Finite Group Databasebeta

← #11897668

Subgroups — #11897668

Order 1152.

786 conjugacy classes of subgroups.

The subgroup lattice has 516 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10596193C211yesmaximal, characteristic, complemented
2#10593956C211yesmaximal, characteristic
3C3×#5084C211yesmaximal, characteristic
4C3×#5078C211yesmaximal, characteristic, complemented
5#10590546C212yesmaximal, complemented
6#10590471C212yesmaximal
7#10590461C212yesmaximal
8#10590434C212yesmaximal, complemented
9C4×#3716C211yesmaximal, characteristic
10#10590296C211yesmaximal, characteristic, complemented
11#10590284C211yesmaximal, characteristic, complemented
12#81954—31nomaximal
13#81056—31nomaximal
14C32×C4⋊Q8C2211yescharacteristic
15#64153—22no—
16#64097—21no—
17#64097C2212yes—
18#64096—21no—
19#64096C2212yes—
20C4×#634C2211yescharacteristic
21C4×#634C2211yescharacteristic
22C3×C4×D12C2211yescharacteristic
23C3×#869C2211yescharacteristic
24#63898C2212yes—
25D3×C4⋊Dic3—21no—
26#63887—22no—
27#63872C2212yes—
28#63857—21no—
29C2×#3716C2211yescharacteristic
30C3×#809C2212yes—
31C3×#808C2212yes—
32C3×#807C2212yes—
33C3×#807C2212yes—
34C3×C4⋊(C3⋊C8)C2211yescharacteristic
35C3×C4×C3⋊C8C2211yescharacteristic
36#63575C2212yes—
37#63573C2211yescharacteristic
38#63572C2212yes—
39#63567C2212yes—
40#63567C2211yescharacteristic
41#63563C2211yescharacteristic
42#63555C2212yes—
43#5730—31no—
44#5722—31no—
45#5722—31no—
46#5722—61no—
47#5543—31no—
48C3×#500—31no—
49C3×#476—31no—
50#5091—31no—
51#5084D311yescharacteristic
52#5078D311yescharacteristic, complemented
53C4×#214—31no—
54#4890—32no—
55#4889—32no—
56#4877—32no—
57#4876—32no—
58#4857—32no—
59#4856—32no—
60#4850—31no—
61#4831—31no—
62#4759—32no—
63#4757—32no—
64C4×#204—31no—
65#4679—31no—
66C2×C32×Q8—21no—
67C2×#634—22no—
68C2×#634D411yescharacteristic
69C2×#634C2311yescharacteristic
70C2×C3×D12C2311yescharacteristic
71C2×C3×C4×D3—21no—
72C2×C3×Dic6—21no—
73C2×D3×Dic3—22no—
74C32×C4⋊C4—21no—
75C32×C4⋊C4C2312yes—
76C32×C42C2311yescharacteristic
77C4⋊(C3⋊Dic3)D411yescharacteristic
78C4⋊(C3⋊Dic3)C2311yescharacteristic
79#3750—21no—
80#3750—22no—
81#3750—22no—
82#3750D412yes—
83C4×C3⋊Dic3—21no—
84C4×C3⋊Dic3—22no—
85C4×C3⋊Dic3C2312yes—
86C3×(C2×D3)⋊C4—21no—
87C3×C4⋊Dic3—21no—
88C3×C4⋊Dic3C2311yescharacteristic
89C3×C4⋊Dic3C2312yes—
90C2×C3×C3⋊C8C2312yes—
91C2×C3×C3⋊C8C2311yescharacteristic
92C2×C3×C3⋊C8C2311yescharacteristic
93Dic3⋊Dic3—22no—
94Dic3⋊Dic3—22no—
95(C2×D3)⋊Dic3—22no—
96#3716Q814yescomplemented
97#3385—91noSylow
98C3×C4⋊Q8—21no—
99C3×C4⋊Q8—31no—
100C3×C4⋊Q8C2×D311yescharacteristic
101C3×C4⋊Q8C2×D311yescharacteristic
102C3×C4×D4—31no—
103#946—62no—
104#944—62no—
105#944—62no—
106#944—64no—
107D4×Dic3—32no—
108C2×#214—31no—
109C2×C4⋊Dic3—61no—
110#924—61no—
111C2×#204—31no—
112#897—61no—
113#893—32no—
114D3×C4⋊C4—61no—
115#890—32no—
116#890—32no—
117#888—32no—
118#888—32no—
119#888—62no—
120#888—61no—
121#888—61no—
122#888—62no—
123#887—32no—
124#887—32no—
125#887—62no—
126#887—61no—
127#887—61no—
128#887—62no—
129#878—62no—
130C4×D12C2×D311yescharacteristic
131#869C2×D311yescharacteristic
132C4×Dic6—31no—
133C4×Dic6—31no—
134C4×Dic6—31no—
135C4×Dic6—31no—
136C4×Dic6—61no—
137C4×Dic6—61no—
138C3×#107—32no—
139C3×#107—32no—
140C3×#106—32no—
141C3×C4⋊C8—31no—
142C3×#102—32no—
143C3×C4×C8—31no—
144#832—31no—
145#821—31no—
146#818—32no—
147#817—31no—
148#816—31no—
149#816—32no—
150#815—32no—
151#815—32no—
152Dic3⋊C8—32no—
153Dic3⋊C8—32no—
154#810—32no—
155#810—31no—
156#809C2×D312yes—
157#808—31no—
158#808C2×D312yes—
159#807—32no—
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⋊Dic3—21no—
172C2×C3⋊Dic3C2×D412yes—
173C2×C3⋊Dic3C2×D412yes—
174#634—22no—
175#634—21no—
176#634—82no—
177#634C2×Q812yes—
178C2×C3×Dic3—22no—
179C2×C3×Dic3—21no—
180C3×D12—21no—
181C3×D12C2×Q812yes—
182C3×C4×D3—42no—
183C3×Dic6—81no—
184D3×Dic3—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—91no—
194#476—31no—
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—61no—
203C2×C3×D4—31no—
204C22×C3×C4—61no—
205C22×Dic3—62no—
206C2×D12C22×D311yescharacteristic
207C2×C4×D3—21no—
208C2×C4×D3—62no—
209C2×Dic6—21no—
210C2×Dic6—31no—
211C2×Dic6—31no—
212C2×Dic6—31no—
213C2×Dic6—31no—
214C2×Dic6—61no—
215C2×Dic6—61no—
216C2×Dic6—62no—
217C2×Dic6—62no—
218C2×Dic6—64no—
219C2×C3×C8—31no—
220C2×C3×C8—31no—
221C2×C3×C8—32no—
222C3×C4⋊C4—22no—
223C3×C4⋊C4—21no—
224C3×C4⋊C4—21no—
225C3×C4⋊C4—22no—
226C3×C4⋊C4—32no—
227C3×C4⋊C4—31no—
228C3×C4⋊C4—61no—
229C3×C4⋊C4C22×D312yes—
230C3×C4⋊C4C22×D312yes—
231C3×C22⋊C4—61no—
232C3×C42—21no—
233C3×C42C22×D311yescharacteristic
234C3×C42C22×D311yescharacteristic
235#217—62no—
236#214—34no—
237(C2×D3)⋊C4—21no—
238(C2×D3)⋊C4—62no—
239C4⋊Dic3—21no—
240C4⋊Dic3—31no—
241C4⋊Dic3—31no—
242C4⋊Dic3—31no—
243C4⋊Dic3—31no—
244C4⋊Dic3—61no—
245C4⋊Dic3—61no—
246C4⋊Dic3—62no—
247C4⋊Dic3—62no—
248C4⋊Dic3C22×D312yes—
249C4⋊Dic3C22×D311yescharacteristic
250Dic3⋊C4—32no—
251Dic3⋊C4—32no—
252Dic3⋊C4—62no—
253Dic3⋊C4—62no—
254Dic3⋊C4—62no—
255Dic3⋊C4—62no—
256Dic3⋊C4—62no—
257Dic3⋊C4—62no—
258Dic3⋊C4—62no—
259Dic3⋊C4—62no—
260Dic3⋊C4—64no—
261Dic3⋊C4—64no—
262Dic3⋊C4—61no—
263Dic3⋊C4—61no—
264C4×Dic3—32no—
265C4×Dic3—32no—
266C4×Dic3—62no—
267C4×Dic3—62no—
268C4×Dic3—62no—
269C4×Dic3—62no—
270C4×Dic3—64no—
271C4×Dic3—61no—
272C4×Dic3—61no—
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—22no—
289C3⋊Dic3—41no—
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—182no—
300C22⋊Q8—181no—
301C4×Q8—91no—
302C4×Q8—92no—
303C4×Q8—91no—
304C4×Q8—181no—
305C4×D4—31no—
306C4×D4—92no—
307C2×C4⋊C4—181no—
308#107—32no—
309#107—32no—
310#107—92no—
311#106—32no—
312#106—91no—
313C4⋊C8—31no—
314C4⋊C8—92no—
315#103—91no—
316#103—92no—
317#102—32no—
318#102—91no—
319#97—92no—
320C4×C8—31no—
321C23×C3—61no—
322C22×D3—21no—
323C3×Q8—81no—
324C3×Q8—81no—
325C3×Q8—82no—
326C3×Q8—241no—
327C3×D4—32no—
328C3×D4—61no—
329C2×C3×C4—24no—
330C2×C3×C4—22no—
331C2×C3×C4—22no—
332C2×C3×C4—21no—
333C2×C3×C4—21no—
334C2×C3×C4—21no—
335C2×C3×C4—61no—
336C2×C3×C4—62no—
337C2×C3×C4—122no—
338C2×C3×C4D3×D411yescharacteristic
339C2×C3×C4D3×D411yescharacteristic
340C2×C3×C4D3×D411yescharacteristic
341C2×C3×C4D3×D411yescharacteristic
342C2×C3×C4C23×D311yescharacteristic
343C2×C3×C4C23×D311yescharacteristic
344C2×Dic3—21no—
345C2×Dic3—22no—
346C2×Dic3—32no—
347C2×Dic3—32no—
348C2×Dic3—32no—
349C2×Dic3—32no—
350C2×Dic3—62no—
351C2×Dic3—62no—
352C2×Dic3—62no—
353C2×Dic3—61no—
354C2×Dic3—61no—
355C2×Dic3—62no—
356C2×Dic3—61no—
357C2×Dic3—61no—
358C2×Dic3—242no—
359D12—21no—
360D12D3×Q812yes—
361C4×D3—42no—
362C4×D3—242no—
363Dic6—32no—
364Dic6—32no—
365Dic6—62no—
366Dic6—62no—
367Dic6—64no—
368Dic6—62no—
369Dic6—62no—
370Dic6—61no—
371Dic6—61no—
372Dic6—81no—
373Dic6—242no—
374Dic6—242no—
375Dic6—244no—
376C3×C8—32no—
377C3×C8—62no—
378C3×C8—61no—
379C3⋊C8—21no—
380C3⋊C8—22no—
381C3⋊C8D3×Q812yes—
382C2×C32D4×Q811yescharacteristic
383C2×C32C2×#13711yescharacteristic
384C2×C32#57611yescharacteristic
385C3×D3—42no—
386C2×Q8—21no—
387C2×Q8—61no—
388C2×Q8—91no—
389C2×Q8—91no—
390C2×Q8—182no—
391C2×D4—31no—
392C22×C4—61no—
393C22×C4—182no—
394SD16—94no—
395C2×C8—31no—
396C2×C8—31no—
397C2×C8—32no—
398C4⋊C4—21no—
399C4⋊C4—31no—
400C4⋊C4—32no—
401C4⋊C4—61no—
402C4⋊C4—91no—
403C4⋊C4—92no—
404C4⋊C4—91no—
405C4⋊C4—182no—
406C4⋊C4—182no—
407C4⋊C4—182no—
408C4⋊C4—182no—
409C4⋊C4—181no—
410C4⋊C4C2×D3212yes—
411C22⋊C4—61no—
412C22⋊C4—182no—
413C42—92no—
414C42—182no—
415C42—181no—
416C42C2×D3211yescharacteristic
417C22×C3—21no—
418C22×C3—62no—
419C22×C3—121no—
420C22×C3—121no—
421C22×C3C2×D3×D411yescharacteristic
422C22×C3C2×D3×D411yescharacteristic
423C2×D3—22no—
424C2×D3—41no—
425C2×D3—41no—
426C3×C4—21no—
427C3×C4—21no—
428C3×C4—21no—
429C3×C4—21no—
430C3×C4—22no—
431C3×C4—41no—
432C3×C4—44no—
433C3×C4—42no—
434C3×C4—42no—
435C3×C4—121no—
436C3×C4—122no—
437C3×C4#91512yes—
438C3×C4#91812yes—
439C3×C4C2×D3×Q811yescharacteristic
440C3×C4C2×D3×Q811yescharacteristic
441C3×C4#100711yescharacteristic
442C3×C4#101011yescharacteristic
443Dic3—42no—
444Dic3—41no—
445Dic3—64no—
446Dic3—64no—
447Dic3—62no—
448Dic3—62no—
449Dic3—62no—
450Dic3—62no—
451Dic3—62no—
452Dic3—62no—
453Dic3—122no—
454Dic3—122no—
455Dic3—121no—
456Dic3—121no—
457C32#338511yescharacteristic, complemented, Sylow
458C23—61no—
459Q8—81no—
460Q8—92no—
461Q8—181no—
462Q8—182no—
463Q8—241no—
464Q8—722no—
465D4—32no—
466D4—61no—
467C2×C4—22no—
468C2×C4—61no—
469C2×C4—62no—
470C2×C4—92no—
471C2×C4—92no—
472C2×C4—122no—
473C2×C4—181no—
474C2×C4—181no—
475C2×C4—722no—
476C2×C4#381111yescharacteristic
477C2×C4#381111yescharacteristic
478C2×C4C22×D3211yescharacteristic
479C8—32no—
480C8—61no—
481C8—62no—
482C2×C3—21no—
483C2×C3—21no—
484C2×C3—21no—
485C2×C3—122no—
486C2×C3#563211yescharacteristic
487C2×C3#572711yescharacteristic
488C2×C3#575711yescharacteristic
489C2×C3C2×#91511yescharacteristic
490C2×C3C2×#91811yescharacteristic
491C2×C3#577411yescharacteristic
492D3—42no—
493C22—62no—
494C22—121no—
495C22—121no—
496C22C2×#381111yescharacteristic
497C4—21no—
498C4—42no—
499C4—121no—
500C4—122no—
501C4—182no—
502C4—182no—
503C4—182no—
504C4—361no—
505C4#6395112yes—
506C4#6431511yescharacteristic
507C4D32×Q811yescharacteristic
508C3—21no—
509C3#8105611yescharacteristic, complemented
510C3#8195411yescharacteristic, complemented
511C2—122no—
512C2#1059510211yescharacteristic
513C2C2×#6395111yescharacteristic
514C2#1059536111yescharacteristic
subgroupG/H
centerC22C2×#3811
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×C4⋊Q8C22
socleC22×C32C22×D4
prime radicalC2×C3×D12C23
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
1. #10596193C2semidirect
4. C3×#5078C2semidirect
5. #10590546C2semidirect
8. #10590434C2semidirect
10. #10590296C2semidirect
11. #10590284C2semidirect
52. #5078D3semidirect
96. #3716Q8semidirect
457. C32#3385semidirect
509. C3#81056semidirect
510. C3#81954semidirect

Maximal subgroups

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

subgroupindex
#105961932
#105939562
C3×#50842
C3×#50782
#105905462
#105904712
#105904612
#105904342
C4×#37162
#105902962
#105902842
#819543
#810563