Finite Group Databasebeta

← #11778592

Subgroups — #11778592

Order 1152.

460 conjugacy classes of subgroups; only the 88 normal subgroups are shown.

normal subgroups only

This group has 460 conjugacy classes of subgroups — too many to draw. Only its 88 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
1C3×#5623C211yesmaximal, characteristic
2C3×#5043C211yesmaximal, characteristic
3#10591214C211yesmaximal, characteristic
4#10591101C211yesmaximal, characteristic
5#10589404C211yesmaximal, characteristic
6#10589152C211yesmaximal, characteristic
7#10589147C211yesmaximal, characteristic
8#71898—31nomaximal
9#71175—31nomaximal
10C32×C22⋊Q8C2211yescharacteristic
11C3×#944—21no—
12C2×C3×C4⋊Dic3C2211yescharacteristic
13C3×#924C2211yescharacteristic
14C2×C3×Dic3⋊C4C2211yescharacteristic
15C3×#889—21no—
16C3×#889—21no—
17C3×#888—21no—
18C3×#878—21no—
19C3×#877—21no—
20C2×#3724—21no—
21#63658C2211yescharacteristic
22#63657C2211yescharacteristic
23C3×#835—21no—
24C3×#830C2211yescharacteristic
25C3×#808—21no—
26#63579—21no—
27#63574—21no—
28#63565—21no—
29C3×#544—31no—
30#5623D311yescharacteristic
31C3×#483—31no—
32#5043—31no—
33#5043D311yescharacteristic
34#4983—31no—
35#4981—31no—
36#4971—31no—
37#4538—31no—
38#4538—31no—
39#4538—31no—
40#4538—61no—
41#4528—31no—
42#4469—31no—
43#4467—31no—
44C2×C32×Q8D411yescharacteristic
45C22×C32×C4C2311yescharacteristic
46C22×C3⋊Dic3—21no—
47C22×C3×Dic3—21no—
48C22×C3×Dic3D411yescharacteristic
49C22×C3×Dic3D411yescharacteristic
50C2×C3×Dic6—21no—
51C2×C3×Dic6D411yescharacteristic
52C32×C4⋊C4—21no—
53C32×C4⋊C4D411yescharacteristic
54C32×C22⋊C4—21no—
55C2×C3⋊(C3⋊C8)—21no—
56C3×#217—21no—
57C3×C4⋊Dic3—21no—
58C3×C4⋊Dic3—21no—
59C3×C4⋊Dic3—21no—
60C3×C4⋊Dic3D411yescharacteristic
61C3×Dic3⋊C4—21no—
62C3×Dic3⋊C4—21no—
63C3×Dic3⋊C4—21no—
64C3×Dic3⋊C4—21no—
65C3×Dic3⋊C4—21no—
66C3×Dic3⋊C4—21no—
67C3×Dic3⋊C4—21no—
68C3×C4×Dic3—21no—
69C3×C4×Dic3—21no—
70C2×C3×C3⋊C8—21no—
71#3724—42no—
72#1611—91noSylow
73C3×C4⋊Q8—61no—
74C3×C4⋊Q8—61no—
75C3×#125—61no—
76C3×#125—61no—
77C3×C22⋊Q8—21no—
78C3×C22⋊Q8—31no—
79C3×C22⋊Q8—61no—
80C3×C22⋊Q8C2×D311yescharacteristic
81C3×C22⋊Q8C2×D311yescharacteristic
82C3×#117—61no—
83C2×C3×C4⋊C4—31no—
84C2×C3×C4⋊C4—31no—
85#944—21no—
86C2×C4⋊Dic3C2×D311yescharacteristic
87#924C2×D311yescharacteristic
88C2×Dic3⋊C4—61no—
89C2×Dic3⋊C4—61no—
90C2×Dic3⋊C4C2×D311yescharacteristic
91#889—21no—
92#889—21no—
93#888—21no—
94#878—21no—
95#877—21no—
96C3×#106—61no—
97C3×#103—61no—
98C3×C22⋊C8—31no—
99#835—21no—
100#835—61no—
101C3⋊#95—31no—
102C3⋊#95—31no—
103C3⋊#95—61no—
104C3⋊#95—61no—
105C3⋊#95—61no—
106#830—31no—
107#830—31no—
108#830—61no—
109#830C2×D311yescharacteristic
110#810—61no—
111#808—21no—
112#808—61no—
113#808—61no—
114C23×C32C2×D411yescharacteristic
115C32×Q8—41no—
116C2×C32×C4—21no—
117C2×C32×C4—21no—
118C2×C32×C4—41no—
119C2×C32×C4C2×D411yescharacteristic
120C2×C32×C4C2×D411yescharacteristic
121C2×C3⋊Dic3—22no—
122C2×C3⋊Dic3—41no—
123C2×C3⋊Dic3—41no—
124C2×C3×Dic3—21no—
125C2×C3×Dic3—21no—
126C2×C3×Dic3—21no—
127C2×C3×Dic3—21no—
128C2×C3×Dic3—21no—
129C2×C3×Dic3—41no—
130C2×C3×Dic3—41no—
131C2×C3×Dic3—41no—
132C2×C3×Dic3—41no—
133C2×C3×Dic3SD1612yes—
134C3×Dic6—41no—
135C3×Dic6—81no—
136C3⋊(C3⋊C8)—41no—
137C3×C3⋊C8—41no—
138#544—31no—
139#483—31no—
140#483—91no—
141#398—91no—
142#328—91no—
143#328—91no—
144#324—91no—
145C2×C3×Q8—21no—
146C2×C3×Q8—31no—
147C2×C3×Q8—61no—
148C2×C3×Q8#6711yescharacteristic
149C2×C3×Q8#6711yescharacteristic
150C22×C3×C4—21no—
151C22×C3×C4—31no—
152C22×C3×C4—31no—
153C22×C3×C4—61no—
154C22×C3×C4C22×D311yescharacteristic
155C22×C3×C4C22×D311yescharacteristic
156C22×Dic3—21no—
157C22×Dic3—61no—
158C22×Dic3—61no—
159C22×Dic3—121no—
160C22×Dic3#6711yescharacteristic
161C22×Dic3#6711yescharacteristic
162C2×Dic6—21no—
163C2×Dic6#6711yescharacteristic
164C2×C3×C8—61no—
165C3×C4⋊C4—21no—
166C3×C4⋊C4—21no—
167C3×C4⋊C4—21no—
168C3×C4⋊C4—31no—
169C3×C4⋊C4—41no—
170C3×C4⋊C4—61no—
171C3×C4⋊C4—61no—
172C3×C4⋊C4—61no—
173C3×C4⋊C4—61no—
174C3×C4⋊C4—61no—
175C3×C4⋊C4—61no—
176C3×C4⋊C4—61no—
177C3×C4⋊C4—61no—
178C3×C4⋊C4—61no—
179C3×C4⋊C4—61no—
180C3×C4⋊C4#6711yescharacteristic
181C3×C4⋊C4#6711yescharacteristic
182C3×C22⋊C4—21no—
183C3×C22⋊C4—21no—
184C3×C22⋊C4—41no—
185C3×C22⋊C4—61no—
186C3×C42—61no—
187C3×C42—61no—
188#217—21no—
189C4⋊Dic3—21no—
190C4⋊Dic3—21no—
191C4⋊Dic3—21no—
192C4⋊Dic3#6711yescharacteristic
193Dic3⋊C4—21no—
194Dic3⋊C4—21no—
195Dic3⋊C4—21no—
196Dic3⋊C4—21no—
197Dic3⋊C4—21no—
198Dic3⋊C4—21no—
199Dic3⋊C4—21no—
200Dic3⋊C4—122no—
201Dic3⋊C4—122no—
202C4×Dic3—21no—
203C4×Dic3—21no—
204C2×C3⋊C8—21no—
205C2×C3⋊C8—61no—
206C2×C3⋊C8—61no—
207C2×C3⋊C8—121no—
208C22×C32—21no—
209C22×C32—21no—
210C22×C32#12011yescharacteristic
211C22×C32C2×SD1611yescharacteristic
212C22×C32#13711yescharacteristic
213C32×C4—21no—
214C32×C4—21no—
215C32×C4—41no—
216C32×C4—41no—
217C3⋊Dic3—42no—
218C3×Dic3—22no—
219C3×Dic3—41no—
220C3×Dic3—41no—
221C3×Dic3—41no—
222C3×Dic3—81no—
223C4⋊Q8—61no—
224C4⋊Q8—61no—
225#125—61no—
226#125—61no—
227C22⋊Q8—31no—
228C22⋊Q8—61no—
229C22⋊Q8D3211yescharacteristic
230#117—61no—
231C2×C4⋊C4—31no—
232C2×C4⋊C4—31no—
233C2×C4⋊C4—181no—
234#106—61no—
235#106—181no—
236#103—61no—
237#103—181no—
238C22⋊C8—31no—
239C22⋊C8—91no—
240#95—91no—
241#95—181no—
242C23×C3—21no—
243C23×C3D3×D411yescharacteristic
244C23×C3C2×#6711yescharacteristic
245C3×Q8—41no—
246C3×Q8—41no—
247C3×Q8—81no—
248C3×Q8—121no—
249C3×Q8—241no—
250C2×C3×C4—21no—
251C2×C3×C4—21no—
252C2×C3×C4—21no—
253C2×C3×C4—21no—
254C2×C3×C4—21no—
255C2×C3×C4—21no—
256C2×C3×C4—32no—
257C2×C3×C4—41no—
258C2×C3×C4—41no—
259C2×C3×C4—41no—
260C2×C3×C4—41no—
261C2×C3×C4—61no—
262C2×C3×C4—61no—
263C2×C3×C4—61no—
264C2×C3×C4—61no—
265C2×C3×C4—61no—
266C2×C3×C4—81no—
267C2×C3×C4—121no—
268C2×C3×C4—121no—
269C2×C3×C4—121no—
270C2×C3×C4—121no—
271C2×C3×C4D3×D411yescharacteristic
272C2×C3×C4C2×#6711yescharacteristic
273C2×C3×C4C2×#6711yescharacteristic
274C2×C3×C4C2×#6711yescharacteristic
275C2×Dic3—21no—
276C2×Dic3—21no—
277C2×Dic3—21no—
278C2×Dic3—21no—
279C2×Dic3—21no—
280C2×Dic3—41no—
281C2×Dic3—41no—
282C2×Dic3—41no—
283C2×Dic3—41no—
284C2×Dic3—62no—
285C2×Dic3—62no—
286C2×Dic3—122no—
287C2×Dic3—121no—
288C2×Dic3—121no—
289C2×Dic3—121no—
290C2×Dic3—121no—
291C2×Dic3—241no—
292C2×Dic3—241no—
293C2×Dic3#21512yes—
294Dic6—41no—
295Dic6—81no—
296C3×C8—121no—
297C3⋊C8—41no—
298C3⋊C8—121no—
299C3⋊C8—121no—
300C3⋊C8—241no—
301C2×C32—21no—
302C2×C32—21no—
303C2×C32#44811yescharacteristic
304C2×C32#45611yescharacteristic
305C2×C32#45811yescharacteristic
306C2×Q8—31no—
307C2×Q8—61no—
308C2×Q8#62511yescharacteristic
309C22×C4—31no—
310C22×C4—31no—
311C22×C4—61no—
312C22×C4—181no—
313C22×C4C2×D3211yescharacteristic
314C2×C8—61no—
315C2×C8—181no—
316C4⋊C4—21no—
317C4⋊C4—31no—
318C4⋊C4—61no—
319C4⋊C4—61no—
320C4⋊C4—61no—
321C4⋊C4—61no—
322C4⋊C4—61no—
323C4⋊C4—61no—
324C4⋊C4—61no—
325C4⋊C4—61no—
326C4⋊C4—61no—
327C4⋊C4—61no—
328C4⋊C4—362no—
329C4⋊C4#62511yescharacteristic
330C22⋊C4—21no—
331C22⋊C4—61no—
332C42—61no—
333C42—61no—
334C22×C3—21no—
335C22×C3—21no—
336C22×C3—21no—
337C22×C3—21no—
338C22×C3—21no—
339C22×C3—21no—
340C22×C3—21no—
341C22×C3—41no—
342C22×C3—41no—
343C22×C3D3×SD1611yescharacteristic
344C22×C3#91511yescharacteristic
345C22×C3#93711yescharacteristic
346C22×C3C2×#21511yescharacteristic
347C22×C3#94211yescharacteristic
348C22×C3#95311yescharacteristic
349C3×C4—21no—
350C3×C4—21no—
351C3×C4—21no—
352C3×C4—21no—
353C3×C4—41no—
354C3×C4—41no—
355C3×C4—41no—
356C3×C4—41no—
357C3×C4—41no—
358C3×C4—41no—
359C3×C4—62no—
360C3×C4—81no—
361C3×C4—81no—
362C3×C4—121no—
363C3×C4—121no—
364C3×C4—121no—
365C3×C4—241no—
366Dic3—22no—
367Dic3—41no—
368Dic3—41no—
369Dic3—41no—
370Dic3—81no—
371Dic3—122no—
372Dic3—122no—
373Dic3—242no—
374C32#161111yescharacteristic, complemented, Sylow
375C23D3×#6711yescharacteristic
376Q8—41no—
377Q8—121no—
378Q8—241no—
379C2×C4—21no—
380C2×C4—21no—
381C2×C4—32no—
382C2×C4—41no—
383C2×C4—61no—
384C2×C4—61no—
385C2×C4—61no—
386C2×C4—61no—
387C2×C4—61no—
388C2×C4—121no—
389C2×C4—121no—
390C2×C4—121no—
391C2×C4—121no—
392C2×C4—182no—
393C2×C4—361no—
394C2×C4—361no—
395C2×C4C2×#62511yescharacteristic
396C2×C4D3×#6711yescharacteristic
397C8—121no—
398C8—361no—
399C2×C3—21no—
400C2×C3—21no—
401C2×C3—21no—
402C2×C3—21no—
403C2×C3—21no—
404C2×C3—21no—
405C2×C3—21no—
406C2×C3—41no—
407C2×C3—41no—
408C2×C3#505311yescharacteristic
409C2×C3#517011yescharacteristic
410C2×C3#520511yescharacteristic
411C2×C3#522711yescharacteristic
412C2×C3#524311yescharacteristic
413C2×C3#524611yescharacteristic
414C22—21no—
415C22—21no—
416C22D3×#21511yescharacteristic
417C22#6394611yescharacteristic
418C22#6397611yescharacteristic
419C4—21no—
420C4—21no—
421C4—41no—
422C4—41no—
423C4—62no—
424C4—121no—
425C4—121no—
426C4—121no—
427C4—241no—
428C4—362no—
429C3—21no—
430C3#7117511yescharacteristic, complemented
431C3#7189811yescharacteristic, complemented
432C2—21no—
433C2—21no—
434C2#1059153311yescharacteristic
435C2#1059158311yescharacteristic
436C2#1059168711yescharacteristic
subgroupG/H
centerC22#63976
commutator, cosocleC22×C32×C4C23
FrattiniC22×C4C2×D32
FittingC32×C22⋊Q8C22
socleC22×C32#120
prime radicalC23×C32C2×D4
hypercenterC22⋊Q8D32
hypocenterC32#1611
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
374. C32#1611semidirect
430. C3#71175semidirect
431. C3#71898semidirect

Maximal subgroups

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

subgroupindex
C3×#56232
C3×#50432
#105912142
#105911012
#105894042
#105891522
#105891472
#718983
#711753