Finite Group Databasebeta

← #11775434

Subgroups — #11775434

Order 1152.

549 conjugacy classes of subgroups; only the 98 normal subgroups are shown.

normal subgroups only

This group has 549 conjugacy classes of subgroups — too many to draw. Only its 98 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#10594910C211yesmaximal, characteristic
2C3×#4719C211yesmaximal, characteristic, complemented
3#10591223C211yesmaximal, characteristic, complemented
4#10589336C211yesmaximal, characteristic, complemented
5C3×#4470C211yesmaximal, characteristic, complemented
6#10589151C211yesmaximal, characteristic, complemented
7#10589150C211yesmaximal, characteristic, complemented
8#70835—31nomaximal
9#68281—31nomaximal
10C2×#3804—21no—
11#64139C2211yescharacteristic
12C3×#930C2211yescharacteristic
13C2×C3×C4×Dic3C2211yescharacteristic
14#63978—21no—
15#63918C411yescharacteristic, complemented
16#63911C411yescharacteristic, complemented
17#63894C411yescharacteristic, complemented
18Dic3×D12C411yescharacteristic, complemented
19#63880—21no—
20#63852—21no—
21C32×C22⋊C8C2211yescharacteristic
22#63658C2211yescharacteristic
23C3×C3⋊#95C2211yescharacteristic
24C3×#830C2211yescharacteristic
25C3×#815—21no—
26C3×Dic3⋊C8—21no—
27#63579—21no—
28#63579—21no—
29#5596—31no—
30#5477—31no—
31C3×#432—31no—
32#4937—31no—
33#4719D311yescharacteristic, complemented
34#4651—31no—
35C3×#327—31no—
36#4537—31no—
37#4470—31no—
38#4470—31no—
39#4470—31no—
40#4470—31no—
41#4470—61no—
42#4470D311yescharacteristic, complemented
43#4451—31no—
44C22×C32×C4C2311yescharacteristic
45C2×#638—21no—
46C22×C3⋊Dic3—21no—
47C2×C4⋊(C3⋊D3)C2×C411yescharacteristic
48C2×C3×#67—21no—
49C22×C3×Dic3—21no—
50C22×C3×Dic3D411yescharacteristic
51C22×C3×Dic3D411yescharacteristic
52C2×C3×D12C2×C411yescharacteristic
53C2×#627—21no—
54C2×#626—21no—
55C2×#626—21no—
56C2×#624—21no—
57#3804—42no—
58#3804—42no—
59C2×D3×Dic3—21no—
60C2×C32×C8—21no—
61#3752—21no—
62C4⋊(C3⋊Dic3)C2×C411yescharacteristic
63C3×(C2×D3)⋊C4—21no—
64C3×C4⋊Dic3C2×C411yescharacteristic
65C3×C4×Dic3C2×C411yescharacteristic
66C3×C4×Dic3C2×C411yescharacteristic
67C3×C4×Dic3D411yescharacteristic
68C3×C4×Dic3D411yescharacteristic
69C2×C3×C3⋊C8—21no—
70Dic3⋊Dic3—21no—
71#3722—21no—
72(C2×D3)⋊Dic3—21no—
73#1514—91noSylow
74C2×#237—61no—
75C2×#235—61no—
76C3×#121—31no—
77C2×C3×C42—31no—
78#940—31no—
79#939—61no—
80D4×Dic3—31no—
81#930—31no—
82#930—31no—
83#930—61no—
84#930—61no—
85#930C2×D311yescharacteristic
86C2×C4×Dic3C2×D311yescharacteristic
87#893—31no—
88#888—31no—
89#885—61no—
90#67⋊C4—61no—
91#875—61no—
92#874—31no—
93C4×D12—31no—
94C4×D12—31no—
95C4×D12—61no—
96#869—31no—
97C3×C4⋊C8—61no—
98C3×C22⋊C8—21no—
99C3×C22⋊C8—31no—
100C3×C22⋊C8C2×D311yescharacteristic
101C3×C22⋊C8C2×D311yescharacteristic
102C3×#97—61no—
103C3×#95—31no—
104C3⋊#95—31no—
105C3⋊#95—31no—
106C3⋊#95—61no—
107C3⋊#95—61no—
108C3⋊#95—61no—
109C3⋊#95—61no—
110C3⋊#95—61no—
111C3⋊#95C2×D311yescharacteristic
112#830C2×D311yescharacteristic
113#815—21no—
114Dic3⋊C8—21no—
115C23×C32C2×D411yescharacteristic
116C22×C3⋊D3—21no—
117C22×C3×D3—21no—
118C2×C32×C4—41no—
119C2×C32×C4C22×C411yescharacteristic
120C2×C32×C4C2×D411yescharacteristic
121#638—41no—
122#638—41no—
123C2×C3⋊Dic3—21no—
124C2×C3⋊Dic3—41no—
125C2×C3⋊Dic3—41no—
126C2×C3⋊Dic3—41no—
127C4⋊(C3⋊D3)—41no—
128C3×#67—41no—
129C3×#67—41no—
130C2×C3×Dic3—21no—
131C2×C3×Dic3—21no—
132C2×C3×Dic3—21no—
133C2×C3×Dic3—41no—
134C2×C3×Dic3—41no—
135C2×C3×Dic3—41no—
136C2×C3×Dic3—41no—
137C2×C3×Dic3C22⋊C411yescharacteristic
138C2×C3×Dic3C22⋊C411yescharacteristic
139C2×C3×Dic3C22⋊C411yescharacteristic
140C2×C3×Dic3C22⋊C411yescharacteristic
141C3×D12—41no—
142#627—42no—
143#626—42no—
144#626—42no—
145#624—42no—
146D3×Dic3—42no—
147C32×C8—41no—
148C3×C3⋊C8—41no—
149#532—91no—
150#432—31no—
151#383—91no—
152#327—31no—
153#327—91no—
154#327—91no—
155#327—91no—
156C2×C3×D4—31no—
157C2×C3×D4—61no—
158C22×C3×C4—21no—
159C22×C3×C4—31no—
160C22×C3×C4—31no—
161C22×C3×C4—61no—
162C22×C3×C4C22×D311yescharacteristic
163C22×C3×C4C22×D311yescharacteristic
164C2×#67—21no—
165C2×#67—61no—
166C2×#67—61no—
167C2×#67—61no—
168C2×#67—61no—
169C2×#67—121no—
170C22×Dic3—21no—
171C22×Dic3—61no—
172C22×Dic3—61no—
173C22×Dic3—61no—
174C22×Dic3—121no—
175C22×Dic3D1211yescharacteristic
176C22×Dic3D1211yescharacteristic
177#237—122no—
178#237—122no—
179#235—122no—
180#235—122no—
181C2×D12—31no—
182C2×D12—31no—
183C2×D12—61no—
184C2×D12—61no—
185C2×D12—61no—
186C2×D12C4×D311yescharacteristic
187C2×C4×D3—61no—
188C2×C4×D3—61no—
189C2×C4×D3—61no—
190C2×Dic6—61no—
191C2×Dic6—61no—
192C2×C3×C8—21no—
193C2×C3×C8—21no—
194C2×C3×C8—41no—
195C2×C3×C8—61no—
196C3×C4⋊C4—31no—
197C3×C22⋊C4—61no—
198C3×C42—31no—
199C3×C42—31no—
200C3×C42—31no—
201C3×C42—31no—
202#217—61no—
203(C2×D3)⋊C4—21no—
204(C2×D3)⋊C4—61no—
205(C2×D3)⋊C4—61no—
206(C2×D3)⋊C4—61no—
207(C2×D3)⋊C4—61no—
208(C2×D3)⋊C4—61no—
209(C2×D3)⋊C4—121no—
210C4⋊Dic3—31no—
211C4⋊Dic3—31no—
212C4⋊Dic3—61no—
213C4⋊Dic3—61no—
214C4⋊Dic3C4×D311yescharacteristic
215Dic3⋊C4—61no—
216C4×Dic3C4×D311yescharacteristic
217C4×Dic3C4×D311yescharacteristic
218C4×Dic3#6711yescharacteristic
219C4×Dic3#6711yescharacteristic
220C2×C3⋊C8—21no—
221C22×C32—21no—
222C22×C32—21no—
223C22×C32C2×C22⋊C411yescharacteristic
224C22×C32AGL(1,ℤ/8)11yescharacteristic
225C22×C32AGL(1,ℤ/8)11yescharacteristic
226C2×C3⋊D3—41no—
227C2×C3⋊D3—41no—
228C2×C3⋊D3—41no—
229C2×C3×D3—41no—
230C2×C3×D3—41no—
231C2×C3×D3—41no—
232C32×C4—21no—
233C32×C4—21no—
234C3⋊Dic3—41no—
235C3⋊Dic3—81no—
236C3×Dic3—21no—
237C3×Dic3—21no—
238C3×Dic3—21no—
239C3×Dic3—21no—
240C3×Dic3—41no—
241C3×Dic3—81no—
242C2×#41—181no—
243C4⋊Q8—91no—
244#127—91no—
245#124—181no—
246#121—31no—
247#121—91no—
248#121—181no—
249C4×D4—91no—
250C4×D4—91no—
251C4×D4—181no—
252C2×C42—31no—
253C4⋊C8—61no—
254C22⋊C8—31no—
255C22⋊C8D3211yescharacteristic
256#97—61no—
257#95—31no—
258#95—91no—
259#95—181no—
260#95—181no—
261C23×C3—21no—
262C23×C3—61no—
263C23×C3C2×D1211yescharacteristic
264C23×C3D3×D411yescharacteristic
265C22×D3—21no—
266C22×D3—61no—
267C22×D3—61no—
268C22×D3—121no—
269C3×D4—121no—
270C3×D4—121no—
271C3×D4—121no—
272C2×C3×C4—21no—
273C2×C3×C4—21no—
274C2×C3×C4—31no—
275C2×C3×C4—31no—
276C2×C3×C4—31no—
277C2×C3×C4—31no—
278C2×C3×C4—41no—
279C2×C3×C4—41no—
280C2×C3×C4—61no—
281C2×C3×C4—61no—
282C2×C3×C4—61no—
283C2×C3×C4—81no—
284C2×C3×C4—121no—
285C2×C3×C4—121no—
286C2×C3×C4—121no—
287C2×C3×C4—121no—
288C2×C3×C4C2×C4×D311yescharacteristic
289C2×C3×C4C2×C4×D311yescharacteristic
290C2×C3×C4D3×D411yescharacteristic
291C2×C3×C4C2×#6711yescharacteristic
292#67—41no—
293#67—41no—
294#67—122no—
295#67—122no—
296#67—121no—
297#67—121no—
298#67—121no—
299#67—121no—
300#67—241no—
301#67—241no—
302C2×Dic3—21no—
303C2×Dic3—21no—
304C2×Dic3—21no—
305C2×Dic3—41no—
306C2×Dic3—41no—
307C2×Dic3—41no—
308C2×Dic3—41no—
309C2×Dic3—61no—
310C2×Dic3—61no—
311C2×Dic3—121no—
312C2×Dic3—122no—
313C2×Dic3—121no—
314C2×Dic3—121no—
315C2×Dic3—121no—
316C2×Dic3—121no—
317C2×Dic3—122no—
318C2×Dic3—121no—
319C2×Dic3—121no—
320C2×Dic3—241no—
321C2×Dic3—241no—
322C2×Dic3(C2×D3)⋊C411yescharacteristic
323C2×Dic3(C2×D3)⋊C411yescharacteristic
324C2×Dic3(C2×D3)⋊C411yescharacteristic
325C2×Dic3(C2×D3)⋊C411yescharacteristic
326D12—41no—
327D12—121no—
328D12—121no—
329D12—122no—
330D12—122no—
331D12—241no—
332C4×D3—122no—
333C4×D3—122no—
334C4×D3—122no—
335Dic6—122no—
336Dic6—122no—
337C3×C8—41no—
338C3×C8—41no—
339C3×C8—81no—
340C3×C8—121no—
341C3⋊C8—41no—
342C2×C32—21no—
343C2×C32—21no—
344C2×C32#41011yescharacteristic
345C2×C32#41811yescharacteristic
346C2×C32#42111yescharacteristic
347C3⋊D3—81no—
348C3×D3—81no—
349#41—362no—
350#41—362no—
351C2×Q8—181no—
352C2×D4—31no—
353C2×D4—61no—
354C2×D4—91no—
355C2×D4—181no—
356C2×D4—181no—
357C2×D4—181no—
358C22×C4—31no—
359C22×C4—31no—
360C22×C4—61no—
361C22×C4—181no—
362C22×C4—181no—
363C22×C4—181no—
364C22×C4C2×D3211yescharacteristic
365C2×C8—21no—
366C2×C8—61no—
367C4⋊C4—31no—
368C4⋊C4—91no—
369C4⋊C4—181no—
370C22⋊C4—61no—
371C22⋊C4—181no—
372C22⋊C4—181no—
373C22⋊C4—181no—
374C42—31no—
375C42—31no—
376C42—31no—
377C42—31no—
378C22×C3—21no—
379C22×C3—21no—
380C22×C3—21no—
381C22×C3—21no—
382C22×C3—21no—
383C22×C3—21no—
384C22×C3—21no—
385C22×C3—41no—
386C22×C3—41no—
387C22×C3—121no—
388C22×C3—121no—
389C22×C3—121no—
390C22×C3D3×C22⋊C411yescharacteristic
391C22×C3#90811yescharacteristic
392C22×C3#90811yescharacteristic
393C22×C3#91111yescharacteristic
394C22×C3#91411yescharacteristic
395C22×C3C2×(C2×D3)⋊C411yescharacteristic
396C2×D3—41no—
397C2×D3—41no—
398C2×D3—41no—
399C2×D3—121no—
400C2×D3—121no—
401C2×D3—121no—
402C2×D3—121no—
403C2×D3—121no—
404C2×D3—121no—
405C2×D3—241no—
406C2×D3—241no—
407C2×D3—241no—
408C3×C4—21no—
409C3×C4—21no—
410C3×C4—21no—
411C3×C4—21no—
412C3×C4—41no—
413C3×C4—41no—
414C3×C4—61no—
415C3×C4—61no—
416C3×C4—61no—
417C3×C4—61no—
418C3×C4—121no—
419C3×C4—241no—
420Dic3—21no—
421Dic3—21no—
422Dic3—21no—
423Dic3—21no—
424Dic3—41no—
425Dic3—81no—
426Dic3—121no—
427Dic3—121no—
428Dic3—241no—
429Dic3—241no—
430Dic3—241no—
431Dic3—242no—
432C32#151411yescharacteristic, complemented, Sylow
433C23—61no—
434C23—181no—
435C23D3×D1211yescharacteristic
436Q8—362no—
437D4—121no—
438D4—121no—
439D4—121no—
440D4—361no—
441D4—362no—
442D4—362no—
443D4—361no—
444D4—361no—
445C2×C4—31no—
446C2×C4—31no—
447C2×C4—31no—
448C2×C4—31no—
449C2×C4—41no—
450C2×C4—61no—
451C2×C4—61no—
452C2×C4—61no—
453C2×C4—121no—
454C2×C4—121no—
455C2×C4—121no—
456C2×C4—121no—
457C2×C4—181no—
458C2×C4—362no—
459C2×C4—362no—
460C2×C4—361no—
461C2×C4—361no—
462C2×C4—361no—
463C2×C4C4×D3211yescharacteristic
464C2×C4D3×#6711yescharacteristic
465C8—41no—
466C8—121no—
467C2×C3—21no—
468C2×C3—21no—
469C2×C3—21no—
470C2×C3—21no—
471C2×C3—21no—
472C2×C3—21no—
473C2×C3—21no—
474C2×C3—41no—
475C2×C3—41no—
476C2×C3—241no—
477C2×C3#474011yescharacteristic
478C2×C3#477011yescharacteristic
479C2×C3#482111yescharacteristic
480C2×C3#500611yescharacteristic
481C2×C3#513111yescharacteristic
482C2×C3#513911yescharacteristic
483D3—81no—
484D3—241no—
485D3—241no—
486D3—481no—
487C22—21no—
488C22—21no—
489C22—121no—
490C22—121no—
491C22—121no—
492C22—361no—
493C22—361no—
494C22—361no—
495C22#6379411yescharacteristic
496C22#6379511yescharacteristic
497C22D3×(C2×D3)⋊C411yescharacteristic
498C4—21no—
499C4—21no—
500C4—61no—
501C4—61no—
502C4—61no—
503C4—61no—
504C4—121no—
505C4—241no—
506C4—361no—
507C4—721no—
508C3—21no—
509C3#6828111yescharacteristic, complemented
510C3#7083511yescharacteristic, complemented
511C2—21no—
512C2—21no—
513C2—241no—
514C2—721no—
515C2#1059040511yescharacteristic
516C2#1059093911yescharacteristic
517C2#1059100511yescharacteristic
subgroupG/H
centerC22D3×(C2×D3)⋊C4
commutatorC2×C32×C4C22×C4
FrattiniC22×C4C2×D32
FittingC32×C22⋊C8C22
socleC22×C32C2×C22⋊C4
prime radical#10594910C2
cosocleC22×C32×C4C23
hypercenterC22⋊C8D32
hypocenterC32#1514
LCSG ▷ C2×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. C3×#4719C2semidirect
3. #10591223C2semidirect
4. #10589336C2semidirect
5. C3×#4470C2semidirect
6. #10589151C2semidirect
7. #10589150C2semidirect
15. #63918C4semidirect
16. #63911C4semidirect
17. #63894C4semidirect
18. Dic3×D12C4semidirect
33. #4719D3semidirect
42. #4470D3semidirect
432. C32#1514semidirect
509. C3#68281semidirect
510. C3#70835semidirect

Maximal subgroups

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

subgroupindex
#105949102
C3×#47192
#105912232
#105893362
C3×#44702
#105891512
#105891502
#708353
#682813