Finite Group Databasebeta

← #11778636

Subgroups — #11778636

Order 1152.

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

normal subgroups only

This group has 521 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#10595038C211yesmaximal, characteristic
2#10592435C211yesmaximal, characteristic, complemented
3#10591315C211yesmaximal, characteristic, complemented
4#10591126C211yesmaximal, characteristic, complemented
5C3×#4468C211yesmaximal, characteristic, complemented
6C3×#4467C211yesmaximal, characteristic, complemented
7#10589151C211yesmaximal, characteristic, complemented
8#68321—31nomaximal
9#68111—31nomaximal
10#64139C2211yescharacteristic
11C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
12C2×C3×(C2×D3)⋊C4C2211yescharacteristic
13C3×#924C2211yescharacteristic
14#63977—21no—
15C2×(C2×D3)⋊Dic3—21no—
16#63952—21no—
17#63910—21no—
18#63907—21no—
19#63861—21no—
20#63854—21no—
21C32×C22⋊C8C2211yescharacteristic
22#63648—21no—
23#63645—21no—
24C3×C3⋊#95C2211yescharacteristic
25C3×#830C2211yescharacteristic
26#63579—21no—
27#63573—21no—
28#63566—21no—
29#5644—31no—
30#5494—31no—
31#5043—31no—
32#4953—31no—
33#4736—31no—
34#4736—31no—
35#4736—61no—
36#4721—31no—
37#4674—31no—
38C3×#328—31no—
39C3×#323—31no—
40#4470—31no—
41#4468D311yescharacteristic, complemented
42#4467D311yescharacteristic, complemented
43#4451—31no—
44C23×C3×D3D411yescharacteristic
45C22×C32×C4C2311yescharacteristic
46C2×#638—21no—
47C22×C3⋊Dic3—21no—
48C2×C4⋊(C3⋊D3)D411yescharacteristic
49C22×C3×Dic3—21no—
50C22×C3×Dic3D411yescharacteristic
51C2×C3×Dic6D411yescharacteristic
52C2×#626—21no—
53C2×#626—21no—
54C2×#624—21no—
55C2×C32×C8—21no—
56#3752—21no—
57C4⋊(C3⋊Dic3)—21no—
58C4⋊(C3⋊Dic3)—21no—
59C4⋊(C3⋊Dic3)D411yescharacteristic
60C3×#217—21no—
61C3×(C2×D3)⋊C4—21no—
62C3×(C2×D3)⋊C4—21no—
63C3×C4⋊Dic3D411yescharacteristic
64C3×Dic3⋊C4—21no—
65C2×C3×C3⋊C8—21no—
66#3724—21no—
67#3722—21no—
68(C2×D3)⋊Dic3—21no—
69(C2×D3)⋊Dic3—21no—
70(C2×D3)⋊Dic3—42no—
71Dic32—21no—
72#1612—91noSylow
73C3×C22⋊Q8—31no—
74C2×C3×C22⋊C4—31no—
75#953—61no—
76C2×#217—61no—
77#947—61no—
78#930—31no—
79#930—31no—
80#930—61no—
81C4×#67—61no—
82C2×(C2×D3)⋊C4—61no—
83C2×(C2×D3)⋊C4C2×D311yescharacteristic
84C2×C4⋊Dic3—31no—
85C2×C4⋊Dic3—31no—
86C2×C4⋊Dic3—61no—
87#924C2×D311yescharacteristic
88#898—61no—
89#895—61no—
90#894—61no—
91#885—61no—
92#884—61no—
93#883—61no—
94#882—61no—
95#67⋊C4—61no—
96#879—61no—
97C3×C22⋊C8—21no—
98C3×C22⋊C8—31no—
99C3×C22⋊C8C2×D311yescharacteristic
100C3×C22⋊C8C2×D311yescharacteristic
101C3×#95—31no—
102#835—61no—
103C3⋊#95—61no—
104C3⋊#95—61no—
105C3⋊#95C2×D311yescharacteristic
106#830C2×D311yescharacteristic
107#821—61no—
108#821—61no—
109#821—62no—
110#818—61no—
111#818—61no—
112#818—62no—
113#817—61no—
114#816—61no—
115#808—61no—
116C23×C32C2×D411yescharacteristic
117C22×C3⋊D3—21no—
118C22×C3×D3—21no—
119C22×C3×D3—21no—
120C22×C3×D3—21no—
121C22×C3×D3—41no—
122C22×C3×D3—41no—
123C2×C32×C4—41no—
124C2×C32×C4C2×D411yescharacteristic
125C2×C32×C4C2×D411yescharacteristic
126#638—41no—
127#638—41no—
128C2×C3⋊Dic3—21no—
129C2×C3⋊Dic3—41no—
130C2×C3⋊Dic3—41no—
131C2×C3⋊Dic3—41no—
132C4⋊(C3⋊D3)—41no—
133C2×C3×Dic3—21no—
134C2×C3×Dic3—21no—
135C2×C3×Dic3—21no—
136C2×C3×Dic3—41no—
137C2×C3×Dic3—41no—
138C2×C3×Dic3—41no—
139C2×C3×Dic3—41no—
140C3×Dic6—41no—
141#626—81no—
142#626—81no—
143#624—81no—
144C32×C8—41no—
145C3×C3⋊C8—41no—
146#538—91no—
147#483—91no—
148#480—91no—
149#397—91no—
150#328—31no—
151#327—91no—
152#323—31no—
153C24×C3—31no—
154C23×D3D1211yescharacteristic
155C2×C3×Q8—31no—
156C22×C3×C4—21no—
157C22×C3×C4—31no—
158C22×C3×C4—61no—
159C22×C3×C4C22×D311yescharacteristic
160C22×C3×C4C22×D311yescharacteristic
161C2×#67—61no—
162C2×#67—61no—
163C2×#67—61no—
164C2×#67—61no—
165C2×#67—121no—
166C22×Dic3—21no—
167C22×Dic3—61no—
168C22×Dic3—61no—
169C22×Dic3—121no—
170C22×Dic3D1211yescharacteristic
171C2×D12—31no—
172C2×D12—31no—
173C2×D12—61no—
174C2×D12—61no—
175C2×D12—61no—
176C2×C4×D3—61no—
177C2×C4×D3—61no—
178C2×Dic6D1211yescharacteristic
179C2×C3×C8—22no—
180C2×C3×C8—21no—
181C2×C3×C8—21no—
182C2×C3×C8—61no—
183C3×C4⋊C4—31no—
184C3×C4⋊C4—61no—
185C3×C22⋊C4—61no—
186C3×C22⋊C4—61no—
187C3×C22⋊C4—61no—
188#217—21no—
189#217—61no—
190#217—61no—
191#217—122no—
192(C2×D3)⋊C4—21no—
193(C2×D3)⋊C4—21no—
194(C2×D3)⋊C4—61no—
195(C2×D3)⋊C4—61no—
196(C2×D3)⋊C4—61no—
197(C2×D3)⋊C4—61no—
198(C2×D3)⋊C4—61no—
199(C2×D3)⋊C4—61no—
200(C2×D3)⋊C4—121no—
201(C2×D3)⋊C4—122no—
202C4⋊Dic3—31no—
203C4⋊Dic3—31no—
204C4⋊Dic3—61no—
205C4⋊Dic3—62no—
206C4⋊Dic3—61no—
207C4⋊Dic3—61no—
208C4⋊Dic3—61no—
209C4⋊Dic3—61no—
210C4⋊Dic3—121no—
211C4⋊Dic3D1211yescharacteristic
212Dic3⋊C4—21no—
213Dic3⋊C4—61no—
214Dic3⋊C4—61no—
215C4×Dic3—61no—
216C4×Dic3—61no—
217C2×C3⋊C8—21no—
218C22×C32—21no—
219C22×C32—21no—
220C22×C32#12011yescharacteristic
221C22×C32#13511yescharacteristic
222C22×C32AGL(1,ℤ/8)11yescharacteristic
223C2×C3⋊D3—41no—
224C2×C3⋊D3—41no—
225C2×C3⋊D3—41no—
226C2×C3×D3—42no—
227C2×C3×D3—41no—
228C2×C3×D3—41no—
229C2×C3×D3—41no—
230C2×C3×D3—81no—
231C32×C4—21no—
232C32×C4—21no—
233C3⋊Dic3—41no—
234C3⋊Dic3—81no—
235C3×Dic3—41no—
236C3×Dic3—41no—
237C3×Dic3—41no—
238C3×Dic3—81no—
239#126—181no—
240#124—181no—
241#123—181no—
242C22⋊Q8—31no—
243#121—91no—
244#121—181no—
245#120—181no—
246C4×D4—181no—
247C2×C4⋊C4—91no—
248C2×C22⋊C4—31no—
249C2×C22⋊C4—181no—
250#107—181no—
251#106—181no—
252#103—181no—
253#102—181no—
254C22⋊C8—31no—
255C22⋊C8D3211yescharacteristic
256#95—31no—
257#95—181no—
258C23×C3—21no—
259C23×C3—61no—
260C23×C3—61no—
261C23×C3—61no—
262C23×C3—121no—
263C23×C3—121no—
264C23×C3C2×D1211yescharacteristic
265C23×C3D3×D411yescharacteristic
266C22×D3—21no—
267C22×D3—21no—
268C22×D3—21no—
269C22×D3—41no—
270C22×D3—41no—
271C22×D3—61no—
272C22×D3—61no—
273C22×D3—121no—
274C3×Q8—121no—
275C2×C3×C4—21no—
276C2×C3×C4—21no—
277C2×C3×C4—41no—
278C2×C3×C4—41no—
279C2×C3×C4—42no—
280C2×C3×C4—61no—
281C2×C3×C4—61no—
282C2×C3×C4—61no—
283C2×C3×C4—121no—
284C2×C3×C4—121no—
285C2×C3×C4—121no—
286C2×C3×C4—121no—
287C2×C3×C4C2×D1211yescharacteristic
288C2×C3×C4D3×D411yescharacteristic
289C2×C3×C4D3×D411yescharacteristic
290C2×C3×C4D3×D411yescharacteristic
291#67—121no—
292#67—121no—
293#67—121no—
294#67—121no—
295#67—241no—
296#67—241no—
297#67—241no—
298#67—241no—
299C2×Dic3—21no—
300C2×Dic3—21no—
301C2×Dic3—21no—
302C2×Dic3—41no—
303C2×Dic3—41no—
304C2×Dic3—41no—
305C2×Dic3—41no—
306C2×Dic3—61no—
307C2×Dic3—61no—
308C2×Dic3—121no—
309C2×Dic3—122no—
310C2×Dic3—121no—
311C2×Dic3—121no—
312C2×Dic3—121no—
313C2×Dic3—121no—
314C2×Dic3—121no—
315C2×Dic3—121no—
316C2×Dic3—241no—
317C2×Dic3—241no—
318D12—121no—
319D12—121no—
320D12—122no—
321D12—241no—
322D12—241no—
323C4×D3—241no—
324C4×D3—241no—
325Dic6—41no—
326C3×C8—42no—
327C3×C8—41no—
328C3×C8—41no—
329C3×C8—121no—
330C3⋊C8—41no—
331C2×C32—21no—
332C2×C32—21no—
333C2×C32#44911yescharacteristic
334C2×C32#45511yescharacteristic
335C2×C32#45811yescharacteristic
336C3⋊D3—81no—
337C3×D3—81no—
338C24—31no—
339C2×Q8—31no—
340C2×D4—91no—
341C2×D4—181no—
342C2×D4—181no—
343C2×D4—181no—
344C22×C4—31no—
345C22×C4—61no—
346C22×C4—181no—
347C22×C4—181no—
348C22×C4C2×D3211yescharacteristic
349C2×C8—21no—
350C2×C8—61no—
351C4⋊C4—31no—
352C4⋊C4—61no—
353C4⋊C4—91no—
354C4⋊C4—181no—
355C4⋊C4—181no—
356C4⋊C4—181no—
357C22⋊C4—61no—
358C22⋊C4—61no—
359C22⋊C4—61no—
360C22⋊C4—181no—
361C22⋊C4—181no—
362C22⋊C4—181no—
363C22⋊C4—181no—
364C22⋊C4—362no—
365C42—181no—
366C22×C3—21no—
367C22×C3—21no—
368C22×C3—21no—
369C22×C3—21no—
370C22×C3—21no—
371C22×C3—21no—
372C22×C3—21no—
373C22×C3—41no—
374C22×C3—41no—
375C22×C3—122no—
376C22×C3—121no—
377C22×C3—121no—
378C22×C3—121no—
379C22×C3—241no—
380C22×C3#88211yescharacteristic
381C22×C3#88211yescharacteristic
382C22×C3#90411yescharacteristic
383C22×C3#90811yescharacteristic
384C22×C3#91411yescharacteristic
385C22×C3#91911yescharacteristic
386C2×D3—42no—
387C2×D3—41no—
388C2×D3—41no—
389C2×D3—41no—
390C2×D3—81no—
391C2×D3—121no—
392C2×D3—121no—
393C2×D3—121no—
394C2×D3—121no—
395C2×D3—121no—
396C2×D3—121no—
397C2×D3—241no—
398C2×D3—241no—
399C2×D3—241no—
400C3×C4—22no—
401C3×C4—21no—
402C3×C4—21no—
403C3×C4—21no—
404C3×C4—21no—
405C3×C4—41no—
406C3×C4—121no—
407C3×C4—121no—
408C3×C4—121no—
409C3×C4—241no—
410Dic3—41no—
411Dic3—41no—
412Dic3—41no—
413Dic3—81no—
414Dic3—121no—
415Dic3—121no—
416Dic3—241no—
417Dic3—242no—
418Dic3—241no—
419Dic3—241no—
420C32#161211yescharacteristic, complemented, Sylow
421C23—61no—
422C23—61no—
423C23—61no—
424C23—121no—
425C23—121no—
426C23—181no—
427C23D3×D1211yescharacteristic
428Q8—121no—
429D4—361no—
430D4—361no—
431D4—361no—
432D4—721no—
433D4—721no—
434C2×C4—41no—
435C2×C4—61no—
436C2×C4—61no—
437C2×C4—61no—
438C2×C4—121no—
439C2×C4—121no—
440C2×C4—121no—
441C2×C4—121no—
442C2×C4—181no—
443C2×C4—361no—
444C2×C4—361no—
445C2×C4—361no—
446C2×C4—721no—
447C2×C4D3×D1211yescharacteristic
448C2×C4#381111yescharacteristic
449C8—41no—
450C8—121no—
451C2×C3—21no—
452C2×C3—21no—
453C2×C3—21no—
454C2×C3—21no—
455C2×C3—21no—
456C2×C3—21no—
457C2×C3—21no—
458C2×C3—41no—
459C2×C3—41no—
460C2×C3—241no—
461C2×C3#473411yescharacteristic
462C2×C3#474211yescharacteristic
463C2×C3#474211yescharacteristic
464C2×C3#474611yescharacteristic
465C2×C3#481011yescharacteristic
466C2×C3#482511yescharacteristic
467D3—81no—
468D3—241no—
469D3—241no—
470D3—481no—
471C22—21no—
472C22—21no—
473C22—122no—
474C22—121no—
475C22—121no—
476C22—121no—
477C22—241no—
478C22—361no—
479C22—361no—
480C22—361no—
481C22#6379411yescharacteristic
482C22#6380811yescharacteristic
483C22#6392311yescharacteristic
484C4—21no—
485C4—21no—
486C4—121no—
487C4—121no—
488C4—121no—
489C4—241no—
490C4—361no—
491C4—721no—
492C3—21no—
493C3#6811111yescharacteristic, complemented
494C3#6832111yescharacteristic, complemented
495C2—21no—
496C2—21no—
497C2—241no—
498C2—721no—
499C2#1059040911yescharacteristic
500C2#1059096711yescharacteristic
501C2#1059101611yescharacteristic
subgroupG/H
centerC22#63923
commutator, cosocleC22×C32×C4C23
FrattiniC22×C4C2×D32
FittingC32×C22⋊C8C22
socleC22×C32#120
prime radical#10595038C2
hypercenterC22⋊C8D32
hypocenterC32#1612
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
2. #10592435C2semidirect
3. #10591315C2semidirect
4. #10591126C2semidirect
5. C3×#4468C2semidirect
6. C3×#4467C2semidirect
7. #10589151C2semidirect
41. #4468D3semidirect
42. #4467D3semidirect
420. C32#1612semidirect
493. C3#68111semidirect
494. C3#68321semidirect

Maximal subgroups

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

subgroupindex
#105950382
#105924352
#105913152
#105911262
C3×#44682
C3×#44672
#105891512
#683213
#681113