Finite Group Databasebeta

← #11778588

Subgroups — #11778588

Order 1152.

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

normal subgroups only

This group has 472 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#10594812C211yesmaximal, characteristic
2#10592670C211yesmaximal, characteristic
3C3×#4983C211yesmaximal, characteristic
4C3×#4971C211yesmaximal, characteristic
5#10589154C211yesmaximal, characteristic
6#10589153C211yesmaximal, characteristic
7#10589147C211yesmaximal, characteristic
8#71175—31nomaximal
9#69713—31nomaximal
10C2×C32×C4⋊C4C2211yescharacteristic
11#64133C2211yescharacteristic
12C3×#924C2211yescharacteristic
13C2×C3×Dic3⋊C4—21no—
14C2×C3×Dic3⋊C4C2211yescharacteristic
15#63964—21no—
16#63955—21no—
17#63846—21no—
18#63845—21no—
19#63840—21no—
20#63839—21no—
21#63657C2211yescharacteristic
22#63637—21no—
23#63635—21no—
24C3×C3⋊#95—21no—
25C3×C3⋊#95C2211yescharacteristic
26C3×#830C2211yescharacteristic
27C3×#810—21no—
28C3×#808—21no—
29#5623—31no—
30#5500—31no—
31C3×#483—31no—
32C3×#398—31no—
33#4983D311yescharacteristic
34#4971—31no—
35#4971—31no—
36#4971—61no—
37#4971D311yescharacteristic
38#4538—31no—
39#4528—31no—
40#4469—31no—
41#4467—31no—
42#4452—31no—
43#4452—31no—
44C22×C32×C4—21no—
45C22×C32×C4C2311yescharacteristic
46C2×#634D411yescharacteristic
47C22×C3×Dic3—21no—
48C22×C3×Dic3D411yescharacteristic
49C22×C3×Dic3D411yescharacteristic
50C2×C3×Dic6D411yescharacteristic
51C2×#627—21no—
52C32×C4⋊C4—21no—
53C32×C4⋊C4—21no—
54#3757—21no—
55C4⋊(C3⋊Dic3)D411yescharacteristic
56#3750—21no—
57C2×C3⋊(C3⋊C8)—21no—
58C3×#217—21no—
59C3×C4⋊Dic3D411yescharacteristic
60C3×Dic3⋊C4—21no—
61C3×Dic3⋊C4—21no—
62C3×Dic3⋊C4—21no—
63C3×Dic3⋊C4—42no—
64C2×C3×C3⋊C8—21no—
65#3724—21no—
66Dic3⋊Dic3—21no—
67Dic3⋊Dic3—21no—
68Dic3⋊Dic3—21no—
69Dic3⋊Dic3—21no—
70Dic32—21no—
71Dic32—21no—
72#1611—91noSylow
73C3×C22⋊Q8—31no—
74C2×C3×C4⋊C4—21no—
75C2×C3×C4⋊C4—31no—
76C2×C3×C4⋊C4—61no—
77C2×C3×C4⋊C4C2×D311yescharacteristic
78C2×C3×C4⋊C4C2×D311yescharacteristic
79#944—61no—
80#926—61no—
81#924—31no—
82#924—31no—
83#924—61no—
84#924—61no—
85#924C2×D311yescharacteristic
86C2×Dic3⋊C4—21no—
87C2×Dic3⋊C4C2×D311yescharacteristic
88#890—61no—
89#890—61no—
90#889—61no—
91#889—61no—
92#888—61no—
93#888—61no—
94#888—61no—
95#878—61no—
96#877—61no—
97C3×#106—61no—
98C3×#103—61no—
99C3×C22⋊C8—31no—
100C3×#95—31no—
101C3×#95—61no—
102C3⋊#95—21no—
103C3⋊#95C2×D311yescharacteristic
104#830—31no—
105#830—31no—
106#830—61no—
107#830C2×D311yescharacteristic
108#810—21no—
109#810—61no—
110#810—61no—
111#810—62no—
112#808—21no—
113#808—61no—
114#808—61no—
115#808—62no—
116C23×C32C2×D411yescharacteristic
117C2×C32×C4—41no—
118C2×C32×C4—41no—
119C2×C32×C4—41no—
120C2×C32×C4—41no—
121C2×C32×C4C2×D411yescharacteristic
122C2×C32×C4C2×D411yescharacteristic
123C2×C3⋊Dic3—21no—
124C2×C3⋊Dic3—21no—
125#634—41no—
126C2×C3×Dic3—21no—
127C2×C3×Dic3—21no—
128C2×C3×Dic3—22no—
129C2×C3×Dic3—21no—
130C2×C3×Dic3—21no—
131C2×C3×Dic3—21no—
132C2×C3×Dic3—41no—
133C2×C3×Dic3—41no—
134C2×C3×Dic3—41no—
135C2×C3×Dic3SD1612yes—
136C3×Dic6—41no—
137#627—81no—
138C3⋊(C3⋊C8)—41no—
139C3×C3⋊C8—41no—
140#544—91no—
141#483—31no—
142#483—91no—
143#398—31no—
144#328—91no—
145#328—91no—
146#324—91no—
147C2×C3×Q8—31no—
148C22×C3×C4—21no—
149C22×C3×C4—21no—
150C22×C3×C4—21no—
151C22×C3×C4—31no—
152C22×C3×C4—31no—
153C22×C3×C4—41no—
154C22×C3×C4—61no—
155C22×C3×C4C22×D311yescharacteristic
156C22×C3×C4C22×D311yescharacteristic
157C22×Dic3—21no—
158C22×Dic3#6711yescharacteristic
159C22×Dic3#6711yescharacteristic
160C2×Dic6—31no—
161C2×Dic6—31no—
162C2×Dic6—61no—
163C2×Dic6—61no—
164C2×Dic6—61no—
165C2×Dic6#6711yescharacteristic
166C2×C3×C8—61no—
167C3×C4⋊C4—22no—
168C3×C4⋊C4—21no—
169C3×C4⋊C4—21no—
170C3×C4⋊C4—21no—
171C3×C4⋊C4—21no—
172C3×C4⋊C4—31no—
173C3×C4⋊C4—41no—
174C3×C4⋊C4—61no—
175C3×C4⋊C4—61no—
176C3×C4⋊C4—61no—
177C3×C4⋊C4—122no—
178C3×C22⋊C4—61no—
179#217—21no—
180#217—61no—
181#217—61no—
182#217—121no—
183C4⋊Dic3—31no—
184C4⋊Dic3—31no—
185C4⋊Dic3—61no—
186C4⋊Dic3—61no—
187C4⋊Dic3—61no—
188C4⋊Dic3—61no—
189C4⋊Dic3—61no—
190C4⋊Dic3#6711yescharacteristic
191Dic3⋊C4—21no—
192Dic3⋊C4—21no—
193Dic3⋊C4—21no—
194Dic3⋊C4—42no—
195Dic3⋊C4—61no—
196Dic3⋊C4—61no—
197Dic3⋊C4—61no—
198Dic3⋊C4—61no—
199Dic3⋊C4—61no—
200Dic3⋊C4—61no—
201Dic3⋊C4—61no—
202Dic3⋊C4—61no—
203Dic3⋊C4—121no—
204C4×Dic3—61no—
205C4×Dic3—61no—
206C4×Dic3—61no—
207C4×Dic3—61no—
208C2×C3⋊C8—21no—
209C2×C3⋊C8—62no—
210C2×C3⋊C8—61no—
211C2×C3⋊C8—61no—
212C22×C32—21no—
213C22×C32—21no—
214C22×C32#12011yescharacteristic
215C22×C32C2×SD1611yescharacteristic
216C22×C32#13711yescharacteristic
217C32×C4—21no—
218C32×C4—21no—
219C32×C4—81no—
220C3⋊Dic3—41no—
221C3⋊Dic3—41no—
222C3×Dic3—22no—
223C3×Dic3—42no—
224C3×Dic3—41no—
225C3×Dic3—41no—
226C3×Dic3—41no—
227C4⋊Q8—181no—
228C4⋊Q8—181no—
229#125—181no—
230#125—181no—
231C22⋊Q8—31no—
232C22⋊Q8—91no—
233C22⋊Q8—181no—
234#117—181no—
235C2×C4⋊C4—31no—
236C2×C4⋊C4—61no—
237C2×C4⋊C4D3211yescharacteristic
238#106—61no—
239#106—181no—
240#103—61no—
241#103—181no—
242C22⋊C8—31no—
243C22⋊C8—91no—
244#95—31no—
245#95—61no—
246C23×C3—21no—
247C23×C3D3×D411yescharacteristic
248C23×C3C2×#6711yescharacteristic
249C3×Q8—121no—
250C2×C3×C4—21no—
251C2×C3×C4—21no—
252C2×C3×C4—32no—
253C2×C3×C4—41no—
254C2×C3×C4—41no—
255C2×C3×C4—42no—
256C2×C3×C4—42no—
257C2×C3×C4—41no—
258C2×C3×C4—41no—
259C2×C3×C4—41no—
260C2×C3×C4—41no—
261C2×C3×C4—41no—
262C2×C3×C4—41no—
263C2×C3×C4—61no—
264C2×C3×C4—61no—
265C2×C3×C4—62no—
266C2×C3×C4—61no—
267C2×C3×C4—61no—
268C2×C3×C4—61no—
269C2×C3×C4—81no—
270C2×C3×C4—81no—
271C2×C3×C4—121no—
272C2×C3×C4—121no—
273C2×C3×C4—121no—
274C2×C3×C4D3×D411yescharacteristic
275C2×C3×C4D3×D411yescharacteristic
276C2×C3×C4D3×D411yescharacteristic
277C2×C3×C4C2×#6711yescharacteristic
278C2×Dic3—21no—
279C2×Dic3—21no—
280C2×Dic3—22no—
281C2×Dic3—21no—
282C2×Dic3—21no—
283C2×Dic3—21no—
284C2×Dic3—41no—
285C2×Dic3—41no—
286C2×Dic3—41no—
287C2×Dic3—61no—
288C2×Dic3—61no—
289C2×Dic3—61no—
290C2×Dic3—61no—
291C2×Dic3—121no—
292C2×Dic3—121no—
293C2×Dic3#21412yes—
294Dic6—41no—
295Dic6—121no—
296Dic6—121no—
297Dic6—122no—
298Dic6—241no—
299Dic6—241no—
300C3×C8—121no—
301C3⋊C8—41no—
302C3⋊C8—122no—
303C3⋊C8—121no—
304C3⋊C8—121no—
305C2×C32—21no—
306C2×C32—21no—
307C2×C32#44811yescharacteristic
308C2×C32#45611yescharacteristic
309C2×C32#45811yescharacteristic
310C2×Q8—31no—
311C2×Q8—91no—
312C2×Q8—181no—
313C22×C4—21no—
314C22×C4—31no—
315C22×C4—31no—
316C22×C4—61no—
317C22×C4C2×D3211yescharacteristic
318C2×C8—61no—
319C2×C8—181no—
320C4⋊C4—21no—
321C4⋊C4—21no—
322C4⋊C4—31no—
323C4⋊C4—61no—
324C4⋊C4—61no—
325C4⋊C4—61no—
326C4⋊C4—91no—
327C4⋊C4—122no—
328C4⋊C4—181no—
329C4⋊C4—181no—
330C4⋊C4—181no—
331C4⋊C4—181no—
332C4⋊C4—181no—
333C4⋊C4—181no—
334C22⋊C4—61no—
335C22⋊C4—181no—
336C42—181no—
337C42—181no—
338C22×C3—21no—
339C22×C3—21no—
340C22×C3—21no—
341C22×C3—21no—
342C22×C3—21no—
343C22×C3—21no—
344C22×C3—21no—
345C22×C3—41no—
346C22×C3—41no—
347C22×C3D3×SD1611yescharacteristic
348C22×C3#91511yescharacteristic
349C22×C3C2×#21411yescharacteristic
350C22×C3#93711yescharacteristic
351C22×C3#93711yescharacteristic
352C22×C3#95111yescharacteristic
353C3×C4—22no—
354C3×C4—21no—
355C3×C4—21no—
356C3×C4—21no—
357C3×C4—21no—
358C3×C4—41no—
359C3×C4—62no—
360C3×C4—82no—
361C3×C4—81no—
362C3×C4—81no—
363C3×C4—122no—
364C3×C4—121no—
365C3×C4—121no—
366C3×C4—121no—
367Dic3—22no—
368Dic3—42no—
369Dic3—41no—
370Dic3—41no—
371Dic3—41no—
372Dic3—121no—
373Dic3—121no—
374Dic3—121no—
375Dic3—121no—
376Dic3—241no—
377Dic3—241no—
378C32#161111yescharacteristic, complemented, Sylow
379C23D3×#6711yescharacteristic
380Q8—121no—
381Q8—361no—
382Q8—721no—
383C2×C4—32no—
384C2×C4—41no—
385C2×C4—41no—
386C2×C4—41no—
387C2×C4—41no—
388C2×C4—61no—
389C2×C4—61no—
390C2×C4—62no—
391C2×C4—61no—
392C2×C4—61no—
393C2×C4—61no—
394C2×C4—121no—
395C2×C4—121no—
396C2×C4—121no—
397C2×C4—181no—
398C2×C4—181no—
399C2×C4D3×#6711yescharacteristic
400C2×C4#381111yescharacteristic
401C8—121no—
402C8—361no—
403C2×C3—21no—
404C2×C3—21no—
405C2×C3—21no—
406C2×C3—21no—
407C2×C3—21no—
408C2×C3—21no—
409C2×C3—21no—
410C2×C3—41no—
411C2×C3—41no—
412C2×C3#504011yescharacteristic
413C2×C3#505311yescharacteristic
414C2×C3#505311yescharacteristic
415C2×C3#509511yescharacteristic
416C2×C3#517011yescharacteristic
417C2×C3#520511yescharacteristic
418C22—21no—
419C22—21no—
420C22D3×#21411yescharacteristic
421C22#6392911yescharacteristic
422C22#6398311yescharacteristic
423C4—21no—
424C4—21no—
425C4—62no—
426C4—81no—
427C4—122no—
428C4—121no—
429C4—121no—
430C4—121no—
431C4—361no—
432C4—361no—
433C3—21no—
434C3#6971311yescharacteristic, complemented
435C3#7117511yescharacteristic, complemented
436C2—21no—
437C2—21no—
438C2#1059139811yescharacteristic
439C2#1059151711yescharacteristic
440C2#1059166111yescharacteristic
subgroupG/H
centerC22#63983
commutator, cosocleC22×C32×C4C23
FrattiniC22×C4C2×D32
FittingC2×C32×C4⋊C4C22
socleC22×C32#120
prime radicalC23×C32C2×D4
hypercenterC2×C4⋊C4D32
hypocenterC32#1611
LCSG ▷ C22×C32×C4 ▷ C22×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C4⋊C4

Complements

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

NH ≅ G/Ntype
378. C32#1611semidirect
434. C3#69713semidirect
435. C3#71175semidirect

Maximal subgroups

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

subgroupindex
#105948122
#105926702
C3×#49832
C3×#49712
#105891542
#105891532
#105891472
#711753
#697133