Finite Group Databasebeta

← #11773475

Subgroups — #11773475

Order 1152.

850 conjugacy classes of subgroups; only the 125 normal subgroups are shown.

normal subgroups only

This group has 850 conjugacy classes of subgroups — too many to draw. Only its 125 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×#63781C211yesmaximal, characteristic
3C2×#63737C212yesmaximal
4C2×#63737C211yesmaximal, characteristic
5#10591370C212yesmaximal
6C23×#157C2211yescharacteristic
7C23×#157C2211yescharacteristic
8C22×C4×C3⋊D3C2211yescharacteristic
9C22×#624C2212yes—
10C22×#624C2212yes—
11C2×#3773—22no—
12C2×#3773—22no—
13C2×#3773C414yescomplemented
14#63781—22no—
15#63737—24no—
16#63737—22no—
17C3×C3⋊#95—22no—
18#63579—22no—
19D3×#95—62no—
20C23×C3⋊D3C2311yescharacteristic
21C22×#157—22no—
22C22×#157—22no—
23C22×#157—21no—
24C22×#157—21no—
25C22×#157—22no—
26C22×#157—22no—
27C22×#157C2×C412yes—
28C22×#157D412yes—
29C22×#157D412yes—
30C22×#157D412yes—
31C22×C32×C4D411yescharacteristic
32C22×C3⋊Dic3D411yescharacteristic
33C2×C4×C3⋊D3—21no—
34C2×C4×C3⋊D3—22no—
35C2×C4×C3⋊D3—22no—
36C2×C4×C3⋊D3—21no—
37C22×C3×Dic3—22no—
38C22×C3×Dic3—22no—
39C2×#624—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×#624—22no—
49C2×#624C2×C414yes—
50C2×#624Q814yes—
51#3773—28no—
52#1445—91nomaximal, Sylow
53C22×C4×D3—62no—
54C22×C4×D3—62no—
55C22×C4×D3—62no—
56C3×#95—62no—
57C3⋊#95—22no—
58C3⋊#95—62no—
59C3⋊#95—62no—
60C23×C32C2×D411yescharacteristic
61C22×C3⋊D3C22×C411yescharacteristic
62C22×C3⋊D3C2×D411yescharacteristic
63C22×C3⋊D3C2×D411yescharacteristic
64C22×C3⋊D3C2×D411yescharacteristic
65C22×C3⋊D3C2×Q812yes—
66C22×C3⋊D3#4112yes—
67C22×C3⋊D3#4112yes—
68C22×C3⋊D3#4111yescharacteristic
69C22×C3⋊D3#4112yes—
70C22×C3⋊D3#4111yescharacteristic
71C2×#157—24no—
72C2×#157—22no—
73C2×#157—22no—
74C2×#157—24no—
75C2×#157—22no—
76C2×#157—24no—
77C2×#157—41no—
78C2×#157—41no—
79C2×#157—42no—
80C2×#157C22⋊C414yes—
81C2×C32×C4—22no—
82C2×C32×C4—21no—
83C2×C3⋊Dic3—22no—
84C2×C3⋊Dic3—21no—
85C4×C3⋊D3—41no—
86C4×C3⋊D3—41no—
87C4×C3⋊D3—42no—
88C2×C3×Dic3—24no—
89C2×C3×Dic3—24no—
90C2×C3×Dic3—42no—
91C2×C3×Dic3—42no—
92C2×C3×Dic3—42no—
93C2×C3×Dic3—42no—
94#624—24no—
95#624—24no—
96#624—24no—
97#624—24no—
98#624—42no—
99#624—42no—
100#624—42no—
101#624—42no—
102C22×C4⋊C4—91no—
103C2×#95—92no—
104C2×#95—91no—
105C2×#95—92no—
106C2×#95—91no—
107C23×D3—62no—
108C22×C3×C4—22no—
109C22×C3×C4—62no—
110C22×C3×C4—62no—
111C22×Dic3—22no—
112C22×Dic3—22no—
113C22×Dic3—62no—
114C2×C4×D3—64no—
115C2×C4×D3—64no—
116C2×C4×D3—64no—
117C2×C4×D3—64no—
118C2×C4×D3—64no—
119C2×C4×D3—64no—
120C2×C4×D3—122no—
121C2×C4×D3—122no—
122C2×C4×D3—122no—
123C2×C4×D3—122no—
124C2×C4×D3—122no—
125C2×C4×D3—122no—
126C2×C4×D3—122no—
127C2×C4×D3—122no—
128C2×C4×D3—122no—
129C2×C4×D3—122no—
130C2×C4×D3—122no—
131C2×C4×D3—122no—
132C22×C32C4×D411yescharacteristic
133C22×C32#12111yescharacteristic
134C22×C32C22⋊Q812yes—
135C22×C32#12312yes—
136C22×C32#12711yescharacteristic
137C2×C3⋊D3C2×C22⋊C411yescharacteristic
138C2×C3⋊D3#11712yes—
139C2×C3⋊D3C4×D411yescharacteristic
140C2×C3⋊D3C4×Q812yes—
141C2×C3⋊D3#12111yescharacteristic
142C2×C3⋊D3C22⋊Q812yes—
143C2×C3⋊D3C22⋊Q812yes—
144C2×C3⋊D3#12311yescharacteristic
145C2×C3⋊D3#12311yescharacteristic
146C2×C3⋊D3#12312yes—
147C2×C3⋊D3#12312yes—
148C2×C3⋊D3#12411yescharacteristic
149C2×C3⋊D3#12411yescharacteristic
150C2×C3⋊D3#12512yes—
151C2×C3⋊D3#12512yes—
152C2×C3⋊D3#12612yes—
153C2×C3⋊D3#12612yes—
154C2×C3⋊D3C4⋊Q811yescharacteristic
155#157—24no—
156#157—42no—
157C32×C4—41no—
158C3⋊Dic3—41no—
159C3×Dic3—44no—
160C3×Dic3—44no—
161C23×C4—92no—
162C23×C4—92no—
163C23×C4—91no—
164C23×C4—91no—
165C23×C4—91no—
166C2×C4⋊C4—94no—
167C2×C4⋊C4—182no—
168C2×C4⋊C4—182no—
169#95—62no—
170#95—182no—
171#95—182no—
172#95—182no—
173#95—184no—
174C23×C3—22no—
175C22×D3—62no—
176C22×D3—62no—
177C22×D3—62no—
178C22×D3—62no—
179C22×D3—62no—
180C22×D3—62no—
181C22×D3—62no—
182C22×D3—62no—
183C22×D3—62no—
184C22×D3—62no—
185C22×D3—62no—
186C22×D3—62no—
187C22×D3—62no—
188C22×D3—62no—
189C2×C3×C4—24no—
190C2×C3×C4—42no—
191C2×C3×C4—42no—
192C2×C3×C4—64no—
193C2×C3×C4—64no—
194C2×C3×C4—122no—
195C2×C3×C4—122no—
196C2×C3×C4—122no—
197C2×C3×C4—122no—
198C2×Dic3—24no—
199C2×Dic3—24no—
200C2×Dic3—42no—
201C2×Dic3—42no—
202C2×Dic3—42no—
203C2×Dic3—42no—
204C2×Dic3—64no—
205C2×Dic3—122no—
206C2×Dic3—122no—
207C4×D3—124no—
208C4×D3—124no—
209C4×D3—124no—
210C4×D3—124no—
211C4×D3—124no—
212C4×D3—124no—
213C4×D3—124no—
214C4×D3—124no—
215C4×D3—124no—
216C4×D3—124no—
217C4×D3—124no—
218C4×D3—124no—
219C2×C32#38712yes—
220C2×C32#39011yescharacteristic
221C2×C32#39711yescharacteristic
222C2×C32#39811yescharacteristic
223C2×C32#39912yes—
224C3⋊D3#38111yescharacteristic
225C3⋊D3#38712yes—
226C3⋊D3#39111yescharacteristic
227C3⋊D3#39711yescharacteristic
228C3⋊D3#39811yescharacteristic
229C3⋊D3#40012yes—
230C24—91no—
231C22×C4—62no—
232C22×C4—62no—
233C22×C4—94no—
234C22×C4—94no—
235C22×C4—92no—
236C22×C4—92no—
237C22×C4—92no—
238C22×C4—92no—
239C22×C4—91no—
240C22×C4—181no—
241C22×C4—182no—
242C22×C4—182no—
243C22×C4—181no—
244C22×C4—182no—
245C22×C4—182no—
246C22×C4—182no—
247C22×C4—182no—
248C22×C4—182no—
249C22×C4—182no—
250C22×C4—182no—
251C22×C4—182no—
252C22×C4—182no—
253C22×C4—182no—
254C22×C4—182no—
255C22×C4—182no—
256C22×C4—181no—
257C22×C4—182no—
258C22×C4—181no—
259C22×C4—182no—
260C22×C4GO+(4,𝔽2)11yescharacteristic
261C4⋊C4—188no—
262C22×C3—22no—
263C22×C3—22no—
264C22×C3—22no—
265C22×C3—22no—
266C22×C3—22no—
267C22×C3—22no—
268C22×C3—22no—
269C2×D3—62no—
270C2×D3—62no—
271C2×D3—62no—
272C2×D3—62no—
273C2×D3—62no—
274C2×D3—62no—
275C2×D3—62no—
276C2×D3—62no—
277C2×D3—62no—
278C2×D3—62no—
279C2×D3—62no—
280C2×D3—62no—
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—
297C3×C4—44no—
298C3×C4—124no—
299C3×C4—124no—
300Dic3—44no—
301Dic3—44no—
302Dic3—124no—
303C32#144511yescharacteristic, complemented, Sylow
304C23—92no—
305C23—92no—
306C23—91no—
307C23—91no—
308C23—91no—
309C23—91no—
310C23—92no—
311C23—92no—
312C23—91no—
313C23—91no—
314C23C2×GO+(4,𝔽2)11yescharacteristic
315C2×C4—22no—
316C2×C4—21no—
317C2×C4—64no—
318C2×C4—64no—
319C2×C4—94no—
320C2×C4—122no—
321C2×C4—122no—
322C2×C4—122no—
323C2×C4—122no—
324C2×C4—184no—
325C2×C4—184no—
326C2×C4—184no—
327C2×C4—184no—
328C2×C4—184no—
329C2×C4—182no—
330C2×C4—184no—
331C2×C4—182no—
332C2×C4—184no—
333C2×C4—182no—
334C2×C4—182no—
335C2×C4—181no—
336C2×C4—361no—
337C2×C4—361no—
338C2×C4—362no—
339C2×C4—362no—
340C2×C4—362no—
341C2×C4—362no—
342C2×C4—362no—
343C2×C4—362no—
344C2×C4—361no—
345C2×C4—361no—
346C2×C3—22no—
347C2×C3—22no—
348C2×C3—22no—
349C2×C3—22no—
350C2×C3—22no—
351C2×C3—22no—
352C2×C3—22no—
353D3—62no—
354D3—62no—
355D3—62no—
356D3—62no—
357D3—62no—
358D3—62no—
359D3—62no—
360D3—62no—
361C22—92no—
362C22—92no—
363C22—92no—
364C22—92no—
365C22—91no—
366C22—91no—
367C22—92no—
368C22—92no—
369C22—92no—
370C22—92no—
371C22—92no—
372C22—91no—
373C22—91no—
374C22—91no—
375C22—91no—
376C22—91no—
377C22—91no—
378C22—92no—
379C22D32⋊Q812yes—
380C22C4×GO+(4,𝔽2)11yescharacteristic
381C22#6423111yescharacteristic
382C22#6423312yes—
383C22#6424211yescharacteristic
384C4—41no—
385C4—124no—
386C4—124no—
387C4—184no—
388C4—362no—
389C4—361no—
390C3—22no—
391C2—91no—
392C2—91no—
393C2—92no—
394C2—92no—
395C2—91no—
396C2—91no—
397C2#1059333812yes—
398C2#1059334011yescharacteristic
399C2#1059340812yes—
400C2#1059345411yescharacteristic
401C2#1059348611yescharacteristic
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#1445
LCSG ▷ C22×C3⋊D3 ▷ C32
UCSC1 ◁ C23 ◁ C22×C4

Complements

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

NH ≅ G/Ntype
13. C2×#3773C4semidirect
303. C32#1445semidirect

Maximal subgroups

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

subgroupindex
C22×#37732
C2×#637812
C2×#637372
#105913702
#14459