Finite Group Databasebeta

← C2×#10593408 #11808491

Subgroups — C2×#10593408 #11808491

Order 1152.

1454 conjugacy classes of subgroups; only the 183 normal subgroups are shown.

normal subgroups only

This group has 1454 conjugacy classes of subgroups — too many to draw. Only its 183 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×#3773C212yesmaximal, complemented
2C22×D32⋊C4C212yesmaximal
3C2×#63921C211yesmaximal, characteristic
4C2×#63900C211yesmaximal, characteristic, complemented
5C2×#63781C211yesmaximal, characteristic, complemented
6#10593408C218yesmaximal, direct product factor
7C23×D32C2211yescharacteristic
8C23×#157C2212yes—
9C22×C4×C3⋊D3C2211yescharacteristic
10C22×#624C2212yes—
11C22×#624C2211yescharacteristic
12C2×#3773—28no—
13C2×#3773C2218yescomplemented
14C2×D32⋊C4—28no—
15C2×D32⋊C4C2218yes—
16C2×C3×(C2×D3)⋊C4—21no—
17C2×C3×C4⋊Dic3—21no—
18C2×#3724—21no—
19C2×(C2×D3)⋊Dic3—21no—
20#63921—22no—
21#63921C2214yes—
22#63900—22no—
23#63900C2214yescomplemented
24#63781C2214yescomplemented
25C2×D3×C4⋊C4—61no—
26C2×D3×C22⋊C4—61no—
27C23×C3⋊D3C2311yescharacteristic
28C23×C3×D3—21no—
29C22×D32—24no—
30C22×D32—24no—
31C22×D32—21no—
32C22×D32—22no—
33C22×D32Q814yes—
34C22×D32C2312yes—
35C22×#157—24no—
36C22×#157—24no—
37C22×#157D418yes—
38C22×#157C2314yes—
39C22×C32×C4D411yescharacteristic
40C22×C3⋊Dic3D411yescharacteristic
41C2×C4×C3⋊D3—24no—
42C2×C4×C3⋊D3D412yes—
43C2×C4×C3⋊D3C2312yes—
44C22×C3×Dic3—22no—
45C22×C3×Dic3—21no—
46C2×#624—24no—
47C2×#624—24no—
48C2×#624—24no—
49C2×#624—22no—
50C2×#624—21no—
51C2×#624C2314yes—
52C2×#624C2312yes—
53#3773—216no—
54D32⋊C4—216no—
55C3×(C2×D3)⋊C4—24no—
56C3×C4⋊Dic3—24no—
57#3724—24no—
58(C2×D3)⋊Dic3—24no—
59C2×#399—91nomaximal, Sylow
60C24×D3—61no—
61C22×C4×D3—61no—
62C22×C4×D3—61no—
63C22×C4×D3—62no—
64C22×C4×D3—61no—
65C2×C3×C4⋊C4—61no—
66C2×C3×C22⋊C4—61no—
67C2×#217—61no—
68C2×(C2×D3)⋊C4—21no—
69C2×(C2×D3)⋊C4—61no—
70C2×C4⋊Dic3—21no—
71C2×Dic3⋊C4—62no—
72D3×C4⋊C4—64no—
73D3×C4⋊C4—64no—
74D3×C22⋊C4—64no—
75D3×C22⋊C4—64no—
76C23×C32C2×D411yescharacteristic
77C22×C3⋊D3C2×D411yescharacteristic
78C22×C3⋊D3C2×D414yes—
79C22×C3⋊D3C2×Q812yes—
80C22×C3⋊D3#4114yes—
81C22×C3⋊D3#4112yes—
82C22×C3⋊D3C2411yescharacteristic
83C22×C3×D3—24no—
84C22×C3×D3—22no—
85C22×C3×D3—42no—
86C22×C3×D3—42no—
87C2×D32—24no—
88C2×D32—22no—
89C2×D32—216no—
90C2×D32—24no—
91C2×D32—24no—
92C2×D32—48no—
93C2×D32—42no—
94C2×D32—42no—
95C2×D32C2×Q814yes—
96C2×#157—216no—
97C2×#157—24no—
98C2×#157—24no—
99C2×#157C2×D418yes—
100C2×C32×C4—22no—
101C2×C32×C4C2×D412yes—
102C2×C3⋊Dic3—22no—
103C2×C3⋊Dic3C2×D412yes—
104C4×C3⋊D3—24no—
105C4×C3⋊D3—24no—
106C2×C3×Dic3—22no—
107C2×C3×Dic3—24no—
108C2×C3×Dic3—44no—
109C2×C3×Dic3—42no—
110#624—24no—
111#624—24no—
112#624—24no—
113#624—44no—
114#624—42no—
115C22×C4⋊C4—91no—
116C22×C4⋊C4—92no—
117C22×C22⋊C4—91no—
118C22×C22⋊C4—92no—
119#399—98no—
120C2×#95—91no—
121C24×C3—61no—
122C23×D3—21no—
123C23×D3—64no—
124C23×D3—62no—
125C23×D3—61no—
126C23×D3—61no—
127C23×D3—62no—
128C23×D3—64no—
129C23×D3—124no—
130C23×D3—124no—
131C22×C3×C4—21no—
132C22×C3×C4—21no—
133C22×C3×C4—62no—
134C22×C3×C4—61no—
135C22×Dic3—22no—
136C22×Dic3—21no—
137C22×Dic3—61no—
138C22×Dic3—61no—
139C2×C4×D3—62no—
140C2×C4×D3—62no—
141C2×C4×D3—62no—
142C2×C4×D3—64no—
143C2×C4×D3—62no—
144C2×C4×D3—62no—
145C2×C4×D3—68no—
146C2×C4×D3—62no—
147C2×C4×D3—64no—
148C2×C4×D3—124no—
149C2×C4×D3—124no—
150C2×C4×D3—124no—
151C2×C4×D3—124no—
152C3×C4⋊C4—64no—
153C3×C22⋊C4—64no—
154#217—64no—
155(C2×D3)⋊C4—24no—
156(C2×D3)⋊C4—64no—
157C4⋊Dic3—24no—
158Dic3⋊C4—68no—
159C22×C32C22⋊Q812yes—
160C22×C32#12312yes—
161C22×C32#12712yes—
162C22×C32C22×D411yescharacteristic
163C2×C3⋊D3C22⋊Q818yes—
164C2×C3⋊D3C22⋊Q812yes—
165C2×C3⋊D3#12318yes—
166C2×C3⋊D3#12312yes—
167C2×C3⋊D3#12712yes—
168C2×C3⋊D3C22×D412yes—
169C2×C3⋊D3C22×Q811yescharacteristic
170C2×C3⋊D3C2×#4112yes—
171C2×C3⋊D3C2×#4111yescharacteristic
172C2×C3×D3—24no—
173C2×C3×D3—42no—
174C2×C3×D3—42no—
175C2×C3×D3—48no—
176D32—28no—
177D32—44no—
178D32—48no—
179#157—28no—
180C32×C4—22no—
181C3⋊Dic3—22no—
182C3×Dic3—44no—
183C3×Dic3—42no—
184C25—91no—
185C23×C4—91no—
186C23×C4—92no—
187C23×C4—92no—
188C23×C4—91no—
189C2×C4⋊C4—61no—
190C2×C4⋊C4—94no—
191C2×C4⋊C4—98no—
192C2×C4⋊C4—182no—
193C2×C4⋊C4—181no—
194C2×C4⋊C4—188no—
195C2×C22⋊C4—61no—
196C2×C22⋊C4—94no—
197C2×C22⋊C4—98no—
198C2×C22⋊C4—182no—
199C2×C22⋊C4—181no—
200C2×C22⋊C4—188no—
201#95—94no—
202C23×C3—21no—
203C23×C3—21no—
204C23×C3—62no—
205C23×C3—64no—
206C23×C3—122no—
207C23×C3—122no—
208C22×D3—22no—
209C22×D3—24no—
210C22×D3—42no—
211C22×D3—42no—
212C22×D3—64no—
213C22×D3—61no—
214C22×D3—61no—
215C22×D3—64no—
216C22×D3—64no—
217C22×D3—62no—
218C22×D3—62no—
219C22×D3—64no—
220C22×D3—64no—
221C22×D3—62no—
222C22×D3—62no—
223C22×D3—61no—
224C22×D3—61no—
225C22×D3—68no—
226C22×D3—64no—
227C22×D3—124no—
228C22×D3—124no—
229C22×D3—1216no—
230C22×D3—124no—
231C22×D3—124no—
232C22×D3—1216no—
233C2×C3×C4—24no—
234C2×C3×C4—22no—
235C2×C3×C4—22no—
236C2×C3×C4—42no—
237C2×C3×C4—64no—
238C2×C3×C4—62no—
239C2×C3×C4—124no—
240C2×C3×C4—122no—
241C2×Dic3—24no—
242C2×Dic3—22no—
243C2×Dic3—44no—
244C2×Dic3—42no—
245C2×Dic3—62no—
246C2×Dic3—62no—
247C2×Dic3—64no—
248C2×Dic3—122no—
249C4×D3—68no—
250C4×D3—68no—
251C4×D3—124no—
252C4×D3—124no—
253C4×D3—124no—
254C4×D3—124no—
255C4×D3—124no—
256C4×D3—128no—
257C4×D3—124no—
258C2×C32#39914yescomplemented
259C2×C32C2×C22⋊Q811yescharacteristic
260C2×C32C2×#12311yescharacteristic
261C2×C32C2×#12711yescharacteristic
262C3⋊D3#39914yescomplemented
263C3⋊D3C2×C22⋊Q812yes—
264C3⋊D3C2×#12312yes—
265C3×D3—44no—
266C24—61no—
267C24—92no—
268C24—94no—
269C24—91no—
270C24—181no—
271C24—182no—
272C24—184no—
273C24—184no—
274C22×C4—61no—
275C22×C4—62no—
276C22×C4—92no—
277C22×C4—94no—
278C22×C4—98no—
279C22×C4—94no—
280C22×C4—91no—
281C22×C4—92no—
282C22×C4—92no—
283C22×C4—184no—
284C22×C4—181no—
285C22×C4—182no—
286C22×C4—184no—
287C22×C4—184no—
288C22×C4—184no—
289C22×C4—184no—
290C22×C4—184no—
291C22×C4GO+(4,𝔽2)11yescharacteristic
292C4⋊C4—64no—
293C4⋊C4—184no—
294C4⋊C4—1816no—
295C22⋊C4—64no—
296C22⋊C4—184no—
297C22⋊C4—1816no—
298C22×C3—21no—
299C22×C3—21no—
300C22×C3—22no—
301C22×C3—22no—
302C22×C3—22no—
303C22×C3—22no—
304C22×C3—22no—
305C22×C3—22no—
306C22×C3—64no—
307C22×C3—128no—
308C22×C3—122no—
309C22×C3—122no—
310C2×D3—24no—
311C2×D3—48no—
312C2×D3—42no—
313C2×D3—42no—
314C2×D3—62no—
315C2×D3—62no—
316C2×D3—62no—
317C2×D3—62no—
318C2×D3—62no—
319C2×D3—62no—
320C2×D3—62no—
321C2×D3—62no—
322C2×D3—62no—
323C2×D3—61no—
324C2×D3—61no—
325C2×D3—68no—
326C2×D3—68no—
327C2×D3—68no—
328C2×D3—62no—
329C2×D3—68no—
330C2×D3—61no—
331C2×D3—61no—
332C2×D3—128no—
333C2×D3—128no—
334C2×D3—1216no—
335C3×C4—24no—
336C3×C4—42no—
337C3×C4—124no—
338C3×C4—122no—
339Dic3—44no—
340Dic3—42no—
341Dic3—64no—
342Dic3—122no—
343C32C2×#39911yescharacteristic, complemented, Sylow
344C23—62no—
345C23—64no—
346C23—94no—
347C23—91no—
348C23—91no—
349C23—92no—
350C23—92no—
351C23—94no—
352C23—94no—
353C23—122no—
354C23—122no—
355C23—182no—
356C23—184no—
357C23—184no—
358C23—1816no—
359C23—184no—
360C23—368no—
361C23—362no—
362C23—362no—
363C23C2×GO+(4,𝔽2)11yescharacteristic
364C2×C4—22no—
365C2×C4—62no—
366C2×C4—64no—
367C2×C4—98no—
368C2×C4—92no—
369C2×C4—122no—
370C2×C4—124no—
371C2×C4—184no—
372C2×C4—184no—
373C2×C4—184no—
374C2×C4—184no—
375C2×C4—184no—
376C2×C4—1816no—
377C2×C4—184no—
378C2×C4—184no—
379C2×C4—182no—
380C2×C4—362no—
381C2×C4—364no—
382C2×C4C2×GO+(4,𝔽2)12yes—
383C2×C3—24no—
384C2×C3—24no—
385C2×C3—21no—
386C2×C3—21no—
387C2×C3—21no—
388C2×C3—21no—
389C2×C3—21no—
390C2×C3—21no—
391C2×C3—124no—
392D3—44no—
393D3—62no—
394D3—62no—
395D3—64no—
396D3—62no—
397D3—62no—
398D3—64no—
399C22—64no—
400C22—98no—
401C22—98no—
402C22—91no—
403C22—91no—
404C22—92no—
405C22—92no—
406C22—92no—
407C22—92no—
408C22—92no—
409C22—128no—
410C22—122no—
411C22—122no—
412C22—188no—
413C22—364no—
414C22—368no—
415C22D32⋊Q812yes—
416C22#6423112yes—
417C22#6423312yes—
418C22C22×GO+(4,𝔽2)11yescharacteristic
419C4—22no—
420C4—122no—
421C4—124no—
422C4—188no—
423C4—182no—
424C3—21no—
425C3—21no—
426C2—92no—
427C2—92no—
428C2—94no—
429C2—124no—
430C2#1059340814yesdirect product factor
431C2C2×D32⋊Q811yescharacteristic
432C2C2×#6423111yescharacteristic
433C2C2×#6423311yescharacteristic
subgroupG/H
centerC23C2×GO+(4,𝔽2)
commutator, cosocleC22×C3⋊D3C24
FrattiniC22C22×GO+(4,𝔽2)
FittingC22×C32×C4D4
socleC23×C32C2×D4
prime radicalC23×D32C22
hypercenterC22×C4GO+(4,𝔽2)
hypocenterC32C2×#399
LCSG ▷ C22×C3⋊D3 ▷ C32
UCSC1 ◁ C23 ◁ C22×C4

Complements

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

NH ≅ G/Ntype
1. C22×#3773C2semidirect
4. C2×#63900C2semidirect
5. C2×#63781C2semidirect
6. #10593408C2direct (N × H)
13. C2×#3773C22semidirect
23. #63900C22semidirect
24. #63781C22semidirect
258. C2×C32#399semidirect
262. C3⋊D3#399semidirect
343. C32C2×#399semidirect
430. C2#10593408direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#37732
C22×D32⋊C42
C2×#639212
C2×#639002
C2×#637812
#105934082
C2×#3999