Finite Group Databasebeta

← #11778367

Subgroups — #11778367

Order 1152.

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

normal subgroups only

This group has 516 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×#5050C211yesmaximal, characteristic
3#10591344C211yesmaximal, characteristic
4#10591185C211yesmaximal, characteristic
5#10589404C211yesmaximal, characteristic
6#10589152C211yesmaximal, characteristic
7#10589147C211yesmaximal, characteristic
8#71904—31nomaximal
9#70983—31nomaximal
10C22×C3×Dic6C2211yescharacteristic
11C32×C22⋊Q8C2211yescharacteristic
12C3×#944—21no—
13C2×C3×#216—21no—
14C3×#924C2211yescharacteristic
15C2×C3×Dic3⋊C4C2211yescharacteristic
16C3×#889—21no—
17C3×#889—21no—
18C3×#888—21no—
19C3×#878—21no—
20C3×#877—21no—
21C2×#3724—21no—
22C2×#3718—21no—
23#63658C2211yescharacteristic
24#63657C2211yescharacteristic
25C3×#830C2211yescharacteristic
26C3×#810—21no—
27#63579—21no—
28#63565—21no—
29C3×#544—31no—
30#5623D311yescharacteristic
31C3×#451—31no—
32#5230—31no—
33#5228—31no—
34#5050—31no—
35#5050D311yescharacteristic
36#4979—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×Dic6—21no—
52C2×C3×Dic6—21no—
53C2×C3×Dic6—42no—
54C2×C3×Dic6D411yescharacteristic
55C32×C4⋊C4—21no—
56C32×C4⋊C4D411yescharacteristic
57C32×C22⋊C4—21no—
58C2×C3⋊(C3⋊C8)—21no—
59C3×#217—21no—
60C3×#216—42no—
61C3×C4⋊Dic3—21no—
62C3×C4⋊Dic3D411yescharacteristic
63C3×Dic3⋊C4—21no—
64C3×Dic3⋊C4—21no—
65C3×Dic3⋊C4—21no—
66C3×Dic3⋊C4—21no—
67C3×Dic3⋊C4—21no—
68C3×Dic3⋊C4—21no—
69C3×Dic3⋊C4—21no—
70C3×C4×Dic3—21no—
71C3×C4×Dic3—21no—
72C2×C3×C3⋊C8—21no—
73#3724—42no—
74#3718—42no—
75#1605—91noSylow
76C22×C3×Q8—31no—
77C22×Dic6C2×D311yescharacteristic
78C2×C3×Q16—61no—
79C3×C4⋊Q8—61no—
80C3×C4⋊Q8—61no—
81C3×#125—61no—
82C3×#125—61no—
83C3×C22⋊Q8—21no—
84C3×C22⋊Q8—31no—
85C3×C22⋊Q8—61no—
86C3×C22⋊Q8C2×D311yescharacteristic
87C3×C22⋊Q8C2×D311yescharacteristic
88C3×#117—61no—
89C2×C3×C4⋊C4—31no—
90#944—21no—
91C2×#216—21no—
92C2×#216—61no—
93C2×#216—61no—
94#924C2×D311yescharacteristic
95C2×Dic3⋊C4—61no—
96C2×Dic3⋊C4—61no—
97C2×Dic3⋊C4C2×D311yescharacteristic
98#889—21no—
99#889—21no—
100#888—21no—
101#878—21no—
102#877—21no—
103C3×#103—61no—
104C3×C22⋊C8—31no—
105#835—61no—
106C3⋊#95—31no—
107C3⋊#95—31no—
108C3⋊#95—61no—
109C3⋊#95—61no—
110C3⋊#95—61no—
111#830—31no—
112#830—31no—
113#830—61no—
114#830C2×D311yescharacteristic
115#810—21no—
116#810—61no—
117C23×C32C2×D411yescharacteristic
118C32×Q8—41no—
119C2×C32×C4—21no—
120C2×C32×C4—21no—
121C2×C32×C4—41no—
122C2×C32×C4C2×D411yescharacteristic
123C2×C32×C4C2×D411yescharacteristic
124C2×C3⋊Dic3—22no—
125C2×C3⋊Dic3—41no—
126C2×C3⋊Dic3—41no—
127C2×C3×Dic3—21no—
128C2×C3×Dic3—21no—
129C2×C3×Dic3—22no—
130C2×C3×Dic3—21no—
131C2×C3×Dic3—21no—
132C2×C3×Dic3—21no—
133C2×C3×Dic3—41no—
134C2×C3×Dic3—41no—
135C2×C3×Dic3—41no—
136C2×C3×Dic3Q1612yescomplemented
137C3×Dic6—22no—
138C3×Dic6—22no—
139C3×Dic6—41no—
140C3×Dic6—41no—
141C3×Dic6—41no—
142C3×Dic6—81no—
143C3⋊(C3⋊C8)—41no—
144C3×C3⋊C8—41no—
145#544—31no—
146#451—31no—
147#451—91no—
148#395—91no—
149#328—91no—
150#328—91no—
151#324—91no—
152C2×C3×Q8—21no—
153C2×C3×Q8—31no—
154C2×C3×Q8—61no—
155C2×C3×Q8—61no—
156C2×C3×Q8—61no—
157C2×C3×Q8—122no—
158C2×C3×Q8#6711yescharacteristic
159C2×C3×Q8#6711yescharacteristic
160C22×C3×C4—21no—
161C22×C3×C4—31no—
162C22×C3×C4—31no—
163C22×C3×C4—61no—
164C22×C3×C4C22×D311yescharacteristic
165C22×C3×C4C22×D311yescharacteristic
166C22×Dic3—21no—
167C22×Dic3—61no—
168C22×Dic3—61no—
169C22×Dic3—121no—
170C22×Dic3#6711yescharacteristic
171C22×Dic3#6711yescharacteristic
172C2×Dic6—21no—
173C2×Dic6—21no—
174C2×Dic6—21no—
175C2×Dic6—42no—
176C2×Dic6#6711yescharacteristic
177C3×Q16—122no—
178C2×C3×C8—61no—
179C3×C4⋊C4—21no—
180C3×C4⋊C4—21no—
181C3×C4⋊C4—21no—
182C3×C4⋊C4—31no—
183C3×C4⋊C4—41no—
184C3×C4⋊C4—61no—
185C3×C4⋊C4—61no—
186C3×C4⋊C4—61no—
187C3×C4⋊C4—61no—
188C3×C4⋊C4—61no—
189C3×C4⋊C4—61no—
190C3×C4⋊C4—61no—
191C3×C4⋊C4—61no—
192C3×C4⋊C4#6711yescharacteristic
193C3×C4⋊C4#6711yescharacteristic
194C3×C22⋊C4—21no—
195C3×C22⋊C4—21no—
196C3×C22⋊C4—41no—
197C3×C22⋊C4—61no—
198C3×C42—61no—
199C3×C42—61no—
200#217—21no—
201#216—42no—
202#216—122no—
203#216—122no—
204C4⋊Dic3—21no—
205C4⋊Dic3#6711yescharacteristic
206Dic3⋊C4—21no—
207Dic3⋊C4—21no—
208Dic3⋊C4—21no—
209Dic3⋊C4—21no—
210Dic3⋊C4—21no—
211Dic3⋊C4—21no—
212Dic3⋊C4—21no—
213Dic3⋊C4—122no—
214Dic3⋊C4—122no—
215C4×Dic3—21no—
216C4×Dic3—21no—
217C2×C3⋊C8—21no—
218C2×C3⋊C8—61no—
219C2×C3⋊C8—61no—
220C2×C3⋊C8—121no—
221C22×C32—21no—
222C22×C32—21no—
223C22×C32#12011yescharacteristic
224C22×C32C2×Q1611yescharacteristic
225C22×C32#13711yescharacteristic
226C32×C4—21no—
227C32×C4—21no—
228C32×C4—41no—
229C32×C4—41no—
230C3⋊Dic3—42no—
231C3×Dic3—22no—
232C3×Dic3—41no—
233C3×Dic3—42no—
234C3×Dic3—41no—
235C3×Dic3—41no—
236C22×Q8—31no—
237C2×Q16—61no—
238C2×Q16—181no—
239C4⋊Q8—61no—
240C4⋊Q8—61no—
241#125—61no—
242#125—61no—
243C22⋊Q8—31no—
244C22⋊Q8—61no—
245C22⋊Q8D3211yescharacteristic
246#117—61no—
247C2×C4⋊C4—31no—
248C2×C4⋊C4—181no—
249#103—61no—
250#103—181no—
251C22⋊C8—31no—
252C22⋊C8—91no—
253#95—91no—
254#95—181no—
255C23×C3—21no—
256C23×C3D3×D411yescharacteristic
257C23×C3C2×#6711yescharacteristic
258C3×Q8—41no—
259C3×Q8—41no—
260C3×Q8—62no—
261C3×Q8—62no—
262C3×Q8—81no—
263C3×Q8—121no—
264C3×Q8—121no—
265C3×Q8—121no—
266C3×Q8—241no—
267C2×C3×C4—21no—
268C2×C3×C4—21no—
269C2×C3×C4—21no—
270C2×C3×C4—21no—
271C2×C3×C4—21no—
272C2×C3×C4—21no—
273C2×C3×C4—32no—
274C2×C3×C4—41no—
275C2×C3×C4—41no—
276C2×C3×C4—41no—
277C2×C3×C4—41no—
278C2×C3×C4—61no—
279C2×C3×C4—61no—
280C2×C3×C4—62no—
281C2×C3×C4—61no—
282C2×C3×C4—61no—
283C2×C3×C4—61no—
284C2×C3×C4—81no—
285C2×C3×C4—121no—
286C2×C3×C4—121no—
287C2×C3×C4—121no—
288C2×C3×C4D3×D411yescharacteristic
289C2×C3×C4C2×#6711yescharacteristic
290C2×C3×C4C2×#6711yescharacteristic
291C2×C3×C4C2×#6711yescharacteristic
292C2×Dic3—21no—
293C2×Dic3—21no—
294C2×Dic3—22no—
295C2×Dic3—21no—
296C2×Dic3—21no—
297C2×Dic3—21no—
298C2×Dic3—41no—
299C2×Dic3—41no—
300C2×Dic3—41no—
301C2×Dic3—62no—
302C2×Dic3—62no—
303C2×Dic3—122no—
304C2×Dic3—121no—
305C2×Dic3—121no—
306C2×Dic3—121no—
307C2×Dic3—121no—
308C2×Dic3—241no—
309C2×Dic3—241no—
310C2×Dic3#21612yescomplemented
311Dic6—22no—
312Dic6—22no—
313Dic6—41no—
314Dic6—41no—
315Dic6—41no—
316Dic6—81no—
317C3×C8—121no—
318C3⋊C8—41no—
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—61no—
329C2×Q8—61no—
330C2×Q8—61no—
331C2×Q8—122no—
332C2×Q8#62511yescharacteristic
333C22×C4—31no—
334C22×C4—31no—
335C22×C4—61no—
336C22×C4—181no—
337C22×C4C2×D3211yescharacteristic
338Q16—122no—
339Q16—362no—
340C2×C8—61no—
341C2×C8—181no—
342C4⋊C4—21no—
343C4⋊C4—31no—
344C4⋊C4—61no—
345C4⋊C4—61no—
346C4⋊C4—61no—
347C4⋊C4—61no—
348C4⋊C4—61no—
349C4⋊C4—61no—
350C4⋊C4—61no—
351C4⋊C4—61no—
352C4⋊C4—362no—
353C4⋊C4#62511yescharacteristic
354C22⋊C4—21no—
355C22⋊C4—61no—
356C42—61no—
357C42—61no—
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×C3D3×Q1611yescharacteristic
368C22×C3#91811yescharacteristic
369C22×C3#93711yescharacteristic
370C22×C3#94211yescharacteristic
371C22×C3C2×#21611yescharacteristic
372C22×C3#95311yescharacteristic
373C3×C4—21no—
374C3×C4—21no—
375C3×C4—21no—
376C3×C4—21no—
377C3×C4—41no—
378C3×C4—41no—
379C3×C4—41no—
380C3×C4—41no—
381C3×C4—41no—
382C3×C4—41no—
383C3×C4—62no—
384C3×C4—81no—
385C3×C4—81no—
386C3×C4—121no—
387C3×C4—122no—
388C3×C4—121no—
389C3×C4—121no—
390Dic3—22no—
391Dic3—41no—
392Dic3—41no—
393Dic3—41no—
394Dic3—42no—
395Dic3—122no—
396Dic3—122no—
397Dic3—242no—
398C32#160511yescharacteristic, complemented, Sylow
399C23D3×#6711yescharacteristic
400Q8—41no—
401Q8—62no—
402Q8—62no—
403Q8—121no—
404Q8—121no—
405Q8—121no—
406Q8—241no—
407C2×C4—21no—
408C2×C4—21no—
409C2×C4—32no—
410C2×C4—41no—
411C2×C4—61no—
412C2×C4—61no—
413C2×C4—62no—
414C2×C4—61no—
415C2×C4—61no—
416C2×C4—61no—
417C2×C4—121no—
418C2×C4—121no—
419C2×C4—121no—
420C2×C4—182no—
421C2×C4—361no—
422C2×C4—361no—
423C2×C4C2×#62511yescharacteristic
424C2×C4D3×#6711yescharacteristic
425C8—121no—
426C8—361no—
427C2×C3—21no—
428C2×C3—21no—
429C2×C3—21no—
430C2×C3—21no—
431C2×C3—21no—
432C2×C3—21no—
433C2×C3—21no—
434C2×C3—41no—
435C2×C3—41no—
436C2×C3#503211yescharacteristic
437C2×C3#518611yescharacteristic
438C2×C3#520511yescharacteristic
439C2×C3#522811yescharacteristic
440C2×C3#524411yescharacteristic
441C2×C3#524611yescharacteristic
442C22—21no—
443C22—21no—
444C22D3×#21611yescharacteristic
445C22#6394811yescharacteristic
446C22#6397611yescharacteristic
447C4—21no—
448C4—21no—
449C4—41no—
450C4—41no—
451C4—62no—
452C4—122no—
453C4—121no—
454C4—121no—
455C4—121no—
456C4—362no—
457C3—21no—
458C3#7098311yescharacteristic, complemented
459C3#7190411yescharacteristic, complemented
460C2—21no—
461C2—21no—
462C2#1059153011yescharacteristic
463C2#1059159411yescharacteristic
464C2#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#1605
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
136. C2×C3×Dic3Q16semidirect
310. C2×Dic3#216semidirect
398. C32#1605semidirect
458. C3#70983semidirect
459. C3#71904semidirect

Maximal subgroups

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

subgroupindex
C3×#56232
C3×#50502
#105913442
#105911852
#105894042
#105891522
#105891472
#719043
#709833