Finite Group Databasebeta

← #11897663

Subgroups — #11897663

Order 1152.

794 conjugacy classes of subgroups.

The subgroup lattice has 520 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10596050C211yesmaximal, characteristic
2C3×Q8×Dic6C211yesmaximal, characteristic, complemented
3C3×#5024C211yesmaximal, characteristic, complemented
4#10590362C212yesmaximal
5C4×#3717C211yesmaximal, characteristic
6#10590313C212yesmaximal
7#10590311C211yesmaximal, characteristic, complemented
8#10590305C212yesmaximal, complemented
9#10590302C212yesmaximal, complemented
10#10590300C211yesmaximal, characteristic
11#10590283C211yesmaximal, characteristic, complemented
12#83706—31nomaximal
13#79976—31nomaximal
14C32×C4×Q8C2211yescharacteristic
15#64155—21no—
16#64105—22no—
17C4⋊C4×C3⋊D3—21no—
18C4×C4⋊(C3⋊D3)C2211yescharacteristic
19C4×C4⋊(C3⋊D3)C2212yes—
20#64079C2212yes—
21#64078C2211yescharacteristic
22C3×Q8×Dic3—21no—
23C3×#888—21no—
24C3×#888—22no—
25C3×#869C2211yescharacteristic
26C3×#869C2212yes—
27C3×C4×Dic6C2211yescharacteristic
28C3×C4×Dic6C2212yes—
29C2×#3717C2211yescharacteristic
30C3×C4⋊(C3⋊C8)C2211yescharacteristic
31C3×C4⋊(C3⋊C8)C2212yes—
32C3×#803C2212yes—
33C3×C4×C3⋊C8C2211yescharacteristic
34#63575C2212yes—
35#63575C2212yes—
36#63575C2212yes—
37#63573C2212yes—
38#63573C2211yescharacteristic
39#63566C2212yes—
40#63566C2211yescharacteristic
41#63564C2212yes—
42#63564C2211yescharacteristic
43C3×Q82—31no—
44#5579—31no—
45#5579—31no—
46#5579—61no—
47Q8×Dic6D311yescharacteristic, complemented
48C3×#446—31no—
49#5087—32no—
50#5084—31no—
51#5081—32no—
52#5078—31no—
53#5026—32no—
54C4×#215—31no—
55#5024D311yescharacteristic, complemented
56#5022—32no—
57#5021—31no—
58#4850—31no—
59#4846—32no—
60#4842—31no—
61#4829—32no—
62#4710—32no—
63#4702—32no—
64C4×#204—31no—
65#4682—31no—
66C2×C32×Q8D411yescharacteristic
67C2×C4⋊(C3⋊D3)C2311yescharacteristic
68C2×C4×C3⋊D3—21no—
69C2×C4×C3⋊D3—22no—
70C2×#634—21no—
71C2×C3×Dic6—22no—
72C2×C3×Dic6—21no—
73C2×C3×Dic6C2311yescharacteristic
74C32×C4⋊C4D411yescharacteristic
75C32×C4⋊C4D412yes—
76C32×C42C2311yescharacteristic
77C32×C42C2312yes—
78#3752—21no—
79#3752—22no—
80C4⋊(C3⋊Dic3)—21no—
81C4⋊(C3⋊Dic3)C2312yes—
82C4⋊(C3⋊Dic3)C2311yescharacteristic
83#3750—22no—
84#3750—22no—
85C3×C4⋊Dic3—22no—
86C3×C4⋊Dic3—21no—
87C3×C4⋊Dic3C2312yes—
88C3×C4⋊Dic3C2311yescharacteristic
89C3×Dic3⋊C4—22no—
90C3×Dic3⋊C4—21no—
91C3×C4×Dic3—22no—
92C3×C4×Dic3—21no—
93C2×C3×C3⋊C8C2312yes—
94C2×C3×C3⋊C8C2311yescharacteristic
95C2×C3×C3⋊C8C2311yescharacteristic
96#3717Q814yescomplemented
97#3385—91noSylow
98C3×C4⋊Q8—31no—
99C3×C4⋊Q8—32no—
100C3×C4⋊Q8—61no—
101C3×C4⋊Q8—62no—
102C3×C4×Q8—21no—
103C3×C4×Q8—31no—
104C3×C4×Q8—32no—
105C3×C4×Q8—61no—
106C3×C4×Q8C2×D311yescharacteristic
107C3×C4×Q8C2×D311yescharacteristic
108#946—62no—
109#946—61no—
110#946—61no—
111Q8×Dic3—21no—
112C2×#215—31no—
113C2×#204—31no—
114#896—64no—
115#896—62no—
116#896—62no—
117D3×C4⋊C4—62no—
118D3×C4⋊C4—61no—
119D3×C4⋊C4—61no—
120#888—21no—
121#888—22no—
122C4×D12—31no—
123C4×D12—32no—
124C4×D12—31no—
125C4×D12—32no—
126C4×D12—61no—
127C4×D12—62no—
128#870—32no—
129#870—32no—
130#870—62no—
131#869—31no—
132#869—31no—
133#869—61no—
134#869C2×D311yescharacteristic
135#869C2×D312yes—
136C4×Dic6C2×D311yescharacteristic
137C4×Dic6C2×D312yes—
138C3×C4⋊C8—32no—
139C3×C4⋊C8—31no—
140C3×#97—32no—
141C3×C4×C8—31no—
142#835—32no—
143#835—31no—
144#821—31no—
145#821—32no—
146#818—32no—
147#818—32no—
148#818—32no—
149#817—31no—
150#817—32no—
151#816—31no—
152#816—32no—
153#809—31no—
154#809—32no—
155#808—32no—
156#808—31no—
157#807—32no—
158#807—32no—
159#807—32no—
160C4⋊(C3⋊C8)C2×D311yescharacteristic
161C4⋊(C3⋊C8)C2×D312yes—
162#803C2×D312yes—
163C4×C3⋊C8C2×D311yescharacteristic
164C22×C3⋊D3—21no—
165C32×Q8—22no—
166C2×C32×C4C2×D412yes—
167C2×C32×C4C2×D412yes—
168C2×C32×C4C2×D411yescharacteristic
169C2×C32×C4C2×D411yescharacteristic
170C2×C32×C4C2411yescharacteristic
171C2×C3⋊Dic3—21no—
172C2×C3⋊Dic3—22no—
173C4⋊(C3⋊D3)—21no—
174C4⋊(C3⋊D3)C2×Q812yes—
175C4×C3⋊D3—42no—
176C4×C3⋊D3—82no—
177#634—81no—
178C2×C3×Dic3—21no—
179C2×C3×Dic3—22no—
180C2×C3×Dic3—21no—
181C3×Dic6—21no—
182C3×Dic6—81no—
183C3×Dic6—82no—
184C3×Dic6C2×Q812yes—
185C3×C3⋊C8—22no—
186C3×C3⋊C8—21no—
187C3×C3⋊C8C2×Q812yes—
188Q82—31no—
189#554—91no—
190#501—92no—
191#500—91no—
192#479—92no—
193#477—91no—
194#476—91no—
195#474—92no—
196#446—31no—
197#440—92no—
198C4×SD16—91no—
199C2×C3×Q8—21no—
200C2×C3×Q8—31no—
201C2×C3×Q8—62no—
202C2×C3×Q8—61no—
203C2×C3×Q8D1211yescharacteristic
204C2×C3×Q8#6711yescharacteristic
205C2×D12—31no—
206C2×D12—31no—
207C2×D12—61no—
208C2×C4×D3—62no—
209C2×C4×D3—61no—
210C2×C4×D3—61no—
211C2×C4×D3—64no—
212C2×C4×D3—62no—
213C2×C4×D3—62no—
214C2×Dic6—22no—
215C2×Dic6—21no—
216C2×Dic6—62no—
217C2×Dic6—61no—
218C2×Dic6—61no—
219C2×Dic6C22×D311yescharacteristic
220C2×C3×C8—31no—
221C2×C3×C8—32no—
222C2×C3×C8—31no—
223C3×C4⋊C4—21no—
224C3×C4⋊C4—22no—
225C3×C4⋊C4—31no—
226C3×C4⋊C4—32no—
227C3×C4⋊C4—62no—
228C3×C4⋊C4—61no—
229C3×C4⋊C4—62no—
230C3×C4⋊C4—61no—
231C3×C4⋊C4D1211yescharacteristic
232C3×C4⋊C4D1212yes—
233C3×C4⋊C4#6711yescharacteristic
234C3×C4⋊C4#6712yes—
235C3×C42—21no—
236C3×C42—22no—
237C3×C42—62no—
238C3×C42—61no—
239C3×C42C22×D311yescharacteristic
240C3×C42C22×D312yes—
241C3×C42C22×D311yescharacteristic
242C3×C42C22×D312yes—
243#215—34no—
244(C2×D3)⋊C4—62no—
245(C2×D3)⋊C4—64no—
246(C2×D3)⋊C4—61no—
247(C2×D3)⋊C4—62no—
248(C2×D3)⋊C4—61no—
249(C2×D3)⋊C4—62no—
250C4⋊Dic3—22no—
251C4⋊Dic3—21no—
252C4⋊Dic3—32no—
253C4⋊Dic3—31no—
254C4⋊Dic3—31no—
255C4⋊Dic3—32no—
256C4⋊Dic3—62no—
257C4⋊Dic3—61no—
258C4⋊Dic3—62no—
259C4⋊Dic3—61no—
260C4⋊Dic3—61no—
261C4⋊Dic3C22×D311yescharacteristic
262C4⋊Dic3C22×D312yes—
263Dic3⋊C4—22no—
264Dic3⋊C4—21no—
265Dic3⋊C4—64no—
266Dic3⋊C4—64no—
267Dic3⋊C4—62no—
268Dic3⋊C4—62no—
269Dic3⋊C4—62no—
270Dic3⋊C4—62no—
271C4×Dic3—22no—
272C4×Dic3—21no—
273C2×C3⋊C8C22×D311yescharacteristic
274C2×C3⋊C8C22×D312yes—
275C2×C3⋊C8C22×D311yescharacteristic
276#204—34no—
277C22×C32C22×D411yescharacteristic
278C2×C3⋊D3—22no—
279C2×C3⋊D3—41no—
280C2×C3⋊D3—41no—
281C32×C4—22no—
282C32×C4—21no—
283C32×C4—22no—
284C32×C4#13712yes—
285C32×C4C22×Q811yescharacteristic
286C32×C42−1+411yescharacteristic
287C3⋊Dic3—41no—
288C3⋊Dic3—42no—
289C3×Dic3—22no—
290C3×Dic3—42no—
291C3×Dic3—41no—
292C2×SD16—91no—
293C4⋊Q8—32no—
294C4⋊Q8—31no—
295C4⋊Q8—61no—
296C4⋊Q8—62no—
297C4⋊Q8—91no—
298#125—92no—
299C22⋊Q8—181no—
300C22⋊Q8—182no—
301C4×Q8—31no—
302C4×Q8—32no—
303C4×Q8—61no—
304C4×Q8D3211yescharacteristic
305C4×D4—91no—
306C4×D4—92no—
307C2×C4⋊C4—181no—
308#107—92no—
309#107—92no—
310#107—92no—
311#106—91no—
312#106—92no—
313C4⋊C8—32no—
314C4⋊C8—31no—
315#103—91no—
316#103—92no—
317#102—91no—
318#102—92no—
319#97—32no—
320C4×C8—31no—
321C22×D3—62no—
322C22×D3—61no—
323C22×D3—61no—
324C3×Q8—22no—
325C3×Q8—22no—
326C3×Q8—32no—
327C3×Q8—42no—
328C3×Q8—61no—
329C3×Q8—241no—
330C3×Q8—242no—
331C2×C3×C4—21no—
332C2×C3×C4—21no—
333C2×C3×C4—22no—
334C2×C3×C4—22no—
335C2×C3×C4—21no—
336C2×C3×C4—61no—
337C2×C3×C4—62no—
338C2×C3×C4—61no—
339C2×C3×C4C2×D1212yes—
340C2×C3×C4C2×D1212yes—
341C2×C3×C4C2×D1211yescharacteristic
342C2×C3×C4C2×D1211yescharacteristic
343C2×C3×C4C2×#6712yes—
344C2×C3×C4C2×#6712yes—
345C2×C3×C4C2×#6711yescharacteristic
346C2×C3×C4C2×#6711yescharacteristic
347C2×C3×C4C23×D311yescharacteristic
348C2×C3×C4C23×D311yescharacteristic
349C2×Dic3—21no—
350C2×Dic3—22no—
351C2×Dic3—21no—
352C2×Dic3—62no—
353C2×Dic3—64no—
354C2×Dic3—61no—
355C2×Dic3—62no—
356C2×Dic3—61no—
357C2×Dic3—62no—
358D12—32no—
359D12—32no—
360D12—62no—
361D12—62no—
362D12—61no—
363D12—61no—
364C4×D3—124no—
365C4×D3—122no—
366C4×D3—122no—
367C4×D3—242no—
368C4×D3—242no—
369C4×D3—244no—
370Dic6—21no—
371Dic6—81no—
372Dic6—82no—
373Dic6—241no—
374Dic6—241no—
375Dic6—242no—
376Dic6D3×Q812yes—
377C3×C8—32no—
378C3×C8—62no—
379C3×C8—61no—
380C3⋊C8—21no—
381C3⋊C8—22no—
382C3⋊C8D3×Q812yes—
383C2×C32D4×Q811yescharacteristic
384C2×C32C2×#13711yescharacteristic
385C2×C32#57611yescharacteristic
386C3⋊D3—42no—
387C2×Q8—31no—
388C2×Q8—61no—
389C2×Q8—62no—
390C2×Q8—181no—
391C2×Q8#62611yescharacteristic
392C2×D4—91no—
393C22×C4—181no—
394C22×C4—182no—
395SD16—94no—
396C2×C8—31no—
397C2×C8—31no—
398C2×C8—32no—
399C4⋊C4—31no—
400C4⋊C4—32no—
401C4⋊C4—61no—
402C4⋊C4—62no—
403C4⋊C4—62no—
404C4⋊C4—61no—
405C4⋊C4—91no—
406C4⋊C4—92no—
407C4⋊C4—182no—
408C4⋊C4—181no—
409C4⋊C4—182no—
410C4⋊C4#62611yescharacteristic
411C4⋊C4#62612yes—
412C22⋊C4—181no—
413C22⋊C4—182no—
414C42—62no—
415C42—61no—
416C42C2×D3211yescharacteristic
417C42C2×D3212yes—
418C22×C3—21no—
419C22×C3C22×D1211yescharacteristic
420C22×C3C22×#6711yescharacteristic
421C2×D3—64no—
422C2×D3—62no—
423C2×D3—62no—
424C2×D3—122no—
425C2×D3—122no—
426C2×D3—121no—
427C2×D3—121no—
428C2×D3—121no—
429C2×D3—121no—
430C3×C4—22no—
431C3×C4—21no—
432C3×C4—22no—
433C3×C4—22no—
434C3×C4—21no—
435C3×C4—22no—
436C3×C4—21no—
437C3×C4—21no—
438C3×C4—22no—
439C3×C4—41no—
440C3×C4—42no—
441C3×C4—42no—
442C3×C4—62no—
443C3×C4—122no—
444C3×C4—121no—
445C3×C4#90912yes—
446C3×C4#94212yes—
447C3×C4C2×D3×Q811yescharacteristic
448C3×C4C2×D3×Q811yescharacteristic
449C3×C4#100711yescharacteristic
450C3×C4#101011yescharacteristic
451Dic3—22no—
452Dic3—42no—
453Dic3—41no—
454Dic3—124no—
455Dic3—122no—
456Dic3—121no—
457Dic3—122no—
458Dic3—121no—
459Dic3—122no—
460C32#338511yescharacteristic, complemented, Sylow
461C23—181no—
462Q8—22no—
463Q8—32no—
464Q8—61no—
465Q8—242no—
466Q8—241no—
467Q8—721no—
468D4—92no—
469D4—181no—
470C2×C4—61no—
471C2×C4—62no—
472C2×C4—61no—
473C2×C4—181no—
474C2×C4—182no—
475C2×C4—362no—
476C2×C4—722no—
477C2×C4C2×#62612yes—
478C2×C4C2×#62611yescharacteristic
479C2×C4C2×#62612yes—
480C2×C4C2×#62611yescharacteristic
481C2×C4C22×D3211yescharacteristic
482C8—32no—
483C8—61no—
484C8—62no—
485C2×C3—21no—
486C2×C3—21no—
487C2×C3—21no—
488C2×C3Q8×D1211yescharacteristic
489C2×C3C2×#90911yescharacteristic
490C2×C3#575211yescharacteristic
491C2×C3C2×#94211yescharacteristic
492C2×C3Q8×#6711yescharacteristic
493C2×C3#583511yescharacteristic
494D3—124no—
495D3—122no—
496D3—122no—
497C22—182no—
498C22—361no—
499C22—361no—
500C22C22×#62611yescharacteristic
501C4—22no—
502C4—21no—
503C4—22no—
504C4—62no—
505C4—121no—
506C4—122no—
507C4—362no—
508C4—361no—
509C4#6383312yes—
510C4#6431511yescharacteristic
511C4D32×Q811yescharacteristic
512C3—21no—
513C3#7997611yescharacteristic, complemented
514C3#8370611yescharacteristic, complemented
515C2—362no—
516C2C2×#6383311yescharacteristic
517C2Q8×#62611yescharacteristic
518C2#1059544911yescharacteristic
subgroupG/H
centerC22C22×#626
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×C4×Q8C22
socleC22×C32C22×D4
prime radicalC2×C4⋊(C3⋊D3)C23
hypercenterC4×Q8D32
hypocenterC32#3385
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C4×Q8

Complements

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

NH ≅ G/Ntype
2. C3×Q8×Dic6C2semidirect
3. C3×#5024C2semidirect
7. #10590311C2semidirect
8. #10590305C2semidirect
9. #10590302C2semidirect
11. #10590283C2semidirect
47. Q8×Dic6D3semidirect
55. #5024D3semidirect
96. #3717Q8semidirect
460. C32#3385semidirect
513. C3#79976semidirect
514. C3#83706semidirect

Maximal subgroups

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

subgroupindex
#105960502
C3×Q8×Dic62
C3×#50242
#105903622
C4×#37172
#105903132
#105903112
#105903052
#105903022
#105903002
#105902832
#837063
#799763