Finite Group Databasebeta

← #11773359

Subgroups — #11773359

Order 1152.

982 conjugacy classes of subgroups; only the 140 normal subgroups are shown.

normal subgroups only

This group has 982 conjugacy classes of subgroups — too many to draw. Only its 140 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
1C22×C4⋊#157C211yesmaximal, characteristic
2C2×C4⋊C4×C3⋊D3C211yesmaximal, characteristic
3C2×#63781C211yesmaximal, characteristic
4C2×#63781C212yesmaximal
5C2×#63781C212yesmaximal
6C23×#157C2212yes—
7C23×#157C2212yes—
8C22×C4×C3⋊D3C2211yescharacteristic
9C22×C4×C3⋊D3C2211yescharacteristic
10C22×C4×C3⋊D3C2211yescharacteristic
11C2×C4⋊#157—22no—
12C2×C4⋊#157—24no—
13C2×C32×C4⋊C4C411yescharacteristic, complemented
14C2×C4⋊(C3⋊Dic3)C411yescharacteristic, complemented
15C2×#3750C411yescharacteristic, complemented
16C2×#3750C411yescharacteristic, complemented
17C4⋊C4×C3⋊D3—22no—
18C4⋊C4×C3⋊D3—22no—
19#63781—22no—
20#63781—24no—
21#63781—24no—
22C2×D3×C4⋊C4—62no—
23C23×C3⋊D3C2311yescharacteristic
24C22×#157—22no—
25C22×#157—22no—
26C22×#157—22no—
27C22×#157—22no—
28C22×#157—22no—
29C22×#157—22no—
30C22×#157—22no—
31C22×#157—22no—
32C22×#157—22no—
33C22×#157—22no—
34C22×#157—22no—
35C22×#157—22no—
36C22×#157D414yes—
37C22×#157Q814yes—
38C22×C32×C4C2×C411yescharacteristic
39C22×C32×C4C2×C411yescharacteristic
40C22×C32×C4C2×C411yescharacteristic
41C22×C3⋊Dic3C2×C411yescharacteristic
42C22×C3⋊Dic3C2×C411yescharacteristic
43C22×C3⋊Dic3C2×C411yescharacteristic
44C2×C4×C3⋊D3—21no—
45C2×C4×C3⋊D3—21no—
46C2×C4×C3⋊D3—22no—
47C2×C4×C3⋊D3—21no—
48C2×C4×C3⋊D3—21no—
49C2×C4×C3⋊D3—22no—
50C2×C4×C3⋊D3—21no—
51C2×C4×C3⋊D3—21no—
52C2×C4×C3⋊D3—22no—
53C2×C4×C3⋊D3—22no—
54C2×C4×C3⋊D3D412yes—
55C2×C4×C3⋊D3D412yes—
56C2×C4×C3⋊D3D412yes—
57C2×C4×C3⋊D3Q812yes—
58C4⋊#157—28no—
59C32×C4⋊C4—22no—
60C4⋊(C3⋊Dic3)—22no—
61#3750—22no—
62#3750—22no—
63#1441—91nomaximal, Sylow
64C22×C4×D3—62no—
65C22×C4×D3—62no—
66C22×C4×D3—62no—
67C2×C3×C4⋊C4—22no—
68C2×C4⋊Dic3—62no—
69C2×Dic3⋊C4—62no—
70C2×Dic3⋊C4—62no—
71D3×C4⋊C4—68no—
72D3×C4⋊C4—68no—
73C23×C32C22×C411yescharacteristic
74C22×C3⋊D3C2×D412yes—
75C22×C3⋊D3C2×D411yescharacteristic
76C22×C3⋊D3C2×D411yescharacteristic
77C22×C3⋊D3C2×D411yescharacteristic
78C22×C3⋊D3C2×Q812yes—
79C22×C3⋊D3C2×Q811yescharacteristic
80C22×C3⋊D3#4111yescharacteristic
81C22×C3⋊D3#4111yescharacteristic
82C22×C3⋊D3#4112yes—
83C22×C3⋊D3#4112yes—
84C2×#157—24no—
85C2×#157—24no—
86C2×#157—24no—
87C2×#157—24no—
88C2×#157—24no—
89C2×#157—24no—
90C2×#157—42no—
91C2×#157—42no—
92C2×#157—42no—
93C2×#157—42no—
94C2×#157—42no—
95C2×#157—42no—
96C2×#157—42no—
97C2×#157—42no—
98C2×C32×C4—21no—
99C2×C32×C4—21no—
100C2×C32×C4—21no—
101C2×C32×C4—22no—
102C2×C32×C4—22no—
103C2×C32×C4C22⋊C412yes—
104C2×C32×C4C4⋊C412yescomplemented
105C2×C3⋊Dic3—21no—
106C2×C3⋊Dic3—21no—
107C2×C3⋊Dic3—21no—
108C2×C3⋊Dic3—22no—
109C2×C3⋊Dic3—22no—
110C2×C3⋊Dic3C22⋊C412yes—
111C2×C3⋊Dic3C4⋊C412yescomplemented
112C4×C3⋊D3—22no—
113C4×C3⋊D3—22no—
114C4×C3⋊D3—22no—
115C4×C3⋊D3—22no—
116C4×C3⋊D3—22no—
117C4×C3⋊D3—24no—
118C4×C3⋊D3—22no—
119C4×C3⋊D3—41no—
120C4×C3⋊D3—42no—
121C4×C3⋊D3—41no—
122C22×C4⋊C4—91no—
123C22×C4⋊C4—91no—
124C2×#95—91no—
125C2×#95—92no—
126C2×#95—92no—
127C23×D3—62no—
128C22×C3×C4—22no—
129C22×C3×C4—22no—
130C22×C3×C4—22no—
131C22×Dic3—62no—
132C22×Dic3—62no—
133C22×Dic3—62no—
134C2×C4×D3—64no—
135C2×C4×D3—64no—
136C2×C4×D3—64no—
137C2×C4×D3—64no—
138C2×C4×D3—64no—
139C2×C4×D3—64no—
140C2×C4×D3—64no—
141C2×C4×D3—64no—
142C2×C4×D3—64no—
143C2×C4×D3—64no—
144C2×C4×D3—124no—
145C2×C4×D3—124no—
146C2×C4×D3—124no—
147C2×C4×D3—124no—
148C3×C4⋊C4—28no—
149C4⋊Dic3—68no—
150Dic3⋊C4—68no—
151Dic3⋊C4—68no—
152C22×C32C2×C22⋊C411yescharacteristic
153C22×C32C2×C4⋊C411yescharacteristic
154C22×C32#11711yescharacteristic
155C22×C32C4×D412yes—
156C22×C32C4×Q812yes—
157C2×C3⋊D3#12011yescharacteristic
158C2×C3⋊D3#12112yes—
159C2×C3⋊D3#12111yescharacteristic
160C2×C3⋊D3#12111yescharacteristic
161C2×C3⋊D3#12112yes—
162C2×C3⋊D3C22⋊Q812yes—
163C2×C3⋊D3C22⋊Q811yescharacteristic
164C2×C3⋊D3C22⋊Q812yes—
165C2×C3⋊D3C22⋊Q812yes—
166C2×C3⋊D3C22⋊Q811yescharacteristic
167C2×C3⋊D3#12312yes—
168C2×C3⋊D3#12311yescharacteristic
169C2×C3⋊D3#12411yescharacteristic
170C2×C3⋊D3#12512yes—
171C2×C3⋊D3#12512yes—
172C2×C3⋊D3#12612yes—
173C2×C3⋊D3C4⋊Q812yes—
174C2×C3⋊D3C4⋊Q811yescharacteristic
175#157—44no—
176#157—44no—
177C32×C4—22no—
178C32×C4—22no—
179C32×C4—41no—
180C3⋊Dic3—22no—
181C3⋊Dic3—22no—
182C3⋊Dic3—41no—
183C23×C4—91no—
184C23×C4—91no—
185C23×C4—92no—
186C23×C4—92no—
187C23×C4—91no—
188C2×C4⋊C4—91no—
189C2×C4⋊C4—91no—
190C2×C4⋊C4—91no—
191C2×C4⋊C4—182no—
192C2×C4⋊C4—182no—
193C2×C4⋊C4—182no—
194C2×C4⋊C4—184no—
195C2×C4⋊C4#15711yescharacteristic, complemented
196#95—184no—
197#95—182no—
198#95—184no—
199C23×C3—22no—
200C22×D3—62no—
201C22×D3—62no—
202C22×D3—62no—
203C22×D3—64no—
204C22×D3—62no—
205C22×D3—64no—
206C22×D3—62no—
207C22×D3—62no—
208C22×D3—64no—
209C22×D3—64no—
210C2×C3×C4—24no—
211C2×C3×C4—24no—
212C2×C3×C4—24no—
213C2×C3×C4—24no—
214C2×C3×C4—24no—
215C2×C3×C4—44no—
216C2×C3×C4—44no—
217C2×Dic3—64no—
218C2×Dic3—64no—
219C2×Dic3—64no—
220C2×Dic3—64no—
221C2×Dic3—64no—
222C2×Dic3—124no—
223C2×Dic3—124no—
224C4×D3—68no—
225C4×D3—68no—
226C4×D3—68no—
227C4×D3—68no—
228C4×D3—124no—
229C4×D3—128no—
230C4×D3—124no—
231C4×D3—124no—
232C4×D3—128no—
233C4×D3—124no—
234C2×C32#38011yescharacteristic
235C2×C32#38611yescharacteristic
236C2×C32#38712yes—
237C2×C32#38912yes—
238C2×C32#39111yescharacteristic
239C3⋊D3#39411yescharacteristic
240C3⋊D3#39511yescharacteristic
241C3⋊D3#39612yes—
242C3⋊D3#39811yescharacteristic
243C3⋊D3#39812yes—
244C3⋊D3#40011yescharacteristic
245C24—91no—
246C22×C4—91no—
247C22×C4—91no—
248C22×C4—92no—
249C22×C4—92no—
250C22×C4—92no—
251C22×C4—92no—
252C22×C4—94no—
253C22×C4—94no—
254C22×C4—91no—
255C22×C4—181no—
256C22×C4—181no—
257C22×C4—182no—
258C22×C4—181no—
259C22×C4—181no—
260C22×C4—182no—
261C22×C4—182no—
262C22×C4—181no—
263C22×C4—181no—
264C22×C4—182no—
265C22×C4—182no—
266C22×C4—182no—
267C22×C4—182no—
268C22×C4—182no—
269C22×C4—182no—
270C22×C4—182no—
271C22×C4—182no—
272C22×C4—182no—
273C22×C4—182no—
274C22×C4—182no—
275C22×C4—182no—
276C22×C4—182no—
277C22×C4C2×#15711yescharacteristic
278C22×C4C2×#15711yescharacteristic
279C22×C4C2×#15711yescharacteristic
280C4⋊C4—22no—
281C4⋊C4—182no—
282C4⋊C4—182no—
283C4⋊C4—188no—
284C4⋊C4—182no—
285C22×C3—22no—
286C22×C3—22no—
287C22×C3—24no—
288C22×C3—24no—
289C22×C3—22no—
290C2×D3—62no—
291C2×D3—62no—
292C2×D3—62no—
293C2×D3—62no—
294C2×D3—62no—
295C2×D3—64no—
296C2×D3—62no—
297C2×D3—64no—
298C2×D3—64no—
299C2×D3—64no—
300C2×D3—64no—
301C2×D3—64no—
302C2×D3—62no—
303C2×D3—64no—
304C2×D3—64no—
305C2×D3—64no—
306C2×D3—62no—
307C2×D3—64no—
308C3×C4—28no—
309C3×C4—44no—
310C3×C4—44no—
311Dic3—68no—
312Dic3—124no—
313Dic3—124no—
314C32#144111yescharacteristic, complemented, Sylow
315C23—91no—
316C23—91no—
317C23—91no—
318C23—91no—
319C23—92no—
320C23—92no—
321C23—92no—
322C23—92no—
323C23—91no—
324C23—91no—
325C23C22×#15711yescharacteristic
326C2×C4—21no—
327C2×C4—22no—
328C2×C4—21no—
329C2×C4—22no—
330C2×C4—21no—
331C2×C4—92no—
332C2×C4—92no—
333C2×C4—182no—
334C2×C4—182no—
335C2×C4—182no—
336C2×C4—182no—
337C2×C4—182no—
338C2×C4—184no—
339C2×C4—182no—
340C2×C4—181no—
341C2×C4—182no—
342C2×C4—181no—
343C2×C4—184no—
344C2×C4—184no—
345C2×C4—184no—
346C2×C4—184no—
347C2×C4—184no—
348C2×C4—184no—
349C2×C4—182no—
350C2×C4—181no—
351C2×C4—361no—
352C2×C4—362no—
353C2×C4—361no—
354C2×C4—362no—
355C2×C4—362no—
356C2×C4—362no—
357C2×C4—362no—
358C2×C4—362no—
359C2×C4—362no—
360C2×C4—362no—
361C2×C4—362no—
362C2×C4C4⋊#15712yescomplemented
363C2×C4C22⋊#15712yes—
364C2×C3—22no—
365C2×C3—22no—
366C2×C3—22no—
367C2×C3—24no—
368C2×C3—24no—
369D3—62no—
370D3—62no—
371D3—64no—
372D3—62no—
373D3—64no—
374D3—62no—
375C22—91no—
376C22—91no—
377C22—91no—
378C22—91no—
379C22—91no—
380C22—92no—
381C22—91no—
382C22—92no—
383C22—91no—
384C22—91no—
385C22—92no—
386C22—92no—
387C22—92no—
388C22—92no—
389C22—92no—
390C22—92no—
391C22—92no—
392C22—92no—
393C22C2×C4⋊#15711yescharacteristic
394C22#6428611yescharacteristic
395C22D4×#15712yes—
396C22Q8×#15712yes—
397C22C2×C22⋊#15711yescharacteristic
398C4—22no—
399C4—22no—
400C4—41no—
401C4—182no—
402C4—182no—
403C4—364no—
404C4—364no—
405C4—361no—
406C3—22no—
407C2—91no—
408C2—92no—
409C2—91no—
410C2—91no—
411C2—92no—
412C2—91no—
413C2#1059375812yes—
414C2#1059375912yes—
415C2#1059381211yescharacteristic
416C2#1059382611yescharacteristic
417C2#1059383711yescharacteristic
subgroupG/H
center, FrattiniC23C22×#157
commutator, socleC23×C32C22×C4
FittingC2×C32×C4⋊C4C4
prime radical, cosocleC23×C3⋊D3C23
hypercenterC2×C4⋊C4#157
hypocenterC32#1441
LCSG ▷ C23×C32 ▷ C32
UCSC1 ◁ C23 ◁ C2×C4⋊C4

Complements

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

NH ≅ G/Ntype
13. C2×C32×C4⋊C4C4semidirect
14. C2×C4⋊(C3⋊Dic3)C4semidirect
15. C2×#3750C4semidirect
16. C2×#3750C4semidirect
104. C2×C32×C4C4⋊C4semidirect
111. C2×C3⋊Dic3C4⋊C4semidirect
195. C2×C4⋊C4#157semidirect
314. C32#1441semidirect
362. C2×C4C4⋊#157semidirect

Maximal subgroups

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

subgroupindex
C22×C4⋊#1572
C2×C4⋊C4×C3⋊D32
C2×#637812
#14419