Finite Group Databasebeta

← #11778646

Subgroups — #11778646

Order 1152.

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

normal subgroups only

This group has 513 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#10594979C211yesmaximal, characteristic
2C3×#4721C211yesmaximal, characteristic, complemented
3#10591326C211yesmaximal, characteristic, complemented
4#10591089C211yesmaximal, characteristic, complemented
5#10589334C211yesmaximal, characteristic, complemented
6C3×#4470C211yesmaximal, characteristic, complemented
7#10589153C211yesmaximal, characteristic, complemented
8#71173—31nomaximal
9#68289—31nomaximal
10C2×#3752C2211yescharacteristic
11C3×#930C2211yescharacteristic
12C2×C3×C4⋊Dic3C2211yescharacteristic
13C3×#924C2211yescharacteristic
14#63981—21no—
15#67⋊Dic3—21no—
16C2×#3722—21no—
17#63907—21no—
18#63890—21no—
19#63886—21no—
20#63848—21no—
21C32×C22⋊C8C2211yescharacteristic
22#63657C2211yescharacteristic
23C3×C3⋊#95C2211yescharacteristic
24C3×#817—21no—
25C3×#816—21no—
26#63579—21no—
27#63576—21no—
28#63562—21no—
29#5644—31no—
30#5617—31no—
31C3×#483—31no—
32#5033—31no—
33#4992—31no—
34#4967—31no—
35#4721D311yescharacteristic, complemented
36#4674—31no—
37C3×#327—31no—
38#4538—31no—
39#4470D311yescharacteristic, complemented
40#4468—31no—
41#4468—31no—
42#4468—61no—
43#4452—31no—
44C23×C3⋊D3D411yescharacteristic
45C22×C32×C4C2311yescharacteristic
46C22×C3⋊Dic3D411yescharacteristic
47C2×C3×#67—21no—
48C22×C3×Dic3—21no—
49C22×C3×Dic3—21no—
50C2×C3×D12D411yescharacteristic
51C2×C3×Dic6D411yescharacteristic
52C2×#626—21no—
53C2×#626—21no—
54C2×D3×Dic3—21no—
55C2×C32×C8—21no—
56#3752—21no—
57#3752—21no—
58C2×C3⋊(C3⋊C8)—21no—
59C3×#217—21no—
60C3×(C2×D3)⋊C4—21no—
61C3×C4⋊Dic3—21no—
62C3×C4⋊Dic3—21no—
63C3×C4⋊Dic3D411yescharacteristic
64C3×C4⋊Dic3D411yescharacteristic
65C3×Dic3⋊C4—21no—
66Dic3⋊Dic3—21no—
67#3722—21no—
68#3722—21no—
69#3722—42no—
70(C2×D3)⋊Dic3—21no—
71Dic32—21no—
72#1612—91noSylow
73C3×C22⋊Q8—31no—
74C3×#121—31no—
75C2×C3×C4⋊C4—31no—
76#947—61no—
77#939—61no—
78#937—61no—
79D4×Dic3—61no—
80#930C2×D311yescharacteristic
81C2×(C2×D3)⋊C4—31no—
82C2×(C2×D3)⋊C4—31no—
83C2×(C2×D3)⋊C4—61no—
84C2×(C2×D3)⋊C4—61no—
85C2×(C2×D3)⋊C4—61no—
86C2×C4⋊Dic3C2×D311yescharacteristic
87#924C2×D311yescharacteristic
88#898—61no—
89#898—61no—
90#895—61no—
91#894—61no—
92#886—61no—
93#885—61no—
94#882—61no—
95#67⋊C4—61no—
96C3×#106—61no—
97C3×#103—61no—
98C3×C22⋊C8—21no—
99C3×C22⋊C8C2×D311yescharacteristic
100C3×C22⋊C8C2×D311yescharacteristic
101C3×#95—31no—
102#832—61no—
103C3⋊#95—61no—
104C3⋊#95—61no—
105C3⋊#95C2×D311yescharacteristic
106#830—31no—
107#830—31no—
108#830—61no—
109#817—21no—
110#816—21no—
111#809—61no—
112#807—61no—
113#807—61no—
114C23×C32C2×D411yescharacteristic
115C22×C3⋊D3—21no—
116C22×C3⋊D3—21no—
117C22×C3⋊D3—21no—
118C22×C3⋊D3—41no—
119C22×C3⋊D3—41no—
120C22×C3×D3—21no—
121C2×C32×C4—41no—
122C2×C32×C4C2×D411yescharacteristic
123C2×C32×C4C2×D411yescharacteristic
124C2×C3⋊Dic3—21no—
125C2×C3⋊Dic3—41no—
126C3×#67—41no—
127C3×#67—41no—
128C2×C3×Dic3—21no—
129C2×C3×Dic3—21no—
130C2×C3×Dic3—21no—
131C2×C3×Dic3—41no—
132C2×C3×Dic3—41no—
133C2×C3×Dic3—41no—
134C2×C3×Dic3—41no—
135C2×C3×Dic3—41no—
136C2×C3×Dic3—41no—
137C3×D12—41no—
138C3×Dic6—41no—
139#626—81no—
140#626—81no—
141D3×Dic3—81no—
142C32×C8—41no—
143C3⋊(C3⋊C8)—41no—
144#538—91no—
145#483—31no—
146#480—91no—
147#397—91no—
148#328—91no—
149#327—31no—
150#323—91no—
151C23×D3—31no—
152C23×D3—31no—
153C23×D3—61no—
154C2×C3×Q8—31no—
155C2×C3×D4—31no—
156C2×C3×D4—61no—
157C22×C3×C4—21no—
158C22×C3×C4—61no—
159C22×C3×C4—61no—
160C22×C3×C4C22×D311yescharacteristic
161C22×C3×C4C22×D311yescharacteristic
162C2×#67—21no—
163C2×#67—61no—
164C2×#67—61no—
165C22×Dic3—21no—
166C22×Dic3—21no—
167C22×Dic3—31no—
168C22×Dic3—31no—
169C22×Dic3—61no—
170C22×Dic3—61no—
171C2×D12—61no—
172C2×D12—61no—
173C2×D12D1211yescharacteristic
174C2×C4×D3—61no—
175C2×Dic6#6711yescharacteristic
176C2×C3×C8—21no—
177C2×C3×C8—21no—
178C2×C3×C8—41no—
179C3×C4⋊C4—31no—
180C3×C4⋊C4—31no—
181C3×C4⋊C4—61no—
182C3×C4⋊C4—61no—
183C3×C4⋊C4—61no—
184C3×C22⋊C4—61no—
185C3×C22⋊C4—61no—
186#217—21no—
187#217—61no—
188(C2×D3)⋊C4—21no—
189(C2×D3)⋊C4—61no—
190(C2×D3)⋊C4—61no—
191(C2×D3)⋊C4—61no—
192(C2×D3)⋊C4—61no—
193(C2×D3)⋊C4—61no—
194(C2×D3)⋊C4—61no—
195(C2×D3)⋊C4—61no—
196(C2×D3)⋊C4—61no—
197(C2×D3)⋊C4—61no—
198(C2×D3)⋊C4—121no—
199(C2×D3)⋊C4—121no—
200(C2×D3)⋊C4—122no—
201(C2×D3)⋊C4—122no—
202C4⋊Dic3—21no—
203C4⋊Dic3—21no—
204C4⋊Dic3—61no—
205C4⋊Dic3D1211yescharacteristic
206C4⋊Dic3#6711yescharacteristic
207Dic3⋊C4—21no—
208Dic3⋊C4—61no—
209C4×Dic3—61no—
210C4×Dic3—61no—
211C2×C3⋊C8—61no—
212C2×C3⋊C8—61no—
213C2×C3⋊C8—121no—
214C22×C32—21no—
215C22×C32—21no—
216C22×C32#12011yescharacteristic
217C22×C32#13511yescharacteristic
218C22×C32AGL(1,ℤ/8)11yescharacteristic
219C2×C3⋊D3—41no—
220C2×C3⋊D3—42no—
221C2×C3⋊D3—41no—
222C2×C3⋊D3—41no—
223C2×C3⋊D3—81no—
224C2×C3×D3—41no—
225C2×C3×D3—41no—
226C2×C3×D3—41no—
227C32×C4—21no—
228C32×C4—21no—
229C3⋊Dic3—41no—
230C3×Dic3—41no—
231C3×Dic3—41no—
232C3×Dic3—41no—
233C3×Dic3—81no—
234C3×Dic3—81no—
235#126—181no—
236#124—181no—
237#123—181no—
238C22⋊Q8—31no—
239#121—31no—
240#121—181no—
241#120—181no—
242C4×D4—181no—
243C2×C4⋊C4—31no—
244C2×C22⋊C4—91no—
245C2×C22⋊C4—181no—
246#107—181no—
247#106—61no—
248#103—61no—
249#102—181no—
250C22⋊C8—91no—
251C22⋊C8D3211yescharacteristic
252#95—31no—
253#95—181no—
254C23×C3—21no—
255C23×C3—61no—
256C23×C3D3×D411yescharacteristic
257C23×C3D3×D411yescharacteristic
258C22×D3—21no—
259C22×D3—61no—
260C22×D3—61no—
261C22×D3—61no—
262C22×D3—61no—
263C22×D3—62no—
264C22×D3—61no—
265C22×D3—61no—
266C22×D3—121no—
267C22×D3—121no—
268C22×D3—121no—
269C22×D3—121no—
270C22×D3—121no—
271C22×D3—121no—
272C22×D3—241no—
273C22×D3—241no—
274C3×Q8—121no—
275C3×D4—121no—
276C3×D4—121no—
277C3×D4—121no—
278C2×C3×C4—21no—
279C2×C3×C4—21no—
280C2×C3×C4—41no—
281C2×C3×C4—41no—
282C2×C3×C4—61no—
283C2×C3×C4—61no—
284C2×C3×C4—61no—
285C2×C3×C4—81no—
286C2×C3×C4—121no—
287C2×C3×C4—121no—
288C2×C3×C4—121no—
289C2×C3×C4—121no—
290C2×C3×C4—121no—
291C2×C3×C4—121no—
292C2×C3×C4C2×D1211yescharacteristic
293C2×C3×C4D3×D411yescharacteristic
294C2×C3×C4D3×D411yescharacteristic
295C2×C3×C4C2×#6711yescharacteristic
296#67—41no—
297#67—41no—
298#67—241no—
299#67—241no—
300C2×Dic3—21no—
301C2×Dic3—21no—
302C2×Dic3—21no—
303C2×Dic3—41no—
304C2×Dic3—41no—
305C2×Dic3—41no—
306C2×Dic3—41no—
307C2×Dic3—41no—
308C2×Dic3—41no—
309C2×Dic3—61no—
310C2×Dic3—61no—
311C2×Dic3—121no—
312C2×Dic3—121no—
313C2×Dic3—121no—
314C2×Dic3—241no—
315C2×Dic3—241no—
316D12—41no—
317D12—241no—
318D12—241no—
319C4×D3—241no—
320Dic6—41no—
321C3×C8—41no—
322C3×C8—41no—
323C3×C8—81no—
324C3⋊C8—121no—
325C3⋊C8—121no—
326C3⋊C8—241no—
327C2×C32—21no—
328C2×C32—21no—
329C2×C32#44911yescharacteristic
330C2×C32#45511yescharacteristic
331C2×C32#45811yescharacteristic
332C3⋊D3—81no—
333C3×D3—81no—
334C24—91no—
335C2×Q8—31no—
336C2×D4—31no—
337C2×D4—61no—
338C2×D4—181no—
339C2×D4—181no—
340C22×C4—61no—
341C22×C4—61no—
342C22×C4—91no—
343C22×C4—181no—
344C22×C4C2×D3211yescharacteristic
345C2×C8—21no—
346C2×C8—181no—
347C4⋊C4—31no—
348C4⋊C4—31no—
349C4⋊C4—61no—
350C4⋊C4—61no—
351C4⋊C4—61no—
352C4⋊C4—181no—
353C22⋊C4—61no—
354C22⋊C4—61no—
355C22⋊C4—181no—
356C22⋊C4—181no—
357C22⋊C4—181no—
358C22⋊C4—181no—
359C22⋊C4—181no—
360C22⋊C4—362no—
361C42—181no—
362C22×C3—21no—
363C22×C3—21no—
364C22×C3—21no—
365C22×C3—21no—
366C22×C3—21no—
367C22×C3—21no—
368C22×C3—21no—
369C22×C3—41no—
370C22×C3—41no—
371C22×C3—121no—
372C22×C3—121no—
373C22×C3—121no—
374C22×C3#88211yescharacteristic
375C22×C3#91111yescharacteristic
376C22×C3#91411yescharacteristic
377C22×C3#91611yescharacteristic
378C22×C3#91611yescharacteristic
379C22×C3#93711yescharacteristic
380C2×D3—41no—
381C2×D3—41no—
382C2×D3—41no—
383C2×D3—122no—
384C2×D3—122no—
385C2×D3—122no—
386C2×D3—121no—
387C2×D3—121no—
388C2×D3—121no—
389C2×D3—121no—
390C2×D3—121no—
391C2×D3—121no—
392C2×D3—241no—
393C2×D3—241no—
394C2×D3—242no—
395C2×D3—241no—
396C2×D3—241no—
397C2×D3—242no—
398C3×C4—21no—
399C3×C4—21no—
400C3×C4—21no—
401C3×C4—21no—
402C3×C4—41no—
403C3×C4—41no—
404C3×C4—121no—
405C3×C4—121no—
406C3×C4—121no—
407C3×C4—241no—
408C3×C4—241no—
409Dic3—41no—
410Dic3—41no—
411Dic3—41no—
412Dic3—81no—
413Dic3—81no—
414Dic3—121no—
415Dic3—121no—
416Dic3—241no—
417C32#161211yescharacteristic, complemented, Sylow
418C23—61no—
419C23—181no—
420C23—181no—
421C23—181no—
422C23—361no—
423C23—361no—
424C23#380211yescharacteristic
425Q8—121no—
426D4—121no—
427D4—121no—
428D4—121no—
429D4—721no—
430D4—721no—
431C2×C4—41no—
432C2×C4—61no—
433C2×C4—61no—
434C2×C4—61no—
435C2×C4—121no—
436C2×C4—121no—
437C2×C4—121no—
438C2×C4—121no—
439C2×C4—121no—
440C2×C4—121no—
441C2×C4—181no—
442C2×C4—361no—
443C2×C4—721no—
444C2×C4D3×D1211yescharacteristic
445C2×C4D3×#6711yescharacteristic
446C8—41no—
447C8—361no—
448C2×C3—21no—
449C2×C3—21no—
450C2×C3—21no—
451C2×C3—21no—
452C2×C3—21no—
453C2×C3—21no—
454C2×C3—21no—
455C2×C3—41no—
456C2×C3—41no—
457C2×C3—241no—
458C2×C3#474211yescharacteristic
459C2×C3#478111yescharacteristic
460C2×C3#482511yescharacteristic
461C2×C3#505311yescharacteristic
462C2×C3#517211yescharacteristic
463C2×C3#520211yescharacteristic
464D3—81no—
465D3—242no—
466D3—241no—
467D3—241no—
468C22—21no—
469C22—21no—
470C22—121no—
471C22—121no—
472C22—121no—
473C22—362no—
474C22—361no—
475C22—361no—
476C22—361no—
477C22—721no—
478C22#6379811yescharacteristic
479C22#6380911yescharacteristic
480C22#6392211yescharacteristic
481C4—21no—
482C4—21no—
483C4—121no—
484C4—121no—
485C4—121no—
486C4—241no—
487C4—241no—
488C4—361no—
489C3—21no—
490C3#6828911yescharacteristic, complemented
491C3#7117311yescharacteristic, complemented
492C2—21no—
493C2—21no—
494C2—241no—
495C2—721no—
496C2#1059040811yescharacteristic
497C2#1059096411yescharacteristic
498C2#1059101111yescharacteristic
subgroupG/H
centerC22#63922
commutator, cosocleC22×C32×C4C23
FrattiniC22×C4C2×D32
FittingC32×C22⋊C8C22
socleC22×C32#120
prime radical#10594979C2
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. C3×#4721C2semidirect
3. #10591326C2semidirect
4. #10591089C2semidirect
5. #10589334C2semidirect
6. C3×#4470C2semidirect
7. #10589153C2semidirect
35. #4721D3semidirect
39. #4470D3semidirect
417. C32#1612semidirect
490. C3#68289semidirect
491. C3#71173semidirect

Maximal subgroups

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

subgroupindex
#105949792
C3×#47212
#105913262
#105910892
#105893342
C3×#44702
#105891532
#711733
#682893