeta

← C2×#86586 #11703517

Subgroups — C2×#86586 #11703517

Order 768.

7478 conjugacy classes of subgroups.

The subgroup lattice has 860 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#544C211yesmaximal, characteristic, complemented
2#86586C2132yesmaximal, direct product factor
3C2×#5727C212yesmaximal, complemented
4C2×#5729C212yesmaximal, complemented
5C2×D3×C4⋊Q8C212yesmaximal, complemented
6C2×#5722C212yesmaximal, complemented
7C2×#5689C212yesmaximal, complemented
8C2×#5685C212yesmaximal, complemented
9C2×#5690C212yesmaximal, complemented
10C2×#5688C212yesmaximal, complemented
11C2×#5636C214yesmaximal, complemented
12C2×#5632C214yesmaximal, complemented
13C2×#5523C211yesmaximal, characteristic
14C2×#5519C211yesmaximal, characteristic, complemented
15C2×#5517C211yesmaximal, characteristic, complemented
16C2×#5522C211yesmaximal, characteristic
17C2×#5504C211yesmaximal, characteristic
18C22×#888C211yesmaximal, characteristic, complemented
19C2×#3503—31nomaximal, Sylow
20C22×D3×Q8C2214yes—
21C22×#235C2211yescharacteristic
22C23×Dic6C2212yes—
23C3×#544C22116yescomplemented
24C2×C3×C4⋊Q8C2212yes—
25C2×C3×C4⋊Q8C2212yes—
26C2×C3×#125C2212yes—
27C2×C3×#125C2212yes—
28C2×C3×C22⋊Q8C2214yes—
29C2×C3×#117C2211yescharacteristic
30C2×C3×#117C2211yescharacteristic
31C22×C3×C4⋊C4C2211yescharacteristic
32C2×#946C2214yes—
33C2×#944C2214yes—
34C2×#944C2214yes—
35C2×C4×#67C2214yes—
36C2×#926C2211yescharacteristic
37C22×C4⋊Dic3C2211yescharacteristic
38C22×Dic3⋊C4C2212yes—
39C22×C4×Dic3C2211yescharacteristic
40#5729C22132yescomplemented
41#5727C22132yescomplemented
42D3×C4⋊Q8C22132yescomplemented
43#5722C22132yescomplemented
44#5690C22132yescomplemented
45#5689C22132yescomplemented
46#5688C22132yescomplemented
47#5685C22132yescomplemented
48#5636C22164yescomplemented
49#5632C22164yescomplemented
50#5523C22116yes—
51#5522C22116yes—
52#5519C22116yescomplemented
53#5517C22116yescomplemented
54C2×#897C2214yes—
55C2×#896C2214yes—
56C2×#896C2214yes—
57C2×#896C2214yes—
58C2×#896C2214yes—
59#5504C22116yes—
60C2×#893C2211yescharacteristic
61C2×#893C2212yes—
62C2×#893C2211yescharacteristic
63C2×#892C2212yes—
64C2×#892C2212yes—
65C2×D3×C4⋊C4C2214yes—
66C2×D3×C4⋊C4C2212yes—
67C2×D3×C4⋊C4C2212yes—
68C2×#890C2212yes—
69C2×#890C2211yescharacteristic
70C2×#890C2211yescharacteristic
71C2×#889C2214yes—
72C2×#889C2214yes—
73C2×#888C2211yescharacteristic
74C2×#888C2212yes—
75C2×#888C2212yes—
76C2×#888C2214yes—
77C2×#888C2212yes—
78C2×#888C2214yes—
79C2×#888C2212yes—
80C2×#888C2212yes—
81C2×#888C2211yescharacteristic
82C2×#888C22116yescomplemented
83C2×#887C2214yes—
84C2×#887C2214yes—
85C2×#887C2211yescharacteristic
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#3503—332no—
103C2×Q82—32no—
104C2×#557—32no—
105C2×#554—32no—
106C2×#554—34no—
107C2×D4×Q8—32no—
108C2×D4×Q8—34no—
109C2×#544—32no—
110C2×#544—32no—
111C2×#544—31no—
112C2×#544D311yescharacteristic, complemented
113C2×#533—32no—
114C2×#533—31no—
115C22×C4⋊Q8—32no—
116C22×C4⋊Q8—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×D3×Q8—416no—
128C2×D3×Q8C23132yes—
129C2×#235Q8116yescomplemented
130C2×#235C2318yes—
131C22×D12C2311yescharacteristic
132C22×C4×D3C2312yes—
133C22×C4×D3C2312yes—
134C22×C4×D3C2314yes—
135C22×C4×D3C2314yes—
136C22×C4×D3C2312yes—
137C22×Dic6—48no—
138C22×Dic6C2314yes—
139C22×Dic6C2312yes—
140C22×Dic6C2312yes—
141C22×Dic6C23116yes—
142C22×Dic6C2314yes—
143C22×Dic6C2314yes—
144C22×Dic6C2311yescharacteristic
145C3×C4⋊Q8C23116yes—
146C3×C4⋊Q8C23116yes—
147C3×#125C23116yes—
148C3×#125C23116yes—
149C3×C22⋊Q8C23132yes—
150C3×#117C2318yes—
151C3×#117C2318yes—
152C2×C3×C4⋊C4C2312yes—
153C2×C3×C4⋊C4C2311yescharacteristic
154C2×C3×C4⋊C4C2314yes—
155C2×C3×C4⋊C4C2314yes—
156C2×C3×C4⋊C4C2311yescharacteristic
157C2×C3×C4⋊C4C2312yes—
158C2×C3×C4⋊C4C2314yes—
159C2×C3×C4⋊C4C2311yescharacteristic
160C2×C3×C4⋊C4C2311yescharacteristic
161C2×C3×C4⋊C4C2318yes—
162C2×C3×C22⋊C4C2312yes—
163C2×C3×C22⋊C4C2312yes—
164C2×C3×C42C2312yes—
165C2×C3×C42C2312yes—
166C2×#217C2312yes—
167#946C23132yes—
168#944C23132yes—
169#944C23132yes—
170C4×#67C23132yes—
171C2×(C2×D3)⋊C4C2312yes—
172C2×(C2×D3)⋊C4C2312yes—
173C2×(C2×D3)⋊C4C2314yes—
174C2×(C2×D3)⋊C4C2314yes—
175#926C2318yes—
176C2×C4⋊Dic3C2312yes—
177C2×C4⋊Dic3C2312yes—
178C2×C4⋊Dic3C2312yes—
179C2×C4⋊Dic3C2311yescharacteristic
180C2×C4⋊Dic3C2312yes—
181C2×C4⋊Dic3C2314yes—
182C2×C4⋊Dic3C2311yescharacteristic
183C2×C4⋊Dic3C2318yes—
184C2×Dic3⋊C4C23116yes—
185C2×Dic3⋊C4C2312yes—
186C2×Dic3⋊C4C2312yes—
187C2×Dic3⋊C4C2312yes—
188C2×Dic3⋊C4C2312yes—
189C2×Dic3⋊C4C2314yes—
190C2×Dic3⋊C4C2314yes—
191C2×Dic3⋊C4C2314yes—
192C2×Dic3⋊C4C2312yes—
193C2×Dic3⋊C4C2312yes—
194C2×Dic3⋊C4C2314yes—
195C2×Dic3⋊C4C2314yes—
196C2×Dic3⋊C4C2314yes—
197C2×C4×Dic3C2311yescharacteristic
198C2×C4×Dic3C2311yescharacteristic
199C2×C4×Dic3C2312yes—
200C2×C4×Dic3C2314yes—
201C2×C4×Dic3C2311yescharacteristic
202C2×C4×Dic3C2312yes—
203C2×C4×Dic3C2312yes—
204C2×C4×Dic3C2311yescharacteristic
205C2×C4×Dic3C2314yes—
206C2×C4×Dic3C2318yes—
207#897C23132yes—
208#896C23132yes—
209#896C23132yes—
210#896C23132yes—
211#896C23132yes—
212#893C2318yes—
213#893C23116yes—
214#893C2318yes—
215#892C23116yes—
216#892C23116yes—
217D3×C4⋊C4C23132yes—
218D3×C4⋊C4C23116yes—
219D3×C4⋊C4C23116yes—
220#890C23116yes—
221#890C2318yes—
222#890C2318yes—
223#889C23132yes—
224#889C23132yes—
225#888C23132yes—
226#888C23132yes—
227#888C23116yes—
228#888C2318yes—
229#888C23116yes—
230#888C23116yes—
231#888C23116yes—
232#888C23116yes—
233#888C2318yes—
234#887C23132yes—
235#887C23132yes—
236#887C2318yes—
237#887C23116yes—
238#887C2318yes—
239#67⋊C4C23116yes—
240#67⋊C4C23132yes—
241#67⋊C4C23116yes—
242#878C23116yes—
243#878C23132yes—
244#878C23116yes—
245C4×D12C23116yes—
246#872C23116yes—
247C42×D3C23116yes—
248#870C23116yes—
249#869C23116yes—
250C4×Dic6C23116yes—
251C4×Dic6C23116yes—
252C4×Dic6C23116yes—
253C22×#41—31no—
254C23×Q8—34no—
255C23×Q8—32no—
256Q82—332no—
257#557—332no—
258#554—332no—
259#554—364no—
260D4×Q8—332no—
261D4×Q8—364no—
262#544—332no—
263#544—332no—
264#544—316no—
265#544C2×D3116yescomplemented
266#533—332no—
267#533—316no—
268C2×C4⋊Q8—34no—
269C2×C4⋊Q8—34no—
270C2×C4⋊Q8—332no—
271C2×C4⋊Q8—31no—
272C2×C4⋊Q8—32no—
273C2×C4⋊Q8—32no—
274C2×C4⋊Q8—34no—
275C2×C4⋊Q8—32no—
276C2×C4⋊Q8—32no—
277C2×C4⋊Q8—316no—
278C2×C4⋊Q8—31no—
279C2×C4⋊Q8—34no—
280C2×C4⋊Q8—32no—
281C2×C4⋊Q8—32no—
282C2×C4⋊Q8C2×D312yes—
283C2×C4⋊Q8C2×D312yes—
284C2×#125—31no—
285C2×#125—31no—
286C2×#125—34no—
287C2×#125—34no—
288C2×#125—32no—
289C2×#125—32no—
290C2×#125C2×D312yes—
291C2×#125C2×D312yes—
292C2×C22⋊Q8—34no—
293C2×C22⋊Q8—34no—
294C2×C22⋊Q8—34no—
295C2×C22⋊Q8—34no—
296C2×C22⋊Q8—34no—
297C2×C22⋊Q8—34no—
298C2×C22⋊Q8—32no—
299C2×C22⋊Q8—32no—
300C2×C22⋊Q8—34no—
301C2×C22⋊Q8C2×D314yes—
302#520—316no—
303#520—316no—
304C4×#41—316no—
305C2×C4×Q8—31no—
306C2×C4×Q8—31no—
307C2×C4×Q8—32no—
308C2×C4×Q8—34no—
309C2×C4×Q8—34no—
310C2×C4×Q8—32no—
311C2×C4×Q8—32no—
312C2×C4×Q8—32no—
313C2×C4×D4—34no—
314C2×C4×D4—31no—
315C2×C4×D4—31no—
316C2×C4×D4—32no—
317C2×C4×D4—32no—
318C2×C4×D4—32no—
319C2×C4×D4—34no—
320C2×C4×D4—32no—
321C2×#117—31no—
322C2×#117—32no—
323C2×#117—32no—
324C2×#117—32no—
325C2×#117C2×D311yescharacteristic
326C2×#117C2×D311yescharacteristic
327C22×C4⋊C4—31no—
328C22×C4⋊C4—32no—
329C22×C4⋊C4—32no—
330C22×C4⋊C4—32no—
331C22×C4⋊C4—34no—
332C22×C4⋊C4C2×D311yescharacteristic
333C22×C42—31no—
334C22×C42—32no—
335C24×C3C2411yescharacteristic
336C23×D3C2412yes—
337C2×C3×Q8—48no—
338C2×C3×Q8C24116yes—
339C22×C3×C4—44no—
340C22×C3×C4C2×Q818yescomplemented
341C22×C3×C4C2412yes—
342C22×C3×C4C2412yes—
343C22×C3×C4C2412yes—
344C22×C3×C4C2414yes—
345C22×C3×C4C2412yes—
346C22×C3×C4C2418yes—
347C22×C3×C4C2411yescharacteristic
348C22×C3×C4C2411yescharacteristic
349C22×C3×C4C2414yes—
350C2×#67C2×Q8116yescomplemented
351C2×#67C2418yes—
352C22×Dic3—24no—
353C22×Dic3—24no—
354C22×Dic3—44no—
355C22×Dic3C2414yes—
356C22×Dic3C2414yes—
357C22×Dic3C2412yes—
358C22×Dic3C2411yescharacteristic
359C22×Dic3C2411yescharacteristic
360C22×Dic3C2414yes—
361C22×Dic3C2412yes—
362C22×Dic3C2418yes—
363C22×Dic3C2412yes—
364C22×Dic3C2411yescharacteristic
365C22×Dic3C2411yescharacteristic
366D3×Q8—464no—
367#235C2×Q8164yescomplemented
368C2×D12C2×Q818yescomplemented
369C2×D12C2414yes—
370C2×C4×D3—28no—
371C2×C4×D3—28no—
372C2×C4×D3—48no—
373C2×C4×D3—48no—
374C2×C4×D3C2×Q8116yescomplemented
375C2×C4×D3C2418yes—
376C2×C4×D3C2418yes—
377C2×C4×D3C24116yes—
378C2×C4×D3C24116yes—
379C2×C4×D3C2418yes—
380C2×Dic6—216no—
381C2×Dic6—28no—
382C2×Dic6—28no—
383C2×Dic6—432no—
384C2×Dic6—48no—
385C2×Dic6—48no—
386C2×Dic6C2×Q818yescomplemented
387C2×Dic6C2418yes—
388C2×Dic6C2418yes—
389C2×Dic6C24116yes—
390C2×Dic6C24116yes—
391C2×Dic6C24116yes—
392C2×Dic6C2414yes—
393C3×C4⋊C4C2418yes—
394C3×C4⋊C4C2414yes—
395C3×C4⋊C4C24116yes—
396C3×C4⋊C4C24116yes—
397C3×C4⋊C4C2414yes—
398C3×C4⋊C4C2418yes—
399C3×C4⋊C4C24116yes—
400C3×C4⋊C4C2414yes—
401C3×C4⋊C4C2414yes—
402C3×C22⋊C4C2418yes—
403C3×C22⋊C4C2418yes—
404C3×C42C2418yes—
405C3×C42C2418yes—
406#217C2418yes—
407(C2×D3)⋊C4C2418yes—
408(C2×D3)⋊C4C2418yes—
409(C2×D3)⋊C4C24116yes—
410(C2×D3)⋊C4C24116yes—
411C4⋊Dic3C2418yes—
412C4⋊Dic3C2418yes—
413C4⋊Dic3C2418yes—
414C4⋊Dic3C2414yes—
415C4⋊Dic3C2418yes—
416C4⋊Dic3C24116yes—
417C4⋊Dic3C2414yes—
418Dic3⋊C4C2418yes—
419Dic3⋊C4C2418yes—
420Dic3⋊C4C2418yes—
421Dic3⋊C4C2418yes—
422Dic3⋊C4C24116yes—
423Dic3⋊C4C24116yes—
424Dic3⋊C4C24116yes—
425Dic3⋊C4C2418yes—
426Dic3⋊C4C2418yes—
427Dic3⋊C4C24116yes—
428Dic3⋊C4C24116yes—
429Dic3⋊C4C24116yes—
430C4×Dic3C2414yes—
431C4×Dic3C2414yes—
432C4×Dic3C2418yes—
433C4×Dic3C24116yes—
434C4×Dic3C2414yes—
435C4×Dic3C2418yes—
436C4×Dic3C2418yes—
437C4×Dic3C2414yes—
438C4×Dic3C24116yes—
439C2×#41—316no—
440C2×#41—38no—
441C22×Q8—332no—
442C22×Q8—31no—
443C22×Q8—32no—
444C22×Q8—34no—
445C22×Q8—32no—
446C22×Q8—34no—
447C22×Q8—34no—
448C22×Q8—316no—
449C22×Q8—128no—
450C22×Q8—1216no—
451C22×Q8C22×D314yes—
452C22×D4—32no—
453C22×D4—31no—
454C23×C4—32no—
455C23×C4—31no—
456C23×C4—31no—
457C23×C4—32no—
458C23×C4—32no—
459C23×C4—32no—
460C23×C4—34no—
461C23×C4—34no—
462C23×C4C22×D312yes—
463C23×C4C22×D311yescharacteristic
464C4⋊Q8—332no—
465C4⋊Q8—332no—
466C4⋊Q8—38no—
467C4⋊Q8—316no—
468C4⋊Q8—316no—
469C4⋊Q8—332no—
470C4⋊Q8—316no—
471C4⋊Q8—316no—
472C4⋊Q8—38no—
473C4⋊Q8—332no—
474C4⋊Q8—316no—
475C4⋊Q8—316no—
476C4⋊Q8C22×D3116yes—
477C4⋊Q8C22×D3116yes—
478#125—38no—
479#125—38no—
480#125—332no—
481#125—332no—
482#125—316no—
483#125—316no—
484#125C22×D3116yes—
485#125C22×D3116yes—
486C22⋊Q8—332no—
487C22⋊Q8—332no—
488C22⋊Q8—332no—
489C22⋊Q8—332no—
490C22⋊Q8—332no—
491C22⋊Q8—332no—
492C22⋊Q8—316no—
493C22⋊Q8—316no—
494C22⋊Q8—332no—
495C22⋊Q8C22×D3132yes—
496C4×Q8—38no—
497C4×Q8—38no—
498C4×Q8—316no—
499C4×Q8—332no—
500C4×Q8—332no—
501C4×Q8—316no—
502C4×Q8—316no—
503C4×Q8—316no—
504C4×D4—332no—
505C4×D4—38no—
506C4×D4—38no—
507C4×D4—316no—
508C4×D4—316no—
509C4×D4—316no—
510C4×D4—332no—
511C4×D4—316no—
512#117—38no—
513#117—316no—
514#117—316no—
515#117—316no—
516#117C22×D318yes—
517#117C22×D318yes—
518C2×C4⋊C4—32no—
519C2×C4⋊C4—31no—
520C2×C4⋊C4—34no—
521C2×C4⋊C4—32no—
522C2×C4⋊C4—34no—
523C2×C4⋊C4—34no—
524C2×C4⋊C4—32no—
525C2×C4⋊C4—38no—
526C2×C4⋊C4—34no—
527C2×C4⋊C4—34no—
528C2×C4⋊C4—316no—
529C2×C4⋊C4—31no—
530C2×C4⋊C4—32no—
531C2×C4⋊C4—32no—
532C2×C4⋊C4—32no—
533C2×C4⋊C4—34no—
534C2×C4⋊C4—32no—
535C2×C4⋊C4—32no—
536C2×C4⋊C4—32no—
537C2×C4⋊C4—34no—
538C2×C4⋊C4—32no—
539C2×C4⋊C4—316no—
540C2×C4⋊C4—316no—
541C2×C4⋊C4—332no—
542C2×C4⋊C4C22×D311yescharacteristic
543C2×C4⋊C4C22×D312yes—
544C2×C4⋊C4C22×D314yes—
545C2×C4⋊C4C22×D312yes—
546C2×C4⋊C4C22×D318yes—
547C2×C4⋊C4C22×D311yescharacteristic
548C2×C4⋊C4C22×D311yescharacteristic
549C2×C4⋊C4C22×D311yescharacteristic
550C2×C4⋊C4C22×D314yes—
551C2×C4⋊C4C22×D314yes—
552C2×C22⋊C4—32no—
553C2×C22⋊C4—34no—
554C2×C22⋊C4—32no—
555C2×C22⋊C4—32no—
556C2×C22⋊C4—34no—
557C2×C22⋊C4C22×D312yes—
558C2×C22⋊C4C22×D312yes—
559C2×C42—31no—
560C2×C42—34no—
561C2×C42—34no—
562C2×C42—32no—
563C2×C42—32no—
564C2×C42—32no—
565C2×C42—31no—
566C2×C42—31no—
567C2×C42—38no—
568C2×C42—31no—
569C2×C42—316no—
570C2×C42C22×D312yes—
571C2×C42C22×D312yes—
572C23×C3—22no—
573C23×C3—22no—
574C23×C3C22×Q814yes—
575C23×C3C2512yes—
576C23×C3C2511yescharacteristic
577C22×D3—24no—
578C22×D3—24no—
579C22×D3C22×Q818yes—
580C22×D3C2514yes—
581C3×Q8—416no—
582C2×C3×C4—28no—
583C2×C3×C4—24no—
584C2×C3×C4—24no—
585C2×C3×C4—24no—
586C2×C3×C4—24no—
587C2×C3×C4—48no—
588C2×C3×C4C22×Q814yes—
589C2×C3×C4C22×Q814yes—
590C2×C3×C4C22×Q8116yescomplemented
591C2×C3×C4C2514yes—
592C2×C3×C4C2514yes—
593C2×C3×C4C2514yes—
594C2×C3×C4C2518yes—
595C2×C3×C4C2514yes—
596C2×C3×C4C2512yes—
597C2×C3×C4C2512yes—
598#67C22×Q8132yescomplemented
599C2×Dic3—24no—
600C2×Dic3—28no—
601C2×Dic3—22no—
602C2×Dic3—24no—
603C2×Dic3—22no—
604C2×Dic3—28no—
605C2×Dic3—28no—
606C2×Dic3—48no—
607C2×Dic3C22×Q818yes—
608C2×Dic3H(5,𝔽2)14yes—
609C2×Dic32−1+414yes—
610C2×Dic3C2514yes—
611C2×Dic3C2512yes—
612C2×Dic3C2512yes—
613C2×Dic3C2518yes—
614C2×Dic3C2514yes—
615C2×Dic3C2514yes—
616C2×Dic3C2512yes—
617C2×Dic3C2512yes—
618D12C22×Q8116yescomplemented
619C4×D3—216no—
620C4×D3—216no—
621C4×D3—416no—
622C4×D3—416no—
623C4×D3C22×Q8132yescomplemented
624Dic6—232no—
625Dic6—216no—
626Dic6—216no—
627Dic6—416no—
628Dic6—416no—
629Dic6C22×Q8116yescomplemented
630C24—32no—
631C24C23×D311yescharacteristic
632#41—364no—
633C2×Q8—38no—
634C2×Q8—34no—
635C2×Q8—38no—
636C2×Q8—316no—
637C2×Q8—38no—
638C2×Q8—316no—
639C2×Q8—316no—
640C2×Q8—48no—
641C2×Q8—616no—
642C2×Q8—68no—
643C2×Q8—68no—
644C2×Q8—128no—
645C2×Q8—128no—
646C2×Q8—1232no—
647C2×Q8—1264no—
648C2×Q8C23×D3116yes—
649C2×D4—316no—
650C2×D4—38no—
651C2×D4—38no—
652C2×D4—34no—
653C22×C4—32no—
654C22×C4—31no—
655C22×C4—31no—
656C22×C4—316no—
657C22×C4—38no—
658C22×C4—34no—
659C22×C4—34no—
660C22×C4—32no—
661C22×C4—31no—
662C22×C4—31no—
663C22×C4—32no—
664C22×C4—34no—
665C22×C4—38no—
666C22×C4—38no—
667C22×C4—38no—
668C22×C4—316no—
669C22×C4—316no—
670C22×C4—44no—
671C22×C4—68no—
672C22×C4—68no—
673C22×C4—64no—
674C22×C4—64no—
675C22×C4—128no—
676C22×C4—128no—
677C22×C4—124no—
678C22×C4D3×Q818yescomplemented
679C22×C4C23×D312yes—
680C22×C4C23×D312yes—
681C22×C4C23×D312yes—
682C22×C4C23×D314yes—
683C22×C4C23×D312yes—
684C22×C4C23×D318yes—
685C22×C4C23×D311yescharacteristic
686C22×C4C23×D311yescharacteristic
687C22×C4C23×D314yes—
688C4⋊C4—38no—
689C4⋊C4—34no—
690C4⋊C4—316no—
691C4⋊C4—38no—
692C4⋊C4—316no—
693C4⋊C4—316no—
694C4⋊C4—38no—
695C4⋊C4—316no—
696C4⋊C4—316no—
697C4⋊C4—34no—
698C4⋊C4—38no—
699C4⋊C4—38no—
700C4⋊C4—38no—
701C4⋊C4—316no—
702C4⋊C4—38no—
703C4⋊C4—38no—
704C4⋊C4—38no—
705C4⋊C4—316no—
706C4⋊C4—38no—
707C4⋊C4C23×D314yes—
708C4⋊C4C23×D318yes—
709C4⋊C4C23×D3116yes—
710C4⋊C4C23×D318yes—
711C4⋊C4C23×D314yes—
712C4⋊C4C23×D314yes—
713C4⋊C4C23×D314yes—
714C4⋊C4C23×D3116yes—
715C4⋊C4C23×D3116yes—
716C22⋊C4—38no—
717C22⋊C4—316no—
718C22⋊C4—38no—
719C22⋊C4—38no—
720C22⋊C4—316no—
721C22⋊C4C23×D318yes—
722C22⋊C4C23×D318yes—
723C42—34no—
724C42—34no—
725C42—38no—
726C42—38no—
727C42—34no—
728C42—34no—
729C42—316no—
730C42—316no—
731C42—38no—
732C42C23×D318yes—
733C42C23×D318yes—
734C22×C3—22no—
735C22×C3—22no—
736C22×C3—28no—
737C22×C3C23×Q814yes—
738C22×C3C23×Q812yes—
739C22×C3C2×H(5,𝔽2)12yes—
740C22×C3C2×2−1+412yes—
741C22×C3C2611yescharacteristic
742C2×D3—24no—
743C2×D3—24no—
744C2×D3—216no—
745C2×D3C23×Q818yes—
746C3×C4—28no—
747C3×C4—24no—
748C3×C4—24no—
749C3×C4—24no—
750C3×C4—24no—
751C3×C4C23×Q814yes—
752C3×C4C23×Q814yes—
753Dic3—24no—
754Dic3—28no—
755Dic3—22no—
756Dic3—24no—
757Dic3—22no—
758Dic3C23×Q818yes—
759Dic3C2×H(5,𝔽2)14yes—
760Dic3C2×2−1+414yes—
761C23—22no—
762C23—22no—
763C23—38no—
764C23—34no—
765C23—64no—
766C23—64no—
767C23C2×D3×Q814yes—
768C23C24×D312yes—
769C23C24×D311yescharacteristic
770Q8—316no—
771Q8—416no—
772Q8—632no—
773Q8—616no—
774Q8—616no—
775Q8—1216no—
776Q8—1216no—
777D4—332no—
778D4—316no—
779C2×C4—28no—
780C2×C4—24no—
781C2×C4—24no—
782C2×C4—24no—
783C2×C4—24no—
784C2×C4—38no—
785C2×C4—34no—
786C2×C4—34no—
787C2×C4—34no—
788C2×C4—32no—
789C2×C4—32no—
790C2×C4—332no—
791C2×C4—34no—
792C2×C4—32no—
793C2×C4—32no—
794C2×C4—34no—
795C2×C4—38no—
796C2×C4—48no—
797C2×C4—616no—
798C2×C4—616no—
799C2×C4—68no—
800C2×C4—68no—
801C2×C4—62no—
802C2×C4—64no—
803C2×C4—68no—
804C2×C4—62no—
805C2×C4—64no—
806C2×C4—1216no—
807C2×C4—1216no—
808C2×C4—128no—
809C2×C4C2×D3×Q814yes—
810C2×C4C2×D3×Q814yes—
811C2×C4C2×D3×Q8116yescomplemented
812C2×C4C24×D314yes—
813C2×C4C24×D314yes—
814C2×C4C24×D314yes—
815C2×C4C24×D318yes—
816C2×C4C24×D314yes—
817C2×C4C24×D312yes—
818C2×C4C24×D312yes—
819C2×C3—24no—
820C2×C3#350314yescomplemented
821C2×C3C24×Q811yescharacteristic
822C2×C3C22×H(5,𝔽2)11yescharacteristic
823C2×C3C22×2−1+411yescharacteristic
824D3—28no—
825C22—22no—
826C22—22no—
827C22—28no—
828C22—38no—
829C22—64no—
830C22—64no—
831C22—616no—
832C22C22×D3×Q814yes—
833C22C22×D3×Q812yes—
834C22D3×H(5,𝔽2)12yes—
835C22D3×2−1+412yes—
836C22C25×D311yescharacteristic
837C4—28no—
838C4—24no—
839C4—24no—
840C4—24no—
841C4—24no—
842C4—38no—
843C4—34no—
844C4—34no—
845C4—62no—
846C4—64no—
847C4—68no—
848C4—62no—
849C4—64no—
850C4C22×D3×Q814yes—
851C4C22×D3×Q814yes—
852C3C2×#350311yescharacteristic, complemented, Sylow
853C2—24no—
854C2—68no—
855C2#8658614yesdirect product factor
856C2C23×D3×Q811yescharacteristic
857C2C2×D3×H(5,𝔽2)11yescharacteristic
858C2C2×D3×2−1+411yescharacteristic
subgroupG/H
centerC23C24×D3
commutator, cosocleC22×C3C26
FrattiniC22C25×D3
FittingC2×C3×#544C2
socleC23×C3C25
prime radicalC22×#235C22
hypercenterC2×#544D3
hypocenterC3C2×#3503
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. #86586C2direct (N × H)
3. C2×#5727C2semidirect
4. C2×#5729C2semidirect
5. C2×D3×C4⋊Q8C2semidirect
6. C2×#5722C2semidirect
7. C2×#5689C2semidirect
8. C2×#5685C2semidirect
9. C2×#5690C2semidirect
10. C2×#5688C2semidirect
11. C2×#5636C2semidirect
12. C2×#5632C2semidirect
14. C2×#5519C2semidirect
15. C2×#5517C2semidirect
18. C22×#888C2semidirect
23. C3×#544C22semidirect
40. #5729C22semidirect
41. #5727C22semidirect
42. D3×C4⋊Q8C22semidirect
43. #5722C22semidirect
44. #5690C22semidirect
45. #5689C22semidirect
46. #5688C22semidirect
47. #5685C22semidirect
48. #5636C22semidirect
49. #5632C22semidirect
52. #5519C22semidirect
53. #5517C22semidirect
82. C2×#888C22semidirect
112. C2×#544D3semidirect
129. C2×#235Q8semidirect
265. #544C2×D3semidirect
340. C22×C3×C4C2×Q8semidirect
350. C2×#67C2×Q8semidirect
367. #235C2×Q8semidirect
368. C2×D12C2×Q8semidirect
374. C2×C4×D3C2×Q8semidirect
386. C2×Dic6C2×Q8semidirect
590. C2×C3×C4C22×Q8semidirect
598. #67C22×Q8semidirect
618. D12C22×Q8semidirect
623. C4×D3C22×Q8semidirect
629. Dic6C22×Q8semidirect
678. C22×C4D3×Q8semidirect
811. C2×C4C2×D3×Q8semidirect
820. C2×C3#3503semidirect
852. C3C2×#3503semidirect
855. C2#86586direct (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
#865862
C2×#57272
C2×#57292
C2×D3×C4⋊Q82
C2×#57222
C2×#56892
C2×#56852
C2×#56902
C2×#56882
C2×#56362
C2×#56322
C2×#55232
C2×#55192
C2×#55172
C2×#55222
C2×#55042
C22×#8882
C2×#35033