Finite Group Databasebeta

← #11778818

Subgroups — #11778818

Order 1152.

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

normal subgroups only

This group has 507 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#10596094C211yesmaximal, characteristic
2C3×#5044C211yesmaximal, characteristic
3#10591227C211yesmaximal, characteristic
4#10591135C211yesmaximal, characteristic
5C3×#4538C211yesmaximal, characteristic
6#10589154C211yesmaximal, characteristic
7#10589148C211yesmaximal, characteristic
8#71179—31nomaximal
9#68331—31nomaximal
10C32×C22⋊Q8C2211yescharacteristic
11#64153—21no—
12#64133C2211yescharacteristic
13C2×#3750C2211yescharacteristic
14#64098—21no—
15#64098—21no—
16#64097—21no—
17#64087—21no—
18#64086—21no—
19C2×C3×C4⋊Dic3C2211yescharacteristic
20C3×#835—21no—
21C3×C3⋊#95C2211yescharacteristic
22C3×#830C2211yescharacteristic
23C3×#830C2211yescharacteristic
24C3×#807—21no—
25#63579—21no—
26#63579—21no—
27#63575—21no—
28#63567—21no—
29#5623—31no—
30#5623—31no—
31#5623—61no—
32C3×#484—31no—
33#5044D311yescharacteristic
34#4985—31no—
35#4970—31no—
36#4722—31no—
37#4659—31no—
38C3×#328—31no—
39#4538D311yescharacteristic
40#4469—31no—
41#4469—31no—
42#4467—31no—
43#4452—31no—
44C2×C32×Q8D411yescharacteristic
45C22×C32×C4C2311yescharacteristic
46C22×C3⋊Dic3D411yescharacteristic
47C22×C3⋊Dic3D411yescharacteristic
48C2×#634—21no—
49C2×#634D411yescharacteristic
50C22×C3×Dic3—21no—
51C22×C3×Dic3—21no—
52C32×C4⋊C4—21no—
53C32×C4⋊C4D411yescharacteristic
54C32×C22⋊C4—21no—
55#3757—21no—
56C4⋊(C3⋊Dic3)—21no—
57C4⋊(C3⋊Dic3)D411yescharacteristic
58#3750—21no—
59#3750—21no—
60#3750—21no—
61#3750—21no—
62#3750—21no—
63#3750—21no—
64#3750—21no—
65C4×C3⋊Dic3—21no—
66C4×C3⋊Dic3—21no—
67C3×C4⋊Dic3—21no—
68C3×C4⋊Dic3—21no—
69C2×C3×C3⋊C8—21no—
70C2×C3×C3⋊C8—21no—
71#1617—91noSylow
72C3×C22⋊Q8—21no—
73C3×C22⋊Q8C2×D311yescharacteristic
74C3×C22⋊Q8C2×D311yescharacteristic
75C2×C3×C4⋊C4—31no—
76#944—62no—
77#944—61no—
78#944—61no—
79C2×C4⋊Dic3C2×D311yescharacteristic
80#924—31no—
81#924—31no—
82#924—61no—
83C2×Dic3⋊C4—31no—
84C2×Dic3⋊C4—31no—
85C2×Dic3⋊C4—61no—
86#889—61no—
87#889—61no—
88#889—62no—
89#889—62no—
90#889—61no—
91#889—61no—
92#888—61no—
93#888—61no—
94#888—62no—
95#878—61no—
96#878—61no—
97#878—62no—
98#877—61no—
99#877—61no—
100#877—62no—
101C3×#107—61no—
102C3×#103—61no—
103C3×C22⋊C8—31no—
104C3×C22⋊C8—31no—
105C3×#95—31no—
106#835—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#807—21no—
118#807—61no—
119C23×C32C2×D411yescharacteristic
120C32×Q8—41no—
121C2×C32×C4—21no—
122C2×C32×C4—21no—
123C2×C32×C4—41no—
124C2×C32×C4C2×D411yescharacteristic
125C2×C32×C4C2×D411yescharacteristic
126C2×C3⋊Dic3—21no—
127C2×C3⋊Dic3—21no—
128C2×C3⋊Dic3—21no—
129C2×C3⋊Dic3—21no—
130C2×C3⋊Dic3—21no—
131C2×C3⋊Dic3—41no—
132C2×C3⋊Dic3Q1612yes—
133#634—41no—
134#634—81no—
135C2×C3×Dic3—41no—
136C2×C3×Dic3—41no—
137C2×C3×Dic3—42no—
138C2×C3×Dic3—41no—
139C2×C3×Dic3—41no—
140C3×C3⋊C8—41no—
141C3×C3⋊C8—41no—
142#544—91no—
143#484—31no—
144#484—91no—
145#400—91no—
146#328—31no—
147#328—91no—
148#324—91no—
149C2×C3×Q8—21no—
150C2×C3×Q8D1211yescharacteristic
151C2×C3×Q8#6711yescharacteristic
152C22×C3×C4—21no—
153C22×C3×C4—61no—
154C22×C3×C4—61no—
155C22×C3×C4C22×D311yescharacteristic
156C22×C3×C4C22×D311yescharacteristic
157C22×Dic3—21no—
158C22×Dic3—21no—
159C22×Dic3—31no—
160C22×Dic3—31no—
161C22×Dic3—31no—
162C22×Dic3—31no—
163C22×Dic3—61no—
164C22×Dic3—61no—
165C2×Dic6—31no—
166C2×Dic6—31no—
167C2×Dic6—61no—
168C2×Dic6—62no—
169C2×Dic6—61no—
170C2×Dic6—61no—
171C2×C3×C8—61no—
172C2×C3×C8—61no—
173C3×C4⋊C4—22no—
174C3×C4⋊C4—21no—
175C3×C4⋊C4—21no—
176C3×C4⋊C4—21no—
177C3×C4⋊C4—61no—
178C3×C4⋊C4—61no—
179C3×C4⋊C4D1211yescharacteristic
180C3×C4⋊C4#6711yescharacteristic
181C3×C22⋊C4—22no—
182C3×C22⋊C4—21no—
183C3×C22⋊C4—21no—
184#217—62no—
185#217—61no—
186#217—61no—
187C4⋊Dic3—21no—
188C4⋊Dic3—21no—
189C4⋊Dic3—31no—
190C4⋊Dic3—31no—
191C4⋊Dic3—61no—
192C4⋊Dic3—62no—
193C4⋊Dic3—61no—
194C4⋊Dic3—61no—
195Dic3⋊C4—62no—
196Dic3⋊C4—61no—
197Dic3⋊C4—61no—
198Dic3⋊C4—62no—
199Dic3⋊C4—61no—
200Dic3⋊C4—61no—
201Dic3⋊C4—62no—
202Dic3⋊C4—61no—
203Dic3⋊C4—61no—
204Dic3⋊C4—62no—
205Dic3⋊C4—61no—
206Dic3⋊C4—61no—
207Dic3⋊C4—62no—
208Dic3⋊C4—62no—
209Dic3⋊C4—62no—
210Dic3⋊C4—61no—
211Dic3⋊C4—61no—
212Dic3⋊C4—61no—
213Dic3⋊C4—61no—
214Dic3⋊C4—61no—
215Dic3⋊C4—61no—
216C4×Dic3—62no—
217C4×Dic3—61no—
218C4×Dic3—61no—
219C4×Dic3—62no—
220C4×Dic3—61no—
221C4×Dic3—61no—
222C2×C3⋊C8—21no—
223C2×C3⋊C8—21no—
224C22×C32—21no—
225C22×C32—21no—
226C22×C32#12011yescharacteristic
227C22×C32C2×Q1611yescharacteristic
228C22×C32#13711yescharacteristic
229C32×C4—21no—
230C32×C4—21no—
231C32×C4—41no—
232C32×C4—41no—
233C3⋊Dic3—22no—
234C3⋊Dic3—41no—
235C3⋊Dic3—41no—
236C3⋊Dic3—41no—
237C3×Dic3—81no—
238C3×Dic3—81no—
239C4⋊Q8—181no—
240C4⋊Q8—181no—
241#125—181no—
242#125—181no—
243C22⋊Q8—91no—
244C22⋊Q8—181no—
245C22⋊Q8D3211yescharacteristic
246#117—181no—
247C2×C4⋊C4—31no—
248C2×C4⋊C4—91no—
249#107—61no—
250#107—181no—
251#103—61no—
252#103—181no—
253C22⋊C8—31no—
254C22⋊C8—31no—
255#95—31no—
256#95—181no—
257#95—181no—
258C23×C3—21no—
259C23×C3D3×D411yescharacteristic
260C23×C3D3×D411yescharacteristic
261C3×Q8—41no—
262C3×Q8—41no—
263C3×Q8—81no—
264C2×C3×C4—22no—
265C2×C3×C4—22no—
266C2×C3×C4—21no—
267C2×C3×C4—21no—
268C2×C3×C4—21no—
269C2×C3×C4—21no—
270C2×C3×C4—21no—
271C2×C3×C4—21no—
272C2×C3×C4—41no—
273C2×C3×C4—41no—
274C2×C3×C4—81no—
275C2×C3×C4—121no—
276C2×C3×C4—121no—
277C2×C3×C4—122no—
278C2×C3×C4—121no—
279C2×C3×C4—121no—
280C2×C3×C4C2×D1211yescharacteristic
281C2×C3×C4D3×D411yescharacteristic
282C2×C3×C4D3×D411yescharacteristic
283C2×C3×C4C2×#6711yescharacteristic
284C2×Dic3—32no—
285C2×Dic3—32no—
286C2×Dic3—41no—
287C2×Dic3—41no—
288C2×Dic3—42no—
289C2×Dic3—41no—
290C2×Dic3—41no—
291C2×Dic3—62no—
292C2×Dic3—62no—
293C2×Dic3—62no—
294C2×Dic3—61no—
295C2×Dic3—61no—
296C2×Dic3—61no—
297C2×Dic3—61no—
298C2×Dic3—62no—
299C2×Dic3—62no—
300C2×Dic3—62no—
301C2×Dic3—61no—
302C2×Dic3—61no—
303C2×Dic3—61no—
304C2×Dic3—61no—
305C2×Dic3—61no—
306C2×Dic3—61no—
307C2×Dic3—121no—
308C2×Dic3—121no—
309C2×Dic3—241no—
310Dic6—121no—
311Dic6—121no—
312Dic6—241no—
313Dic6—242no—
314Dic6—241no—
315Dic6—241no—
316C3×C8—121no—
317C3×C8—121no—
318C3⋊C8—41no—
319C3⋊C8—41no—
320C2×C32—21no—
321C2×C32—21no—
322C2×C32#45111yescharacteristic
323C2×C32#45411yescharacteristic
324C2×C32#45811yescharacteristic
325C2×Q8—91no—
326C2×Q8—181no—
327C2×Q8#62611yescharacteristic
328C22×C4—61no—
329C22×C4—61no—
330C22×C4—91no—
331C22×C4—91no—
332C22×C4C2×D3211yescharacteristic
333C2×C8—61no—
334C2×C8—61no—
335C4⋊C4—21no—
336C4⋊C4—61no—
337C4⋊C4—61no—
338C4⋊C4—91no—
339C4⋊C4—181no—
340C4⋊C4—181no—
341C4⋊C4—181no—
342C4⋊C4—181no—
343C4⋊C4—181no—
344C4⋊C4—181no—
345C4⋊C4—181no—
346C4⋊C4—181no—
347C4⋊C4#62611yescharacteristic
348C22⋊C4—21no—
349C22⋊C4—181no—
350C42—181no—
351C42—181no—
352C22×C3—21no—
353C22×C3—21no—
354C22×C3—21no—
355C22×C3—21no—
356C22×C3—21no—
357C22×C3—21no—
358C22×C3—21no—
359C22×C3—41no—
360C22×C3—41no—
361C22×C3#88211yescharacteristic
362C22×C3#91511yescharacteristic
363C22×C3D3×Q1611yescharacteristic
364C22×C3D3×Q1611yescharacteristic
365C22×C3#91811yescharacteristic
366C22×C3#93711yescharacteristic
367C3×C4—21no—
368C3×C4—21no—
369C3×C4—21no—
370C3×C4—21no—
371C3×C4—41no—
372C3×C4—41no—
373C3×C4—42no—
374C3×C4—42no—
375C3×C4—41no—
376C3×C4—41no—
377C3×C4—41no—
378C3×C4—41no—
379C3×C4—241no—
380C3×C4—241no—
381Dic3—64no—
382Dic3—62no—
383Dic3—62no—
384Dic3—81no—
385Dic3—81no—
386Dic3—122no—
387Dic3—122no—
388Dic3—122no—
389Dic3—121no—
390Dic3—121no—
391Dic3—121no—
392Dic3—121no—
393Dic3—121no—
394Dic3—121no—
395C32#161711yescharacteristic, complemented, Sylow
396C23#381111yescharacteristic
397Q8—41no—
398Q8—361no—
399Q8—721no—
400C2×C4—21no—
401C2×C4—21no—
402C2×C4—41no—
403C2×C4—92no—
404C2×C4—121no—
405C2×C4—121no—
406C2×C4—122no—
407C2×C4—121no—
408C2×C4—121no—
409C2×C4—181no—
410C2×C4—181no—
411C2×C4—181no—
412C2×C4—181no—
413C2×C4—181no—
414C2×C4—361no—
415C2×C4C2×#62611yescharacteristic
416C2×C4#381111yescharacteristic
417C8—121no—
418C8—121no—
419C2×C3—21no—
420C2×C3—21no—
421C2×C3—21no—
422C2×C3—21no—
423C2×C3—21no—
424C2×C3—21no—
425C2×C3—21no—
426C2×C3—41no—
427C2×C3—41no—
428C2×C3#474211yescharacteristic
429C2×C3#480911yescharacteristic
430C2×C3#482711yescharacteristic
431C2×C3#505311yescharacteristic
432C2×C3#518611yescharacteristic
433C2×C3#520111yescharacteristic
434C22—21no—
435C22—21no—
436C22#6394411yescharacteristic
437C22#6395111yescharacteristic
438C22#6398111yescharacteristic
439C4—21no—
440C4—21no—
441C4—41no—
442C4—41no—
443C4—182no—
444C4—241no—
445C4—241no—
446C4—361no—
447C4—361no—
448C4—361no—
449C3—21no—
450C3#6833111yescharacteristic, complemented
451C3#7117911yescharacteristic, complemented
452C2—21no—
453C2—21no—
454C2#1059153511yescharacteristic
455C2#1059160311yescharacteristic
456C2#1059168611yescharacteristic
subgroupG/H
centerC22#63981
commutator, cosocleC22×C32×C4C23
FrattiniC22×C4C2×D32
FittingC32×C22⋊Q8C22
socleC22×C32#120
prime radicalC23×C32C2×D4
hypercenterC22⋊Q8D32
hypocenterC32#1617
LCSG ▷ C22×C32×C4 ▷ C22×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22⋊Q8

Complements

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

NH ≅ G/Ntype
395. C32#1617semidirect
450. C3#68331semidirect
451. C3#71179semidirect

Maximal subgroups

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

subgroupindex
#105960942
C3×#50442
#105912272
#105911352
C3×#45382
#105891542
#105891482
#711793
#683313