Finite Group Databasebeta

← #11920411

Subgroups — #11920411

Order 1152.

544 conjugacy classes of subgroups; only the 56 normal subgroups are shown.

normal subgroups only

This group has 544 conjugacy classes of subgroups — too many to draw. Only its 56 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#41×C22⋊C9C211yesmaximal, characteristic
2C2×(C22⋊C9)⋊Q8C211yesmaximal, characteristic, complemented
3#10589518C212yesmaximal, complemented
4#10589516C212yesmaximal, complemented
5#10589511C211yesmaximal, characteristic, complemented
6#84084—31nomaximal
7Q8×C22⋊C9C2211yescharacteristic
8D4×C22⋊C9—21no—
9D4×C22⋊C9C2211yescharacteristic
10C2×C4×C22⋊C9—21no—
11C2×C4×C22⋊C9C2211yescharacteristic
12C2×(C22⋊C9)⋊C4—21no—
13(C22⋊C9)⋊Q8—21no—
14(C22⋊C9)⋊Q8C2212yes—
15#63511—41nomaximal
16(C22⋊C9)⋊C8C2212yes—
17C22×C3×#41D311yescharacteristic
18C2×#951—31no—
19C2×#951—31no—
20C2×#924—31no—
21#5239—32no—
22#5239—32no—
23#5232—31no—
24#5232—31no—
25#5228—32no—
26#5218—32no—
27#5207—31no—
28C22×C22⋊C9—21no—
29C22×C22⋊C9D411yescharacteristic
30C9×#41—41no—
31C2×Dic18—41no—
32C4×C22⋊C9—21no—
33C4×C22⋊C9D411yescharacteristic
34C4×C22⋊C9C2311yescharacteristic
35(C22⋊C9)⋊C4—22no—
36#3674—42no—
37#3672—42no—
38#3667—41no—
39#3007—91noSylow
40C2×C3×#41—31no—
41C2×C3×#41—31no—
42C2×C3×#41—31no—
43C2×C3×#41—31no—
44C2×C3×#41—61no—
45C2×C3×#41—61no—
46C22×C3×Q8C2×D311yescharacteristic
47C22×C3×D4—21no—
48C22×C3×D4C2×D311yescharacteristic
49C23×C3×C4—21no—
50C23×C3×C4C2×D311yescharacteristic
51C22×Dic6—31no—
52C2×#217—61no—
53#951—62no—
54#951—62no—
55#951—61no—
56#951—61no—
57#951—61no—
58#951—61no—
59C2×#216—32no—
60C2×#216—32no—
61C2×#214—32no—
62C2×#214—32no—
63C2×C4⋊Dic3—31no—
64#924—32no—
65#924—32no—
66#924—61no—
67#924—61no—
68C2×Dic3⋊C4—61no—
69C2×#208—31no—
70C2×#208—31no—
71#835—32no—
72#835—32no—
73#832—32no—
74#832—32no—
75#830—32no—
76#830—32no—
77C2×C22⋊C9—21no—
78C2×C22⋊C9—41no—
79C2×C22⋊C9C2×D411yescharacteristic
80Q8×C9—41no—
81D4×C9—41no—
82D4×C9—81no—
83C2×C4×C9—41no—
84C2×C4×C9—81no—
85C2×Dic9—81no—
86Dic18—42no—
87Dic18—81no—
88C9⋊C8—42no—
89C22×#41D911yescharacteristic
90C2×#137—91no—
91C2×#137—91no—
92C2×C22⋊Q8—91no—
93#452—92no—
94#452—92no—
95#451—92no—
96#450—92no—
97#417—91no—
98#417—91no—
99#407—91no—
100C24×C3—21no—
101C24×C3#6711yescharacteristic
102C3×#41—32no—
103C3×#41—32no—
104C3×#41—31no—
105C3×#41—31no—
106C3×#41—31no—
107C3×#41—61no—
108C3×#41—61no—
109C3×#41—61no—
110C3×#41—62no—
111C3×#41—62no—
112C3×#41S411yescharacteristic
113C2×C3×Q8—31no—
114C2×C3×Q8—31no—
115C2×C3×Q8—61no—
116C2×C3×D4—31no—
117C2×C3×D4—31no—
118C2×C3×D4—61no—
119C2×C3×D4—61no—
120C2×C3×D4—61no—
121C2×C3×D4—61no—
122C2×C3×D4—61no—
123C22×C3×C4—21no—
124C22×C3×C4—31no—
125C22×C3×C4—31no—
126C22×C3×C4—31no—
127C22×C3×C4—31no—
128C22×C3×C4—61no—
129C22×C3×C4—61no—
130C22×C3×C4—61no—
131C22×C3×C4—61no—
132C22×C3×C4#6711yescharacteristic
133C22×C3×C4C22×D311yescharacteristic
134C22×Dic3—61no—
135C22×Dic3—61no—
136C2×Dic6—32no—
137C2×Dic6—61no—
138C2×Dic6—61no—
139C2×Dic6—61no—
140C2×Dic6—61no—
141C2×Dic6—61no—
142#217—62no—
143#217—62no—
144#216—64no—
145#216—62no—
146#216—62no—
147#214—64no—
148#214—62no—
149#214—62no—
150C4⋊Dic3—32no—
151C4⋊Dic3—61no—
152Dic3⋊C4—62no—
153Dic3⋊C4—62no—
154#208—61no—
155#208—61no—
156#208—61no—
157#208—61no—
158C2×C3⋊C8—32no—
159C2×C3⋊C8—32no—
160C22×C9—41no—
161C22×C9—81no—
162C22⋊C9#13711yescharacteristic, complemented
163C4×C9—41no—
164C4×C9—41no—
165C4×C9—81no—
166Dic9—82no—
167C2×#41—31no—
168C2×#41—31no—
169C2×#41—31no—
170C2×#41—31no—
171C2×#41—61no—
172C2×#41—61no—
173C22×Q8—91no—
174C22×Q8C2×D911yescharacteristic
175C22×D4—21no—
176C22×D4C2×D911yescharacteristic
177C23×C4—21no—
178C23×C4C2×D911yescharacteristic
179#137—182no—
180#137—182no—
181#137—181no—
182#137—181no—
183#137—181no—
184#137—181no—
185C2×Q16—92no—
186C2×Q16—92no—
187C2×SD16—92no—
188C2×SD16—92no—
189C2×M16—91no—
190C2×M16—91no—
191C22⋊Q8—92no—
192C22⋊Q8—92no—
193C22⋊Q8—181no—
194C22⋊Q8—181no—
195C2×C4⋊C4—91no—
196C2×C4⋊C4—181no—
197C2×C22⋊C4—181no—
198#103—92no—
199#103—92no—
200#102—92no—
201#102—92no—
202C22⋊C8—92no—
203C22⋊C8—92no—
204C23×C3—21no—
205C23×C3—31no—
206C23×C3—31no—
207C23×C3—41no—
208C23×C3—61no—
209C23×C3—61no—
210C23×C3—61no—
211C23×C3—121no—
212C23×C3C2×#6711yescharacteristic
213C3×Q8—32no—
214C3×Q8—31no—
215C3×Q8—61no—
216C3×Q8C2×S411yescharacteristic
217C3×D4—21no—
218C3×D4—32no—
219C3×D4—31no—
220C3×D4—61no—
221C3×D4—61no—
222C3×D4—61no—
223C3×D4—62no—
224C3×D4—61no—
225C3×D4C2×S411yescharacteristic
226C2×C3×C4—21no—
227C2×C3×C4—31no—
228C2×C3×C4—31no—
229C2×C3×C4—31no—
230C2×C3×C4—31no—
231C2×C3×C4—31no—
232C2×C3×C4—31no—
233C2×C3×C4—31no—
234C2×C3×C4—61no—
235C2×C3×C4—61no—
236C2×C3×C4—61no—
237C2×C3×C4—61no—
238C2×C3×C4—62no—
239C2×C3×C4—61no—
240C2×C3×C4—61no—
241C2×C3×C4C2×S411yescharacteristic
242C2×Dic3—62no—
243C2×Dic3—62no—
244C2×Dic3—121no—
245C2×Dic3—122no—
246C2×Dic3—121no—
247Dic6—62no—
248Dic6—62no—
249Dic6—121no—
250Dic6—121no—
251C3⋊C8—62no—
252C3⋊C8—62no—
253C2×C9—41no—
254C2×C9—81no—
255C2×C9—161no—
256C24—21no—
257C24#61111yescharacteristic
258#41—32no—
259#41—32no—
260#41—31no—
261#41—31no—
262#41—31no—
263#41—61no—
264#41—61no—
265#41—61no—
266#41—62no—
267#41—62no—
268#41(C22⋊C9)⋊C211yescharacteristic
269C2×Q8—31no—
270C2×Q8—31no—
271C2×Q8—61no—
272C2×Q8—92no—
273C2×Q8—181no—
274C2×Q8—181no—
275C2×Q8—181no—
276C2×Q8—181no—
277C2×Q8—181no—
278C2×D4—31no—
279C2×D4—31no—
280C2×D4—61no—
281C2×D4—61no—
282C2×D4—61no—
283C2×D4—61no—
284C2×D4—61no—
285C22×C4—21no—
286C22×C4—31no—
287C22×C4—31no—
288C22×C4—31no—
289C22×C4—31no—
290C22×C4—61no—
291C22×C4—61no—
292C22×C4—61no—
293C22×C4—61no—
294C22×C4—181no—
295C22×C4—181no—
296C22×C4#61111yescharacteristic
297C22×C4C22×D911yescharacteristic
298Q16—184no—
299Q16—182no—
300Q16—182no—
301SD16—184no—
302SD16—182no—
303SD16—182no—
304M16—181no—
305M16—181no—
306M16—181no—
307M16—181no—
308C2×C8—92no—
309C2×C8—92no—
310C4⋊C4—92no—
311C4⋊C4—181no—
312C4⋊C4—182no—
313C4⋊C4—182no—
314C22⋊C4—182no—
315C22⋊C4—182no—
316C22×C3—21no—
317C22×C3—31no—
318C22×C3—31no—
319C22×C3—31no—
320C22×C3—61no—
321C22×C3—61no—
322C22×C3—61no—
323C22×C3—61no—
324C22×C3—61no—
325C22×C3—121no—
326C22×C3—121no—
327C22×C3—121no—
328C22×C3—121no—
329C22×C3#95111yescharacteristic
330C22×C3GL(2,ℤ/4)11yescharacteristic
331C3×C4—21no—
332C3×C4—31no—
333C3×C4—31no—
334C3×C4—61no—
335C3×C4GL(2,ℤ/4)11yescharacteristic
336C3×C4C22×S411yescharacteristic
337Dic3—122no—
338Dic3—122no—
339C9—41noSylow
340C23—21no—
341C23—31no—
342C23—31no—
343C23—41no—
344C23—61no—
345C23—61no—
346C23—61no—
347C23—121no—
348C23C2×#61111yescharacteristic
349Q8—32no—
350Q8—31no—
351Q8—61no—
352Q8—182no—
353Q8—182no—
354Q8—361no—
355Q8—361no—
356Q8C2×(C22⋊C9)⋊C211yescharacteristic
357D4—21no—
358D4—32no—
359D4—31no—
360D4—61no—
361D4—61no—
362D4—61no—
363D4—62no—
364D4—61no—
365D4C2×(C22⋊C9)⋊C211yescharacteristic
366C2×C4—21no—
367C2×C4—31no—
368C2×C4—31no—
369C2×C4—31no—
370C2×C4—31no—
371C2×C4—31no—
372C2×C4—31no—
373C2×C4—31no—
374C2×C4—61no—
375C2×C4—61no—
376C2×C4—61no—
377C2×C4—61no—
378C2×C4—62no—
379C2×C4—61no—
380C2×C4—61no—
381C2×C4—182no—
382C2×C4—182no—
383C2×C4—361no—
384C2×C4—362no—
385C2×C4—361no—
386C2×C4C2×(C22⋊C9)⋊C211yescharacteristic
387C8—182no—
388C8—182no—
389C2×C3—21no—
390C2×C3—31no—
391C2×C3—31no—
392C2×C3—41no—
393C2×C3—61no—
394C2×C3—121no—
395C2×C3C2×GL(2,ℤ/4)11yescharacteristic
396C22—21no—
397C22—31no—
398C22—31no—
399C22—31no—
400C22—61no—
401C22—61no—
402C22—61no—
403C22—61no—
404C22—61no—
405C22—121no—
406C22—121no—
407C22—121no—
408C22—121no—
409C22#6351111yescharacteristic, complemented
410C22#6369411yescharacteristic
411C4—21no—
412C4—31no—
413C4—31no—
414C4—61no—
415C4—362no—
416C4—362no—
417C4#6369411yescharacteristic
418C4C22×(C22⋊C9)⋊C211yescharacteristic
419C3#8551211yescharacteristic
420C2—21no—
421C2—31no—
422C2—31no—
423C2—41no—
424C2—61no—
425C2—121no—
426C2C2×#6369411yescharacteristic
subgroupG/H
centerC2C2×#63694
commutator, cosocleC4×C22⋊C9C23
FrattiniC3×C4C22×S4
Fitting, prime radicalC22×C3×#41D3
socleC23×C3C2×#67
hypercenter#41(C22⋊C9)⋊C2
hypocenterC22⋊C9#137
LCSG ▷ C4×C22⋊C9 ▷ C2×C22⋊C9 ▷ C22⋊C9
UCSC1 ◁ C2 ◁ C2×C4 ◁ #41

Complements

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

NH ≅ G/Ntype
2. C2×(C22⋊C9)⋊Q8C2semidirect
3. #10589518C2semidirect
4. #10589516C2semidirect
5. #10589511C2semidirect
162. C22⋊C9#137semidirect
409. C22#63511semidirect

Maximal subgroups

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

subgroupindex
#41×C22⋊C92
C2×(C22⋊C9)⋊Q82
#105895182
#105895162
#105895112
#840843
#635114