Finite Group Databasebeta

← #11786442

Subgroups — #11786442

Order 1152.

634 conjugacy classes of subgroups; only the 81 normal subgroups are shown.

normal subgroups only

This group has 634 conjugacy classes of subgroups — too many to draw. Only its 81 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
1D32×C4⋊C4C211yesmaximal, characteristic
2#10593403C211yesmaximal, characteristic
3#10593396C211yesmaximal, characteristic, complemented
4C2×D32⋊C8C211yesmaximal, characteristic
5#10590573C211yesmaximal, characteristic, complemented
6#10590163C211yesmaximal, characteristic, complemented
7#10590049C211yesmaximal, characteristic, complemented
8C2×C4×D32—21no—
9C2×C4×D32C2211yescharacteristic
10C2×C4⋊#157C2211yescharacteristic
11C2×#3787C2211yescharacteristic
12C2×D32⋊C4—21no—
13C4⋊C4×C3⋊D3C2211yescharacteristic
14C3×D3×C4⋊C4—21no—
15#63900C2211yescharacteristic
16#63900C2211yescharacteristic
17D3×C4⋊Dic3—21no—
18#63883—21no—
19D3×Dic3⋊C4—22no—
20C2×#3710C2211yescharacteristic
21#63743—22no—
22#63737—21no—
23D32⋊C8C414yescomplemented
24C3×#807—21no—
25#63575—21no—
26C2×D3×C4⋊C4—61no—
27D3×#107—61no—
28C22×D32D411yescharacteristic
29C22×#157—21no—
30C2×C4×C3⋊D3—21no—
31C2×C4×C3⋊D3C2311yescharacteristic
32C2×C3×C4×D3—21no—
33C2×C3×C4×D3—22no—
34C2×#624—21no—
35C2×#624—21no—
36C2×#624D411yescharacteristic
37C2×D3×Dic3—21no—
38C2×D3×Dic3—22no—
39C4×D32—21no—
40C4×D32—21no—
41C4×D32—42no—
42C4×D32—42no—
43C4×D32C2×C412yes—
44C4×D32Q812yes—
45C2×#622—21no—
46C4⋊#157—21no—
47C4⋊#157—21no—
48#3787—21no—
49#3787C2×C412yescomplemented
50D32⋊C4—42no—
51C32×C4⋊C4D411yescharacteristic
52C4⋊(C3⋊Dic3)D411yescharacteristic
53#3750—21no—
54C3×C4⋊Dic3—21no—
55C3×C4⋊Dic3—21no—
56C3×Dic3⋊C4—22no—
57C2×C3×C3⋊C8—21no—
58#3724—21no—
59#3724D412yes—
60Dic3⋊Dic3—22no—
61#3710—21no—
62#3710C2×C412yescomplemented
63#1852—91nomaximal, Sylow
64C22×C4×D3—61no—
65C22×C4×D3—62no—
66C2×C3×C4⋊C4—61no—
67C2×C4⋊Dic3—61no—
68C2×Dic3⋊C4—62no—
69C2×D3×C8—61no—
70D3×C4⋊C4—21no—
71D3×C4⋊C4—61no—
72D3×C4⋊C4—61no—
73D3×C4⋊C4—61no—
74D3×C4⋊C4—61no—
75D3×C4⋊C4—62no—
76D3×C4⋊C4—62no—
77D3×C4⋊C4—61no—
78C3×#107—61no—
79#818—61no—
80#807—21no—
81#807—61no—
82C22×C3⋊D3C2×D411yescharacteristic
83C22×C3×D3—21no—
84C2×D32—21no—
85C2×D32—21no—
86C2×D32—21no—
87C2×D32C4⋊C412yes—
88C2×D32D812yes—
89C2×D32Q1612yes—
90C2×#157—41no—
91C2×#157—41no—
92C2×#157—41no—
93C2×C32×C4—21no—
94C2×C32×C4C2×D411yescharacteristic
95C2×C3⋊Dic3—21no—
96C2×C3⋊Dic3C2×D411yescharacteristic
97C4×C3⋊D3—41no—
98C4×C3⋊D3—41no—
99C4×C3⋊D3C22×C411yescharacteristic
100C4×C3⋊D3C2×Q811yescharacteristic
101C4×C3⋊D3#4111yescharacteristic
102C4×C3⋊D3#4111yescharacteristic
103C2×C3×Dic3—21no—
104C2×C3×Dic3—22no—
105C2×C3×Dic3—41no—
106C3×C4×D3—22no—
107C3×C4×D3—22no—
108C3×C4×D3—44no—
109#624—21no—
110#624—41no—
111#624—41no—
112#624—41no—
113#624—41no—
114#624C4⋊C412yes—
115D3×Dic3—22no—
116D3×Dic3—22no—
117D3×Dic3—44no—
118#622—22no—
119C3×C3⋊C8—22no—
120C22×C4⋊C4—91no—
121C2×#107—91no—
122C2×#107—91no—
123C2×C22⋊C8—91no—
124#380—91no—
125#340—91no—
126#340—91no—
127C23×D3—61no—
128C22×C3×C4—61no—
129C22×C3×C4—62no—
130C22×Dic3—61no—
131C22×Dic3—62no—
132C2×C4×D3—21no—
133C2×C4×D3—22no—
134C2×C4×D3—62no—
135C2×C4×D3—62no—
136C2×C4×D3—61no—
137C2×C4×D3—61no—
138C2×C4×D3—61no—
139C2×C4×D3—62no—
140C2×C4×D3—62no—
141C2×C4×D3—61no—
142C2×C4×D3—62no—
143C2×C4×D3—62no—
144C2×C4×D3—62no—
145C2×C4×D3—121no—
146C2×C4×D3—121no—
147C2×C4×D3—124no—
148C2×C4×D3—124no—
149C2×C3×C8—61no—
150C3×C4⋊C4—21no—
151C3×C4⋊C4—21no—
152C3×C4⋊C4—62no—
153C3×C4⋊C4—61no—
154C3×C4⋊C4—61no—
155C4⋊Dic3—21no—
156C4⋊Dic3—21no—
157C4⋊Dic3—61no—
158C4⋊Dic3—61no—
159C4⋊Dic3—62no—
160Dic3⋊C4—22no—
161Dic3⋊C4—62no—
162Dic3⋊C4—62no—
163Dic3⋊C4—62no—
164Dic3⋊C4—121no—
165Dic3⋊C4—121no—
166C2×C3⋊C8—21no—
167D3×C8—62no—
168D3×C8—62no—
169C22×C32#12011yescharacteristic
170C2×C3⋊D3C2×C4⋊C411yescharacteristic
171C2×C3⋊D3#12311yescharacteristic
172C2×C3⋊D3C2×D811yescharacteristic
173C2×C3⋊D3C2×Q1611yescharacteristic
174C2×C3⋊D3AGL(1,ℤ/8)11yescharacteristic
175C2×C3⋊D3#13711yescharacteristic
176C2×C3×D3—22no—
177C2×C3×D3—22no—
178C2×C3×D3—22no—
179D32—22no—
180D32—22no—
181D32—22no—
182D32#10714yescomplemented
183#157—81no—
184C32×C4—41no—
185C32×C4C4×D411yescharacteristic
186C32×C4C22⋊Q811yescharacteristic
187C3⋊Dic3—41no—
188C3⋊Dic3C4×D411yescharacteristic
189C3⋊Dic3C22⋊Q811yescharacteristic
190C3×Dic3—22no—
191C3×Dic3—42no—
192C3×Dic3—81no—
193C23×C4—91no—
194C23×C4—181no—
195C22×C8—91no—
196C22×C8—91no—
197C2×C4⋊C4—61no—
198C2×C4⋊C4—91no—
199C2×C4⋊C4—91no—
200C2×C4⋊C4—91no—
201C2×C4⋊C4—91no—
202C2×C4⋊C4—181no—
203C2×C4⋊C4—182no—
204C2×C4⋊C4—181no—
205C2×C22⋊C4—181no—
206#107—61no—
207#107—181no—
208#107—182no—
209C22⋊C8—94no—
210#95—181no—
211C23×C3—61no—
212C22×D3—21no—
213C22×D3—62no—
214C22×D3—62no—
215C22×D3—62no—
216C22×D3—61no—
217C22×D3—61no—
218C22×D3—62no—
219C22×D3—62no—
220C22×D3—62no—
221C2×C3×C4—22no—
222C2×C3×C4—21no—
223C2×C3×C4—21no—
224C2×C3×C4—41no—
225C2×C3×C4—62no—
226C2×C3×C4—62no—
227C2×C3×C4—61no—
228C2×C3×C4—62no—
229C2×C3×C4—124no—
230C2×C3×C4—121no—
231C2×Dic3—21no—
232C2×Dic3—22no—
233C2×Dic3—41no—
234C2×Dic3—61no—
235C2×Dic3—61no—
236C2×Dic3—62no—
237C2×Dic3—62no—
238C2×Dic3—62no—
239C2×Dic3—121no—
240C2×Dic3—124no—
241C4×D3—22no—
242C4×D3—22no—
243C4×D3—44no—
244C4×D3—62no—
245C4×D3—61no—
246C4×D3—61no—
247C4×D3—61no—
248C4×D3—61no—
249C4×D3—61no—
250C4×D3—61no—
251C4×D3—61no—
252C4×D3—61no—
253C4×D3—62no—
254C4×D3—62no—
255C4×D3—62no—
256C4×D3—122no—
257C4×D3—122no—
258C4×D3—122no—
259C4×D3—122no—
260C4×D3—124no—
261C4×D3—241no—
262C4×D3—241no—
263C4×D3—241no—
264C4×D3—241no—
265C3×C8—62no—
266C3⋊C8—22no—
267C2×C32#38511yescharacteristic
268C2×C32#44711yescharacteristic
269C2×C32#45111yescharacteristic
270C3⋊D3C2×#10711yescharacteristic
271C3⋊D3#42811yescharacteristic
272C3⋊D3#48011yescharacteristic
273C3⋊D3#48411yescharacteristic
274C3×D3—24no—
275C24—91no—
276C22×C4—62no—
277C22×C4—61no—
278C22×C4—91no—
279C22×C4—92no—
280C22×C4—92no—
281C22×C4—91no—
282C22×C4—181no—
283C22×C4—181no—
284C22×C4—181no—
285C22×C4—181no—
286C22×C4—181no—
287C22×C4—182no—
288C22×C4—181no—
289C22×C4—181no—
290C22×C4—362no—
291C22×C4—362no—
292C2×C8—61no—
293C2×C8—92no—
294C2×C8—92no—
295C2×C8—181no—
296C2×C8—181no—
297C2×C8—181no—
298C4⋊C4—62no—
299C4⋊C4—61no—
300C4⋊C4—61no—
301C4⋊C4—92no—
302C4⋊C4—91no—
303C4⋊C4—181no—
304C4⋊C4—182no—
305C4⋊C4—181no—
306C4⋊C4—181no—
307C4⋊C4—181no—
308C4⋊C4GO+(4,𝔽2)11yescharacteristic
309C22⋊C4—362no—
310C22×C3—21no—
311C22×C3—21no—
312C22×C3—62no—
313C22×C3—62no—
314C22×C3—62no—
315C2×D3—22no—
316C2×D3—22no—
317C2×D3—22no—
318C2×D3—64no—
319C2×D3—61no—
320C2×D3—61no—
321C2×D3—61no—
322C2×D3—61no—
323C2×D3—61no—
324C2×D3—61no—
325C2×D3—61no—
326C2×D3—61no—
327C2×D3—61no—
328C2×D3—61no—
329C2×D3—61no—
330C2×D3—61no—
331C2×D3—64no—
332C2×D3—64no—
333C2×D3—64no—
334C3×C4—21no—
335C3×C4—21no—
336C3×C4—21no—
337C3×C4—21no—
338C3×C4—42no—
339C3×C4—62no—
340C3×C4—81no—
341C3×C4—122no—
342C3×C4—241no—
343Dic3—22no—
344Dic3—42no—
345Dic3—61no—
346Dic3—61no—
347Dic3—61no—
348Dic3—61no—
349Dic3—81no—
350Dic3—122no—
351Dic3—241no—
352C32#185211yescharacteristic, complemented, Sylow
353C23—61no—
354C23—92no—
355C23—92no—
356C23—92no—
357C23—91no—
358C23—181no—
359C23—181no—
360C23—181no—
361C2×C4—21no—
362C2×C4—61no—
363C2×C4—62no—
364C2×C4—62no—
365C2×C4—62no—
366C2×C4—92no—
367C2×C4—91no—
368C2×C4—91no—
369C2×C4—91no—
370C2×C4—91no—
371C2×C4—91no—
372C2×C4—124no—
373C2×C4—121no—
374C2×C4—181no—
375C2×C4—182no—
376C2×C4—182no—
377C2×C4—181no—
378C2×C4—361no—
379C2×C4—361no—
380C2×C4—361no—
381C2×C4—361no—
382C2×C4—364no—
383C2×C4—361no—
384C2×C4—361no—
385C2×C4—361no—
386C2×C4—361no—
387C2×C4—361no—
388C2×C4C2×GO+(4,𝔽2)11yescharacteristic
389C8—62no—
390C8—182no—
391C2×C3—21no—
392C2×C3—21no—
393C2×C3—21no—
394C2×C3—21no—
395C2×C3—21no—
396C2×C3—21no—
397C2×C3—64no—
398D3—24no—
399D3—61no—
400D3—61no—
401D3—61no—
402D3—61no—
403D3—61no—
404D3—61no—
405D3—61no—
406D3—61no—
407C22—62no—
408C22—62no—
409C22—62no—
410C22—94no—
411C22—91no—
412C22—91no—
413C22—91no—
414C22—91no—
415C22—91no—
416C22—91no—
417C22—182no—
418C22—182no—
419C22—182no—
420C22#6424111yescharacteristic
421C4—41no—
422C4—62no—
423C4—91no—
424C4—91no—
425C4—122no—
426C4—241no—
427C4—361no—
428C4—721no—
429C4D32⋊Q811yescharacteristic
430C4C4×GO+(4,𝔽2)11yescharacteristic
431C3—21no—
432C3—21no—
433C2—64no—
434C2—91no—
435C2—91no—
436C2—91no—
437C2—91no—
438C2#1059339811yescharacteristic
439C2#1059345711yescharacteristic
440C2#1059347211yescharacteristic
subgroupG/H
centerC22#64241
commutatorC4×C3⋊D3C22×C4
FrattiniC2×C4C2×GO+(4,𝔽2)
FittingC32×C4⋊C4D4
socleC22×C32#120
prime radicalC22×D32D4
cosocleC2×C4×C3⋊D3C23
hypercenterC4⋊C4GO+(4,𝔽2)
hypocenterC32#1852
LCSG ▷ C4×C3⋊D3 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C2×C4 ◁ C4⋊C4

Complements

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

NH ≅ G/Ntype
3. #10593396C2semidirect
5. #10590573C2semidirect
6. #10590163C2semidirect
7. #10590049C2semidirect
23. D32⋊C8C4semidirect
49. #3787C2×C4semidirect
62. #3710C2×C4semidirect
182. D32#107semidirect
352. C32#1852semidirect

Maximal subgroups

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

subgroupindex
D32×C4⋊C42
#105934032
#105933962
C2×D32⋊C82
#105905732
#105901632
#105900492
#18529