Finite Group Databasebeta

← C2×#10593402 #11808128

Subgroups — C2×#10593402 #11808128

Order 1152.

1798 conjugacy classes of subgroups; only the 183 normal subgroups are shown.

normal subgroups only

This group has 1798 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×#3797C211yesmaximal, characteristic, complemented
2C22×D32⋊C4C212yesmaximal
3C2×#63921C211yesmaximal, characteristic
4C2×#63781C211yesmaximal, characteristic, complemented
5C2×#63737C212yesmaximal, complemented
6#10593402C218yesmaximal, direct product factor
7C23×D32C2211yescharacteristic
8C23×#157C2212yes—
9C22×C4×C3⋊D3C2211yescharacteristic
10C22×C3×Dic6—21no—
11C22×#627—21no—
12C22×#624C2211yescharacteristic
13C22×#624C2212yes—
14C2×#3797—22no—
15C2×#3797—28no—
16C2×#3797C2214yescomplemented
17C2×D32⋊C4—28no—
18C2×D32⋊C4C2218yes—
19C2×C3×(C2×D3)⋊C4—21no—
20C2×(C2×D3)⋊Dic3—21no—
21#63921—22no—
22#63921C2214yes—
23#63781C2214yescomplemented
24#63737C2218yescomplemented
25C22×D3×Q8—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×D32Q814yescomplemented
34C22×D32C2312yes—
35C22×#157—24no—
36C22×#157—24no—
37C22×#157—24no—
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×C3×Dic6—28no—
47C2×C3×Dic6—24no—
48C2×#627—28no—
49C2×#627—24no—
50C2×#624—22no—
51C2×#624—24no—
52C2×#624—24no—
53C2×#624—21no—
54C2×#624D418yes—
55C2×#624C2312yes—
56C2×#624C2314yes—
57#3797—216no—
58#3797—216no—
59D32⋊C4—216no—
60C3×(C2×D3)⋊C4—24no—
61(C2×D3)⋊Dic3—24no—
62C2×#393—91nomaximal, Sylow
63C24×D3—61no—
64C22×C3×Q8—61no—
65C2×D3×Q8—64no—
66C2×D3×Q8—616no—
67C2×D3×Q8—64no—
68C22×C4×D3—62no—
69C22×C4×D3—61no—
70C22×C4×D3—61no—
71C22×C4×D3—61no—
72C22×Dic6—21no—
73C22×Dic6—62no—
74C2×C3×C22⋊C4—61no—
75C2×#217—61no—
76C2×(C2×D3)⋊C4—21no—
77C2×(C2×D3)⋊C4—61no—
78D3×C22⋊C4—64no—
79D3×C22⋊C4—64no—
80C23×C32C2×D411yescharacteristic
81C22×C3⋊D3C2×D411yescharacteristic
82C22×C3⋊D3C2×D414yes—
83C22×C3⋊D3C2×Q812yes—
84C22×C3⋊D3#4114yes—
85C22×C3⋊D3#4112yes—
86C22×C3⋊D3C2411yescharacteristic
87C22×C3×D3—24no—
88C22×C3×D3—22no—
89C22×C3×D3—42no—
90C22×C3×D3—42no—
91C2×D32—24no—
92C2×D32—22no—
93C2×D32—216no—
94C2×D32—24no—
95C2×D32—24no—
96C2×D32—42no—
97C2×D32—48no—
98C2×D32—42no—
99C2×D32C2×Q814yescomplemented
100C2×#157—24no—
101C2×#157—24no—
102C2×#157—24no—
103C2×#157—48no—
104C2×C32×C4—22no—
105C2×C32×C4C2×D412yes—
106C2×C3⋊Dic3—22no—
107C2×C3⋊Dic3C2×D412yes—
108C4×C3⋊D3—24no—
109C4×C3⋊D3—24no—
110C2×C3×Dic3—28no—
111C2×C3×Dic3—24no—
112C2×C3×Dic3—22no—
113C2×C3×Dic3—42no—
114C3×Dic6—216no—
115#627—216no—
116#624—28no—
117#624—24no—
118#624—24no—
119#624—42no—
120#624C2×D418yes—
121C23×Q8—91no—
122C22×C22⋊C4—91no—
123C22×C22⋊C4—92no—
124#393—98no—
125C2×#95—91no—
126C2×#95—92no—
127C24×C3—61no—
128C23×D3—21no—
129C23×D3—64no—
130C23×D3—62no—
131C23×D3—61no—
132C23×D3—61no—
133C23×D3—62no—
134C23×D3—64no—
135C23×D3—124no—
136C23×D3—124no—
137C2×C3×Q8—68no—
138C2×C3×Q8—64no—
139C22×C3×C4—21no—
140C22×C3×C4—21no—
141C22×C3×C4—62no—
142C22×C3×C4—61no—
143C22×Dic3—22no—
144C22×Dic3—21no—
145C22×Dic3—61no—
146C22×Dic3—61no—
147D3×Q8—632no—
148D3×Q8—632no—
149C2×C4×D3—68no—
150C2×C4×D3—64no—
151C2×C4×D3—62no—
152C2×C4×D3—62no—
153C2×C4×D3—62no—
154C2×C4×D3—62no—
155C2×C4×D3—62no—
156C2×C4×D3—64no—
157C2×C4×D3—68no—
158C2×C4×D3—68no—
159C2×C4×D3—62no—
160C2×C4×D3—124no—
161C2×C4×D3—124no—
162C2×Dic6—28no—
163C2×Dic6—24no—
164C2×Dic6—68no—
165C2×Dic6—616no—
166C3×C22⋊C4—64no—
167#217—64no—
168(C2×D3)⋊C4—24no—
169(C2×D3)⋊C4—64no—
170C22×C32#12012yes—
171C22×C32C22⋊Q812yes—
172C22×C32#12412yes—
173C22×C32C22×D411yescharacteristic
174C2×C3⋊D3#12012yes—
175C2×C3⋊D3C22⋊Q818yes—
176C2×C3⋊D3C22⋊Q812yes—
177C2×C3⋊D3#12418yes—
178C2×C3⋊D3#12412yes—
179C2×C3⋊D3C22×D412yes—
180C2×C3⋊D3C22×Q811yescharacteristic
181C2×C3⋊D3C2×#4112yes—
182C2×C3⋊D3C2×#4111yescharacteristic
183C2×C3×D3—24no—
184C2×C3×D3—42no—
185C2×C3×D3—42no—
186C2×C3×D3—48no—
187D32—28no—
188D32—44no—
189D32—48no—
190#157—44no—
191C32×C4—22no—
192C3⋊Dic3—22no—
193C3×Dic3—28no—
194C3×Dic3—42no—
195C25—91no—
196C22×Q8—61no—
197C22×Q8—94no—
198C22×Q8—181no—
199C22×Q8—188no—
200C22×Q8—182no—
201C23×C4—92no—
202C23×C4—91no—
203C23×C4—91no—
204C23×C4—92no—
205C2×C22⋊C4—61no—
206C2×C22⋊C4—94no—
207C2×C22⋊C4—98no—
208C2×C22⋊C4—182no—
209C2×C22⋊C4—181no—
210C2×C22⋊C4—188no—
211#95—94no—
212#95—98no—
213C23×C3—21no—
214C23×C3—21no—
215C23×C3—62no—
216C23×C3—64no—
217C23×C3—122no—
218C23×C3—122no—
219C22×D3—22no—
220C22×D3—24no—
221C22×D3—42no—
222C22×D3—42no—
223C22×D3—64no—
224C22×D3—61no—
225C22×D3—64no—
226C22×D3—61no—
227C22×D3—64no—
228C22×D3—62no—
229C22×D3—62no—
230C22×D3—64no—
231C22×D3—62no—
232C22×D3—64no—
233C22×D3—62no—
234C22×D3—61no—
235C22×D3—61no—
236C22×D3—68no—
237C22×D3—64no—
238C22×D3—124no—
239C22×D3—124no—
240C22×D3—1216no—
241C22×D3—124no—
242C22×D3—124no—
243C22×D3—1216no—
244C3×Q8—616no—
245C2×C3×C4—24no—
246C2×C3×C4—22no—
247C2×C3×C4—22no—
248C2×C3×C4—42no—
249C2×C3×C4—64no—
250C2×C3×C4—68no—
251C2×C3×C4—62no—
252C2×C3×C4—122no—
253C2×Dic3—24no—
254C2×Dic3—28no—
255C2×Dic3—22no—
256C2×Dic3—42no—
257C2×Dic3—62no—
258C2×Dic3—62no—
259C2×Dic3—64no—
260C2×Dic3—122no—
261C4×D3—68no—
262C4×D3—616no—
263C4×D3—68no—
264C4×D3—68no—
265C4×D3—68no—
266C4×D3—124no—
267C4×D3—124no—
268C4×D3—124no—
269C4×D3—124no—
270Dic6—216no—
271Dic6—632no—
272C2×C32#39314yescomplemented
273C2×C32C2×#12011yescharacteristic
274C2×C32C2×C22⋊Q811yescharacteristic
275C2×C32C2×#12411yescharacteristic
276C3⋊D3#39314yescomplemented
277C3⋊D3C2×C22⋊Q812yes—
278C3⋊D3C2×#12412yes—
279C3×D3—44no—
280C24—61no—
281C24—92no—
282C24—94no—
283C24—91no—
284C24—181no—
285C24—182no—
286C24—184no—
287C24—184no—
288C2×Q8—68no—
289C2×Q8—64no—
290C2×Q8—184no—
291C2×Q8—188no—
292C2×Q8—1816no—
293C2×Q8—1816no—
294C22×C4—62no—
295C22×C4—61no—
296C22×C4—94no—
297C22×C4—98no—
298C22×C4—92no—
299C22×C4—91no—
300C22×C4—92no—
301C22×C4—92no—
302C22×C4—94no—
303C22×C4—184no—
304C22×C4—182no—
305C22×C4—184no—
306C22×C4—181no—
307C22×C4—184no—
308C22×C4—184no—
309C22×C4—184no—
310C22×C4—184no—
311C22×C4GO+(4,𝔽2)11yescharacteristic
312C22⋊C4—64no—
313C22⋊C4—184no—
314C22⋊C4—1816no—
315C22×C3—21no—
316C22×C3—21no—
317C22×C3—22no—
318C22×C3—22no—
319C22×C3—22no—
320C22×C3—22no—
321C22×C3—22no—
322C22×C3—22no—
323C22×C3—64no—
324C22×C3—128no—
325C22×C3—122no—
326C22×C3—122no—
327C2×D3—24no—
328C2×D3—48no—
329C2×D3—42no—
330C2×D3—42no—
331C2×D3—62no—
332C2×D3—62no—
333C2×D3—62no—
334C2×D3—62no—
335C2×D3—62no—
336C2×D3—62no—
337C2×D3—62no—
338C2×D3—61no—
339C2×D3—61no—
340C2×D3—68no—
341C2×D3—68no—
342C2×D3—68no—
343C2×D3—62no—
344C2×D3—68no—
345C2×D3—62no—
346C2×D3—61no—
347C2×D3—61no—
348C2×D3—62no—
349C2×D3—128no—
350C2×D3—128no—
351C2×D3—1216no—
352C3×C4—24no—
353C3×C4—42no—
354C3×C4—68no—
355C3×C4—122no—
356Dic3—28no—
357Dic3—42no—
358Dic3—64no—
359Dic3—122no—
360C32C2×#39311yescharacteristic, complemented, Sylow
361C23—62no—
362C23—64no—
363C23—94no—
364C23—91no—
365C23—91no—
366C23—92no—
367C23—92no—
368C23—94no—
369C23—94no—
370C23—122no—
371C23—122no—
372C23—182no—
373C23—184no—
374C23—184no—
375C23—1816no—
376C23—184no—
377C23—368no—
378C23—362no—
379C23—362no—
380C23C2×GO+(4,𝔽2)11yescharacteristic
381Q8—616no—
382Q8—1816no—
383C2×C4—22no—
384C2×C4—64no—
385C2×C4—68no—
386C2×C4—62no—
387C2×C4—98no—
388C2×C4—92no—
389C2×C4—122no—
390C2×C4—184no—
391C2×C4—184no—
392C2×C4—184no—
393C2×C4—188no—
394C2×C4—184no—
395C2×C4—182no—
396C2×C4—184no—
397C2×C4—184no—
398C2×C4—184no—
399C2×C4—362no—
400C2×C4—368no—
401C2×C4C2×GO+(4,𝔽2)12yes—
402C2×C3—24no—
403C2×C3—24no—
404C2×C3—21no—
405C2×C3—21no—
406C2×C3—21no—
407C2×C3—21no—
408C2×C3—21no—
409C2×C3—21no—
410C2×C3—124no—
411D3—44no—
412D3—62no—
413D3—62no—
414D3—64no—
415D3—62no—
416D3—62no—
417D3—64no—
418C22—64no—
419C22—98no—
420C22—98no—
421C22—91no—
422C22—91no—
423C22—92no—
424C22—92no—
425C22—92no—
426C22—92no—
427C22—92no—
428C22—128no—
429C22—122no—
430C22—122no—
431C22—188no—
432C22—364no—
433C22—368no—
434C22D32⋊Q812yes—
435C22#6422112yes—
436C22#6424112yes—
437C22C22×GO+(4,𝔽2)11yescharacteristic
438C4—22no—
439C4—68no—
440C4—122no—
441C4—182no—
442C4—364no—
443C3—21no—
444C3—21no—
445C2—92no—
446C2—92no—
447C2—94no—
448C2—124no—
449C2#1059340214yesdirect product factor
450C2C2×D32⋊Q811yescharacteristic
451C2C2×#6422111yescharacteristic
452C2C2×#6424111yescharacteristic
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×#393
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×#3797C2semidirect
4. C2×#63781C2semidirect
5. C2×#63737C2semidirect
6. #10593402C2direct (N × H)
16. C2×#3797C22semidirect
23. #63781C22semidirect
24. #63737C22semidirect
33. C22×D32Q8semidirect
99. C2×D32C2×Q8semidirect
272. C2×C32#393semidirect
276. C3⋊D3#393semidirect
360. C32C2×#393semidirect
449. C2#10593402direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#37972
C22×D32⋊C42
C2×#639212
C2×#637812
C2×#637372
#105934022
C2×#3939