Finite Group Databasebeta

← #11801909

Subgroups — #11801909

Order 1152.

1630 conjugacy classes of subgroups; only the 207 normal subgroups are shown.

normal subgroups only

This group has 1630 conjugacy classes of subgroups — too many to draw. Only its 207 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
2C2×#64286C211yesmaximal, characteristic, complemented
3C2×C4×#624C211yesmaximal, characteristic, complemented
4#10593514C214yesmaximal, complemented
5#10593405C212yesmaximal, complemented
6C4×D32⋊C4C214yesmaximal, complemented
7#10593341C212yesmaximal, complemented
8C22×C4×C3⋊D3C2211yescharacteristic
9C2×C3×#235—21no—
10C2×#3811C2212yes—
11C22×#624C2212yes—
12C2×#3805—21no—
13#64306—24no—
14#64306C418yescomplemented
15C2×#3802C2211yescharacteristic
16C2×C4×D32C2212yes—
17C2×#3798—21no—
18C2×#3797C2211yescharacteristic
19C2×#3796—21no—
20C2×C22⋊#157C2212yes—
21#64286—24no—
22C2×C4⋊#157C2212yes—
23C2×C4×#157C2212yes—
24C2×D32⋊C4C2218yes—
25C2×C3×C4×Dic3—21no—
26C2×Dic32—21no—
27C4×#624—21no—
28C4×#624—21no—
29C4×#624C2212yes—
30C4×#624C2212yes—
31#63737C2218yes—
32C2×D3×#41—61no—
33C2×C42×D3—61no—
34C23×C3⋊D3C2311yescharacteristic
35C22×D32C2312yes—
36C22×#157C2314yes—
37C22×C32×C4D411yescharacteristic
38C22×C3⋊Dic3D411yescharacteristic
39C2×C4×C3⋊D3C2×C414yes—
40C2×C4×C3⋊D3D411yescharacteristic
41C2×C4×C3⋊D3D411yescharacteristic
42C2×C4×C3⋊D3D414yes—
43C2×C4×C3⋊D3C2311yescharacteristic
44C2×C4×C3⋊D3C2311yescharacteristic
45C2×C3×#67—22no—
46C22×C3×Dic3—22no—
47C3×#235—28no—
48C2×C3×D12—21no—
49C2×C3×C4×D3—22no—
50C2×C3×Dic6—21no—
51#3811—24no—
52#3811C2×C418yes—
53C2×#627—21no—
54C2×#626—22no—
55C2×#625—21no—
56C2×#624—22no—
57C2×#624—28no—
58C2×#624C2312yes—
59C2×#624C2314yes—
60#3805—28no—
61C2×D3×Dic3—22no—
62#3802—22no—
63#3802C2×C414yescomplemented
64C4×D32—24no—
65C4×D32C2×C418yescomplemented
66#3798—28no—
67#3797—22no—
68#3797C2×C414yescomplemented
69#3796—28no—
70C22⋊#157—24no—
71C4⋊#157—24no—
72C4×#157—24no—
73D32⋊C4—216no—
74C3×C4×Dic3—22no—
75C3×C4×Dic3—22no—
76Dic32—22no—
77Dic32—22no—
78#2297—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—62no—
92C22×C4×D3—61no—
93C22×C4×D3—61no—
94C2×C3×C42—61no—
95C2×C4×Dic3—21no—
96C2×C4×Dic3—62no—
97C42×D3—62no—
98C42×D3—62no—
99C42×D3—62no—
100C42×D3—62no—
101C23×C32C2×D411yescharacteristic
102C22×C3⋊D3—24no—
103C22×C3⋊D3C22×C412yes—
104C22×C3⋊D3C2×D411yescharacteristic
105C22×C3⋊D3C2×D412yes—
106C22×C3⋊D3C2411yescharacteristic
107C22×C3×D3—22no—
108C2×D32—22no—
109C2×D32—28no—
110C2×D32C22×C414yes—
111C2×#157—24no—
112C2×#157—28no—
113C2×C32×C4C22⋊C414yescomplemented
114C2×C32×C4C2×D411yescharacteristic
115C2×C32×C4C2×D411yescharacteristic
116C2×C3⋊Dic3C22⋊C414yescomplemented
117C2×C3⋊Dic3C2×D411yescharacteristic
118C2×C3⋊Dic3C2×D411yescharacteristic
119C4×C3⋊D3C22⋊C414yescomplemented
120C4×C3⋊D3C22⋊C414yescomplemented
121C4×C3⋊D3C22×C412yes—
122C4×C3⋊D3C22×C412yes—
123C4×C3⋊D3C2×D412yes—
124C4×C3⋊D3C2×D412yes—
125C3×#67—28no—
126C2×C3×Dic3—28no—
127C2×C3×Dic3—24no—
128C2×C3×Dic3—22no—
129C3×D12—24no—
130C3×C4×D3—28no—
131C3×Dic6—24no—
132#627—24no—
133#626—28no—
134#625—24no—
135#624—28no—
136#624—22no—
137#624—24no—
138#624C22×C414yes—
139#624#4118yescomplemented
140D3×Dic3—28no—
141C22×#41—91no—
142C2×#117—91no—
143C22×C42—91no—
144#391—92no—
145#390—92no—
146#386—94no—
147C4×C22⋊C4—94no—
148C23×D3—62no—
149C23×D3—61no—
150C23×D3—61no—
151C3×#41—68no—
152C2×C3×Q8—61no—
153C2×C3×D4—61no—
154C2×C3×D4—62no—
155C22×C3×C4—21no—
156C22×C3×C4—21no—
157C22×C3×C4—62no—
158C22×C3×C4—62no—
159C2×#67—22no—
160C2×#67—62no—
161C2×#67—62no—
162C22×Dic3—22no—
163C22×Dic3—61no—
164C22×Dic3—61no—
165C22×Dic3—62no—
166#239—68no—
167D3×Q8—64no—
168D3×Q8—64no—
169#237—68no—
170#237—616no—
171D3×D4—64no—
172D3×D4—68no—
173D3×D4—64no—
174D3×D4—68no—
175#235—28no—
176#235—616no—
177C2×D12—21no—
178C2×D12—62no—
179C2×C4×D3—22no—
180C2×C4×D3—68no—
181C2×C4×D3—64no—
182C2×C4×D3—62no—
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—61no—
190C2×C4×D3—61no—
191C2×C4×D3—64no—
192C2×C4×D3—64no—
193C2×C4×D3—64no—
194C2×C4×D3—64no—
195C2×C4×D3—68no—
196C2×C4×D3—64no—
197C2×C4×D3—616no—
198C2×C4×D3—62no—
199C2×Dic6—21no—
200C2×Dic6—62no—
201C3×C42—62no—
202C3×C42—62no—
203C4×Dic3—22no—
204C4×Dic3—22no—
205C4×Dic3—64no—
206C4×Dic3—64no—
207C22×C32—22no—
208C22×C32C2×C22⋊C412yes—
209C22×C32C22×D411yescharacteristic
210C2×C3⋊D3—22no—
211C2×C3⋊D3—24no—
212C2×C3⋊D3—24no—
213C2×C3⋊D3C2×C22⋊C412yes—
214C2×C3⋊D3C23×C411yescharacteristic
215C2×C3⋊D3C22×D411yescharacteristic
216C2×C3⋊D3C2×#4114yes—
217C2×C3×D3—24no—
218C2×C3×D3—44no—
219D32—28no—
220D32—44no—
221#157—44no—
222C32×C4C2×C22⋊C412yes—
223C32×C4C2×C22⋊C412yes—
224C3⋊Dic3C2×C22⋊C412yes—
225C3⋊Dic3C2×C22⋊C412yes—
226C3×Dic3—24no—
227C3×Dic3—28no—
228C2×#41—61no—
229C2×#41—98no—
230C2×#41—181no—
231C2×#41—181no—
232C2×#41—181no—
233C2×#41—184no—
234C22×Q8—91no—
235C22×D4—92no—
236C22×D4—91no—
237C23×C4—92no—
238C23×C4—92no—
239C23×C4—91no—
240#117—184no—
241C2×C4⋊C4—92no—
242C2×C22⋊C4—92no—
243C2×C22⋊C4—98no—
244C2×C42—61no—
245C2×C42—92no—
246C2×C42—92no—
247C2×C42—92no—
248C2×C42—181no—
249C2×C42—181no—
250C2×C42—181no—
251#95—98no—
252C23×C3—21no—
253C23×C3—21no—
254C23×C3—62no—
255C22×D3—22no—
256C22×D3—64no—
257C22×D3—62no—
258C22×D3—61no—
259C22×D3—62no—
260C22×D3—61no—
261C22×D3—61no—
262C22×D3—62no—
263C22×D3—61no—
264C22×D3—62no—
265C22×D3—64no—
266C22×D3—68no—
267C22×D3—128no—
268C22×D3—124no—
269C3×Q8—64no—
270C3×D4—64no—
271C3×D4—68no—
272C2×C3×C4—21no—
273C2×C3×C4—21no—
274C2×C3×C4—21no—
275C2×C3×C4—21no—
276C2×C3×C4—24no—
277C2×C3×C4—24no—
278C2×C3×C4—68no—
279C2×C3×C4—64no—
280C2×C3×C4—62no—
281C2×C3×C4—68no—
282#67—28no—
283#67—68no—
284#67—68no—
285C2×Dic3—24no—
286C2×Dic3—22no—
287C2×Dic3—28no—
288C2×Dic3—64no—
289C2×Dic3—64no—
290C2×Dic3—61no—
291C2×Dic3—61no—
292C2×Dic3—61no—
293C2×Dic3—61no—
294C2×Dic3—68no—
295D12—24no—
296D12—68no—
297C4×D3—28no—
298C4×D3—64no—
299C4×D3—68no—
300C4×D3—64no—
301C4×D3—64no—
302C4×D3—64no—
303C4×D3—64no—
304C4×D3—62no—
305C4×D3—62no—
306C4×D3—62no—
307C4×D3—62no—
308C4×D3—62no—
309C4×D3—62no—
310C4×D3—62no—
311C4×D3—62no—
312C4×D3—68no—
313C4×D3—616no—
314C4×D3—64no—
315C4×D3—68no—
316Dic6—24no—
317Dic6—68no—
318C2×C32—22no—
319C2×C32C22×C22⋊C411yescharacteristic
320C2×C32#52512yes—
321C3⋊D3—22no—
322C3⋊D3C4×#4112yes—
323C3⋊D3#53212yes—
324C3×D3—44no—
325C24—92no—
326C24—91no—
327#41—68no—
328#41—188no—
329#41—188no—
330#41—188no—
331C2×Q8—61no—
332C2×Q8—94no—
333C2×Q8—181no—
334C2×Q8—182no—
335C2×D4—62no—
336C2×D4—61no—
337C2×D4—98no—
338C2×D4—94no—
339C2×D4—182no—
340C2×D4—182no—
341C2×D4—181no—
342C2×D4—184no—
343C22×C4—62no—
344C22×C4—62no—
345C22×C4—92no—
346C22×C4—94no—
347C22×C4—98no—
348C22×C4—91no—
349C22×C4—91no—
350C22×C4—91no—
351C22×C4—91no—
352C22×C4—91no—
353C22×C4—94no—
354C22×C4—94no—
355C22×C4—94no—
356C22×C4—184no—
357C22×C4—188no—
358C22×C4—182no—
359C22×C4—182no—
360C22×C4GO+(4,𝔽2)11yescharacteristic
361C4⋊C4—184no—
362C22⋊C4—1816no—
363C22⋊C4—184no—
364C42—62no—
365C42—62no—
366C42—182no—
367C42—182no—
368C42—184no—
369C22×C3—24no—
370C22×C3—21no—
371C22×C3—21no—
372C22×C3—22no—
373C22×C3—22no—
374C22×C3—42no—
375C22×C3—64no—
376C22×C3—124no—
377C2×D3—24no—
378C2×D3—44no—
379C2×D3—61no—
380C2×D3—61no—
381C2×D3—62no—
382C2×D3—61no—
383C2×D3—61no—
384C2×D3—64no—
385C2×D3—64no—
386C2×D3—62no—
387C2×D3—64no—
388C2×D3—68no—
389C2×D3—68no—
390C2×D3—128no—
391C2×D3—124no—
392C2×D3—124no—
393C2×D3—122no—
394C2×D3—128no—
395C3×C4—22no—
396C3×C4—22no—
397C3×C4—22no—
398C3×C4—22no—
399C3×C4—64no—
400C3×C4—68no—
401Dic3—24no—
402Dic3—28no—
403Dic3—62no—
404Dic3—62no—
405Dic3—62no—
406Dic3—62no—
407C32#229711yescharacteristic, complemented, Sylow
408C23—62no—
409C23—94no—
410C23—91no—
411C23—91no—
412C23—92no—
413C23—92no—
414C23—184no—
415C23—182no—
416C23—188no—
417C23C2×GO+(4,𝔽2)11yescharacteristic
418Q8—64no—
419Q8—184no—
420D4—68no—
421D4—64no—
422D4—188no—
423D4—184no—
424C2×C4—68no—
425C2×C4—64no—
426C2×C4—62no—
427C2×C4—68no—
428C2×C4—98no—
429C2×C4—94no—
430C2×C4—91no—
431C2×C4—91no—
432C2×C4—94no—
433C2×C4—92no—
434C2×C4—92no—
435C2×C4—92no—
436C2×C4—92no—
437C2×C4—94no—
438C2×C4—94no—
439C2×C4—182no—
440C2×C4—184no—
441C2×C4—188no—
442C2×C4—188no—
443C2×C4—184no—
444C2×C4—188no—
445C2×C4D32⋊C414yescomplemented
446C2×C4C2×GO+(4,𝔽2)11yescharacteristic
447C2×C4C2×GO+(4,𝔽2)11yescharacteristic
448C2×C3—24no—
449C2×C3—22no—
450C2×C3—22no—
451C2×C3—21no—
452C2×C3—21no—
453C2×C3—42no—
454C2×C3—124no—
455D3—44no—
456D3—62no—
457D3—62no—
458D3—62no—
459D3—62no—
460D3—64no—
461D3—122no—
462C22—22no—
463C22—64no—
464C22—94no—
465C22—91no—
466C22—91no—
467C22—92no—
468C22—124no—
469C22—184no—
470C22—184no—
471C22—188no—
472C22—182no—
473C22—364no—
474C22C2×D32⋊C412yes—
475C22C22×GO+(4,𝔽2)11yescharacteristic
476C4—68no—
477C4—64no—
478C4—92no—
479C4—92no—
480C4—364no—
481C4C2×D32⋊C412yes—
482C4C2×D32⋊C412yes—
483C3—21no—
484C3—21no—
485C2—22no—
486C2—92no—
487C2—92no—
488C2—124no—
489C2—182no—
490C2#1059651012yes—
491C2C22×D32⋊C411yescharacteristic
subgroupG/H
centerC2×C4C2×GO+(4,𝔽2)
commutatorC2×C3⋊D3C23×C4
FrattiniC22C22×GO+(4,𝔽2)
FittingC22×C32×C4D4
socleC22×C32C22×D4
prime radicalC2×#64306C2
cosocleC22×C3⋊D3C24
hypercenterC22×C4GO+(4,𝔽2)
hypocenterC32#2297
LCSG ▷ C2×C3⋊D3 ▷ C32
UCSC1 ◁ C2×C4 ◁ C22×C4

Complements

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

NH ≅ G/Ntype
2. C2×#64286C2semidirect
3. C2×C4×#624C2semidirect
4. #10593514C2semidirect
5. #10593405C2semidirect
6. C4×D32⋊C4C2semidirect
7. #10593341C2semidirect
14. #64306C4semidirect
63. #3802C2×C4semidirect
65. C4×D32C2×C4semidirect
68. #3797C2×C4semidirect
113. C2×C32×C4C22⋊C4semidirect
116. C2×C3⋊Dic3C22⋊C4semidirect
119. C4×C3⋊D3C22⋊C4semidirect
120. C4×C3⋊D3C22⋊C4semidirect
139. #624#41semidirect
407. C32#2297semidirect
445. 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
C2×#642862
C2×C4×#6242
#105935142
#105934052
C4×D32⋊C42
#105933412
#22979