Finite Group Databasebeta

← #11778372

Subgroups — #11778372

Order 1152.

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

normal subgroups only

This group has 515 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#10594813C211yesmaximal, characteristic
2C3×#4739C211yesmaximal, characteristic
3#10591346C211yesmaximal, characteristic
4#10591185C211yesmaximal, characteristic
5#10589335C211yesmaximal, characteristic
6C3×#4467C211yesmaximal, characteristic
7#10589153C211yesmaximal, characteristic
8#70983—31nomaximal
9#68327—31nomaximal
10C22×C3×Dic6C2211yescharacteristic
11C2×#3750C2211yescharacteristic
12C3×#924C2211yescharacteristic
13C3×#924C2211yescharacteristic
14C2×C3×Dic12—21no—
15#63982—21no—
16C2×Dic3⋊Dic3—21no—
17#63957—21no—
18#63847—21no—
19#63847—21no—
20#63839—21no—
21#63839—21no—
22C2×#3718—21no—
23C32×C22⋊C8C2211yescharacteristic
24#63657C2211yescharacteristic
25C3×C3⋊#95C2211yescharacteristic
26C3×#816—21no—
27#63579—21no—
28#63565—21no—
29#5623—31no—
30#5623—31no—
31C3×#451—31no—
32#5230—31no—
33#5228—31no—
34#5050—31no—
35#4739D311yescharacteristic
36#4656—31no—
37C3×#328—31no—
38#4538—31no—
39#4469—31no—
40#4469—31no—
41#4469—61no—
42#4467D311yescharacteristic
43#4452—31no—
44C22×C32×C4C2311yescharacteristic
45C22×C3⋊Dic3D411yescharacteristic
46C22×C3⋊Dic3D411yescharacteristic
47C22×C3×Dic3—21no—
48C22×C3×Dic3—21no—
49C2×C3×Dic6—21no—
50C2×C3×Dic6—21no—
51C2×C3×Dic6—42no—
52C2×C3×Dic6D411yescharacteristic
53C2×C3×Dic6D411yescharacteristic
54C2×#627—21no—
55C2×C32×C8—21no—
56#3750—21no—
57#3750—21no—
58C2×C3⋊(C3⋊C8)—21no—
59C3×#217—21no—
60C3×#217—21no—
61C3×C4⋊Dic3D411yescharacteristic
62C3×C4⋊Dic3D411yescharacteristic
63C3×Dic3⋊C4—21no—
64C3×Dic3⋊C4—21no—
65C3×Dic12—42no—
66#3724—21no—
67#3724—21no—
68#3724—21no—
69Dic3⋊Dic3—21no—
70Dic3⋊Dic3—21no—
71Dic3⋊Dic3—42no—
72Dic32—21no—
73Dic32—21no—
74#3718—42no—
75#1605—91noSylow
76C22×C3×Q8—31no—
77C22×Dic6C2×D311yescharacteristic
78C2×C3×Q16—61no—
79C3×C22⋊Q8—31no—
80C3×C22⋊Q8—31no—
81#944—61no—
82#944—61no—
83C2×#216—61no—
84C2×#216—61no—
85C2×C4⋊Dic3—61no—
86#924C2×D311yescharacteristic
87#924C2×D311yescharacteristic
88C2×Dic3⋊C4—31no—
89C2×Dic3⋊C4—31no—
90C2×Dic3⋊C4—61no—
91C2×Dic3⋊C4—61no—
92C2×Dic12—21no—
93#889—61no—
94#889—61no—
95#889—61no—
96#889—61no—
97#888—61no—
98#888—61no—
99#878—61no—
100#878—61no—
101#877—61no—
102#877—61no—
103C3×#103—61no—
104C3×C22⋊C8—21no—
105C3×C22⋊C8C2×D311yescharacteristic
106C3×C22⋊C8C2×D311yescharacteristic
107C3×#95—31no—
108#835—61no—
109C3⋊#95—61no—
110C3⋊#95—61no—
111C3⋊#95C2×D311yescharacteristic
112#830—31no—
113#830—31no—
114#830—61no—
115#816—21no—
116#810—61no—
117C23×C32C2×D411yescharacteristic
118C2×C32×C4—41no—
119C2×C32×C4C2×D411yescharacteristic
120C2×C32×C4C2×D411yescharacteristic
121C2×C3⋊Dic3—21no—
122C2×C3⋊Dic3—21no—
123C2×C3⋊Dic3—21no—
124C2×C3⋊Dic3—41no—
125C2×C3⋊Dic3Q1612yescomplemented
126C2×C3×Dic3—22no—
127C2×C3×Dic3—22no—
128C2×C3×Dic3—21no—
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×Dic3—41no—
136C3×Dic6—22no—
137C3×Dic6—22no—
138C3×Dic6—41no—
139C3×Dic6—41no—
140C3×Dic6—41no—
141C3×Dic6—41no—
142#627—81no—
143C32×C8—41no—
144C3⋊(C3⋊C8)—41no—
145#544—91no—
146#451—31no—
147#451—91no—
148#395—91no—
149#328—31no—
150#328—91no—
151#324—91no—
152C2×C3×Q8—31no—
153C2×C3×Q8—31no—
154C2×C3×Q8—61no—
155C2×C3×Q8—61no—
156C2×C3×Q8—122no—
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—
170C2×Dic6—21no—
171C2×Dic6—21no—
172C2×Dic6—42no—
173C2×Dic6—61no—
174C2×Dic6—61no—
175C2×Dic6D1211yescharacteristic
176C2×Dic6#6711yescharacteristic
177C3×Q16—122no—
178C2×C3×C8—21no—
179C2×C3×C8—21no—
180C2×C3×C8—41no—
181C3×C4⋊C4—31no—
182C3×C4⋊C4—31no—
183C3×C4⋊C4—61no—
184C3×C4⋊C4—61no—
185C3×C22⋊C4—61no—
186C3×C22⋊C4—61no—
187#217—21no—
188#217—21no—
189#216—122no—
190#216—122no—
191C4⋊Dic3—61no—
192C4⋊Dic3—61no—
193C4⋊Dic3—122no—
194C4⋊Dic3D1211yescharacteristic
195C4⋊Dic3#6711yescharacteristic
196Dic3⋊C4—21no—
197Dic3⋊C4—21no—
198Dic3⋊C4—61no—
199Dic3⋊C4—61no—
200Dic3⋊C4—61no—
201Dic3⋊C4—61no—
202Dic3⋊C4—61no—
203Dic3⋊C4—61no—
204Dic3⋊C4—61no—
205Dic3⋊C4—61no—
206Dic3⋊C4—61no—
207Dic3⋊C4—61no—
208Dic3⋊C4—61no—
209Dic3⋊C4—61no—
210Dic3⋊C4—121no—
211Dic3⋊C4—121no—
212Dic3⋊C4—122no—
213C4×Dic3—61no—
214C4×Dic3—61no—
215C4×Dic3—61no—
216C4×Dic3—61no—
217C2×C3⋊C8—61no—
218C2×C3⋊C8—61no—
219C2×C3⋊C8—121no—
220Dic12—42no—
221C22×C32—21no—
222C22×C32—21no—
223C22×C32#12011yescharacteristic
224C22×C32C2×Q1611yescharacteristic
225C22×C32#13711yescharacteristic
226C32×C4—21no—
227C32×C4—21no—
228C3⋊Dic3—22no—
229C3⋊Dic3—41no—
230C3×Dic3—42no—
231C3×Dic3—41no—
232C3×Dic3—41no—
233C3×Dic3—41no—
234C3×Dic3—41no—
235C3×Dic3—42no—
236C22×Q8—31no—
237C2×Q16—61no—
238C2×Q16—181no—
239C4⋊Q8—181no—
240C4⋊Q8—181no—
241#125—181no—
242#125—181no—
243C22⋊Q8—31no—
244C22⋊Q8—31no—
245C22⋊Q8—181no—
246#117—181no—
247C2×C4⋊C4—91no—
248C2×C4⋊C4—181no—
249#103—61no—
250#103—181no—
251C22⋊C8—91no—
252C22⋊C8D3211yescharacteristic
253#95—31no—
254#95—181no—
255C23×C3—21no—
256C23×C3D3×D411yescharacteristic
257C23×C3D3×D411yescharacteristic
258C3×Q8—62no—
259C3×Q8—62no—
260C3×Q8—121no—
261C3×Q8—121no—
262C3×Q8—121no—
263C3×Q8—121no—
264C2×C3×C4—21no—
265C2×C3×C4—21no—
266C2×C3×C4—41no—
267C2×C3×C4—41no—
268C2×C3×C4—62no—
269C2×C3×C4—62no—
270C2×C3×C4—61no—
271C2×C3×C4—61no—
272C2×C3×C4—61no—
273C2×C3×C4—61no—
274C2×C3×C4—81no—
275C2×C3×C4—121no—
276C2×C3×C4—121no—
277C2×C3×C4—121no—
278C2×C3×C4—121no—
279C2×C3×C4C2×D1211yescharacteristic
280C2×C3×C4D3×D411yescharacteristic
281C2×C3×C4D3×D411yescharacteristic
282C2×C3×C4C2×#6711yescharacteristic
283C2×Dic3—22no—
284C2×Dic3—22no—
285C2×Dic3—21no—
286C2×Dic3—21no—
287C2×Dic3—21no—
288C2×Dic3—21no—
289C2×Dic3—32no—
290C2×Dic3—32no—
291C2×Dic3—41no—
292C2×Dic3—41no—
293C2×Dic3—41no—
294C2×Dic3—41no—
295C2×Dic3—62no—
296C2×Dic3—61no—
297C2×Dic3—61no—
298C2×Dic3—61no—
299C2×Dic3—61no—
300C2×Dic3—61no—
301C2×Dic3—61no—
302C2×Dic3—121no—
303C2×Dic3—121no—
304C2×Dic3—121no—
305C2×Dic3—121no—
306C2×Dic3—121no—
307C2×Dic3—241no—
308Dic6—22no—
309Dic6—22no—
310Dic6—41no—
311Dic6—41no—
312Dic6—41no—
313Dic6—41no—
314Dic6—241no—
315Dic6—241no—
316C3×C8—41no—
317C3×C8—41no—
318C3×C8—81no—
319C3⋊C8—121no—
320C3⋊C8—121no—
321C3⋊C8—241no—
322C2×C32—21no—
323C2×C32—21no—
324C2×C32#45111yescharacteristic
325C2×C32#45611yescharacteristic
326C2×C32B(4,𝔽2)11yescharacteristic
327C2×Q8—31no—
328C2×Q8—31no—
329C2×Q8—61no—
330C2×Q8—61no—
331C2×Q8—122no—
332C2×Q8—181no—
333C22×C4—61no—
334C22×C4—61no—
335C22×C4—91no—
336C22×C4—91no—
337C22×C4C2×D3211yescharacteristic
338Q16—122no—
339Q16—362no—
340C2×C8—21no—
341C2×C8—181no—
342C4⋊C4—31no—
343C4⋊C4—31no—
344C4⋊C4—61no—
345C4⋊C4—61no—
346C4⋊C4—181no—
347C4⋊C4—181no—
348C4⋊C4—181no—
349C4⋊C4—181no—
350C4⋊C4—181no—
351C4⋊C4—181no—
352C4⋊C4—181no—
353C4⋊C4—362no—
354C22⋊C4—61no—
355C22⋊C4—61no—
356C42—181no—
357C42—181no—
358C22×C3—21no—
359C22×C3—21no—
360C22×C3—21no—
361C22×C3—21no—
362C22×C3—21no—
363C22×C3—21no—
364C22×C3—21no—
365C22×C3—41no—
366C22×C3—41no—
367C22×C3#88211yescharacteristic
368C22×C3#91511yescharacteristic
369C22×C3D3×Q1611yescharacteristic
370C22×C3D3×Q1611yescharacteristic
371C22×C3#91811yescharacteristic
372C22×C3#93711yescharacteristic
373C3×C4—21no—
374C3×C4—21no—
375C3×C4—21no—
376C3×C4—21no—
377C3×C4—41no—
378C3×C4—41no—
379C3×C4—122no—
380C3×C4—121no—
381C3×C4—121no—
382C3×C4—122no—
383C3×C4—121no—
384C3×C4—121no—
385Dic3—42no—
386Dic3—41no—
387Dic3—41no—
388Dic3—42no—
389Dic3—41no—
390Dic3—41no—
391Dic3—62no—
392Dic3—62no—
393Dic3—122no—
394Dic3—121no—
395Dic3—121no—
396Dic3—241no—
397C32#160511yescharacteristic, complemented, Sylow
398C23#380211yescharacteristic
399Q8—62no—
400Q8—62no—
401Q8—121no—
402Q8—121no—
403Q8—121no—
404Q8—121no—
405Q8—721no—
406C2×C4—41no—
407C2×C4—62no—
408C2×C4—62no—
409C2×C4—61no—
410C2×C4—61no—
411C2×C4—61no—
412C2×C4—61no—
413C2×C4—92no—
414C2×C4—121no—
415C2×C4—121no—
416C2×C4—121no—
417C2×C4—121no—
418C2×C4—181no—
419C2×C4—181no—
420C2×C4—181no—
421C2×C4—361no—
422C2×C4D3×D1211yescharacteristic
423C2×C4D3×#6711yescharacteristic
424C8—41no—
425C8—361no—
426C2×C3—21no—
427C2×C3—21no—
428C2×C3—21no—
429C2×C3—21no—
430C2×C3—21no—
431C2×C3—21no—
432C2×C3—21no—
433C2×C3—41no—
434C2×C3—41no—
435C2×C3#474111yescharacteristic
436C2×C3#480911yescharacteristic
437C2×C3#482611yescharacteristic
438C2×C3#503211yescharacteristic
439C2×C3#518611yescharacteristic
440C2×C3#520511yescharacteristic
441C22—21no—
442C22—21no—
443C22#6380211yescharacteristic
444C22#6381111yescharacteristic
445C22#6392211yescharacteristic
446C4—21no—
447C4—21no—
448C4—122no—
449C4—121no—
450C4—121no—
451C4—122no—
452C4—121no—
453C4—121no—
454C4—182no—
455C4—361no—
456C3—21no—
457C3#6832711yescharacteristic, complemented
458C3#7098311yescharacteristic, complemented
459C2—21no—
460C2—21no—
461C2#1059040711yescharacteristic
462C2#1059095011yescharacteristic
463C2#1059101711yescharacteristic
subgroupG/H
centerC22#63922
commutator, cosocleC22×C32×C4C23
FrattiniC22×C4C2×D32
FittingC32×C22⋊C8C22
socleC22×C32#120
prime radicalC23×C32C2×D4
hypercenterC22⋊C8D32
hypocenterC32#1605
LCSG ▷ C22×C32×C4 ▷ C22×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22⋊C8

Complements

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

NH ≅ G/Ntype
125. C2×C3⋊Dic3Q16semidirect
397. C32#1605semidirect
457. C3#68327semidirect
458. C3#70983semidirect

Maximal subgroups

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

subgroupindex
#105948132
C3×#47392
#105913462
#105911852
#105893352
C3×#44672
#105891532
#709833
#683273