Finite Group Databasebeta

← C2×#86128 #11703392

Subgroups — C2×#86128 #11703392

Order 768.

7758 conjugacy classes of subgroups.

The subgroup lattice has 896 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#529C211yesmaximal, characteristic, complemented
2#86128C2132yesmaximal, direct product factor
3C2×#5710C214yesmaximal, complemented
4C2×#5690C212yesmaximal, complemented
5C2×#5681C212yesmaximal, complemented
6C2×#5655C214yesmaximal, complemented
7C2×#5624C212yesmaximal, complemented
8C2×#5596C212yesmaximal, complemented
9C2×#5585C211yesmaximal, characteristic, complemented
10C2×Q8×Dic6C211yesmaximal, characteristic, complemented
11C2×#5543C211yesmaximal, characteristic, complemented
12C2×#5553C211yesmaximal, characteristic, complemented
13C2×#5552C212yesmaximal, complemented
14C2×#5555C212yesmaximal, complemented
15C2×#5534C212yesmaximal, complemented
16C2×#5523C212yesmaximal, complemented
17C2×#5477C211yesmaximal, characteristic, complemented
18C22×C4×Dic6C211yesmaximal, characteristic, complemented
19C2×#3522—31nomaximal, Sylow
20C22×#237C2214yes—
21C22×#235C2212yes—
22C22×#235C2212yes—
23C23×Dic6C2211yescharacteristic
24C3×#529C22116yescomplemented
25C2×C3×#126C2212yes—
26C2×C3×#125C2211yescharacteristic
27C2×C3×#124C2211yescharacteristic
28C2×C3×#123C2212yes—
29C2×C3×C22⋊Q8C2211yescharacteristic
30C2×C3×#121C2211yescharacteristic
31C2×C3×C4×Q8C2211yescharacteristic
32C2×C3×C4×D4C2211yescharacteristic
33C2×C3×C4×D4C2212yes—
34C2×C3×#117C2212yes—
35C22×C3×C42C2211yescharacteristic
36C2×#947C2212yes—
37C2×Q8×Dic3C2212yes—
38C2×#940C2212yes—
39C2×#939C2214yes—
40C2×D4×Dic3C2212yes—
41C2×#930C2212yes—
42C2×#930C2212yes—
43C2×#930C2212yes—
44C22×C4⋊Dic3C2212yes—
45C22×C4⋊Dic3C2211yescharacteristic
46C2×#924C2212yes—
47C22×Dic3⋊C4C2212yes—
48C22×C4×Dic3C2212yes—
49#5710C22164yescomplemented
50#5690C22132yescomplemented
51#5681C22132yescomplemented
52#5655C22164yescomplemented
53#5624C22132yescomplemented
54#5596C22132yescomplemented
55#5585C22116yescomplemented
56Q8×Dic6C22116yescomplemented
57#5555C22132yescomplemented
58#5553C22116yescomplemented
59#5552C22132yescomplemented
60#5543C22116yescomplemented
61#5534C22132yescomplemented
62#5523C22132yescomplemented
63C2×#898C2214yes—
64C2×#897C2214yes—
65C2×#896C2214yes—
66C2×#896C2214yes—
67C2×#894C2214yes—
68C2×#893C2212yes—
69C2×#893C2212yes—
70C2×#892C2214yes—
71C2×D3×C4⋊C4C2214yes—
72C2×#890C2212yes—
73C2×#888C2212yes—
74C2×#888C2214yes—
75C2×#886C2214yes—
76C2×#886C2214yes—
77C2×#885C2214yes—
78C2×#885C2214yes—
79C2×#884C2214yes—
80C2×#883C2214yes—
81C2×#67⋊C4C2214yes—
82C2×#67⋊C4C2214yes—
83C2×#67⋊C4C2214yes—
84C2×#878C2214yes—
85#5477C22116yescomplemented
86C2×#875C2212yes—
87C2×#875C2212yes—
88C2×#874C2211yescharacteristic
89C2×C4×D12C2212yes—
90C2×C4×D12C2212yes—
91C2×C4×D12C2212yes—
92C2×#869C2211yescharacteristic
93C2×#869C2212yes—
94C2×C4×Dic6C2211yescharacteristic
95C2×C4×Dic6C2211yescharacteristic
96C2×C4×Dic6C2212yes—
97C2×C4×Dic6C2212yes—
98C2×C4×Dic6C2212yes—
99C2×C4×Dic6C2211yescharacteristic
100C2×C4×Dic6C2211yescharacteristic
101C2×C4×Dic6C22116yescomplemented
102#3522—332no—
103C2×#559—32no—
104C2×#559—31no—
105C2×Q82—31no—
106C2×#554—32no—
107C2×#554—31no—
108C2×#550—31no—
109C2×#548—32no—
110C2×#547—34no—
111C2×#547—32no—
112C2×#542—34no—
113C2×#542—32no—
114C2×#532—31no—
115C2×#532—32no—
116C2×#529—32no—
117C2×#529D311yescharacteristic, complemented
118C2×#520—32no—
119C22×C4×Q8—31no—
120C22×C3×Q8C2311yescharacteristic
121C22×C3×D4C2312yes—
122C22×C3×D4C2311yescharacteristic
123C23×C3×C4C2311yescharacteristic
124C23×C3×C4C2311yescharacteristic
125C23×C3×C4C2312yes—
126C23×C3×C4C2311yescharacteristic
127C22×#67C2314yes—
128C22×#67C2314yes—
129C22×#67C2314yes—
130C23×Dic3C2312yes—
131C23×Dic3C2312yes—
132C23×Dic3C2314yes—
133C2×#237—416no—
134C2×#237C23132yes—
135C2×#235—216no—
136C2×#235—48no—
137C2×#235C23116yes—
138C2×#235C23116yes—
139C22×D12C2312yes—
140C22×D12C2312yes—
141C22×D12C2312yes—
142C22×C4×D3C2314yes—
143C22×C4×D3C2314yes—
144C22×C4×D3C2314yes—
145C22×Dic6—28no—
146C22×Dic6C2311yescharacteristic
147C22×Dic6C2312yes—
148C22×Dic6C2318yes—
149C22×Dic6C2312yes—
150C22×Dic6C2314yes—
151C22×Dic6C2311yescharacteristic
152C3×#126C23116yes—
153C3×#125C2318yes—
154C3×#124C2318yes—
155C3×#123C23116yes—
156C3×C22⋊Q8C2318yes—
157C3×#121C2318yes—
158C3×C4×Q8C2318yes—
159C3×C4×D4C2318yes—
160C3×C4×D4C23116yes—
161C3×#117C23116yes—
162C2×C3×C4⋊C4C2311yescharacteristic
163C2×C3×C4⋊C4C2312yes—
164C2×C3×C4⋊C4C2311yescharacteristic
165C2×C3×C4⋊C4C2312yes—
166C2×C3×C4⋊C4C2312yes—
167C2×C3×C4⋊C4C2312yes—
168C2×C3×C22⋊C4C2312yes—
169C2×C3×C22⋊C4C2312yes—
170C2×C3×C22⋊C4C2312yes—
171C2×C3×C22⋊C4C2312yes—
172C2×C3×C22⋊C4C2312yes—
173C2×C3×C42C2311yescharacteristic
174C2×C3×C42C2311yescharacteristic
175C2×C3×C42C2311yescharacteristic
176C2×C3×C42C2311yescharacteristic
177C2×C3×C42C2312yes—
178C2×C3×C42C2318yes—
179C2×#217C2314yes—
180#947C23116yes—
181Q8×Dic3C23116yes—
182#940C23116yes—
183#939C23132yes—
184D4×Dic3C23116yes—
185#930C23116yes—
186#930C23116yes—
187#930C23116yes—
188C2×(C2×D3)⋊C4C2314yes—
189C2×(C2×D3)⋊C4C2314yes—
190C2×(C2×D3)⋊C4C2314yes—
191C2×(C2×D3)⋊C4C2314yes—
192C2×(C2×D3)⋊C4C2314yes—
193C2×(C2×D3)⋊C4C2314yes—
194C2×C4⋊Dic3C2311yescharacteristic
195C2×C4⋊Dic3C2311yescharacteristic
196C2×C4⋊Dic3C2312yes—
197C2×C4⋊Dic3C2312yes—
198C2×C4⋊Dic3C2318yes—
199C2×C4⋊Dic3C2312yes—
200C2×C4⋊Dic3C2314yes—
201C2×C4⋊Dic3C2314yes—
202C2×C4⋊Dic3C23116yes—
203#924C23116yes—
204C2×Dic3⋊C4C23116yes—
205C2×Dic3⋊C4C2312yes—
206C2×Dic3⋊C4C2312yes—
207C2×Dic3⋊C4C2312yes—
208C2×Dic3⋊C4C2312yes—
209C2×Dic3⋊C4C2314yes—
210C2×Dic3⋊C4C2314yes—
211C2×C4×Dic3C2312yes—
212C2×C4×Dic3C2312yes—
213C2×C4×Dic3C2312yes—
214C2×C4×Dic3C2312yes—
215C2×C4×Dic3C2314yes—
216C2×C4×Dic3C23116yes—
217#898C23132yes—
218#897C23132yes—
219#896C23132yes—
220#896C23132yes—
221#894C23132yes—
222#893C23116yes—
223#893C23116yes—
224#892C23132yes—
225D3×C4⋊C4C23132yes—
226#890C23116yes—
227#888C23132yes—
228#888C23116yes—
229#886C23132yes—
230#886C23132yes—
231#885C23132yes—
232#885C23132yes—
233#884C23132yes—
234#883C23132yes—
235#67⋊C4C23132yes—
236#67⋊C4C23132yes—
237#67⋊C4C23132yes—
238#878C23132yes—
239#875C23116yes—
240#875C23116yes—
241#874C2318yes—
242C4×D12C23116yes—
243C4×D12C23116yes—
244C4×D12C23116yes—
245#869C2318yes—
246#869C23116yes—
247C4×Dic6C23116yes—
248C4×Dic6C23116yes—
249C4×Dic6C2318yes—
250C4×Dic6C2318yes—
251C4×Dic6C2318yes—
252C4×Dic6C2318yes—
253C4×Dic6C23116yes—
254C22×#41—34no—
255C22×#41—32no—
256C22×#41—32no—
257C23×Q8—31no—
258#559—332no—
259#559—316no—
260Q82—316no—
261#554—332no—
262#554—316no—
263#550—316no—
264#548—332no—
265#547—364no—
266#547—332no—
267#542—364no—
268#542—332no—
269#532—332no—
270#532—316no—
271C2×C4⋊Q8—32no—
272C2×C4⋊Q8—34no—
273C2×C4⋊Q8—31no—
274C2×C4⋊Q8—32no—
275C2×#127—32no—
276C2×#127—31no—
277#529—332no—
278#529C2×D3116yescomplemented
279C2×#126—34no—
280C2×#126C2×D312yes—
281C2×#125—32no—
282C2×#125C2×D311yescharacteristic
283C2×#124—32no—
284C2×#124—34no—
285C2×#124—34no—
286C2×#124—32no—
287C2×#124—32no—
288C2×#124C2×D311yescharacteristic
289C2×#123—34no—
290C2×#123—34no—
291C2×#123—34no—
292C2×#123—34no—
293C2×#123C2×D312yes—
294C2×C22⋊Q8—32no—
295C2×C22⋊Q8—34no—
296C2×C22⋊Q8—34no—
297C2×C22⋊Q8—34no—
298C2×C22⋊Q8—34no—
299C2×C22⋊Q8C2×D311yescharacteristic
300C2×#121—34no—
301C2×#121—32no—
302C2×#121—32no—
303C2×#121—32no—
304C2×#121—34no—
305C2×#121C2×D311yescharacteristic
306#520—332no—
307C2×C4×Q8—32no—
308C2×C4×Q8—31no—
309C2×C4×Q8—32no—
310C2×C4×Q8—31no—
311C2×C4×Q8—31no—
312C2×C4×Q8—31no—
313C2×C4×Q8—32no—
314C2×C4×Q8—32no—
315C2×C4×Q8—316no—
316C2×C4×Q8C2×D311yescharacteristic
317C2×C4×D4—32no—
318C2×C4×D4—32no—
319C2×C4×D4—32no—
320C2×C4×D4—34no—
321C2×C4×D4—34no—
322C2×C4×D4—34no—
323C2×C4×D4—32no—
324C2×C4×D4—32no—
325C2×C4×D4—32no—
326C2×C4×D4C2×D312yes—
327C2×C4×D4C2×D311yescharacteristic
328C2×#117—34no—
329C2×#117C2×D312yes—
330C22×C4⋊C4—32no—
331C22×C4⋊C4—31no—
332C22×C4⋊C4—32no—
333C22×C4⋊C4—34no—
334C22×C42—32no—
335C22×C42C2×D311yescharacteristic
336C24×C3C2412yes—
337C24×C3C2411yescharacteristic
338C23×D3C2414yes—
339C2×C3×Q8—24no—
340C2×C3×Q8C2414yes—
341C2×C3×D4—28no—
342C2×C3×D4—24no—
343C2×C3×D4C2414yes—
344C2×C3×D4C2418yes—
345C22×C3×C4—24no—
346C22×C3×C4—24no—
347C22×C3×C4—28no—
348C22×C3×C4—24no—
349C22×C3×C4C2411yescharacteristic
350C22×C3×C4C2414yes—
351C22×C3×C4C2412yes—
352C22×C3×C4C2411yescharacteristic
353C22×C3×C4C2411yescharacteristic
354C22×C3×C4C2414yes—
355C22×C3×C4C2412yes—
356C22×C3×C4C2412yes—
357C22×C3×C4C2418yes—
358C22×C3×C4C2411yescharacteristic
359C22×C3×C4C2414yes—
360C22×C3×C4C2411yescharacteristic
361C22×C3×C4C2411yescharacteristic
362C2×#67—216no—
363C2×#67—216no—
364C2×#67—48no—
365C2×#67C24116yes—
366C2×#67C24116yes—
367C2×#67C24116yes—
368C22×Dic3—28no—
369C22×Dic3—28no—
370C22×Dic3—48no—
371C22×Dic3C2418yes—
372C22×Dic3C2418yes—
373C22×Dic3C2412yes—
374C22×Dic3C2412yes—
375C22×Dic3C2412yes—
376C22×Dic3C2414yes—
377C22×Dic3C24116yes—
378C22×Dic3C2412yes—
379#237—464no—
380#235—264no—
381#235—432no—
382C2×D12—28no—
383C2×D12—28no—
384C2×D12—44no—
385C2×D12C2418yes—
386C2×D12C2418yes—
387C2×D12C2418yes—
388C2×C4×D3—216no—
389C2×C4×D3—48no—
390C2×C4×D3—48no—
391C2×C4×D3C24116yes—
392C2×C4×D3C24116yes—
393C2×C4×D3C24116yes—
394C2×Dic6—24no—
395C2×Dic6—28no—
396C2×Dic6—232no—
397C2×Dic6—44no—
398C2×Dic6—48no—
399C2×Dic6#4118yescomplemented
400C2×Dic6C2414yes—
401C2×Dic6C2418yes—
402C2×Dic6C2418yes—
403C2×Dic6C24116yes—
404C2×Dic6C2414yes—
405C3×C4⋊C4C2414yes—
406C3×C4⋊C4C2418yes—
407C3×C4⋊C4C2414yes—
408C3×C4⋊C4C2418yes—
409C3×C4⋊C4C2418yes—
410C3×C4⋊C4C2418yes—
411C3×C22⋊C4C2418yes—
412C3×C22⋊C4C2418yes—
413C3×C22⋊C4C2418yes—
414C3×C22⋊C4C2418yes—
415C3×C22⋊C4C2418yes—
416C3×C42C2414yes—
417C3×C42C2414yes—
418C3×C42C2414yes—
419C3×C42C2414yes—
420C3×C42C2418yes—
421#217C24116yes—
422(C2×D3)⋊C4C24116yes—
423(C2×D3)⋊C4C24116yes—
424(C2×D3)⋊C4C24116yes—
425(C2×D3)⋊C4C24116yes—
426(C2×D3)⋊C4C24116yes—
427(C2×D3)⋊C4C24116yes—
428C4⋊Dic3C2414yes—
429C4⋊Dic3C2414yes—
430C4⋊Dic3C2418yes—
431C4⋊Dic3C2418yes—
432C4⋊Dic3C2418yes—
433C4⋊Dic3C24116yes—
434C4⋊Dic3C24116yes—
435Dic3⋊C4C2418yes—
436Dic3⋊C4C2418yes—
437Dic3⋊C4C2418yes—
438Dic3⋊C4C2418yes—
439Dic3⋊C4C24116yes—
440Dic3⋊C4C24116yes—
441C4×Dic3C2418yes—
442C4×Dic3C2418yes—
443C4×Dic3C2418yes—
444C4×Dic3C2418yes—
445C4×Dic3C24116yes—
446C2×#41—332no—
447C2×#41—316no—
448C2×#41—316no—
449C2×#41—616no—
450C2×#41—128no—
451C2×#41—1216no—
452C22×Q8—31no—
453C22×Q8—32no—
454C22×Q8—31no—
455C22×Q8—38no—
456C22×Q8—34no—
457C22×Q8—32no—
458C22×Q8—68no—
459C22×Q8C22×D311yescharacteristic
460C22×D4—34no—
461C22×D4—34no—
462C22×D4—34no—
463C22×D4—32no—
464C22×D4—32no—
465C22×D4—32no—
466C22×D4C22×D311yescharacteristic
467C22×D4C22×D312yes—
468C23×C4—32no—
469C23×C4—32no—
470C23×C4—34no—
471C23×C4—34no—
472C23×C4—34no—
473C23×C4—34no—
474C23×C4C22×D311yescharacteristic
475C23×C4C22×D312yes—
476C23×C4C22×D311yescharacteristic
477C23×C4C22×D311yescharacteristic
478C4⋊Q8—316no—
479C4⋊Q8—332no—
480C4⋊Q8—38no—
481C4⋊Q8—316no—
482#127—316no—
483#127—38no—
484#126—332no—
485#126C22×D3116yes—
486#125—316no—
487#125C22×D318yes—
488#124—316no—
489#124—332no—
490#124—332no—
491#124—316no—
492#124—316no—
493#124C22×D318yes—
494#123—332no—
495#123—332no—
496#123—332no—
497#123—332no—
498#123C22×D3116yes—
499C22⋊Q8—316no—
500C22⋊Q8—332no—
501C22⋊Q8—332no—
502C22⋊Q8—332no—
503C22⋊Q8—332no—
504C22⋊Q8C22×D318yes—
505#121—332no—
506#121—316no—
507#121—316no—
508#121—316no—
509#121—332no—
510#121C22×D318yes—
511C4×Q8—316no—
512C4×Q8—38no—
513C4×Q8—316no—
514C4×Q8—38no—
515C4×Q8—38no—
516C4×Q8—38no—
517C4×Q8—316no—
518C4×Q8—316no—
519C4×Q8C22×D318yes—
520C4×D4—316no—
521C4×D4—316no—
522C4×D4—316no—
523C4×D4—332no—
524C4×D4—332no—
525C4×D4—332no—
526C4×D4—316no—
527C4×D4—316no—
528C4×D4—316no—
529C4×D4C22×D3116yes—
530C4×D4C22×D318yes—
531#117—332no—
532#117C22×D3116yes—
533C2×C4⋊C4—32no—
534C2×C4⋊C4—31no—
535C2×C4⋊C4—34no—
536C2×C4⋊C4—34no—
537C2×C4⋊C4—32no—
538C2×C4⋊C4—32no—
539C2×C4⋊C4—31no—
540C2×C4⋊C4—32no—
541C2×C4⋊C4—32no—
542C2×C4⋊C4—32no—
543C2×C4⋊C4—316no—
544C2×C4⋊C4—38no—
545C2×C4⋊C4—316no—
546C2×C4⋊C4—32no—
547C2×C4⋊C4—34no—
548C2×C4⋊C4—34no—
549C2×C4⋊C4—332no—
550C2×C4⋊C4C22×D312yes—
551C2×C4⋊C4C22×D312yes—
552C2×C4⋊C4C22×D311yescharacteristic
553C2×C4⋊C4C22×D311yescharacteristic
554C2×C4⋊C4C22×D312yes—
555C2×C4⋊C4C22×D312yes—
556C2×C22⋊C4—34no—
557C2×C22⋊C4—34no—
558C2×C22⋊C4—34no—
559C2×C22⋊C4—34no—
560C2×C22⋊C4—34no—
561C2×C22⋊C4—34no—
562C2×C22⋊C4—34no—
563C2×C22⋊C4C22×D312yes—
564C2×C22⋊C4C22×D312yes—
565C2×C22⋊C4C22×D312yes—
566C2×C22⋊C4C22×D312yes—
567C2×C22⋊C4C22×D312yes—
568C2×C42—32no—
569C2×C42—34no—
570C2×C42—32no—
571C2×C42—32no—
572C2×C42—32no—
573C2×C42—316no—
574C2×C42C22×D311yescharacteristic
575C2×C42C22×D312yes—
576C2×C42C22×D311yescharacteristic
577C2×C42C22×D311yescharacteristic
578C2×C42C22×D311yescharacteristic
579C2×C42C22×D318yes—
580C23×C3—22no—
581C23×C3—22no—
582C23×C3—24no—
583C23×C3—24no—
584C23×C3—24no—
585C23×C3H(5,𝔽2)14yes—
586C23×C3C2514yes—
587C23×C3C2512yes—
588C23×C3C2511yescharacteristic
589C22×D3—28no—
590C22×D3—28no—
591C22×D3—28no—
592C22×D3C2518yes—
593C3×Q8—28no—
594C3×D4—216no—
595C3×D4—28no—
596C2×C3×C4—22no—
597C2×C3×C4—24no—
598C2×C3×C4—24no—
599C2×C3×C4—22no—
600C2×C3×C4—22no—
601C2×C3×C4—28no—
602C2×C3×C4—22no—
603C2×C3×C4—24no—
604C2×C3×C4—28no—
605C2×C3×C4—216no—
606C2×C3×C4—28no—
607C2×C3×C4C2×#4114yes—
608C2×C3×C42−1+414yes—
609C2×C3×C4C2512yes—
610C2×C3×C4C2514yes—
611C2×C3×C4C2512yes—
612C2×C3×C4C2512yes—
613C2×C3×C4C2514yes—
614C2×C3×C4C2514yes—
615C2×C3×C4C2512yes—
616C2×C3×C4C2512yes—
617C2×C3×C4C2512yes—
618#67—232no—
619#67—232no—
620#67—416no—
621C2×Dic3—24no—
622C2×Dic3—28no—
623C2×Dic3—24no—
624C2×Dic3—24no—
625C2×Dic3—216no—
626C2×Dic3—216no—
627C2×Dic3—416no—
628C2×Dic3C2×#4118yes—
629C2×Dic3C2514yes—
630C2×Dic3C2514yes—
631C2×Dic3C2514yes—
632C2×Dic3C2518yes—
633C2×Dic3C2514yes—
634D12—216no—
635D12—216no—
636D12—48no—
637C4×D3—232no—
638C4×D3—416no—
639C4×D3—416no—
640Dic6—28no—
641Dic6—216no—
642Dic6—48no—
643Dic6—416no—
644Dic6C2×#41116yescomplemented
645C24—34no—
646C24C23×D312yes—
647C24C23×D311yescharacteristic
648#41—664no—
649#41—1232no—
650#41—1264no—
651C2×Q8—24no—
652C2×Q8—38no—
653C2×Q8—34no—
654C2×Q8—38no—
655C2×Q8—34no—
656C2×Q8—316no—
657C2×Q8—38no—
658C2×Q8—68no—
659C2×Q8—632no—
660C2×Q8—64no—
661C2×Q8—124no—
662C2×Q8—128no—
663C2×Q8C23×D314yes—
664C2×D4—28no—
665C2×D4—24no—
666C2×D4—316no—
667C2×D4—316no—
668C2×D4—316no—
669C2×D4—38no—
670C2×D4—38no—
671C2×D4—38no—
672C2×D4—616no—
673C2×D4—616no—
674C2×D4—68no—
675C2×D4—68no—
676C2×D4—124no—
677C2×D4—128no—
678C2×D4C23×D314yes—
679C2×D4C23×D318yes—
680C22×C4—24no—
681C22×C4—24no—
682C22×C4—28no—
683C22×C4—24no—
684C22×C4—32no—
685C22×C4—38no—
686C22×C4—38no—
687C22×C4—32no—
688C22×C4—32no—
689C22×C4—32no—
690C22×C4—34no—
691C22×C4—316no—
692C22×C4—316no—
693C22×C4—316no—
694C22×C4—316no—
695C22×C4—616no—
696C22×C4—68no—
697C22×C4—68no—
698C22×C4—128no—
699C22×C4—128no—
700C22×C4—128no—
701C22×C4C23×D314yes—
702C22×C4C23×D314yes—
703C22×C4C23×D314yes—
704C22×C4C23×D318yes—
705C22×C4C23×D311yescharacteristic
706C22×C4C23×D312yes—
707C22×C4C23×D311yescharacteristic
708C22×C4C23×D311yescharacteristic
709C22×C4C23×D311yescharacteristic
710C22×C4C23×D312yes—
711C22×C4C23×D312yes—
712C22×C4C23×D311yescharacteristic
713C22×C4C23×D311yescharacteristic
714C4⋊C4—38no—
715C4⋊C4—34no—
716C4⋊C4—316no—
717C4⋊C4—316no—
718C4⋊C4—38no—
719C4⋊C4—38no—
720C4⋊C4—34no—
721C4⋊C4—38no—
722C4⋊C4—38no—
723C4⋊C4—38no—
724C4⋊C4—38no—
725C4⋊C4—316no—
726C4⋊C4—316no—
727C4⋊C4C23×D318yes—
728C4⋊C4C23×D318yes—
729C4⋊C4C23×D314yes—
730C4⋊C4C23×D314yes—
731C4⋊C4C23×D318yes—
732C4⋊C4C23×D318yes—
733C22⋊C4—316no—
734C22⋊C4—316no—
735C22⋊C4—316no—
736C22⋊C4—316no—
737C22⋊C4—316no—
738C22⋊C4—316no—
739C22⋊C4—316no—
740C22⋊C4C23×D318yes—
741C22⋊C4C23×D318yes—
742C22⋊C4C23×D318yes—
743C22⋊C4C23×D318yes—
744C22⋊C4C23×D318yes—
745C42—38no—
746C42—38no—
747C42—38no—
748C42—38no—
749C42—316no—
750C42C23×D314yes—
751C42C23×D314yes—
752C42C23×D314yes—
753C42C23×D314yes—
754C42C23×D318yes—
755C22×C3—22no—
756C22×C3—22no—
757C22×C3—28no—
758C22×C3—24no—
759C22×C3—24no—
760C22×C3—24no—
761C22×C3—48no—
762C22×C3C22×#4112yes—
763C22×C3C2×H(5,𝔽2)14yes—
764C22×C3C2×H(5,𝔽2)12yes—
765C22×C3C2×2−1+412yes—
766C22×C3C2611yescharacteristic
767C2×D3—28no—
768C2×D3—28no—
769C2×D3—28no—
770C2×D3—416no—
771C3×C4—22no—
772C3×C4—24no—
773C3×C4—24no—
774C3×C4—22no—
775C3×C4—22no—
776C3×C4—22no—
777C3×C4—24no—
778C3×C4C22×#4114yes—
779C3×C4C2×2−1+414yes—
780Dic3—24no—
781Dic3—28no—
782Dic3—24no—
783Dic3—24no—
784Dic3C22×#4118yes—
785C23—22no—
786C23—22no—
787C23—24no—
788C23—24no—
789C23—24no—
790C23—38no—
791C23—68no—
792C23—68no—
793C23—68no—
794C23#100914yes—
795C23C24×D314yes—
796C23C24×D312yes—
797C23C24×D311yescharacteristic
798Q8—28no—
799Q8—316no—
800Q8—616no—
801Q8—68no—
802Q8—128no—
803Q8—1216no—
804D4—216no—
805D4—28no—
806D4—632no—
807D4—632no—
808D4—616no—
809D4—616no—
810D4—128no—
811D4—1216no—
812C2×C4—24no—
813C2×C4—22no—
814C2×C4—22no—
815C2×C4—22no—
816C2×C4—28no—
817C2×C4—24no—
818C2×C4—22no—
819C2×C4—24no—
820C2×C4—28no—
821C2×C4—216no—
822C2×C4—28no—
823C2×C4—38no—
824C2×C4—34no—
825C2×C4—34no—
826C2×C4—34no—
827C2×C4—34no—
828C2×C4—38no—
829C2×C4—632no—
830C2×C4—616no—
831C2×C4—64no—
832C2×C4—64no—
833C2×C4—64no—
834C2×C4—616no—
835C2×C4—68no—
836C2×C4—1216no—
837C2×C4—1216no—
838C2×C4—1216no—
839C2×C4D3×#4114yes—
840C2×C4#101014yes—
841C2×C4C24×D312yes—
842C2×C4C24×D314yes—
843C2×C4C24×D312yes—
844C2×C4C24×D312yes—
845C2×C4C24×D312yes—
846C2×C4C24×D314yes—
847C2×C4C24×D314yes—
848C2×C4C24×D312yes—
849C2×C4C24×D312yes—
850C2×C3—24no—
851C2×C3—44no—
852C2×C3#352214yescomplemented
853C2×C3C23×#4111yescharacteristic
854C2×C3C22×H(5,𝔽2)11yescharacteristic
855C2×C3C22×2−1+411yescharacteristic
856D3—48no—
857C22—22no—
858C22—22no—
859C22—28no—
860C22—24no—
861C22—24no—
862C22—24no—
863C22—48no—
864C22—68no—
865C22—68no—
866C22—68no—
867C22—1216no—
868C22C2×D3×#4112yes—
869C22C2×#100914yes—
870C22C2×#100912yes—
871C22C2×#101012yes—
872C22C25×D311yescharacteristic
873C4—22no—
874C4—24no—
875C4—24no—
876C4—22no—
877C4—22no—
878C4—22no—
879C4—24no—
880C4—38no—
881C4—64no—
882C4—64no—
883C4—64no—
884C4—68no—
885C4C2×D3×#4114yes—
886C4C2×#101014yes—
887C3C2×#352211yescharacteristic, complemented, Sylow
888C2—24no—
889C2—44no—
890C2—128no—
891C2#8612814yesdirect product factor
892C2C22×#101011yescharacteristic
893C2C22×D3×#4111yescharacteristic
894C2C22×#100911yescharacteristic
subgroupG/H
centerC23C24×D3
commutator, cosocleC22×C3C26
FrattiniC22C25×D3
FittingC2×C3×#529C2
socleC23×C3C25
hypercenterC2×#529D3
hypocenterC3C2×#3522
LCSG ▷ C22×C3 ▷ C3
UCSC1 ◁ C23 ◁ C2×#529

Complements

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

NH ≅ G/Ntype
1. C2×C3×#529C2semidirect
2. #86128C2direct (N × H)
3. C2×#5710C2semidirect
4. C2×#5690C2semidirect
5. C2×#5681C2semidirect
6. C2×#5655C2semidirect
7. C2×#5624C2semidirect
8. C2×#5596C2semidirect
9. C2×#5585C2semidirect
10. C2×Q8×Dic6C2semidirect
11. C2×#5543C2semidirect
12. C2×#5553C2semidirect
13. C2×#5552C2semidirect
14. C2×#5555C2semidirect
15. C2×#5534C2semidirect
16. C2×#5523C2semidirect
17. C2×#5477C2semidirect
18. C22×C4×Dic6C2semidirect
24. C3×#529C22semidirect
49. #5710C22semidirect
50. #5690C22semidirect
51. #5681C22semidirect
52. #5655C22semidirect
53. #5624C22semidirect
54. #5596C22semidirect
55. #5585C22semidirect
56. Q8×Dic6C22semidirect
57. #5555C22semidirect
58. #5553C22semidirect
59. #5552C22semidirect
60. #5543C22semidirect
61. #5534C22semidirect
62. #5523C22semidirect
85. #5477C22semidirect
101. C2×C4×Dic6C22semidirect
117. C2×#529D3semidirect
278. #529C2×D3semidirect
399. C2×Dic6#41semidirect
644. Dic6C2×#41semidirect
852. C2×C3#3522semidirect
887. C3C2×#3522semidirect
891. C2#86128direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C3×#5292
#861282
C2×#57102
C2×#56902
C2×#56812
C2×#56552
C2×#56242
C2×#55962
C2×#55852
C2×Q8×Dic62
C2×#55432
C2×#55532
C2×#55522
C2×#55552
C2×#55342
C2×#55232
C2×#54772
C22×C4×Dic62
C2×#35223