Finite Group Databasebeta

← #11773215

Subgroups — #11773215

Order 1152.

1114 conjugacy classes of subgroups.

The subgroup lattice has 451 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C4⋊#157C211yesmaximal, characteristic
2C2×#63900C211yesmaximal, characteristic
3C2×C4×#624C211yesmaximal, characteristic
4C2×#63737C214yesmaximal
5C23×#157C2212yes—
6C22×C4×C3⋊D3C2211yescharacteristic
7C22×#624C2212yes—
8C22×#624C2212yes—
9C2×C4⋊#157—22no—
10C2×C4⋊#157—22no—
11C2×C4⋊#157C414yescomplemented
12C2×C3×C4⋊Dic3—21no—
13C2×C3×C4×Dic3—21no—
14C2×#3724—21no—
15C2×Dic32—21no—
16#63900—22no—
17#63900C414yescomplemented
18C4×#624—22no—
19C4×#624C414yescomplemented
20#63737—28no—
21C2×D3×C4⋊C4—61no—
22C2×C42×D3—61no—
23C23×C3⋊D3C2311yescharacteristic
24C22×#157—22no—
25C22×#157—22no—
26C22×#157—24no—
27C22×#157—24no—
28C22×#157C2×C414yes—
29C22×C32×C4D411yescharacteristic
30C22×C3⋊Dic3D411yescharacteristic
31C2×C4×C3⋊D3C2×C412yes—
32C2×C4×C3⋊D3C2×C412yes—
33C2×C4×C3⋊D3C2×C412yes—
34C2×C4×C3⋊D3D412yes—
35C2×C4×C3⋊D3D412yes—
36C2×C4×C3⋊D3Q812yes—
37C22×C3×Dic3—22no—
38C22×C3×Dic3—22no—
39C2×#624—22no—
40C2×#624—22no—
41C2×#624—22no—
42C2×#624—24no—
43C2×#624—24no—
44C2×#624—22no—
45C2×#624C2×C414yes—
46C2×#624C2×C414yes—
47C2×#624D414yes—
48C2×#624Q814yes—
49C4⋊#157—28no—
50C3×C4⋊Dic3—24no—
51C3×C4×Dic3—24no—
52#3724—24no—
53Dic32—24no—
54C4⋊#95—91nomaximal, Sylow
55C22×C4×D3—62no—
56C22×C4×D3—61no—
57C22×C4×D3—61no—
58C22×C4×D3—62no—
59C2×C3×C4⋊C4—61no—
60C2×C3×C42—61no—
61C2×C4⋊Dic3—21no—
62C2×Dic3⋊C4—62no—
63C2×C4×Dic3—21no—
64C2×C4×Dic3—62no—
65D3×C4⋊C4—64no—
66D3×C4⋊C4—64no—
67C42×D3—64no—
68C42×D3—64no—
69C23×C32C2×D411yescharacteristic
70C22×C3⋊D3C22×C411yescharacteristic
71C22×C3⋊D3C22×C411yescharacteristic
72C22×C3⋊D3C22×C411yescharacteristic
73C22×C3⋊D3C2×D411yescharacteristic
74C22×C3⋊D3C2×D411yescharacteristic
75C22×C3⋊D3C2×D412yes—
76C22×C3⋊D3C2×Q811yescharacteristic
77C22×C3⋊D3C2×Q812yes—
78C22×C3⋊D3#4112yes—
79C22×C3⋊D3#4112yes—
80C2×#157—24no—
81C2×#157—28no—
82C2×#157—44no—
83C2×#157—42no—
84C2×#157—42no—
85C2×C32×C4C22⋊C412yes—
86C2×C32×C4C22⋊C412yes—
87C2×C32×C4C4⋊C412yes—
88C2×C3⋊Dic3C22⋊C412yes—
89C2×C3⋊Dic3C22⋊C412yes—
90C2×C3⋊Dic3C4⋊C412yes—
91C4×C3⋊D3C4214yes—
92C4×C3⋊D3C22⋊C414yes—
93C4×C3⋊D3C4⋊C414yes—
94C4×C3⋊D3C4⋊C414yes—
95C2×C3×Dic3—24no—
96C2×C3×Dic3—24no—
97C2×C3×Dic3—24no—
98C2×C3×Dic3—24no—
99C2×C3×Dic3—44no—
100#624—24no—
101#624—24no—
102#624—24no—
103#624—28no—
104#624—42no—
105#624—42no—
106#624C4⋊C418yescomplemented
107C22×C4⋊C4—91no—
108C22×C4⋊C4—91no—
109C22×C42—91no—
110C2×#95—94no—
111C23×D3—61no—
112C23×D3—61no—
113C22×C3×C4—21no—
114C22×C3×C4—21no—
115C22×C3×C4—62no—
116C22×C3×C4—62no—
117C22×Dic3—22no—
118C22×Dic3—22no—
119C22×Dic3—61no—
120C22×Dic3—61no—
121C2×C4×D3—64no—
122C2×C4×D3—64no—
123C2×C4×D3—64no—
124C2×C4×D3—62no—
125C2×C4×D3—62no—
126C2×C4×D3—62no—
127C2×C4×D3—62no—
128C2×C4×D3—62no—
129C2×C4×D3—62no—
130C2×C4×D3—62no—
131C2×C4×D3—62no—
132C2×C4×D3—62no—
133C2×C4×D3—62no—
134C2×C4×D3—62no—
135C2×C4×D3—62no—
136C2×C4×D3—64no—
137C2×C4×D3—64no—
138C2×C4×D3—64no—
139C2×C4×D3—64no—
140C2×C4×D3—64no—
141C2×C4×D3—124no—
142C2×C4×D3—124no—
143C3×C4⋊C4—64no—
144C3×C42—64no—
145C4⋊Dic3—24no—
146Dic3⋊C4—68no—
147C4×Dic3—24no—
148C4×Dic3—68no—
149C22×C32C2×C22⋊C411yescharacteristic
150C22×C32C2×C22⋊C411yescharacteristic
151C22×C32C2×C4⋊C411yescharacteristic
152C22×C32#12112yes—
153C22×C32C22⋊Q812yes—
154C2×C3⋊D3C2×C4211yescharacteristic
155C2×C3⋊D3C2×C22⋊C411yescharacteristic
156C2×C3⋊D3C2×C4⋊C412yes—
157C2×C3⋊D3C2×C4⋊C411yescharacteristic
158C2×C3⋊D3C2×C4⋊C411yescharacteristic
159C2×C3⋊D3#11712yes—
160C2×C3⋊D3C4×D412yes—
161C2×C3⋊D3C4×D412yes—
162C2×C3⋊D3C4×Q812yes—
163C2×C3⋊D3C4×Q812yes—
164C2×C3⋊D3#12112yes—
165C2×C3⋊D3C22⋊Q812yes—
166C2×C3⋊D3#12411yescharacteristic
167C2×C3⋊D3#12411yescharacteristic
168C2×C3⋊D3#12512yes—
169C2×C3⋊D3#12711yescharacteristic
170C2×C3⋊D3C4⋊Q812yes—
171C2×C3⋊D3C4⋊Q811yescharacteristic
172#157—44no—
173C32×C4#9514yescomplemented
174C3⋊Dic3#9514yescomplemented
175C3×Dic3—28no—
176C3×Dic3—44no—
177C23×C4—92no—
178C23×C4—92no—
179C23×C4—91no—
180C23×C4—92no—
181C2×C4⋊C4—61no—
182C2×C4⋊C4—94no—
183C2×C4⋊C4—94no—
184C2×C4⋊C4—182no—
185C2×C4⋊C4—181no—
186C2×C4⋊C4—182no—
187C2×C4⋊C4—182no—
188C2×C42—61no—
189C2×C42—94no—
190C2×C42—182no—
191C2×C42—181no—
192#95—188no—
193C23×C3—21no—
194C23×C3—21no—
195C22×D3—61no—
196C22×D3—61no—
197C22×D3—61no—
198C22×D3—61no—
199C22×D3—61no—
200C22×D3—61no—
201C22×D3—61no—
202C22×D3—61no—
203C22×D3—62no—
204C22×D3—61no—
205C22×D3—61no—
206C22×D3—62no—
207C22×D3—62no—
208C22×D3—61no—
209C22×D3—61no—
210C22×D3—62no—
211C22×D3—62no—
212C22×D3—62no—
213C22×D3—62no—
214C22×D3—62no—
215C2×C3×C4—22no—
216C2×C3×C4—22no—
217C2×C3×C4—22no—
218C2×C3×C4—22no—
219C2×C3×C4—22no—
220C2×C3×C4—22no—
221C2×C3×C4—64no—
222C2×C3×C4—64no—
223C2×C3×C4—64no—
224C2×C3×C4—64no—
225C2×C3×C4—124no—
226C2×Dic3—24no—
227C2×Dic3—24no—
228C2×Dic3—24no—
229C2×Dic3—24no—
230C2×Dic3—44no—
231C2×Dic3—62no—
232C2×Dic3—62no—
233C2×Dic3—62no—
234C2×Dic3—62no—
235C2×Dic3—62no—
236C2×Dic3—62no—
237C4×D3—68no—
238C4×D3—64no—
239C4×D3—64no—
240C4×D3—64no—
241C4×D3—64no—
242C4×D3—64no—
243C4×D3—64no—
244C4×D3—64no—
245C4×D3—64no—
246C4×D3—68no—
247C4×D3—68no—
248C4×D3—68no—
249C4×D3—128no—
250C4×D3—124no—
251C4×D3—124no—
252C2×C32C2×#9511yescharacteristic
253C2×C32#38012yes—
254C2×C32#38912yes—
255C2×C32#39011yescharacteristic
256C2×C32#39111yescharacteristic
257C3⋊D3C4×C4⋊C412yes—
258C3⋊D3#38211yescharacteristic
259C3⋊D3#38411yescharacteristic
260C3⋊D3#38912yes—
261C3⋊D3#39011yescharacteristic
262C3⋊D3#39111yescharacteristic
263C24—91no—
264C22×C4—62no—
265C22×C4—62no—
266C22×C4—94no—
267C22×C4—94no—
268C22×C4—94no—
269C22×C4—94no—
270C22×C4—91no—
271C22×C4—92no—
272C22×C4—92no—
273C22×C4—92no—
274C22×C4—92no—
275C22×C4—92no—
276C22×C4—92no—
277C22×C4—94no—
278C22×C4—182no—
279C22×C4—182no—
280C22×C4—182no—
281C22×C4—182no—
282C22×C4—184no—
283C22×C4—184no—
284C22×C4—184no—
285C22×C4—182no—
286C22×C4—182no—
287C22×C4—184no—
288C22×C4GO+(4,𝔽2)11yescharacteristic
289C4⋊C4—64no—
290C4⋊C4—184no—
291C4⋊C4—188no—
292C42—64no—
293C42—184no—
294C22×C3—22no—
295C22×C3—22no—
296C22×C3—22no—
297C22×C3—22no—
298C22×C3—21no—
299C22×C3—21no—
300C22×C3—21no—
301C22×C3—21no—
302C22×C3—21no—
303C22×C3—21no—
304C2×D3—61no—
305C2×D3—61no—
306C2×D3—61no—
307C2×D3—61no—
308C2×D3—62no—
309C2×D3—61no—
310C2×D3—61no—
311C2×D3—61no—
312C2×D3—61no—
313C2×D3—62no—
314C2×D3—62no—
315C2×D3—62no—
316C2×D3—62no—
317C2×D3—61no—
318C2×D3—61no—
319C2×D3—62no—
320C2×D3—62no—
321C2×D3—62no—
322C2×D3—62no—
323C2×D3—62no—
324C2×D3—62no—
325C2×D3—62no—
326C2×D3—62no—
327C2×D3—62no—
328C2×D3—62no—
329C2×D3—62no—
330C2×D3—61no—
331C2×D3—61no—
332C2×D3—61no—
333C2×D3—62no—
334C2×D3—62no—
335C2×D3—61no—
336C2×D3—61no—
337C2×D3—61no—
338C2×D3—62no—
339C2×D3—62no—
340C3×C4—24no—
341C3×C4—24no—
342C3×C4—68no—
343C3×C4—124no—
344Dic3—28no—
345Dic3—44no—
346Dic3—64no—
347Dic3—64no—
348C32C4⋊#9511yescharacteristic, complemented, Sylow
349C23—92no—
350C23—92no—
351C23—92no—
352C23—92no—
353C23—91no—
354C23—91no—
355C23—91no—
356C23—91no—
357C23—91no—
358C23—91no—
359C23C2×GO+(4,𝔽2)11yescharacteristic
360C2×C4—64no—
361C2×C4—64no—
362C2×C4—64no—
363C2×C4—64no—
364C2×C4—98no—
365C2×C4—92no—
366C2×C4—92no—
367C2×C4—92no—
368C2×C4—94no—
369C2×C4—94no—
370C2×C4—94no—
371C2×C4—94no—
372C2×C4—124no—
373C2×C4—184no—
374C2×C4—184no—
375C2×C4—184no—
376C2×C4—188no—
377C2×C4—184no—
378C2×C4—188no—
379C2×C4—362no—
380C2×C4—362no—
381C2×C4—362no—
382C2×C4—364no—
383C2×C4—362no—
384C2×C4D32⋊C412yes—
385C2×C4D32⋊C412yes—
386C2×C4#377312yes—
387C2×C3—21no—
388C2×C3—21no—
389C2×C3—22no—
390C2×C3—22no—
391C2×C3—21no—
392C2×C3—21no—
393C2×C3—22no—
394C2×C3—22no—
395C2×C3—21no—
396C2×C3—21no—
397D3—62no—
398D3—62no—
399D3—61no—
400D3—61no—
401D3—61no—
402D3—61no—
403D3—62no—
404D3—62no—
405D3—61no—
406D3—61no—
407D3—61no—
408D3—61no—
409C22—91no—
410C22—91no—
411C22—92no—
412C22—92no—
413C22—92no—
414C22—92no—
415C22—92no—
416C22—92no—
417C22—91no—
418C22—91no—
419C22—92no—
420C22—92no—
421C22—92no—
422C22—92no—
423C22—91no—
424C22—91no—
425C22—91no—
426C22—91no—
427C22D32⋊Q812yes—
428C22#6423012yes—
429C22C2×D32⋊C411yescharacteristic
430C22C2×D32⋊C411yescharacteristic
431C22C2×#377311yescharacteristic
432C4—68no—
433C4—94no—
434C4—124no—
435C4—364no—
436C4#6373714yescomplemented
437C3—21no—
438C3—21no—
439C2—91no—
440C2—91no—
441C2—91no—
442C2—92no—
443C2—92no—
444C2—91no—
445C2#1059334111yescharacteristic
446C2#1059340312yes—
447C2#1059340511yescharacteristic
448C2#1059341212yes—
449C2C2×#6373711yescharacteristic
subgroupG/H
center, FrattiniC23C2×GO+(4,𝔽2)
commutatorC2×C3⋊D3C2×C42
FittingC22×C32×C4D4
socleC23×C32C2×D4
prime radical, cosocleC23×C3⋊D3C23
hypercenterC22×C4GO+(4,𝔽2)
hypocenterC32C4⋊#95
LCSG ▷ C2×C3⋊D3 ▷ C32
UCSC1 ◁ C23 ◁ C22×C4

Complements

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

NH ≅ G/Ntype
11. C2×C4⋊#157C4semidirect
17. #63900C4semidirect
19. C4×#624C4semidirect
106. #624C4⋊C4semidirect
173. C32×C4#95semidirect
174. C3⋊Dic3#95semidirect
348. C32C4⋊#95semidirect
436. C4#63737semidirect

Maximal subgroups

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

subgroupindex
C22×C4⋊#1572
C2×#639002
C2×C4×#6242
C2×#637372
C4⋊#959