Finite Group Databasebeta

← #11779734

Subgroups — #11779734

Order 1152.

676 conjugacy classes of subgroups; only the 92 normal subgroups are shown.

normal subgroups only

This group has 676 conjugacy classes of subgroups — too many to draw. Only its 92 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#10594004C211yesmaximal, characteristic
2#10592540C211yesmaximal, characteristic, complemented
3#10590273C211yesmaximal, characteristic, complemented
4#10590272C211yesmaximal, characteristic, complemented
5C3×#4485C211yesmaximal, characteristic, complemented
6C3×#4483C211yesmaximal, characteristic, complemented
7#10589082C211yesmaximal, characteristic, complemented
8#68392—31nomaximal
9#68182—31nomaximal
10C2×#3802—21no—
11C2×D3×D12—21no—
12C2×#3744—21no—
13C4×C4⋊(C3⋊D3)C2211yescharacteristic
14#64078C2211yescharacteristic, complemented
15C3×#874C2211yescharacteristic
16C3×C4×D12C2211yescharacteristic
17#63922—22no—
18#63916—21no—
19#63908—21no—
20C32×C4⋊C8C2211yescharacteristic, complemented
21#63643—21no—
22C3×C4⋊(C3⋊C8)C2211yescharacteristic, complemented
23C3×C4×C3⋊C8C2211yescharacteristic, complemented
24#63575—21no—
25#63563—21no—
26#63563—22no—
27#5717—31no—
28D4×D12—31no—
29#5070—31no—
30#5007—31no—
31#4846—31no—
32#4841—31no—
33#4841—31no—
34#4841—61no—
35#4694—31no—
36C3×#331—31no—
37C3×D4⋊C8—31no—
38#4485D311yescharacteristic, complemented
39#4483—31no—
40#4483D311yescharacteristic, complemented
41#4459—31no—
42C22×D32—22no—
43C2×C4⋊(C3⋊D3)D411yescharacteristic
44C2×C4×C3⋊D3—21no—
45C2×#634—21no—
46C2×C3×D12—21no—
47C2×C3×D12—21no—
48C2×C3×D12D411yescharacteristic
49C2×C3×D12D412yes—
50C2×C3×C4×D3—21no—
51C2×#626—22no—
52C2×#625—22no—
53#3802—42no—
54#3802—42no—
55D3×D12—42no—
56D3×D12—42no—
57C2×C32×C8—21no—
58C32×C42C2311yescharacteristic
59#3752—21no—
60C4⋊(C3⋊Dic3)—21no—
61C4⋊(C3⋊Dic3)—21no—
62C4⋊(C3⋊Dic3)D411yescharacteristic
63#3744—42no—
64C3×(C2×D3)⋊C4—21no—
65C3×C4⋊Dic3D411yescharacteristic
66C2×C3×C3⋊C8—21no—
67C2×C3×C3⋊C8—21no—
68(C2×D3)⋊Dic3—22no—
69#1639—91noSylow
70C2×D3×D4—61no—
71C2×D3×D4—61no—
72C2×D3×D4—61no—
73C22×D12—61no—
74C3×#127—31no—
75C3×C4×D4—31no—
76#938—61no—
77#938—61no—
78#937—62no—
79#930—61no—
80C2×#204—61no—
81C2×#204—61no—
82C2×#204—62no—
83#895—61no—
84#882—62no—
85#874C2×D311yescharacteristic
86C4×D12—31no—
87C4×D12—31no—
88C4×D12—61no—
89C4×D12C2×D311yescharacteristic
90#869—31no—
91#869—31no—
92#869—61no—
93C3×C4⋊C8—21no—
94C3×C4⋊C8—31no—
95C3×C4⋊C8C2×D311yescharacteristic, complemented
96C3×C4⋊C8C2×D311yescharacteristic, complemented
97C3×C4×C8—31no—
98#832—61no—
99#832—62no—
100#821—62no—
101#821—61no—
102#818—61no—
103#816—61no—
104#816—61no—
105#816—62no—
106#807—61no—
107C4⋊(C3⋊C8)C2×D311yescharacteristic, complemented
108C4×C3⋊C8C2×D311yescharacteristic, complemented
109C22×C3⋊D3—21no—
110C22×C3×D3—21no—
111C22×C3×D3—22no—
112C2×D32—44no—
113C2×D32—44no—
114C2×D32—82no—
115C2×C32×C4C2×D411yescharacteristic
116C2×C32×C4C2×D411yescharacteristic
117C2×C32×C4C2×D411yescharacteristic
118C2×C3⋊Dic3—21no—
119C2×C3⋊Dic3—41no—
120C4⋊(C3⋊D3)—21no—
121C4⋊(C3⋊D3)D812yes—
122C4×C3⋊D3—41no—
123C4×C3⋊D3—41no—
124#634—41no—
125#634—41no—
126C2×C3×Dic3—21no—
127C3×D12—21no—
128C3×D12—42no—
129C3×D12—41no—
130C3×D12—41no—
131C3×D12—41no—
132C3×D12—41no—
133C3×D12SD1612yescomplemented
134C3×C4×D3—41no—
135C3×C4×D3—41no—
136#626—44no—
137#625—44no—
138C32×C8—41no—
139C3×C3⋊C8—41no—
140C3×C3⋊C8—41no—
141D42—91no—
142#486—91no—
143#474—91no—
144#461—91no—
145#331—31no—
146D4⋊C8—31no—
147D4⋊C8—91no—
148C23×D3—62no—
149C23×D3—62no—
150C2×C3×D4—31no—
151C2×C3×D4—32no—
152C2×C3×D4—61no—
153C2×C3×D4—61no—
154C22×C3×C4—61no—
155C2×#67—62no—
156C2×#67—62no—
157C2×#67—62no—
158D3×D4—122no—
159D3×D4—122no—
160D3×D4—122no—
161D3×D4—122no—
162D3×D4—122no—
163D3×D4—122no—
164C2×D12—21no—
165C2×D12—21no—
166C2×D12—31no—
167C2×D12—31no—
168C2×D12—61no—
169C2×D12—62no—
170C2×D12—122no—
171C2×D12—122no—
172C2×D12D1211yescharacteristic
173C2×D12D1212yes—
174C2×C4×D3—21no—
175C2×C4×D3—61no—
176C2×C4×D3—61no—
177C2×C4×D3—121no—
178C2×Dic6—62no—
179C2×Dic6—61no—
180C2×Dic6—61no—
181C2×C3×C8—22no—
182C2×C3×C8—21no—
183C2×C3×C8—21no—
184C2×C3×C8—61no—
185C2×C3×C8—61no—
186C3×C4⋊C4—31no—
187C3×C22⋊C4—61no—
188C3×C42—21no—
189C3×C42C22×D311yescharacteristic
190C3×C42C22×D311yescharacteristic
191#217—62no—
192(C2×D3)⋊C4—21no—
193(C2×D3)⋊C4—62no—
194(C2×D3)⋊C4—61no—
195(C2×D3)⋊C4—61no—
196(C2×D3)⋊C4—121no—
197C4⋊Dic3—31no—
198C4⋊Dic3—31no—
199C4⋊Dic3—61no—
200C4⋊Dic3—61no—
201C4⋊Dic3—61no—
202C4⋊Dic3—61no—
203C4⋊Dic3—61no—
204C4⋊Dic3—121no—
205C4⋊Dic3—121no—
206C4⋊Dic3D1211yescharacteristic
207C2×C3⋊C8—21no—
208C2×C3⋊C8—21no—
209#204—122no—
210#204—122no—
211#204—124no—
212C22×C32#12011yescharacteristic
213C2×C3⋊D3—22no—
214C2×C3⋊D3—41no—
215C2×C3⋊D3—41no—
216C2×C3×D3—22no—
217C2×C3×D3—41no—
218C2×C3×D3—41no—
219C2×C3×D3—42no—
220C2×C3×D3—42no—
221C2×C3×D3—42no—
222D32—88no—
223C32×C4—21no—
224C32×C4C2×D811yescharacteristic
225C32×C4C2×SD1611yescharacteristic
226C32×C4AGL(1,ℤ/8)11yescharacteristic
227C32×C4AGL(1,ℤ/8)11yescharacteristic
228C3⋊Dic3—41no—
229C3⋊Dic3—81no—
230C3×Dic3—41no—
231C22×D4—181no—
232C22×D4—181no—
233C2×SD16—181no—
234C4⋊Q8—91no—
235#127—31no—
236#121—181no—
237#121—181no—
238#120—182no—
239C4×D4—31no—
240C4×D4—91no—
241#107—181no—
242C4⋊C8—31no—
243C4⋊C8D3211yescharacteristic, complemented
244#103—181no—
245#102—181no—
246#102—182no—
247C4×C8—31no—
248C23×C3—61no—
249C23×C3—62no—
250C22×D3—21no—
251C22×D3—22no—
252C22×D3—61no—
253C22×D3—61no—
254C22×D3—121no—
255C22×D3—124no—
256C22×D3—124no—
257C22×D3—124no—
258C22×D3—124no—
259C22×D3—242no—
260C22×D3—242no—
261C3×D4—32no—
262C3×D4—61no—
263C3×D4—122no—
264C3×D4—121no—
265C3×D4—121no—
266C3×D4—121no—
267C3×D4—121no—
268C2×C3×C4—21no—
269C2×C3×C4—21no—
270C2×C3×C4—21no—
271C2×C3×C4—61no—
272C2×C3×C4—121no—
273C2×C3×C4—121no—
274C2×C3×C4C2×D1211yescharacteristic
275C2×C3×C4C2×D1211yescharacteristic
276C2×C3×C4D3×D411yescharacteristic
277C2×C3×C4D3×D411yescharacteristic
278C2×C3×C4D3×D411yescharacteristic
279C2×C3×C4D3×D411yescharacteristic
280#67—124no—
281#67—124no—
282#67—124no—
283C2×Dic3—21no—
284C2×Dic3—61no—
285C2×Dic3—61no—
286C2×Dic3—121no—
287C2×Dic3—122no—
288C2×Dic3—121no—
289C2×Dic3—121no—
290D12—21no—
291D12—32no—
292D12—32no—
293D12—42no—
294D12—41no—
295D12—41no—
296D12—41no—
297D12—41no—
298D12—62no—
299D12—61no—
300D12—61no—
301D12—121no—
302D12—124no—
303D12#20412yescomplemented
304C4×D3—41no—
305C4×D3—41no—
306C4×D3—121no—
307C4×D3—121no—
308C4×D3—121no—
309C4×D3—121no—
310C4×D3—241no—
311C4×D3—241no—
312Dic6—122no—
313Dic6—122no—
314Dic6—121no—
315Dic6—121no—
316Dic6—121no—
317Dic6—121no—
318C3×C8—42no—
319C3×C8—41no—
320C3×C8—41no—
321C3×C8—121no—
322C3×C8—121no—
323C3⋊C8—41no—
324C3⋊C8—41no—
325C2×C32#44711yescharacteristic
326C2×C32#45011yescharacteristic
327C2×C32#45511yescharacteristic
328C3⋊D3—42no—
329C3×D3—42no—
330C3×D3—82no—
331C24—182no—
332C2×Q8—181no—
333C2×D4—31no—
334C2×D4—32no—
335C2×D4—61no—
336C2×D4—61no—
337C2×D4—91no—
338C2×D4—182no—
339C2×D4—182no—
340C2×D4—362no—
341C2×D4—362no—
342C2×D4—362no—
343C2×D4—362no—
344C22×C4—61no—
345C22×C4—181no—
346SD16—362no—
347C2×C8—21no—
348C2×C8—61no—
349C2×C8—61no—
350C4⋊C4—31no—
351C4⋊C4—91no—
352C4⋊C4—181no—
353C4⋊C4—181no—
354C22⋊C4—61no—
355C22⋊C4—182no—
356C22⋊C4—181no—
357C42C2×D3211yescharacteristic
358C22×C3—21no—
359C22×C3—62no—
360C22×C3—121no—
361C22×C3—121no—
362C22×C3—122no—
363C22×C3—122no—
364C22×C3—122no—
365C22×C3#88211yescharacteristic
366C22×C3#88211yescharacteristic
367C2×D3—22no—
368C2×D3—41no—
369C2×D3—41no—
370C2×D3—42no—
371C2×D3—42no—
372C2×D3—42no—
373C2×D3—62no—
374C2×D3—62no—
375C2×D3—122no—
376C2×D3—121no—
377C2×D3—121no—
378C2×D3—121no—
379C2×D3—121no—
380C2×D3—241no—
381C2×D3—241no—
382C2×D3—248no—
383C2×D3—248no—
384C3×C4—21no—
385C3×C4—21no—
386C3×C4—21no—
387C3×C4—21no—
388C3×C4—21no—
389C3×C4—21no—
390C3×C4—41no—
391C3×C4—121no—
392C3×C4C2×#20411yescharacteristic
393C3×C4#90811yescharacteristic
394C3×C4D3×D811yescharacteristic
395C3×C4D3×D811yescharacteristic
396C3×C4#91111yescharacteristic
397C3×C4D3×SD1611yescharacteristic
398C3×C4#91411yescharacteristic
399C3×C4#91411yescharacteristic
400Dic3—41no—
401Dic3—121no—
402Dic3—121no—
403Dic3—241no—
404Dic3—242no—
405Dic3—241no—
406Dic3—241no—
407C32#163911yescharacteristic, complemented, Sylow
408C23—61no—
409C23—62no—
410C23—181no—
411C23—364no—
412C23—364no—
413C23—722no—
414Q8—361no—
415Q8—361no—
416D4—32no—
417D4—61no—
418D4—92no—
419D4—122no—
420D4—121no—
421D4—121no—
422D4—121no—
423D4—121no—
424D4—181no—
425D4—364no—
426D4—364no—
427C2×C4—61no—
428C2×C4—121no—
429C2×C4—121no—
430C2×C4—181no—
431C2×C4—361no—
432C2×C4—361no—
433C2×C4—361no—
434C2×C4D3×D1211yescharacteristic
435C2×C4D3×D1211yescharacteristic
436C2×C4#381111yescharacteristic
437C8—41no—
438C8—121no—
439C8—121no—
440C2×C3—21no—
441C2×C3—21no—
442C2×C3—21no—
443C2×C3—122no—
444C2×C3—242no—
445C2×C3#473111yescharacteristic
446C2×C3#474611yescharacteristic
447C2×C3#477311yescharacteristic
448C2×C3#477311yescharacteristic
449C2×C3#477611yescharacteristic
450C2×C3#482511yescharacteristic
451D3—42no—
452D3—82no—
453D3—122no—
454D3—122no—
455D3—242no—
456C22—62no—
457C22—121no—
458C22—121no—
459C22—122no—
460C22—122no—
461C22—122no—
462C22—182no—
463C22—361no—
464C22—361no—
465C22—728no—
466C22#6392311yescharacteristic
467C4—21no—
468C4—121no—
469C4—361no—
470C4—721no—
471C4D3×#20411yescharacteristic
472C4#6379511yescharacteristic
473C4#6392611yescharacteristic
474C4#6394111yescharacteristic
475C3—21no—
476C3#6818211yescharacteristic, complemented
477C3#6839211yescharacteristic, complemented
478C2—122no—
479C2—242no—
480C2—362no—
481C2#1059059811yescharacteristic
482C2#1059094611yescharacteristic
483C2#1059101611yescharacteristic
subgroupG/H
centerC22#63923
commutator, cosocleC32×C42C23
FrattiniC42C2×D32
FittingC32×C4⋊C8C22
socleC22×C32#120
prime radical#10594004C2
hypercenterC4⋊C8D32
hypocenterC32#1639
LCSG ▷ C32×C42 ▷ C22×C32 ▷ C32
UCSC1 ◁ C22 ◁ C42 ◁ C4⋊C8

Complements

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

NH ≅ G/Ntype
2. #10592540C2semidirect
3. #10590273C2semidirect
4. #10590272C2semidirect
5. C3×#4485C2semidirect
6. C3×#4483C2semidirect
7. #10589082C2semidirect
14. #64078C22semidirect
20. C32×C4⋊C8C22semidirect
22. C3×C4⋊(C3⋊C8)C22semidirect
23. C3×C4×C3⋊C8C22semidirect
38. #4485D3semidirect
40. #4483D3semidirect
95. C3×C4⋊C8C2×D3semidirect
96. C3×C4⋊C8C2×D3semidirect
107. C4⋊(C3⋊C8)C2×D3semidirect
108. C4×C3⋊C8C2×D3semidirect
133. C3×D12SD16semidirect
243. C4⋊C8D32semidirect
303. D12#204semidirect
407. C32#1639semidirect
476. C3#68182semidirect
477. C3#68392semidirect

Maximal subgroups

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

subgroupindex
#105940042
#105925402
#105902732
#105902722
C3×#44852
C3×#44832
#105890822
#683923
#681823