Finite Group Databasebeta

← #11778366

Subgroups — #11778366

Order 1152.

579 conjugacy classes of subgroups; only the 82 normal subgroups are shown.

normal subgroups only

This group has 579 conjugacy classes of subgroups — too many to draw. Only its 82 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#10596094C211yesmaximal, characteristic
2C3×#5050C211yesmaximal, characteristic
3#10591346C211yesmaximal, characteristic
4#10591186C211yesmaximal, characteristic
5C3×#4538C211yesmaximal, characteristic
6#10589154C211yesmaximal, characteristic
7#10589148C211yesmaximal, characteristic
8#70983—31nomaximal
9#68327—31nomaximal
10C22×C3×Dic6C2211yescharacteristic
11C32×C22⋊Q8C2211yescharacteristic
12#64153—21no—
13#64133C2211yescharacteristic
14C2×#3750C2211yescharacteristic
15#64098—21no—
16#64098—21no—
17#64097—21no—
18#64087—21no—
19#64086—21no—
20C2×C3×#216—21no—
21C2×Dic3⋊Dic3—21no—
22C2×#3719—21no—
23C3×C3⋊#95C2211yescharacteristic
24C3×#830C2211yescharacteristic
25C3×#830C2211yescharacteristic
26C3×#810—21no—
27#63579—21no—
28#63566—21no—
29#5623—31no—
30#5623—31no—
31#5623—61no—
32C3×#451—31no—
33#5230—31no—
34#5228—31no—
35#5050D311yescharacteristic
36#4739—31no—
37#4656—31no—
38C3×#328—31no—
39#4538D311yescharacteristic
40#4469—31no—
41#4469—31no—
42#4467—31no—
43#4452—31no—
44C2×C32×Q8D411yescharacteristic
45C22×C32×C4C2311yescharacteristic
46C22×C3⋊Dic3D411yescharacteristic
47C22×C3⋊Dic3D411yescharacteristic
48C2×#634—21no—
49C2×#634D411yescharacteristic
50C22×C3×Dic3—21no—
51C22×C3×Dic3—21no—
52C2×C3×Dic6—21no—
53C2×C3×Dic6—21no—
54C2×C3×Dic6—42no—
55C32×C4⋊C4—21no—
56C32×C4⋊C4D411yescharacteristic
57C32×C22⋊C4—21no—
58#3757—21no—
59C4⋊(C3⋊Dic3)—21no—
60C4⋊(C3⋊Dic3)D411yescharacteristic
61#3750—21no—
62#3750—21no—
63#3750—21no—
64#3750—21no—
65#3750—21no—
66#3750—21no—
67#3750—21no—
68C4×C3⋊Dic3—21no—
69C4×C3⋊Dic3—21no—
70C3×#216—42no—
71C2×C3×C3⋊C8—21no—
72C2×C3×C3⋊C8—21no—
73Dic3⋊Dic3—42no—
74#3719—42no—
75#1605—91noSylow
76C22×C3×Q8—31no—
77C22×Dic6C2×D311yescharacteristic
78C2×C3×Q16—61no—
79C3×C22⋊Q8—21no—
80C3×C22⋊Q8C2×D311yescharacteristic
81C3×C22⋊Q8C2×D311yescharacteristic
82#944—62no—
83#944—61no—
84#944—61no—
85C2×#216—21no—
86C2×#216—61no—
87C2×C4⋊Dic3—61no—
88#924—31no—
89#924—31no—
90#924—61no—
91C2×Dic3⋊C4—31no—
92C2×Dic3⋊C4—31no—
93C2×Dic3⋊C4—61no—
94C2×Dic3⋊C4—61no—
95C2×Dic12—61no—
96#889—61no—
97#889—61no—
98#889—62no—
99#889—62no—
100#889—61no—
101#889—61no—
102#888—61no—
103#888—61no—
104#888—62no—
105#878—61no—
106#878—61no—
107#878—62no—
108#877—61no—
109#877—61no—
110#877—62no—
111C3×#103—61no—
112C3×C22⋊C8—31no—
113C3×C22⋊C8—31no—
114C3×#95—31no—
115#835—61no—
116C3⋊#95—61no—
117C3⋊#95—61no—
118C3⋊#95C2×D311yescharacteristic
119#830C2×D311yescharacteristic
120#830C2×D311yescharacteristic
121#816—61no—
122#810—21no—
123C23×C32C2×D411yescharacteristic
124C32×Q8—41no—
125C2×C32×C4—21no—
126C2×C32×C4—21no—
127C2×C32×C4—41no—
128C2×C32×C4C2×D411yescharacteristic
129C2×C32×C4C2×D411yescharacteristic
130C2×C3⋊Dic3—21no—
131C2×C3⋊Dic3—21no—
132C2×C3⋊Dic3—21no—
133C2×C3⋊Dic3—21no—
134C2×C3⋊Dic3—21no—
135C2×C3⋊Dic3—41no—
136C2×C3⋊Dic3Q1612yescomplemented
137#634—41no—
138#634—81no—
139C2×C3×Dic3—22no—
140C2×C3×Dic3—22no—
141C2×C3×Dic3—41no—
142C2×C3×Dic3—41no—
143C2×C3×Dic3—41no—
144C2×C3×Dic3—41no—
145C3×Dic6—22no—
146C3×Dic6—22no—
147C3×Dic6—41no—
148C3×Dic6—41no—
149C3×C3⋊C8—41no—
150C3×C3⋊C8—41no—
151#544—91no—
152#451—31no—
153#451—91no—
154#395—91no—
155#328—31no—
156#328—91no—
157#324—91no—
158C2×C3×Q8—21no—
159C2×C3×Q8—61no—
160C2×C3×Q8—61no—
161C2×C3×Q8—122no—
162C2×C3×Q8D1211yescharacteristic
163C2×C3×Q8#6711yescharacteristic
164C22×C3×C4—21no—
165C22×C3×C4—61no—
166C22×C3×C4—61no—
167C22×C3×C4C22×D311yescharacteristic
168C22×C3×C4C22×D311yescharacteristic
169C22×Dic3—21no—
170C22×Dic3—21no—
171C22×Dic3—31no—
172C22×Dic3—31no—
173C22×Dic3—31no—
174C22×Dic3—31no—
175C22×Dic3—61no—
176C22×Dic3—61no—
177C2×Dic6—21no—
178C2×Dic6—21no—
179C2×Dic6—31no—
180C2×Dic6—31no—
181C2×Dic6—42no—
182C2×Dic6—61no—
183C2×Dic6—62no—
184C2×Dic6—61no—
185C2×Dic6—61no—
186C3×Q16—122no—
187C2×C3×C8—61no—
188C2×C3×C8—61no—
189C3×C4⋊C4—22no—
190C3×C4⋊C4—21no—
191C3×C4⋊C4—21no—
192C3×C4⋊C4—21no—
193C3×C4⋊C4D1211yescharacteristic
194C3×C4⋊C4#6711yescharacteristic
195C3×C22⋊C4—22no—
196C3×C22⋊C4—21no—
197C3×C22⋊C4—21no—
198#217—62no—
199#217—61no—
200#217—61no—
201#216—42no—
202#216—122no—
203C4⋊Dic3—31no—
204C4⋊Dic3—31no—
205C4⋊Dic3—61no—
206C4⋊Dic3—62no—
207C4⋊Dic3—61no—
208C4⋊Dic3—61no—
209C4⋊Dic3—122no—
210Dic3⋊C4—62no—
211Dic3⋊C4—61no—
212Dic3⋊C4—61no—
213Dic3⋊C4—62no—
214Dic3⋊C4—61no—
215Dic3⋊C4—61no—
216Dic3⋊C4—62no—
217Dic3⋊C4—61no—
218Dic3⋊C4—61no—
219Dic3⋊C4—62no—
220Dic3⋊C4—61no—
221Dic3⋊C4—61no—
222Dic3⋊C4—62no—
223Dic3⋊C4—62no—
224Dic3⋊C4—62no—
225Dic3⋊C4—61no—
226Dic3⋊C4—61no—
227Dic3⋊C4—61no—
228Dic3⋊C4—61no—
229Dic3⋊C4—61no—
230Dic3⋊C4—61no—
231Dic3⋊C4—122no—
232C4×Dic3—62no—
233C4×Dic3—61no—
234C4×Dic3—61no—
235C4×Dic3—62no—
236C4×Dic3—61no—
237C4×Dic3—61no—
238C2×C3⋊C8—21no—
239C2×C3⋊C8—21no—
240Dic12—122no—
241C22×C32—21no—
242C22×C32—21no—
243C22×C32#12011yescharacteristic
244C22×C32C2×Q1611yescharacteristic
245C22×C32#13711yescharacteristic
246C32×C4—21no—
247C32×C4—21no—
248C32×C4—41no—
249C32×C4—41no—
250C3⋊Dic3—22no—
251C3⋊Dic3—41no—
252C3⋊Dic3—41no—
253C3⋊Dic3—41no—
254C3×Dic3—42no—
255C3×Dic3—42no—
256C22×Q8—31no—
257C2×Q16—61no—
258C2×Q16—181no—
259C4⋊Q8—181no—
260C4⋊Q8—181no—
261#125—181no—
262#125—181no—
263C22⋊Q8—91no—
264C22⋊Q8—181no—
265C22⋊Q8D3211yescharacteristic
266#117—181no—
267C2×C4⋊C4—91no—
268C2×C4⋊C4—181no—
269#103—61no—
270#103—181no—
271C22⋊C8—31no—
272C22⋊C8—31no—
273#95—31no—
274#95—181no—
275C23×C3—21no—
276C23×C3D3×D411yescharacteristic
277C23×C3D3×D411yescharacteristic
278C3×Q8—41no—
279C3×Q8—41no—
280C3×Q8—62no—
281C3×Q8—62no—
282C3×Q8—81no—
283C3×Q8—121no—
284C3×Q8—121no—
285C2×C3×C4—22no—
286C2×C3×C4—22no—
287C2×C3×C4—21no—
288C2×C3×C4—21no—
289C2×C3×C4—21no—
290C2×C3×C4—21no—
291C2×C3×C4—21no—
292C2×C3×C4—21no—
293C2×C3×C4—41no—
294C2×C3×C4—41no—
295C2×C3×C4—62no—
296C2×C3×C4—62no—
297C2×C3×C4—81no—
298C2×C3×C4—121no—
299C2×C3×C4—121no—
300C2×C3×C4—121no—
301C2×C3×C4—121no—
302C2×C3×C4C2×D1211yescharacteristic
303C2×C3×C4D3×D411yescharacteristic
304C2×C3×C4D3×D411yescharacteristic
305C2×C3×C4C2×#6711yescharacteristic
306C2×Dic3—22no—
307C2×Dic3—22no—
308C2×Dic3—32no—
309C2×Dic3—32no—
310C2×Dic3—41no—
311C2×Dic3—41no—
312C2×Dic3—41no—
313C2×Dic3—41no—
314C2×Dic3—62no—
315C2×Dic3—62no—
316C2×Dic3—62no—
317C2×Dic3—61no—
318C2×Dic3—61no—
319C2×Dic3—61no—
320C2×Dic3—61no—
321C2×Dic3—62no—
322C2×Dic3—62no—
323C2×Dic3—62no—
324C2×Dic3—61no—
325C2×Dic3—61no—
326C2×Dic3—61no—
327C2×Dic3—61no—
328C2×Dic3—61no—
329C2×Dic3—61no—
330C2×Dic3—121no—
331C2×Dic3—121no—
332C2×Dic3—241no—
333Dic6—22no—
334Dic6—22no—
335Dic6—41no—
336Dic6—41no—
337Dic6—121no—
338Dic6—121no—
339Dic6—241no—
340Dic6—242no—
341Dic6—241no—
342Dic6—241no—
343C3×C8—121no—
344C3×C8—121no—
345C3⋊C8—41no—
346C3⋊C8—41no—
347C2×C32—21no—
348C2×C32—21no—
349C2×C32#45111yescharacteristic
350C2×C32#45611yescharacteristic
351C2×C32B(4,𝔽2)11yescharacteristic
352C2×Q8—61no—
353C2×Q8—61no—
354C2×Q8—91no—
355C2×Q8—122no—
356C2×Q8—181no—
357C2×Q8#62611yescharacteristic
358C22×C4—61no—
359C22×C4—61no—
360C22×C4—91no—
361C22×C4—91no—
362C22×C4C2×D3211yescharacteristic
363Q16—122no—
364Q16—362no—
365C2×C8—61no—
366C2×C8—61no—
367C4⋊C4—21no—
368C4⋊C4—91no—
369C4⋊C4—181no—
370C4⋊C4—181no—
371C4⋊C4—181no—
372C4⋊C4—181no—
373C4⋊C4—181no—
374C4⋊C4—181no—
375C4⋊C4—181no—
376C4⋊C4—181no—
377C4⋊C4—362no—
378C4⋊C4#62611yescharacteristic
379C22⋊C4—21no—
380C22⋊C4—181no—
381C42—181no—
382C42—181no—
383C22×C3—21no—
384C22×C3—21no—
385C22×C3—21no—
386C22×C3—21no—
387C22×C3—21no—
388C22×C3—21no—
389C22×C3—21no—
390C22×C3—41no—
391C22×C3—41no—
392C22×C3#88211yescharacteristic
393C22×C3#91511yescharacteristic
394C22×C3D3×Q1611yescharacteristic
395C22×C3D3×Q1611yescharacteristic
396C22×C3#91811yescharacteristic
397C22×C3#93711yescharacteristic
398C3×C4—21no—
399C3×C4—21no—
400C3×C4—21no—
401C3×C4—21no—
402C3×C4—41no—
403C3×C4—41no—
404C3×C4—42no—
405C3×C4—42no—
406C3×C4—41no—
407C3×C4—41no—
408C3×C4—41no—
409C3×C4—41no—
410C3×C4—122no—
411C3×C4—122no—
412Dic3—42no—
413Dic3—42no—
414Dic3—64no—
415Dic3—62no—
416Dic3—62no—
417Dic3—122no—
418Dic3—122no—
419Dic3—122no—
420Dic3—121no—
421Dic3—121no—
422Dic3—121no—
423Dic3—121no—
424Dic3—121no—
425Dic3—121no—
426C32#160511yescharacteristic, complemented, Sylow
427C23#381111yescharacteristic
428Q8—41no—
429Q8—62no—
430Q8—62no—
431Q8—121no—
432Q8—121no—
433Q8—361no—
434Q8—721no—
435C2×C4—21no—
436C2×C4—21no—
437C2×C4—41no—
438C2×C4—62no—
439C2×C4—62no—
440C2×C4—92no—
441C2×C4—121no—
442C2×C4—121no—
443C2×C4—121no—
444C2×C4—121no—
445C2×C4—181no—
446C2×C4—181no—
447C2×C4—181no—
448C2×C4—181no—
449C2×C4—181no—
450C2×C4—361no—
451C2×C4C2×#62611yescharacteristic
452C2×C4#381111yescharacteristic
453C8—121no—
454C8—121no—
455C2×C3—21no—
456C2×C3—21no—
457C2×C3—21no—
458C2×C3—21no—
459C2×C3—21no—
460C2×C3—21no—
461C2×C3—21no—
462C2×C3—41no—
463C2×C3—41no—
464C2×C3#474111yescharacteristic
465C2×C3#480911yescharacteristic
466C2×C3#482611yescharacteristic
467C2×C3#503211yescharacteristic
468C2×C3#518611yescharacteristic
469C2×C3#520511yescharacteristic
470C22—21no—
471C22—21no—
472C22#6394411yescharacteristic
473C22#6395111yescharacteristic
474C22#6398111yescharacteristic
475C4—21no—
476C4—21no—
477C4—41no—
478C4—41no—
479C4—122no—
480C4—122no—
481C4—182no—
482C4—361no—
483C4—361no—
484C4—361no—
485C3—21no—
486C3#6832711yescharacteristic, complemented
487C3#7098311yescharacteristic, complemented
488C2—21no—
489C2—21no—
490C2#1059153211yescharacteristic
491C2#1059160311yescharacteristic
492C2#1059166811yescharacteristic
subgroupG/H
centerC22#63981
commutator, cosocleC22×C32×C4C23
FrattiniC22×C4C2×D32
FittingC32×C22⋊Q8C22
socleC22×C32#120
prime radicalC23×C32C2×D4
hypercenterC22⋊Q8D32
hypocenterC32#1605
LCSG ▷ C22×C32×C4 ▷ C22×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22⋊Q8

Complements

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

NH ≅ G/Ntype
136. C2×C3⋊Dic3Q16semidirect
426. C32#1605semidirect
486. C3#68327semidirect
487. C3#70983semidirect

Maximal subgroups

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

subgroupindex
#105960942
C3×#50502
#105913462
#105911862
C3×#45382
#105891542
#105891482
#709833
#683273