Finite Group Databasebeta

← #11778292

Subgroups — #11778292

Order 1152.

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

normal subgroups only

This group has 597 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×#5040C211yesmaximal, characteristic
3#10591346C211yesmaximal, characteristic, complemented
4#10591186C211yesmaximal, characteristic, complemented
5C3×#4537C211yesmaximal, characteristic
6#10589154C211yesmaximal, characteristic, complemented
7#10589148C211yesmaximal, characteristic, complemented
8#70974—31nomaximal
9#68294—31nomaximal
10C22×C3×Dic6C2211yescharacteristic
11C32×#121C2211yescharacteristic
12#64144—21no—
13#64144—21no—
14D4×C3⋊Dic3—21no—
15#64133C2211yescharacteristic
16C2×#3750C2211yescharacteristic
17#64098—21no—
18#64088—21no—
19#64087—21no—
20C2×C3×#214—21no—
21C2×Dic3⋊Dic3—21no—
22C2×#3719—21no—
23C3×C3⋊#95C2211yescharacteristic
24C3×#830C2211yescharacteristic
25C3×#830C2211yescharacteristic
26C3×#810—21no—
27#63579—21no—
28#63566—21no—
29#5602—31no—
30#5602—31no—
31#5602—61no—
32C3×#448—31no—
33#5230—31no—
34#5228—31no—
35#5040D311yescharacteristic
36#4739—31no—
37#4656—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—
53C2×C3×Dic6—21no—
54C2×C3×Dic6—21no—
55C2×C3×Dic6—42no—
56C32×C4⋊C4D411yescharacteristic
57C32×C22⋊C4—21no—
58#3757—21no—
59#3757—21no—
60#3757—21no—
61#3757—21no—
62C4⋊(C3⋊Dic3)—21no—
63C4⋊(C3⋊Dic3)D411yescharacteristic
64#3750—21no—
65#3750—21no—
66#3750—21no—
67#3750—21no—
68#3750—21no—
69C4×C3⋊Dic3—21no—
70C3×#214—42no—
71C2×C3×C3⋊C8—21no—
72C2×C3×C3⋊C8—21no—
73Dic3⋊Dic3—42no—
74#3719—42no—
75#1603—91noSylow
76C22×C3×Q8—31no—
77C22×Dic6C2×D311yescharacteristic
78C2×C3×SD16—61no—
79C3×#121—21no—
80C3×#121C2×D311yescharacteristic
81C3×#121C2×D311yescharacteristic
82C2×#216—61no—
83#935—61no—
84#935—61no—
85#935—62no—
86#935—62no—
87#935—61no—
88#935—61no—
89D4×Dic3—61no—
90D4×Dic3—61no—
91D4×Dic3—62no—
92C2×#214—21no—
93C2×C4⋊Dic3—61no—
94#924—31no—
95#924—31no—
96#924—61no—
97C2×Dic3⋊C4—31no—
98C2×Dic3⋊C4—31no—
99C2×Dic3⋊C4—61no—
100C2×Dic3⋊C4—61no—
101C2×Dic12—61no—
102#889—62no—
103#889—61no—
104#889—61no—
105#879—61no—
106#879—61no—
107#879—62no—
108#878—61no—
109#878—61no—
110#878—62no—
111C3×#103—61no—
112C3×C22⋊C8—31no—
113C3×C22⋊C8—31no—
114C3×#95—31no—
115#835—61no—
116C3⋊#95—61no—
117C3⋊#95—61no—
118C3⋊#95C2×D311yescharacteristic
119#830C2×D311yescharacteristic
120#830C2×D311yescharacteristic
121#816—61no—
122#810—21no—
123C23×C32—21no—
124C23×C32C2×D411yescharacteristic
125C32×D4—41no—
126C32×D4—41no—
127C32×D4—41no—
128C2×C32×C4—21no—
129C2×C32×C4—41no—
130C2×C32×C4C2×D411yescharacteristic
131C2×C32×C4C2×D411yescharacteristic
132C2×C3⋊Dic3—21no—
133C2×C3⋊Dic3—21no—
134C2×C3⋊Dic3—21no—
135C2×C3⋊Dic3—21no—
136C2×C3⋊Dic3—21no—
137C2×C3⋊Dic3—21no—
138C2×C3⋊Dic3—41no—
139C2×C3⋊Dic3—81no—
140#634—41no—
141C2×C3×Dic3—22no—
142C2×C3×Dic3—22no—
143C2×C3×Dic3—41no—
144C2×C3×Dic3—41no—
145C2×C3×Dic3—41no—
146C2×C3×Dic3—41no—
147C3×Dic6—22no—
148C3×Dic6—22no—
149C3×Dic6—41no—
150C3×Dic6—41no—
151C3×C3⋊C8—41no—
152C3×C3⋊C8—41no—
153#539—91no—
154#451—91no—
155#448—31no—
156#395—91no—
157#328—91no—
158#327—31no—
159#324—91no—
160C2×C3×Q8—61no—
161C2×C3×Q8—61no—
162C2×C3×Q8—122no—
163C2×C3×D4—22no—
164C2×C3×D4—21no—
165C2×C3×D4—21no—
166C2×C3×D4—21no—
167C2×C3×D4D1211yescharacteristic
168C2×C3×D4#6711yescharacteristic
169C22×C3×C4—21no—
170C22×C3×C4—61no—
171C22×C3×C4—61no—
172C22×C3×C4C22×D311yescharacteristic
173C22×C3×C4C22×D311yescharacteristic
174C22×Dic3—21no—
175C22×Dic3—21no—
176C22×Dic3—31no—
177C22×Dic3—31no—
178C22×Dic3—31no—
179C22×Dic3—31no—
180C22×Dic3—61no—
181C22×Dic3—61no—
182C22×Dic3—62no—
183C22×Dic3—61no—
184C22×Dic3—61no—
185C2×Dic6—21no—
186C2×Dic6—21no—
187C2×Dic6—31no—
188C2×Dic6—31no—
189C2×Dic6—42no—
190C2×Dic6—61no—
191C3×SD16—122no—
192C2×C3×C8—61no—
193C2×C3×C8—61no—
194C3×C4⋊C4—21no—
195C3×C4⋊C4D1211yescharacteristic
196C3×C4⋊C4#6711yescharacteristic
197C3×C22⋊C4—22no—
198C3×C22⋊C4—21no—
199C3×C22⋊C4—21no—
200#217—62no—
201#217—61no—
202#217—61no—
203#217—62no—
204#217—61no—
205#217—61no—
206#217—62no—
207#217—61no—
208#217—61no—
209#217—62no—
210#217—61no—
211#217—61no—
212#216—122no—
213#214—42no—
214C4⋊Dic3—31no—
215C4⋊Dic3—31no—
216C4⋊Dic3—61no—
217C4⋊Dic3—62no—
218C4⋊Dic3—61no—
219C4⋊Dic3—61no—
220C4⋊Dic3—122no—
221Dic3⋊C4—62no—
222Dic3⋊C4—62no—
223Dic3⋊C4—61no—
224Dic3⋊C4—61no—
225Dic3⋊C4—62no—
226Dic3⋊C4—61no—
227Dic3⋊C4—61no—
228Dic3⋊C4—62no—
229Dic3⋊C4—62no—
230Dic3⋊C4—61no—
231Dic3⋊C4—61no—
232Dic3⋊C4—61no—
233Dic3⋊C4—61no—
234Dic3⋊C4—61no—
235Dic3⋊C4—61no—
236Dic3⋊C4—122no—
237C4×Dic3—62no—
238C4×Dic3—61no—
239C4×Dic3—61no—
240C2×C3⋊C8—21no—
241C2×C3⋊C8—21no—
242Dic12—122no—
243C22×C32—21no—
244C22×C32—21no—
245C22×C32—41no—
246C22×C32—41no—
247C22×C32—41no—
248C22×C32#12011yescharacteristic
249C22×C32#13511yescharacteristic
250C22×C32#13711yescharacteristic
251C32×C4—21no—
252C32×C4—21no—
253C32×C4—41no—
254C3⋊Dic3—41no—
255C3⋊Dic3—41no—
256C3⋊Dic3—41no—
257C3⋊Dic3—41no—
258C3×Dic3—42no—
259C3×Dic3—42no—
260C22×Q8—31no—
261C2×Q16—181no—
262C2×SD16—61no—
263#126—181no—
264#125—181no—
265#123—181no—
266#123—181no—
267C22⋊Q8—91no—
268C22⋊Q8—181no—
269#121D3211yescharacteristic
270C4×D4—181no—
271C2×C4⋊C4—91no—
272C2×C4⋊C4—181no—
273#103—61no—
274#103—181no—
275C22⋊C8—31no—
276C22⋊C8—31no—
277#95—31no—
278#95—181no—
279C23×C3—22no—
280C23×C3—21no—
281C23×C3—21no—
282C23×C3—21no—
283C23×C3D3×D411yescharacteristic
284C23×C3D3×D411yescharacteristic
285C3×Q8—62no—
286C3×Q8—62no—
287C3×Q8—121no—
288C3×Q8—121no—
289C3×D4—41no—
290C3×D4—41no—
291C3×D4—42no—
292C3×D4—42no—
293C3×D4—41no—
294C3×D4—41no—
295C3×D4—41no—
296C3×D4—41no—
297C3×D4—81no—
298C2×C3×C4—22no—
299C2×C3×C4—21no—
300C2×C3×C4—21no—
301C2×C3×C4—21no—
302C2×C3×C4—21no—
303C2×C3×C4—41no—
304C2×C3×C4—41no—
305C2×C3×C4—62no—
306C2×C3×C4—62no—
307C2×C3×C4—81no—
308C2×C3×C4—121no—
309C2×C3×C4—121no—
310C2×C3×C4—121no—
311C2×C3×C4—121no—
312C2×C3×C4C2×D1211yescharacteristic
313C2×C3×C4D3×D411yescharacteristic
314C2×C3×C4D3×D411yescharacteristic
315C2×C3×C4C2×#6711yescharacteristic
316C2×Dic3—22no—
317C2×Dic3—22no—
318C2×Dic3—41no—
319C2×Dic3—41no—
320C2×Dic3—41no—
321C2×Dic3—41no—
322C2×Dic3—62no—
323C2×Dic3—62no—
324C2×Dic3—62no—
325C2×Dic3—62no—
326C2×Dic3—61no—
327C2×Dic3—61no—
328C2×Dic3—61no—
329C2×Dic3—61no—
330C2×Dic3—61no—
331C2×Dic3—61no—
332C2×Dic3—61no—
333C2×Dic3—61no—
334C2×Dic3—61no—
335C2×Dic3—61no—
336C2×Dic3—61no—
337C2×Dic3—61no—
338C2×Dic3—121no—
339C2×Dic3—121no—
340C2×Dic3—121no—
341C2×Dic3—121no—
342C2×Dic3—241no—
343C2×Dic3—242no—
344C2×Dic3—241no—
345C2×Dic3—241no—
346Dic6—22no—
347Dic6—22no—
348Dic6—41no—
349Dic6—41no—
350Dic6—121no—
351Dic6—121no—
352Dic6—241no—
353C3×C8—121no—
354C3×C8—121no—
355C3⋊C8—41no—
356C3⋊C8—41no—
357C2×C32—21no—
358C2×C32—21no—
359C2×C32—81no—
360C2×C32#45211yescharacteristic
361C2×C32#45611yescharacteristic
362C2×C32B(4,𝔽2)11yescharacteristic
363C2×Q8—61no—
364C2×Q8—61no—
365C2×Q8—91no—
366C2×Q8—122no—
367C2×D4—21no—
368C2×D4#62611yescharacteristic
369C22×C4—61no—
370C22×C4—61no—
371C22×C4—91no—
372C22×C4—91no—
373C22×C4—181no—
374C22×C4C2×D3211yescharacteristic
375Q16—362no—
376SD16—122no—
377C2×C8—61no—
378C2×C8—61no—
379C4⋊C4—91no—
380C4⋊C4—181no—
381C4⋊C4—181no—
382C4⋊C4—181no—
383C4⋊C4—181no—
384C4⋊C4—181no—
385C4⋊C4—181no—
386C4⋊C4—362no—
387C4⋊C4#62611yescharacteristic
388C22⋊C4—21no—
389C22⋊C4—181no—
390C22⋊C4—181no—
391C22⋊C4—181no—
392C22⋊C4—181no—
393C42—181no—
394C22×C3—21no—
395C22×C3—21no—
396C22×C3—21no—
397C22×C3—21no—
398C22×C3—21no—
399C22×C3—21no—
400C22×C3—21no—
401C22×C3—41no—
402C22×C3—41no—
403C22×C3—42no—
404C22×C3—42no—
405C22×C3—42no—
406C22×C3—41no—
407C22×C3—41no—
408C22×C3—41no—
409C22×C3—41no—
410C22×C3—41no—
411C22×C3—41no—
412C22×C3#88211yescharacteristic
413C22×C3#91211yescharacteristic
414C22×C3#91511yescharacteristic
415C22×C3#91511yescharacteristic
416C22×C3#91611yescharacteristic
417C22×C3#93711yescharacteristic
418C3×C4—21no—
419C3×C4—21no—
420C3×C4—21no—
421C3×C4—21no—
422C3×C4—41no—
423C3×C4—41no—
424C3×C4—42no—
425C3×C4—41no—
426C3×C4—41no—
427C3×C4—122no—
428C3×C4—122no—
429Dic3—42no—
430Dic3—42no—
431Dic3—122no—
432Dic3—122no—
433Dic3—122no—
434Dic3—122no—
435Dic3—121no—
436Dic3—121no—
437Dic3—121no—
438Dic3—121no—
439Dic3—121no—
440Dic3—121no—
441Dic3—121no—
442Dic3—121no—
443C32#160311yescharacteristic, complemented, Sylow
444C23—21no—
445C23#381111yescharacteristic
446Q8—62no—
447Q8—62no—
448Q8—121no—
449Q8—121no—
450Q8—361no—
451D4—41no—
452D4—41no—
453D4—41no—
454C2×C4—21no—
455C2×C4—41no—
456C2×C4—62no—
457C2×C4—62no—
458C2×C4—121no—
459C2×C4—121no—
460C2×C4—121no—
461C2×C4—121no—
462C2×C4—181no—
463C2×C4—181no—
464C2×C4—181no—
465C2×C4—181no—
466C2×C4—181no—
467C2×C4—181no—
468C2×C4—361no—
469C2×C4—721no—
470C2×C4C2×#62611yescharacteristic
471C2×C4#381111yescharacteristic
472C8—121no—
473C8—121no—
474C2×C3—21no—
475C2×C3—21no—
476C2×C3—21no—
477C2×C3—21no—
478C2×C3—21no—
479C2×C3—21no—
480C2×C3—21no—
481C2×C3—41no—
482C2×C3—41no—
483C2×C3—82no—
484C2×C3—81no—
485C2×C3—81no—
486C2×C3#474111yescharacteristic
487C2×C3#478311yescharacteristic
488C2×C3#482611yescharacteristic
489C2×C3#503211yescharacteristic
490C2×C3#517311yescharacteristic
491C2×C3#520511yescharacteristic
492C22—21no—
493C22—21no—
494C22—41no—
495C22—41no—
496C22—41no—
497C22#6393111yescharacteristic
498C22#6393611yescharacteristic
499C22#6398111yescharacteristic
500C4—21no—
501C4—21no—
502C4—41no—
503C4—122no—
504C4—122no—
505C4—361no—
506C4—361no—
507C4—361no—
508C4—361no—
509C3—21no—
510C3#6829411yescharacteristic, complemented
511C3#7097411yescharacteristic, complemented
512C2—21no—
513C2—21no—
514C2—81no—
515C2#1059146611yescharacteristic
516C2#1059153211yescharacteristic
517C2#1059166811yescharacteristic
subgroupG/H
centerC22#63981
commutator, cosocleC22×C32×C4C23
FrattiniC22×C4C2×D32
Fitting, prime radicalC32×#121C22
socleC22×C32#120
hypercenter#121D32
hypocenterC32#1603
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. #10591346C2semidirect
4. #10591186C2semidirect
6. #10589154C2semidirect
7. #10589148C2semidirect
443. C32#1603semidirect
510. C3#68294semidirect
511. C3#70974semidirect

Maximal subgroups

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

subgroupindex
#105960732
C3×#50402
#105913462
#105911862
C3×#45372
#105891542
#105891482
#709743
#682943