Finite Group Databasebeta

← #11778702

Subgroups — #11778702

Order 1152.

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

normal subgroups only

This group has 524 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#10594971C211yesmaximal, characteristic
2#10592669C211yesmaximal, characteristic, complemented
3C3×#4993C211yesmaximal, characteristic
4C3×#4970C211yesmaximal, characteristic, complemented
5#10589154C211yesmaximal, characteristic, complemented
6#10589153C211yesmaximal, characteristic, complemented
7#10589145C211yesmaximal, characteristic
8#71176—31nomaximal
9#69716—31nomaximal
10C2×C32×C4⋊C4C2211yescharacteristic
11#64133C2211yescharacteristic
12C2×C3×(C2×D3)⋊C4—21no—
13C2×C3×(C2×D3)⋊C4C2211yescharacteristic
14C3×#924C2211yescharacteristic
15C2×C3×Dic3⋊C4—21no—
16D3×#217—21no—
17#63964—21no—
18#63899—21no—
19#63896—21no—
20#63893—21no—
21#63887—21no—
22#63657C2211yescharacteristic
23#63637—21no—
24#63634—21no—
25C3×C3⋊#95C2211yescharacteristic
26C3×#830C2211yescharacteristic
27C3×#810—21no—
28C3×#807—21no—
29#5634—31no—
30#5483—31no—
31C3×#484—31no—
32C3×#399—31no—
33#4993D311yescharacteristic
34#4970—31no—
35#4970—31no—
36#4970—61no—
37#4970D311yescharacteristic, complemented
38#4538—31no—
39#4525—31no—
40#4468—31no—
41#4467—31no—
42#4452—31no—
43#4452—31no—
44C23×C3×D3D411yescharacteristic
45C22×C32×C4—21no—
46C22×C32×C4C2311yescharacteristic
47C2×#634D411yescharacteristic
48C22×C3×Dic3—21no—
49C22×C3×Dic3D411yescharacteristic
50C2×C3×Dic6D411yescharacteristic
51C2×#627—21no—
52C2×D3×Dic3—21no—
53C2×D3×Dic3—21no—
54C32×C4⋊C4—21no—
55C32×C4⋊C4—21no—
56#3757—21no—
57C4⋊(C3⋊Dic3)D411yescharacteristic
58#3750—21no—
59C2×C3⋊(C3⋊C8)—21no—
60C3×#217—21no—
61C3×(C2×D3)⋊C4—21no—
62C3×(C2×D3)⋊C4—21no—
63C3×(C2×D3)⋊C4—42no—
64C3×C4⋊Dic3D411yescharacteristic
65C3×Dic3⋊C4—21no—
66C3×Dic3⋊C4—42no—
67C2×C3×C3⋊C8—21no—
68#3724—21no—
69Dic3⋊Dic3—21no—
70Dic3⋊Dic3—21no—
71(C2×D3)⋊Dic3—21no—
72(C2×D3)⋊Dic3—21no—
73#1614—91noSylow
74C3×C22⋊Q8—31no—
75C2×C3×C4⋊C4—21no—
76C2×C3×C4⋊C4—61no—
77C2×C3×C4⋊C4C2×D311yescharacteristic
78C2×C3×C4⋊C4C2×D311yescharacteristic
79C2×C3×C22⋊C4—31no—
80C2×C3×C22⋊C4—61no—
81C2×#217—61no—
82#946—61no—
83C2×(C2×D3)⋊C4—21no—
84C2×(C2×D3)⋊C4C2×D311yescharacteristic
85#924—31no—
86#924—31no—
87#924—61no—
88#924—61no—
89#924C2×D311yescharacteristic
90C2×Dic3⋊C4—21no—
91#897—61no—
92#896—61no—
93#896—61no—
94D3×C22⋊C4—61no—
95#878—61no—
96#878—61no—
97#878—61no—
98#878—61no—
99#878—61no—
100C3×#107—61no—
101C3×#103—61no—
102C3×C22⋊C8—31no—
103C3×#95—31no—
104C3⋊#95C2×D311yescharacteristic
105#830—31no—
106#830—31no—
107#830—61no—
108#830C2×D311yescharacteristic
109#810—21no—
110#810—61no—
111#810—61no—
112#810—62no—
113#807—21no—
114#807—61no—
115#807—61no—
116#807—62no—
117C23×C32C2×D411yescharacteristic
118C22×C3×D3—21no—
119C22×C3×D3—21no—
120C22×C3×D3—41no—
121C22×C3×D3—41no—
122C22×C3×D3Q1612yes—
123C2×C32×C4—41no—
124C2×C32×C4—41no—
125C2×C32×C4—41no—
126C2×C32×C4—41no—
127C2×C32×C4C2×D411yescharacteristic
128C2×C32×C4C2×D411yescharacteristic
129C2×C3⋊Dic3—21no—
130C2×C3⋊Dic3—21no—
131#634—41no—
132C2×C3×Dic3—22no—
133C2×C3×Dic3—21no—
134C2×C3×Dic3—21no—
135C2×C3×Dic3—21no—
136C2×C3×Dic3—41no—
137C2×C3×Dic3—41no—
138C2×C3×Dic3—41no—
139C3×Dic6—41no—
140#627—81no—
141D3×Dic3—81no—
142D3×Dic3—81no—
143C3⋊(C3⋊C8)—41no—
144C3×C3⋊C8—41no—
145#543—91no—
146#484—31no—
147#484—91no—
148#399—31no—
149#328—91no—
150#328—91no—
151#323—91no—
152C24×C3—31no—
153C23×D3#6711yescharacteristic
154C2×C3×Q8—31no—
155C22×C3×C4—21no—
156C22×C3×C4—21no—
157C22×C3×C4—21no—
158C22×C3×C4—31no—
159C22×C3×C4—41no—
160C22×C3×C4—61no—
161C22×C3×C4C22×D311yescharacteristic
162C22×C3×C4C22×D311yescharacteristic
163C22×Dic3—21no—
164C22×Dic3—61no—
165C22×Dic3—61no—
166C22×Dic3#6711yescharacteristic
167C2×C4×D3—61no—
168C2×C4×D3—61no—
169C2×Dic6—31no—
170C2×Dic6—31no—
171C2×Dic6—61no—
172C2×Dic6—61no—
173C2×Dic6—61no—
174C2×Dic6#6711yescharacteristic
175C2×C3×C8—61no—
176C3×C4⋊C4—22no—
177C3×C4⋊C4—21no—
178C3×C4⋊C4—21no—
179C3×C4⋊C4—21no—
180C3×C4⋊C4—21no—
181C3×C4⋊C4—31no—
182C3×C4⋊C4—41no—
183C3×C4⋊C4—61no—
184C3×C4⋊C4—122no—
185C3×C22⋊C4—61no—
186C3×C22⋊C4—61no—
187C3×C22⋊C4—61no—
188C3×C22⋊C4—122no—
189#217—21no—
190#217—61no—
191#217—61no—
192#217—61no—
193#217—61no—
194#217—121no—
195(C2×D3)⋊C4—21no—
196(C2×D3)⋊C4—21no—
197(C2×D3)⋊C4—42no—
198(C2×D3)⋊C4—61no—
199(C2×D3)⋊C4—61no—
200C4⋊Dic3—31no—
201C4⋊Dic3—31no—
202C4⋊Dic3—61no—
203C4⋊Dic3—61no—
204C4⋊Dic3—61no—
205C4⋊Dic3#6711yescharacteristic
206Dic3⋊C4—21no—
207Dic3⋊C4—42no—
208Dic3⋊C4—61no—
209Dic3⋊C4—61no—
210Dic3⋊C4—61no—
211Dic3⋊C4—61no—
212Dic3⋊C4—61no—
213Dic3⋊C4—61no—
214Dic3⋊C4—121no—
215C2×C3⋊C8—21no—
216C2×C3⋊C8—62no—
217C2×C3⋊C8—61no—
218C2×C3⋊C8—61no—
219C22×C32—21no—
220C22×C32—21no—
221C22×C32#12011yescharacteristic
222C22×C32C2×Q1611yescharacteristic
223C22×C32#13711yescharacteristic
224C2×C3×D3—22no—
225C2×C3×D3—41no—
226C2×C3×D3—41no—
227C2×C3×D3—42no—
228C2×C3×D3—81no—
229C32×C4—21no—
230C32×C4—21no—
231C32×C4—81no—
232C3⋊Dic3—41no—
233C3⋊Dic3—41no—
234C3×Dic3—42no—
235C3×Dic3—41no—
236C3×Dic3—41no—
237C3×Dic3—41no—
238C22⋊Q8—31no—
239C22⋊Q8—91no—
240C22⋊Q8—181no—
241C22⋊Q8—181no—
242C22⋊Q8—181no—
243C22⋊Q8—181no—
244C22⋊Q8—181no—
245C2×C4⋊C4—61no—
246C2×C4⋊C4D3211yescharacteristic
247C2×C22⋊C4—31no—
248C2×C22⋊C4—61no—
249C2×C22⋊C4—181no—
250#107—61no—
251#107—181no—
252#103—61no—
253#103—181no—
254C22⋊C8—31no—
255C22⋊C8—91no—
256#95—31no—
257C23×C3—21no—
258C23×C3—32no—
259C23×C3—61no—
260C23×C3—61no—
261C23×C3—121no—
262C23×C3—121no—
263C23×C3D3×D411yescharacteristic
264C23×C3C2×#6711yescharacteristic
265C22×D3—21no—
266C22×D3—21no—
267C22×D3—41no—
268C22×D3—41no—
269C22×D3#21612yes—
270C3×Q8—121no—
271C2×C3×C4—21no—
272C2×C3×C4—21no—
273C2×C3×C4—41no—
274C2×C3×C4—41no—
275C2×C3×C4—42no—
276C2×C3×C4—41no—
277C2×C3×C4—41no—
278C2×C3×C4—41no—
279C2×C3×C4—42no—
280C2×C3×C4—41no—
281C2×C3×C4—41no—
282C2×C3×C4—41no—
283C2×C3×C4—62no—
284C2×C3×C4—61no—
285C2×C3×C4—61no—
286C2×C3×C4—61no—
287C2×C3×C4—81no—
288C2×C3×C4—81no—
289C2×C3×C4—121no—
290C2×C3×C4—121no—
291C2×C3×C4—121no—
292C2×C3×C4D3×D411yescharacteristic
293C2×C3×C4D3×D411yescharacteristic
294C2×C3×C4D3×D411yescharacteristic
295C2×C3×C4C2×#6711yescharacteristic
296C2×Dic3—22no—
297C2×Dic3—21no—
298C2×Dic3—21no—
299C2×Dic3—21no—
300C2×Dic3—41no—
301C2×Dic3—41no—
302C2×Dic3—41no—
303C2×Dic3—61no—
304C2×Dic3—61no—
305C2×Dic3—61no—
306C2×Dic3—61no—
307C2×Dic3—121no—
308C2×Dic3—121no—
309C2×Dic3—241no—
310C2×Dic3—241no—
311C4×D3—241no—
312C4×D3—241no—
313Dic6—41no—
314Dic6—121no—
315Dic6—121no—
316Dic6—122no—
317Dic6—241no—
318Dic6—241no—
319C3×C8—121no—
320C3⋊C8—41no—
321C3⋊C8—122no—
322C3⋊C8—121no—
323C3⋊C8—121no—
324C2×C32—21no—
325C2×C32—21no—
326C2×C32#45111yescharacteristic
327C2×C32#45311yescharacteristic
328C2×C32#45811yescharacteristic
329C3×D3—42no—
330C24—31no—
331C2×Q8—31no—
332C2×Q8—91no—
333C2×Q8—181no—
334C22×C4—21no—
335C22×C4—31no—
336C22×C4—61no—
337C22×C4—181no—
338C22×C4—181no—
339C22×C4C2×D3211yescharacteristic
340C2×C8—61no—
341C2×C8—181no—
342C4⋊C4—21no—
343C4⋊C4—21no—
344C4⋊C4—31no—
345C4⋊C4—61no—
346C4⋊C4—91no—
347C4⋊C4—122no—
348C4⋊C4—181no—
349C4⋊C4—181no—
350C4⋊C4—181no—
351C4⋊C4—181no—
352C22⋊C4—61no—
353C22⋊C4—61no—
354C22⋊C4—61no—
355C22⋊C4—122no—
356C22⋊C4—181no—
357C22⋊C4—181no—
358C22⋊C4—181no—
359C22×C3—21no—
360C22×C3—21no—
361C22×C3—21no—
362C22×C3—21no—
363C22×C3—21no—
364C22×C3—21no—
365C22×C3—21no—
366C22×C3—41no—
367C22×C3—41no—
368C22×C3—62no—
369C22×C3—122no—
370C22×C3—121no—
371C22×C3—121no—
372C22×C3—241no—
373C22×C3D3×Q1611yescharacteristic
374C22×C3#91811yescharacteristic
375C22×C3#93711yescharacteristic
376C22×C3#93711yescharacteristic
377C22×C3C2×#21611yescharacteristic
378C22×C3#95111yescharacteristic
379C2×D3—22no—
380C2×D3—41no—
381C2×D3—41no—
382C2×D3—42no—
383C2×D3—81no—
384C3×C4—22no—
385C3×C4—21no—
386C3×C4—21no—
387C3×C4—21no—
388C3×C4—21no—
389C3×C4—41no—
390C3×C4—82no—
391C3×C4—81no—
392C3×C4—81no—
393C3×C4—122no—
394C3×C4—121no—
395C3×C4—121no—
396C3×C4—121no—
397Dic3—42no—
398Dic3—41no—
399Dic3—41no—
400Dic3—41no—
401Dic3—121no—
402Dic3—121no—
403Dic3—121no—
404Dic3—121no—
405Dic3—241no—
406Dic3—241no—
407C32#161411yescharacteristic, complemented, Sylow
408C23—32no—
409C23—61no—
410C23—61no—
411C23—121no—
412C23—121no—
413C23D3×#6711yescharacteristic
414Q8—121no—
415Q8—361no—
416Q8—721no—
417C2×C4—41no—
418C2×C4—41no—
419C2×C4—41no—
420C2×C4—41no—
421C2×C4—62no—
422C2×C4—61no—
423C2×C4—61no—
424C2×C4—61no—
425C2×C4—121no—
426C2×C4—121no—
427C2×C4—121no—
428C2×C4—181no—
429C2×C4—181no—
430C2×C4—721no—
431C2×C4—721no—
432C2×C4D3×#6711yescharacteristic
433C2×C4#381111yescharacteristic
434C8—121no—
435C8—361no—
436C2×C3—21no—
437C2×C3—21no—
438C2×C3—21no—
439C2×C3—21no—
440C2×C3—21no—
441C2×C3—21no—
442C2×C3—21no—
443C2×C3—41no—
444C2×C3—41no—
445C2×C3—122no—
446C2×C3#505011yescharacteristic
447C2×C3#505311yescharacteristic
448C2×C3#505311yescharacteristic
449C2×C3#507711yescharacteristic
450C2×C3#518611yescharacteristic
451C2×C3#519811yescharacteristic
452D3—42no—
453C22—21no—
454C22—21no—
455C22—62no—
456C22—122no—
457C22—121no—
458C22—121no—
459C22—241no—
460C22D3×#21611yescharacteristic
461C22#6394311yescharacteristic
462C22#6398311yescharacteristic
463C4—21no—
464C4—21no—
465C4—81no—
466C4—122no—
467C4—121no—
468C4—121no—
469C4—121no—
470C4—361no—
471C4—361no—
472C3—21no—
473C3#6971611yescharacteristic, complemented
474C3#7117611yescharacteristic, complemented
475C2—21no—
476C2—21no—
477C2—122no—
478C2#1059139811yescharacteristic
479C2#1059152311yescharacteristic
480C2#1059165311yescharacteristic
subgroupG/H
centerC22#63983
commutator, cosocleC22×C32×C4C23
FrattiniC22×C4C2×D32
FittingC2×C32×C4⋊C4C22
socleC22×C32#120
prime radicalC23×C3×D3D4
hypercenterC2×C4⋊C4D32
hypocenterC32#1614
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. #10592669C2semidirect
4. C3×#4970C2semidirect
5. #10589154C2semidirect
6. #10589153C2semidirect
37. #4970D3semidirect
407. C32#1614semidirect
473. C3#69716semidirect
474. C3#71176semidirect

Maximal subgroups

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

subgroupindex
#105949712
#105926692
C3×#49932
C3×#49702
#105891542
#105891532
#105891452
#711763
#697163