Finite Group Databasebeta

← #11897679

Subgroups — #11897679

Order 1152.

728 conjugacy classes of subgroups.

The subgroup lattice has 501 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10593960C211yesmaximal, characteristic
2#10593856C211yesmaximal, characteristic, complemented
3#10592549C211yesmaximal, characteristic, complemented
4C3×#4842C211yesmaximal, characteristic
5C3×#4831C211yesmaximal, characteristic, complemented
6#10590892C212yesmaximal, complemented
7#10590809C212yesmaximal, complemented
8#10590762C212yesmaximal
9#10590747C212yesmaximal
10C4×#3716C211yesmaximal, characteristic
11#10590311C211yesmaximal, characteristic, complemented
12#81056—31nomaximal
13#79976—31nomaximal
14#64078C2211yescharacteristic
15C4×#634C2211yescharacteristic
16C3×C4×D12C2211yescharacteristic
17C3×#869C2211yescharacteristic
18C3×C4×Dic6C2211yescharacteristic
19#63919—21no—
20#63918C2212yes—
21#63896—22no—
22Dic3×D12C2212yes—
23D3×C4⋊Dic3—21no—
24#63869C2212yes—
25#63856—21no—
26#63844C2212yes—
27#63843—21no—
28#63839—22no—
29C2×#3716C2211yescharacteristic
30C32×C4⋊C8C2211yescharacteristic
31#63645C2212yes—
32#63643C2212yes—
33C3×#821C2212yes—
34C3×#817C2212yes—
35C3×#815C2212yes—
36C3×Dic3⋊C8C2212yes—
37C3×C4×C3⋊C8C2211yescharacteristic
38#63575C2212yes—
39#63575C2212yes—
40#63573C2211yescharacteristic
41#63567C2211yescharacteristic
42#63563C2211yescharacteristic
43#5722—31no—
44#5579—31no—
45Q8×Dic6—31no—
46#5543—31no—
47C3×#476—31no—
48C3×#446—31no—
49#5078—31no—
50C4×#214—31no—
51#4857—32no—
52#4856—32no—
53#4850—31no—
54#4850—31no—
55#4850—61no—
56#4846—32no—
57#4842D311yescharacteristic
58#4831D311yescharacteristic, complemented
59#4829—32no—
60#4759—32no—
61#4757—32no—
62#4710—32no—
63#4702—32no—
64C4×#204—31no—
65#4682—31no—
66C2×#634—21no—
67C2×#634C2311yescharacteristic
68C2×C3×D12C2311yescharacteristic
69C2×C3×C4×D3—21no—
70C2×C3×Dic6—21no—
71C2×C3×Dic6D411yescharacteristic
72C2×#627—22no—
73C2×D3×Dic3—22no—
74C2×C32×C8C2312yes—
75C32×C42C2311yescharacteristic
76C4⋊(C3⋊Dic3)—21no—
77C4⋊(C3⋊Dic3)C2311yescharacteristic
78C4⋊(C3⋊Dic3)C2312yes—
79#3750—21no—
80C4×C3⋊Dic3—21no—
81C3×(C2×D3)⋊C4—21no—
82C3×C4⋊Dic3—21no—
83C3×C4⋊Dic3D411yescharacteristic
84C3×C4⋊Dic3C2311yescharacteristic
85C3×C4⋊Dic3C2312yes—
86C3×Dic3⋊C4D412yes—
87C3×C4×Dic3C2312yes—
88C2×C3×C3⋊C8C2311yescharacteristic
89C2×C3×C3⋊C8C2311yescharacteristic
90#3724—22no—
91#3724—22no—
92Dic3⋊Dic3—22no—
93Dic3⋊Dic3—22no—
94(C2×D3)⋊Dic3—22no—
95Dic32—22no—
96#3716Q814yescomplemented
97#3385—91noSylow
98C3×C4⋊Q8—31no—
99C3×C4×Q8—31no—
100C3×C4×D4—31no—
101#946—61no—
102Q8×Dic3—61no—
103#944—62no—
104D4×Dic3—32no—
105C2×#214—31no—
106C2×C4⋊Dic3—61no—
107#924—61no—
108C2×#204—31no—
109#896—62no—
110D3×C4⋊C4—61no—
111#890—32no—
112#888—32no—
113#888—61no—
114#888—62no—
115#888—61no—
116#887—32no—
117#887—61no—
118#878—62no—
119C4×D12—32no—
120C4×D12C2×D311yescharacteristic
121#870—32no—
122#869—31no—
123#869—31no—
124#869—32no—
125#869—61no—
126#869C2×D311yescharacteristic
127C4×Dic6—31no—
128C4×Dic6—31no—
129C4×Dic6—32no—
130C4×Dic6—61no—
131C4×Dic6C2×D311yescharacteristic
132C3×#106—32no—
133C3×C4⋊C8—21no—
134C3×C4⋊C8—32no—
135C3×C4⋊C8C2×D311yescharacteristic
136C3×C4⋊C8C2×D311yescharacteristic
137C3×#102—32no—
138C3×#97—32no—
139C3×C4×C8—31no—
140#832—31no—
141#821—31no—
142#821C2×D312yes—
143#818—32no—
144#818—32no—
145#818—32no—
146#818—32no—
147#818—62no—
148#817—31no—
149#817C2×D312yes—
150#816—32no—
151#816—32no—
152#816—31no—
153#816—62no—
154#815C2×D312yes—
155Dic3⋊C8C2×D312yes—
156#810—31no—
157#808—31no—
158#807—32no—
159#807—32no—
160C4×C3⋊C8C2×D311yescharacteristic
161C22×C3×D3—21no—
162C2×C32×C4C2×D411yescharacteristic
163C2×C32×C4C2×D411yescharacteristic
164C2×C32×C4C2411yescharacteristic
165C2×C3⋊Dic3—21no—
166C2×C3⋊Dic3—22no—
167C2×C3⋊Dic3—21no—
168#634—21no—
169#634—81no—
170#634C2×Q812yes—
171C2×C3×Dic3—22no—
172C2×C3×Dic3—21no—
173C2×C3×Dic3C2×D412yes—
174C2×C3×Dic3C2×D412yes—
175C3×D12—21no—
176C3×D12C2×Q812yes—
177C3×C4×D3—42no—
178C3×Dic6—22no—
179C3×Dic6—81no—
180#627—82no—
181D3×Dic3—82no—
182C32×C8—22no—
183C3×C3⋊C8—21no—
184C3×C3⋊C8C2×Q812yes—
185Q82—91no—
186#554—91no—
187#501—92no—
188#500—91no—
189#479—92no—
190#477—91no—
191#476—31no—
192#474—92no—
193#446—31no—
194#440—92no—
195C4×SD16—91no—
196C2×C3×Q8—31no—
197C2×C3×Q8—61no—
198C2×C3×D4—31no—
199C22×C3×C4—61no—
200C22×Dic3—62no—
201C2×D12C22×D311yescharacteristic
202C2×C4×D3—21no—
203C2×C4×D3—62no—
204C2×Dic6—21no—
205C2×Dic6—31no—
206C2×Dic6—31no—
207C2×Dic6—61no—
208C2×Dic6—62no—
209C2×Dic6—61no—
210C2×Dic6—61no—
211C2×Dic6—62no—
212C2×Dic6—121no—
213C2×Dic6D1211yescharacteristic
214C2×C3×C8—22no—
215C2×C3×C8—31no—
216C2×C3×C8—31no—
217C2×C3×C8C22×D312yes—
218C2×C3×C8C22×D312yes—
219C3×C4⋊C4—31no—
220C3×C4⋊C4—32no—
221C3×C4⋊C4—32no—
222C3×C4⋊C4—31no—
223C3×C4⋊C4—61no—
224C3×C22⋊C4—61no—
225C3×C42—21no—
226C3×C42—32no—
227C3×C42C22×D311yescharacteristic
228C3×C42C22×D311yescharacteristic
229#217—62no—
230#214—34no—
231(C2×D3)⋊C4—21no—
232(C2×D3)⋊C4—62no—
233C4⋊Dic3—21no—
234C4⋊Dic3—32no—
235C4⋊Dic3—31no—
236C4⋊Dic3—32no—
237C4⋊Dic3—31no—
238C4⋊Dic3—62no—
239C4⋊Dic3—61no—
240C4⋊Dic3—62no—
241C4⋊Dic3—61no—
242C4⋊Dic3—61no—
243C4⋊Dic3—62no—
244C4⋊Dic3—121no—
245C4⋊Dic3D1211yescharacteristic
246C4⋊Dic3C22×D311yescharacteristic
247C4⋊Dic3C22×D312yes—
248Dic3⋊C4—62no—
249Dic3⋊C4—62no—
250Dic3⋊C4—62no—
251Dic3⋊C4—61no—
252Dic3⋊C4—61no—
253Dic3⋊C4—62no—
254Dic3⋊C4—62no—
255Dic3⋊C4—62no—
256Dic3⋊C4—121no—
257Dic3⋊C4D1212yes—
258C4×Dic3—62no—
259C4×Dic3—61no—
260C4×Dic3—61no—
261C4×Dic3—62no—
262C4×Dic3—121no—
263C4×Dic3C22×D312yes—
264C2×C3⋊C8C22×D311yescharacteristic
265C2×C3⋊C8C22×D311yescharacteristic
266#204—34no—
267C22×C32C22×D411yescharacteristic
268C2×C3×D3—22no—
269C2×C3×D3—41no—
270C2×C3×D3—41no—
271C32×C4—21no—
272C32×C4#13712yes—
273C32×C4C22×Q811yescharacteristic
274C32×C42−1+411yescharacteristic
275C3⋊Dic3—22no—
276C3⋊Dic3—42no—
277C3⋊Dic3—41no—
278C3×Dic3—22no—
279C3×Dic3—22no—
280C3×Dic3—41no—
281C3×Dic3—42no—
282C2×SD16—91no—
283C4⋊Q8—31no—
284C4⋊Q8—92no—
285C4⋊Q8—91no—
286C4⋊Q8—181no—
287C4⋊Q8—182no—
288#125—92no—
289C22⋊Q8—182no—
290C22⋊Q8—181no—
291C4×Q8—31no—
292C4×Q8—92no—
293C4×Q8—91no—
294C4×Q8—181no—
295C4×D4—31no—
296C4×D4—92no—
297C2×C4⋊C4—181no—
298#107—92no—
299#107—92no—
300#107—92no—
301#106—32no—
302#106—91no—
303C4⋊C8—32no—
304C4⋊C8D3211yescharacteristic
305#103—91no—
306#103—92no—
307#102—32no—
308#102—91no—
309#97—32no—
310C4×C8—31no—
311C23×C3—61no—
312C22×D3—21no—
313C3×Q8—62no—
314C3×Q8—241no—
315C3×D4—32no—
316C3×D4—61no—
317C2×C3×C4—21no—
318C2×C3×C4—21no—
319C2×C3×C4—21no—
320C2×C3×C4—32no—
321C2×C3×C4—32no—
322C2×C3×C4—62no—
323C2×C3×C4—61no—
324C2×C3×C4—122no—
325C2×C3×C4C2×D1211yescharacteristic
326C2×C3×C4C2×D1211yescharacteristic
327C2×C3×C4D3×D411yescharacteristic
328C2×C3×C4D3×D411yescharacteristic
329C2×C3×C4C23×D311yescharacteristic
330C2×C3×C4C23×D311yescharacteristic
331C2×Dic3—22no—
332C2×Dic3—21no—
333C2×Dic3—61no—
334C2×Dic3—61no—
335C2×Dic3—61no—
336C2×Dic3—62no—
337C2×Dic3—61no—
338C2×Dic3—62no—
339C2×Dic3—121no—
340C2×Dic3—121no—
341C2×Dic3—122no—
342C2×Dic3—242no—
343C2×Dic3C2×D1212yes—
344C2×Dic3C2×D1212yes—
345D12—21no—
346D12D3×Q812yes—
347C4×D3—42no—
348C4×D3—242no—
349Dic6—22no—
350Dic6—32no—
351Dic6—32no—
352Dic6—62no—
353Dic6—61no—
354Dic6—61no—
355Dic6—81no—
356Dic6—121no—
357Dic6—242no—
358Dic6—242no—
359Dic6—241no—
360Dic6—241no—
361Dic6—242no—
362C3×C8—22no—
363C3×C8—22no—
364C3×C8—32no—
365C3×C8—42no—
366C3×C8—61no—
367C3⋊C8—21no—
368C3⋊C8D3×Q812yes—
369C2×C32D4×Q811yescharacteristic
370C2×C32C2×#13711yescharacteristic
371C2×C32#57611yescharacteristic
372C3×D3—42no—
373C2×Q8—31no—
374C2×Q8—61no—
375C2×Q8—91no—
376C2×Q8—182no—
377C2×Q8—181no—
378C2×D4—31no—
379C22×C4—61no—
380C22×C4—182no—
381SD16—94no—
382C2×C8—31no—
383C2×C8—31no—
384C2×C8C2×D3212yes—
385C4⋊C4—31no—
386C4⋊C4—32no—
387C4⋊C4—32no—
388C4⋊C4—31no—
389C4⋊C4—61no—
390C4⋊C4—91no—
391C4⋊C4—92no—
392C4⋊C4—182no—
393C4⋊C4—182no—
394C4⋊C4—182no—
395C4⋊C4—182no—
396C4⋊C4—181no—
397C4⋊C4—181no—
398C22⋊C4—61no—
399C22⋊C4—182no—
400C42—32no—
401C42—182no—
402C42—181no—
403C42C2×D3211yescharacteristic
404C22×C3—21no—
405C22×C3—62no—
406C22×C3—121no—
407C22×C3—121no—
408C22×C3C22×D1211yescharacteristic
409C22×C3C2×D3×D411yescharacteristic
410C2×D3—22no—
411C2×D3—41no—
412C2×D3—41no—
413C3×C4—21no—
414C3×C4—21no—
415C3×C4—21no—
416C3×C4—22no—
417C3×C4—21no—
418C3×C4—41no—
419C3×C4—62no—
420C3×C4—62no—
421C3×C4—121no—
422C3×C4—122no—
423C3×C4#90912yes—
424C3×C4#91512yes—
425C3×C4C2×D3×Q811yescharacteristic
426C3×C4C2×D3×Q811yescharacteristic
427C3×C4#101011yescharacteristic
428C3×C4#101011yescharacteristic
429Dic3—22no—
430Dic3—22no—
431Dic3—41no—
432Dic3—42no—
433Dic3—62no—
434Dic3—62no—
435Dic3—122no—
436Dic3—121no—
437Dic3—122no—
438Dic3—121no—
439Dic3—122no—
440Dic3—242no—
441Dic3—241no—
442C32#338511yescharacteristic, complemented, Sylow
443C23—61no—
444Q8—62no—
445Q8—92no—
446Q8—181no—
447Q8—241no—
448Q8—721no—
449Q8—722no—
450D4—32no—
451D4—61no—
452C2×C4—32no—
453C2×C4—32no—
454C2×C4—62no—
455C2×C4—61no—
456C2×C4—122no—
457C2×C4—181no—
458C2×C4—181no—
459C2×C4—182no—
460C2×C4—722no—
461C2×C4D3×D1211yescharacteristic
462C2×C4D3×D1211yescharacteristic
463C2×C4C22×D3211yescharacteristic
464C8—22no—
465C8—32no—
466C8—61no—
467C2×C3—21no—
468C2×C3—21no—
469C2×C3—21no—
470C2×C3—122no—
471C2×C3Q8×D1211yescharacteristic
472C2×C3#563211yescharacteristic
473C2×C3C2×#90911yescharacteristic
474C2×C3#575211yescharacteristic
475C2×C3C2×#91511yescharacteristic
476C2×C3#577411yescharacteristic
477D3—42no—
478C22—62no—
479C22—121no—
480C22—121no—
481C22C2×D3×D1211yescharacteristic
482C4—21no—
483C4—62no—
484C4—62no—
485C4—121no—
486C4—122no—
487C4—182no—
488C4—362no—
489C4—361no—
490C4#6380012yes—
491C4#6430911yescharacteristic
492C4D32×Q811yescharacteristic
493C3—21no—
494C3#7997611yescharacteristic, complemented
495C3#8105611yescharacteristic, complemented
496C2—122no—
497C2#1059438311yescharacteristic
498C2C2×#6380011yescharacteristic
499C2#1059471411yescharacteristic
subgroupG/H
centerC22C2×D3×D12
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×C4⋊C8C22
socleC22×C32C22×D4
prime radicalC2×C3×D12C23
hypercenterC4⋊C8D32
hypocenterC32#3385
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
2. #10593856C2semidirect
3. #10592549C2semidirect
5. C3×#4831C2semidirect
6. #10590892C2semidirect
7. #10590809C2semidirect
11. #10590311C2semidirect
58. #4831D3semidirect
96. #3716Q8semidirect
442. C32#3385semidirect
494. C3#79976semidirect
495. C3#81056semidirect

Maximal subgroups

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

subgroupindex
#105939602
#105938562
#105925492
C3×#48422
C3×#48312
#105908922
#105908092
#105907622
#105907472
C4×#37162
#105903112
#810563
#799763