Finite Group Databasebeta

← C2×#86126 #11703439

Subgroups — C2×#86126 #11703439

Order 768.

7854 conjugacy classes of subgroups.

The subgroup lattice has 924 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#529C211yesmaximal, characteristic, complemented
2#86126C2132yesmaximal, direct product factor
3C2×#5709C214yesmaximal, complemented
4C2×#5691C212yesmaximal, complemented
5C2×#5668C212yesmaximal, complemented
6C2×#5663C214yesmaximal, complemented
7C2×#5631C212yesmaximal, complemented
8C2×#5599C212yesmaximal, complemented
9C2×#5567C211yesmaximal, characteristic, complemented
10C2×#5577C211yesmaximal, characteristic, complemented
11C2×#5565C212yesmaximal, complemented
12C2×#5553C212yesmaximal, complemented
13C2×#5553C211yesmaximal, characteristic, complemented
14C2×#5555C211yesmaximal, characteristic, complemented
15C2×#5535C212yesmaximal, complemented
16C2×#5523C212yesmaximal, complemented
17C2×#5477C211yesmaximal, characteristic, complemented
18C2×C4×#235C211yesmaximal, characteristic, complemented
19C2×#3517—31nomaximal, Sylow
20C22×#239C2212yes—
21C22×#237C2212yes—
22C22×#235C2211yescharacteristic
23C22×#235C2212yes—
24C22×#235C2212yes—
25C3×#529C22116yescomplemented
26C2×C3×#126C2212yes—
27C2×C3×#125C2211yescharacteristic
28C2×C3×#124C2211yescharacteristic
29C2×C3×#123C2212yes—
30C2×C3×C22⋊Q8C2211yescharacteristic
31C2×C3×#121C2211yescharacteristic
32C2×C3×C4×Q8C2211yescharacteristic
33C2×C3×C4×D4C2211yescharacteristic
34C2×C3×C4×D4C2212yes—
35C2×C3×#117C2212yes—
36C22×C3×C42C2211yescharacteristic
37C2×#944C2212yes—
38C2×#940C2212yes—
39C2×#940C2214yes—
40C2×#939C2214yes—
41C2×#930C2212yes—
42C2×#930C2212yes—
43C2×#930C2212yes—
44C2×#930C2212yes—
45C2×C4×#67C2212yes—
46C2×C4×#67C2212yes—
47C2×#926C2211yescharacteristic
48C22×C4⋊Dic3C2212yes—
49#5709C22164yescomplemented
50#5691C22132yescomplemented
51#5668C22132yescomplemented
52#5663C22164yescomplemented
53#5631C22132yescomplemented
54#5599C22132yescomplemented
55#5577C22116yescomplemented
56#5567C22116yescomplemented
57#5565C22132yescomplemented
58#5555C22116yescomplemented
59#5553C22116yescomplemented
60#5553C22132yescomplemented
61#5535C22132yescomplemented
62#5523C22132yescomplemented
63C2×#898C2214yes—
64C2×#897C2212yes—
65C2×#895C2212yes—
66C2×#895C2214yes—
67C2×#894C2214yes—
68C2×#894C2214yes—
69C2×#893C2214yes—
70C2×#893C2212yes—
71C2×#892C2214yes—
72C2×D3×C4⋊C4C2214yes—
73C2×#889C2214yes—
74C2×#887C2212yes—
75C2×#886C2214yes—
76C2×#884C2214yes—
77C2×#884C2214yes—
78C2×#884C2214yes—
79C2×#884C2214yes—
80C2×#884C2214yes—
81C2×#883C2214yes—
82C2×#67⋊C4C2214yes—
83C2×#67⋊C4C2214yes—
84C2×#67⋊C4C2214yes—
85#5477C22116yescomplemented
86C2×#875C2212yes—
87C2×#874C2211yescharacteristic
88C2×#874C2212yes—
89C4×#235C22116yescomplemented
90C2×C4×D12C2211yescharacteristic
91C2×C4×D12C2212yes—
92C2×C4×D12C2212yes—
93C2×C4×D12C2211yescharacteristic
94C2×C4×D12C2212yes—
95C2×#872C2212yes—
96C2×C42×D3C2212yes—
97C2×#870C2212yes—
98C2×#869C2211yescharacteristic
99C2×C4×Dic6C2211yescharacteristic
100C2×C4×Dic6C2212yes—
101C2×C4×Dic6C2211yescharacteristic
102#3517—332no—
103C2×#557—31no—
104C2×#553—34no—
105C2×#553—32no—
106C2×#550—32no—
107C2×#550—31no—
108C2×#550—31no—
109C2×#550—32no—
110C2×#547—32no—
111C2×#547—31no—
112C2×#540—34no—
113C2×#540—32no—
114C2×#532—31no—
115C2×#532—32no—
116C2×#529—32no—
117C2×#529D311yescharacteristic, complemented
118C2×#520—32no—
119C2×C4×#41—31no—
120C22×C3×Q8C2311yescharacteristic
121C22×C3×D4C2311yescharacteristic
122C22×C3×D4C2312yes—
123C23×C3×C4C2311yescharacteristic
124C23×C3×C4C2312yes—
125C23×C3×C4C2311yescharacteristic
126C23×C3×C4C2311yescharacteristic
127C22×#67C2314yes—
128C22×#67C2312yes—
129C22×#67C2314yes—
130C22×#67C2314yes—
131C22×#67C2314yes—
132C23×Dic3C2314yes—
133C2×#239—48no—
134C2×#239C23116yes—
135C2×#237—48no—
136C2×#237C23116yes—
137C2×#235—28no—
138C2×#235—216no—
139C2×#235—48no—
140C2×#235C2318yes—
141C2×#235C23116yes—
142C2×#235C23116yes—
143C22×D12C2312yes—
144C22×D12C2311yescharacteristic
145C22×D12C2312yes—
146C22×D12C2314yes—
147C22×D12C2312yes—
148C22×D12C2314yes—
149C22×C4×D3C2312yes—
150C22×C4×D3C2314yes—
151C22×C4×D3C2312yes—
152C22×C4×D3C2314yes—
153C22×C4×D3C2314yes—
154C22×C4×D3C2312yes—
155C22×Dic6C2312yes—
156C22×Dic6C2311yescharacteristic
157C3×#126C23116yes—
158C3×#125C2318yes—
159C3×#124C2318yes—
160C3×#123C23116yes—
161C3×C22⋊Q8C2318yes—
162C3×#121C2318yes—
163C3×C4×Q8C2318yes—
164C3×C4×D4C2318yes—
165C3×C4×D4C23116yes—
166C3×#117C23116yes—
167C2×C3×C4⋊C4C2311yescharacteristic
168C2×C3×C4⋊C4C2312yes—
169C2×C3×C4⋊C4C2312yes—
170C2×C3×C4⋊C4C2312yes—
171C2×C3×C4⋊C4C2311yescharacteristic
172C2×C3×C4⋊C4C2312yes—
173C2×C3×C22⋊C4C2312yes—
174C2×C3×C22⋊C4C2312yes—
175C2×C3×C22⋊C4C2312yes—
176C2×C3×C22⋊C4C2312yes—
177C2×C3×C22⋊C4C2312yes—
178C2×C3×C42C2311yescharacteristic
179C2×C3×C42C2312yes—
180C2×C3×C42C2311yescharacteristic
181C2×C3×C42C2311yescharacteristic
182C2×C3×C42C2311yescharacteristic
183C2×C3×C42C2318yes—
184C2×#217C2312yes—
185#944C23116yes—
186#940C23132yes—
187#940C23116yes—
188#939C23132yes—
189#930C23116yes—
190#930C23116yes—
191#930C23116yes—
192#930C23116yes—
193C4×#67C23116yes—
194C4×#67C23116yes—
195C2×(C2×D3)⋊C4C2312yes—
196C2×(C2×D3)⋊C4C2312yes—
197C2×(C2×D3)⋊C4C2314yes—
198C2×(C2×D3)⋊C4C2314yes—
199C2×(C2×D3)⋊C4C2314yes—
200C2×(C2×D3)⋊C4C2314yes—
201C2×(C2×D3)⋊C4C2314yes—
202#926C2318yes—
203C2×C4⋊Dic3C2312yes—
204C2×C4⋊Dic3C2311yescharacteristic
205C2×C4⋊Dic3C2311yescharacteristic
206C2×C4⋊Dic3C2312yes—
207C2×C4⋊Dic3C2314yes—
208C2×C4⋊Dic3C23116yes—
209C2×Dic3⋊C4C2312yes—
210C2×Dic3⋊C4C2312yes—
211C2×Dic3⋊C4C2314yes—
212C2×Dic3⋊C4C2314yes—
213C2×Dic3⋊C4C2314yes—
214C2×C4×Dic3C2312yes—
215C2×C4×Dic3C2312yes—
216C2×C4×Dic3C2314yes—
217C2×C4×Dic3C2312yes—
218#898C23132yes—
219#897C23116yes—
220#895C23132yes—
221#895C23116yes—
222#894C23132yes—
223#894C23132yes—
224#893C23132yes—
225#893C23116yes—
226#892C23132yes—
227D3×C4⋊C4C23132yes—
228#889C23132yes—
229#887C23116yes—
230#886C23132yes—
231#884C23132yes—
232#884C23132yes—
233#884C23132yes—
234#884C23132yes—
235#884C23132yes—
236#883C23132yes—
237#67⋊C4C23132yes—
238#67⋊C4C23132yes—
239#67⋊C4C23132yes—
240#875C23116yes—
241#874C2318yes—
242#874C23116yes—
243C4×D12C23116yes—
244C4×D12C2318yes—
245C4×D12C2318yes—
246C4×D12C23116yes—
247C4×D12C23116yes—
248#872C23116yes—
249C42×D3C23116yes—
250#870C23116yes—
251#869C2318yes—
252C4×Dic6C2318yes—
253C4×Dic6C2318yes—
254C4×Dic6C23116yes—
255C22×#41—32no—
256C22×#41—32no—
257C22×#41—31no—
258C22×#41—32no—
259C22×#41—32no—
260#557—316no—
261#553—364no—
262#553—332no—
263#550—332no—
264#550—316no—
265#550—316no—
266#550—332no—
267#547—332no—
268#547—316no—
269#540—364no—
270#540—332no—
271#532—332no—
272#532—316no—
273C2×C4⋊Q8—32no—
274C2×C4⋊Q8—31no—
275C2×#127—32no—
276C2×#127—34no—
277C2×#127—31no—
278C2×#127—32no—
279#529—332no—
280#529C2×D3116yescomplemented
281C2×#126—34no—
282C2×#126C2×D312yes—
283C2×#125—34no—
284C2×#125—32no—
285C2×#125C2×D311yescharacteristic
286C2×#124—32no—
287C2×#124C2×D311yescharacteristic
288C2×#123—34no—
289C2×#123—34no—
290C2×#123—34no—
291C2×#123—34no—
292C2×#123C2×D312yes—
293C2×C22⋊Q8—32no—
294C2×C22⋊Q8C2×D311yescharacteristic
295C2×#121—34no—
296C2×#121—32no—
297C2×#121—32no—
298C2×#121—32no—
299C2×#121—32no—
300C2×#121—32no—
301C2×#121—34no—
302C2×#121—34no—
303C2×#121—34no—
304C2×#121—34no—
305C2×#121—34no—
306C2×#121—34no—
307C2×#121C2×D311yescharacteristic
308#520—332no—
309C4×#41—316no—
310C2×C4×Q8—32no—
311C2×C4×Q8—31no—
312C2×C4×Q8—31no—
313C2×C4×Q8—32no—
314C2×C4×Q8C2×D311yescharacteristic
315C2×C4×D4—32no—
316C2×C4×D4—32no—
317C2×C4×D4—32no—
318C2×C4×D4—34no—
319C2×C4×D4—34no—
320C2×C4×D4—34no—
321C2×C4×D4—34no—
322C2×C4×D4—31no—
323C2×C4×D4—31no—
324C2×C4×D4—32no—
325C2×C4×D4—32no—
326C2×C4×D4—32no—
327C2×C4×D4C2×D311yescharacteristic
328C2×C4×D4C2×D312yes—
329C2×#117—31no—
330C2×#117—34no—
331C2×#117—32no—
332C2×#117C2×D312yes—
333C22×C4⋊C4—32no—
334C22×C4⋊C4—34no—
335C22×C42—32no—
336C22×C42C2×D311yescharacteristic
337C24×C3C2411yescharacteristic
338C24×C3C2412yes—
339C23×D3C2412yes—
340C23×D3C2414yes—
341C2×C3×Q8—24no—
342C2×C3×Q8C2414yes—
343C2×C3×D4—24no—
344C2×C3×D4—44no—
345C2×C3×D4C2414yes—
346C2×C3×D4C2418yes—
347C22×C3×C4—28no—
348C22×C3×C4—24no—
349C22×C3×C4—24no—
350C22×C3×C4—42no—
351C22×C3×C4C2412yes—
352C22×C3×C4C2411yescharacteristic
353C22×C3×C4C2411yescharacteristic
354C22×C3×C4C2412yes—
355C22×C3×C4C2411yescharacteristic
356C22×C3×C4C2411yescharacteristic
357C22×C3×C4C2412yes—
358C22×C3×C4C2418yes—
359C22×C3×C4C2414yes—
360C22×C3×C4C2414yes—
361C22×C3×C4C2414yes—
362C22×C3×C4C2411yescharacteristic
363C22×C3×C4C2411yescharacteristic
364C2×#67—216no—
365C2×#67—28no—
366C2×#67—48no—
367C2×#67—48no—
368C2×#67—48no—
369C2×#67C24116yes—
370C2×#67C2418yes—
371C2×#67C24116yes—
372C2×#67C24116yes—
373C2×#67C24116yes—
374C22×Dic3—48no—
375C22×Dic3C2412yes—
376C22×Dic3C2412yes—
377C22×Dic3C2414yes—
378C22×Dic3C24116yes—
379C22×Dic3C2412yes—
380#239—432no—
381#237—432no—
382#235—232no—
383#235—264no—
384#235—432no—
385C2×D12—24no—
386C2×D12—28no—
387C2×D12—28no—
388C2×D12—44no—
389C2×D12—48no—
390C2×D12—48no—
391C2×D12C2414yes—
392C2×D12C2418yes—
393C2×D12C2418yes—
394C2×D12C2418yes—
395C2×D12C24116yes—
396C2×D12C24116yes—
397C2×C4×D3—28no—
398C2×C4×D3—28no—
399C2×C4×D3—216no—
400C2×C4×D3—44no—
401C2×C4×D3—48no—
402C2×C4×D3—48no—
403C2×C4×D3C2418yes—
404C2×C4×D3C2418yes—
405C2×C4×D3C24116yes—
406C2×C4×D3C2418yes—
407C2×C4×D3C24116yes—
408C2×C4×D3C24116yes—
409C2×Dic6—28no—
410C2×Dic6#4118yescomplemented
411C2×Dic6C2418yes—
412C2×Dic6C2414yes—
413C3×C4⋊C4C2414yes—
414C3×C4⋊C4C2418yes—
415C3×C4⋊C4C2418yes—
416C3×C4⋊C4C2418yes—
417C3×C4⋊C4C2414yes—
418C3×C4⋊C4C2418yes—
419C3×C22⋊C4C2418yes—
420C3×C22⋊C4C2418yes—
421C3×C22⋊C4C2418yes—
422C3×C22⋊C4C2418yes—
423C3×C22⋊C4C2418yes—
424C3×C42C2414yes—
425C3×C42C2418yes—
426C3×C42C2414yes—
427C3×C42C2414yes—
428C3×C42C2414yes—
429#217C2418yes—
430(C2×D3)⋊C4C2418yes—
431(C2×D3)⋊C4C2418yes—
432(C2×D3)⋊C4C24116yes—
433(C2×D3)⋊C4C24116yes—
434(C2×D3)⋊C4C24116yes—
435(C2×D3)⋊C4C24116yes—
436(C2×D3)⋊C4C24116yes—
437C4⋊Dic3C2418yes—
438C4⋊Dic3C2414yes—
439C4⋊Dic3C2414yes—
440C4⋊Dic3C2418yes—
441C4⋊Dic3C24116yes—
442Dic3⋊C4C2418yes—
443Dic3⋊C4C2418yes—
444Dic3⋊C4C24116yes—
445Dic3⋊C4C24116yes—
446Dic3⋊C4C24116yes—
447C4×Dic3C2418yes—
448C4×Dic3C2418yes—
449C4×Dic3C24116yes—
450C4×Dic3C2418yes—
451C2×#41—316no—
452C2×#41—316no—
453C2×#41—38no—
454C2×#41—316no—
455C2×#41—316no—
456C2×#41—68no—
457C2×#41—616no—
458C2×#41—128no—
459C2×#41—128no—
460C2×#41—128no—
461C22×Q8—31no—
462C22×Q8—32no—
463C22×Q8C22×D311yescharacteristic
464C22×D4—32no—
465C22×D4—34no—
466C22×D4—34no—
467C22×D4—34no—
468C22×D4—34no—
469C22×D4—31no—
470C22×D4—32no—
471C22×D4—32no—
472C22×D4—32no—
473C22×D4—34no—
474C22×D4—34no—
475C22×D4C22×D311yescharacteristic
476C22×D4C22×D312yes—
477C23×C4—34no—
478C23×C4—34no—
479C23×C4—32no—
480C23×C4—32no—
481C23×C4—34no—
482C23×C4—34no—
483C23×C4—32no—
484C23×C4C22×D312yes—
485C23×C4C22×D311yescharacteristic
486C23×C4C22×D311yescharacteristic
487C23×C4C22×D311yescharacteristic
488C4⋊Q8—316no—
489C4⋊Q8—38no—
490#127—316no—
491#127—332no—
492#127—38no—
493#127—316no—
494#126—332no—
495#126C22×D3116yes—
496#125—332no—
497#125—316no—
498#125C22×D318yes—
499#124—316no—
500#124C22×D318yes—
501#123—332no—
502#123—332no—
503#123—332no—
504#123—332no—
505#123C22×D3116yes—
506C22⋊Q8—316no—
507C22⋊Q8C22×D318yes—
508#121—332no—
509#121—316no—
510#121—316no—
511#121—316no—
512#121—316no—
513#121—316no—
514#121—332no—
515#121—332no—
516#121—332no—
517#121—332no—
518#121—332no—
519#121—332no—
520#121C22×D318yes—
521C4×Q8—316no—
522C4×Q8—38no—
523C4×Q8—38no—
524C4×Q8—316no—
525C4×Q8C22×D318yes—
526C4×D4—316no—
527C4×D4—316no—
528C4×D4—316no—
529C4×D4—332no—
530C4×D4—332no—
531C4×D4—332no—
532C4×D4—332no—
533C4×D4—38no—
534C4×D4—38no—
535C4×D4—316no—
536C4×D4—316no—
537C4×D4—316no—
538C4×D4C22×D318yes—
539C4×D4C22×D3116yes—
540#117—38no—
541#117—332no—
542#117—316no—
543#117C22×D3116yes—
544C2×C4⋊C4—32no—
545C2×C4⋊C4—31no—
546C2×C4⋊C4—34no—
547C2×C4⋊C4—34no—
548C2×C4⋊C4—32no—
549C2×C4⋊C4—316no—
550C2×C4⋊C4—32no—
551C2×C4⋊C4—31no—
552C2×C4⋊C4—34no—
553C2×C4⋊C4—32no—
554C2×C4⋊C4—34no—
555C2×C4⋊C4—332no—
556C2×C4⋊C4C22×D312yes—
557C2×C4⋊C4C22×D312yes—
558C2×C4⋊C4C22×D311yescharacteristic
559C2×C4⋊C4C22×D312yes—
560C2×C4⋊C4C22×D311yescharacteristic
561C2×C4⋊C4C22×D312yes—
562C2×C22⋊C4—32no—
563C2×C22⋊C4—34no—
564C2×C22⋊C4—32no—
565C2×C22⋊C4—32no—
566C2×C22⋊C4—34no—
567C2×C22⋊C4—34no—
568C2×C22⋊C4—34no—
569C2×C22⋊C4—34no—
570C2×C22⋊C4C22×D312yes—
571C2×C22⋊C4C22×D312yes—
572C2×C22⋊C4C22×D312yes—
573C2×C22⋊C4C22×D312yes—
574C2×C22⋊C4C22×D312yes—
575C2×C42—32no—
576C2×C42—32no—
577C2×C42—34no—
578C2×C42—32no—
579C2×C42—316no—
580C2×C42C22×D311yescharacteristic
581C2×C42C22×D311yescharacteristic
582C2×C42C22×D312yes—
583C2×C42C22×D311yescharacteristic
584C2×C42C22×D318yes—
585C2×C42C22×D311yescharacteristic
586C23×C3—22no—
587C23×C3—24no—
588C23×C3—24no—
589C23×C3—22no—
590C23×C3—24no—
591C23×C3—22no—
592C23×C3C2512yes—
593C23×C3C2514yes—
594C23×C3C2511yescharacteristic
595C22×D3—24no—
596C22×D3—28no—
597C22×D3—24no—
598C22×D3—28no—
599C22×D3—24no—
600C22×D3—28no—
601C22×D3C2514yes—
602C22×D3C2518yes—
603C3×Q8—28no—
604C3×D4—28no—
605C3×D4—48no—
606C2×C3×C4—22no—
607C2×C3×C4—24no—
608C2×C3×C4—22no—
609C2×C3×C4—24no—
610C2×C3×C4—22no—
611C2×C3×C4—22no—
612C2×C3×C4—24no—
613C2×C3×C4—216no—
614C2×C3×C4—28no—
615C2×C3×C4—28no—
616C2×C3×C4—44no—
617C2×C3×C4C2×#4114yes—
618C2×C3×C4H(5,𝔽2)14yes—
619C2×C3×C4C2514yes—
620C2×C3×C4C2512yes—
621C2×C3×C4C2512yes—
622C2×C3×C4C2514yes—
623C2×C3×C4C2512yes—
624C2×C3×C4C2512yes—
625C2×C3×C4C2514yes—
626C2×C3×C4C2512yes—
627C2×C3×C4C2512yes—
628#67—232no—
629#67—216no—
630#67—416no—
631#67—416no—
632#67—416no—
633C2×Dic3—28no—
634C2×Dic3—24no—
635C2×Dic3—24no—
636C2×Dic3—416no—
637C2×Dic3C2×#4118yes—
638C2×Dic3C2514yes—
639C2×Dic3C2514yes—
640C2×Dic3C2518yes—
641C2×Dic3C2514yes—
642D12—28no—
643D12—216no—
644D12—216no—
645D12—48no—
646D12—416no—
647D12—416no—
648C4×D3—216no—
649C4×D3—216no—
650C4×D3—232no—
651C4×D3—48no—
652C4×D3—416no—
653C4×D3—416no—
654Dic6—216no—
655Dic6C2×#41116yescomplemented
656C24—32no—
657C24—34no—
658C24C23×D311yescharacteristic
659C24C23×D312yes—
660#41—632no—
661#41—664no—
662#41—1232no—
663#41—1232no—
664#41—1232no—
665C2×Q8—24no—
666C2×Q8—38no—
667C2×Q8—34no—
668C2×Q8—38no—
669C2×Q8—68no—
670C2×Q8C23×D314yes—
671C2×D4—24no—
672C2×D4—38no—
673C2×D4—316no—
674C2×D4—316no—
675C2×D4—316no—
676C2×D4—316no—
677C2×D4—34no—
678C2×D4—38no—
679C2×D4—38no—
680C2×D4—38no—
681C2×D4—316no—
682C2×D4—316no—
683C2×D4—44no—
684C2×D4—68no—
685C2×D4—616no—
686C2×D4—64no—
687C2×D4—68no—
688C2×D4—68no—
689C2×D4—128no—
690C2×D4—124no—
691C2×D4—128no—
692C2×D4—128no—
693C2×D4—128no—
694C2×D4—128no—
695C2×D4C23×D314yes—
696C2×D4C23×D318yes—
697C22×C4—28no—
698C22×C4—24no—
699C22×C4—24no—
700C22×C4—32no—
701C22×C4—32no—
702C22×C4—32no—
703C22×C4—34no—
704C22×C4—316no—
705C22×C4—38no—
706C22×C4—38no—
707C22×C4—316no—
708C22×C4—38no—
709C22×C4—316no—
710C22×C4—316no—
711C22×C4—42no—
712C22×C4—616no—
713C22×C4—68no—
714C22×C4—68no—
715C22×C4—128no—
716C22×C4—128no—
717C22×C4—124no—
718C22×C4—128no—
719C22×C4C23×D314yes—
720C22×C4C23×D314yes—
721C22×C4C23×D318yes—
722C22×C4C23×D311yescharacteristic
723C22×C4C23×D311yescharacteristic
724C22×C4C23×D312yes—
725C22×C4C23×D311yescharacteristic
726C22×C4C23×D311yescharacteristic
727C22×C4C23×D312yes—
728C22×C4C23×D312yes—
729C22×C4C23×D314yes—
730C22×C4C23×D311yescharacteristic
731C22×C4C23×D311yescharacteristic
732C4⋊C4—38no—
733C4⋊C4—34no—
734C4⋊C4—316no—
735C4⋊C4—316no—
736C4⋊C4—38no—
737C4⋊C4—38no—
738C4⋊C4—34no—
739C4⋊C4—316no—
740C4⋊C4—38no—
741C4⋊C4—316no—
742C4⋊C4C23×D318yes—
743C4⋊C4C23×D318yes—
744C4⋊C4C23×D314yes—
745C4⋊C4C23×D318yes—
746C4⋊C4C23×D314yes—
747C4⋊C4C23×D318yes—
748C22⋊C4—38no—
749C22⋊C4—316no—
750C22⋊C4—38no—
751C22⋊C4—38no—
752C22⋊C4—316no—
753C22⋊C4—316no—
754C22⋊C4—316no—
755C22⋊C4—316no—
756C22⋊C4C23×D318yes—
757C22⋊C4C23×D318yes—
758C22⋊C4C23×D318yes—
759C22⋊C4C23×D318yes—
760C22⋊C4C23×D318yes—
761C42—38no—
762C42—38no—
763C42—38no—
764C42—316no—
765C42C23×D314yes—
766C42C23×D314yes—
767C42C23×D314yes—
768C42C23×D314yes—
769C42C23×D318yes—
770C22×C3—22no—
771C22×C3—24no—
772C22×C3—24no—
773C22×C3—22no—
774C22×C3—24no—
775C22×C3—22no—
776C22×C3—48no—
777C22×C3—44no—
778C22×C3C22×#4112yes—
779C22×C3C2×H(5,𝔽2)12yes—
780C22×C3#58512yes—
781C22×C3C2611yescharacteristic
782C2×D3—24no—
783C2×D3—28no—
784C2×D3—24no—
785C2×D3—28no—
786C2×D3—24no—
787C2×D3—28no—
788C2×D3—48no—
789C2×D3—416no—
790C3×C4—22no—
791C3×C4—24no—
792C3×C4—22no—
793C3×C4—24no—
794C3×C4—22no—
795C3×C4—22no—
796C3×C4—24no—
797C3×C4C22×#4114yes—
798C3×C4C2×H(5,𝔽2)14yes—
799Dic3—28no—
800Dic3—24no—
801Dic3—24no—
802Dic3C22×#4118yes—
803C23—22no—
804C23—24no—
805C23—22no—
806C23—24no—
807C23—22no—
808C23—24no—
809C23—34no—
810C23—38no—
811C23—64no—
812C23—68no—
813C23—64no—
814C23—68no—
815C23—64no—
816C23—68no—
817C23C24×D312yes—
818C23C24×D314yes—
819C23C24×D311yescharacteristic
820Q8—28no—
821Q8—316no—
822Q8—616no—
823D4—28no—
824D4—48no—
825D4—616no—
826D4—632no—
827D4—68no—
828D4—616no—
829D4—616no—
830D4—1216no—
831D4—128no—
832D4—1216no—
833D4—1216no—
834D4—1216no—
835D4—1216no—
836C2×C4—22no—
837C2×C4—24no—
838C2×C4—22no—
839C2×C4—24no—
840C2×C4—22no—
841C2×C4—22no—
842C2×C4—24no—
843C2×C4—28no—
844C2×C4—216no—
845C2×C4—28no—
846C2×C4—38no—
847C2×C4—34no—
848C2×C4—34no—
849C2×C4—34no—
850C2×C4—38no—
851C2×C4—44no—
852C2×C4—616no—
853C2×C4—632no—
854C2×C4—64no—
855C2×C4—68no—
856C2×C4—64no—
857C2×C4—616no—
858C2×C4—1216no—
859C2×C4—1216no—
860C2×C4—128no—
861C2×C4—1216no—
862C2×C4D3×#4114yes—
863C2×C4#100914yes—
864C2×C4C24×D312yes—
865C2×C4C24×D312yes—
866C2×C4C24×D314yes—
867C2×C4C24×D312yes—
868C2×C4C24×D312yes—
869C2×C4C24×D314yes—
870C2×C4C24×D314yes—
871C2×C4C24×D312yes—
872C2×C4C24×D312yes—
873C2×C3—44no—
874C2×C3—42no—
875C2×C3#351714yescomplemented
876C2×C3C23×#4111yescharacteristic
877C2×C3C22×H(5,𝔽2)11yescharacteristic
878C2×C3C2×#58511yescharacteristic
879D3—44no—
880D3—48no—
881C22—22no—
882C22—24no—
883C22—22no—
884C22—24no—
885C22—22no—
886C22—24no—
887C22—44no—
888C22—48no—
889C22—64no—
890C22—68no—
891C22—64no—
892C22—68no—
893C22—64no—
894C22—68no—
895C22—128no—
896C22—1216no—
897C22C2×D3×#4112yes—
898C22C2×#100912yes—
899C22#596412yes—
900C22C25×D311yescharacteristic
901C4—22no—
902C4—24no—
903C4—22no—
904C4—24no—
905C4—22no—
906C4—22no—
907C4—24no—
908C4—38no—
909C4—64no—
910C4—68no—
911C4—64no—
912C4C2×D3×#4114yes—
913C4C2×#100914yes—
914C3C2×#351711yescharacteristic, complemented, Sylow
915C2—42no—
916C2—44no—
917C2—124no—
918C2—128no—
919C2#8612614yesdirect product factor
920C2C22×D3×#4111yescharacteristic
921C2C22×#100911yescharacteristic
922C2C2×#596411yescharacteristic
subgroupG/H
centerC23C24×D3
commutator, cosocleC22×C3C26
FrattiniC22C25×D3
FittingC2×C3×#529C2
socleC23×C3C25
hypercenterC2×#529D3
hypocenterC3C2×#3517
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. #86126C2direct (N × H)
3. C2×#5709C2semidirect
4. C2×#5691C2semidirect
5. C2×#5668C2semidirect
6. C2×#5663C2semidirect
7. C2×#5631C2semidirect
8. C2×#5599C2semidirect
9. C2×#5567C2semidirect
10. C2×#5577C2semidirect
11. C2×#5565C2semidirect
12. C2×#5553C2semidirect
13. C2×#5553C2semidirect
14. C2×#5555C2semidirect
15. C2×#5535C2semidirect
16. C2×#5523C2semidirect
17. C2×#5477C2semidirect
18. C2×C4×#235C2semidirect
25. C3×#529C22semidirect
49. #5709C22semidirect
50. #5691C22semidirect
51. #5668C22semidirect
52. #5663C22semidirect
53. #5631C22semidirect
54. #5599C22semidirect
55. #5577C22semidirect
56. #5567C22semidirect
57. #5565C22semidirect
58. #5555C22semidirect
59. #5553C22semidirect
60. #5553C22semidirect
61. #5535C22semidirect
62. #5523C22semidirect
85. #5477C22semidirect
89. C4×#235C22semidirect
117. C2×#529D3semidirect
280. #529C2×D3semidirect
410. C2×Dic6#41semidirect
655. Dic6C2×#41semidirect
875. C2×C3#3517semidirect
914. C3C2×#3517semidirect
919. C2#86126direct (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
#861262
C2×#57092
C2×#56912
C2×#56682
C2×#56632
C2×#56312
C2×#55992
C2×#55672
C2×#55772
C2×#55652
C2×#55532
C2×#55552
C2×#55352
C2×#55232
C2×#54772
C2×C4×#2352
C2×#35173