Finite Group Databasebeta

← #11778785

Subgroups — #11778785

Order 1152.

639 conjugacy classes of subgroups; only the 82 normal subgroups are shown.

normal subgroups only

This group has 639 conjugacy classes of subgroups — too many to draw. Only its 82 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#10596068C211yesmaximal, characteristic
2C3×#5034C211yesmaximal, characteristic, complemented
3#10591227C211yesmaximal, characteristic, complemented
4#10591125C211yesmaximal, characteristic, complemented
5C3×#4537C211yesmaximal, characteristic, complemented
6#10589151C211yesmaximal, characteristic, complemented
7#10589148C211yesmaximal, characteristic, complemented
8#71171—31nomaximal
9#68299—31nomaximal
10C2×#3830—21no—
11C32×#121C2211yescharacteristic
12#64148—21no—
13#64148—21no—
14#64139C2211yescharacteristic
15C2×#3750C2211yescharacteristic
16#64105—21no—
17#64093—21no—
18#64087—21no—
19C2×C3×C4⋊Dic3C2211yescharacteristic
20C3×#832—21no—
21C3×C3⋊#95C2211yescharacteristic
22C3×#830C2211yescharacteristic
23C3×#830C2211yescharacteristic
24C3×#808—21no—
25#63579—21no—
26#63579—21no—
27#63573—21no—
28#63564—21no—
29#5597—31no—
30#5597—31no—
31#5597—61no—
32C3×#481—31no—
33#5034D311yescharacteristic, complemented
34#4985—31no—
35#4968—31no—
36#4735—31no—
37#4659—31no—
38C3×#327—31no—
39#4537D311yescharacteristic, complemented
40#4470—31no—
41#4469—31no—
42#4469—31no—
43#4451—31no—
44C2×C32×D4—21no—
45C2×C32×D4D411yescharacteristic
46C22×C32×C4C2311yescharacteristic
47C2×#638—21no—
48C2×#638—21no—
49C2×#638—21no—
50C22×C3⋊Dic3—21no—
51C22×C3⋊Dic3D411yescharacteristic
52C22×C3⋊Dic3D411yescharacteristic
53#3830—42no—
54#3830—42no—
55C2×C4⋊(C3⋊D3)D411yescharacteristic
56C2×C4×C3⋊D3—21no—
57C2×#634—21no—
58C22×C3×Dic3—21no—
59C22×C3×Dic3—21no—
60C32×C4⋊C4D411yescharacteristic
61C32×C22⋊C4—21no—
62#3757—21no—
63#3752—21no—
64#3752—21no—
65C4⋊(C3⋊Dic3)D411yescharacteristic
66#3750—21no—
67#3750—21no—
68#3750—21no—
69C3×C4⋊Dic3—21no—
70C3×C4⋊Dic3—21no—
71C2×C3×C3⋊C8—21no—
72C2×C3×C3⋊C8—21no—
73#1616—91noSylow
74C2×#237—61no—
75C2×#237—61no—
76C2×#237—62no—
77C3×#121—21no—
78C3×#121C2×D311yescharacteristic
79C3×#121C2×D311yescharacteristic
80C2×C3×C4⋊C4—31no—
81#939—61no—
82#939—61no—
83#939—62no—
84#939—62no—
85#939—61no—
86#939—61no—
87#930—31no—
88#930—31no—
89#930—61no—
90C2×C4⋊Dic3C2×D311yescharacteristic
91C2×Dic3⋊C4—31no—
92C2×Dic3⋊C4—31no—
93C2×Dic3⋊C4—61no—
94#896—62no—
95#896—61no—
96#896—61no—
97#884—61no—
98#884—61no—
99#884—62no—
100#878—61no—
101#878—61no—
102#878—62no—
103C3×#106—61no—
104C3×#102—61no—
105C3×C22⋊C8—31no—
106C3×C22⋊C8—31no—
107C3×#95—31no—
108#832—21no—
109C3⋊#95—61no—
110C3⋊#95—61no—
111C3⋊#95—61no—
112C3⋊#95—61no—
113C3⋊#95C2×D311yescharacteristic
114#830C2×D311yescharacteristic
115#830C2×D311yescharacteristic
116#821—61no—
117#817—61no—
118#809—61no—
119#808—21no—
120#808—61no—
121C23×C32—21no—
122C23×C32C2×D411yescharacteristic
123C22×C3⋊D3—21no—
124C32×D4—41no—
125C32×D4—41no—
126C32×D4—41no—
127C2×C32×C4—21no—
128C2×C32×C4—41no—
129C2×C32×C4C2×D411yescharacteristic
130C2×C32×C4C2×D411yescharacteristic
131#638—42no—
132#638—41no—
133#638—41no—
134#638—81no—
135C2×C3⋊Dic3—21no—
136C2×C3⋊Dic3—21no—
137C2×C3⋊Dic3—21no—
138C2×C3⋊Dic3—21no—
139C2×C3⋊Dic3—42no—
140C2×C3⋊Dic3—41no—
141C2×C3⋊Dic3SD1612yes—
142C4⋊(C3⋊D3)—41no—
143C4×C3⋊D3—42no—
144#634—42no—
145C2×C3×Dic3—41no—
146C2×C3×Dic3—41no—
147C2×C3×Dic3—42no—
148C2×C3×Dic3—41no—
149C2×C3×Dic3—41no—
150C3×C3⋊C8—41no—
151C3×C3⋊C8—41no—
152#537—91no—
153#481—31no—
154#481—91no—
155#400—91no—
156#327—31no—
157#327—91no—
158#324—91no—
159C2×C3×D4—22no—
160C2×C3×D4—21no—
161C2×C3×D4—21no—
162C2×C3×D4—21no—
163C2×C3×D4D1211yescharacteristic
164C2×C3×D4#6711yescharacteristic
165C22×C3×C4—21no—
166C22×C3×C4—61no—
167C22×C3×C4—61no—
168C22×C3×C4C22×D311yescharacteristic
169C22×C3×C4C22×D311yescharacteristic
170C2×#67—62no—
171C2×#67—61no—
172C2×#67—61no—
173C2×#67—62no—
174C2×#67—61no—
175C2×#67—61no—
176C2×#67—62no—
177C2×#67—61no—
178C2×#67—61no—
179C22×Dic3—21no—
180C22×Dic3—21no—
181C22×Dic3—31no—
182C22×Dic3—31no—
183C22×Dic3—31no—
184C22×Dic3—31no—
185C22×Dic3—61no—
186C22×Dic3—61no—
187C22×Dic3—62no—
188C22×Dic3—61no—
189C22×Dic3—61no—
190#237—122no—
191#237—122no—
192#237—124no—
193#237—124no—
194#237—122no—
195#237—122no—
196C2×D12—31no—
197C2×D12—31no—
198C2×D12—61no—
199C2×C4×D3—62no—
200C2×C4×D3—61no—
201C2×C4×D3—61no—
202C2×Dic6—62no—
203C2×Dic6—61no—
204C2×Dic6—61no—
205C2×C3×C8—61no—
206C2×C3×C8—61no—
207C3×C4⋊C4—21no—
208C3×C4⋊C4—61no—
209C3×C4⋊C4—61no—
210C3×C4⋊C4D1211yescharacteristic
211C3×C4⋊C4#6711yescharacteristic
212C3×C22⋊C4—22no—
213C3×C22⋊C4—21no—
214C3×C22⋊C4—21no—
215#217—62no—
216#217—61no—
217#217—61no—
218(C2×D3)⋊C4—62no—
219(C2×D3)⋊C4—61no—
220(C2×D3)⋊C4—61no—
221(C2×D3)⋊C4—62no—
222(C2×D3)⋊C4—61no—
223(C2×D3)⋊C4—61no—
224C4⋊Dic3—21no—
225C4⋊Dic3—21no—
226C4⋊Dic3—31no—
227C4⋊Dic3—31no—
228C4⋊Dic3—61no—
229Dic3⋊C4—62no—
230Dic3⋊C4—62no—
231Dic3⋊C4—61no—
232Dic3⋊C4—61no—
233Dic3⋊C4—62no—
234Dic3⋊C4—61no—
235Dic3⋊C4—61no—
236Dic3⋊C4—61no—
237Dic3⋊C4—61no—
238C2×C3⋊C8—21no—
239C2×C3⋊C8—21no—
240C22×C32—21no—
241C22×C32—21no—
242C22×C32—41no—
243C22×C32—41no—
244C22×C32—41no—
245C22×C32#12011yescharacteristic
246C22×C32C2×SD1611yescharacteristic
247C22×C32AGL(1,ℤ/8)11yescharacteristic
248C2×C3⋊D3—41no—
249C2×C3⋊D3—41no—
250C2×C3⋊D3—41no—
251C32×C4—21no—
252C32×C4—21no—
253C32×C4—41no—
254C3⋊Dic3—22no—
255C3⋊Dic3—41no—
256C3⋊Dic3—41no—
257C3×Dic3—81no—
258C3×Dic3—81no—
259C2×#41—181no—
260C22⋊Q8—181no—
261C22⋊Q8—181no—
262#121—91no—
263#121—181no—
264#121—181no—
265#121—181no—
266#121D3211yescharacteristic
267C2×C4⋊C4—31no—
268C2×C4⋊C4—91no—
269#106—61no—
270#106—181no—
271#102—61no—
272#102—181no—
273C22⋊C8—31no—
274C22⋊C8—31no—
275#95—31no—
276#95—181no—
277#95—181no—
278C23×C3—22no—
279C23×C3—21no—
280C23×C3—21no—
281C23×C3—21no—
282C23×C3D3×D411yescharacteristic
283C23×C3D3×D411yescharacteristic
284C22×D3—62no—
285C22×D3—61no—
286C22×D3—61no—
287C3×D4—41no—
288C3×D4—41no—
289C3×D4—42no—
290C3×D4—42no—
291C3×D4—41no—
292C3×D4—41no—
293C3×D4—41no—
294C3×D4—41no—
295C3×D4—81no—
296C2×C3×C4—22no—
297C2×C3×C4—21no—
298C2×C3×C4—21no—
299C2×C3×C4—21no—
300C2×C3×C4—21no—
301C2×C3×C4—41no—
302C2×C3×C4—41no—
303C2×C3×C4—81no—
304C2×C3×C4—121no—
305C2×C3×C4—121no—
306C2×C3×C4—122no—
307C2×C3×C4—121no—
308C2×C3×C4—121no—
309C2×C3×C4C2×D1211yescharacteristic
310C2×C3×C4D3×D411yescharacteristic
311C2×C3×C4D3×D411yescharacteristic
312C2×C3×C4C2×#6711yescharacteristic
313#67—124no—
314#67—122no—
315#67—122no—
316#67—122no—
317#67—122no—
318#67—121no—
319#67—121no—
320#67—121no—
321#67—121no—
322#67—242no—
323#67—241no—
324#67—241no—
325C2×Dic3—32no—
326C2×Dic3—32no—
327C2×Dic3—41no—
328C2×Dic3—41no—
329C2×Dic3—42no—
330C2×Dic3—41no—
331C2×Dic3—41no—
332C2×Dic3—62no—
333C2×Dic3—62no—
334C2×Dic3—62no—
335C2×Dic3—61no—
336C2×Dic3—61no—
337C2×Dic3—61no—
338C2×Dic3—61no—
339C2×Dic3—62no—
340C2×Dic3—62no—
341C2×Dic3—61no—
342C2×Dic3—61no—
343C2×Dic3—61no—
344C2×Dic3—61no—
345C2×Dic3—124no—
346C2×Dic3—122no—
347C2×Dic3—122no—
348C2×Dic3—121no—
349C2×Dic3—121no—
350C2×Dic3—241no—
351D12—121no—
352D12—121no—
353D12—241no—
354C4×D3—124no—
355C4×D3—122no—
356C4×D3—122no—
357Dic6—124no—
358Dic6—122no—
359Dic6—122no—
360C3×C8—121no—
361C3×C8—121no—
362C3⋊C8—41no—
363C3⋊C8—41no—
364C2×C32—21no—
365C2×C32—21no—
366C2×C32—81no—
367C2×C32#45011yescharacteristic
368C2×C32#45411yescharacteristic
369C2×C32#45811yescharacteristic
370C3⋊D3—81no—
371#41—362no—
372#41—362no—
373C2×Q8—181no—
374C2×D4—21no—
375C2×D4—91no—
376C2×D4—181no—
377C2×D4—181no—
378C2×D4—181no—
379C2×D4#62611yescharacteristic
380C22×C4—61no—
381C22×C4—61no—
382C22×C4—91no—
383C22×C4—91no—
384C22×C4—181no—
385C22×C4—181no—
386C22×C4C2×D3211yescharacteristic
387C2×C8—61no—
388C2×C8—61no—
389C4⋊C4—61no—
390C4⋊C4—61no—
391C4⋊C4—91no—
392C4⋊C4—181no—
393C4⋊C4—181no—
394C4⋊C4—181no—
395C4⋊C4#62611yescharacteristic
396C22⋊C4—21no—
397C22⋊C4—181no—
398C22⋊C4—181no—
399C22⋊C4—181no—
400C22×C3—21no—
401C22×C3—21no—
402C22×C3—21no—
403C22×C3—21no—
404C22×C3—21no—
405C22×C3—21no—
406C22×C3—21no—
407C22×C3—41no—
408C22×C3—41no—
409C22×C3—42no—
410C22×C3—42no—
411C22×C3—42no—
412C22×C3—41no—
413C22×C3—41no—
414C22×C3—41no—
415C22×C3—41no—
416C22×C3—41no—
417C22×C3—41no—
418C22×C3#88211yescharacteristic
419C22×C3#91111yescharacteristic
420C22×C3D3×SD1611yescharacteristic
421C22×C3D3×SD1611yescharacteristic
422C22×C3#91411yescharacteristic
423C22×C3#93711yescharacteristic
424C2×D3—122no—
425C2×D3—122no—
426C2×D3—122no—
427C2×D3—121no—
428C2×D3—121no—
429C2×D3—121no—
430C2×D3—121no—
431C2×D3—121no—
432C2×D3—121no—
433C3×C4—21no—
434C3×C4—21no—
435C3×C4—21no—
436C3×C4—21no—
437C3×C4—41no—
438C3×C4—41no—
439C3×C4—42no—
440C3×C4—41no—
441C3×C4—41no—
442C3×C4—241no—
443C3×C4—241no—
444Dic3—64no—
445Dic3—62no—
446Dic3—62no—
447Dic3—81no—
448Dic3—81no—
449Dic3—122no—
450Dic3—122no—
451Dic3—121no—
452Dic3—121no—
453Dic3—121no—
454Dic3—121no—
455C32#161611yescharacteristic, complemented, Sylow
456C23—21no—
457C23—181no—
458C23#381111yescharacteristic
459Q8—362no—
460D4—41no—
461D4—41no—
462D4—41no—
463D4—361no—
464D4—362no—
465D4—361no—
466D4—361no—
467D4—721no—
468C2×C4—21no—
469C2×C4—41no—
470C2×C4—92no—
471C2×C4—121no—
472C2×C4—121no—
473C2×C4—122no—
474C2×C4—121no—
475C2×C4—121no—
476C2×C4—181no—
477C2×C4—181no—
478C2×C4—181no—
479C2×C4—181no—
480C2×C4—362no—
481C2×C4—362no—
482C2×C4—361no—
483C2×C4C2×#62611yescharacteristic
484C2×C4#381111yescharacteristic
485C8—121no—
486C8—121no—
487C2×C3—21no—
488C2×C3—21no—
489C2×C3—21no—
490C2×C3—21no—
491C2×C3—21no—
492C2×C3—21no—
493C2×C3—21no—
494C2×C3—41no—
495C2×C3—41no—
496C2×C3—82no—
497C2×C3—81no—
498C2×C3—81no—
499C2×C3#474211yescharacteristic
500C2×C3#477611yescharacteristic
501C2×C3#482711yescharacteristic
502C2×C3#505311yescharacteristic
503C2×C3#516911yescharacteristic
504C2×C3#520111yescharacteristic
505D3—242no—
506D3—241no—
507D3—241no—
508C22—21no—
509C22—21no—
510C22—41no—
511C22—41no—
512C22—41no—
513C22—361no—
514C22—361no—
515C22—361no—
516C22#6393011yescharacteristic
517C22#6393711yescharacteristic
518C22#6398111yescharacteristic
519C4—21no—
520C4—21no—
521C4—41no—
522C4—182no—
523C4—241no—
524C4—241no—
525C4—361no—
526C4—361no—
527C3—21no—
528C3#6829911yescharacteristic, complemented
529C3#7117111yescharacteristic, complemented
530C2—21no—
531C2—21no—
532C2—81no—
533C2—721no—
534C2#1059146711yescharacteristic
535C2#1059153511yescharacteristic
536C2#1059168611yescharacteristic
subgroupG/H
centerC22#63981
commutator, cosocleC22×C32×C4C23
FrattiniC22×C4C2×D32
FittingC32×#121C22
socleC22×C32#120
prime radical#10596068C2
hypercenter#121D32
hypocenterC32#1616
LCSG ▷ C22×C32×C4 ▷ C22×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4 ◁ #121

Complements

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

NH ≅ G/Ntype
2. C3×#5034C2semidirect
3. #10591227C2semidirect
4. #10591125C2semidirect
5. C3×#4537C2semidirect
6. #10589151C2semidirect
7. #10589148C2semidirect
33. #5034D3semidirect
39. #4537D3semidirect
455. C32#1616semidirect
528. C3#68299semidirect
529. C3#71171semidirect

Maximal subgroups

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

subgroupindex
#105960682
C3×#50342
#105912272
#105911252
C3×#45372
#105891512
#105891482
#711713
#682993