Finite Group Databasebeta

← C2×#10596117 #11910288

Subgroups — C2×#10596117 #11910288

Order 1152.

3072 conjugacy classes of subgroups.

The subgroup lattice has 588 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C32×C22⋊Q8C211yesmaximal, characteristic, complemented
2C2×#64155C211yesmaximal, characteristic, complemented
3C2×#64153C211yesmaximal, characteristic, complemented
4C2×#64138C211yesmaximal, characteristic
5C2×#64133C211yesmaximal, characteristic, complemented
6#10596117C2116yesmaximal, direct product factor
7C2×#64107C211yesmaximal, characteristic, complemented
8C2×#64107C211yesmaximal, characteristic, complemented
9C2×#64105C211yesmaximal, characteristic, complemented
10C2×#64099C211yesmaximal, characteristic, complemented
11C2×#64098C211yesmaximal, characteristic, complemented
12C2×#64097C211yesmaximal, characteristic, complemented
13C2×#64094C211yesmaximal, characteristic
14C2×#64092C211yesmaximal, characteristic
15C2×#64088C211yesmaximal, characteristic, complemented
16C2×#64088C211yesmaximal, characteristic, complemented
17C2×#5646—34nomaximal
18C22×C32×Q8C2211yescharacteristic
19C23×C32×C4C2211yescharacteristic
20C22×#638C2211yescharacteristic
21C22×C4×C3⋊D3C2211yescharacteristic
22C22×#634C2211yescharacteristic
23C22×#634C2211yescharacteristic
24C32×C22⋊Q8C2218yescomplemented
25C2×C32×C4⋊C4C2211yescharacteristic
26C2×C32×C4⋊C4C2211yescharacteristic
27C2×C32×C4⋊C4C2211yescharacteristic
28C2×C32×C22⋊C4C2211yescharacteristic
29C2×C32×C22⋊C4C2211yescharacteristic
30C2×#3757C2211yescharacteristic
31C2×#3757C2211yescharacteristic
32C2×#3757C2211yescharacteristic
33#64155C2218yescomplemented
34#64153C2218yescomplemented
35#64138C2218yes—
36C2×#3752C2211yescharacteristic
37C2×#3752C2211yescharacteristic
38C2×#3752C2211yescharacteristic
39C2×#3752C2211yescharacteristic
40C2×#3752C2211yescharacteristic
41C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
42C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
43C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
44C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
45#64133C2218yescomplemented
46C2×#3750C2211yescharacteristic
47C2×#3750C2211yescharacteristic
48C2×#3750C2211yescharacteristic
49C2×#3750C2211yescharacteristic
50C2×#3750C2211yescharacteristic
51C2×#3750C2211yescharacteristic
52C2×#3750C2211yescharacteristic
53C2×#3750C2211yescharacteristic
54C2×#3750C2211yescharacteristic
55C2×C4×C3⋊Dic3C2211yescharacteristic
56C2×C4×C3⋊Dic3C2211yescharacteristic
57C2×C4×C3⋊Dic3C2211yescharacteristic
58#64107C2218yescomplemented
59#64107C2218yescomplemented
60#64105C2218yescomplemented
61#64099C2218yescomplemented
62#64098C2218yescomplemented
63#64097C2218yescomplemented
64#64094C2218yes—
65#64092C2218yes—
66#64088C2218yescomplemented
67#64088C2218yescomplemented
68C2×C3×C22⋊Q8D314yescomplemented
69C2×#946—34no—
70C2×#944—34no—
71C2×#929—34no—
72C2×#924—34no—
73#5646—364no—
74C2×#898—34no—
75C2×#898—34no—
76C2×#896—34no—
77C2×#890—34no—
78C2×#889—34no—
79C2×#888—34no—
80C2×#885—34no—
81C2×#883—34no—
82C2×#879—34no—
83C2×#879—34no—
84C24×C32C2311yescharacteristic
85C23×C3⋊D3C2311yescharacteristic
86C2×C32×Q8—42no—
87C2×C32×Q8C2314yes—
88C22×C32×C4—42no—
89C22×C32×C4C2311yescharacteristic
90C22×C32×C4C2311yescharacteristic
91C22×C32×C4C2311yescharacteristic
92C22×C32×C4C2311yescharacteristic
93C22×C32×C4C2311yescharacteristic
94C22×C32×C4C2311yescharacteristic
95C22×C32×C4C2314yes—
96C2×#638—42no—
97C2×#638C2314yes—
98C22×C3⋊Dic3C2311yescharacteristic
99C22×C3⋊Dic3C2311yescharacteristic
100C22×C3⋊Dic3C2311yescharacteristic
101C22×C3⋊Dic3C2311yescharacteristic
102C22×C3⋊Dic3C2311yescharacteristic
103C22×C3⋊Dic3C2311yescharacteristic
104C22×C3⋊Dic3C2311yescharacteristic
105C2×C4×C3⋊D3—42no—
106C2×C4×C3⋊D3C2314yes—
107C2×#634—42no—
108C2×#634—42no—
109C2×#634C2314yes—
110C2×#634C2314yes—
111C32×C4⋊C4C2314yes—
112C32×C4⋊C4C2314yes—
113C32×C4⋊C4C2314yes—
114C32×C22⋊C4C2314yes—
115C32×C22⋊C4C2314yes—
116#3757C2314yes—
117#3757C2314yes—
118#3757C2314yes—
119#3752C2314yes—
120#3752C2314yes—
121#3752C2314yes—
122#3752C2314yes—
123#3752C2314yes—
124C4⋊(C3⋊Dic3)C2314yes—
125C4⋊(C3⋊Dic3)C2314yes—
126C4⋊(C3⋊Dic3)C2314yes—
127C4⋊(C3⋊Dic3)C2314yes—
128#3750C2314yes—
129#3750C2314yes—
130#3750C2314yes—
131#3750C2314yes—
132#3750C2314yes—
133#3750C2314yes—
134#3750C2314yes—
135#3750C2314yes—
136#3750C2314yes—
137C4×C3⋊Dic3C2314yes—
138C4×C3⋊Dic3C2314yes—
139C4×C3⋊Dic3C2314yes—
140C2×#563—91noSylow
141C22×C3×Q8C2×D314yes—
142C23×C3×C4C2×D314yes—
143C22×#67—34no—
144C22×C4×D3—34no—
145C22×Dic6—34no—
146C22×Dic6—34no—
147C3×C22⋊Q8C2×D3132yescomplemented
148C2×C3×C4⋊C4C2×D314yes—
149C2×C3×C4⋊C4C2×D314yes—
150C2×C3×C4⋊C4C2×D314yes—
151C2×C3×C22⋊C4C2×D314yes—
152C2×C3×C22⋊C4C2×D314yes—
153C2×#217—34no—
154C2×#217—34no—
155C2×#217—34no—
156#946—332no—
157#944—332no—
158#929—332no—
159C2×(C2×D3)⋊C4—34no—
160C2×(C2×D3)⋊C4—34no—
161C2×(C2×D3)⋊C4—34no—
162C2×(C2×D3)⋊C4—34no—
163C2×(C2×D3)⋊C4—34no—
164C2×C4⋊Dic3—34no—
165C2×C4⋊Dic3—34no—
166C2×C4⋊Dic3—34no—
167C2×C4⋊Dic3—34no—
168#924—332no—
169C2×Dic3⋊C4—34no—
170C2×Dic3⋊C4—34no—
171C2×Dic3⋊C4—34no—
172C2×Dic3⋊C4—34no—
173C2×Dic3⋊C4—34no—
174C2×Dic3⋊C4—34no—
175C2×Dic3⋊C4—34no—
176C2×Dic3⋊C4—34no—
177C2×Dic3⋊C4—34no—
178C2×C4×Dic3—34no—
179C2×C4×Dic3—34no—
180C2×C4×Dic3—34no—
181#898—332no—
182#898—332no—
183#896—332no—
184#890—332no—
185#889—332no—
186#888—332no—
187#885—332no—
188#883—332no—
189#879—332no—
190#879—332no—
191C23×C32—22no—
192C23×C32—22no—
193C23×C32—22no—
194C23×C32C2412yes—
195C23×C32C2411yescharacteristic
196C22×C3⋊D3—22no—
197C22×C3⋊D3—22no—
198C22×C3⋊D3—22no—
199C22×C3⋊D3C2412yes—
200C32×Q8—44no—
201C2×C32×C4—22no—
202C2×C32×C4—22no—
203C2×C32×C4—22no—
204C2×C32×C4—22no—
205C2×C32×C4—22no—
206C2×C32×C4—22no—
207C2×C32×C4—44no—
208C2×C32×C4C2412yes—
209C2×C32×C4C2412yes—
210C2×C32×C4C2412yes—
211C2×C32×C4C2412yes—
212C2×C32×C4C2412yes—
213C2×C32×C4C2412yes—
214#638—44no—
215C2×C3⋊Dic3—22no—
216C2×C3⋊Dic3—22no—
217C2×C3⋊Dic3—22no—
218C2×C3⋊Dic3—22no—
219C2×C3⋊Dic3—22no—
220C2×C3⋊Dic3—22no—
221C2×C3⋊Dic3—22no—
222C2×C3⋊Dic3C2412yes—
223C2×C3⋊Dic3C2412yes—
224C2×C3⋊Dic3C2412yes—
225C2×C3⋊Dic3C2412yes—
226C2×C3⋊Dic3C2412yes—
227C2×C3⋊Dic3C2412yes—
228C2×C3⋊Dic3C2412yes—
229C4×C3⋊D3—44no—
230#634—44no—
231#634—44no—
232#563—916no—
233C2×C4⋊Q8—91no—
234C2×C4⋊Q8—91no—
235C2×#126—91no—
236C2×#126—91no—
237C2×#126—91no—
238C2×#126—91no—
239C2×#125—91no—
240C2×#125—91no—
241C2×#124—91no—
242C2×#123—91no—
243C2×#123—91no—
244C2×C22⋊Q8—91no—
245C2×C22⋊Q8—91no—
246C2×C22⋊Q8—91no—
247C2×C22⋊Q8C3⋊D311yescharacteristic, complemented
248C24×C3C22×D314yes—
249C23×D3—34no—
250C2×C3×Q8—48no—
251C2×C3×Q8C22×D3116yes—
252C22×C3×C4—48no—
253C22×C3×C4C22×D314yes—
254C22×C3×C4C22×D314yes—
255C22×C3×C4C22×D314yes—
256C22×C3×C4C22×D314yes—
257C22×C3×C4C22×D314yes—
258C22×C3×C4C22×D314yes—
259C22×C3×C4C22×D3116yes—
260C2×#67—316no—
261C2×#67—128no—
262C22×Dic3—34no—
263C22×Dic3—34no—
264C22×Dic3—34no—
265C22×Dic3—34no—
266C22×Dic3—34no—
267C22×Dic3—34no—
268C22×Dic3—34no—
269C2×C4×D3—316no—
270C2×C4×D3—128no—
271C2×Dic6—316no—
272C2×Dic6—316no—
273C2×Dic6—128no—
274C2×Dic6—128no—
275C3×C4⋊C4C22×D3116yes—
276C3×C4⋊C4C22×D3116yes—
277C3×C4⋊C4C22×D3116yes—
278C3×C22⋊C4C22×D3116yes—
279C3×C22⋊C4C22×D3116yes—
280#217—316no—
281#217—316no—
282#217—316no—
283(C2×D3)⋊C4—316no—
284(C2×D3)⋊C4—316no—
285(C2×D3)⋊C4—316no—
286(C2×D3)⋊C4—316no—
287(C2×D3)⋊C4—316no—
288C4⋊Dic3—316no—
289C4⋊Dic3—316no—
290C4⋊Dic3—316no—
291C4⋊Dic3—316no—
292Dic3⋊C4—316no—
293Dic3⋊C4—316no—
294Dic3⋊C4—316no—
295Dic3⋊C4—316no—
296Dic3⋊C4—316no—
297Dic3⋊C4—316no—
298Dic3⋊C4—316no—
299Dic3⋊C4—316no—
300Dic3⋊C4—316no—
301C4×Dic3—316no—
302C4×Dic3—316no—
303C4×Dic3—316no—
304C22×C32—22no—
305C22×C32—22no—
306C22×C32—22no—
307C22×C32—44no—
308C22×C32H(5,𝔽2)12yes—
309C22×C322−1+412yes—
310C22×C322−1+412yes—
311C22×C32C2511yescharacteristic
312C2×C3⋊D3—22no—
313C2×C3⋊D3—22no—
314C2×C3⋊D3—22no—
315C2×C3⋊D3—44no—
316C32×C4—22no—
317C32×C4—22no—
318C32×C4—22no—
319C32×C4—22no—
320C32×C4—22no—
321C32×C4—22no—
322C3⋊Dic3—22no—
323C3⋊Dic3—22no—
324C3⋊Dic3—22no—
325C3⋊Dic3—22no—
326C3⋊Dic3—22no—
327C3⋊Dic3—22no—
328C3⋊Dic3—22no—
329C22×Q8—91no—
330C22×Q8—91no—
331C22×Q8C2×C3⋊D311yescharacteristic
332C22×D4—91no—
333C23×C4—91no—
334C23×C4C2×C3⋊D311yescharacteristic
335C4⋊Q8—98no—
336C4⋊Q8—98no—
337#126—98no—
338#126—98no—
339#126—98no—
340#126—98no—
341#125—98no—
342#125—98no—
343#124—98no—
344#123—98no—
345#123—98no—
346C22⋊Q8—98no—
347C22⋊Q8—98no—
348C22⋊Q8—98no—
349C22⋊Q8C2×C3⋊D318yescomplemented
350C2×C4⋊C4—91no—
351C2×C4⋊C4—91no—
352C2×C4⋊C4—91no—
353C2×C4⋊C4—91no—
354C2×C4⋊C4—91no—
355C2×C4⋊C4—91no—
356C2×C4⋊C4—91no—
357C2×C4⋊C4—91no—
358C2×C4⋊C4—91no—
359C2×C4⋊C4—91no—
360C2×C4⋊C4—91no—
361C2×C4⋊C4—91no—
362C2×C4⋊C4—91no—
363C2×C4⋊C4C2×C3⋊D311yescharacteristic
364C2×C4⋊C4C2×C3⋊D311yescharacteristic
365C2×C4⋊C4C2×C3⋊D311yescharacteristic
366C2×C22⋊C4—91no—
367C2×C22⋊C4—91no—
368C2×C22⋊C4—91no—
369C2×C22⋊C4—91no—
370C2×C22⋊C4—91no—
371C2×C22⋊C4—91no—
372C2×C22⋊C4—91no—
373C2×C22⋊C4—91no—
374C2×C22⋊C4C2×C3⋊D311yescharacteristic
375C2×C22⋊C4C2×C3⋊D311yescharacteristic
376C2×C42—91no—
377C2×C42—91no—
378C2×C42—91no—
379C23×C3—28no—
380C23×C3—28no—
381C23×C3—28no—
382C23×C3C23×D318yes—
383C23×C3C23×D314yes—
384C22×D3—38no—
385C22×D3—68no—
386C22×D3—68no—
387C22×D3—68no—
388C3×Q8—416no—
389C2×C3×C4—28no—
390C2×C3×C4—28no—
391C2×C3×C4—28no—
392C2×C3×C4—28no—
393C2×C3×C4—28no—
394C2×C3×C4—28no—
395C2×C3×C4—416no—
396C2×C3×C4C23×D318yes—
397C2×C3×C4C23×D318yes—
398C2×C3×C4C23×D318yes—
399C2×C3×C4C23×D318yes—
400C2×C3×C4C23×D318yes—
401C2×C3×C4C23×D318yes—
402#67—1216no—
403C2×Dic3—38no—
404C2×Dic3—38no—
405C2×Dic3—38no—
406C2×Dic3—38no—
407C2×Dic3—38no—
408C2×Dic3—38no—
409C2×Dic3—38no—
410C2×Dic3—68no—
411C2×Dic3—68no—
412C2×Dic3—68no—
413C2×Dic3—68no—
414C2×Dic3—68no—
415C2×Dic3—68no—
416C2×Dic3—68no—
417C4×D3—1216no—
418Dic6—1216no—
419Dic6—1216no—
420C2×C32—42no—
421C2×C32#56314yescomplemented
422C2×C32C2×H(5,𝔽2)11yescharacteristic
423C2×C32C2×2−1+411yescharacteristic
424C2×C32C2×2−1+411yescharacteristic
425C3⋊D3—42no—
426C24—91no—
427C24C22×C3⋊D311yescharacteristic
428C2×Q8—42no—
429C2×Q8—94no—
430C2×Q8—94no—
431C2×Q8—362no—
432C2×Q8—362no—
433C2×Q8C22×C3⋊D314yes—
434C2×D4—94no—
435C2×D4—362no—
436C22×C4—42no—
437C22×C4—91no—
438C22×C4—91no—
439C22×C4—91no—
440C22×C4—91no—
441C22×C4—91no—
442C22×C4—91no—
443C22×C4—91no—
444C22×C4—94no—
445C22×C4—362no—
446C22×C4C22×C3⋊D311yescharacteristic
447C22×C4C22×C3⋊D311yescharacteristic
448C22×C4C22×C3⋊D311yescharacteristic
449C22×C4C22×C3⋊D311yescharacteristic
450C22×C4C22×C3⋊D311yescharacteristic
451C22×C4C22×C3⋊D311yescharacteristic
452C22×C4C22×C3⋊D314yes—
453C4⋊C4—94no—
454C4⋊C4—94no—
455C4⋊C4—94no—
456C4⋊C4—94no—
457C4⋊C4—94no—
458C4⋊C4—94no—
459C4⋊C4—94no—
460C4⋊C4—94no—
461C4⋊C4—94no—
462C4⋊C4—94no—
463C4⋊C4—94no—
464C4⋊C4—94no—
465C4⋊C4—94no—
466C4⋊C4C22×C3⋊D314yes—
467C4⋊C4C22×C3⋊D314yes—
468C4⋊C4C22×C3⋊D314yes—
469C22⋊C4—94no—
470C22⋊C4—94no—
471C22⋊C4—94no—
472C22⋊C4—94no—
473C22⋊C4—94no—
474C22⋊C4—94no—
475C22⋊C4—94no—
476C22⋊C4—94no—
477C22⋊C4C22×C3⋊D314yes—
478C22⋊C4C22×C3⋊D314yes—
479C42—94no—
480C42—94no—
481C42—94no—
482C22×C3—28no—
483C22×C3—28no—
484C22×C3—28no—
485C22×C3—416no—
486C22×C3#100418yes—
487C22×C3#100718yes—
488C22×C3#101018yes—
489C22×C3C24×D314yes—
490C2×D3—68no—
491C2×D3—68no—
492C2×D3—68no—
493C2×D3—1216no—
494C3×C4—28no—
495C3×C4—28no—
496C3×C4—28no—
497C3×C4—28no—
498C3×C4—28no—
499C3×C4—28no—
500Dic3—68no—
501Dic3—68no—
502Dic3—68no—
503Dic3—68no—
504Dic3—68no—
505Dic3—68no—
506Dic3—68no—
507C32C2×#56311yescharacteristic, complemented, Sylow
508C23—22no—
509C23—22no—
510C23—22no—
511C23—92no—
512C23—182no—
513C23—182no—
514C23—182no—
515C23C23×C3⋊D312yes—
516C23C23×C3⋊D311yescharacteristic
517Q8—44no—
518Q8—364no—
519Q8—364no—
520D4—364no—
521C2×C4—22no—
522C2×C4—22no—
523C2×C4—22no—
524C2×C4—22no—
525C2×C4—22no—
526C2×C4—22no—
527C2×C4—44no—
528C2×C4—92no—
529C2×C4—92no—
530C2×C4—92no—
531C2×C4—92no—
532C2×C4—92no—
533C2×C4—92no—
534C2×C4—92no—
535C2×C4—182no—
536C2×C4—182no—
537C2×C4—182no—
538C2×C4—182no—
539C2×C4—182no—
540C2×C4—182no—
541C2×C4—182no—
542C2×C4—364no—
543C2×C4C23×C3⋊D312yes—
544C2×C4C23×C3⋊D312yes—
545C2×C4C23×C3⋊D312yes—
546C2×C4C23×C3⋊D312yes—
547C2×C4C23×C3⋊D312yes—
548C2×C4C23×C3⋊D312yes—
549C2×C3—48no—
550C2×C3#5646116yescomplemented
551C2×C3C2×#100414yes—
552C2×C3C2×#100714yes—
553C2×C3C2×#101014yes—
554D3—128no—
555C22—22no—
556C22—22no—
557C22—22no—
558C22—44no—
559C22—182no—
560C22—182no—
561C22—182no—
562C22—364no—
563C22#6436112yes—
564C22#6436412yes—
565C22#6436712yes—
566C22C24×C3⋊D311yescharacteristic
567C4—22no—
568C4—22no—
569C4—22no—
570C4—22no—
571C4—22no—
572C4—22no—
573C4—182no—
574C4—182no—
575C4—182no—
576C4—182no—
577C4—182no—
578C4—182no—
579C4—182no—
580C3C2×#564614yescomplemented
581C2—42no—
582C2—362no—
583C2#1059611714yesdirect product factor
584C2C2×#6436111yescharacteristic
585C2C2×#6436411yescharacteristic
586C2C2×#6436711yescharacteristic
subgroupG/H
centerC23C23×C3⋊D3
commutator, cosocleC22×C32C25
FrattiniC22C24×C3⋊D3
FittingC2×C32×C22⋊Q8C2
socleC23×C32C24
prime radicalC22×#638C22
hypercenterC2×C22⋊Q8C3⋊D3
hypocenterC32C2×#563
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C23 ◁ C2×C22⋊Q8

Complements

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

NH ≅ G/Ntype
1. C2×C32×C22⋊Q8C2semidirect
2. C2×#64155C2semidirect
3. C2×#64153C2semidirect
5. C2×#64133C2semidirect
6. #10596117C2direct (N × H)
7. C2×#64107C2semidirect
8. C2×#64107C2semidirect
9. C2×#64105C2semidirect
10. C2×#64099C2semidirect
11. C2×#64098C2semidirect
12. C2×#64097C2semidirect
15. C2×#64088C2semidirect
16. C2×#64088C2semidirect
24. C32×C22⋊Q8C22semidirect
33. #64155C22semidirect
34. #64153C22semidirect
45. #64133C22semidirect
58. #64107C22semidirect
59. #64107C22semidirect
60. #64105C22semidirect
61. #64099C22semidirect
62. #64098C22semidirect
63. #64097C22semidirect
66. #64088C22semidirect
67. #64088C22semidirect
68. C2×C3×C22⋊Q8D3semidirect
147. C3×C22⋊Q8C2×D3semidirect
247. C2×C22⋊Q8C3⋊D3semidirect
349. C22⋊Q8C2×C3⋊D3semidirect
421. C2×C32#563semidirect
507. C32C2×#563semidirect
550. C2×C3#5646semidirect
580. C3C2×#5646semidirect
583. C2#10596117direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C32×C22⋊Q82
C2×#641552
C2×#641532
C2×#641382
C2×#641332
#105961172
C2×#641072
C2×#641052
C2×#640992
C2×#640982
C2×#640972
C2×#640942
C2×#640922
C2×#640882
C2×#56463