Finite Group Databasebeta

← #11773448

Subgroups — #11773448

Order 1152.

1026 conjugacy classes of subgroups; only the 141 normal subgroups are shown.

normal subgroups only

This group has 1026 conjugacy classes of subgroups — too many to draw. Only its 141 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×#3773C211yesmaximal, characteristic
2C2×#63883C212yesmaximal
3C2×#63781C211yesmaximal, characteristic
4C2×#63737C212yesmaximal
5C2×#63737C211yesmaximal, characteristic
6C23×#157C2211yescharacteristic
7C23×#157C2211yescharacteristic
8C22×C4×C3⋊D3C2211yescharacteristic
9C22×#624C2212yes—
10C22×#624C2212yes—
11C2×#3773—24no—
12C2×#3773—22no—
13C2×C3×Dic3⋊C4—22no—
14C2×Dic3⋊Dic3—22no—
15#63883—24no—
16#63883—24no—
17#63781—22no—
18#63737—24no—
19#63737C414yescomplemented
20C2×D3×C4⋊C4—62no—
21C23×C3⋊D3C2311yescharacteristic
22C22×#157—22no—
23C22×#157—22no—
24C22×#157—21no—
25C22×#157—22no—
26C22×#157—22no—
27C22×#157—21no—
28C22×#157C2×C412yes—
29C22×#157D412yes—
30C22×#157Q812yes—
31C22×#157Q812yes—
32C22×C32×C4D411yescharacteristic
33C22×C3⋊Dic3D411yescharacteristic
34C2×C4×C3⋊D3—22no—
35C2×C4×C3⋊D3—22no—
36C2×C4×C3⋊D3—21no—
37C2×C4×C3⋊D3—21no—
38C22×C3×Dic3—22no—
39C22×C3×Dic3—22no—
40C2×#624—22no—
41C2×#624—22no—
42C2×#624—22no—
43C2×#624—22no—
44C2×#624—22no—
45C2×#624—22no—
46C2×#624—22no—
47C2×#624—22no—
48C2×#624C2×C414yes—
49C2×#624D414yes—
50C2×#624D414yes—
51C2×#624Q814yes—
52#3773—28no—
53C3×Dic3⋊C4—28no—
54Dic3⋊Dic3—28no—
55#1444—91nomaximal, Sylow
56C22×C4×D3—62no—
57C22×C4×D3—62no—
58C22×C4×D3—62no—
59C2×C3×C4⋊C4—62no—
60C2×C4⋊Dic3—62no—
61C2×Dic3⋊C4—22no—
62C2×Dic3⋊C4—62no—
63D3×C4⋊C4—68no—
64D3×C4⋊C4—68no—
65C23×C32C2×D411yescharacteristic
66C22×C3⋊D3C22×C411yescharacteristic
67C22×C3⋊D3C2×D411yescharacteristic
68C22×C3⋊D3C2×D412yes—
69C22×C3⋊D3C2×D412yes—
70C22×C3⋊D3C2×Q811yescharacteristic
71C22×C3⋊D3C2×Q812yes—
72C22×C3⋊D3C2×Q811yescharacteristic
73C22×C3⋊D3#4112yes—
74C22×C3⋊D3#4111yescharacteristic
75C22×C3⋊D3#4111yescharacteristic
76C2×#157—24no—
77C2×#157—22no—
78C2×#157—24no—
79C2×#157—22no—
80C2×#157—24no—
81C2×#157—22no—
82C2×#157—41no—
83C2×#157—42no—
84C2×#157—41no—
85C2×#157C4⋊C414yescomplemented
86C2×C32×C4—22no—
87C2×C32×C4—21no—
88C2×C3⋊Dic3—22no—
89C2×C3⋊Dic3—21no—
90C4×C3⋊D3—41no—
91C4×C3⋊D3—42no—
92C4×C3⋊D3—41no—
93C2×C3×Dic3—24no—
94C2×C3×Dic3—24no—
95C2×C3×Dic3—24no—
96C2×C3×Dic3—24no—
97C2×C3×Dic3—42no—
98C2×C3×Dic3—42no—
99#624—24no—
100#624—24no—
101#624—24no—
102#624—24no—
103#624—24no—
104#624—42no—
105#624—42no—
106#624C4⋊C418yescomplemented
107C22×C4⋊C4—92no—
108C22×C4⋊C4—91no—
109C2×#95—91no—
110C2×#95—91no—
111C2×#95—92no—
112C23×D3—62no—
113C22×C3×C4—22no—
114C22×C3×C4—62no—
115C22×C3×C4—62no—
116C22×Dic3—22no—
117C22×Dic3—22no—
118C22×Dic3—62no—
119C2×C4×D3—64no—
120C2×C4×D3—64no—
121C2×C4×D3—64no—
122C2×C4×D3—64no—
123C2×C4×D3—64no—
124C2×C4×D3—64no—
125C2×C4×D3—64no—
126C2×C4×D3—64no—
127C2×C4×D3—64no—
128C2×C4×D3—64no—
129C2×C4×D3—122no—
130C2×C4×D3—122no—
131C2×C4×D3—122no—
132C2×C4×D3—122no—
133C2×C4×D3—122no—
134C2×C4×D3—122no—
135C2×C4×D3—122no—
136C2×C4×D3—122no—
137C3×C4⋊C4—68no—
138C4⋊Dic3—68no—
139Dic3⋊C4—28no—
140Dic3⋊C4—68no—
141C22×C32C4×D411yescharacteristic
142C22×C32#12012yes—
143C22×C32#12111yescharacteristic
144C22×C32C22⋊Q812yes—
145C22×C32C4⋊Q811yescharacteristic
146C2×C3⋊D3C2×C4⋊C411yescharacteristic
147C2×C3⋊D3C2×C4⋊C412yes—
148C2×C3⋊D3C4×D412yes—
149C2×C3⋊D3C4×Q811yescharacteristic
150C2×C3⋊D3#12011yescharacteristic
151C2×C3⋊D3#12112yes—
152C2×C3⋊D3C22⋊Q812yes—
153C2×C3⋊D3C22⋊Q812yes—
154C2×C3⋊D3C22⋊Q812yes—
155C2×C3⋊D3C22⋊Q811yescharacteristic
156C2×C3⋊D3#12311yescharacteristic
157C2×C3⋊D3#12312yes—
158C2×C3⋊D3#12512yes—
159C2×C3⋊D3#12511yescharacteristic
160C2×C3⋊D3#12711yescharacteristic
161C2×C3⋊D3C4⋊Q811yescharacteristic
162C2×C3⋊D3C4⋊Q812yes—
163C2×C3⋊D3C4⋊Q812yes—
164#157—24no—
165#157—42no—
166C32×C4—41no—
167C3⋊Dic3—41no—
168C3×Dic3—28no—
169C3×Dic3—44no—
170C23×C4—92no—
171C23×C4—92no—
172C23×C4—91no—
173C23×C4—91no—
174C23×C4—91no—
175C2×C4⋊C4—62no—
176C2×C4⋊C4—184no—
177C2×C4⋊C4—184no—
178C2×C4⋊C4—182no—
179C2×C4⋊C4—184no—
180C2×C4⋊C4—182no—
181#95—94no—
182#95—182no—
183#95—184no—
184C23×C3—22no—
185C22×D3—62no—
186C22×D3—62no—
187C22×D3—62no—
188C22×D3—62no—
189C22×D3—62no—
190C22×D3—62no—
191C22×D3—62no—
192C22×D3—62no—
193C22×D3—62no—
194C22×D3—62no—
195C22×D3—62no—
196C22×D3—62no—
197C22×D3—62no—
198C22×D3—62no—
199C2×C3×C4—24no—
200C2×C3×C4—42no—
201C2×C3×C4—42no—
202C2×C3×C4—64no—
203C2×C3×C4—64no—
204C2×C3×C4—64no—
205C2×C3×C4—64no—
206C2×C3×C4—122no—
207C2×C3×C4—122no—
208C2×Dic3—24no—
209C2×Dic3—24no—
210C2×Dic3—24no—
211C2×Dic3—24no—
212C2×Dic3—42no—
213C2×Dic3—42no—
214C2×Dic3—64no—
215C2×Dic3—122no—
216C2×Dic3—122no—
217C4×D3—68no—
218C4×D3—68no—
219C4×D3—68no—
220C4×D3—68no—
221C4×D3—124no—
222C4×D3—124no—
223C4×D3—124no—
224C4×D3—124no—
225C4×D3—124no—
226C4×D3—124no—
227C4×D3—124no—
228C4×D3—124no—
229C2×C32#38512yes—
230C2×C32#38911yescharacteristic
231C2×C32#39211yescharacteristic
232C2×C32#39512yes—
233C2×C32#39811yescharacteristic
234C3⋊D3#38411yescharacteristic
235C3⋊D3#38511yescharacteristic
236C3⋊D3#38912yes—
237C3⋊D3#39511yescharacteristic
238C3⋊D3#39812yes—
239C3⋊D3#39911yescharacteristic
240C24—91no—
241C22×C4—62no—
242C22×C4—62no—
243C22×C4—94no—
244C22×C4—94no—
245C22×C4—94no—
246C22×C4—94no—
247C22×C4—92no—
248C22×C4—92no—
249C22×C4—92no—
250C22×C4—92no—
251C22×C4—91no—
252C22×C4—181no—
253C22×C4—182no—
254C22×C4—182no—
255C22×C4—181no—
256C22×C4—182no—
257C22×C4—182no—
258C22×C4—182no—
259C22×C4—182no—
260C22×C4—182no—
261C22×C4—182no—
262C22×C4—182no—
263C22×C4—182no—
264C22×C4—182no—
265C22×C4—182no—
266C22×C4—182no—
267C22×C4—181no—
268C22×C4—182no—
269C22×C4—181no—
270C22×C4GO+(4,𝔽2)11yescharacteristic
271C4⋊C4—68no—
272C4⋊C4—188no—
273C4⋊C4—188no—
274C22×C3—22no—
275C22×C3—22no—
276C22×C3—22no—
277C22×C3—22no—
278C22×C3—22no—
279C22×C3—22no—
280C22×C3—22no—
281C2×D3—62no—
282C2×D3—62no—
283C2×D3—62no—
284C2×D3—62no—
285C2×D3—62no—
286C2×D3—62no—
287C2×D3—62no—
288C2×D3—62no—
289C2×D3—62no—
290C2×D3—62no—
291C2×D3—62no—
292C2×D3—62no—
293C2×D3—62no—
294C2×D3—62no—
295C2×D3—62no—
296C2×D3—62no—
297C2×D3—62no—
298C2×D3—62no—
299C2×D3—62no—
300C2×D3—62no—
301C2×D3—62no—
302C2×D3—62no—
303C2×D3—62no—
304C2×D3—62no—
305C2×D3—62no—
306C2×D3—62no—
307C2×D3—62no—
308C2×D3—62no—
309C3×C4—44no—
310C3×C4—68no—
311C3×C4—124no—
312Dic3—28no—
313Dic3—44no—
314Dic3—124no—
315C32#144411yescharacteristic, complemented, Sylow
316C23—92no—
317C23—92no—
318C23—91no—
319C23—91no—
320C23—91no—
321C23—91no—
322C23—92no—
323C23—92no—
324C23—91no—
325C23—91no—
326C23C2×GO+(4,𝔽2)11yescharacteristic
327C2×C4—22no—
328C2×C4—21no—
329C2×C4—64no—
330C2×C4—64no—
331C2×C4—64no—
332C2×C4—64no—
333C2×C4—98no—
334C2×C4—94no—
335C2×C4—122no—
336C2×C4—122no—
337C2×C4—184no—
338C2×C4—184no—
339C2×C4—184no—
340C2×C4—184no—
341C2×C4—184no—
342C2×C4—182no—
343C2×C4—182no—
344C2×C4—184no—
345C2×C4—184no—
346C2×C4—182no—
347C2×C4—184no—
348C2×C4—182no—
349C2×C4—181no—
350C2×C4—361no—
351C2×C4—362no—
352C2×C4—361no—
353C2×C4—362no—
354C2×C4—362no—
355C2×C4—361no—
356C2×C4—362no—
357C2×C4—361no—
358C2×C3—22no—
359C2×C3—22no—
360C2×C3—22no—
361C2×C3—22no—
362C2×C3—22no—
363C2×C3—22no—
364C2×C3—22no—
365D3—62no—
366D3—62no—
367D3—62no—
368D3—62no—
369D3—62no—
370D3—62no—
371D3—62no—
372D3—62no—
373C22—91no—
374C22—91no—
375C22—92no—
376C22—92no—
377C22—92no—
378C22—92no—
379C22—92no—
380C22—91no—
381C22—91no—
382C22—91no—
383C22—91no—
384C22—92no—
385C22—92no—
386C22—92no—
387C22—92no—
388C22—91no—
389C22—92no—
390C22—91no—
391C22D32⋊Q812yes—
392C22#6422211yescharacteristic
393C22C4×GO+(4,𝔽2)11yescharacteristic
394C22#6424112yes—
395C22#6424211yescharacteristic
396C4—41no—
397C4—68no—
398C4—124no—
399C4—184no—
400C4—362no—
401C4—361no—
402C3—22no—
403C2—91no—
404C2—91no—
405C2—91no—
406C2—92no—
407C2—92no—
408C2—91no—
409C2#1059334011yescharacteristic
410C2#1059339812yes—
411C2#1059341011yescharacteristic
412C2#1059341112yes—
413C2#1059353011yescharacteristic
subgroupG/H
center, FrattiniC23C2×GO+(4,𝔽2)
commutatorC22×C3⋊D3C22×C4
FittingC22×C32×C4D4
socleC23×C32C2×D4
prime radical, cosocleC23×C3⋊D3C23
hypercenterC22×C4GO+(4,𝔽2)
hypocenterC32#1444
LCSG ▷ C22×C3⋊D3 ▷ C32
UCSC1 ◁ C23 ◁ C22×C4

Complements

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

NH ≅ G/Ntype
19. #63737C4semidirect
85. C2×#157C4⋊C4semidirect
106. #624C4⋊C4semidirect
315. C32#1444semidirect

Maximal subgroups

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

subgroupindex
C22×#37732
C2×#638832
C2×#637812
C2×#637372
#14449