Finite Group Databasebeta

← #11802747

Subgroups — #11802747

Order 1152.

1490 conjugacy classes of subgroups; only the 199 normal subgroups are shown.

normal subgroups only

This group has 1490 conjugacy classes of subgroups — too many to draw. Only its 199 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
1C2×#64306C211yesmaximal, characteristic
2C22×C4⋊#157C211yesmaximal, characteristic, complemented
3#10594969C211yesmaximal, characteristic, complemented
4#10593515C214yesmaximal, complemented
5#10593405C212yesmaximal, complemented
6#10593403C214yesmaximal, complemented
7#10593341C212yesmaximal, complemented
8C23×#157C2212yes—
9C22×C4×C3⋊D3C2211yescharacteristic
10C2×C3×#235—21no—
11C2×#3811C2212yes—
12C2×#3805—21no—
13#64306—24no—
14#64306C418yescomplemented
15C2×#3802C2211yescharacteristic
16C2×C4×D32C2212yes—
17C2×#3798—21no—
18C2×#3797C2211yescharacteristic
19C2×#3796—21no—
20C2×C4⋊#157—24no—
21C2×C4⋊#157C2212yes—
22C2×C4⋊#157C2212yes—
23C2×D32⋊C4C2218yes—
24C3×#926—21no—
25#63974C2212yes—
26#63957—21no—
27#63900C2212yes—
28C4×#624C2212yes—
29#63874—21no—
30#63849—21no—
31#63737C2218yes—
32C2×D3×#41—61no—
33D3×#117—61no—
34C23×C3⋊D3C2311yescharacteristic
35C22×D32C2312yes—
36C22×#157—24no—
37C22×#157—44no—
38C22×#157C2314yes—
39C22×C32×C4D411yescharacteristic
40C22×C3⋊Dic3D411yescharacteristic
41C2×C4×C3⋊D3C2×C414yes—
42C2×C4×C3⋊D3D411yescharacteristic
43C2×C4×C3⋊D3D411yescharacteristic
44C2×C4×C3⋊D3D414yes—
45C2×C4×C3⋊D3C2311yescharacteristic
46C2×C4×C3⋊D3C2311yescharacteristic
47C2×C3×#67—22no—
48C3×#235—28no—
49C2×C3×D12—21no—
50C2×C3×C4×D3—22no—
51C2×C3×Dic6—21no—
52#3811—24no—
53#3811C2×C418yes—
54C2×#627—21no—
55C2×#626—22no—
56C2×#625—21no—
57C2×#624C2314yes—
58C2×#624C2312yes—
59#3805—28no—
60C2×D3×Dic3—22no—
61#3802—22no—
62#3802C2×C414yescomplemented
63C4×D32—24no—
64C4×D32C2×C418yescomplemented
65#3798—28no—
66#3797—22no—
67#3797C2×C414yescomplemented
68#3796—28no—
69C4⋊#157—24no—
70C4⋊#157—24no—
71D32⋊C4—48no—
72C3×#217—22no—
73C3×C4⋊Dic3—22no—
74C3×C4×Dic3—22no—
75#3724—22no—
76#3722—22no—
77Dic32—22no—
78#2311—91nomaximal, Sylow
79C2×C3×#41—61no—
80D3×#41—68no—
81D3×#41—68no—
82C2×#239—61no—
83C2×D3×Q8—61no—
84C2×#237—61no—
85C2×#237—62no—
86C2×D3×D4—61no—
87C2×D3×D4—62no—
88C2×#235—21no—
89C2×#235—62no—
90C22×C4×D3—62no—
91C22×C4×D3—61no—
92C22×C4×D3—61no—
93C3×#117—61no—
94#926—21no—
95#892—62no—
96D3×C4⋊C4—62no—
97D3×C22⋊C4—62no—
98#877—62no—
99#872—62no—
100C42×D3—62no—
101C23×C32C2×D411yescharacteristic
102C22×C3⋊D3—22no—
103C22×C3⋊D3—22no—
104C22×C3⋊D3C22×C412yes—
105C22×C3⋊D3C2×D411yescharacteristic
106C22×C3⋊D3C2×D412yes—
107C22×C3⋊D3C2411yescharacteristic
108C22×C3×D3—22no—
109C2×D32—22no—
110C2×D32—24no—
111C2×D32—24no—
112C2×D32C22×C414yes—
113C2×#157—24no—
114C2×#157—28no—
115C2×#157—48no—
116C2×C32×C4C22⋊C414yescomplemented
117C2×C32×C4C2×D411yescharacteristic
118C2×C32×C4C2×D411yescharacteristic
119C2×C3⋊Dic3C22⋊C414yescomplemented
120C2×C3⋊Dic3C2×D411yescharacteristic
121C2×C3⋊Dic3C2×D411yescharacteristic
122C4×C3⋊D3C22⋊C414yescomplemented
123C4×C3⋊D3C22⋊C414yescomplemented
124C4×C3⋊D3C22×C412yes—
125C4×C3⋊D3C22×C412yes—
126C4×C3⋊D3C2×D412yes—
127C4×C3⋊D3C2×D412yes—
128C3×#67—28no—
129C2×C3×Dic3—22no—
130C2×C3×Dic3—24no—
131C3×D12—24no—
132C3×C4×D3—28no—
133C3×Dic6—24no—
134#627—24no—
135#626—28no—
136#625—24no—
137#624—22no—
138#624—24no—
139#624—24no—
140#624C22×C414yes—
141D3×Dic3—28no—
142C22×#41—91no—
143C2×#117—91no—
144C22×C4⋊C4—91no—
145#391—92no—
146#390—92no—
147#386—94no—
148#380—94no—
149C23×D3—62no—
150C23×D3—61no—
151C23×D3—61no—
152C3×#41—68no—
153C2×C3×Q8—61no—
154C2×C3×D4—61no—
155C2×C3×D4—62no—
156C22×C3×C4—21no—
157C22×C3×C4—21no—
158C22×C3×C4—62no—
159C2×#67—22no—
160C2×#67—62no—
161C2×#67—62no—
162C22×Dic3—61no—
163C22×Dic3—61no—
164C22×Dic3—62no—
165#239—68no—
166D3×Q8—64no—
167D3×Q8—64no—
168#237—68no—
169#237—616no—
170D3×D4—64no—
171D3×D4—68no—
172D3×D4—64no—
173D3×D4—68no—
174#235—28no—
175#235—616no—
176C2×D12—21no—
177C2×D12—62no—
178C2×C4×D3—22no—
179C2×C4×D3—68no—
180C2×C4×D3—62no—
181C2×C4×D3—61no—
182C2×C4×D3—61no—
183C2×C4×D3—61no—
184C2×C4×D3—61no—
185C2×C4×D3—61no—
186C2×C4×D3—61no—
187C2×C4×D3—61no—
188C2×C4×D3—61no—
189C2×C4×D3—64no—
190C2×C4×D3—64no—
191C2×C4×D3—64no—
192C2×C4×D3—64no—
193C2×C4×D3—64no—
194C2×C4×D3—68no—
195C2×C4×D3—62no—
196C2×Dic6—21no—
197C2×Dic6—62no—
198C3×C4⋊C4—62no—
199C3×C22⋊C4—62no—
200C3×C42—62no—
201#217—22no—
202(C2×D3)⋊C4—64no—
203C4⋊Dic3—22no—
204Dic3⋊C4—64no—
205C4×Dic3—22no—
206C4×Dic3—64no—
207C22×C32—22no—
208C22×C32C2×C22⋊C412yes—
209C22×C32C22×D411yescharacteristic
210C2×C3⋊D3—22no—
211C2×C3⋊D3—24no—
212C2×C3⋊D3—22no—
213C2×C3⋊D3—22no—
214C2×C3⋊D3C2×C22⋊C412yes—
215C2×C3⋊D3C23×C411yescharacteristic
216C2×C3⋊D3C22×D411yescharacteristic
217C2×C3⋊D3H(5,𝔽2)12yes—
218C2×C3⋊D32−1+412yes—
219C2×C3×D3—24no—
220C2×C3×D3—44no—
221D32—28no—
222D32—42no—
223D32—42no—
224#157—44no—
225C32×C4C2×C22⋊C412yes—
226C32×C4C2×C22⋊C412yes—
227C3⋊Dic3C2×C22⋊C412yes—
228C3⋊Dic3C2×C22⋊C412yes—
229C3×Dic3—24no—
230C3×Dic3—44no—
231C2×#41—61no—
232C2×#41—98no—
233C2×#41—181no—
234C2×#41—181no—
235C2×#41—181no—
236C2×#41—184no—
237C22×Q8—91no—
238C22×D4—92no—
239C22×D4—91no—
240C23×C4—92no—
241C23×C4—91no—
242C23×C4—92no—
243#117—61no—
244#117—181no—
245#117—181no—
246#117—181no—
247C2×C4⋊C4—92no—
248C2×C4⋊C4—92no—
249C2×C4⋊C4—92no—
250C2×C4⋊C4—184no—
251C2×C22⋊C4—92no—
252C2×C22⋊C4—98no—
253C2×C42—92no—
254#95—98no—
255C23×C3—21no—
256C23×C3—21no—
257C23×C3—62no—
258C22×D3—22no—
259C22×D3—64no—
260C22×D3—61no—
261C22×D3—61no—
262C22×D3—62no—
263C22×D3—62no—
264C22×D3—61no—
265C22×D3—61no—
266C22×D3—62no—
267C22×D3—62no—
268C22×D3—64no—
269C22×D3—124no—
270C22×D3—124no—
271C22×D3—122no—
272C22×D3—122no—
273C22×D3—122no—
274C22×D3—122no—
275C3×Q8—64no—
276C3×D4—64no—
277C3×D4—68no—
278C2×C3×C4—21no—
279C2×C3×C4—21no—
280C2×C3×C4—21no—
281C2×C3×C4—21no—
282C2×C3×C4—24no—
283C2×C3×C4—24no—
284C2×C3×C4—68no—
285C2×C3×C4—62no—
286C2×C3×C4—64no—
287#67—28no—
288#67—68no—
289#67—68no—
290C2×Dic3—22no—
291C2×Dic3—24no—
292C2×Dic3—64no—
293C2×Dic3—64no—
294C2×Dic3—61no—
295C2×Dic3—61no—
296C2×Dic3—61no—
297C2×Dic3—61no—
298C2×Dic3—68no—
299D12—24no—
300D12—68no—
301C4×D3—28no—
302C4×D3—64no—
303C4×D3—64no—
304C4×D3—64no—
305C4×D3—64no—
306C4×D3—64no—
307C4×D3—62no—
308C4×D3—62no—
309C4×D3—62no—
310C4×D3—62no—
311C4×D3—62no—
312C4×D3—62no—
313C4×D3—62no—
314C4×D3—62no—
315C4×D3—64no—
316C4×D3—68no—
317C4×D3—124no—
318C4×D3—124no—
319Dic6—24no—
320Dic6—68no—
321C2×C32—22no—
322C2×C32C22×C22⋊C411yescharacteristic
323C2×C32#53712yes—
324C3⋊D3—22no—
325C3⋊D3#52012yes—
326C3⋊D3#53511yescharacteristic
327C3⋊D3#53611yescharacteristic
328C3×D3—44no—
329C24—92no—
330C24—91no—
331#41—68no—
332#41—188no—
333#41—188no—
334#41—188no—
335C2×Q8—61no—
336C2×Q8—94no—
337C2×Q8—181no—
338C2×Q8—182no—
339C2×D4—62no—
340C2×D4—61no—
341C2×D4—98no—
342C2×D4—94no—
343C2×D4—182no—
344C2×D4—182no—
345C2×D4—181no—
346C2×D4—184no—
347C22×C4—62no—
348C22×C4—92no—
349C22×C4—98no—
350C22×C4—94no—
351C22×C4—91no—
352C22×C4—91no—
353C22×C4—91no—
354C22×C4—91no—
355C22×C4—91no—
356C22×C4—94no—
357C22×C4—94no—
358C22×C4—94no—
359C22×C4—184no—
360C22×C4—182no—
361C22×C4—184no—
362C22×C4—364no—
363C22×C4GO+(4,𝔽2)11yescharacteristic
364C4⋊C4—62no—
365C4⋊C4—182no—
366C4⋊C4—184no—
367C4⋊C4—184no—
368C22⋊C4—62no—
369C22⋊C4—182no—
370C22⋊C4—368no—
371C42—62no—
372C42—182no—
373C22×C3—21no—
374C22×C3—21no—
375C22×C3—22no—
376C22×C3—22no—
377C22×C3—42no—
378C22×C3—42no—
379C22×C3—64no—
380C22×C3—124no—
381C2×D3—24no—
382C2×D3—44no—
383C2×D3—61no—
384C2×D3—61no—
385C2×D3—61no—
386C2×D3—61no—
387C2×D3—62no—
388C2×D3—62no—
389C2×D3—62no—
390C2×D3—62no—
391C2×D3—62no—
392C2×D3—62no—
393C2×D3—128no—
394C2×D3—122no—
395C2×D3—122no—
396C2×D3—124no—
397C2×D3—122no—
398C2×D3—124no—
399C2×D3—122no—
400C2×D3—122no—
401C2×D3—122no—
402C2×D3—124no—
403C2×D3—124no—
404C3×C4—22no—
405C3×C4—22no—
406C3×C4—22no—
407C3×C4—22no—
408C3×C4—64no—
409C3×C4—124no—
410Dic3—24no—
411Dic3—44no—
412Dic3—62no—
413Dic3—62no—
414Dic3—62no—
415Dic3—62no—
416C32#231111yescharacteristic, complemented, Sylow
417C23—62no—
418C23—94no—
419C23—91no—
420C23—91no—
421C23—92no—
422C23—92no—
423C23—182no—
424C23—182no—
425C23—182no—
426C23—184no—
427C23—184no—
428C23C2×GO+(4,𝔽2)11yescharacteristic
429Q8—64no—
430Q8—184no—
431D4—68no—
432D4—64no—
433D4—188no—
434D4—184no—
435C2×C4—62no—
436C2×C4—68no—
437C2×C4—64no—
438C2×C4—94no—
439C2×C4—91no—
440C2×C4—91no—
441C2×C4—94no—
442C2×C4—92no—
443C2×C4—92no—
444C2×C4—92no—
445C2×C4—92no—
446C2×C4—94no—
447C2×C4—94no—
448C2×C4—182no—
449C2×C4—188no—
450C2×C4—184no—
451C2×C4—184no—
452C2×C4—188no—
453C2×C4—184no—
454C2×C4—368no—
455C2×C4D32⋊C414yescomplemented
456C2×C4C2×GO+(4,𝔽2)11yescharacteristic
457C2×C4C2×GO+(4,𝔽2)11yescharacteristic
458C2×C3—22no—
459C2×C3—22no—
460C2×C3—21no—
461C2×C3—21no—
462C2×C3—42no—
463C2×C3—42no—
464C2×C3—124no—
465D3—44no—
466D3—62no—
467D3—61no—
468D3—61no—
469D3—62no—
470D3—61no—
471D3—61no—
472D3—122no—
473D3—122no—
474C22—22no—
475C22—64no—
476C22—92no—
477C22—92no—
478C22—91no—
479C22—91no—
480C22—92no—
481C22—124no—
482C22—182no—
483C22—184no—
484C22—182no—
485C22—188no—
486C22—182no—
487C22—362no—
488C22—362no—
489C22C2×D32⋊C412yes—
490C22C22×GO+(4,𝔽2)11yescharacteristic
491C4—64no—
492C4—92no—
493C4—92no—
494C4—124no—
495C4—364no—
496C4C2×D32⋊C412yes—
497C4C2×D32⋊C412yes—
498C3—21no—
499C3—21no—
500C2—22no—
501C2—91no—
502C2—92no—
503C2—91no—
504C2—124no—
505C2—182no—
506C2#1059651312yes—
507C2C22×D32⋊C411yescharacteristic
subgroupG/H
center, FrattiniC22C22×GO+(4,𝔽2)
commutatorC2×C3⋊D3C23×C4
FittingC22×C32×C4D4
socleC22×C32C22×D4
prime radicalC2×#64306C2
cosocleC22×C3⋊D3C24
hypercenterC22×C4GO+(4,𝔽2)
hypocenterC32#2311
LCSG ▷ C2×C3⋊D3 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4

Complements

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

NH ≅ G/Ntype
2. C22×C4⋊#157C2semidirect
3. #10594969C2semidirect
4. #10593515C2semidirect
5. #10593405C2semidirect
6. #10593403C2semidirect
7. #10593341C2semidirect
14. #64306C4semidirect
62. #3802C2×C4semidirect
64. C4×D32C2×C4semidirect
67. #3797C2×C4semidirect
116. C2×C32×C4C22⋊C4semidirect
119. C2×C3⋊Dic3C22⋊C4semidirect
122. C4×C3⋊D3C22⋊C4semidirect
123. C4×C3⋊D3C22⋊C4semidirect
416. C32#2311semidirect
455. C2×C4D32⋊C4semidirect

Maximal subgroups

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

subgroupindex
C2×#643062
C22×C4⋊#1572
#105949692
#105935152
#105934052
#105934032
#105933412
#23119