Finite Group Databasebeta

← #11778296

Subgroups — #11778296

Order 1152.

527 conjugacy classes of subgroups; only the 84 normal subgroups are shown.

normal subgroups only

This group has 527 conjugacy classes of subgroups — too many to draw. Only its 84 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
1C3×#5515C211yesmaximal, characteristic
2C3×#4979C211yesmaximal, characteristic, complemented
3#10591185C211yesmaximal, characteristic, complemented
4#10591171C211yesmaximal, characteristic
5#10589394C211yesmaximal, characteristic, complemented
6#10589153C211yesmaximal, characteristic, complemented
7#10589149C211yesmaximal, characteristic
8#71889—31nomaximal
9#69705—31nomaximal
10C22×C3×Dic6C2211yescharacteristic
11C2×C32×C4⋊C4C2211yescharacteristic
12C3×#930C2211yescharacteristic
13C3×#929—21no—
14C3×C4×#67—21no—
15C3×#924C2211yescharacteristic
16C2×C3×Dic3⋊C4—21no—
17C3×#898—21no—
18C3×#896—21no—
19C3×#894—21no—
20C3×#889—21no—
21C2×#3718—21no—
22C2×#3715—21no—
23#63657C2211yescharacteristic
24#63657C2211yescharacteristic
25C3×C3⋊#95—21no—
26C3×C3⋊#95C2211yescharacteristic
27#63565—21no—
28#63565—21no—
29C3×#539—31no—
30#5515D311yescharacteristic
31C3×#395—31no—
32#5228—31no—
33#5227—31no—
34#5050—31no—
35#5040—31no—
36#4979D311yescharacteristic, complemented
37#4538—31no—
38#4537—31no—
39#4528—31no—
40#4528—31no—
41#4528—61no—
42#4452—31no—
43#4451—31no—
44C22×C32×C4D411yescharacteristic
45C22×C32×C4D411yescharacteristic
46C22×C32×C4C2311yescharacteristic
47C2×C3×#67—21no—
48C22×C3×Dic3—21no—
49C22×C3×Dic3—21no—
50C2×C3×D12D411yescharacteristic
51C2×C3×C4×D3—21no—
52C2×C3×Dic6—21no—
53C2×C3×Dic6—21no—
54C2×C3×Dic6—42no—
55C2×C3×Dic6D411yescharacteristic
56C32×C4⋊C4—21no—
57C32×C4⋊C4—21no—
58C2×C3⋊(C3⋊C8)—21no—
59C2×C3⋊(C3⋊C8)—21no—
60C3×#217—21no—
61C3×(C2×D3)⋊C4—21no—
62C3×(C2×D3)⋊C4—21no—
63C3×(C2×D3)⋊C4—21no—
64C3×(C2×D3)⋊C4—21no—
65C3×C4⋊Dic3D411yescharacteristic
66C3×C4⋊Dic3D411yescharacteristic
67C3×Dic3⋊C4—21no—
68C3×Dic3⋊C4—21no—
69C3×Dic3⋊C4—21no—
70C3×Dic3⋊C4—21no—
71C3×Dic3⋊C4—42no—
72C3×C4×Dic3—21no—
73#3718—42no—
74#3715—42no—
75#1603—91noSylow
76C22×C3×Q8—31no—
77C22×Dic6C2×D311yescharacteristic
78C3×#126—61no—
79C3×#125—61no—
80C3×#123—61no—
81C3×#123—61no—
82C3×C22⋊Q8—31no—
83C3×C22⋊Q8—61no—
84C3×#121—31no—
85C3×C4×D4—61no—
86C2×C3×C4⋊C4—21no—
87C2×C3×C4⋊C4—61no—
88C2×C3×C4⋊C4C2×D311yescharacteristic
89C2×C3×C4⋊C4C2×D311yescharacteristic
90C2×#216—61no—
91C2×#216—61no—
92C2×#215—61no—
93C2×#214—61no—
94#930C2×D311yescharacteristic
95#929—21no—
96C4×#67—21no—
97#924C2×D311yescharacteristic
98C2×Dic3⋊C4—21no—
99#898—21no—
100#896—21no—
101#894—21no—
102#889—21no—
103C3×#95—31no—
104C3×#95—61no—
105#835—61no—
106#835—61no—
107C3⋊#95—21no—
108C3⋊#95C2×D311yescharacteristic
109#830—31no—
110#830—31no—
111#830—31no—
112#830—31no—
113#830—61no—
114#830—61no—
115#810—61no—
116#810—61no—
117C23×C32C2×D411yescharacteristic
118C22×C3×D3—21no—
119C2×C32×C4—21no—
120C2×C32×C4—21no—
121C2×C32×C4—21no—
122C2×C32×C4—21no—
123C2×C32×C4—41no—
124C2×C32×C4—41no—
125C2×C32×C4C2×D411yescharacteristic
126C2×C32×C4C2×D411yescharacteristic
127C3×#67—41no—
128C3×#67—41no—
129C2×C3×Dic3—22no—
130C2×C3×Dic3—22no—
131C2×C3×Dic3—21no—
132C2×C3×Dic3—21no—
133C2×C3×Dic3—21no—
134C2×C3×Dic3—41no—
135C2×C3×Dic3—41no—
136C2×C3×Dic3—41no—
137C2×C3×Dic3—41no—
138C3×D12—41no—
139C3×C4×D3—81no—
140C3×Dic6—22no—
141C3×Dic6—22no—
142C3×Dic6—41no—
143C3×Dic6—41no—
144C3×Dic6—41no—
145C3⋊(C3⋊C8)—41no—
146C3⋊(C3⋊C8)—41no—
147#539—31no—
148#451—91no—
149#448—91no—
150#395—31no—
151#328—91no—
152#327—91no—
153#324—91no—
154C2×C3×Q8—31no—
155C2×C3×Q8—61no—
156C2×C3×Q8—61no—
157C2×C3×Q8—122no—
158C2×C3×D4—31no—
159C2×C3×D4—61no—
160C22×C3×C4—21no—
161C22×C3×C4—21no—
162C22×C3×C4—21no—
163C22×C3×C4—61no—
164C22×C3×C4—61no—
165C22×C3×C4—61no—
166C22×C3×C4#6711yescharacteristic
167C22×C3×C4#6711yescharacteristic
168C22×C3×C4#6711yescharacteristic
169C22×C3×C4#6711yescharacteristic
170C22×C3×C4C22×D311yescharacteristic
171C22×C3×C4C22×D311yescharacteristic
172C2×#67—21no—
173C22×Dic3—21no—
174C22×Dic3—21no—
175C2×D12#6711yescharacteristic
176C2×C4×D3—21no—
177C2×Dic6—21no—
178C2×Dic6—21no—
179C2×Dic6—42no—
180C2×Dic6#6711yescharacteristic
181C3×C4⋊C4—21no—
182C3×C4⋊C4—21no—
183C3×C4⋊C4—21no—
184C3×C4⋊C4—21no—
185C3×C4⋊C4—31no—
186C3×C4⋊C4—31no—
187C3×C4⋊C4—41no—
188C3×C4⋊C4—41no—
189C3×C4⋊C4—61no—
190C3×C4⋊C4—61no—
191C3×C4⋊C4—61no—
192C3×C4⋊C4—61no—
193C3×C4⋊C4—122no—
194C3×C22⋊C4—61no—
195C3×C22⋊C4—61no—
196C3×C22⋊C4—61no—
197C3×C22⋊C4—61no—
198C3×C22⋊C4—61no—
199C3×C42—61no—
200#217—21no—
201#216—122no—
202#216—122no—
203#215—122no—
204#214—122no—
205(C2×D3)⋊C4—21no—
206(C2×D3)⋊C4—21no—
207(C2×D3)⋊C4—21no—
208(C2×D3)⋊C4—21no—
209C4⋊Dic3#6711yescharacteristic
210C4⋊Dic3#6711yescharacteristic
211Dic3⋊C4—21no—
212Dic3⋊C4—21no—
213Dic3⋊C4—21no—
214Dic3⋊C4—21no—
215Dic3⋊C4—42no—
216C4×Dic3—21no—
217C2×C3⋊C8—61no—
218C2×C3⋊C8—61no—
219C2×C3⋊C8—61no—
220C2×C3⋊C8—61no—
221C2×C3⋊C8—121no—
222C2×C3⋊C8—121no—
223C22×C32—21no—
224C22×C32—21no—
225C22×C32#12011yescharacteristic
226C22×C32#13511yescharacteristic
227C22×C32#13711yescharacteristic
228C2×C3×D3—41no—
229C2×C3×D3—41no—
230C2×C3×D3—41no—
231C32×C4—21no—
232C32×C4—21no—
233C32×C4—41no—
234C32×C4—41no—
235C3×Dic3—42no—
236C3×Dic3—41no—
237C3×Dic3—41no—
238C3×Dic3—42no—
239C3×Dic3—41no—
240C22×Q8—31no—
241C2×Q16—181no—
242C2×SD16—181no—
243#126—61no—
244#125—61no—
245#123—61no—
246#123—61no—
247C22⋊Q8—31no—
248C22⋊Q8—61no—
249#121—31no—
250C4×D4—61no—
251C2×C4⋊C4—61no—
252C2×C4⋊C4D3211yescharacteristic
253#103—181no—
254#103—181no—
255C22⋊C8—91no—
256C22⋊C8—91no—
257#95—31no—
258#95—61no—
259C23×C3—21no—
260C23×C3—61no—
261C23×C3C2×#6711yescharacteristic
262C23×C3C2×#6711yescharacteristic
263C22×D3—21no—
264C3×Q8—62no—
265C3×Q8—62no—
266C3×Q8—121no—
267C3×Q8—121no—
268C3×Q8—121no—
269C3×D4—121no—
270C3×D4—121no—
271C3×D4—121no—
272C2×C3×C4—22no—
273C2×C3×C4—21no—
274C2×C3×C4—21no—
275C2×C3×C4—21no—
276C2×C3×C4—21no—
277C2×C3×C4—21no—
278C2×C3×C4—21no—
279C2×C3×C4—21no—
280C2×C3×C4—21no—
281C2×C3×C4—21no—
282C2×C3×C4—21no—
283C2×C3×C4—41no—
284C2×C3×C4—41no—
285C2×C3×C4—41no—
286C2×C3×C4—41no—
287C2×C3×C4—41no—
288C2×C3×C4—41no—
289C2×C3×C4—41no—
290C2×C3×C4—62no—
291C2×C3×C4—62no—
292C2×C3×C4—61no—
293C2×C3×C4—61no—
294C2×C3×C4—61no—
295C2×C3×C4—81no—
296C2×C3×C4—81no—
297C2×C3×C4—121no—
298C2×C3×C4—121no—
299C2×C3×C4—121no—
300C2×C3×C4—121no—
301C2×C3×C4—241no—
302C2×C3×C4D3×D411yescharacteristic
303C2×C3×C4D3×D411yescharacteristic
304C2×C3×C4C2×#6711yescharacteristic
305C2×C3×C4C2×#6711yescharacteristic
306#67—41no—
307#67—41no—
308C2×Dic3—22no—
309C2×Dic3—22no—
310C2×Dic3—21no—
311C2×Dic3—21no—
312C2×Dic3—21no—
313C2×Dic3—41no—
314C2×Dic3—41no—
315C2×Dic3—41no—
316C2×Dic3—41no—
317D12—41no—
318C4×D3—81no—
319Dic6—22no—
320Dic6—22no—
321Dic6—41no—
322Dic6—41no—
323Dic6—41no—
324C3⋊C8—121no—
325C3⋊C8—121no—
326C3⋊C8—121no—
327C3⋊C8—121no—
328C3⋊C8—241no—
329C3⋊C8—241no—
330C2×C32—21no—
331C2×C32—21no—
332C2×C32#45211yescharacteristic
333C2×C32#45611yescharacteristic
334C2×C32B(4,𝔽2)11yescharacteristic
335C3×D3—81no—
336C2×Q8—31no—
337C2×Q8—61no—
338C2×Q8—61no—
339C2×Q8—122no—
340C2×D4—31no—
341C2×D4—61no—
342C22×C4—61no—
343C22×C4—61no—
344C22×C4—61no—
345C22×C4#62511yescharacteristic
346C22×C4#62511yescharacteristic
347C22×C4C2×D3211yescharacteristic
348Q16—362no—
349SD16—362no—
350C2×C8—181no—
351C2×C8—181no—
352C4⋊C4—21no—
353C4⋊C4—21no—
354C4⋊C4—31no—
355C4⋊C4—31no—
356C4⋊C4—61no—
357C4⋊C4—61no—
358C4⋊C4—61no—
359C4⋊C4—61no—
360C4⋊C4—122no—
361C22⋊C4—61no—
362C22⋊C4—61no—
363C22⋊C4—61no—
364C22⋊C4—61no—
365C22⋊C4—61no—
366C42—61no—
367C22×C3—21no—
368C22×C3—21no—
369C22×C3—21no—
370C22×C3—21no—
371C22×C3—21no—
372C22×C3—21no—
373C22×C3—21no—
374C22×C3—41no—
375C22×C3—41no—
376C22×C3—121no—
377C22×C3—121no—
378C22×C3—121no—
379C22×C3#93711yescharacteristic
380C22×C3#94211yescharacteristic
381C22×C3#95011yescharacteristic
382C22×C3#95011yescharacteristic
383C22×C3#95111yescharacteristic
384C22×C3#95311yescharacteristic
385C2×D3—41no—
386C2×D3—41no—
387C2×D3—41no—
388C3×C4—21no—
389C3×C4—21no—
390C3×C4—21no—
391C3×C4—21no—
392C3×C4—41no—
393C3×C4—41no—
394C3×C4—42no—
395C3×C4—41no—
396C3×C4—41no—
397C3×C4—41no—
398C3×C4—41no—
399C3×C4—81no—
400C3×C4—122no—
401C3×C4—122no—
402C3×C4—121no—
403C3×C4—121no—
404C3×C4—121no—
405Dic3—42no—
406Dic3—41no—
407Dic3—41no—
408Dic3—41no—
409Dic3—42no—
410C32#160311yescharacteristic, complemented, Sylow
411C23—61no—
412C23C2×#62511yescharacteristic
413Q8—62no—
414Q8—62no—
415Q8—121no—
416Q8—121no—
417Q8—121no—
418D4—121no—
419D4—121no—
420D4—121no—
421C2×C4—21no—
422C2×C4—21no—
423C2×C4—21no—
424C2×C4—21no—
425C2×C4—41no—
426C2×C4—41no—
427C2×C4—62no—
428C2×C4—62no—
429C2×C4—61no—
430C2×C4—61no—
431C2×C4—61no—
432C2×C4—121no—
433C2×C4—121no—
434C2×C4—121no—
435C2×C4—121no—
436C2×C4—241no—
437C2×C4D3×#6711yescharacteristic
438C2×C4D3×#6711yescharacteristic
439C8—361no—
440C8—361no—
441C2×C3—21no—
442C2×C3—21no—
443C2×C3—21no—
444C2×C3—21no—
445C2×C3—21no—
446C2×C3—21no—
447C2×C3—21no—
448C2×C3—41no—
449C2×C3—41no—
450C2×C3—241no—
451C2×C3#503211yescharacteristic
452C2×C3#504711yescharacteristic
453C2×C3#509511yescharacteristic
454C2×C3#523911yescharacteristic
455C2×C3#524411yescharacteristic
456C2×C3#524611yescharacteristic
457D3—81no—
458C22—21no—
459C22—21no—
460C22—121no—
461C22—121no—
462C22—121no—
463C22#6382211yescharacteristic
464C22#6382711yescharacteristic
465C22#6397611yescharacteristic
466C4—21no—
467C4—21no—
468C4—41no—
469C4—41no—
470C4—122no—
471C4—122no—
472C4—121no—
473C4—121no—
474C4—121no—
475C3—21no—
476C3#6970511yescharacteristic, complemented
477C3#7188911yescharacteristic, complemented
478C2—21no—
479C2—21no—
480C2—241no—
481C2#1059117011yescharacteristic
482C2#1059153011yescharacteristic
483C2#1059164811yescharacteristic
subgroupG/H
centerC22#63976
commutator, cosocleC22×C32×C4C23
FrattiniC22×C4C2×D32
FittingC2×C32×C4⋊C4C22
socleC22×C32#120
prime radicalC3×#930C22
hypercenterC2×C4⋊C4D32
hypocenterC32#1603
LCSG ▷ C22×C32×C4 ▷ C22×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C4⋊C4

Complements

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

NH ≅ G/Ntype
2. C3×#4979C2semidirect
3. #10591185C2semidirect
5. #10589394C2semidirect
6. #10589153C2semidirect
36. #4979D3semidirect
410. C32#1603semidirect
476. C3#69705semidirect
477. C3#71889semidirect

Maximal subgroups

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

subgroupindex
C3×#55152
C3×#49792
#105911852
#105911712
#105893942
#105891532
#105891492
#718893
#697053