Finite Group Databasebeta

← #11778298

Subgroups — #11778298

Order 1152.

527 conjugacy classes of subgroups; only the 78 normal subgroups are shown.

normal subgroups only

This group has 527 conjugacy classes of subgroups — too many to draw. Only its 78 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#10594974C211yesmaximal, characteristic
2C3×#4738C211yesmaximal, characteristic
3#10591346C211yesmaximal, characteristic, complemented
4#10591185C211yesmaximal, characteristic, complemented
5#10589335C211yesmaximal, characteristic, complemented
6C3×#4467C211yesmaximal, characteristic, complemented
7#10589149C211yesmaximal, characteristic
8#70974—31nomaximal
9#68326—31nomaximal
10C22×C3×Dic6C2211yescharacteristic
11C2×#3750C2211yescharacteristic
12C3×#930C2211yescharacteristic
13C3×#924C2211yescharacteristic
14C2×C3×#204—21no—
15#67⋊Dic3—21no—
16C2×Dic3⋊Dic3—21no—
17#63962—21no—
18#63887—21no—
19#63884—21no—
20#63858—21no—
21#63846—21no—
22C2×#3718—21no—
23C32×C22⋊C8C2211yescharacteristic
24#63657C2211yescharacteristic
25C3×C3⋊#95C2211yescharacteristic
26C3×#816—21no—
27#63579—21no—
28#63565—21no—
29#5645—31no—
30#5602—31no—
31C3×#448—31no—
32#5230—31no—
33#5228—31no—
34#5050—31no—
35#4738D311yescharacteristic
36#4656—31no—
37C3×#328—31no—
38#4537—31no—
39#4469—31no—
40#4469—31no—
41#4469—61no—
42#4467D311yescharacteristic, complemented
43#4451—31no—
44C22×C32×C4C2311yescharacteristic
45C22×C3⋊Dic3D411yescharacteristic
46C22×C3⋊Dic3D411yescharacteristic
47C2×C3×#67—21no—
48C22×C3×Dic3—21no—
49C22×C3×Dic3—21no—
50C2×C3×D12D411yescharacteristic
51C2×C3×Dic6—21no—
52C2×C3×Dic6—21no—
53C2×C3×Dic6—42no—
54C2×C3×Dic6D411yescharacteristic
55C2×D3×Dic3—21no—
56C2×C32×C8—21no—
57#3750—21no—
58#3750—21no—
59C2×C3⋊(C3⋊C8)—21no—
60C3×#217—21no—
61C3×(C2×D3)⋊C4—21no—
62C3×C4⋊Dic3D411yescharacteristic
63C3×C4⋊Dic3D411yescharacteristic
64C3×Dic3⋊C4—21no—
65C3×#204—42no—
66Dic3⋊Dic3—21no—
67Dic3⋊Dic3—21no—
68Dic3⋊Dic3—21no—
69Dic3⋊Dic3—42no—
70(C2×D3)⋊Dic3—21no—
71(C2×D3)⋊Dic3—21no—
72(C2×D3)⋊Dic3—21no—
73Dic32—21no—
74#3718—42no—
75#1603—91noSylow
76C22×C3×Q8—31no—
77C22×Dic6C2×D311yescharacteristic
78C2×C3×SD16—61no—
79C3×C22⋊Q8—31no—
80C3×#121—31no—
81#946—61no—
82C2×#216—61no—
83C2×#216—61no—
84#935—61no—
85#935—61no—
86D4×Dic3—61no—
87#930C2×D311yescharacteristic
88C2×C4⋊Dic3—61no—
89#924C2×D311yescharacteristic
90C2×Dic3⋊C4—31no—
91C2×Dic3⋊C4—31no—
92C2×Dic3⋊C4—61no—
93C2×Dic3⋊C4—61no—
94C2×#204—21no—
95#898—61no—
96#894—61no—
97#890—61no—
98#889—61no—
99#886—61no—
100#67⋊C4—61no—
101#879—61no—
102#878—61no—
103C3×#103—61no—
104C3×C22⋊C8—21no—
105C3×C22⋊C8C2×D311yescharacteristic
106C3×C22⋊C8C2×D311yescharacteristic
107C3×#95—31no—
108#835—61no—
109C3⋊#95—61no—
110C3⋊#95—61no—
111C3⋊#95C2×D311yescharacteristic
112#830—31no—
113#830—31no—
114#830—61no—
115#816—21no—
116#810—61no—
117C23×C32C2×D411yescharacteristic
118C22×C3×D3—21no—
119C2×C32×C4—41no—
120C2×C32×C4C2×D411yescharacteristic
121C2×C32×C4C2×D411yescharacteristic
122C2×C3⋊Dic3—21no—
123C2×C3⋊Dic3—21no—
124C2×C3⋊Dic3—21no—
125C2×C3⋊Dic3—21no—
126C2×C3⋊Dic3—41no—
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×Dic6—22no—
140C3×Dic6—22no—
141C3×Dic6—41no—
142C3×Dic6—41no—
143C3×Dic6—41no—
144D3×Dic3—81no—
145C32×C8—41no—
146C3⋊(C3⋊C8)—41no—
147#539—91no—
148#451—91no—
149#448—31no—
150#395—91no—
151#328—31no—
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—61no—
162C22×C3×C4—61no—
163C22×C3×C4C22×D311yescharacteristic
164C22×C3×C4C22×D311yescharacteristic
165C2×#67—21no—
166C22×Dic3—21no—
167C22×Dic3—21no—
168C22×Dic3—31no—
169C22×Dic3—31no—
170C22×Dic3—31no—
171C22×Dic3—31no—
172C22×Dic3—61no—
173C22×Dic3—61no—
174C22×Dic3—61no—
175C2×D12#6711yescharacteristic
176C2×C4×D3—61no—
177C2×Dic6—21no—
178C2×Dic6—21no—
179C2×Dic6—42no—
180C2×Dic6D1211yescharacteristic
181C3×SD16—122no—
182C2×C3×C8—21no—
183C2×C3×C8—21no—
184C2×C3×C8—41no—
185C3×C4⋊C4—31no—
186C3×C4⋊C4—31no—
187C3×C4⋊C4—61no—
188C3×C22⋊C4—61no—
189C3×C22⋊C4—61no—
190#217—21no—
191#217—61no—
192#217—61no—
193#217—61no—
194#216—122no—
195#216—122no—
196(C2×D3)⋊C4—21no—
197(C2×D3)⋊C4—61no—
198(C2×D3)⋊C4—61no—
199(C2×D3)⋊C4—61no—
200C4⋊Dic3—61no—
201C4⋊Dic3—61no—
202C4⋊Dic3—61no—
203C4⋊Dic3—122no—
204C4⋊Dic3D1211yescharacteristic
205C4⋊Dic3#6711yescharacteristic
206Dic3⋊C4—21no—
207Dic3⋊C4—61no—
208Dic3⋊C4—61no—
209Dic3⋊C4—61no—
210Dic3⋊C4—61no—
211Dic3⋊C4—61no—
212Dic3⋊C4—61no—
213Dic3⋊C4—61no—
214Dic3⋊C4—121no—
215Dic3⋊C4—121no—
216Dic3⋊C4—122no—
217C4×Dic3—61no—
218C4×Dic3—61no—
219C2×C3⋊C8—61no—
220C2×C3⋊C8—61no—
221C2×C3⋊C8—121no—
222#204—42no—
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—
233C3⋊Dic3—41no—
234C3⋊Dic3—41no—
235C3×Dic3—42no—
236C3×Dic3—41no—
237C3×Dic3—41no—
238C3×Dic3—41no—
239C3×Dic3—42no—
240C22×Q8—31no—
241C2×Q16—181no—
242C2×SD16—61no—
243#126—181no—
244#125—181no—
245#123—181no—
246#123—181no—
247C22⋊Q8—31no—
248C22⋊Q8—181no—
249#121—31no—
250C4×D4—181no—
251C2×C4⋊C4—91no—
252C2×C4⋊C4—181no—
253#103—61no—
254#103—181no—
255C22⋊C8—91no—
256C22⋊C8D3211yescharacteristic
257#95—31no—
258#95—181no—
259C23×C3—21no—
260C23×C3—61no—
261C23×C3D3×D411yescharacteristic
262C23×C3D3×D411yescharacteristic
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—21no—
273C2×C3×C4—21no—
274C2×C3×C4—41no—
275C2×C3×C4—41no—
276C2×C3×C4—62no—
277C2×C3×C4—62no—
278C2×C3×C4—61no—
279C2×C3×C4—61no—
280C2×C3×C4—61no—
281C2×C3×C4—81no—
282C2×C3×C4—121no—
283C2×C3×C4—121no—
284C2×C3×C4—121no—
285C2×C3×C4—121no—
286C2×C3×C4C2×D1211yescharacteristic
287C2×C3×C4D3×D411yescharacteristic
288C2×C3×C4D3×D411yescharacteristic
289C2×C3×C4C2×#6711yescharacteristic
290#67—41no—
291#67—41no—
292C2×Dic3—22no—
293C2×Dic3—22no—
294C2×Dic3—21no—
295C2×Dic3—21no—
296C2×Dic3—21no—
297C2×Dic3—41no—
298C2×Dic3—41no—
299C2×Dic3—41no—
300C2×Dic3—41no—
301C2×Dic3—62no—
302C2×Dic3—61no—
303C2×Dic3—61no—
304C2×Dic3—61no—
305C2×Dic3—61no—
306C2×Dic3—61no—
307C2×Dic3—61no—
308C2×Dic3—61no—
309C2×Dic3—61no—
310C2×Dic3—121no—
311C2×Dic3—121no—
312C2×Dic3—121no—
313C2×Dic3—121no—
314C2×Dic3—121no—
315C2×Dic3—241no—
316C2×Dic3—241no—
317D12—41no—
318C4×D3—241no—
319Dic6—22no—
320Dic6—22no—
321Dic6—41no—
322Dic6—41no—
323Dic6—41no—
324C3×C8—41no—
325C3×C8—41no—
326C3×C8—81no—
327C3⋊C8—121no—
328C3⋊C8—121no—
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—91no—
345C22×C4—91no—
346C22×C4—181no—
347C22×C4C2×D3211yescharacteristic
348Q16—362no—
349SD16—122no—
350C2×C8—21no—
351C2×C8—181no—
352C4⋊C4—31no—
353C4⋊C4—31no—
354C4⋊C4—61no—
355C4⋊C4—181no—
356C4⋊C4—181no—
357C4⋊C4—181no—
358C4⋊C4—181no—
359C4⋊C4—181no—
360C4⋊C4—362no—
361C22⋊C4—61no—
362C22⋊C4—61no—
363C22⋊C4—181no—
364C22⋊C4—181no—
365C22⋊C4—181no—
366C42—181no—
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#88211yescharacteristic
380C22×C3#91511yescharacteristic
381C22×C3#91611yescharacteristic
382C22×C3#91611yescharacteristic
383C22×C3#91811yescharacteristic
384C22×C3#93711yescharacteristic
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—122no—
395C3×C4—121no—
396C3×C4—122no—
397C3×C4—121no—
398C3×C4—121no—
399Dic3—42no—
400Dic3—41no—
401Dic3—41no—
402Dic3—42no—
403Dic3—41no—
404Dic3—122no—
405Dic3—121no—
406Dic3—121no—
407Dic3—121no—
408Dic3—121no—
409Dic3—241no—
410C32#160311yescharacteristic, complemented, Sylow
411C23—61no—
412C23#380211yescharacteristic
413Q8—62no—
414Q8—62no—
415Q8—121no—
416Q8—121no—
417Q8—121no—
418D4—121no—
419D4—121no—
420D4—121no—
421C2×C4—41no—
422C2×C4—62no—
423C2×C4—62no—
424C2×C4—61no—
425C2×C4—61no—
426C2×C4—61no—
427C2×C4—121no—
428C2×C4—121no—
429C2×C4—121no—
430C2×C4—121no—
431C2×C4—181no—
432C2×C4—181no—
433C2×C4—181no—
434C2×C4—181no—
435C2×C4—361no—
436C2×C4—721no—
437C2×C4D3×D1211yescharacteristic
438C2×C4D3×#6711yescharacteristic
439C8—41no—
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#474111yescharacteristic
452C2×C3#480811yescharacteristic
453C2×C3#482611yescharacteristic
454C2×C3#503211yescharacteristic
455C2×C3#517311yescharacteristic
456C2×C3#520511yescharacteristic
457D3—81no—
458C22—21no—
459C22—21no—
460C22—121no—
461C22—121no—
462C22—121no—
463C22#6380911yescharacteristic
464C22#6381111yescharacteristic
465C22#6392211yescharacteristic
466C4—21no—
467C4—21no—
468C4—122no—
469C4—121no—
470C4—122no—
471C4—121no—
472C4—121no—
473C4—361no—
474C4—361no—
475C3—21no—
476C3#6832611yescharacteristic, complemented
477C3#7097411yescharacteristic, complemented
478C2—21no—
479C2—21no—
480C2—241no—
481C2#1059040711yescharacteristic
482C2#1059096111yescharacteristic
483C2#1059101711yescharacteristic
subgroupG/H
centerC22#63922
commutator, cosocleC22×C32×C4C23
FrattiniC22×C4C2×D32
FittingC32×C22⋊C8C22
socleC22×C32#120
prime radicalC3×#930C22
hypercenterC22⋊C8D32
hypocenterC32#1603
LCSG ▷ C22×C32×C4 ▷ C22×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22⋊C8

Complements

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

NH ≅ G/Ntype
3. #10591346C2semidirect
4. #10591185C2semidirect
5. #10589335C2semidirect
6. C3×#4467C2semidirect
42. #4467D3semidirect
410. C32#1603semidirect
476. C3#68326semidirect
477. C3#70974semidirect

Maximal subgroups

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

subgroupindex
#105949742
C3×#47382
#105913462
#105911852
#105893352
C3×#44672
#105891492
#709743
#683263