Finite Group Databasebeta

← #11796305

Subgroups — #11796305

Order 1152.

603 conjugacy classes of subgroups; only the 108 normal subgroups are shown.

normal subgroups only

This group has 603 conjugacy classes of subgroups — too many to draw. Only its 108 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
1#10596296C211yesmaximal, characteristic
2C3×#5240C211yesmaximal, characteristic
3C3×#5237C211yesmaximal, characteristic
4#10589177C214yesmaximal, complemented
5#70147—31nomaximal
6#70058—31nomaximal
7C2×C32×#41C2211yescharacteristic
8C22×#634C411yescharacteristic, complemented
9#64153—21no—
10#64145—21no—
11#64144C412yescomplemented
12#64144C2212yes—
13#64135C411yescharacteristic, complemented
14#64133—21no—
15#64133—21no—
16C3×#926—21no—
17C2×C3×#208—21no—
18C3×#836—21no—
19C3×#834—21no—
20C3×#834C2212yes—
21C3×#833C2212yes—
22#5825—31no—
23#5825—31no—
24#5825—61no—
25C3×#413—31no—
26C3×#410—31no—
27#5240D311yescharacteristic
28#5237D311yescharacteristic
29#4476—34no—
30#4472—34no—
31C32×#41—41no—
32C32×#41—41no—
33C2×C32×Q8D411yescharacteristic
34C2×C32×D4C2×C411yescharacteristic
35C2×C32×D4D411yescharacteristic
36C2×C32×D4C2311yescharacteristic
37C22×C32×C4C2×C411yescharacteristic
38C22×C32×C4D411yescharacteristic
39C22×C32×C4D411yescharacteristic
40C22×C3⋊Dic3C2×C412yes—
41C2×#634—21no—
42C2×#634—21no—
43C2×#634—41no—
44C2×#634—41no—
45#3757—22no—
46#3757—22no—
47#3757C2×C412yes—
48C4⋊(C3⋊Dic3)—21no—
49#3750—22no—
50#3750—22no—
51C4×C3⋊Dic3—21no—
52C3×#217—22no—
53C3×C4⋊Dic3—41no—
54C3×C4×Dic3—41no—
55C3×#208—22no—
56C3×#208—41no—
57C2×C3×C3⋊C8—41no—
58#2123—91noSylow
59C2×C3×#41—21no—
60C2×C3×#41C2×D311yescharacteristic
61C2×C3×#41C2×D311yescharacteristic
62C22×Dic6—31no—
63C22×Dic6—31no—
64C22×Dic6—61no—
65C2×C3×M16—61no—
66C3×#117—61no—
67#944—62no—
68#944—61no—
69#944—61no—
70#936—62no—
71#936—61no—
72#936—61no—
73#935—32no—
74#935—32no—
75#935—32no—
76#935—32no—
77#935—62no—
78#935—62no—
79#926—21no—
80#926—31no—
81#926—31no—
82#926—61no—
83#924—62no—
84#924—62no—
85#924—61no—
86#924—61no—
87#924—61no—
88#924—61no—
89C2×#208—21no—
90C3×#101—61no—
91C3×#100—32no—
92C3×#99—32no—
93C3×#99—61no—
94#836—21no—
95#834—21no—
96#834C2×D312yes—
97#833C2×D312yes—
98C23×C32C22⋊C411yescharacteristic
99C23×C32C22×C411yescharacteristic
100C23×C32C2×D411yescharacteristic
101C32×Q8—41no—
102C32×D4—41no—
103C32×D4—41no—
104C32×D4—41no—
105C2×C32×C4—21no—
106C2×C32×C4—21no—
107C2×C32×C4—21no—
108C2×C32×C4—21no—
109C2×C32×C4—21no—
110C2×C32×C4—21no—
111C2×C32×C4C22⋊C411yescharacteristic
112C2×C32×C4C22⋊C411yescharacteristic
113C2×C32×C4C22⋊C411yescharacteristic
114C2×C32×C4C2×D411yescharacteristic
115C2×C3⋊Dic3—22no—
116C2×C3⋊Dic3—22no—
117C2×C3⋊Dic3—42no—
118#634—42no—
119#634—41no—
120#634—41no—
121C2×C3×Dic3—42no—
122C3×C3⋊C8—42no—
123#536—91no—
124#413—31no—
125#410—31no—
126#352—94no—
127C3×#41—41no—
128C3×#41—41no—
129C3×#41—41no—
130C3×#41—41no—
131C3×#41—42no—
132C3×#41—42no—
133C2×C3×Q8—21no—
134C2×C3×Q8D1211yescharacteristic
135C2×C3×Q8#6711yescharacteristic
136C2×C3×D4—21no—
137C2×C3×D4—21no—
138C2×C3×D4—21no—
139C2×C3×D4C4×D311yescharacteristic
140C2×C3×D4C4×D311yescharacteristic
141C2×C3×D4D1211yescharacteristic
142C2×C3×D4#6711yescharacteristic
143C2×C3×D4C22×D311yescharacteristic
144C2×C3×D4C22×D311yescharacteristic
145C22×C3×C4—21no—
146C22×C3×C4—21no—
147C22×C3×C4—21no—
148C22×C3×C4C4×D311yescharacteristic
149C22×C3×C4C4×D311yescharacteristic
150C22×C3×C4D1211yescharacteristic
151C22×C3×C4D1211yescharacteristic
152C22×C3×C4#6711yescharacteristic
153C22×C3×C4#6711yescharacteristic
154C22×Dic3—32no—
155C22×Dic3—32no—
156C22×Dic3—62no—
157C2×Dic6—62no—
158C2×Dic6—62no—
159C2×Dic6—61no—
160C2×Dic6—61no—
161C2×Dic6—61no—
162C2×Dic6—61no—
163C2×Dic6—122no—
164C2×Dic6—122no—
165C2×Dic6—121no—
166C2×Dic6—121no—
167C2×Dic6—121no—
168C2×Dic6—121no—
169C3×M16—62no—
170C3×M16—121no—
171C2×C3×C8—121no—
172C3×C4⋊C4—121no—
173C3×C22⋊C4—62no—
174C3×C42—121no—
175#217—22no—
176#217—32no—
177#217—32no—
178#217—62no—
179#217—64no—
180#217—64no—
181#217—62no—
182#217—62no—
183#217—62no—
184#217—62no—
185C4⋊Dic3—41no—
186C4⋊Dic3—62no—
187C4⋊Dic3—61no—
188C4⋊Dic3—61no—
189Dic3⋊C4—64no—
190Dic3⋊C4—64no—
191Dic3⋊C4—62no—
192Dic3⋊C4—62no—
193Dic3⋊C4—62no—
194Dic3⋊C4—62no—
195C4×Dic3—41no—
196C4×Dic3—62no—
197C4×Dic3—61no—
198C4×Dic3—61no—
199#208—22no—
200#208—41no—
201C2×C3⋊C8—41no—
202C22×C32—21no—
203C22×C32—21no—
204C22×C32—21no—
205C22×C32—41no—
206C22×C32—41no—
207C22×C32—41no—
208C22×C32C2×C22⋊C411yescharacteristic
209C32×C4—21no—
210C32×C4—21no—
211C32×C4—21no—
212C32×C4#9911yescharacteristic
213C32×C4#9911yescharacteristic
214C3⋊Dic3—42no—
215C3⋊Dic3—42no—
216C3×Dic3—82no—
217C2×#41D3211yescharacteristic
218C22×Q8—91no—
219C2×M16—61no—
220C4⋊Q8—181no—
221#124—181no—
222#123—92no—
223#123—92no—
224C22⋊Q8—181no—
225C22⋊Q8—181no—
226#117—61no—
227#117—91no—
228#101—61no—
229#100—32no—
230#99—32no—
231#99—61no—
232C23×C3—21no—
233C23×C3—21no—
234C23×C3—21no—
235C23×C3(C2×D3)⋊C411yescharacteristic
236C23×C3(C2×D3)⋊C411yescharacteristic
237C23×C3C2×C4×D311yescharacteristic
238C23×C3C2×C4×D311yescharacteristic
239C23×C3C2×D1211yescharacteristic
240C23×C3C2×#6711yescharacteristic
241C3×Q8—41no—
242C3×Q8—41no—
243C3×Q8—42no—
244C3×D4—41no—
245C3×D4—41no—
246C3×D4—41no—
247C3×D4—41no—
248C3×D4—41no—
249C3×D4—41no—
250C3×D4—42no—
251C3×D4—42no—
252C3×D4—42no—
253C2×C3×C4—22no—
254C2×C3×C4—22no—
255C2×C3×C4—21no—
256C2×C3×C4—21no—
257C2×C3×C4—21no—
258C2×C3×C4—21no—
259C2×C3×C4—21no—
260C2×C3×C4—21no—
261C2×C3×C4—21no—
262C2×C3×C4—21no—
263C2×C3×C4—21no—
264C2×C3×C4—21no—
265C2×C3×C4—21no—
266C2×C3×C4—21no—
267C2×C3×C4—21no—
268C2×C3×C4—21no—
269C2×C3×C4—21no—
270C2×C3×C4—21no—
271C2×C3×C4—41no—
272C2×C3×C4—41no—
273C2×C3×C4—41no—
274C2×C3×C4—41no—
275C2×C3×C4—122no—
276C2×C3×C4(C2×D3)⋊C411yescharacteristic
277C2×C3×C4(C2×D3)⋊C411yescharacteristic
278C2×C3×C4(C2×D3)⋊C411yescharacteristic
279C2×C3×C4(C2×D3)⋊C411yescharacteristic
280C2×C3×C4(C2×D3)⋊C411yescharacteristic
281C2×C3×C4(C2×D3)⋊C411yescharacteristic
282C2×C3×C4C2×D1211yescharacteristic
283C2×C3×C4C2×#6711yescharacteristic
284C2×Dic3—42no—
285C2×Dic3—64no—
286C2×Dic3—64no—
287C2×Dic3—62no—
288C2×Dic3—62no—
289C2×Dic3—62no—
290C2×Dic3—62no—
291C2×Dic3—124no—
292C2×Dic3—122no—
293C2×Dic3—122no—
294Dic6—124no—
295Dic6—122no—
296Dic6—122no—
297Dic6—122no—
298Dic6—122no—
299Dic6—121no—
300Dic6—121no—
301Dic6—121no—
302Dic6—121no—
303C3×C8—122no—
304C3⋊C8—42no—
305C2×C32—21no—
306C2×C32—41no—
307C2×C32—41no—
308C2×C32—41no—
309C2×C32C2×#9911yescharacteristic
310#41—41no—
311#41—41no—
312C2×Q8—181no—
313C2×Q8—181no—
314C2×Q8—361no—
315C2×Q8—361no—
316C2×Q8#62611yescharacteristic
317C2×D4#62411yescharacteristic
318C2×D4#62611yescharacteristic
319C2×D4C2×D3211yescharacteristic
320C22×C4—92no—
321C22×C4#62411yescharacteristic
322C22×C4#62611yescharacteristic
323C22×C4#62611yescharacteristic
324M16—62no—
325M16—121no—
326C2×C8—121no—
327C4⋊C4—121no—
328C4⋊C4—182no—
329C4⋊C4—181no—
330C4⋊C4—182no—
331C22⋊C4—62no—
332C22⋊C4—92no—
333C22⋊C4—182no—
334C22⋊C4—182no—
335C42—121no—
336C42—181no—
337C22×C3—22no—
338C22×C3—21no—
339C22×C3—21no—
340C22×C3—21no—
341C22×C3—21no—
342C22×C3—21no—
343C22×C3—21no—
344C22×C3—21no—
345C22×C3—41no—
346C22×C3—41no—
347C22×C3—41no—
348C22×C3—41no—
349C22×C3—41no—
350C22×C3—41no—
351C22×C3—41no—
352C22×C3—41no—
353C22×C3—42no—
354C22×C3—42no—
355C22×C3—42no—
356C22×C3C2×(C2×D3)⋊C411yescharacteristic
357C22×C3C2×(C2×D3)⋊C411yescharacteristic
358C3×C4—22no—
359C3×C4—21no—
360C3×C4—21no—
361C3×C4—21no—
362C3×C4—21no—
363C3×C4—21no—
364C3×C4—21no—
365C3×C4—21no—
366C3×C4—21no—
367C3×C4—41no—
368C3×C4—41no—
369C3×C4—242no—
370C3×C4#80611yescharacteristic
371C3×C4#80611yescharacteristic
372C3×C4#80611yescharacteristic
373C3×C4#80611yescharacteristic
374Dic3—82no—
375Dic3—124no—
376Dic3—124no—
377Dic3—122no—
378Dic3—122no—
379Dic3—122no—
380Dic3—122no—
381C32#212311yescharacteristic, complemented, Sylow
382C23#372211yescharacteristic
383C23C2×#62411yescharacteristic
384C23C2×#62611yescharacteristic
385Q8—41no—
386Q8—362no—
387Q8—361no—
388Q8—361no—
389D4—41no—
390D4—41no—
391D4—41no—
392C2×C4—21no—
393C2×C4—21no—
394C2×C4—21no—
395C2×C4—21no—
396C2×C4—21no—
397C2×C4—21no—
398C2×C4—122no—
399C2×C4—182no—
400C2×C4—182no—
401C2×C4—362no—
402C2×C4#372211yescharacteristic
403C2×C4#372211yescharacteristic
404C2×C4#372211yescharacteristic
405C2×C4C2×#62611yescharacteristic
406C8—122no—
407C2×C3—22no—
408C2×C3—21no—
409C2×C3—21no—
410C2×C3—21no—
411C2×C3—42no—
412C2×C3—41no—
413C2×C3—41no—
414C2×C3—41no—
415C2×C3—41no—
416C2×C3—41no—
417C2×C3—41no—
418C2×C3—81no—
419C2×C3—81no—
420C2×C3C2×#80611yescharacteristic
421C2×C3C2×#80611yescharacteristic
422C22—21no—
423C22—21no—
424C22—21no—
425C22—41no—
426C22—41no—
427C22—41no—
428C22C2×#372211yescharacteristic
429C4—21no—
430C4—21no—
431C4—21no—
432C4—242no—
433C4—362no—
434C4—362no—
435C4#6358111yescharacteristic
436C4#6358111yescharacteristic
437C3—21no—
438C3#7005811yescharacteristic, complemented
439C3#7014711yescharacteristic, complemented
440C2—21no—
441C2—41no—
442C2—41no—
443C2—41no—
444C2C2×#6358111yescharacteristic
subgroupG/H
centerC2C2×#63581
commutatorC23×C32C22×C4
FrattiniC2×D4C2×D32
Fitting, prime radicalC2×C32×#41C22
socleC2×C32C2×#99
cosocleC2×C32×D4C23
hypercenterC2×#41D32
hypocenterC32#2123
LCSG ▷ C23×C32 ▷ C22×C32 ▷ C2×C32 ▷ C32
UCSC1 ◁ C2 ◁ C2×C4 ◁ C2×#41

Complements

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

NH ≅ G/Ntype
4. #10589177C2semidirect
8. C22×#634C4semidirect
11. #64144C4semidirect
13. #64135C4semidirect
381. C32#2123semidirect
438. C3#70058semidirect
439. C3#70147semidirect

Maximal subgroups

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

subgroupindex
#105962962
C3×#52402
C3×#52372
#105891772
#701473
#700583