Finite Group Databasebeta

← #11897675

Subgroups — #11897675

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#10596201C211yesmaximal, characteristic
2#10593856C211yesmaximal, characteristic, complemented
3C3×#5091C211yesmaximal, characteristic, complemented
4C3×#5078C211yesmaximal, characteristic, complemented
5#10590563C212yesmaximal, complemented
6#10590494C212yesmaximal, complemented
7#10590484C212yesmaximal
8#10590430C212yesmaximal
9C4×#3717C211yesmaximal, characteristic
10#10590300C211yesmaximal, characteristic
11#10590296C211yesmaximal, characteristic, complemented
12#81954—31nomaximal
13#81137—31nomaximal
14C32×C4⋊Q8C2211yescharacteristic
15#64155—22no—
16#64106—21no—
17#64102C2212yes—
18C4⋊C4×C3⋊D3—21no—
19#64099C2212yes—
20C4×C4⋊(C3⋊D3)C2211yescharacteristic
21C4×#634C2211yescharacteristic
22C3×#869C2211yescharacteristic
23C3×C4×Dic6C2211yescharacteristic
24#63919C2212yes—
25#63918—21no—
26#63844—21no—
27#63843C2212yes—
28#63839—22no—
29C2×#3717C2211yescharacteristic
30C3×#810C2212yes—
31C3×#807C2212yes—
32C3×#807C2212yes—
33C3×#807C2212yes—
34C3×C4⋊(C3⋊C8)C2211yescharacteristic
35C3×C4×C3⋊C8C2211yescharacteristic
36#63573C2212yes—
37#63573C2211yescharacteristic
38#63572C2212yes—
39#63566C2211yescharacteristic
40#63564C2212yes—
41#63564C2211yescharacteristic
42#63555C2212yes—
43#5730—31no—
44#5730—31no—
45#5730—61no—
46#5722—31no—
47Q8×Dic6—31no—
48C3×#500—31no—
49C3×#477—31no—
50#5091D311yescharacteristic, complemented
51#5084—31no—
52#5078D311yescharacteristic, complemented
53C4×#215—31no—
54#4890—32no—
55#4890—32no—
56#4889—32no—
57#4877—32no—
58#4876—32no—
59#4876—32no—
60#4842—31no—
61#4831—31no—
62#4817—32no—
63#4799—32no—
64C4×#204—31no—
65#4679—31no—
66C2×C32×Q8—21no—
67C2×C4⋊(C3⋊D3)C2311yescharacteristic
68C2×C4×C3⋊D3—21no—
69C2×C4×C3⋊D3—22no—
70C2×#634D411yescharacteristic
71C2×C3×Dic6—21no—
72C2×C3×Dic6C2311yescharacteristic
73C2×#627—22no—
74C32×C4⋊C4—21no—
75C32×C4⋊C4C2312yes—
76C32×C42C2311yescharacteristic
77#3752—21no—
78#3752—22no—
79C4⋊(C3⋊Dic3)—22no—
80C4⋊(C3⋊Dic3)D411yescharacteristic
81C4⋊(C3⋊Dic3)C2311yescharacteristic
82#3750—22no—
83#3750D412yes—
84C4×C3⋊Dic3C2312yes—
85C3×C4⋊Dic3—21no—
86C3×C4⋊Dic3C2312yes—
87C3×C4⋊Dic3C2311yescharacteristic
88C3×Dic3⋊C4—21no—
89C3×C4×Dic3—21no—
90C2×C3×C3⋊C8C2312yes—
91C2×C3×C3⋊C8C2311yescharacteristic
92C2×C3×C3⋊C8C2311yescharacteristic
93#3724—22no—
94Dic3⋊Dic3—22no—
95Dic32—22no—
96#3717Q814yescomplemented
97#3385—91noSylow
98C3×C4⋊Q8—21no—
99C3×C4⋊Q8—31no—
100C3×C4⋊Q8C2×D311yescharacteristic
101C3×C4⋊Q8C2×D311yescharacteristic
102C3×C4×Q8—31no—
103#946—62no—
104#946—62no—
105#946—64no—
106Q8×Dic3—32no—
107#944—62no—
108C2×#215—31no—
109C2×#204—31no—
110#897—61no—
111#897—61no—
112#897—62no—
113#893—32no—
114#893—32no—
115#893—62no—
116D3×C4⋊C4—61no—
117D3×C4⋊C4—61no—
118D3×C4⋊C4—62no—
119#890—32no—
120#890—32no—
121#890—62no—
122#888—32no—
123#888—32no—
124#888—61no—
125#888—62no—
126#887—32no—
127#887—61no—
128C4×D12—31no—
129C4×D12—31no—
130C4×D12—61no—
131#869—61no—
132#869C2×D311yescharacteristic
133C4×Dic6—31no—
134C4×Dic6—31no—
135C4×Dic6—61no—
136C4×Dic6—61no—
137C4×Dic6C2×D311yescharacteristic
138C3×#107—32no—
139C3×#107—32no—
140C3×#107—32no—
141C3×C4⋊C8—31no—
142C3×#103—32no—
143C3×C4×C8—31no—
144#835—31no—
145#821—31no—
146#821—32no—
147#817—31no—
148#817—32no—
149#816—31no—
150#815—32no—
151#815—32no—
152Dic3⋊C8—32no—
153Dic3⋊C8—32no—
154#810C2×D312yes—
155#809—32no—
156#809—31no—
157#808—31no—
158#808—32no—
159#807C2×D312yes—
160#807C2×D312yes—
161#807C2×D312yes—
162C4⋊(C3⋊C8)C2×D311yescharacteristic
163C4×C3⋊C8C2×D311yescharacteristic
164C22×C3⋊D3—21no—
165C32×Q8—81no—
166C2×C32×C4—22no—
167C2×C32×C4C2×D411yescharacteristic
168C2×C32×C4C2×D411yescharacteristic
169C2×C32×C4C2411yescharacteristic
170C2×C3⋊Dic3—21no—
171C2×C3⋊Dic3C2×D412yes—
172C2×C3⋊Dic3C2×D412yes—
173C4⋊(C3⋊D3)—21no—
174C4⋊(C3⋊D3)C2×Q812yes—
175C4×C3⋊D3—42no—
176C4×C3⋊D3—82no—
177#634—22no—
178C2×C3×Dic3—21no—
179C2×C3×Dic3—22no—
180C2×C3×Dic3—21no—
181C3×Dic6—21no—
182C3×Dic6—81no—
183C3×Dic6C2×Q812yes—
184#627—82no—
185C3×C3⋊C8—21no—
186C3×C3⋊C8—22no—
187C3×C3⋊C8C2×Q812yes—
188Q82—91no—
189#554—91no—
190#501—92no—
191#500—31no—
192#479—92no—
193#477—31no—
194#476—91no—
195#474—92no—
196#446—91no—
197#440—92no—
198C4×SD16—91no—
199C2×C3×Q8—22no—
200C2×C3×Q8—21no—
201C2×C3×Q8—21no—
202C2×C3×Q8—31no—
203C2×C3×Q8—61no—
204C2×D12—31no—
205C2×D12—31no—
206C2×D12—61no—
207C2×C4×D3—62no—
208C2×C4×D3—61no—
209C2×C4×D3—61no—
210C2×C4×D3—62no—
211C2×C4×D3—62no—
212C2×C4×D3—64no—
213C2×Dic6—21no—
214C2×Dic6—31no—
215C2×Dic6—31no—
216C2×Dic6—61no—
217C2×Dic6—62no—
218C2×Dic6—62no—
219C2×Dic6C22×D311yescharacteristic
220C2×C3×C8—31no—
221C2×C3×C8—31no—
222C2×C3×C8—32no—
223C3×C4⋊C4—22no—
224C3×C4⋊C4—21no—
225C3×C4⋊C4—21no—
226C3×C4⋊C4—22no—
227C3×C4⋊C4—32no—
228C3×C4⋊C4—31no—
229C3×C4⋊C4—61no—
230C3×C4⋊C4—61no—
231C3×C4⋊C4C22×D312yes—
232C3×C4⋊C4C22×D312yes—
233C3×C42—21no—
234C3×C42—61no—
235C3×C42C22×D311yescharacteristic
236C3×C42C22×D311yescharacteristic
237#215—34no—
238(C2×D3)⋊C4—62no—
239(C2×D3)⋊C4—62no—
240(C2×D3)⋊C4—62no—
241(C2×D3)⋊C4—64no—
242(C2×D3)⋊C4—61no—
243(C2×D3)⋊C4—61no—
244C4⋊Dic3—21no—
245C4⋊Dic3—31no—
246C4⋊Dic3—31no—
247C4⋊Dic3—31no—
248C4⋊Dic3—31no—
249C4⋊Dic3—61no—
250C4⋊Dic3—61no—
251C4⋊Dic3—62no—
252C4⋊Dic3—62no—
253C4⋊Dic3—62no—
254C4⋊Dic3—64no—
255C4⋊Dic3C22×D311yescharacteristic
256C4⋊Dic3C22×D312yes—
257Dic3⋊C4—21no—
258Dic3⋊C4—32no—
259Dic3⋊C4—32no—
260Dic3⋊C4—62no—
261Dic3⋊C4—62no—
262Dic3⋊C4—62no—
263Dic3⋊C4—62no—
264Dic3⋊C4—62no—
265Dic3⋊C4—62no—
266Dic3⋊C4—64no—
267C4×Dic3—21no—
268C4×Dic3—32no—
269C4×Dic3—32no—
270C4×Dic3—62no—
271C4×Dic3—62no—
272C4×Dic3—62no—
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—21no—
282C32×C4—42no—
283C32×C4#13712yes—
284C32×C4C22×Q811yescharacteristic
285C32×C42−1+411yescharacteristic
286C3⋊Dic3—22no—
287C3⋊Dic3—22no—
288C3⋊Dic3—41no—
289C3×Dic3—22no—
290C3×Dic3—41no—
291C3×Dic3—42no—
292C2×SD16—91no—
293C4⋊Q8—31no—
294C4⋊Q8—92no—
295C4⋊Q8—181no—
296C4⋊Q8—182no—
297C4⋊Q8D3211yescharacteristic
298#125—92no—
299C22⋊Q8—181no—
300C22⋊Q8—182no—
301C4×Q8—31no—
302C4×Q8—91no—
303C4×Q8—92no—
304C4×Q8—181no—
305C4×D4—92no—
306C4×D4—91no—
307C2×C4⋊C4—181no—
308#107—32no—
309#107—32no—
310#107—32no—
311#106—91no—
312#106—92no—
313C4⋊C8—31no—
314C4⋊C8—92no—
315#103—32no—
316#103—91no—
317#102—91no—
318#102—92no—
319#97—92no—
320C4×C8—31no—
321C22×D3—62no—
322C22×D3—61no—
323C22×D3—61no—
324C3×Q8—32no—
325C3×Q8—61no—
326C3×Q8—81no—
327C3×Q8—81no—
328C3×Q8—82no—
329C3×Q8—241no—
330C2×C3×C4—24no—
331C2×C3×C4—22no—
332C2×C3×C4—22no—
333C2×C3×C4—21no—
334C2×C3×C4—21no—
335C2×C3×C4—21no—
336C2×C3×C4—61no—
337C2×C3×C4—62no—
338C2×C3×C4—61no—
339C2×C3×C4D3×D411yescharacteristic
340C2×C3×C4D3×D411yescharacteristic
341C2×C3×C4D3×D411yescharacteristic
342C2×C3×C4D3×D411yescharacteristic
343C2×C3×C4C23×D311yescharacteristic
344C2×C3×C4C23×D311yescharacteristic
345C2×Dic3—21no—
346C2×Dic3—21no—
347C2×Dic3—22no—
348C2×Dic3—32no—
349C2×Dic3—32no—
350C2×Dic3—32no—
351C2×Dic3—32no—
352C2×Dic3—62no—
353C2×Dic3—62no—
354C2×Dic3—62no—
355C2×Dic3—61no—
356C2×Dic3—61no—
357D12—32no—
358D12—32no—
359D12—62no—
360D12—62no—
361D12—61no—
362D12—61no—
363C4×D3—124no—
364C4×D3—122no—
365C4×D3—122no—
366C4×D3—242no—
367C4×D3—242no—
368C4×D3—244no—
369Dic6—21no—
370Dic6—62no—
371Dic6—62no—
372Dic6—81no—
373Dic6—122no—
374Dic6—242no—
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—21no—
388C2×Q8—31no—
389C2×Q8—61no—
390C2×Q8—91no—
391C2×Q8—182no—
392C2×D4—91no—
393C22×C4—182no—
394C22×C4—181no—
395SD16—94no—
396C2×C8—31no—
397C2×C8—31no—
398C2×C8—32no—
399C4⋊C4—21no—
400C4⋊C4—31no—
401C4⋊C4—32no—
402C4⋊C4—61no—
403C4⋊C4—61no—
404C4⋊C4—91no—
405C4⋊C4—92no—
406C4⋊C4—91no—
407C4⋊C4—182no—
408C4⋊C4—182no—
409C4⋊C4—182no—
410C4⋊C4—182no—
411C4⋊C4C2×D3212yes—
412C22⋊C4—182no—
413C22⋊C4—181no—
414C42—61no—
415C42—92no—
416C42—182no—
417C42C2×D3211yescharacteristic
418C22×C3—21no—
419C22×C3C2×D3×D411yescharacteristic
420C22×C3C2×D3×D411yescharacteristic
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—21no—
431C3×C4—21no—
432C3×C4—21no—
433C3×C4—21no—
434C3×C4—22no—
435C3×C4—41no—
436C3×C4—44no—
437C3×C4—42no—
438C3×C4—42no—
439C3×C4—62no—
440C3×C4—121no—
441C3×C4—122no—
442C3×C4#91812yes—
443C3×C4#91812yes—
444C3×C4C2×D3×Q811yescharacteristic
445C3×C4C2×D3×Q811yescharacteristic
446C3×C4#100711yescharacteristic
447C3×C4#101011yescharacteristic
448Dic3—22no—
449Dic3—42no—
450Dic3—41no—
451Dic3—62no—
452Dic3—62no—
453Dic3—62no—
454Dic3—62no—
455Dic3—122no—
456Dic3—122no—
457Dic3—122no—
458Dic3—121no—
459Dic3—121no—
460C32#338511yescharacteristic, complemented, Sylow
461C23—181no—
462Q8—32no—
463Q8—61no—
464Q8—81no—
465Q8—182no—
466Q8—241no—
467Q8—722no—
468D4—92no—
469D4—181no—
470C2×C4—22no—
471C2×C4—61no—
472C2×C4—61no—
473C2×C4—62no—
474C2×C4—92no—
475C2×C4—92no—
476C2×C4—181no—
477C2×C4—362no—
478C2×C4—722no—
479C2×C4#381111yescharacteristic
480C2×C4#381111yescharacteristic
481C2×C4C22×D3211yescharacteristic
482C8—32no—
483C8—61no—
484C8—62no—
485C2×C3—21no—
486C2×C3—21no—
487C2×C3—21no—
488C2×C3#563211yescharacteristic
489C2×C3#572711yescharacteristic
490C2×C3#575711yescharacteristic
491C2×C3C2×#91811yescharacteristic
492C2×C3C2×#91811yescharacteristic
493C2×C3#577411yescharacteristic
494D3—124no—
495D3—122no—
496D3—122no—
497C22—182no—
498C22—361no—
499C22—361no—
500C22C2×#381111yescharacteristic
501C4—21no—
502C4—42no—
503C4—62no—
504C4—122no—
505C4—121no—
506C4—182no—
507C4—182no—
508C4—361no—
509C4#6394512yes—
510C4#6431511yescharacteristic
511C4D32×Q811yescharacteristic
512C3—21no—
513C3#8113711yescharacteristic, complemented
514C3#8195411yescharacteristic, complemented
515C2—362no—
516C2#1059510211yescharacteristic
517C2C2×#6394511yescharacteristic
518C2#1059536111yescharacteristic
subgroupG/H
centerC22C2×#3811
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 ◁ C42 ◁ C4⋊Q8

Complements

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

NH ≅ G/Ntype
2. #10593856C2semidirect
3. C3×#5091C2semidirect
4. C3×#5078C2semidirect
5. #10590563C2semidirect
6. #10590494C2semidirect
11. #10590296C2semidirect
50. #5091D3semidirect
52. #5078D3semidirect
96. #3717Q8semidirect
460. C32#3385semidirect
513. C3#81137semidirect
514. C3#81954semidirect

Maximal subgroups

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

subgroupindex
#105962012
#105938562
C3×#50912
C3×#50782
#105905632
#105904942
#105904842
#105904302
C4×#37172
#105903002
#105902962
#819543
#811373