Finite Group Databasebeta

← #11878911

Subgroups — #11878911

Order 1152.

822 conjugacy classes of subgroups.

The subgroup lattice has 583 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×D3×C4⋊Q8C211yesmaximal, characteristic
2#10593873C211yesmaximal, characteristic
3#10592789C211yesmaximal, characteristic, complemented
4C3×#5090C211yesmaximal, characteristic, complemented
5#10591626C212yesmaximal, complemented
6#10591623C212yesmaximal, complemented
7#10591595C212yesmaximal
8#10591594C212yesmaximal
9#10590388C211yesmaximal, characteristic, complemented
10#10590384C211yesmaximal, characteristic, complemented
11#10590248C211yesmaximal, characteristic
12#83222—31nomaximal
13#80480—31nomaximal
14C2×C3×D3×Q8C2212yes—
15C32×C4⋊Q8C2211yescharacteristic
16C2×#3756C2212yes—
17C4×#634C2211yescharacteristic
18C3×#944C2212yes—
19C2×C3×#216C2212yes—
20C3×D3×C4⋊C4—21no—
21C3×D3×C4⋊C4—21no—
22C3×#888—21no—
23C3×#888—21no—
24C3×C42×D3C2211yescharacteristic
25C3×#869C2211yescharacteristic
26C3×C4×Dic6C2211yescharacteristic
27#63918C2211yescharacteristic
28C4×#627—21no—
29#63867—21no—
30#63866C2211yescharacteristic
31#63857C2211yescharacteristic
32#63856C2211yescharacteristic
33#63855—21no—
34#63851—21no—
35C2×#3719C2212yes—
36C2×#3718C2212yes—
37#63662C2212yes—
38C4⋊(C3⋊(C3⋊C8))C2211yescharacteristic
39C3×#835C2212yes—
40C3×C4⋊(C3⋊C8)C2211yescharacteristic
41#63566C2212yes—
42#63565C2212yes—
43(C2×D3)⋊(C3⋊C8)C2212yes—
44Dic3×C3⋊C8C2212yes—
45C2×C3×C4⋊Q8—31no—
46D3×C4⋊Q8D311yescharacteristic
47#5578—31no—
48#5470—31no—
49C3×#462—31no—
50#5228—32no—
51#5228—32no—
52#5186—32no—
53#5183—32no—
54#5092—32no—
55#5090—31no—
56#5090—31no—
57#5090—31no—
58#5090—31no—
59#5090—61no—
60#5090D311yescharacteristic, complemented
61#5079—32no—
62#5031—31no—
63#4925—31no—
64#4849—31no—
65#4833—31no—
66#4809—32no—
67#4792—32no—
68C2×C32×Q8C2312yes—
69C2×#634C2311yescharacteristic
70C3×D3×Q8—42no—
71C3×D3×Q8—42no—
72C2×C3×C4×D3—22no—
73C2×C3×C4×D3D411yescharacteristic
74C2×C3×C4×D3D411yescharacteristic
75C2×C3×C4×D3C2311yescharacteristic
76C2×C3×Dic6—22no—
77C2×C3×Dic6C2311yescharacteristic
78C2×C3×Dic6C2312yes—
79C2×#627—21no—
80C32×C4⋊C4—21no—
81C32×C4⋊C4—21no—
82C32×C42C2311yescharacteristic
83#3756—42no—
84C4⋊(C3⋊Dic3)C2311yescharacteristic
85#3750—21no—
86C4×C3⋊Dic3—21no—
87C2×C3⋊(C3⋊C8)C2312yes—
88C3×#216—42no—
89C3×C4⋊Dic3—21no—
90C3×C4⋊Dic3—21no—
91C3×C4⋊Dic3C2311yescharacteristic
92C3×Dic3⋊C4—21no—
93C3×Dic3⋊C4—22no—
94C3×Dic3⋊C4—22no—
95C3×C4×Dic3—21no—
96C3×C4×Dic3D411yescharacteristic
97C3×C4×Dic3D411yescharacteristic
98C3×C4×Dic3C2311yescharacteristic
99C2×C3×C3⋊C8C2312yes—
100#3724—21no—
101Dic3⋊Dic3—21no—
102Dic3⋊Dic3—21no—
103Dic3⋊Dic3—21no—
104Dic3⋊Dic3—21no—
105(C2×D3)⋊Dic3—21no—
106(C2×D3)⋊Dic3—21no—
107#3719—42no—
108#3718—42no—
109#3209—91noSylow
110C22×C3×Q8—32no—
111C2×D3×Q8C2×D312yes—
112C2×C3×Q16—32no—
113C3×C4⋊Q8—21no—
114C3×C4⋊Q8—32no—
115C3×C4⋊Q8—31no—
116C3×C4⋊Q8—61no—
117C3×C4⋊Q8—61no—
118C3×C4⋊Q8C2×D311yescharacteristic
119C3×C4⋊Q8C2×D311yescharacteristic
120C3×C4×Q8—31no—
121C2×C3×C4⋊C4—61no—
122C2×C3×C4⋊C4—61no—
123C2×C3×C42—31no—
124#946—31no—
125#944—31no—
126#944C2×D312yes—
127C2×#216—32no—
128C2×#216—32no—
129C2×#216—32no—
130C2×#216—32no—
131C2×#216—32no—
132C2×#216—62no—
133C2×#216C2×D312yes—
134#926—61no—
135#924—31no—
136#924—31no—
137#924—61no—
138C2×Dic12—32no—
139#897—31no—
140#896—61no—
141D3×C4⋊C4—21no—
142D3×C4⋊C4—21no—
143#889—61no—
144#888—21no—
145#888—21no—
146#888—31no—
147#872—61no—
148C42×D3C2×D311yescharacteristic
149#870—61no—
150#869—31no—
151#869—31no—
152#869C2×D311yescharacteristic
153C4×Dic6—31no—
154C4×Dic6—31no—
155C4×Dic6—61no—
156C4×Dic6—61no—
157C4×Dic6—61no—
158C4×Dic6C2×D311yescharacteristic
159C3×C4⋊C8—31no—
160C3×#103—32no—
161#835—32no—
162#835—32no—
163#835—32no—
164#835—32no—
165#835—62no—
166#835C2×D312yes—
167#830—32no—
168(C2×D3)⋊C8—32no—
169#816—32no—
170C8×Dic3—32no—
171#810—32no—
172C4⋊(C3⋊C8)—31no—
173C4⋊(C3⋊C8)—31no—
174C4⋊(C3⋊C8)—61no—
175C4⋊(C3⋊C8)C2×D311yescharacteristic
176C4×C3⋊C8—32no—
177C22×C3×D3C2×D411yescharacteristic
178C32×Q8—22no—
179C32×Q8—22no—
180C2×C32×C4—22no—
181C2×C32×C4C2×D411yescharacteristic
182C2×C32×C4C2×D411yescharacteristic
183C2×C32×C4C2411yescharacteristic
184C2×C3⋊Dic3—21no—
185C2×C3⋊Dic3—21no—
186#634—21no—
187#634—21no—
188C2×C3×Dic3—21no—
189C2×C3×Dic3—21no—
190C2×C3×Dic3—22no—
191C2×C3×Dic3C2×D411yescharacteristic
192C2×C3×Dic3C2×D411yescharacteristic
193C2×C3×Dic3C2×D411yescharacteristic
194C3×C4×D3—21no—
195C3×C4×D3—21no—
196C3×C4×D3—22no—
197C3×C4×D3—44no—
198C3×C4×D3Q1614yescomplemented
199C3×Dic6—21no—
200C3×Dic6—22no—
201C3×Dic6—22no—
202C3×Dic6—21no—
203C3×Dic6—44no—
204#627—42no—
205C3⋊(C3⋊C8)—22no—
206C3×C3⋊C8—22no—
207#533—91no—
208C2×C4⋊Q8—31no—
209#494—92no—
210#487—92no—
211#462—31no—
212#462—91no—
213#462—91no—
214#462—91no—
215#451—92no—
216#451—92no—
217#431—91no—
218C2×C3×Q8—22no—
219C2×C3×Q8—32no—
220C2×C3×Q8—31no—
221C2×C3×Q8—62no—
222C2×C3×Q8—122no—
223C2×C3×Q8—122no—
224C2×C3×Q8C22×D312yes—
225C2×C3×Q8C22×D312yes—
226C22×C3×C4—31no—
227C22×C3×C4—31no—
228C22×C3×C4—31no—
229C22×C3×C4—62no—
230D3×Q8—42no—
231D3×Q8—42no—
232C2×C4×D3—22no—
233C2×C4×D3#6711yescharacteristic
234C2×C4×D3#6711yescharacteristic
235C2×C4×D3C22×D311yescharacteristic
236C2×Dic6—22no—
237C2×Dic6—31no—
238C2×Dic6—31no—
239C2×Dic6—61no—
240C2×Dic6—61no—
241C2×Dic6—61no—
242C2×Dic6C22×D312yes—
243C2×Dic6C22×D311yescharacteristic
244C3×Q16—122no—
245C2×C3×C8—32no—
246C3×C4⋊C4—21no—
247C3×C4⋊C4—21no—
248C3×C4⋊C4—21no—
249C3×C4⋊C4—21no—
250C3×C4⋊C4—31no—
251C3×C4⋊C4—41no—
252C3×C4⋊C4—41no—
253C3×C4⋊C4—62no—
254C3×C4⋊C4—62no—
255C3×C4⋊C4—61no—
256C3×C4⋊C4—61no—
257C3×C4⋊C4—61no—
258C3×C42—21no—
259C3×C42—31no—
260C3×C42—31no—
261C3×C42—31no—
262C3×C42—61no—
263C3×C42C22×D311yescharacteristic
264C3×C42C22×D311yescharacteristic
265#217—61no—
266#217—61no—
267#216—42no—
268#216—122no—
269#216—122no—
270#216—122no—
271#216—122no—
272#216—122no—
273#216—124no—
274(C2×D3)⋊C4—61no—
275(C2×D3)⋊C4—61no—
276C4⋊Dic3—21no—
277C4⋊Dic3—21no—
278C4⋊Dic3—31no—
279C4⋊Dic3—31no—
280C4⋊Dic3—61no—
281C4⋊Dic3—61no—
282C4⋊Dic3—61no—
283C4⋊Dic3—61no—
284C4⋊Dic3—61no—
285C4⋊Dic3C22×D311yescharacteristic
286Dic3⋊C4—21no—
287Dic3⋊C4—22no—
288Dic3⋊C4—22no—
289Dic3⋊C4—61no—
290Dic3⋊C4—61no—
291Dic3⋊C4—61no—
292Dic3⋊C4—61no—
293Dic3⋊C4—61no—
294Dic3⋊C4—61no—
295Dic3⋊C4—61no—
296Dic3⋊C4—61no—
297Dic3⋊C4—121no—
298C4×Dic3—21no—
299C4×Dic3—61no—
300C4×Dic3—61no—
301C4×Dic3—121no—
302C4×Dic3#6711yescharacteristic
303C4×Dic3#6711yescharacteristic
304C4×Dic3C22×D311yescharacteristic
305C2×C3⋊C8—32no—
306C2×C3⋊C8—32no—
307C2×C3⋊C8—62no—
308C2×C3⋊C8C22×D312yes—
309Dic12—122no—
310C22×C32C22×D411yescharacteristic
311C2×C3×D3—21no—
312C2×C3×D3—21no—
313C2×C3×D3C2×Q1612yes—
314C32×C4—21no—
315C32×C4—42no—
316C32×C4C2×Q1612yes—
317C32×C4H(5,𝔽2)11yescharacteristic
318C32×C4H(5,𝔽2)11yescharacteristic
319C3⋊Dic3—41no—
320C3⋊Dic3—41no—
321C3×Dic3—21no—
322C3×Dic3—42no—
323C3×Dic3—41no—
324C3×Dic3—41no—
325C3×Dic3C2×Q1612yes—
326C3×Dic3#13712yes—
327C22×Q8—32no—
328C2×Q16—32no—
329C2×Q16—92no—
330C2×Q16—92no—
331C2×Q16—92no—
332C4⋊Q8—32no—
333C4⋊Q8—31no—
334C4⋊Q8—61no—
335C4⋊Q8—61no—
336C4⋊Q8—91no—
337C4⋊Q8—91no—
338C4⋊Q8D3211yescharacteristic
339#125—181no—
340C22⋊Q8—91no—
341C22⋊Q8—91no—
342C22⋊Q8—181no—
343C4×Q8—31no—
344C4×Q8—91no—
345C4×Q8—181no—
346#117—181no—
347C2×C4⋊C4—61no—
348C2×C4⋊C4—61no—
349C2×C42—31no—
350C4⋊C8—31no—
351C4⋊C8—91no—
352#103—32no—
353#103—92no—
354#103—92no—
355#103—92no—
356C22⋊C8—92no—
357C4×C8—92no—
358C23×C3—31no—
359C22×D3C2×#6711yescharacteristic
360C3×Q8—22no—
361C3×Q8—22no—
362C3×Q8—22no—
363C3×Q8—22no—
364C3×Q8—42no—
365C3×Q8—42no—
366C3×Q8—61no—
367C3×Q8—62no—
368C3×Q8—61no—
369C3×Q8—62no—
370C3×Q8—124no—
371C2×C3×C4—22no—
372C2×C3×C4—22no—
373C2×C3×C4—21no—
374C2×C3×C4—21no—
375C2×C3×C4—21no—
376C2×C3×C4—31no—
377C2×C3×C4—31no—
378C2×C3×C4—34no—
379C2×C3×C4—31no—
380C2×C3×C4—42no—
381C2×C3×C4—62no—
382C2×C3×C4—61no—
383C2×C3×C4—61no—
384C2×C3×C4—62no—
385C2×C3×C4—61no—
386C2×C3×C4—61no—
387C2×C3×C4—124no—
388C2×C3×C4D3×D411yescharacteristic
389C2×C3×C4D3×D411yescharacteristic
390C2×C3×C4C2×#6711yescharacteristic
391C2×C3×C4C2×#6711yescharacteristic
392C2×C3×C4C23×D311yescharacteristic
393C2×C3×C4C23×D311yescharacteristic
394C2×Dic3—21no—
395C2×Dic3—21no—
396C2×Dic3—22no—
397C2×Dic3—61no—
398C2×Dic3—61no—
399C2×Dic3—61no—
400C2×Dic3—61no—
401C2×Dic3—121no—
402C2×Dic3—121no—
403C2×Dic3C2×#6711yescharacteristic
404C2×Dic3C2×#6711yescharacteristic
405C2×Dic3C2×#6711yescharacteristic
406C4×D3—21no—
407C4×D3—21no—
408C4×D3—22no—
409C4×D3—44no—
410C4×D3#21614yescomplemented
411Dic6—22no—
412Dic6—21no—
413Dic6—22no—
414Dic6—21no—
415Dic6—44no—
416Dic6—62no—
417Dic6—61no—
418Dic6—61no—
419Dic6—61no—
420Dic6—61no—
421Dic6—121no—
422Dic6—122no—
423Dic6—122no—
424C3×C8—62no—
425C3⋊C8—22no—
426C3⋊C8—62no—
427C3⋊C8—62no—
428C3⋊C8—122no—
429C2×C32#53511yescharacteristic
430C2×C32C22×Q1611yescharacteristic
431C2×C32C2×#13711yescharacteristic
432C3×D3—22no—
433C2×Q8—32no—
434C2×Q8—31no—
435C2×Q8—62no—
436C2×Q8—91no—
437C2×Q8—122no—
438C2×Q8—122no—
439C2×Q8—181no—
440C2×Q8C2×D3212yes—
441C22×C4—31no—
442C22×C4—31no—
443C22×C4—31no—
444C22×C4—62no—
445Q16—122no—
446Q16—362no—
447Q16—362no—
448Q16—362no—
449C2×C8—32no—
450C2×C8—92no—
451C4⋊C4—21no—
452C4⋊C4—21no—
453C4⋊C4—31no—
454C4⋊C4—62no—
455C4⋊C4—62no—
456C4⋊C4—61no—
457C4⋊C4—61no—
458C4⋊C4—61no—
459C4⋊C4—91no—
460C4⋊C4—181no—
461C4⋊C4—181no—
462C4⋊C4—181no—
463C4⋊C4—181no—
464C4⋊C4—181no—
465C4⋊C4—181no—
466C22⋊C4—181no—
467C22⋊C4—181no—
468C42—31no—
469C42—31no—
470C42—31no—
471C42—61no—
472C42—181no—
473C42C2×D3211yescharacteristic
474C22×C3—21no—
475C22×C3—32no—
476C22×C3—61no—
477C22×C3—61no—
478C22×C3C2×D3×D411yescharacteristic
479C22×C3C22×#6711yescharacteristic
480C2×D3—21no—
481C2×D3—21no—
482C2×D3C2×#21612yes—
483C3×C4—21no—
484C3×C4—21no—
485C3×C4—21no—
486C3×C4—21no—
487C3×C4—22no—
488C3×C4—32no—
489C3×C4—32no—
490C3×C4—41no—
491C3×C4—42no—
492C3×C4—42no—
493C3×C4—61no—
494C3×C4—82no—
495C3×C4—121no—
496C3×C4—121no—
497C3×C4—122no—
498C3×C4D3×Q1612yes—
499C3×C4C2×#21612yes—
500C3×C4#100411yescharacteristic
501C3×C4#100411yescharacteristic
502C3×C4#100411yescharacteristic
503C3×C4#100911yescharacteristic
504Dic3—21no—
505Dic3—41no—
506Dic3—42no—
507Dic3—41no—
508Dic3—122no—
509Dic3—121no—
510Dic3—121no—
511Dic3—121no—
512Dic3—121no—
513Dic3—241no—
514Dic3#94212yes—
515Dic3C2×#21612yes—
516C32#320911yescharacteristic, complemented, Sylow
517C23—31no—
518Q8—22no—
519Q8—22no—
520Q8—61no—
521Q8—62no—
522Q8—61no—
523Q8—62no—
524Q8—124no—
525Q8—181no—
526Q8—181no—
527Q8—362no—
528C2×C4—22no—
529C2×C4—31no—
530C2×C4—31no—
531C2×C4—34no—
532C2×C4—31no—
533C2×C4—62no—
534C2×C4—61no—
535C2×C4—61no—
536C2×C4—61no—
537C2×C4—61no—
538C2×C4—62no—
539C2×C4—124no—
540C2×C4—181no—
541C2×C4—181no—
542C2×C4D3×#6711yescharacteristic
543C2×C4D3×#6711yescharacteristic
544C2×C4C22×D3211yescharacteristic
545C8—62no—
546C8—182no—
547C2×C3—21no—
548C2×C3—21no—
549C2×C3—21no—
550C2×C3—62no—
551C2×C3#560711yescharacteristic
552C2×C3C2×D3×Q1611yescharacteristic
553C2×C3D3×#13711yescharacteristic
554C2×C3#580511yescharacteristic
555C2×C3C2×#94211yescharacteristic
556C2×C3C22×#21611yescharacteristic
557D3—22no—
558C22—32no—
559C22—61no—
560C22—61no—
561C22C2×D3×#6711yescharacteristic
562C4—21no—
563C4—32no—
564C4—32no—
565C4—42no—
566C4—61no—
567C4—122no—
568C4—121no—
569C4—121no—
570C4—361no—
571C4—361no—
572C4D3×#21612yes—
573C4#6431311yescharacteristic
574C4#6431411yescharacteristic
575C3—21no—
576C3#8048011yescharacteristic, complemented
577C3#8322211yescharacteristic, complemented
578C2—62no—
579C2#1059523111yescharacteristic
580C2D3×#94211yescharacteristic
581C2C2×D3×#21611yescharacteristic
subgroupG/H
centerC22C2×D3×#67
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×C4⋊Q8C22
socleC22×C32C22×D4
prime radicalC22×C3×D3C2×D4
hypercenterC4⋊Q8D32
hypocenterC32#3209
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C42 ◁ C4⋊Q8

Complements

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

NH ≅ G/Ntype
3. #10592789C2semidirect
4. C3×#5090C2semidirect
5. #10591626C2semidirect
6. #10591623C2semidirect
9. #10590388C2semidirect
10. #10590384C2semidirect
60. #5090D3semidirect
198. C3×C4×D3Q16semidirect
410. C4×D3#216semidirect
516. C32#3209semidirect
576. C3#80480semidirect
577. C3#83222semidirect

Maximal subgroups

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

subgroupindex
C3×D3×C4⋊Q82
#105938732
#105927892
C3×#50902
#105916262
#105916232
#105915952
#105915942
#105903882
#105903842
#105902482
#832223
#804803