Finite Group Databasebeta

← #11778744

Subgroups — #11778744

Order 1152.

525 conjugacy classes of subgroups; only the 80 normal subgroups are shown.

normal subgroups only

This group has 525 conjugacy classes of subgroups — too many to draw. Only its 80 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#10596073C211yesmaximal, characteristic
2C3×#5034C211yesmaximal, characteristic
3#10591227C211yesmaximal, characteristic, complemented
4#10591135C211yesmaximal, characteristic, complemented
5C3×#4537C211yesmaximal, characteristic
6#10589154C211yesmaximal, characteristic, complemented
7#10589148C211yesmaximal, characteristic, complemented
8#71170—31nomaximal
9#68298—31nomaximal
10C32×#121C2211yescharacteristic
11#64144—21no—
12#64144—21no—
13D4×C3⋊Dic3—21no—
14#64133C2211yescharacteristic
15C2×#3750C2211yescharacteristic
16#64098—21no—
17#64088—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#63575—21no—
28#63567—21no—
29#5602—31no—
30#5602—31no—
31#5602—61no—
32C3×#481—31no—
33#5034D311yescharacteristic
34#4985—31no—
35#4970—31no—
36#4722—31no—
37#4659—31no—
38C3×#327—31no—
39#4537D311yescharacteristic
40#4469—31no—
41#4469—31no—
42#4467—31no—
43#4452—31no—
44C2×C32×D4—21no—
45C2×C32×D4D411yescharacteristic
46C22×C32×C4C2311yescharacteristic
47C22×C3⋊Dic3—21no—
48C22×C3⋊Dic3D411yescharacteristic
49C22×C3⋊Dic3D411yescharacteristic
50C2×#634D411yescharacteristic
51C22×C3×Dic3—21no—
52C22×C3×Dic3—21no—
53C32×C4⋊C4D411yescharacteristic
54C32×C22⋊C4—21no—
55#3757—21no—
56#3757—21no—
57#3757—21no—
58#3757—21no—
59C4⋊(C3⋊Dic3)—21no—
60C4⋊(C3⋊Dic3)D411yescharacteristic
61#3750—21no—
62#3750—21no—
63#3750—21no—
64#3750—21no—
65#3750—21no—
66C4×C3⋊Dic3—21no—
67C3×C4⋊Dic3—21no—
68C3×C4⋊Dic3—21no—
69C2×C3×C3⋊C8—21no—
70C2×C3×C3⋊C8—21no—
71#1615—91noSylow
72C3×#121—21no—
73C3×#121C2×D311yescharacteristic
74C3×#121C2×D311yescharacteristic
75C2×C3×C4⋊C4—31no—
76#935—61no—
77#935—61no—
78#935—62no—
79#935—62no—
80#935—61no—
81#935—61no—
82D4×Dic3—61no—
83D4×Dic3—61no—
84D4×Dic3—62no—
85C2×C4⋊Dic3C2×D311yescharacteristic
86#924—31no—
87#924—31no—
88#924—61no—
89C2×Dic3⋊C4—31no—
90C2×Dic3⋊C4—31no—
91C2×Dic3⋊C4—61no—
92#889—62no—
93#889—61no—
94#889—61no—
95#879—61no—
96#879—61no—
97#879—62no—
98#878—61no—
99#878—61no—
100#878—62no—
101C3×#106—61no—
102C3×#102—61no—
103C3×C22⋊C8—31no—
104C3×C22⋊C8—31no—
105C3×#95—31no—
106#832—21no—
107C3⋊#95—61no—
108C3⋊#95—61no—
109C3⋊#95—61no—
110C3⋊#95—61no—
111C3⋊#95C2×D311yescharacteristic
112#830C2×D311yescharacteristic
113#830C2×D311yescharacteristic
114#818—61no—
115#816—61no—
116#810—61no—
117#808—21no—
118#807—61no—
119C23×C32—21no—
120C23×C32C2×D411yescharacteristic
121C32×D4—41no—
122C32×D4—41no—
123C32×D4—41no—
124C2×C32×C4—21no—
125C2×C32×C4—41no—
126C2×C32×C4C2×D411yescharacteristic
127C2×C32×C4C2×D411yescharacteristic
128C2×C3⋊Dic3—21no—
129C2×C3⋊Dic3—21no—
130C2×C3⋊Dic3—21no—
131C2×C3⋊Dic3—21no—
132C2×C3⋊Dic3—21no—
133C2×C3⋊Dic3—21no—
134C2×C3⋊Dic3—41no—
135C2×C3⋊Dic3—81no—
136#634—41no—
137C2×C3×Dic3—41no—
138C2×C3×Dic3—41no—
139C2×C3×Dic3—42no—
140C2×C3×Dic3—41no—
141C2×C3×Dic3—41no—
142C3×C3⋊C8—41no—
143C3×C3⋊C8—41no—
144#539—91no—
145#484—91no—
146#481—31no—
147#400—91no—
148#328—91no—
149#327—31no—
150#324—91no—
151C2×C3×D4—22no—
152C2×C3×D4—21no—
153C2×C3×D4—21no—
154C2×C3×D4—21no—
155C2×C3×D4D1211yescharacteristic
156C2×C3×D4#6711yescharacteristic
157C22×C3×C4—21no—
158C22×C3×C4—61no—
159C22×C3×C4—61no—
160C22×C3×C4C22×D311yescharacteristic
161C22×C3×C4C22×D311yescharacteristic
162C22×Dic3—21no—
163C22×Dic3—21no—
164C22×Dic3—31no—
165C22×Dic3—31no—
166C22×Dic3—31no—
167C22×Dic3—31no—
168C22×Dic3—61no—
169C22×Dic3—61no—
170C22×Dic3—62no—
171C22×Dic3—61no—
172C22×Dic3—61no—
173C2×Dic6—31no—
174C2×Dic6—31no—
175C2×Dic6—61no—
176C2×C3×C8—61no—
177C2×C3×C8—61no—
178C3×C4⋊C4—21no—
179C3×C4⋊C4—61no—
180C3×C4⋊C4—61no—
181C3×C4⋊C4D1211yescharacteristic
182C3×C4⋊C4#6711yescharacteristic
183C3×C22⋊C4—22no—
184C3×C22⋊C4—21no—
185C3×C22⋊C4—21no—
186#217—62no—
187#217—61no—
188#217—61no—
189#217—62no—
190#217—61no—
191#217—61no—
192#217—62no—
193#217—61no—
194#217—61no—
195#217—62no—
196#217—61no—
197#217—61no—
198C4⋊Dic3—21no—
199C4⋊Dic3—21no—
200C4⋊Dic3—31no—
201C4⋊Dic3—31no—
202C4⋊Dic3—61no—
203C4⋊Dic3—62no—
204C4⋊Dic3—61no—
205C4⋊Dic3—61no—
206Dic3⋊C4—62no—
207Dic3⋊C4—62no—
208Dic3⋊C4—61no—
209Dic3⋊C4—61no—
210Dic3⋊C4—62no—
211Dic3⋊C4—61no—
212Dic3⋊C4—61no—
213Dic3⋊C4—62no—
214Dic3⋊C4—62no—
215Dic3⋊C4—61no—
216Dic3⋊C4—61no—
217Dic3⋊C4—61no—
218Dic3⋊C4—61no—
219Dic3⋊C4—61no—
220Dic3⋊C4—61no—
221C4×Dic3—62no—
222C4×Dic3—61no—
223C4×Dic3—61no—
224C2×C3⋊C8—21no—
225C2×C3⋊C8—21no—
226C22×C32—21no—
227C22×C32—21no—
228C22×C32—41no—
229C22×C32—41no—
230C22×C32—41no—
231C22×C32#12011yescharacteristic
232C22×C32#13511yescharacteristic
233C22×C32#13711yescharacteristic
234C32×C4—21no—
235C32×C4—21no—
236C32×C4—41no—
237C3⋊Dic3—41no—
238C3⋊Dic3—41no—
239C3⋊Dic3—41no—
240C3⋊Dic3—41no—
241C3×Dic3—81no—
242C3×Dic3—81no—
243#126—181no—
244#125—181no—
245#123—181no—
246#123—181no—
247C22⋊Q8—91no—
248C22⋊Q8—181no—
249#121D3211yescharacteristic
250C4×D4—181no—
251C2×C4⋊C4—31no—
252C2×C4⋊C4—91no—
253#107—181no—
254#106—61no—
255#103—181no—
256#102—61no—
257C22⋊C8—31no—
258C22⋊C8—31no—
259#95—31no—
260#95—181no—
261#95—181no—
262C23×C3—22no—
263C23×C3—21no—
264C23×C3—21no—
265C23×C3—21no—
266C23×C3D3×D411yescharacteristic
267C23×C3D3×D411yescharacteristic
268C3×D4—41no—
269C3×D4—41no—
270C3×D4—42no—
271C3×D4—42no—
272C3×D4—41no—
273C3×D4—41no—
274C3×D4—41no—
275C3×D4—41no—
276C3×D4—81no—
277C2×C3×C4—22no—
278C2×C3×C4—21no—
279C2×C3×C4—21no—
280C2×C3×C4—21no—
281C2×C3×C4—21no—
282C2×C3×C4—41no—
283C2×C3×C4—41no—
284C2×C3×C4—81no—
285C2×C3×C4—121no—
286C2×C3×C4—121no—
287C2×C3×C4—122no—
288C2×C3×C4—121no—
289C2×C3×C4—121no—
290C2×C3×C4C2×D1211yescharacteristic
291C2×C3×C4D3×D411yescharacteristic
292C2×C3×C4D3×D411yescharacteristic
293C2×C3×C4C2×#6711yescharacteristic
294C2×Dic3—41no—
295C2×Dic3—41no—
296C2×Dic3—42no—
297C2×Dic3—41no—
298C2×Dic3—41no—
299C2×Dic3—62no—
300C2×Dic3—62no—
301C2×Dic3—62no—
302C2×Dic3—62no—
303C2×Dic3—61no—
304C2×Dic3—61no—
305C2×Dic3—61no—
306C2×Dic3—61no—
307C2×Dic3—61no—
308C2×Dic3—61no—
309C2×Dic3—61no—
310C2×Dic3—61no—
311C2×Dic3—61no—
312C2×Dic3—61no—
313C2×Dic3—61no—
314C2×Dic3—61no—
315C2×Dic3—121no—
316C2×Dic3—121no—
317C2×Dic3—121no—
318C2×Dic3—121no—
319C2×Dic3—241no—
320C2×Dic3—242no—
321C2×Dic3—241no—
322C2×Dic3—241no—
323Dic6—121no—
324Dic6—121no—
325Dic6—241no—
326C3×C8—121no—
327C3×C8—121no—
328C3⋊C8—41no—
329C3⋊C8—41no—
330C2×C32—21no—
331C2×C32—21no—
332C2×C32—81no—
333C2×C32#45211yescharacteristic
334C2×C32#45411yescharacteristic
335C2×C32#45811yescharacteristic
336C2×Q8—91no—
337C2×D4—21no—
338C2×D4#62611yescharacteristic
339C22×C4—61no—
340C22×C4—61no—
341C22×C4—91no—
342C22×C4—91no—
343C22×C4—181no—
344C22×C4C2×D3211yescharacteristic
345C2×C8—61no—
346C2×C8—61no—
347C4⋊C4—61no—
348C4⋊C4—61no—
349C4⋊C4—91no—
350C4⋊C4—181no—
351C4⋊C4—181no—
352C4⋊C4—181no—
353C4⋊C4—181no—
354C4⋊C4—181no—
355C4⋊C4—181no—
356C4⋊C4#62611yescharacteristic
357C22⋊C4—21no—
358C22⋊C4—181no—
359C22⋊C4—181no—
360C22⋊C4—181no—
361C22⋊C4—181no—
362C42—181no—
363C22×C3—21no—
364C22×C3—21no—
365C22×C3—21no—
366C22×C3—21no—
367C22×C3—21no—
368C22×C3—21no—
369C22×C3—21no—
370C22×C3—41no—
371C22×C3—41no—
372C22×C3—42no—
373C22×C3—42no—
374C22×C3—42no—
375C22×C3—41no—
376C22×C3—41no—
377C22×C3—41no—
378C22×C3—41no—
379C22×C3—41no—
380C22×C3—41no—
381C22×C3#88211yescharacteristic
382C22×C3#91211yescharacteristic
383C22×C3#91511yescharacteristic
384C22×C3#91511yescharacteristic
385C22×C3#91611yescharacteristic
386C22×C3#93711yescharacteristic
387C3×C4—21no—
388C3×C4—21no—
389C3×C4—21no—
390C3×C4—21no—
391C3×C4—41no—
392C3×C4—41no—
393C3×C4—42no—
394C3×C4—41no—
395C3×C4—41no—
396C3×C4—241no—
397C3×C4—241no—
398Dic3—81no—
399Dic3—81no—
400Dic3—122no—
401Dic3—122no—
402Dic3—122no—
403Dic3—122no—
404Dic3—121no—
405Dic3—121no—
406Dic3—121no—
407Dic3—121no—
408Dic3—121no—
409Dic3—121no—
410Dic3—121no—
411Dic3—121no—
412C32#161511yescharacteristic, complemented, Sylow
413C23—21no—
414C23#381111yescharacteristic
415Q8—361no—
416D4—41no—
417D4—41no—
418D4—41no—
419C2×C4—21no—
420C2×C4—41no—
421C2×C4—121no—
422C2×C4—121no—
423C2×C4—122no—
424C2×C4—121no—
425C2×C4—121no—
426C2×C4—181no—
427C2×C4—181no—
428C2×C4—181no—
429C2×C4—181no—
430C2×C4—181no—
431C2×C4—181no—
432C2×C4—361no—
433C2×C4—721no—
434C2×C4C2×#62611yescharacteristic
435C2×C4#381111yescharacteristic
436C8—121no—
437C8—121no—
438C2×C3—21no—
439C2×C3—21no—
440C2×C3—21no—
441C2×C3—21no—
442C2×C3—21no—
443C2×C3—21no—
444C2×C3—21no—
445C2×C3—41no—
446C2×C3—41no—
447C2×C3—82no—
448C2×C3—81no—
449C2×C3—81no—
450C2×C3#474211yescharacteristic
451C2×C3#478311yescharacteristic
452C2×C3#482711yescharacteristic
453C2×C3#505311yescharacteristic
454C2×C3#517311yescharacteristic
455C2×C3#520111yescharacteristic
456C22—21no—
457C22—21no—
458C22—41no—
459C22—41no—
460C22—41no—
461C22#6393111yescharacteristic
462C22#6393611yescharacteristic
463C22#6398111yescharacteristic
464C4—21no—
465C4—21no—
466C4—41no—
467C4—241no—
468C4—241no—
469C4—361no—
470C4—361no—
471C4—361no—
472C4—361no—
473C3—21no—
474C3#6829811yescharacteristic, complemented
475C3#7117011yescharacteristic, complemented
476C2—21no—
477C2—21no—
478C2—81no—
479C2#1059146611yescharacteristic
480C2#1059153511yescharacteristic
481C2#1059168611yescharacteristic
subgroupG/H
centerC22#63981
commutator, cosocleC22×C32×C4C23
FrattiniC22×C4C2×D32
Fitting, prime radicalC32×#121C22
socleC22×C32#120
hypercenter#121D32
hypocenterC32#1615
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
3. #10591227C2semidirect
4. #10591135C2semidirect
6. #10589154C2semidirect
7. #10589148C2semidirect
412. C32#1615semidirect
474. C3#68298semidirect
475. C3#71170semidirect

Maximal subgroups

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

subgroupindex
#105960732
C3×#50342
#105912272
#105911352
C3×#45372
#105891542
#105891482
#711703
#682983