Finite Group Databasebeta

← C2×#86936 #11703393

Subgroups — C2×#86936 #11703393

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×#554C211yesmaximal, characteristic, complemented
2#86936C2132yesmaximal, direct product factor
3C2×#5722C211yesmaximal, characteristic, complemented
4C2×#5725C211yesmaximal, characteristic, complemented
5C2×#5690C212yesmaximal, complemented
6C2×#5691C212yesmaximal, complemented
7C2×#5633C212yesmaximal, complemented
8C2×#5631C214yesmaximal, complemented
9C2×#5640C214yesmaximal, complemented
10C2×#5643C212yesmaximal, complemented
11C2×C4×D3×Q8C211yesmaximal, characteristic, complemented
12C2×#5585C211yesmaximal, characteristic, complemented
13C2×#5548C212yesmaximal, complemented
14C2×#5557C211yesmaximal, characteristic, complemented
15C2×#5559C212yesmaximal, complemented
16C2×#5553C211yesmaximal, characteristic, complemented
17C2×#5507C212yesmaximal, complemented
18C2×#5504C212yesmaximal, complemented
19C2×#3522—31nomaximal, Sylow
20C22×#239C2212yes—
21C22×D3×Q8C2211yescharacteristic
22C22×#235C2212yes—
23C22×#235C2214yes—
24C3×#554C22116yescomplemented
25C2×C3×C4⋊Q8C2211yescharacteristic
26C2×C3×#125C2212yes—
27C2×C3×C22⋊Q8C2212yes—
28C2×C3×C22⋊Q8C2214yes—
29C2×C3×C4×Q8C2211yescharacteristic
30C2×C3×C4×D4C2212yes—
31C2×C3×C4×D4C2211yescharacteristic
32C22×C3×C4⋊C4C2212yes—
33C2×#947C2212yes—
34C2×#947C2212yes—
35C2×Q8×Dic3C2211yescharacteristic
36C2×#944C2214yes—
37C2×#940C2212yes—
38C2×#938C2211yescharacteristic
39C2×#936C2211yescharacteristic
40C2×#930C2212yes—
41C2×#929C2214yes—
42C2×C4×#67C2214yes—
43C2×C4×#67C2212yes—
44C2×C4×#67C2214yes—
45C2×#926C2212yes—
46#5725C22116yescomplemented
47#5722C22116yescomplemented
48#5691C22132yescomplemented
49#5690C22132yescomplemented
50#5643C22132yescomplemented
51#5640C22164yescomplemented
52#5633C22132yescomplemented
53#5631C22164yescomplemented
54#5585C22116yescomplemented
55C4×D3×Q8C22116yescomplemented
56#5559C22132yescomplemented
57#5557C22116yescomplemented
58#5553C22116yescomplemented
59#5548C22132yescomplemented
60C2×#898C2214yes—
61C2×#897C2211yescharacteristic
62C2×#897C2214yes—
63C2×#896C2214yes—
64C2×#896C2214yes—
65#5507C22132yescomplemented
66C2×#895C2212yes—
67C2×#895C2212yes—
68C2×#894C2214yes—
69C2×#894C2214yes—
70#5504C22132yescomplemented
71C2×#893C2212yes—
72C2×#893C2212yes—
73C2×#893C2212yes—
74C2×#893C2214yes—
75C2×#893C2212yes—
76C2×#892C2214yes—
77C2×D3×C4⋊C4C2211yescharacteristic
78C2×D3×C4⋊C4C2212yes—
79C2×D3×C4⋊C4C2214yes—
80C2×#890C2211yescharacteristic
81C2×#888C2212yes—
82C2×#888C2212yes—
83C2×#887C2212yes—
84C2×#887C2212yes—
85C2×#887C2211yescharacteristic
86C2×#887C2212yes—
87C2×#885C2214yes—
88C2×#885C2214yes—
89C2×#884C2214yes—
90C2×#884C2214yes—
91C2×#883C2214yes—
92C2×#883C2212yes—
93C2×#879C2212yes—
94C2×#875C2212yes—
95C2×#874C2211yescharacteristic
96C2×C4×D12C2212yes—
97C2×C42×D3C2211yescharacteristic
98C2×C42×D3C2212yes—
99C2×C4×Dic6C2212yes—
100C2×C4×Dic6C2211yescharacteristic
101C2×C4×Dic6C2211yescharacteristic
102#3522—332no—
103C2×#559—31no—
104C2×#559—32no—
105C2×Q82—31no—
106C2×#554—32no—
107C2×#554D311yescharacteristic, complemented
108C2×#550—31no—
109C2×#548—32no—
110C2×#547—34no—
111C2×#547—32no—
112C2×#542—32no—
113C2×#542—34no—
114C2×#532—31no—
115C2×#532—32no—
116C2×#529—32no—
117C2×#529—31no—
118C2×#520—32no—
119C22×C4×Q8—31no—
120C22×C3×Q8C2311yescharacteristic
121C22×C3×Q8C2312yes—
122C22×C3×D4C2311yescharacteristic
123C23×C3×C4C2312yes—
124C23×C3×C4C2314yes—
125C22×#67C2312yes—
126C22×#67C2314yes—
127C22×#67C2314yes—
128C2×#239—48no—
129C2×#239C23116yes—
130C2×D3×Q8—28no—
131C2×D3×Q8C2318yes—
132C2×#235—216no—
133C2×#235—416no—
134C2×#235C23116yes—
135C2×#235C23132yes—
136C22×D12C2314yes—
137C22×D12C2312yes—
138C22×D12C2312yes—
139C22×D12C2312yes—
140C22×C4×D3C2312yes—
141C22×C4×D3C2314yes—
142C22×C4×D3C2312yes—
143C22×C4×D3C2311yescharacteristic
144C22×C4×D3C2311yescharacteristic
145C22×C4×D3C2311yescharacteristic
146C22×C4×D3C2314yes—
147C22×C4×D3C2314yes—
148C22×Dic6C2312yes—
149C22×Dic6C2311yescharacteristic
150C22×Dic6C2314yes—
151C22×Dic6C2311yescharacteristic
152C3×C4⋊Q8C2318yes—
153C3×#125C23116yes—
154C3×C22⋊Q8C23116yes—
155C3×C22⋊Q8C23132yes—
156C3×C4×Q8C2318yes—
157C3×C4×D4C23116yes—
158C3×C4×D4C2318yes—
159C2×C3×C4⋊C4C2312yes—
160C2×C3×C4⋊C4C2312yes—
161C2×C3×C4⋊C4C2311yescharacteristic
162C2×C3×C4⋊C4C2312yes—
163C2×C3×C4⋊C4C2311yescharacteristic
164C2×C3×C4⋊C4C2314yes—
165C2×C3×C4⋊C4C2314yes—
166C2×C3×C4⋊C4C23116yes—
167C2×C3×C22⋊C4C2312yes—
168C2×C3×C22⋊C4C2314yes—
169C2×C3×C42C2311yescharacteristic
170C2×C3×C42C2312yes—
171C2×#217C2312yes—
172C2×#217C2312yes—
173C2×#217C2312yes—
174#947C23116yes—
175#947C23116yes—
176Q8×Dic3C2318yes—
177#944C23132yes—
178#940C23116yes—
179#938C2318yes—
180#936C2318yes—
181#930C23116yes—
182#929C23132yes—
183C4×#67C23116yes—
184C4×#67C23132yes—
185C4×#67C23132yes—
186C2×(C2×D3)⋊C4C2314yes—
187C2×(C2×D3)⋊C4C2314yes—
188C2×(C2×D3)⋊C4C2314yes—
189C2×(C2×D3)⋊C4C2312yes—
190C2×(C2×D3)⋊C4C2314yes—
191C2×(C2×D3)⋊C4C2314yes—
192C2×(C2×D3)⋊C4C2314yes—
193#926C23116yes—
194C2×C4⋊Dic3C2311yescharacteristic
195C2×C4⋊Dic3C2312yes—
196C2×C4⋊Dic3C2311yescharacteristic
197C2×C4⋊Dic3C2312yes—
198C2×C4⋊Dic3C2312yes—
199C2×Dic3⋊C4C2312yes—
200C2×Dic3⋊C4C2312yes—
201C2×Dic3⋊C4C2312yes—
202C2×Dic3⋊C4C2312yes—
203C2×Dic3⋊C4C2312yes—
204C2×Dic3⋊C4C2314yes—
205C2×Dic3⋊C4C2314yes—
206C2×C4×Dic3C2312yes—
207C2×C4×Dic3C2311yescharacteristic
208C2×C4×Dic3C2312yes—
209C2×C4×Dic3C2311yescharacteristic
210C2×C4×Dic3C2312yes—
211C2×C4×Dic3C2312yes—
212C2×C4×Dic3C2311yescharacteristic
213C2×C4×Dic3C2314yes—
214#898C23132yes—
215#897C23132yes—
216#897C2318yes—
217#896C23132yes—
218#896C23132yes—
219#895C23116yes—
220#895C23116yes—
221#894C23132yes—
222#894C23132yes—
223#893C23132yes—
224#893C23116yes—
225#893C23116yes—
226#893C23116yes—
227#893C23116yes—
228#892C23132yes—
229D3×C4⋊C4C23132yes—
230D3×C4⋊C4C2318yes—
231D3×C4⋊C4C23116yes—
232#890C2318yes—
233#888C23116yes—
234#888C23116yes—
235#887C23116yes—
236#887C23116yes—
237#887C23116yes—
238#887C2318yes—
239#885C23132yes—
240#885C23132yes—
241#884C23132yes—
242#884C23132yes—
243#883C23132yes—
244#883C23116yes—
245#879C23116yes—
246#875C23116yes—
247#874C2318yes—
248C4×D12C23116yes—
249C42×D3C23116yes—
250C42×D3C2318yes—
251C4×Dic6C23116yes—
252C4×Dic6C2318yes—
253C4×Dic6C2318yes—
254C22×#41—32no—
255C22×#41—32no—
256C22×#41—34no—
257C23×Q8—31no—
258#559—316no—
259#559—332no—
260Q82—316no—
261#554—332no—
262#554C2×D3116yescomplemented
263#550—316no—
264#548—332no—
265#547—364no—
266#547—332no—
267#542—364no—
268#542—332no—
269#532—316no—
270#532—332no—
271C2×C4⋊Q8—34no—
272C2×C4⋊Q8—32no—
273C2×C4⋊Q8—32no—
274C2×C4⋊Q8C2×D311yescharacteristic
275C2×#127—32no—
276C2×#127—31no—
277#529—332no—
278#529—316no—
279C2×#126—34no—
280C2×#126—32no—
281C2×#125—31no—
282C2×#125C2×D312yes—
283C2×#124—32no—
284C2×#124—32no—
285C2×#124—31no—
286C2×#124—34no—
287C2×#124—34no—
288C2×#124—32no—
289C2×#123—34no—
290C2×#123—34no—
291C2×#123—34no—
292C2×#123—32no—
293C2×#123—34no—
294C2×C22⋊Q8—31no—
295C2×C22⋊Q8—34no—
296C2×C22⋊Q8—34no—
297C2×C22⋊Q8—34no—
298C2×C22⋊Q8C2×D314yes—
299C2×C22⋊Q8C2×D312yes—
300C2×#121—31no—
301C2×#121—32no—
302C2×#121—32no—
303C2×#121—32no—
304C2×#121—34no—
305C2×#121—34no—
306#520—332no—
307C2×C4×Q8—31no—
308C2×C4×Q8—316no—
309C2×C4×Q8—31no—
310C2×C4×Q8—32no—
311C2×C4×Q8—32no—
312C2×C4×Q8—32no—
313C2×C4×Q8—31no—
314C2×C4×Q8—32no—
315C2×C4×Q8—31no—
316C2×C4×Q8C2×D311yescharacteristic
317C2×C4×D4—34no—
318C2×C4×D4—34no—
319C2×C4×D4—32no—
320C2×C4×D4—32no—
321C2×C4×D4—32no—
322C2×C4×D4—34no—
323C2×C4×D4—32no—
324C2×C4×D4—32no—
325C2×C4×D4—32no—
326C2×C4×D4C2×D311yescharacteristic
327C2×C4×D4C2×D312yes—
328C2×#117—32no—
329C2×#117—34no—
330C22×C4⋊C4—32no—
331C22×C4⋊C4—31no—
332C22×C4⋊C4—34no—
333C22×C4⋊C4C2×D312yes—
334C22×C42—31no—
335C22×C42—32no—
336C24×C3C2412yes—
337C23×D3C2414yes—
338C23×D3C2411yescharacteristic
339C2×C3×Q8—24no—
340C2×C3×Q8—44no—
341C2×C3×Q8C2414yes—
342C2×C3×Q8C2418yes—
343C2×C3×D4—24no—
344C2×C3×D4C2414yes—
345C22×C3×C4—28no—
346C22×C3×C4—48no—
347C22×C3×C4C2411yescharacteristic
348C22×C3×C4C2412yes—
349C22×C3×C4C2414yes—
350C22×C3×C4C2412yes—
351C22×C3×C4C2412yes—
352C22×C3×C4C2418yes—
353C22×C3×C4C24116yes—
354C22×C3×C4C2411yescharacteristic
355C22×C3×C4C2411yescharacteristic
356C2×#67—28no—
357C2×#67—216no—
358C2×#67—48no—
359C2×#67C2418yes—
360C2×#67C24116yes—
361C2×#67C24116yes—
362C22×Dic3C2411yescharacteristic
363C22×Dic3C2412yes—
364C22×Dic3C2412yes—
365C22×Dic3C2411yescharacteristic
366C22×Dic3C2411yescharacteristic
367C22×Dic3C2412yes—
368C22×Dic3C2412yes—
369#239—432no—
370D3×Q8—232no—
371#235—264no—
372#235—464no—
373C2×D12—216no—
374C2×D12—28no—
375C2×D12—28no—
376C2×D12—44no—
377C2×D12C2418yes—
378C2×D12C2418yes—
379C2×D12C24116yes—
380C2×D12C2418yes—
381C2×C4×D3—28no—
382C2×C4×D3—24no—
383C2×C4×D3—24no—
384C2×C4×D3—24no—
385C2×C4×D3—216no—
386C2×C4×D3—28no—
387C2×C4×D3—48no—
388C2×C4×D3—48no—
389C2×C4×D3C2414yes—
390C2×C4×D3C2414yes—
391C2×C4×D3C2418yes—
392C2×C4×D3C2418yes—
393C2×C4×D3C2414yes—
394C2×C4×D3C24116yes—
395C2×C4×D3C24116yes—
396C2×C4×D3C24116yes—
397C2×Dic6—24no—
398C2×Dic6—28no—
399C2×Dic6—48no—
400C2×Dic6#4118yescomplemented
401C2×Dic6C2414yes—
402C2×Dic6C2418yes—
403C2×Dic6C24116yes—
404C2×Dic6C2414yes—
405C3×C4⋊C4C2418yes—
406C3×C4⋊C4C2418yes—
407C3×C4⋊C4C2414yes—
408C3×C4⋊C4C2418yes—
409C3×C4⋊C4C2414yes—
410C3×C4⋊C4C24116yes—
411C3×C4⋊C4C24116yes—
412C3×C22⋊C4C2418yes—
413C3×C22⋊C4C24116yes—
414C3×C42C2414yes—
415C3×C42C2418yes—
416#217C2418yes—
417#217C2418yes—
418#217C2418yes—
419(C2×D3)⋊C4C24116yes—
420(C2×D3)⋊C4C24116yes—
421(C2×D3)⋊C4C24116yes—
422(C2×D3)⋊C4C2418yes—
423(C2×D3)⋊C4C24116yes—
424(C2×D3)⋊C4C24116yes—
425(C2×D3)⋊C4C24116yes—
426C4⋊Dic3C2414yes—
427C4⋊Dic3C2418yes—
428C4⋊Dic3C2414yes—
429C4⋊Dic3C2418yes—
430C4⋊Dic3C2418yes—
431Dic3⋊C4C2418yes—
432Dic3⋊C4C2418yes—
433Dic3⋊C4C2418yes—
434Dic3⋊C4C2418yes—
435Dic3⋊C4C2418yes—
436Dic3⋊C4C24116yes—
437Dic3⋊C4C24116yes—
438C4×Dic3C2418yes—
439C4×Dic3C2414yes—
440C4×Dic3C2418yes—
441C4×Dic3C2414yes—
442C4×Dic3C2418yes—
443C4×Dic3C2418yes—
444C4×Dic3C2414yes—
445C4×Dic3C24116yes—
446C2×#41—316no—
447C2×#41—316no—
448C2×#41—332no—
449C2×#41—616no—
450C2×#41—1216no—
451C2×#41—128no—
452C22×Q8—38no—
453C22×Q8—31no—
454C22×Q8—31no—
455C22×Q8—32no—
456C22×Q8—34no—
457C22×Q8—68no—
458C22×Q8C22×D311yescharacteristic
459C22×Q8C22×D312yes—
460C22×D4—34no—
461C22×D4—32no—
462C22×D4—34no—
463C22×D4—32no—
464C22×D4—32no—
465C22×D4—34no—
466C22×D4—32no—
467C22×D4C22×D311yescharacteristic
468C23×C4—31no—
469C23×C4—32no—
470C23×C4—34no—
471C23×C4—32no—
472C23×C4—31no—
473C23×C4—31no—
474C23×C4—34no—
475C23×C4—34no—
476C23×C4C22×D312yes—
477C23×C4C22×D314yes—
478C4⋊Q8—332no—
479C4⋊Q8—316no—
480C4⋊Q8—316no—
481C4⋊Q8C22×D318yes—
482#127—316no—
483#127—38no—
484#126—332no—
485#126—316no—
486#125—38no—
487#125C22×D3116yes—
488#124—316no—
489#124—316no—
490#124—38no—
491#124—332no—
492#124—332no—
493#124—316no—
494#123—332no—
495#123—332no—
496#123—332no—
497#123—316no—
498#123—332no—
499C22⋊Q8—38no—
500C22⋊Q8—332no—
501C22⋊Q8—332no—
502C22⋊Q8—332no—
503C22⋊Q8C22×D3132yes—
504C22⋊Q8C22×D3116yes—
505#121—38no—
506#121—316no—
507#121—316no—
508#121—316no—
509#121—332no—
510#121—332no—
511C4×Q8—38no—
512C4×Q8—38no—
513C4×Q8—316no—
514C4×Q8—316no—
515C4×Q8—316no—
516C4×Q8—38no—
517C4×Q8—316no—
518C4×Q8—38no—
519C4×Q8C22×D318yes—
520C4×D4—332no—
521C4×D4—332no—
522C4×D4—316no—
523C4×D4—316no—
524C4×D4—316no—
525C4×D4—332no—
526C4×D4—316no—
527C4×D4—316no—
528C4×D4—316no—
529C4×D4C22×D318yes—
530C4×D4C22×D3116yes—
531#117—316no—
532#117—332no—
533C2×C4⋊C4—32no—
534C2×C4⋊C4—32no—
535C2×C4⋊C4—34no—
536C2×C4⋊C4—32no—
537C2×C4⋊C4—31no—
538C2×C4⋊C4—32no—
539C2×C4⋊C4—32no—
540C2×C4⋊C4—32no—
541C2×C4⋊C4—31no—
542C2×C4⋊C4—32no—
543C2×C4⋊C4—34no—
544C2×C4⋊C4—32no—
545C2×C4⋊C4—316no—
546C2×C4⋊C4—38no—
547C2×C4⋊C4—332no—
548C2×C4⋊C4C22×D311yescharacteristic
549C2×C4⋊C4C22×D314yes—
550C2×C4⋊C4C22×D312yes—
551C2×C4⋊C4C22×D312yes—
552C2×C4⋊C4C22×D3116yes—
553C2×C4⋊C4C22×D311yescharacteristic
554C2×C4⋊C4C22×D312yes—
555C2×C4⋊C4C22×D314yes—
556C2×C22⋊C4—32no—
557C2×C22⋊C4—32no—
558C2×C22⋊C4—32no—
559C2×C22⋊C4—34no—
560C2×C22⋊C4—34no—
561C2×C22⋊C4—32no—
562C2×C22⋊C4—34no—
563C2×C22⋊C4—34no—
564C2×C22⋊C4—34no—
565C2×C22⋊C4—34no—
566C2×C22⋊C4C22×D312yes—
567C2×C22⋊C4C22×D314yes—
568C2×C42—32no—
569C2×C42—31no—
570C2×C42—34no—
571C2×C42—32no—
572C2×C42—31no—
573C2×C42—32no—
574C2×C42—31no—
575C2×C42—32no—
576C2×C42—38no—
577C2×C42—316no—
578C2×C42C22×D312yes—
579C2×C42C22×D311yescharacteristic
580C23×C3—24no—
581C23×C3—24no—
582C23×C3—24no—
583C23×C3C2514yes—
584C23×C3C2511yescharacteristic
585C22×D3—22no—
586C22×D3—22no—
587C22×D3—28no—
588C22×D3—28no—
589C22×D3—28no—
590C22×D3H(5,𝔽2)14yes—
591C22×D3C2518yes—
592C22×D3C2512yes—
593C3×Q8—28no—
594C3×Q8—48no—
595C3×D4—28no—
596C2×C3×C4—24no—
597C2×C3×C4—24no—
598C2×C3×C4—28no—
599C2×C3×C4—24no—
600C2×C3×C4—22no—
601C2×C3×C4—216no—
602C2×C3×C4—416no—
603C2×C3×C4C2×#4114yes—
604C2×C3×C42−1+414yes—
605C2×C3×C4C2512yes—
606C2×C3×C4C2514yes—
607C2×C3×C4C2518yes—
608C2×C3×C4C2514yes—
609C2×C3×C4C2514yes—
610C2×C3×C4C2512yes—
611C2×C3×C4C2512yes—
612#67—216no—
613#67—232no—
614#67—416no—
615C2×Dic3—22no—
616C2×Dic3—24no—
617C2×Dic3—24no—
618C2×Dic3—22no—
619C2×Dic3—24no—
620C2×Dic3—22no—
621C2×Dic3C2×#4118yes—
622C2×Dic3C2512yes—
623C2×Dic3C2514yes—
624C2×Dic3C2514yes—
625C2×Dic3C2512yes—
626C2×Dic3C2512yes—
627C2×Dic3C2514yes—
628C2×Dic3C2514yes—
629D12—232no—
630D12—216no—
631D12—216no—
632D12—48no—
633C4×D3—216no—
634C4×D3—28no—
635C4×D3—28no—
636C4×D3—28no—
637C4×D3—232no—
638C4×D3—216no—
639C4×D3—416no—
640C4×D3—416no—
641Dic6—28no—
642Dic6—216no—
643Dic6—416no—
644Dic6C2×#41116yescomplemented
645C24—31no—
646C24—34no—
647C24C23×D312yes—
648#41—664no—
649#41—1264no—
650#41—1232no—
651C2×Q8—24no—
652C2×Q8—38no—
653C2×Q8—34no—
654C2×Q8—34no—
655C2×Q8—38no—
656C2×Q8—316no—
657C2×Q8—44no—
658C2×Q8—68no—
659C2×Q8—632no—
660C2×Q8—64no—
661C2×Q8—128no—
662C2×Q8C23×D314yes—
663C2×Q8C23×D318yes—
664C2×D4—24no—
665C2×D4—316no—
666C2×D4—38no—
667C2×D4—316no—
668C2×D4—38no—
669C2×D4—38no—
670C2×D4—316no—
671C2×D4—38no—
672C2×D4—616no—
673C2×D4—616no—
674C2×D4—68no—
675C2×D4—68no—
676C2×D4—68no—
677C2×D4—124no—
678C2×D4—128no—
679C2×D4C23×D314yes—
680C22×C4—28no—
681C22×C4—32no—
682C22×C4—31no—
683C22×C4—32no—
684C22×C4—31no—
685C22×C4—31no—
686C22×C4—32no—
687C22×C4—32no—
688C22×C4—34no—
689C22×C4—34no—
690C22×C4—38no—
691C22×C4—38no—
692C22×C4—34no—
693C22×C4—316no—
694C22×C4—316no—
695C22×C4—316no—
696C22×C4—48no—
697C22×C4—68no—
698C22×C4—616no—
699C22×C4—68no—
700C22×C4—64no—
701C22×C4—64no—
702C22×C4—64no—
703C22×C4—128no—
704C22×C4—128no—
705C22×C4C23×D318yes—
706C22×C4C23×D312yes—
707C22×C4C23×D312yes—
708C22×C4C23×D311yescharacteristic
709C22×C4C23×D314yes—
710C22×C4C23×D312yes—
711C22×C4C23×D3116yes—
712C22×C4C23×D311yescharacteristic
713C22×C4C23×D311yescharacteristic
714C4⋊C4—38no—
715C4⋊C4—38no—
716C4⋊C4—316no—
717C4⋊C4—38no—
718C4⋊C4—34no—
719C4⋊C4—38no—
720C4⋊C4—38no—
721C4⋊C4—38no—
722C4⋊C4—34no—
723C4⋊C4—38no—
724C4⋊C4—316no—
725C4⋊C4—38no—
726C4⋊C4C23×D314yes—
727C4⋊C4C23×D3116yes—
728C4⋊C4C23×D318yes—
729C4⋊C4C23×D318yes—
730C4⋊C4C23×D314yes—
731C4⋊C4C23×D318yes—
732C4⋊C4C23×D3116yes—
733C22⋊C4—38no—
734C22⋊C4—38no—
735C22⋊C4—38no—
736C22⋊C4—316no—
737C22⋊C4—316no—
738C22⋊C4—38no—
739C22⋊C4—316no—
740C22⋊C4—316no—
741C22⋊C4—316no—
742C22⋊C4—316no—
743C22⋊C4C23×D318yes—
744C22⋊C4C23×D3116yes—
745C42—38no—
746C42—34no—
747C42—34no—
748C42—38no—
749C42—34no—
750C42—38no—
751C42—316no—
752C42—38no—
753C42C23×D318yes—
754C42C23×D314yes—
755C22×C3—24no—
756C22×C3—24no—
757C22×C3—24no—
758C22×C3—48no—
759C22×C3C22×#4112yes—
760C22×C3C2×H(5,𝔽2)12yes—
761C22×C3C2×2−1+412yes—
762C22×C3C2611yescharacteristic
763C2×D3—22no—
764C2×D3—22no—
765C2×D3—28no—
766C2×D3—28no—
767C2×D3—28no—
768C2×D3—28no—
769C2×D3—416no—
770C2×D3C2×H(5,𝔽2)14yes—
771C3×C4—24no—
772C3×C4—24no—
773C3×C4—28no—
774C3×C4—24no—
775C3×C4—22no—
776C3×C4C22×#4114yes—
777C3×C4C2×2−1+414yes—
778Dic3—22no—
779Dic3—24no—
780Dic3—24no—
781Dic3—22no—
782Dic3—24no—
783Dic3—22no—
784Dic3C22×#4118yes—
785C23—24no—
786C23—24no—
787C23—24no—
788C23—34no—
789C23—32no—
790C23—38no—
791C23—62no—
792C23—62no—
793C23—68no—
794C23—68no—
795C23—68no—
796C23C24×D314yes—
797C23C24×D311yescharacteristic
798Q8—28no—
799Q8—316no—
800Q8—48no—
801Q8—616no—
802Q8—68no—
803Q8—1216no—
804D4—28no—
805D4—632no—
806D4—632no—
807D4—616no—
808D4—616no—
809D4—616no—
810D4—128no—
811D4—1216no—
812C2×C4—24no—
813C2×C4—24no—
814C2×C4—24no—
815C2×C4—28no—
816C2×C4—22no—
817C2×C4—216no—
818C2×C4—38no—
819C2×C4—34no—
820C2×C4—32no—
821C2×C4—34no—
822C2×C4—32no—
823C2×C4—32no—
824C2×C4—34no—
825C2×C4—34no—
826C2×C4—416no—
827C2×C4—616no—
828C2×C4—632no—
829C2×C4—616no—
830C2×C4—68no—
831C2×C4—62no—
832C2×C4—64no—
833C2×C4—62no—
834C2×C4—62no—
835C2×C4—64no—
836C2×C4—64no—
837C2×C4—68no—
838C2×C4—68no—
839C2×C4—1216no—
840C2×C4—1216no—
841C2×C4#100714yes—
842C2×C4D3×#4114yes—
843C2×C4C24×D314yes—
844C2×C4C24×D314yes—
845C2×C4C24×D312yes—
846C2×C4C24×D318yes—
847C2×C4C24×D314yes—
848C2×C4C24×D312yes—
849C2×C4C24×D312yes—
850C2×C3—44no—
851C2×C3#352214yescomplemented
852C2×C3C23×#4111yescharacteristic
853C2×C3C22×H(5,𝔽2)11yescharacteristic
854C2×C3C22×2−1+411yescharacteristic
855D3—24no—
856D3—48no—
857C22—24no—
858C22—24no—
859C22—24no—
860C22—34no—
861C22—48no—
862C22—62no—
863C22—62no—
864C22—68no—
865C22—68no—
866C22—68no—
867C22—68no—
868C22—1216no—
869C22C2×#100712yes—
870C22C2×D3×#4112yes—
871C22D3×H(5,𝔽2)12yes—
872C22C25×D311yescharacteristic
873C4—24no—
874C4—24no—
875C4—24no—
876C4—28no—
877C4—22no—
878C4—38no—
879C4—62no—
880C4—64no—
881C4—62no—
882C4—62no—
883C4—64no—
884C4—64no—
885C4C2×#100714yes—
886C4C2×D3×#4114yes—
887C3C2×#352211yescharacteristic, complemented, Sylow
888C2—44no—
889C2—64no—
890C2—128no—
891C2#8693614yesdirect product factor
892C2C22×#100711yescharacteristic
893C2C22×D3×#4111yescharacteristic
894C2C2×D3×H(5,𝔽2)11yescharacteristic
subgroupG/H
centerC23C24×D3
commutator, cosocleC22×C3C26
FrattiniC22C25×D3
FittingC2×C3×#554C2
socleC23×C3C25
hypercenterC2×#554D3
hypocenterC3C2×#3522
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. #86936C2direct (N × H)
3. C2×#5722C2semidirect
4. C2×#5725C2semidirect
5. C2×#5690C2semidirect
6. C2×#5691C2semidirect
7. C2×#5633C2semidirect
8. C2×#5631C2semidirect
9. C2×#5640C2semidirect
10. C2×#5643C2semidirect
11. C2×C4×D3×Q8C2semidirect
12. C2×#5585C2semidirect
13. C2×#5548C2semidirect
14. C2×#5557C2semidirect
15. C2×#5559C2semidirect
16. C2×#5553C2semidirect
17. C2×#5507C2semidirect
18. C2×#5504C2semidirect
24. C3×#554C22semidirect
46. #5725C22semidirect
47. #5722C22semidirect
48. #5691C22semidirect
49. #5690C22semidirect
50. #5643C22semidirect
51. #5640C22semidirect
52. #5633C22semidirect
53. #5631C22semidirect
54. #5585C22semidirect
55. C4×D3×Q8C22semidirect
56. #5559C22semidirect
57. #5557C22semidirect
58. #5553C22semidirect
59. #5548C22semidirect
65. #5507C22semidirect
70. #5504C22semidirect
107. C2×#554D3semidirect
262. #554C2×D3semidirect
400. C2×Dic6#41semidirect
644. Dic6C2×#41semidirect
851. C2×C3#3522semidirect
887. C3C2×#3522semidirect
891. C2#86936direct (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
#869362
C2×#57222
C2×#57252
C2×#56902
C2×#56912
C2×#56332
C2×#56312
C2×#56402
C2×#56432
C2×C4×D3×Q82
C2×#55852
C2×#55482
C2×#55572
C2×#55592
C2×#55532
C2×#55072
C2×#55042
C2×#35223