Finite Group Databasebeta

← #11897678

Subgroups — #11897678

Order 1152.

734 conjugacy classes of subgroups.

The subgroup lattice has 505 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10593958C211yesmaximal, characteristic
2Dic62C211yesmaximal, characteristic, complemented
3#10592541C211yesmaximal, characteristic
4C3×#4850C211yesmaximal, characteristic, complemented
5C3×#4831C211yesmaximal, characteristic, complemented
6#10590894C212yesmaximal, complemented
7#10590815C212yesmaximal, complemented
8#10590795C212yesmaximal
9#10590764C212yesmaximal
10C4×#3717C211yesmaximal, characteristic
11#10590311C211yesmaximal, characteristic, complemented
12#81137—31nomaximal
13#79976—31nomaximal
14C4×C4⋊(C3⋊D3)C2211yescharacteristic
15#64078C2211yescharacteristic
16C3×#869C2211yescharacteristic
17C3×C4×Dic6C2211yescharacteristic
18C3×C4×Dic6C2211yescharacteristic
19#63918—21no—
20#63918C2212yes—
21#63900—21no—
22#63894C2212yes—
23#63888—22no—
24#63871—21no—
25#63869C2212yes—
26Dic3×Dic6—21no—
27Dic3×Dic6C2212yes—
28#63840—22no—
29C2×#3717C2211yescharacteristic
30C32×C4⋊C8C2211yescharacteristic
31#63648C2212yes—
32#63644C2212yes—
33C3×#818C2212yes—
34C3×#816C2212yes—
35C3×#815C2212yes—
36C3×Dic3⋊C8C2212yes—
37C3×C4×C3⋊C8C2211yescharacteristic
38#63575C2212yes—
39#63575C2212yes—
40#63573C2211yescharacteristic
41#63566C2211yescharacteristic
42#63564C2211yescharacteristic
43#5730—31no—
44#5579—31no—
45Q8×Dic6—31no—
46Q8×Dic6—31no—
47C3×#477—31no—
48C3×#446—31no—
49#5078—31no—
50C4×#215—31no—
51#4890—32no—
52#4876—32no—
53#4850D311yescharacteristic, complemented
54#4846—32no—
55#4842—31no—
56#4842—31no—
57#4842—61no—
58#4831D311yescharacteristic, complemented
59#4829—32no—
60#4817—32no—
61#4799—32no—
62#4710—32no—
63#4702—32no—
64C4×#204—31no—
65#4682—31no—
66C2×C4⋊(C3⋊D3)C2311yescharacteristic
67C2×C4×C3⋊D3—21no—
68C2×#634—21no—
69C2×C3×Dic6—21no—
70C2×C3×Dic6D411yescharacteristic
71C2×C3×Dic6C2311yescharacteristic
72C2×#627—22no—
73C2×#624—22no—
74C2×C32×C8C2312yes—
75C32×C42C2311yescharacteristic
76#3752—21no—
77C4⋊(C3⋊Dic3)—21no—
78C4⋊(C3⋊Dic3)C2311yescharacteristic
79C4⋊(C3⋊Dic3)C2312yes—
80C3×C4⋊Dic3—21no—
81C3×C4⋊Dic3D411yescharacteristic
82C3×C4⋊Dic3C2311yescharacteristic
83C3×C4⋊Dic3C2312yes—
84C3×Dic3⋊C4—21no—
85C3×Dic3⋊C4D412yes—
86C3×C4×Dic3—21no—
87C3×C4×Dic3C2312yes—
88C2×C3×C3⋊C8C2311yescharacteristic
89C2×C3×C3⋊C8C2311yescharacteristic
90#3724—22no—
91Dic3⋊Dic3—22no—
92Dic3⋊Dic3—22no—
93Dic3⋊Dic3—22no—
94#3722—22no—
95Dic32—22no—
96#3717Q814yescomplemented
97#3385—91noSylow
98C3×C4⋊Q8—31no—
99C3×C4×Q8—31no—
100C3×C4×Q8—31no—
101#946—61no—
102#946—62no—
103Q8×Dic3—32no—
104Q8×Dic3—61no—
105C2×#215—31no—
106C2×#204—31no—
107#897—61no—
108#896—62no—
109#893—32no—
110D3×C4⋊C4—61no—
111D3×C4⋊C4—61no—
112#890—32no—
113#888—32no—
114#888—61no—
115#888—62no—
116#888—62no—
117C4×D12—31no—
118C4×D12—31no—
119C4×D12—32no—
120C4×D12—61no—
121#870—32no—
122#869—31no—
123#869—31no—
124#869—32no—
125#869—61no—
126#869—61no—
127#869C2×D311yescharacteristic
128C4×Dic6—32no—
129C4×Dic6—61no—
130C4×Dic6C2×D311yescharacteristic
131C4×Dic6C2×D311yescharacteristic
132C3×#107—32no—
133C3×C4⋊C8—21no—
134C3×C4⋊C8—32no—
135C3×C4⋊C8C2×D311yescharacteristic
136C3×C4⋊C8C2×D311yescharacteristic
137C3×#103—32no—
138C3×#97—32no—
139C3×C4×C8—31no—
140#835—31no—
141#821—32no—
142#821—32no—
143#821—31no—
144#821—62no—
145#818—32no—
146#818—32no—
147#818C2×D312yes—
148#817—32no—
149#817—32no—
150#817—31no—
151#817—62no—
152#816—31no—
153#816C2×D312yes—
154#815C2×D312yes—
155Dic3⋊C8C2×D312yes—
156#809—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—22no—
166C2×C3⋊Dic3—21no—
167C4⋊(C3⋊D3)—21no—
168C4⋊(C3⋊D3)C2×Q812yes—
169C4×C3⋊D3—42no—
170#634—81no—
171C2×C3×Dic3—21no—
172C2×C3×Dic3—22no—
173C2×C3×Dic3—21no—
174C2×C3×Dic3C2×D412yes—
175C2×C3×Dic3C2×D412yes—
176C3×Dic6—22no—
177C3×Dic6—21no—
178C3×Dic6—81no—
179C3×Dic6C2×Q812yes—
180#627—82no—
181#624—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—31no—
191#476—91no—
192#474—92no—
193#446—31no—
194#440—92no—
195C4×SD16—91no—
196C2×C3×Q8—31no—
197C2×C3×Q8—31no—
198C2×C3×Q8—61no—
199C2×D12—31no—
200C2×D12—31no—
201C2×D12—61no—
202C2×C4×D3—61no—
203C2×C4×D3—61no—
204C2×C4×D3—62no—
205C2×C4×D3—62no—
206C2×C4×D3—121no—
207C2×Dic6—21no—
208C2×Dic6—62no—
209C2×Dic6—61no—
210C2×Dic6—61no—
211C2×Dic6—62no—
212C2×Dic6—121no—
213C2×Dic6D1211yescharacteristic
214C2×Dic6C22×D311yescharacteristic
215C2×C3×C8—22no—
216C2×C3×C8—31no—
217C2×C3×C8—31no—
218C2×C3×C8C22×D312yes—
219C2×C3×C8C22×D312yes—
220C3×C4⋊C4—31no—
221C3×C4⋊C4—32no—
222C3×C4⋊C4—32no—
223C3×C4⋊C4—31no—
224C3×C4⋊C4—61no—
225C3×C4⋊C4—61no—
226C3×C42—21no—
227C3×C42—32no—
228C3×C42—61no—
229C3×C42C22×D311yescharacteristic
230C3×C42C22×D311yescharacteristic
231#215—34no—
232(C2×D3)⋊C4—62no—
233(C2×D3)⋊C4—61no—
234(C2×D3)⋊C4—61no—
235(C2×D3)⋊C4—62no—
236(C2×D3)⋊C4—121no—
237C4⋊Dic3—21no—
238C4⋊Dic3—32no—
239C4⋊Dic3—31no—
240C4⋊Dic3—31no—
241C4⋊Dic3—32no—
242C4⋊Dic3—61no—
243C4⋊Dic3—62no—
244C4⋊Dic3—62no—
245C4⋊Dic3—61no—
246C4⋊Dic3—61no—
247C4⋊Dic3—62no—
248C4⋊Dic3—62no—
249C4⋊Dic3—121no—
250C4⋊Dic3D1211yescharacteristic
251C4⋊Dic3C22×D312yes—
252C4⋊Dic3C22×D311yescharacteristic
253Dic3⋊C4—21no—
254Dic3⋊C4—62no—
255Dic3⋊C4—62no—
256Dic3⋊C4—62no—
257Dic3⋊C4—62no—
258Dic3⋊C4—62no—
259Dic3⋊C4D1212yes—
260C4×Dic3—21no—
261C4×Dic3—62no—
262C4×Dic3—62no—
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—41no—
276C3⋊Dic3—42no—
277C3×Dic3—22no—
278C3×Dic3—22no—
279C3×Dic3—22no—
280C3×Dic3—42no—
281C3×Dic3—41no—
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—31no—
293C4×Q8—92no—
294C4×Q8—181no—
295C4×D4—92no—
296C4×D4—91no—
297C2×C4⋊C4—181no—
298#107—32no—
299#107—92no—
300#107—92no—
301#106—91no—
302#106—92no—
303C4⋊C8—32no—
304C4⋊C8D3211yescharacteristic
305#103—32no—
306#103—91no—
307#102—91no—
308#102—92no—
309#97—32no—
310C4×C8—31no—
311C22×D3—61no—
312C22×D3—61no—
313C22×D3—121no—
314C3×Q8—32no—
315C3×Q8—62no—
316C3×Q8—61no—
317C3×Q8—241no—
318C2×C3×C4—21no—
319C2×C3×C4—21no—
320C2×C3×C4—21no—
321C2×C3×C4—32no—
322C2×C3×C4—32no—
323C2×C3×C4—61no—
324C2×C3×C4—61no—
325C2×C3×C4—62no—
326C2×C3×C4C2×D1211yescharacteristic
327C2×C3×C4C2×D1211yescharacteristic
328C2×C3×C4D3×D411yescharacteristic
329C2×C3×C4D3×D411yescharacteristic
330C2×C3×C4C23×D311yescharacteristic
331C2×C3×C4C23×D311yescharacteristic
332C2×Dic3—21no—
333C2×Dic3—21no—
334C2×Dic3—22no—
335C2×Dic3—62no—
336C2×Dic3—61no—
337C2×Dic3—62no—
338C2×Dic3—61no—
339C2×Dic3—122no—
340C2×Dic3—121no—
341C2×Dic3C2×D1212yes—
342C2×Dic3C2×D1212yes—
343D12—32no—
344D12—32no—
345D12—62no—
346D12—61no—
347D12—61no—
348D12—121no—
349C4×D3—122no—
350C4×D3—122no—
351C4×D3—242no—
352C4×D3—242no—
353C4×D3—242no—
354Dic6—22no—
355Dic6—21no—
356Dic6—81no—
357Dic6—242no—
358Dic6—242no—
359Dic6—241no—
360Dic6—241no—
361Dic6—242no—
362Dic6D3×Q812yes—
363C3×C8—22no—
364C3×C8—22no—
365C3×C8—32no—
366C3×C8—42no—
367C3×C8—61no—
368C3⋊C8—21no—
369C3⋊C8D3×Q812yes—
370C2×C32D4×Q811yescharacteristic
371C2×C32C2×#13711yescharacteristic
372C2×C32#57611yescharacteristic
373C3⋊D3—42no—
374C2×Q8—31no—
375C2×Q8—31no—
376C2×Q8—61no—
377C2×Q8—182no—
378C2×Q8—181no—
379C2×D4—91no—
380C22×C4—182no—
381C22×C4—181no—
382SD16—94no—
383C2×C8—31no—
384C2×C8—31no—
385C2×C8C2×D3212yes—
386C4⋊C4—31no—
387C4⋊C4—32no—
388C4⋊C4—31no—
389C4⋊C4—32no—
390C4⋊C4—61no—
391C4⋊C4—61no—
392C4⋊C4—92no—
393C4⋊C4—91no—
394C4⋊C4—182no—
395C4⋊C4—182no—
396C4⋊C4—182no—
397C4⋊C4—182no—
398C4⋊C4—181no—
399C22⋊C4—182no—
400C22⋊C4—181no—
401C42—32no—
402C42—61no—
403C42—182no—
404C42C2×D3211yescharacteristic
405C22×C3—21no—
406C22×C3C22×D1211yescharacteristic
407C22×C3C2×D3×D411yescharacteristic
408C2×D3—62no—
409C2×D3—62no—
410C2×D3—122no—
411C2×D3—121no—
412C2×D3—121no—
413C2×D3—121no—
414C2×D3—121no—
415C2×D3—241no—
416C2×D3—241no—
417C3×C4—21no—
418C3×C4—21no—
419C3×C4—21no—
420C3×C4—22no—
421C3×C4—21no—
422C3×C4—41no—
423C3×C4—62no—
424C3×C4—62no—
425C3×C4—62no—
426C3×C4—121no—
427C3×C4—122no—
428C3×C4#90912yes—
429C3×C4#91812yes—
430C3×C4C2×D3×Q811yescharacteristic
431C3×C4C2×D3×Q811yescharacteristic
432C3×C4#101011yescharacteristic
433C3×C4#101011yescharacteristic
434Dic3—22no—
435Dic3—22no—
436Dic3—22no—
437Dic3—42no—
438Dic3—41no—
439Dic3—121no—
440Dic3—122no—
441Dic3—121no—
442Dic3—122no—
443Dic3—242no—
444Dic3—241no—
445C32#338511yescharacteristic, complemented, Sylow
446C23—181no—
447Q8—32no—
448Q8—61no—
449Q8—62no—
450Q8—241no—
451Q8—721no—
452Q8—722no—
453D4—92no—
454D4—181no—
455C2×C4—32no—
456C2×C4—32no—
457C2×C4—61no—
458C2×C4—61no—
459C2×C4—62no—
460C2×C4—182no—
461C2×C4—181no—
462C2×C4—362no—
463C2×C4—722no—
464C2×C4D3×D1211yescharacteristic
465C2×C4D3×D1211yescharacteristic
466C2×C4C22×D3211yescharacteristic
467C8—22no—
468C8—32no—
469C8—61no—
470C2×C3—21no—
471C2×C3—21no—
472C2×C3—21no—
473C2×C3Q8×D1211yescharacteristic
474C2×C3#563211yescharacteristic
475C2×C3C2×#90911yescharacteristic
476C2×C3#575211yescharacteristic
477C2×C3C2×#91811yescharacteristic
478C2×C3#577411yescharacteristic
479D3—122no—
480D3—122no—
481D3—242no—
482C22—182no—
483C22—361no—
484C22—361no—
485C22C2×D3×D1211yescharacteristic
486C4—21no—
487C4—62no—
488C4—62no—
489C4—62no—
490C4—122no—
491C4—121no—
492C4—361no—
493C4—362no—
494C4#6380112yes—
495C4#6430911yescharacteristic
496C4D32×Q811yescharacteristic
497C3—21no—
498C3#7997611yescharacteristic, complemented
499C3#8113711yescharacteristic, complemented
500C2—362no—
501C2#1059438311yescharacteristic
502C2C2×#6380111yescharacteristic
503C2#1059471411yescharacteristic
subgroupG/H
centerC22C2×D3×D12
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×C4⋊C8C22
socleC22×C32C22×D4
prime radicalC2×C4⋊(C3⋊D3)C23
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. Dic62C2semidirect
4. C3×#4850C2semidirect
5. C3×#4831C2semidirect
6. #10590894C2semidirect
7. #10590815C2semidirect
11. #10590311C2semidirect
53. #4850D3semidirect
58. #4831D3semidirect
96. #3717Q8semidirect
445. C32#3385semidirect
498. C3#79976semidirect
499. C3#81137semidirect

Maximal subgroups

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

subgroupindex
#105939582
Dic622
#105925412
C3×#48502
C3×#48312
#105908942
#105908152
#105907952
#105907642
C4×#37172
#105903112
#811373
#799763