Finite Group Databasebeta

← #11778071

Subgroups — #11778071

Order 1152.

643 conjugacy classes of subgroups; only the 78 normal subgroups are shown.

normal subgroups only

This group has 643 conjugacy classes of subgroups — too many to draw. Only its 78 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10594980C211yesmaximal, characteristic, complemented
2#10592431C211yesmaximal, characteristic
3#10591321C211yesmaximal, characteristic, complemented
4#10591183C211yesmaximal, characteristic, complemented
5C3×#4469C211yesmaximal, characteristic, complemented
6C3×#4467C211yesmaximal, characteristic, complemented
7#10589151C211yesmaximal, characteristic, complemented
8#68324—31nomaximal
9#68130—31nomaximal
10C22×C4⋊(C3⋊D3)C2211yescharacteristic
11#64139C2211yescharacteristic
12C2×#3745—21no—
13C3×#924C2211yescharacteristic
14C2×C3×Dic3⋊C4C2211yescharacteristic
15#63966—21no—
16C2×#3722—21no—
17C2×#3722—21no—
18#63952—21no—
19#63897—21no—
20#63888—21no—
21#63848—21no—
22#63845—21no—
23C2×#3717—21no—
24C32×C22⋊C8C2211yescharacteristic
25#63648—21no—
26C3×C3⋊#95C2211yescharacteristic
27C3×#830C2211yescharacteristic
28#63564—21no—
29#5645—31no—
30#5515—31no—
31#5046—31no—
32#4991—31no—
33#4732—31no—
34#4732—31no—
35#4732—61no—
36#4731—31no—
37#4672—31no—
38C3×#328—31no—
39C3×#324—31no—
40#4470—31no—
41#4469D311yescharacteristic, complemented
42#4467D311yescharacteristic, complemented
43#4451—31no—
44C23×C3⋊D3—21no—
45C22×C32×C4C2311yescharacteristic
46C2×#638—21no—
47C2×C4⋊(C3⋊D3)—21no—
48C2×C4⋊(C3⋊D3)—21no—
49C2×C4⋊(C3⋊D3)—42no—
50C2×C4⋊(C3⋊D3)D411yescharacteristic
51C22×C3×Dic3—21no—
52C22×C3×Dic3D411yescharacteristic
53C22×C3×Dic3D411yescharacteristic
54C2×C3×Dic6D411yescharacteristic
55C2×#624—21no—
56C2×C32×C8—21no—
57#3752—21no—
58C4⋊(C3⋊Dic3)D411yescharacteristic
59#3745—42no—
60C3×#217—21no—
61C3×C4⋊Dic3D411yescharacteristic
62C3×Dic3⋊C4—21no—
63C3×Dic3⋊C4—21no—
64C3×Dic3⋊C4—21no—
65C2×C3×C3⋊C8—21no—
66#3724—21no—
67Dic3⋊Dic3—21no—
68Dic3⋊Dic3—21no—
69#3722—21no—
70#3722—21no—
71#3722—21no—
72#3722—42no—
73#3722—42no—
74Dic32—21no—
75#3717—42no—
76#1597—91noSylow
77C22×D12—31no—
78C22×D12—31no—
79C22×D12—61no—
80C3×C22⋊Q8—31no—
81C2×C3×C4⋊C4—31no—
82#946—61no—
83C2×#215—61no—
84#930—31no—
85#930—31no—
86#930—61no—
87#929—61no—
88C4×#67—61no—
89C2×(C2×D3)⋊C4—61no—
90C2×(C2×D3)⋊C4—61no—
91C2×(C2×D3)⋊C4—61no—
92C2×(C2×D3)⋊C4—61no—
93#924C2×D311yescharacteristic
94C2×Dic3⋊C4C2×D311yescharacteristic
95C2×D24—61no—
96C2×D24—61no—
97C2×D24—62no—
98C2×#204—61no—
99#898—61no—
100#898—61no—
101#896—61no—
102#894—61no—
103#894—61no—
104#890—61no—
105#889—61no—
106#886—61no—
107#67⋊C4—61no—
108C3×C22⋊C8—21no—
109C3×C22⋊C8—31no—
110C3×C22⋊C8C2×D311yescharacteristic
111C3×C22⋊C8C2×D311yescharacteristic
112C3×#95—31no—
113C3⋊#95C2×D311yescharacteristic
114#830C2×D311yescharacteristic
115#821—61no—
116#821—61no—
117#821—62no—
118#821—61no—
119#809—61no—
120C23×C32C2×D411yescharacteristic
121C22×C3⋊D3—22no—
122C22×C3⋊D3—21no—
123C22×C3⋊D3—41no—
124C22×C3⋊D3—41no—
125C22×C3⋊D3—41no—
126C22×C3⋊D3—41no—
127C22×C3⋊D3—41no—
128C22×C3⋊D3—41no—
129C2×C32×C4—41no—
130C2×C32×C4C2×D411yescharacteristic
131C2×C32×C4C2×D411yescharacteristic
132#638—41no—
133#638—41no—
134C2×C3⋊Dic3—21no—
135C4⋊(C3⋊D3)—22no—
136C4⋊(C3⋊D3)—22no—
137C4⋊(C3⋊D3)—41no—
138C4⋊(C3⋊D3)—41no—
139C4⋊(C3⋊D3)—41no—
140C2×C3×Dic3—21no—
141C2×C3×Dic3—21no—
142C2×C3×Dic3—21no—
143C2×C3×Dic3—21no—
144C2×C3×Dic3—21no—
145C2×C3×Dic3—21no—
146C2×C3×Dic3—41no—
147C2×C3×Dic3—41no—
148C2×C3×Dic3—41no—
149C2×C3×Dic3—41no—
150C3×Dic6—41no—
151#624—81no—
152C32×C8—41no—
153C3×C3⋊C8—41no—
154#539—91no—
155#450—91no—
156#447—91no—
157#394—91no—
158#328—31no—
159#327—91no—
160#324—31no—
161C23×D3—61no—
162C23×D3—61no—
163C23×D3—121no—
164C2×C3×Q8—31no—
165C22×C3×C4—21no—
166C22×C3×C4—31no—
167C22×C3×C4—31no—
168C22×C3×C4—61no—
169C22×C3×C4C22×D311yescharacteristic
170C22×C3×C4C22×D311yescharacteristic
171C2×#67—61no—
172C2×#67—61no—
173C2×#67—121no—
174C22×Dic3—21no—
175C22×Dic3D1211yescharacteristic
176C22×Dic3D1211yescharacteristic
177C2×D12—31no—
178C2×D12—31no—
179C2×D12—61no—
180C2×D12—62no—
181C2×D12—61no—
182C2×D12—61no—
183C2×D12—61no—
184C2×D12—61no—
185C2×D12—121no—
186C2×D12—122no—
187C2×D12—122no—
188C2×D12—124no—
189C2×C4×D3—61no—
190C2×C4×D3—61no—
191C2×Dic6D1211yescharacteristic
192C2×C3×C8—22no—
193C2×C3×C8—21no—
194C2×C3×C8—21no—
195C2×C3×C8—61no—
196C3×C4⋊C4—31no—
197C3×C4⋊C4—61no—
198C3×C4⋊C4—61no—
199C3×C4⋊C4—61no—
200C3×C22⋊C4—61no—
201#217—21no—
202#215—122no—
203(C2×D3)⋊C4—61no—
204(C2×D3)⋊C4—61no—
205(C2×D3)⋊C4—61no—
206(C2×D3)⋊C4—61no—
207(C2×D3)⋊C4—61no—
208(C2×D3)⋊C4—61no—
209(C2×D3)⋊C4—61no—
210(C2×D3)⋊C4—61no—
211(C2×D3)⋊C4—121no—
212(C2×D3)⋊C4—122no—
213(C2×D3)⋊C4—122no—
214(C2×D3)⋊C4—122no—
215(C2×D3)⋊C4—122no—
216C4⋊Dic3—31no—
217C4⋊Dic3—31no—
218C4⋊Dic3—61no—
219C4⋊Dic3—61no—
220C4⋊Dic3—61no—
221C4⋊Dic3D1211yescharacteristic
222Dic3⋊C4—21no—
223Dic3⋊C4—21no—
224Dic3⋊C4—21no—
225Dic3⋊C4—61no—
226Dic3⋊C4—61no—
227Dic3⋊C4—61no—
228Dic3⋊C4—61no—
229C4×Dic3—61no—
230C4×Dic3—61no—
231C2×C3⋊C8—21no—
232D24—122no—
233D24—122no—
234D24—124no—
235#204—122no—
236C22×C32—21no—
237C22×C32—21no—
238C22×C32#12011yescharacteristic
239C22×C32#13511yescharacteristic
240C22×C32AGL(1,ℤ/8)11yescharacteristic
241C2×C3⋊D3—42no—
242C2×C3⋊D3—42no—
243C2×C3⋊D3—42no—
244C2×C3⋊D3—41no—
245C2×C3⋊D3—41no—
246C2×C3⋊D3—41no—
247C2×C3⋊D3—81no—
248C2×C3⋊D3—81no—
249C2×C3⋊D3—81no—
250C2×C3⋊D3—81no—
251C32×C4—21no—
252C32×C4—21no—
253C3⋊Dic3—41no—
254C3×Dic3—41no—
255C3×Dic3—41no—
256C3×Dic3—41no—
257C3×Dic3—41no—
258C3×Dic3—81no—
259C22×D4—91no—
260C2×SD16—181no—
261C2×D8—181no—
262#126—181no—
263#125—181no—
264#123—181no—
265#123—181no—
266C22⋊Q8—31no—
267C22⋊Q8—181no—
268#121—91no—
269C4×D4—181no—
270C2×C4⋊C4—31no—
271C2×C22⋊C4—181no—
272C2×C22⋊C4—181no—
273#102—181no—
274#102—181no—
275C22⋊C8—31no—
276C22⋊C8D3211yescharacteristic
277#95—31no—
278C23×C3—21no—
279C23×C3C2×D1211yescharacteristic
280C23×C3D3×D411yescharacteristic
281C22×D3—62no—
282C22×D3—62no—
283C22×D3—61no—
284C22×D3—61no—
285C22×D3—122no—
286C22×D3—121no—
287C22×D3—122no—
288C22×D3—121no—
289C22×D3—121no—
290C22×D3—121no—
291C22×D3—121no—
292C22×D3—121no—
293C22×D3—121no—
294C22×D3—122no—
295C22×D3—121no—
296C22×D3—121no—
297C22×D3—121no—
298C22×D3—121no—
299C22×D3—121no—
300C22×D3—121no—
301C22×D3—241no—
302C22×D3—241no—
303C22×D3—241no—
304C22×D3—241no—
305C3×Q8—121no—
306C2×C3×C4—21no—
307C2×C3×C4—21no—
308C2×C3×C4—41no—
309C2×C3×C4—41no—
310C2×C3×C4—42no—
311C2×C3×C4—61no—
312C2×C3×C4—61no—
313C2×C3×C4—61no—
314C2×C3×C4—61no—
315C2×C3×C4—61no—
316C2×C3×C4—61no—
317C2×C3×C4—121no—
318C2×C3×C4—121no—
319C2×C3×C4—121no—
320C2×C3×C4—121no—
321C2×C3×C4C2×D1211yescharacteristic
322C2×C3×C4D3×D411yescharacteristic
323C2×C3×C4D3×D411yescharacteristic
324C2×C3×C4D3×D411yescharacteristic
325#67—121no—
326#67—121no—
327#67—121no—
328#67—121no—
329#67—241no—
330#67—241no—
331C2×Dic3—21no—
332C2×Dic3—21no—
333C2×Dic3—21no—
334C2×Dic3—21no—
335C2×Dic3—21no—
336C2×Dic3—21no—
337C2×Dic3—41no—
338C2×Dic3—41no—
339C2×Dic3—41no—
340C2×Dic3—41no—
341C2×Dic3—61no—
342C2×Dic3—61no—
343C2×Dic3—121no—
344D12—62no—
345D12—64no—
346D12—62no—
347D12—62no—
348D12—62no—
349D12—122no—
350D12—121no—
351D12—121no—
352D12—122no—
353D12—121no—
354D12—121no—
355D12—121no—
356D12—121no—
357D12—122no—
358D12—122no—
359C4×D3—241no—
360C4×D3—241no—
361Dic6—41no—
362C3×C8—42no—
363C3×C8—41no—
364C3×C8—41no—
365C3×C8—121no—
366C3⋊C8—41no—
367C2×C32—21no—
368C2×C32—21no—
369C2×C32#44911yescharacteristic
370C2×C32#45411yescharacteristic
371C2×C32B(4,𝔽2)11yescharacteristic
372C3⋊D3—82no—
373C3⋊D3—81no—
374C24—181no—
375C2×Q8—31no—
376C2×D4—91no—
377C2×D4—181no—
378C2×D4—181no—
379C2×D4—181no—
380C2×D4—362no—
381C22×C4—31no—
382C22×C4—31no—
383C22×C4—61no—
384C22×C4—181no—
385C22×C4C2×D3211yescharacteristic
386SD16—362no—
387D8—362no—
388C2×C8—21no—
389C2×C8—61no—
390C4⋊C4—31no—
391C4⋊C4—61no—
392C4⋊C4—61no—
393C4⋊C4—61no—
394C4⋊C4—91no—
395C4⋊C4—181no—
396C4⋊C4—181no—
397C4⋊C4—181no—
398C22⋊C4—61no—
399C22⋊C4—181no—
400C22⋊C4—181no—
401C22⋊C4—181no—
402C22⋊C4—181no—
403C22⋊C4—362no—
404C22⋊C4—362no—
405C42—181no—
406C22×C3—21no—
407C22×C3—21no—
408C22×C3—21no—
409C22×C3—21no—
410C22×C3—21no—
411C22×C3—21no—
412C22×C3—21no—
413C22×C3—41no—
414C22×C3—41no—
415C22×C3#88211yescharacteristic
416C22×C3#88211yescharacteristic
417C22×C3#90411yescharacteristic
418C22×C3#90811yescharacteristic
419C22×C3#91411yescharacteristic
420C22×C3#91911yescharacteristic
421C2×D3—124no—
422C2×D3—122no—
423C2×D3—122no—
424C2×D3—122no—
425C2×D3—122no—
426C2×D3—121no—
427C2×D3—121no—
428C2×D3—121no—
429C2×D3—122no—
430C2×D3—122no—
431C2×D3—121no—
432C2×D3—121no—
433C2×D3—121no—
434C2×D3—242no—
435C2×D3—242no—
436C2×D3—241no—
437C2×D3—241no—
438C2×D3—241no—
439C2×D3—241no—
440C2×D3—241no—
441C2×D3—241no—
442C2×D3—241no—
443C2×D3—242no—
444C2×D3—242no—
445C2×D3—242no—
446C2×D3—242no—
447C2×D3—241no—
448C2×D3—241no—
449C2×D3—241no—
450C2×D3—241no—
451C3×C4—22no—
452C3×C4—21no—
453C3×C4—21no—
454C3×C4—21no—
455C3×C4—21no—
456C3×C4—41no—
457C3×C4—121no—
458C3×C4—121no—
459C3×C4—121no—
460C3×C4—121no—
461C3×C4—241no—
462Dic3—41no—
463Dic3—41no—
464Dic3—41no—
465Dic3—41no—
466Dic3—81no—
467Dic3—121no—
468Dic3—121no—
469Dic3—241no—
470C32#159711yescharacteristic, complemented, Sylow
471C23—182no—
472C23—181no—
473C23—361no—
474C23—361no—
475C23—361no—
476C23—361no—
477C23—361no—
478C23—361no—
479C23D3×D1211yescharacteristic
480Q8—121no—
481D4—182no—
482D4—182no—
483D4—361no—
484D4—361no—
485D4—361no—
486D4—361no—
487D4—361no—
488C2×C4—41no—
489C2×C4—61no—
490C2×C4—61no—
491C2×C4—61no—
492C2×C4—61no—
493C2×C4—61no—
494C2×C4—61no—
495C2×C4—121no—
496C2×C4—121no—
497C2×C4—121no—
498C2×C4—121no—
499C2×C4—181no—
500C2×C4—721no—
501C2×C4D3×D1211yescharacteristic
502C2×C4#381111yescharacteristic
503C8—41no—
504C8—121no—
505C2×C3—21no—
506C2×C3—21no—
507C2×C3—21no—
508C2×C3—21no—
509C2×C3—21no—
510C2×C3—21no—
511C2×C3—21no—
512C2×C3—41no—
513C2×C3—41no—
514C2×C3#473411yescharacteristic
515C2×C3#474111yescharacteristic
516C2×C3#474111yescharacteristic
517C2×C3#475311yescharacteristic
518C2×C3#481011yescharacteristic
519C2×C3#482711yescharacteristic
520D3—244no—
521D3—242no—
522D3—241no—
523D3—242no—
524D3—241no—
525D3—481no—
526C22—21no—
527C22—21no—
528C22—362no—
529C22—362no—
530C22—361no—
531C22—361no—
532C22—362no—
533C22—361no—
534C22—721no—
535C22—721no—
536C22—721no—
537C22—721no—
538C22#6379411yescharacteristic
539C22#6380811yescharacteristic
540C22#6392311yescharacteristic
541C4—21no—
542C4—21no—
543C4—121no—
544C4—121no—
545C4—121no—
546C4—121no—
547C4—241no—
548C4—361no—
549C3—21no—
550C3#6813011yescharacteristic, complemented
551C3#6832411yescharacteristic, complemented
552C2—21no—
553C2—21no—
554C2—722no—
555C2—721no—
556C2#1059041011yescharacteristic
557C2#1059096711yescharacteristic
558C2#1059102211yescharacteristic
subgroupG/H
centerC22#63923
commutator, cosocleC22×C32×C4C23
FrattiniC22×C4C2×D32
FittingC32×C22⋊C8C22
socleC22×C32#120
prime radical#10592431C2
hypercenterC22⋊C8D32
hypocenterC32#1597
LCSG ▷ C22×C32×C4 ▷ C22×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22⋊C8

Complements

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

NH ≅ G/Ntype
1. #10594980C2semidirect
3. #10591321C2semidirect
4. #10591183C2semidirect
5. C3×#4469C2semidirect
6. C3×#4467C2semidirect
7. #10589151C2semidirect
41. #4469D3semidirect
42. #4467D3semidirect
470. C32#1597semidirect
550. C3#68130semidirect
551. C3#68324semidirect

Maximal subgroups

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

subgroupindex
#105949802
#105924312
#105913212
#105911832
C3×#44692
C3×#44672
#105891512
#683243
#681303