Finite Group Databasebeta

← #11780211

Subgroups — #11780211

Order 1152.

608 conjugacy classes of subgroups; only the 98 normal subgroups are shown.

normal subgroups only

This group has 608 conjugacy classes of subgroups — too many to draw. Only its 98 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
1D4×#634C211yesmaximal, characteristic
2C3×#5007C211yesmaximal, characteristic
3#10590388C211yesmaximal, characteristic, complemented
4#10590311C211yesmaximal, characteristic, complemented
5C3×D4⋊(C3⋊C8)C211yesmaximal, characteristic
6#10589094C211yesmaximal, characteristic, complemented
7#10589085C211yesmaximal, characteristic, complemented
8#71114—31nomaximal
9#68192—31nomaximal
10C22×#634—21no—
11C32×C4×D4C2211yescharacteristic
12D4×C3⋊Dic3—21no—
13#64133—21no—
14#64097—21no—
15#64087—22no—
16#64078C2211yescharacteristic
17C4×#634C2211yescharacteristic
18C3×#869C2211yescharacteristic
19C2×#3719—21no—
20C3×#832—21no—
21C3×#807—21no—
22C3×C4⋊(C3⋊C8)C2211yescharacteristic
23C3×C4⋊(C3⋊C8)C2211yescharacteristic
24C3×C4×C3⋊C8C2211yescharacteristic
25#63575—22no—
26#63566—21no—
27D4×Dic6—31no—
28D4×Dic6—31no—
29D4×Dic6—61no—
30C3×#474—31no—
31#5090—31no—
32#5078—31no—
33#5007D311yescharacteristic
34#4849—31no—
35#4682—31no—
36C3×D4⋊C8—31no—
37D4⋊(C3⋊C8)D311yescharacteristic
38#4486—31no—
39#4484—31no—
40#4482—31no—
41#4456—31no—
42C2×C32×D4D411yescharacteristic
43C22×C32×C4—21no—
44C22×C3⋊Dic3—22no—
45C2×#634—22no—
46C2×#634—21no—
47C2×#634—42no—
48C2×#634—42no—
49C2×#634D411yescharacteristic
50C2×C3×Dic6—21no—
51C32×C4⋊C4D411yescharacteristic
52C32×C22⋊C4—21no—
53C32×C42C2311yescharacteristic
54#3757—22no—
55C4⋊(C3⋊Dic3)—21no—
56C4⋊(C3⋊Dic3)D411yescharacteristic
57C4⋊(C3⋊Dic3)D412yes—
58#3750—22no—
59#3750—21no—
60C4×C3⋊Dic3—21no—
61C3×C4⋊Dic3—21no—
62C3×C4⋊Dic3—21no—
63C2×C3×C3⋊C8—21no—
64C2×C3×C3⋊C8—21no—
65C2×C3×C3⋊C8—21no—
66#3719—42no—
67#1649—91noSylow
68C22×Dic6—61no—
69C22×Dic6—61no—
70C22×Dic6—62no—
71C3×C4⋊Q8—31no—
72C3×C4×D4—21no—
73C3×C4×D4C2×D311yescharacteristic
74C3×C4×D4C2×D311yescharacteristic
75C2×#216—61no—
76D4×Dic3—62no—
77D4×Dic3—61no—
78D4×Dic3—61no—
79#924—61no—
80#924—61no—
81#924—62no—
82C2×Dic12—61no—
83#888—62no—
84#888—61no—
85#888—61no—
86#878—62no—
87#878—62no—
88#878—64no—
89#869—31no—
90#869—31no—
91#869—61no—
92#869C2×D311yescharacteristic
93C4×Dic6—31no—
94C4×Dic6—31no—
95C4×Dic6—61no—
96C3×#107—61no—
97C3×C4⋊C8—31no—
98C3×C4⋊C8—31no—
99C3×#102—61no—
100C3×C4×C8—31no—
101#835—61no—
102#832—21no—
103#818—62no—
104#816—61no—
105#807—21no—
106#807—62no—
107C4⋊(C3⋊C8)C2×D311yescharacteristic
108C4⋊(C3⋊C8)C2×D311yescharacteristic
109C4×C3⋊C8C2×D311yescharacteristic
110C23×C32—21no—
111C32×D4—21no—
112C32×D4Q1612yescomplemented
113C2×C32×C4—21no—
114C2×C32×C4—41no—
115C2×C32×C4—41no—
116C2×C32×C4C2×D411yescharacteristic
117C2×C32×C4C2×D411yescharacteristic
118C2×C32×C4C2×D411yescharacteristic
119C2×C3⋊Dic3—21no—
120C2×C3⋊Dic3—21no—
121C2×C3⋊Dic3—22no—
122C2×C3⋊Dic3—44no—
123#634—21no—
124#634—44no—
125#634—41no—
126#634—41no—
127#634D812yes—
128C2×C3×Dic3—41no—
129C3×Dic6—41no—
130C3×Dic6—41no—
131C3×C3⋊C8—22no—
132C3×C3⋊C8—41no—
133C3×C3⋊C8—41no—
134D4×Q8—91no—
135#500—91no—
136#474—31no—
137#462—91no—
138#332—91no—
139Q8⋊C8—91no—
140D4⋊C8—31no—
141C2×C3×Q8—61no—
142C2×C3×D4—21no—
143C2×C3×D4D1211yescharacteristic
144C2×C3×D4#6711yescharacteristic
145C22×C3×C4—22no—
146C22×C3×C4—21no—
147C22×C3×C4—21no—
148C22×Dic3—64no—
149C22×Dic3—62no—
150C22×Dic3—62no—
151C2×Dic6—21no—
152C2×Dic6—31no—
153C2×Dic6—31no—
154C2×Dic6—61no—
155C2×Dic6—62no—
156C2×Dic6—64no—
157C2×Dic6—62no—
158C2×Dic6—62no—
159C2×Dic6—61no—
160C2×Dic6—61no—
161C2×Dic6—122no—
162C2×Dic6—122no—
163C2×Dic6—124no—
164C2×Dic6—124no—
165C2×Dic6—122no—
166C2×Dic6—122no—
167C2×C3×C8—61no—
168C2×C3×C8—61no—
169C2×C3×C8—61no—
170C3×C4⋊C4—21no—
171C3×C4⋊C4—61no—
172C3×C4⋊C4—61no—
173C3×C4⋊C4D1211yescharacteristic
174C3×C4⋊C4#6711yescharacteristic
175C3×C22⋊C4—22no—
176C3×C22⋊C4—21no—
177C3×C22⋊C4—21no—
178C3×C42—21no—
179C3×C42C22×D311yescharacteristic
180C3×C42C22×D311yescharacteristic
181#217—64no—
182#217—62no—
183#217—62no—
184#216—122no—
185C4⋊Dic3—21no—
186C4⋊Dic3—21no—
187C4⋊Dic3—32no—
188C4⋊Dic3—31no—
189C4⋊Dic3—32no—
190C4⋊Dic3—31no—
191C4⋊Dic3—61no—
192C4⋊Dic3—62no—
193C4⋊Dic3—62no—
194C4⋊Dic3—61no—
195C4⋊Dic3—61no—
196Dic3⋊C4—62no—
197Dic3⋊C4—64no—
198Dic3⋊C4—62no—
199Dic3⋊C4—62no—
200Dic3⋊C4—61no—
201Dic3⋊C4—61no—
202C4×Dic3—62no—
203C4×Dic3—61no—
204C4×Dic3—61no—
205C2×C3⋊C8—21no—
206C2×C3⋊C8—21no—
207C2×C3⋊C8—21no—
208Dic12—122no—
209C22×C32—22no—
210C22×C32—41no—
211C22×C32—41no—
212C22×C32#12011yescharacteristic
213C32×C4—21no—
214C32×C4—41no—
215C32×C4C2×D811yescharacteristic
216C32×C4C2×Q1611yescharacteristic
217C32×C4AGL(1,ℤ/8)11yescharacteristic
218C32×C4#13711yescharacteristic
219C3⋊Dic3—22no—
220C3⋊Dic3—42no—
221C3⋊Dic3—41no—
222C3×Dic3—81no—
223C22×Q8—181no—
224C2×Q16—181no—
225C4⋊Q8—31no—
226C4⋊Q8—91no—
227C4⋊Q8—181no—
228C22⋊Q8—182no—
229C22⋊Q8—181no—
230C4×Q8—91no—
231C4×D4—181no—
232C4×D4D3211yescharacteristic
233#107—61no—
234#107—182no—
235C4⋊C8—31no—
236C4⋊C8—31no—
237#103—181no—
238#102—61no—
239C4×C8—31no—
240C23×C3—22no—
241C23×C3—21no—
242C23×C3—21no—
243C3×Q8—121no—
244C3×Q8—121no—
245C3×D4—22no—
246C3×D4—21no—
247C3×D4—21no—
248C3×D4—22no—
249C3×D4Dic1212yescomplemented
250C3×D4#21612yescomplemented
251C2×C3×C4—22no—
252C2×C3×C4—21no—
253C2×C3×C4—21no—
254C2×C3×C4—21no—
255C2×C3×C4—21no—
256C2×C3×C4—21no—
257C2×C3×C4—42no—
258C2×C3×C4—42no—
259C2×C3×C4—41no—
260C2×C3×C4—41no—
261C2×C3×C4—41no—
262C2×C3×C4—41no—
263C2×C3×C4—121no—
264C2×C3×C4C2×D1211yescharacteristic
265C2×C3×C4D3×D411yescharacteristic
266C2×C3×C4D3×D411yescharacteristic
267C2×C3×C4D3×D411yescharacteristic
268C2×C3×C4D3×D411yescharacteristic
269C2×C3×C4C2×#6711yescharacteristic
270C2×Dic3—41no—
271C2×Dic3—62no—
272C2×Dic3—61no—
273C2×Dic3—61no—
274C2×Dic3—62no—
275C2×Dic3—64no—
276C2×Dic3—61no—
277C2×Dic3—62no—
278C2×Dic3—61no—
279C2×Dic3—62no—
280C2×Dic3—128no—
281C2×Dic3—124no—
282C2×Dic3—124no—
283Dic6—32no—
284Dic6—32no—
285Dic6—41no—
286Dic6—41no—
287Dic6—62no—
288Dic6—62no—
289Dic6—61no—
290Dic6—61no—
291Dic6—128no—
292Dic6—124no—
293Dic6—124no—
294Dic6—122no—
295Dic6—122no—
296Dic6—121no—
297Dic6—121no—
298Dic6—121no—
299Dic6—121no—
300C3×C8—62no—
301C3×C8—121no—
302C3×C8—121no—
303C3⋊C8—22no—
304C3⋊C8—41no—
305C3⋊C8—41no—
306C2×C32—42no—
307C2×C32#44711yescharacteristic
308C2×C32#45111yescharacteristic
309C2×C32#45611yescharacteristic
310C2×Q8—61no—
311C2×Q8—91no—
312C2×Q8—182no—
313C2×Q8—181no—
314C2×Q8—362no—
315C2×Q8—362no—
316C2×D4#62611yescharacteristic
317C22×C4—21no—
318C22×C4—182no—
319Q16—362no—
320C2×C8—61no—
321C2×C8—61no—
322C2×C8—61no—
323C4⋊C4—61no—
324C4⋊C4—61no—
325C4⋊C4—91no—
326C4⋊C4—92no—
327C4⋊C4—182no—
328C4⋊C4—181no—
329C4⋊C4—181no—
330C4⋊C4#62611yescharacteristic
331C22⋊C4—21no—
332C22⋊C4—182no—
333C42—181no—
334C42C2×D3211yescharacteristic
335C22×C3—24no—
336C22×C3—22no—
337C22×C3—22no—
338C22×C3—21no—
339C22×C3—42no—
340C22×C3—42no—
341C22×C3—41no—
342C22×C3—41no—
343C22×C3—41no—
344C22×C3—41no—
345C22×C3#88211yescharacteristic
346C22×C3#93711yescharacteristic
347C3×C4—21no—
348C3×C4—21no—
349C3×C4—21no—
350C3×C4—21no—
351C3×C4—21no—
352C3×C4—21no—
353C3×C4—41no—
354C3×C4—42no—
355C3×C4—41no—
356C3×C4—41no—
357C3×C4—241no—
358C3×C4C2×Dic1211yescharacteristic
359C3×C4#90911yescharacteristic
360C3×C4D3×D811yescharacteristic
361C3×C4D3×D811yescharacteristic
362C3×C4#91111yescharacteristic
363C3×C4#91411yescharacteristic
364C3×C4C2×#21611yescharacteristic
365C3×C4#95111yescharacteristic
366Dic3—64no—
367Dic3—62no—
368Dic3—62no—
369Dic3—81no—
370Dic3—124no—
371Dic3—122no—
372Dic3—122no—
373Dic3—121no—
374Dic3—122no—
375Dic3—121no—
376C32#164911yescharacteristic, complemented, Sylow
377C23—21no—
378Q8—92no—
379Q8—121no—
380Q8—121no—
381Q8—181no—
382Q8—364no—
383Q8—361no—
384Q8—361no—
385D4—21no—
386D4#371912yescomplemented
387C2×C4—21no—
388C2×C4—41no—
389C2×C4—41no—
390C2×C4—121no—
391C2×C4—181no—
392C2×C4—181no—
393C2×C4—182no—
394C2×C4—364no—
395C2×C4C2×#62611yescharacteristic
396C2×C4#381111yescharacteristic
397C2×C4#381111yescharacteristic
398C8—62no—
399C8—121no—
400C8—121no—
401C2×C3—21no—
402C2×C3—21no—
403C2×C3—21no—
404C2×C3—44no—
405C2×C3—42no—
406C2×C3—42no—
407C2×C3#473911yescharacteristic
408C2×C3#477311yescharacteristic
409C2×C3#482611yescharacteristic
410C2×C3#505011yescharacteristic
411C2×C3#515611yescharacteristic
412C2×C3#520511yescharacteristic
413C22—22no—
414C22—41no—
415C22—41no—
416C22#6398111yescharacteristic
417C4—21no—
418C4—41no—
419C4—182no—
420C4—241no—
421C4—361no—
422C4—362no—
423C4#6383111yescharacteristic
424C4C2×#371911yescharacteristic
425C4#6392611yescharacteristic
426C4#6393711yescharacteristic
427C3—21no—
428C3#6819211yescharacteristic, complemented
429C3#7111411yescharacteristic, complemented
430C2—42no—
431C2#1059119011yescharacteristic
432C2#1059145611yescharacteristic
433C2#1059166811yescharacteristic
subgroupG/H
centerC22#63981
commutator, cosocleC32×C42C23
FrattiniC42C2×D32
FittingC32×C4×D4C22
socleC22×C32#120
prime radicalC2×C32×D4D4
hypercenterC4×D4D32
hypocenterC32#1649
LCSG ▷ C32×C42 ▷ C22×C32 ▷ C32
UCSC1 ◁ C22 ◁ C42 ◁ C4×D4

Complements

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

NH ≅ G/Ntype
3. #10590388C2semidirect
4. #10590311C2semidirect
6. #10589094C2semidirect
7. #10589085C2semidirect
112. C32×D4Q16semidirect
249. C3×D4Dic12semidirect
250. C3×D4#216semidirect
376. C32#1649semidirect
386. D4#3719semidirect
428. C3#68192semidirect
429. C3#71114semidirect

Maximal subgroups

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

subgroupindex
D4×#6342
C3×#50072
#105903882
#105903112
C3×D4⋊(C3⋊C8)2
#105890942
#105890852
#711143
#681923