Finite Group Databasebeta

← C2×#86993 #11703403

Subgroups — C2×#86993 #11703403

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×#556C211yesmaximal, characteristic, complemented
2#86993C2132yesmaximal, direct product factor
3C2×#5721C211yesmaximal, characteristic, complemented
4C2×#5728C211yesmaximal, characteristic, complemented
5C2×#5708C214yesmaximal, complemented
6C2×#5701C214yesmaximal, complemented
7C2×#5671C212yesmaximal, complemented
8C2×#5680C212yesmaximal
9C2×#5632C212yesmaximal, complemented
10C2×#5625C212yesmaximal, complemented
11C2×#5578C212yesmaximal, complemented
12C2×C4×D3×Q8C211yesmaximal, characteristic, complemented
13C2×#5569C212yesmaximal, complemented
14C2×#5567C211yesmaximal, characteristic, complemented
15C2×#5557C211yesmaximal, characteristic
16C2×D4×Dic6C211yesmaximal, characteristic, complemented
17C2×#5529C212yesmaximal, complemented
18C2×#5516C212yesmaximal, complemented
19C2×#3523—31nomaximal, Sylow
20C22×D3×Q8C2211yescharacteristic
21C23×Dic6C2212yes—
22C3×#556C22116yescomplemented
23C2×C3×C4⋊Q8C2211yescharacteristic
24C2×C3×#126C2214yes—
25C2×C3×#124C2212yes—
26C2×C3×C22⋊Q8C2212yes—
27C2×C3×C4×Q8C2211yescharacteristic
28C2×C3×C4×Q8C2212yes—
29C2×C3×C4×D4C2211yescharacteristic
30C2×C3×#117C2212yes—
31C2×#946C2212yes—
32C2×Q8×Dic3C2212yes—
33C2×Q8×Dic3C2212yes—
34C2×Q8×Dic3C2211yescharacteristic
35C2×#944C2212yes—
36C2×#944C2212yes—
37C2×#938C2211yescharacteristic
38C2×#936C2211yescharacteristic
39C2×D4×Dic3C2212yes—
40C2×C4×#67C2212yes—
41C2×#926C2212yes—
42C2×#924C2212yes—
43#5728C22116yescomplemented
44#5721C22116yescomplemented
45#5708C22164yescomplemented
46#5701C22164yescomplemented
47#5680C22132yes—
48#5671C22132yescomplemented
49#5632C22132yescomplemented
50#5625C22132yescomplemented
51#5578C22132yescomplemented
52C4×D3×Q8C22116yescomplemented
53#5569C22132yescomplemented
54#5567C22116yescomplemented
55#5557C22116yes—
56D4×Dic6C22116yescomplemented
57#5529C22132yescomplemented
58#5516C22132yescomplemented
59C2×#897C2211yescharacteristic
60C2×#897C2212yes—
61C2×#896C2214yes—
62C2×#892C2212yes—
63C2×D3×C4⋊C4C2212yes—
64C2×D3×C4⋊C4C2211yescharacteristic
65C2×#890C2211yescharacteristic
66C2×#890C2214yes—
67C2×#890C2212yes—
68C2×#890C2212yes—
69C2×#889C2214yes—
70C2×#889C2214yes—
71C2×#889C2214yes—
72C2×#888C2212yes—
73C2×#888C2214yes—
74C2×#887C2212yes—
75C2×#887C2212yes—
76C2×#887C2211yescharacteristic
77C2×#887C2212yes—
78C2×#887C2212yes—
79C2×#883C2212yes—
80C2×#883C2214yes—
81C2×#67⋊C4C2214yes—
82C2×#879C2212yes—
83C2×#879C2214yes—
84C2×#879C2214yes—
85C2×#879C2214yes—
86C2×#878C2214yes—
87C2×#878C2214yes—
88C2×#877C2214yes—
89C2×#877C2214yes—
90C2×#872C2214yes—
91C2×C42×D3C2211yescharacteristic
92C2×C42×D3C2212yes—
93C2×#870C2212yes—
94C2×#870C2214yes—
95C2×#869C2211yescharacteristic
96C2×C4×Dic6C2211yescharacteristic
97C2×C4×Dic6C2212yes—
98C2×C4×Dic6C2212yes—
99C2×C4×Dic6C2214yes—
100C2×C4×Dic6C2211yescharacteristic
101C2×C4×Dic6C2214yes—
102#3523—332no—
103C2×#557—31no—
104C2×#557—31no—
105C2×#557—32no—
106C2×#556—32no—
107C2×#556D311yescharacteristic, complemented
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×#529—31no—
118C2×#519—32no—
119C22×C4×Q8—31no—
120C22×C3×Q8C2311yescharacteristic
121C22×C3×Q8C2312yes—
122C22×C3×D4C2311yescharacteristic
123C23×C3×C4C2312yes—
124C22×#67C2312yes—
125C23×Dic3C2314yes—
126C2×D3×Q8—28no—
127C2×D3×Q8C2318yes—
128C22×C4×D3C2312yes—
129C22×C4×D3C2311yescharacteristic
130C22×C4×D3C2311yescharacteristic
131C22×C4×D3C2312yes—
132C22×C4×D3C2311yescharacteristic
133C22×Dic6—216no—
134C22×Dic6C23116yes—
135C22×Dic6C2314yes—
136C22×Dic6C2312yes—
137C22×Dic6C2312yes—
138C22×Dic6C2311yescharacteristic
139C22×Dic6C2311yescharacteristic
140C3×C4⋊Q8C2318yes—
141C3×#126C23132yes—
142C3×#124C23116yes—
143C3×C22⋊Q8C23116yes—
144C3×C4×Q8C2318yes—
145C3×C4×Q8C23116yes—
146C3×C4×D4C2318yes—
147C3×#117C23116yes—
148C2×C3×C4⋊C4C2311yescharacteristic
149C2×C3×C4⋊C4C2312yes—
150C2×C3×C4⋊C4C2312yes—
151C2×C3×C4⋊C4C2311yescharacteristic
152C2×C3×C4⋊C4C2314yes—
153C2×C3×C4⋊C4C2312yes—
154C2×C3×C22⋊C4C2314yes—
155C2×C3×C22⋊C4C2312yes—
156C2×C3×C22⋊C4C2314yes—
157C2×C3×C42C2311yescharacteristic
158C2×C3×C42C2312yes—
159C2×C3×C42C2314yes—
160C2×#217C2312yes—
161C2×#217C2312yes—
162C2×#217C2312yes—
163C2×#217C2314yes—
164#946C23116yes—
165Q8×Dic3C23116yes—
166Q8×Dic3C23116yes—
167Q8×Dic3C2318yes—
168#944C23116yes—
169#944C23116yes—
170#938C2318yes—
171#936C2318yes—
172D4×Dic3C23116yes—
173C4×#67C23116yes—
174C2×(C2×D3)⋊C4C2312yes—
175C2×(C2×D3)⋊C4C2314yes—
176#926C23116yes—
177C2×C4⋊Dic3C2312yes—
178C2×C4⋊Dic3C2312yes—
179C2×C4⋊Dic3C2312yes—
180C2×C4⋊Dic3C2311yescharacteristic
181C2×C4⋊Dic3C2312yes—
182C2×C4⋊Dic3C2311yescharacteristic
183C2×C4⋊Dic3C2312yes—
184C2×C4⋊Dic3C2314yes—
185C2×C4⋊Dic3C2314yes—
186#924C23116yes—
187C2×Dic3⋊C4C2312yes—
188C2×Dic3⋊C4C2314yes—
189C2×Dic3⋊C4C2312yes—
190C2×Dic3⋊C4C2314yes—
191C2×Dic3⋊C4C2314yes—
192C2×Dic3⋊C4C2312yes—
193C2×Dic3⋊C4C2314yes—
194C2×Dic3⋊C4C2312yes—
195C2×Dic3⋊C4C2312yes—
196C2×Dic3⋊C4C2314yes—
197C2×Dic3⋊C4C2314yes—
198C2×Dic3⋊C4C2314yes—
199C2×C4×Dic3C2312yes—
200C2×C4×Dic3C2312yes—
201C2×C4×Dic3C2311yescharacteristic
202C2×C4×Dic3C2314yes—
203C2×C4×Dic3C2314yes—
204C2×C4×Dic3C2314yes—
205C2×C4×Dic3C2312yes—
206C2×C4×Dic3C2311yescharacteristic
207C2×C4×Dic3C2312yes—
208C2×C4×Dic3C2311yescharacteristic
209#897C23116yes—
210#897C2318yes—
211#896C23132yes—
212#892C23116yes—
213D3×C4⋊C4C23116yes—
214D3×C4⋊C4C2318yes—
215#890C23116yes—
216#890C23132yes—
217#890C23116yes—
218#890C2318yes—
219#889C23132yes—
220#889C23132yes—
221#889C23132yes—
222#888C23132yes—
223#888C23116yes—
224#887C23116yes—
225#887C23116yes—
226#887C23116yes—
227#887C2318yes—
228#887C23116yes—
229#883C23132yes—
230#883C23116yes—
231#67⋊C4C23132yes—
232#879C23132yes—
233#879C23132yes—
234#879C23132yes—
235#879C23116yes—
236#878C23132yes—
237#878C23132yes—
238#877C23132yes—
239#877C23132yes—
240#872C23132yes—
241C42×D3C23116yes—
242C42×D3C2318yes—
243#870C23116yes—
244#870C23132yes—
245#869C2318yes—
246C4×Dic6C23116yes—
247C4×Dic6C23116yes—
248C4×Dic6C23132yes—
249C4×Dic6C23132yes—
250C4×Dic6C2318yes—
251C4×Dic6C2318yes—
252C23×Q8—31no—
253C23×Q8—32no—
254#557—316no—
255#557—316no—
256#557—332no—
257#556—332no—
258#556C2×D3116yescomplemented
259#552—364no—
260#552—332no—
261D4×Q8—332no—
262D4×Q8—316no—
263#541—364no—
264#541—332no—
265#533—316no—
266#533—332no—
267C2×C4⋊Q8—32no—
268C2×C4⋊Q8—32no—
269C2×C4⋊Q8—32no—
270C2×C4⋊Q8—34no—
271C2×C4⋊Q8—31no—
272C2×C4⋊Q8C2×D311yescharacteristic
273#529—332no—
274#529—316no—
275C2×#126—34no—
276C2×#126—32no—
277C2×#126—34no—
278C2×#126—34no—
279C2×#126C2×D314yes—
280C2×#125—31no—
281C2×#125—34no—
282C2×#125—32no—
283C2×#125—34no—
284C2×#125—34no—
285C2×#125—34no—
286C2×#125—32no—
287C2×#125—32no—
288C2×#125—34no—
289C2×#124—31no—
290C2×#124C2×D312yes—
291C2×#123—32no—
292C2×#123—34no—
293C2×C22⋊Q8—32no—
294C2×C22⋊Q8—32no—
295C2×C22⋊Q8—31no—
296C2×C22⋊Q8—34no—
297C2×C22⋊Q8—32no—
298C2×C22⋊Q8—34no—
299C2×C22⋊Q8—34no—
300C2×C22⋊Q8C2×D312yes—
301C2×#121—31no—
302#519—332no—
303C2×C4×Q8—31no—
304C2×C4×Q8—32no—
305C2×C4×Q8—32no—
306C2×C4×Q8—316no—
307C2×C4×Q8—31no—
308C2×C4×Q8—32no—
309C2×C4×Q8—32no—
310C2×C4×Q8—32no—
311C2×C4×Q8—32no—
312C2×C4×Q8—31no—
313C2×C4×Q8—32no—
314C2×C4×Q8—34no—
315C2×C4×Q8—34no—
316C2×C4×Q8—31no—
317C2×C4×Q8—32no—
318C2×C4×Q8C2×D311yescharacteristic
319C2×C4×Q8C2×D312yes—
320C2×C4×D4—32no—
321C2×C4×D4—32no—
322C2×C4×D4—34no—
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×C42—31no—
334C24×C3C2412yes—
335C23×D3C2411yescharacteristic
336C2×C3×Q8—24no—
337C2×C3×Q8—28no—
338C2×C3×Q8C2414yes—
339C2×C3×Q8C2418yes—
340C2×C3×D4—24no—
341C2×C3×D4C2414yes—
342C22×C3×C4—28no—
343C22×C3×C4C2412yes—
344C22×C3×C4C2414yes—
345C22×C3×C4C2411yescharacteristic
346C22×C3×C4C2412yes—
347C22×C3×C4C2412yes—
348C22×C3×C4C2418yes—
349C22×C3×C4C2411yescharacteristic
350C22×C3×C4C2411yescharacteristic
351C2×#67—28no—
352C2×#67C2418yes—
353C22×Dic3—216no—
354C22×Dic3C24116yes—
355C22×Dic3C2411yescharacteristic
356C22×Dic3C2411yescharacteristic
357C22×Dic3C2412yes—
358C22×Dic3C2412yes—
359C22×Dic3C2412yes—
360C22×Dic3C2414yes—
361C22×Dic3C2411yescharacteristic
362C22×Dic3C2412yes—
363D3×Q8—232no—
364C2×C4×D3—28no—
365C2×C4×D3—24no—
366C2×C4×D3—24no—
367C2×C4×D3—24no—
368C2×C4×D3—28no—
369C2×C4×D3C2414yes—
370C2×C4×D3C2418yes—
371C2×C4×D3C2418yes—
372C2×C4×D3C2414yes—
373C2×C4×D3C2414yes—
374C2×Dic6—28no—
375C2×Dic6—24no—
376C2×Dic6—216no—
377C2×Dic6—28no—
378C2×Dic6—264no—
379C2×Dic6#4118yes—
380C2×Dic6C2414yes—
381C2×Dic6C24116yes—
382C2×Dic6C2418yes—
383C2×Dic6C2418yes—
384C2×Dic6C2414yes—
385C3×C4⋊C4C2414yes—
386C3×C4⋊C4C2418yes—
387C3×C4⋊C4C2418yes—
388C3×C4⋊C4C2414yes—
389C3×C4⋊C4C24116yes—
390C3×C4⋊C4C2418yes—
391C3×C22⋊C4C24116yes—
392C3×C22⋊C4C2418yes—
393C3×C22⋊C4C24116yes—
394C3×C42C2414yes—
395C3×C42C2418yes—
396C3×C42C24116yes—
397#217C2418yes—
398#217C2418yes—
399#217C2418yes—
400#217C24116yes—
401(C2×D3)⋊C4C2418yes—
402(C2×D3)⋊C4C24116yes—
403C4⋊Dic3C2418yes—
404C4⋊Dic3C2418yes—
405C4⋊Dic3C2418yes—
406C4⋊Dic3C2414yes—
407C4⋊Dic3C2418yes—
408C4⋊Dic3C2414yes—
409C4⋊Dic3C2418yes—
410C4⋊Dic3C24116yes—
411C4⋊Dic3C24116yes—
412Dic3⋊C4C2418yes—
413Dic3⋊C4C24116yes—
414Dic3⋊C4C2418yes—
415Dic3⋊C4C24116yes—
416Dic3⋊C4C24116yes—
417Dic3⋊C4C2418yes—
418Dic3⋊C4C24116yes—
419Dic3⋊C4C2418yes—
420Dic3⋊C4C2418yes—
421Dic3⋊C4C24116yes—
422Dic3⋊C4C24116yes—
423Dic3⋊C4C24116yes—
424C4×Dic3C2418yes—
425C4×Dic3C2418yes—
426C4×Dic3C2414yes—
427C4×Dic3C24116yes—
428C4×Dic3C24116yes—
429C4×Dic3C24116yes—
430C4×Dic3C2418yes—
431C4×Dic3C2414yes—
432C4×Dic3C2418yes—
433C4×Dic3C2414yes—
434C22×Q8—38no—
435C22×Q8—31no—
436C22×Q8—31no—
437C22×Q8—32no—
438C22×Q8—34no—
439C22×Q8—32no—
440C22×Q8—316no—
441C22×Q8—616no—
442C22×Q8—68no—
443C22×Q8C22×D312yes—
444C22×Q8C22×D311yescharacteristic
445C22×D4—32no—
446C22×D4C22×D311yescharacteristic
447C23×C4—34no—
448C23×C4—31no—
449C23×C4—32no—
450C23×C4—32no—
451C23×C4—31no—
452C23×C4—31no—
453C23×C4C22×D312yes—
454C4⋊Q8—316no—
455C4⋊Q8—316no—
456C4⋊Q8—316no—
457C4⋊Q8—332no—
458C4⋊Q8—38no—
459C4⋊Q8C22×D318yes—
460#126—332no—
461#126—316no—
462#126—332no—
463#126—332no—
464#126C22×D3132yes—
465#125—38no—
466#125—332no—
467#125—316no—
468#125—332no—
469#125—332no—
470#125—332no—
471#125—316no—
472#125—316no—
473#125—332no—
474#124—38no—
475#124C22×D3116yes—
476#123—316no—
477#123—332no—
478C22⋊Q8—316no—
479C22⋊Q8—316no—
480C22⋊Q8—38no—
481C22⋊Q8—332no—
482C22⋊Q8—316no—
483C22⋊Q8—332no—
484C22⋊Q8—332no—
485C22⋊Q8C22×D3116yes—
486#121—38no—
487C4×Q8—38no—
488C4×Q8—316no—
489C4×Q8—316no—
490C4×Q8—38no—
491C4×Q8—316no—
492C4×Q8—316no—
493C4×Q8—316no—
494C4×Q8—316no—
495C4×Q8—38no—
496C4×Q8—316no—
497C4×Q8—332no—
498C4×Q8—332no—
499C4×Q8—38no—
500C4×Q8—316no—
501C4×Q8C22×D318yes—
502C4×Q8C22×D3116yes—
503C4×D4—316no—
504C4×D4—316no—
505C4×D4—332no—
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—32no—
515C2×C4⋊C4—31no—
516C2×C4⋊C4—32no—
517C2×C4⋊C4—32no—
518C2×C4⋊C4—34no—
519C2×C4⋊C4—34no—
520C2×C4⋊C4—32no—
521C2×C4⋊C4—34no—
522C2×C4⋊C4—32no—
523C2×C4⋊C4—34no—
524C2×C4⋊C4—32no—
525C2×C4⋊C4—34no—
526C2×C4⋊C4—32no—
527C2×C4⋊C4—34no—
528C2×C4⋊C4—32no—
529C2×C4⋊C4—31no—
530C2×C4⋊C4—34no—
531C2×C4⋊C4—34no—
532C2×C4⋊C4—32no—
533C2×C4⋊C4—34no—
534C2×C4⋊C4—316no—
535C2×C4⋊C4—38no—
536C2×C4⋊C4C22×D311yescharacteristic
537C2×C4⋊C4C22×D312yes—
538C2×C4⋊C4C22×D312yes—
539C2×C4⋊C4C22×D312yes—
540C2×C4⋊C4C22×D311yescharacteristic
541C2×C4⋊C4C22×D314yes—
542C2×C22⋊C4—32no—
543C2×C22⋊C4—32no—
544C2×C22⋊C4—34no—
545C2×C22⋊C4—32no—
546C2×C22⋊C4—32no—
547C2×C22⋊C4—34no—
548C2×C22⋊C4C22×D314yes—
549C2×C22⋊C4C22×D314yes—
550C2×C22⋊C4C22×D312yes—
551C2×C42—32no—
552C2×C42—31no—
553C2×C42—34no—
554C2×C42—34no—
555C2×C42—34no—
556C2×C42—32no—
557C2×C42—32no—
558C2×C42—31no—
559C2×C42—32no—
560C2×C42—31no—
561C2×C42—316no—
562C2×C42—38no—
563C2×C42C22×D314yes—
564C2×C42C22×D311yescharacteristic
565C2×C42C22×D312yes—
566C23×C3—24no—
567C23×C3—24no—
568C23×C3—24no—
569C23×C3C2514yes—
570C23×C3C2511yescharacteristic
571C22×D3—22no—
572C22×D3—22no—
573C22×D32−1+414yes—
574C22×D3C2512yes—
575C3×Q8—28no—
576C3×Q8—216no—
577C3×D4—28no—
578C2×C3×C4—24no—
579C2×C3×C4—24no—
580C2×C3×C4—24no—
581C2×C3×C4—22no—
582C2×C3×C4—28no—
583C2×C3×C4—216no—
584C2×C3×C4C2×#4114yes—
585C2×C3×C42−1+414yes—
586C2×C3×C4C2514yes—
587C2×C3×C4C2518yes—
588C2×C3×C4C2512yes—
589C2×C3×C4C2514yes—
590C2×C3×C4C2514yes—
591C2×C3×C4C2512yes—
592C2×C3×C4C2512yes—
593#67—216no—
594C2×Dic3—22no—
595C2×Dic3—28no—
596C2×Dic3—24no—
597C2×Dic3—22no—
598C2×Dic3—22no—
599C2×Dic3—24no—
600C2×Dic3—24no—
601C2×Dic3—232no—
602C2×Dic3C2×#4118yes—
603C2×Dic3C2512yes—
604C2×Dic3C2512yes—
605C2×Dic3C2514yes—
606C2×Dic3C2514yes—
607C2×Dic3C2514yes—
608C2×Dic3C2518yes—
609C2×Dic3C2512yes—
610C2×Dic3C2514yes—
611C4×D3—216no—
612C4×D3—28no—
613C4×D3—28no—
614C4×D3—28no—
615C4×D3—216no—
616Dic6—216no—
617Dic6—28no—
618Dic6—232no—
619Dic6—216no—
620Dic6C2×#41116yes—
621C24—31no—
622C24C23×D312yes—
623C2×Q8—24no—
624C2×Q8—28no—
625C2×Q8—38no—
626C2×Q8—34no—
627C2×Q8—34no—
628C2×Q8—38no—
629C2×Q8—316no—
630C2×Q8—38no—
631C2×Q8—616no—
632C2×Q8—68no—
633C2×Q8—664no—
634C2×Q8—632no—
635C2×Q8—68no—
636C2×Q8—64no—
637C2×Q8C23×D318yes—
638C2×Q8C23×D314yes—
639C2×D4—24no—
640C2×D4—38no—
641C2×D4—68no—
642C2×D4C23×D314yes—
643C22×C4—28no—
644C22×C4—32no—
645C22×C4—316no—
646C22×C4—31no—
647C22×C4—31no—
648C22×C4—32no—
649C22×C4—32no—
650C22×C4—32no—
651C22×C4—34no—
652C22×C4—31no—
653C22×C4—34no—
654C22×C4—34no—
655C22×C4—38no—
656C22×C4—38no—
657C22×C4—34no—
658C22×C4—68no—
659C22×C4—68no—
660C22×C4—64no—
661C22×C4—616no—
662C22×C4—64no—
663C22×C4—64no—
664C22×C4C23×D318yes—
665C22×C4C23×D312yes—
666C22×C4C23×D314yes—
667C22×C4C23×D311yescharacteristic
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—316no—
679C4⋊C4—38no—
680C4⋊C4—316no—
681C4⋊C4—38no—
682C4⋊C4—316no—
683C4⋊C4—38no—
684C4⋊C4—316no—
685C4⋊C4—38no—
686C4⋊C4—316no—
687C4⋊C4—38no—
688C4⋊C4—34no—
689C4⋊C4—316no—
690C4⋊C4—316no—
691C4⋊C4—38no—
692C4⋊C4—316no—
693C4⋊C4C23×D314yes—
694C4⋊C4C23×D318yes—
695C4⋊C4C23×D318yes—
696C4⋊C4C23×D318yes—
697C4⋊C4C23×D314yes—
698C4⋊C4C23×D3116yes—
699C22⋊C4—38no—
700C22⋊C4—38no—
701C22⋊C4—316no—
702C22⋊C4—38no—
703C22⋊C4—38no—
704C22⋊C4—316no—
705C22⋊C4C23×D3116yes—
706C22⋊C4C23×D3116yes—
707C22⋊C4C23×D318yes—
708C42—38no—
709C42—34no—
710C42—38no—
711C42—34no—
712C42—38no—
713C42—34no—
714C42—316no—
715C42—316no—
716C42—316no—
717C42—38no—
718C42C23×D314yes—
719C42C23×D318yes—
720C42C23×D3116yes—
721C22×C3—24no—
722C22×C3—24no—
723C22×C3—24no—
724C22×C3—48no—
725C22×C3C22×#4112yes—
726C22×C3C2×2−1+412yes—
727C22×C3C2×2−1+412yes—
728C22×C3C2611yescharacteristic
729C2×D3—22no—
730C2×D3—22no—
731C2×D3—28no—
732C2×D3C2×2−1+414yes—
733C3×C4—24no—
734C3×C4—24no—
735C3×C4—24no—
736C3×C4—22no—
737C3×C4—28no—
738C3×C4C22×#4114yes—
739C3×C4C2×2−1+414yes—
740Dic3—22no—
741Dic3—28no—
742Dic3—24no—
743Dic3—22no—
744Dic3—22no—
745Dic3—24no—
746Dic3—24no—
747Dic3C22×#4118yes—
748C23—24no—
749C23—24no—
750C23—24no—
751C23—34no—
752C23—32no—
753C23—62no—
754C23—62no—
755C23C24×D314yes—
756C23C24×D311yescharacteristic
757Q8—28no—
758Q8—216no—
759Q8—316no—
760Q8—632no—
761Q8—616no—
762Q8—616no—
763Q8—68no—
764D4—28no—
765D4—616no—
766C2×C4—24no—
767C2×C4—24no—
768C2×C4—28no—
769C2×C4—24no—
770C2×C4—22no—
771C2×C4—216no—
772C2×C4—38no—
773C2×C4—34no—
774C2×C4—32no—
775C2×C4—32no—
776C2×C4—34no—
777C2×C4—34no—
778C2×C4—34no—
779C2×C4—32no—
780C2×C4—38no—
781C2×C4—616no—
782C2×C4—616no—
783C2×C4—68no—
784C2×C4—632no—
785C2×C4—68no—
786C2×C4—62no—
787C2×C4—62no—
788C2×C4—64no—
789C2×C4—62no—
790C2×C4—64no—
791C2×C4—64no—
792C2×C4—68no—
793C2×C4—68no—
794C2×C4D3×#4114yes—
795C2×C4#101014yes—
796C2×C4C24×D314yes—
797C2×C4C24×D318yes—
798C2×C4C24×D312yes—
799C2×C4C24×D314yes—
800C2×C4C24×D314yes—
801C2×C4C24×D312yes—
802C2×C4C24×D312yes—
803C2×C3—44no—
804C2×C3#352314yescomplemented
805C2×C3C23×#4111yescharacteristic
806C2×C3C22×2−1+411yescharacteristic
807C2×C3C22×2−1+411yescharacteristic
808D3—24no—
809C22—24no—
810C22—24no—
811C22—24no—
812C22—34no—
813C22—48no—
814C22—62no—
815C22—62no—
816C22—68no—
817C22C2×D3×#4112yes—
818C22C2×#101012yes—
819C22D3×2−1+412yes—
820C22C25×D311yescharacteristic
821C4—28no—
822C4—24no—
823C4—24no—
824C4—24no—
825C4—22no—
826C4—38no—
827C4—62no—
828C4—64no—
829C4—68no—
830C4—62no—
831C4—62no—
832C4—64no—
833C4—64no—
834C4C2×D3×#4114yes—
835C4C2×#101014yes—
836C3C2×#352311yescharacteristic, complemented, Sylow
837C2—44no—
838C2—64no—
839C2#8699314yesdirect product factor
840C2C22×#101011yescharacteristic
841C2C22×D3×#4111yescharacteristic
842C2C2×D3×2−1+411yescharacteristic
subgroupG/H
centerC23C24×D3
commutator, cosocleC22×C3C26
FrattiniC22C25×D3
FittingC2×C3×#556C2
socleC23×C3C25
prime radicalC2×#938C22
hypercenterC2×#556D3
hypocenterC3C2×#3523
LCSG ▷ C22×C3 ▷ C3
UCSC1 ◁ C23 ◁ C2×#556

Complements

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

NH ≅ G/Ntype
1. C2×C3×#556C2semidirect
2. #86993C2direct (N × H)
3. C2×#5721C2semidirect
4. C2×#5728C2semidirect
5. C2×#5708C2semidirect
6. C2×#5701C2semidirect
7. C2×#5671C2semidirect
9. C2×#5632C2semidirect
10. C2×#5625C2semidirect
11. C2×#5578C2semidirect
12. C2×C4×D3×Q8C2semidirect
13. C2×#5569C2semidirect
14. C2×#5567C2semidirect
16. C2×D4×Dic6C2semidirect
17. C2×#5529C2semidirect
18. C2×#5516C2semidirect
22. C3×#556C22semidirect
43. #5728C22semidirect
44. #5721C22semidirect
45. #5708C22semidirect
46. #5701C22semidirect
48. #5671C22semidirect
49. #5632C22semidirect
50. #5625C22semidirect
51. #5578C22semidirect
52. C4×D3×Q8C22semidirect
53. #5569C22semidirect
54. #5567C22semidirect
56. D4×Dic6C22semidirect
57. #5529C22semidirect
58. #5516C22semidirect
107. C2×#556D3semidirect
258. #556C2×D3semidirect
804. C2×C3#3523semidirect
836. C3C2×#3523semidirect
839. C2#86993direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C3×#5562
#869932
C2×#57212
C2×#57282
C2×#57082
C2×#57012
C2×#56712
C2×#56802
C2×#56322
C2×#56252
C2×#55782
C2×C4×D3×Q82
C2×#55692
C2×#55672
C2×#55572
C2×D4×Dic62
C2×#55292
C2×#55162
C2×#35233