Finite Group Databasebeta

← #11897571

Subgroups — #11897571

Order 1152.

797 conjugacy classes of subgroups.

The subgroup lattice has 523 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10593960C211yesmaximal, characteristic, complemented
2Dic6×D12C211yesmaximal, characteristic, complemented
3#10592379C211yesmaximal, characteristic, complemented
4C3×C4×D24C211yesmaximal, characteristic
5C3×#4679C211yesmaximal, characteristic, complemented
6#10590894C212yesmaximal, complemented
7#10590772C212yesmaximal, complemented
8#10590771C212yesmaximal
9#10590757C212yesmaximal, complemented
10#10590272C211yesmaximal, characteristic, complemented
11#10590268C211yesmaximal, characteristic, complemented
12#79975—31nomaximal
13#79576—31nomaximal
14C2×D3×Dic6—21no—
15#64078C2211yescharacteristic
16#64078C2211yescharacteristic
17C2×C3×D24C2211yescharacteristic
18C3×C4×D12C2211yescharacteristic
19C3×C4×D12C2211yescharacteristic
20C3×C4×Dic6C2211yescharacteristic
21#63918C2212yes—
22#63896—22no—
23#63893—22no—
24Dic3×D12C2212yes—
25Dic3×D12C2212yes—
26D3×C4⋊Dic3—21no—
27#63869C2212yes—
28#63857—21no—
29#63856—21no—
30C32×C4×C8C2211yescharacteristic
31#63644C2212yes—
32#63644C2212yes—
33C3×#821C2211yescharacteristic
34C3×#821C2211yescharacteristic
35C3×#818C2211yescharacteristic
36C3×#815C2212yes—
37C3×Dic3⋊C8C2212yes—
38C3×C4⋊(C3⋊C8)C2211yescharacteristic
39#63575C2212yes—
40#63573C2212yes—
41#63563C2212yes—
42#63563C2212yes—
43#5579—31no—
44Q8×D12—31no—
45#5543—31no—
46D4×Dic6—31no—
47C3×#446—31no—
48C3×C4×D8—31no—
49#5152—32no—
50#5008—31no—
51#5007—31no—
52#4876—32no—
53#4847—32no—
54#4846—31no—
55#4842—31no—
56#4842—32no—
57#4763—32no—
58#4761—32no—
59#4711—32no—
60#4702—32no—
61C4×D24D311yescharacteristic
62#4680—31no—
63#4680—31no—
64#4680—61no—
65#4679D311yescharacteristic, complemented
66C2×#634—21no—
67C2×#634—21no—
68C2×C3×D12C2311yescharacteristic
69C2×C3×D12C2311yescharacteristic
70C2×C3×C4×D3—21no—
71C2×C3×C4×D3—21no—
72C2×C3×Dic6D411yescharacteristic
73C2×#627—22no—
74C2×D3×Dic3—22no—
75C2×D3×Dic3—22no—
76D3×Dic6—44no—
77C2×C32×C8C2311yescharacteristic
78C2×C32×C8C2311yescharacteristic
79C32×C42C2311yescharacteristic
80C4⋊(C3⋊Dic3)—21no—
81C4⋊(C3⋊Dic3)—21no—
82C4⋊(C3⋊Dic3)C2312yes—
83C4⋊(C3⋊Dic3)C2312yes—
84C3×(C2×D3)⋊C4—21no—
85C3×(C2×D3)⋊C4—21no—
86C3×C4⋊Dic3D411yescharacteristic
87C3×C4⋊Dic3C2311yescharacteristic
88C3×C4⋊Dic3C2311yescharacteristic
89C3×Dic3⋊C4D412yes—
90C3×C4×Dic3C2312yes—
91C2×C3×C3⋊C8C2312yes—
92C3×D24Q814yescomplemented
93#3724—22no—
94Dic3⋊Dic3—22no—
95Dic3⋊Dic3—22no—
96(C2×D3)⋊Dic3—22no—
97(C2×D3)⋊Dic3—22no—
98#3384—91noSylow
99C2×D3×Q8—61no—
100C22×Dic6—61no—
101C2×C3×D8—31no—
102C3×C4×Q8—31no—
103C3×C4×D4—31no—
104C3×C4×D4—31no—
105#946—61no—
106D4×Dic3—32no—
107D4×Dic3—32no—
108C2×C4⋊Dic3—61no—
109#924—61no—
110#924—61no—
111C2×D24C2×D311yescharacteristic
112#897—62no—
113#897—61no—
114#896—62no—
115D3×C4⋊C4—61no—
116#890—32no—
117#888—32no—
118#878—62no—
119#878—62no—
120C4×D12—32no—
121C4×D12—32no—
122C4×D12C2×D311yescharacteristic
123C4×D12C2×D311yescharacteristic
124#870—32no—
125#869—31no—
126#869—31no—
127#869—31no—
128#869—31no—
129#869—32no—
130#869—61no—
131#869—61no—
132C4×Dic6C2×D311yescharacteristic
133C3×#107—31no—
134C3×C4⋊C8—32no—
135C3×C4⋊C8—31no—
136C3×#102—31no—
137C3×#102—31no—
138C3×#97—32no—
139C3×C4×C8—21no—
140C3×C4×C8C2×D311yescharacteristic
141C3×C4×C8C2×D311yescharacteristic
142#832—32no—
143#832—32no—
144#821—32no—
145#821—32no—
146#821C2×D311yescharacteristic
147#821C2×D311yescharacteristic
148#818—32no—
149#818C2×D311yescharacteristic
150#817—32no—
151#817—32no—
152#817—32no—
153#817—32no—
154#817—32no—
155#817—62no—
156#817—62no—
157#815C2×D312yes—
158Dic3⋊C8C2×D312yes—
159#808—32no—
160#807—32no—
161C4⋊(C3⋊C8)C2×D311yescharacteristic
162C22×C3×D3—21no—
163C22×C3×D3—21no—
164C2×C32×C4C2×D411yescharacteristic
165C2×C32×C4C2×D411yescharacteristic
166C2×C32×C4C2411yescharacteristic
167C2×C3⋊Dic3—22no—
168C2×C3⋊Dic3—22no—
169#634—42no—
170#634—81no—
171C2×C3×Dic3—21no—
172C2×C3×Dic3—21no—
173C2×C3×Dic3C2×D412yes—
174C2×C3×Dic3C2×D412yes—
175C3×D12—21no—
176C3×D12—21no—
177C3×D12C2×Q812yes—
178C3×D12C2×Q812yescomplemented
179C3×C4×D3—42no—
180C3×C4×D3—42no—
181C3×Dic6—22no—
182#627—44no—
183D3×Dic3—44no—
184D3×Dic3—82no—
185C32×C8—21no—
186C32×C8C2×Q812yescomplemented
187C3×C3⋊C8—22no—
188#554—91no—
189D4×Q8—91no—
190#501—92no—
191#498—91no—
192#478—92no—
193#476—92no—
194#476—91no—
195#474—91no—
196#446—31no—
197#442—92no—
198C4×D8—31no—
199C2×C3×Q8—31no—
200C2×C3×D4—31no—
201C2×C3×D4—31no—
202C22×C3×C4—61no—
203C22×C3×C4—61no—
204C22×Dic3—62no—
205C22×Dic3—62no—
206D3×Q8—124no—
207C2×D12C22×D311yescharacteristic
208C2×D12C22×D311yescharacteristic
209C2×C4×D3—21no—
210C2×C4×D3—21no—
211C2×C4×D3—62no—
212C2×C4×D3—62no—
213C2×Dic6—62no—
214C2×Dic6—61no—
215C2×Dic6—61no—
216C2×Dic6—62no—
217C2×Dic6—61no—
218C2×Dic6—61no—
219C2×Dic6—121no—
220C2×Dic6—121no—
221C2×Dic6—124no—
222C2×Dic6D1211yescharacteristic
223C3×D8—34no—
224C2×C3×C8—21no—
225C2×C3×C8—21no—
226C2×C3×C8—32no—
227C2×C3×C8C22×D311yescharacteristic
228C2×C3×C8C22×D311yescharacteristic
229C2×C3×C8C22×D311yescharacteristic
230C2×C3×C8C22×D311yescharacteristic
231C3×C4⋊C4—31no—
232C3×C4⋊C4—32no—
233C3×C4⋊C4—31no—
234C3×C4⋊C4—31no—
235C3×C22⋊C4—61no—
236C3×C22⋊C4—61no—
237C3×C42—21no—
238C3×C42—32no—
239C3×C42C22×D311yescharacteristic
240C3×C42C22×D311yescharacteristic
241#217—62no—
242#217—62no—
243(C2×D3)⋊C4—21no—
244(C2×D3)⋊C4—21no—
245(C2×D3)⋊C4—62no—
246(C2×D3)⋊C4—62no—
247C4⋊Dic3—32no—
248C4⋊Dic3—32no—
249C4⋊Dic3—32no—
250C4⋊Dic3—32no—
251C4⋊Dic3—62no—
252C4⋊Dic3—62no—
253C4⋊Dic3—62no—
254C4⋊Dic3—61no—
255C4⋊Dic3—61no—
256C4⋊Dic3—61no—
257C4⋊Dic3—61no—
258C4⋊Dic3—62no—
259C4⋊Dic3—121no—
260C4⋊Dic3—121no—
261C4⋊Dic3D1211yescharacteristic
262C4⋊Dic3C22×D311yescharacteristic
263C4⋊Dic3C22×D311yescharacteristic
264Dic3⋊C4—62no—
265Dic3⋊C4—62no—
266Dic3⋊C4—62no—
267Dic3⋊C4—62no—
268Dic3⋊C4D1212yes—
269C4×Dic3C22×D312yes—
270C2×C3⋊C8C22×D312yes—
271D24Dic614yescomplemented
272C22×C32C22×D411yescharacteristic
273C2×C3×D3—22no—
274C2×C3×D3—22no—
275C2×C3×D3—41no—
276C2×C3×D3—41no—
277C2×C3×D3—41no—
278C2×C3×D3—41no—
279C32×C4—21no—
280C32×C4AGL(1,ℤ/8)12yes—
281C32×C4C22×Q811yescharacteristic
282C32×C42−1+411yescharacteristic
283C3⋊Dic3—42no—
284C3⋊Dic3—42no—
285C3×Dic3—22no—
286C3×Dic3—22no—
287C3×Dic3—41no—
288C3×Dic3—41no—
289C22×Q8—181no—
290C2×D8—31no—
291C4⋊Q8—92no—
292C4⋊Q8—91no—
293C4⋊Q8—91no—
294#125—92no—
295C22⋊Q8—182no—
296C22⋊Q8—182no—
297C22⋊Q8—181no—
298C22⋊Q8—181no—
299C4×Q8—31no—
300C4×D4—31no—
301C4×D4—31no—
302C4×D4—92no—
303C4×D4—92no—
304C2×C4⋊C4—181no—
305#107—31no—
306#107—92no—
307#106—92no—
308#106—92no—
309#106—92no—
310C4⋊C8—32no—
311C4⋊C8—31no—
312#102—31no—
313#102—31no—
314#102—92no—
315#102—92no—
316#97—32no—
317C4×C8D3211yescharacteristic
318C23×C3—61no—
319C23×C3—61no—
320C22×D3—21no—
321C22×D3—21no—
322C3×Q8—62no—
323C3×D4—32no—
324C3×D4—32no—
325C3×D4—61no—
326C3×D4—61no—
327C2×C3×C4—21no—
328C2×C3×C4—21no—
329C2×C3×C4—21no—
330C2×C3×C4—32no—
331C2×C3×C4—32no—
332C2×C3×C4—61no—
333C2×C3×C4—61no—
334C2×C3×C4—122no—
335C2×C3×C4—122no—
336C2×C3×C4C2×D1211yescharacteristic
337C2×C3×C4C2×D1211yescharacteristic
338C2×C3×C4D3×D411yescharacteristic
339C2×C3×C4D3×D411yescharacteristic
340C2×C3×C4C23×D311yescharacteristic
341C2×C3×C4C23×D311yescharacteristic
342C2×Dic3—21no—
343C2×Dic3—21no—
344C2×Dic3—62no—
345C2×Dic3—62no—
346C2×Dic3—62no—
347C2×Dic3—62no—
348C2×Dic3—122no—
349C2×Dic3—122no—
350C2×Dic3—124no—
351C2×Dic3—242no—
352C2×Dic3C2×D1212yes—
353C2×Dic3C2×D1212yes—
354D12—21no—
355D12—21no—
356D12C2×Dic612yes—
357D12C2×Dic612yescomplemented
358C4×D3—42no—
359C4×D3—42no—
360C4×D3—124no—
361C4×D3—242no—
362Dic6—22no—
363Dic6—124no—
364Dic6—124no—
365Dic6—122no—
366Dic6—122no—
367Dic6—242no—
368Dic6—241no—
369Dic6—241no—
370Dic6—242no—
371C3×C8—22no—
372C3×C8—21no—
373C3×C8—21no—
374C3×C8—22no—
375C3×C8—62no—
376C3×C8C2×Dic612yescomplemented
377C3×C8D3×Q812yescomplemented
378C3⋊C8—22no—
379C2×C32D4×Q811yescharacteristic
380C2×C32C2×AGL(1,ℤ/8)11yescharacteristic
381C2×C32#57711yescharacteristic
382C3×D3—42no—
383C3×D3—42no—
384C2×Q8—31no—
385C2×Q8—182no—
386C2×Q8—181no—
387C2×Q8—181no—
388C2×Q8—364no—
389C2×D4—31no—
390C2×D4—31no—
391C22×C4—61no—
392C22×C4—61no—
393C22×C4—182no—
394C22×C4—182no—
395D8—34no—
396C2×C8—32no—
397C2×C8C2×D3211yescharacteristic
398C2×C8C2×D3211yescharacteristic
399C4⋊C4—31no—
400C4⋊C4—32no—
401C4⋊C4—31no—
402C4⋊C4—31no—
403C4⋊C4—92no—
404C4⋊C4—92no—
405C4⋊C4—182no—
406C4⋊C4—182no—
407C4⋊C4—182no—
408C4⋊C4—181no—
409C4⋊C4—181no—
410C22⋊C4—61no—
411C22⋊C4—61no—
412C22⋊C4—182no—
413C22⋊C4—182no—
414C42—32no—
415C42C2×D3211yescharacteristic
416C22×C3—21no—
417C22×C3—62no—
418C22×C3—62no—
419C22×C3—121no—
420C22×C3—121no—
421C22×C3—121no—
422C22×C3—121no—
423C22×C3C22×D1211yescharacteristic
424C22×C3C2×D3×D411yescharacteristic
425C2×D3—22no—
426C2×D3—22no—
427C2×D3—41no—
428C2×D3—41no—
429C2×D3—41no—
430C2×D3—41no—
431C3×C4—22no—
432C3×C4—21no—
433C3×C4—21no—
434C3×C4—21no—
435C3×C4—21no—
436C3×C4—22no—
437C3×C4—62no—
438C3×C4—62no—
439C3×C4—121no—
440C3×C4—121no—
441C3×C4#90812yes—
442C3×C4#91112yes—
443C3×C4C22×Dic611yescharacteristic
444C3×C4C2×D3×Q811yescharacteristic
445C3×C4#101011yescharacteristic
446C3×C4#101011yescharacteristic
447Dic3—22no—
448Dic3—22no—
449Dic3—41no—
450Dic3—41no—
451Dic3—122no—
452Dic3—122no—
453Dic3—122no—
454Dic3—122no—
455Dic3—242no—
456Dic3—242no—
457C32#338411yescharacteristic, complemented, Sylow
458C23—61no—
459C23—61no—
460Q8—62no—
461Q8—364no—
462Q8—362no—
463Q8—721no—
464D4—32no—
465D4—32no—
466D4—61no—
467D4—61no—
468C2×C4—32no—
469C2×C4—32no—
470C2×C4—61no—
471C2×C4—61no—
472C2×C4—122no—
473C2×C4—122no—
474C2×C4—182no—
475C2×C4—182no—
476C2×C4—364no—
477C2×C4—722no—
478C2×C4D3×D1211yescharacteristic
479C2×C4D3×D1211yescharacteristic
480C2×C4C22×D3211yescharacteristic
481C8—21no—
482C8—62no—
483C8D3×Dic612yescomplemented
484C2×C3—21no—
485C2×C3—21no—
486C2×C3—21no—
487C2×C3—122no—
488C2×C3—122no—
489C2×C3D4×Dic611yescharacteristic
490C2×C3Q8×D1211yescharacteristic
491C2×C3C2×#90811yescharacteristic
492C2×C3#575111yescharacteristic
493C2×C3C2×#91111yescharacteristic
494C2×C3#577011yescharacteristic
495D3—42no—
496D3—42no—
497C22—62no—
498C22—62no—
499C22—121no—
500C22—121no—
501C22—121no—
502C22—121no—
503C22C2×D3×D1211yescharacteristic
504C4—21no—
505C4—62no—
506C4—62no—
507C4—121no—
508C4—121no—
509C4—362no—
510C4—362no—
511C4#6379512yes—
512C4C2×D3×Dic611yescharacteristic
513C4#6429811yescharacteristic
514C3—21no—
515C3#7957611yescharacteristic, complemented
516C3#7997511yescharacteristic, complemented
517C2—122no—
518C2—122no—
519C2Dic6×D1211yescharacteristic
520C2C2×#6379511yescharacteristic
521C2#1059467911yescharacteristic
subgroupG/H
centerC22C2×D3×D12
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×C4×C8C22
socleC22×C32C22×D4
prime radicalC2×C3×D24C22
hypercenterC4×C8D32
hypocenterC32#3384
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C42 ◁ C4×C8

Complements

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

NH ≅ G/Ntype
1. #10593960C2semidirect
2. Dic6×D12C2semidirect
3. #10592379C2semidirect
5. C3×#4679C2semidirect
6. #10590894C2semidirect
7. #10590772C2semidirect
9. #10590757C2semidirect
10. #10590272C2semidirect
11. #10590268C2semidirect
65. #4679D3semidirect
92. C3×D24Q8semidirect
178. C3×D12C2×Q8semidirect
186. C32×C8C2×Q8semidirect
271. D24Dic6semidirect
357. D12C2×Dic6semidirect
376. C3×C8C2×Dic6semidirect
377. C3×C8D3×Q8semidirect
457. C32#3384semidirect
483. C8D3×Dic6semidirect
515. C3#79576semidirect
516. C3#79975semidirect

Maximal subgroups

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

subgroupindex
#105939602
Dic6×D122
#105923792
C3×C4×D242
C3×#46792
#105908942
#105907722
#105907712
#105907572
#105902722
#105902682
#799753
#795763