Finite Group Databasebeta

← #11778518

Subgroups — #11778518

Order 1152.

541 conjugacy classes of subgroups; only the 80 normal subgroups are shown.

normal subgroups only

This group has 541 conjugacy classes of subgroups — too many to draw. Only its 80 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#10596073C211yesmaximal, characteristic
2C3×#5033C211yesmaximal, characteristic
3#10591358C211yesmaximal, characteristic, complemented
4#10591124C211yesmaximal, characteristic, complemented
5C3×#4537C211yesmaximal, characteristic
6#10589154C211yesmaximal, characteristic, complemented
7#10589148C211yesmaximal, characteristic, complemented
8#71166—31nomaximal
9#68296—31nomaximal
10C32×#121C2211yescharacteristic
11#64144—21no—
12#64144—21no—
13D4×C3⋊Dic3—21no—
14#64133C2211yescharacteristic
15C2×#3750C2211yescharacteristic
16#64098—21no—
17#64088—21no—
18#64087—21no—
19C2×C3×C4⋊Dic3C2211yescharacteristic
20C2×Dic3⋊Dic3—21no—
21C3×#832—21no—
22C3×C3⋊#95C2211yescharacteristic
23C3×#830C2211yescharacteristic
24C3×#830C2211yescharacteristic
25C3×#807—21no—
26#63579—21no—
27#63573—21no—
28#63567—21no—
29#5602—31no—
30#5602—31no—
31#5602—61no—
32C3×#480—31no—
33#5033D311yescharacteristic
34#4983—31no—
35#4971—31no—
36#4721—31no—
37#4661—31no—
38C3×#327—31no—
39#4537D311yescharacteristic
40#4469—31no—
41#4469—31no—
42#4467—31no—
43#4452—31no—
44C2×C32×D4—21no—
45C2×C32×D4D411yescharacteristic
46C22×C32×C4C2311yescharacteristic
47C22×C3⋊Dic3—21no—
48C22×C3⋊Dic3D411yescharacteristic
49C22×C3⋊Dic3D411yescharacteristic
50C2×#634D411yescharacteristic
51C22×C3×Dic3—21no—
52C22×C3×Dic3—21no—
53C32×C4⋊C4D411yescharacteristic
54C32×C22⋊C4—21no—
55#3757—21no—
56#3757—21no—
57#3757—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—
66C4×C3⋊Dic3—21no—
67C3×C4⋊Dic3—21no—
68C3×C4⋊Dic3—21no—
69C2×C3×C3⋊C8—21no—
70C2×C3×C3⋊C8—21no—
71Dic3⋊Dic3—42no—
72#1609—91noSylow
73C3×#121—21no—
74C3×#121C2×D311yescharacteristic
75C3×#121C2×D311yescharacteristic
76C2×C3×C4⋊C4—31no—
77#935—61no—
78#935—61no—
79#935—62no—
80#935—62no—
81#935—61no—
82#935—61no—
83D4×Dic3—61no—
84D4×Dic3—61no—
85D4×Dic3—62no—
86C2×C4⋊Dic3—61no—
87C2×C4⋊Dic3C2×D311yescharacteristic
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—
95#889—62no—
96#889—61no—
97#889—61no—
98#879—61no—
99#879—61no—
100#879—62no—
101#878—61no—
102#878—61no—
103#878—62no—
104C3×#107—61no—
105C3×#102—61no—
106C3×C22⋊C8—31no—
107C3×C22⋊C8—31no—
108C3×#95—31no—
109#832—21no—
110C3⋊#95—61no—
111C3⋊#95—61no—
112C3⋊#95C2×D311yescharacteristic
113#830C2×D311yescharacteristic
114#830C2×D311yescharacteristic
115#817—61no—
116#816—61no—
117#810—61no—
118#808—61no—
119#807—21no—
120C23×C32—21no—
121C23×C32C2×D411yescharacteristic
122C32×D4—41no—
123C32×D4—41no—
124C32×D4—41no—
125C2×C32×C4—21no—
126C2×C32×C4—41no—
127C2×C32×C4C2×D411yescharacteristic
128C2×C32×C4C2×D411yescharacteristic
129C2×C3⋊Dic3—21no—
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⋊Dic3—81no—
137#634—41no—
138C2×C3×Dic3—22no—
139C2×C3×Dic3—41no—
140C2×C3×Dic3—41no—
141C2×C3×Dic3—41no—
142C2×C3×Dic3—41no—
143C2×C3×Dic3—41no—
144C3×C3⋊C8—41no—
145C3×C3⋊C8—41no—
146#539—91no—
147#483—91no—
148#480—31no—
149#398—91no—
150#328—91no—
151#327—31no—
152#324—91no—
153C2×C3×D4—22no—
154C2×C3×D4—21no—
155C2×C3×D4—21no—
156C2×C3×D4—21no—
157C2×C3×D4D1211yescharacteristic
158C2×C3×D4#6711yescharacteristic
159C22×C3×C4—21no—
160C22×C3×C4—61no—
161C22×C3×C4—61no—
162C22×C3×C4C22×D311yescharacteristic
163C22×C3×C4C22×D311yescharacteristic
164C22×Dic3—21no—
165C22×Dic3—21no—
166C22×Dic3—31no—
167C22×Dic3—31no—
168C22×Dic3—31no—
169C22×Dic3—31no—
170C22×Dic3—61no—
171C22×Dic3—61no—
172C22×Dic3—62no—
173C22×Dic3—61no—
174C22×Dic3—61no—
175C2×Dic6—31no—
176C2×Dic6—31no—
177C2×Dic6—61no—
178C2×C3×C8—61no—
179C2×C3×C8—61no—
180C3×C4⋊C4—21no—
181C3×C4⋊C4—61no—
182C3×C4⋊C4—61no—
183C3×C4⋊C4D1211yescharacteristic
184C3×C4⋊C4#6711yescharacteristic
185C3×C22⋊C4—22no—
186C3×C22⋊C4—21no—
187C3×C22⋊C4—21no—
188#217—62no—
189#217—61no—
190#217—61no—
191#217—62no—
192#217—61no—
193#217—61no—
194#217—62no—
195#217—61no—
196#217—61no—
197#217—62no—
198#217—61no—
199#217—61no—
200C4⋊Dic3—21no—
201C4⋊Dic3—21no—
202C4⋊Dic3—31no—
203C4⋊Dic3—31no—
204C4⋊Dic3—61no—
205C4⋊Dic3—62no—
206C4⋊Dic3—61no—
207C4⋊Dic3—61no—
208C4⋊Dic3—122no—
209Dic3⋊C4—62no—
210Dic3⋊C4—62no—
211Dic3⋊C4—61no—
212Dic3⋊C4—61no—
213Dic3⋊C4—62no—
214Dic3⋊C4—61no—
215Dic3⋊C4—61no—
216Dic3⋊C4—62no—
217Dic3⋊C4—62no—
218Dic3⋊C4—61no—
219Dic3⋊C4—61no—
220Dic3⋊C4—61no—
221Dic3⋊C4—61no—
222Dic3⋊C4—61no—
223Dic3⋊C4—61no—
224Dic3⋊C4—122no—
225C4×Dic3—62no—
226C4×Dic3—61no—
227C4×Dic3—61no—
228C2×C3⋊C8—21no—
229C2×C3⋊C8—21no—
230C22×C32—21no—
231C22×C32—21no—
232C22×C32—41no—
233C22×C32—41no—
234C22×C32—41no—
235C22×C32#12011yescharacteristic
236C22×C32#13511yescharacteristic
237C22×C32AGL(1,ℤ/8)11yescharacteristic
238C32×C4—21no—
239C32×C4—21no—
240C32×C4—41no—
241C3⋊Dic3—41no—
242C3⋊Dic3—41no—
243C3⋊Dic3—41no—
244C3⋊Dic3—41no—
245C3×Dic3—42no—
246C3×Dic3—81no—
247#126—181no—
248#125—181no—
249#123—181no—
250#123—181no—
251C22⋊Q8—91no—
252C22⋊Q8—181no—
253#121D3211yescharacteristic
254C4×D4—181no—
255C2×C4⋊C4—31no—
256C2×C4⋊C4—91no—
257C2×C4⋊C4—181no—
258#107—61no—
259#106—181no—
260#103—181no—
261#102—61no—
262C22⋊C8—31no—
263C22⋊C8—31no—
264#95—31no—
265#95—181no—
266C23×C3—22no—
267C23×C3—21no—
268C23×C3—21no—
269C23×C3—21no—
270C23×C3D3×D411yescharacteristic
271C23×C3D3×D411yescharacteristic
272C3×D4—41no—
273C3×D4—41no—
274C3×D4—42no—
275C3×D4—42no—
276C3×D4—41no—
277C3×D4—41no—
278C3×D4—41no—
279C3×D4—41no—
280C3×D4—81no—
281C2×C3×C4—22no—
282C2×C3×C4—21no—
283C2×C3×C4—21no—
284C2×C3×C4—21no—
285C2×C3×C4—21no—
286C2×C3×C4—41no—
287C2×C3×C4—41no—
288C2×C3×C4—62no—
289C2×C3×C4—81no—
290C2×C3×C4—121no—
291C2×C3×C4—121no—
292C2×C3×C4—121no—
293C2×C3×C4—121no—
294C2×C3×C4—121no—
295C2×C3×C4C2×D1211yescharacteristic
296C2×C3×C4D3×D411yescharacteristic
297C2×C3×C4D3×D411yescharacteristic
298C2×C3×C4C2×#6711yescharacteristic
299C2×Dic3—22no—
300C2×Dic3—41no—
301C2×Dic3—41no—
302C2×Dic3—41no—
303C2×Dic3—41no—
304C2×Dic3—41no—
305C2×Dic3—62no—
306C2×Dic3—62no—
307C2×Dic3—62no—
308C2×Dic3—62no—
309C2×Dic3—61no—
310C2×Dic3—61no—
311C2×Dic3—61no—
312C2×Dic3—61no—
313C2×Dic3—61no—
314C2×Dic3—61no—
315C2×Dic3—61no—
316C2×Dic3—61no—
317C2×Dic3—61no—
318C2×Dic3—61no—
319C2×Dic3—61no—
320C2×Dic3—61no—
321C2×Dic3—121no—
322C2×Dic3—121no—
323C2×Dic3—121no—
324C2×Dic3—121no—
325C2×Dic3—241no—
326C2×Dic3—242no—
327C2×Dic3—241no—
328C2×Dic3—241no—
329Dic6—121no—
330Dic6—121no—
331Dic6—241no—
332C3×C8—121no—
333C3×C8—121no—
334C3⋊C8—41no—
335C3⋊C8—41no—
336C2×C32—21no—
337C2×C32—21no—
338C2×C32—81no—
339C2×C32#44911yescharacteristic
340C2×C32#45611yescharacteristic
341C2×C32#45811yescharacteristic
342C2×Q8—91no—
343C2×D4—21no—
344C2×D4#62611yescharacteristic
345C22×C4—61no—
346C22×C4—61no—
347C22×C4—91no—
348C22×C4—91no—
349C22×C4—181no—
350C22×C4C2×D3211yescharacteristic
351C2×C8—61no—
352C2×C8—61no—
353C4⋊C4—61no—
354C4⋊C4—61no—
355C4⋊C4—91no—
356C4⋊C4—181no—
357C4⋊C4—181no—
358C4⋊C4—181no—
359C4⋊C4—181no—
360C4⋊C4—181no—
361C4⋊C4—181no—
362C4⋊C4—362no—
363C4⋊C4#62611yescharacteristic
364C22⋊C4—21no—
365C22⋊C4—181no—
366C22⋊C4—181no—
367C22⋊C4—181no—
368C22⋊C4—181no—
369C42—181no—
370C22×C3—21no—
371C22×C3—21no—
372C22×C3—21no—
373C22×C3—21no—
374C22×C3—21no—
375C22×C3—21no—
376C22×C3—21no—
377C22×C3—41no—
378C22×C3—41no—
379C22×C3—42no—
380C22×C3—42no—
381C22×C3—42no—
382C22×C3—41no—
383C22×C3—41no—
384C22×C3—41no—
385C22×C3—41no—
386C22×C3—41no—
387C22×C3—41no—
388C22×C3#88211yescharacteristic
389C22×C3#91111yescharacteristic
390C22×C3#91111yescharacteristic
391C22×C3#91211yescharacteristic
392C22×C3#91611yescharacteristic
393C22×C3#93711yescharacteristic
394C3×C4—21no—
395C3×C4—21no—
396C3×C4—21no—
397C3×C4—21no—
398C3×C4—41no—
399C3×C4—41no—
400C3×C4—42no—
401C3×C4—41no—
402C3×C4—41no—
403C3×C4—122no—
404C3×C4—241no—
405Dic3—42no—
406Dic3—81no—
407Dic3—122no—
408Dic3—122no—
409Dic3—122no—
410Dic3—122no—
411Dic3—121no—
412Dic3—121no—
413Dic3—121no—
414Dic3—121no—
415Dic3—121no—
416Dic3—121no—
417Dic3—121no—
418Dic3—121no—
419C32#160911yescharacteristic, complemented, Sylow
420C23—21no—
421C23#381111yescharacteristic
422Q8—361no—
423D4—41no—
424D4—41no—
425D4—41no—
426C2×C4—21no—
427C2×C4—41no—
428C2×C4—62no—
429C2×C4—121no—
430C2×C4—121no—
431C2×C4—121no—
432C2×C4—121no—
433C2×C4—121no—
434C2×C4—181no—
435C2×C4—181no—
436C2×C4—181no—
437C2×C4—181no—
438C2×C4—181no—
439C2×C4—181no—
440C2×C4—361no—
441C2×C4—721no—
442C2×C4C2×#62611yescharacteristic
443C2×C4#381111yescharacteristic
444C8—121no—
445C8—121no—
446C2×C3—21no—
447C2×C3—21no—
448C2×C3—21no—
449C2×C3—21no—
450C2×C3—21no—
451C2×C3—21no—
452C2×C3—21no—
453C2×C3—41no—
454C2×C3—41no—
455C2×C3—82no—
456C2×C3—81no—
457C2×C3—81no—
458C2×C3#474211yescharacteristic
459C2×C3#478111yescharacteristic
460C2×C3#482611yescharacteristic
461C2×C3#505311yescharacteristic
462C2×C3#515811yescharacteristic
463C2×C3#520511yescharacteristic
464C22—21no—
465C22—21no—
466C22—41no—
467C22—41no—
468C22—41no—
469C22#6392711yescharacteristic
470C22#6393611yescharacteristic
471C22#6398111yescharacteristic
472C4—21no—
473C4—21no—
474C4—41no—
475C4—122no—
476C4—241no—
477C4—361no—
478C4—361no—
479C4—361no—
480C4—361no—
481C3—21no—
482C3#6829611yescharacteristic, complemented
483C3#7116611yescharacteristic, complemented
484C2—21no—
485C2—21no—
486C2—81no—
487C2#1059145711yescharacteristic
488C2#1059153511yescharacteristic
489C2#1059166811yescharacteristic
subgroupG/H
centerC22#63981
commutator, cosocleC22×C32×C4C23
FrattiniC22×C4C2×D32
Fitting, prime radicalC32×#121C22
socleC22×C32#120
hypercenter#121D32
hypocenterC32#1609
LCSG ▷ C22×C32×C4 ▷ C22×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4 ◁ #121

Complements

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

NH ≅ G/Ntype
3. #10591358C2semidirect
4. #10591124C2semidirect
6. #10589154C2semidirect
7. #10589148C2semidirect
419. C32#1609semidirect
482. C3#68296semidirect
483. C3#71166semidirect

Maximal subgroups

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

subgroupindex
#105960732
C3×#50332
#105913582
#105911242
C3×#45372
#105891542
#105891482
#711663
#682963