Finite Group Databasebeta

← #11778295

Subgroups — #11778295

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#10595986C211yesmaximal, characteristic
2C3×#4979C211yesmaximal, characteristic, complemented
3#10591186C211yesmaximal, characteristic, complemented
4#10591174C211yesmaximal, characteristic
5C3×#4528C211yesmaximal, characteristic, complemented
6#10589154C211yesmaximal, characteristic, complemented
7#10589151C211yesmaximal, characteristic
8#69705—31nomaximal
9#68132—31nomaximal
10C22×C3×Dic6C2211yescharacteristic
11C2×C32×C4⋊C4C2211yescharacteristic
12#64139C2211yescharacteristic
13#64138—21no—
14C4×#638—21no—
15#64133C2211yescharacteristic
16#64107—21no—
17#64105—21no—
18#64103—21no—
19#64098—21no—
20C2×C3×Dic3⋊C4—21no—
21C2×#3719—21no—
22C2×#3717—21no—
23C3×C3⋊#95—21no—
24C3×C3⋊#95C2211yescharacteristic
25C3×#830C2211yescharacteristic
26C3×#830C2211yescharacteristic
27#63566—21no—
28#63566—21no—
29#5515—31no—
30#5515—31no—
31#5515—61no—
32C3×#395—31no—
33#5228—31no—
34#5227—31no—
35#4979D311yescharacteristic, complemented
36#4739—31no—
37#4738—31no—
38C3×#324—31no—
39#4528D311yescharacteristic, complemented
40#4470—31no—
41#4467—31no—
42#4452—31no—
43#4451—31no—
44C22×C32×C4D411yescharacteristic
45C22×C32×C4D411yescharacteristic
46C22×C32×C4C2311yescharacteristic
47C2×#638—21no—
48C2×C4⋊(C3⋊D3)D411yescharacteristic
49C2×C4×C3⋊D3—21no—
50C2×#634D411yescharacteristic
51C22×C3×Dic3—21no—
52C22×C3×Dic3—21no—
53C2×C3×Dic6—21no—
54C2×C3×Dic6—21no—
55C2×C3×Dic6—42no—
56C32×C4⋊C4—21no—
57C32×C4⋊C4—21no—
58#3757—21no—
59#3752—21no—
60#3752—21no—
61#3752—21no—
62#3752—21no—
63C4⋊(C3⋊Dic3)D411yescharacteristic
64C4⋊(C3⋊Dic3)D411yescharacteristic
65#3750—21no—
66#3750—21no—
67#3750—21no—
68#3750—21no—
69C4×C3⋊Dic3—21no—
70C3×Dic3⋊C4—42no—
71C2×C3×C3⋊C8—21no—
72C2×C3×C3⋊C8—21no—
73#3719—42no—
74#3717—42no—
75#1603—91noSylow
76C22×C3×Q8—31no—
77C22×Dic6C2×D311yescharacteristic
78C2×C3×C4⋊C4—21no—
79C2×C3×C4⋊C4—61no—
80C2×C3×C4⋊C4C2×D311yescharacteristic
81C2×C3×C4⋊C4C2×D311yescharacteristic
82C2×#216—61no—
83C2×#215—61no—
84#930—31no—
85#930—31no—
86#930—61no—
87#929—62no—
88#929—61no—
89#929—61no—
90C4×#67—62no—
91C4×#67—61no—
92C4×#67—61no—
93#924—31no—
94#924—31no—
95#924—61no—
96C2×Dic3⋊C4—21no—
97C2×Dic12—61no—
98C2×#204—61no—
99#898—61no—
100#898—61no—
101#898—62no—
102#896—61no—
103#896—61no—
104#896—62no—
105#894—61no—
106#894—61no—
107#894—62no—
108#889—61no—
109#889—61no—
110#889—62no—
111C3×C22⋊C8—31no—
112C3×C22⋊C8—31no—
113C3×#95—31no—
114C3×#95—61no—
115#835—61no—
116#835—61no—
117C3⋊#95—21no—
118C3⋊#95C2×D311yescharacteristic
119#830C2×D311yescharacteristic
120#830C2×D311yescharacteristic
121#816—61no—
122#816—61no—
123C23×C32C2×D411yescharacteristic
124C22×C3⋊D3—21no—
125C2×C32×C4—21no—
126C2×C32×C4—21no—
127C2×C32×C4—21no—
128C2×C32×C4—21no—
129C2×C32×C4—41no—
130C2×C32×C4—41no—
131C2×C32×C4C2×D411yescharacteristic
132C2×C32×C4C2×D411yescharacteristic
133#638—41no—
134#638—41no—
135C2×C3⋊Dic3—21no—
136C2×C3⋊Dic3—21no—
137C2×C3⋊Dic3—21no—
138C4⋊(C3⋊D3)—41no—
139C4×C3⋊D3—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—91no—
156#395—31no—
157#328—91no—
158#327—91no—
159#324—31no—
160C2×C3×Q8—61no—
161C2×C3×Q8—61no—
162C2×C3×Q8—122no—
163C22×C3×C4—21no—
164C22×C3×C4—21no—
165C22×C3×C4—21no—
166C22×C3×C4—61no—
167C22×C3×C4—61no—
168C22×C3×C4D1211yescharacteristic
169C22×C3×C4D1211yescharacteristic
170C22×C3×C4#6711yescharacteristic
171C22×C3×C4#6711yescharacteristic
172C22×C3×C4C22×D311yescharacteristic
173C22×C3×C4C22×D311yescharacteristic
174C2×#67—62no—
175C2×#67—61no—
176C2×#67—61no—
177C22×Dic3—21no—
178C22×Dic3—21no—
179C2×D12—31no—
180C2×D12—31no—
181C2×D12—61no—
182C2×C4×D3—62no—
183C2×C4×D3—61no—
184C2×C4×D3—61no—
185C2×Dic6—21no—
186C2×Dic6—21no—
187C2×Dic6—31no—
188C2×Dic6—31no—
189C2×Dic6—42no—
190C2×Dic6—61no—
191C2×C3×C8—61no—
192C2×C3×C8—61no—
193C3×C4⋊C4—22no—
194C3×C4⋊C4—22no—
195C3×C4⋊C4—21no—
196C3×C4⋊C4—21no—
197C3×C4⋊C4—21no—
198C3×C4⋊C4—21no—
199C3×C4⋊C4—122no—
200#217—62no—
201#217—61no—
202#217—61no—
203#216—122no—
204#215—122no—
205(C2×D3)⋊C4—62no—
206(C2×D3)⋊C4—61no—
207(C2×D3)⋊C4—61no—
208(C2×D3)⋊C4—62no—
209(C2×D3)⋊C4—61no—
210(C2×D3)⋊C4—61no—
211(C2×D3)⋊C4—62no—
212(C2×D3)⋊C4—61no—
213(C2×D3)⋊C4—61no—
214(C2×D3)⋊C4—62no—
215(C2×D3)⋊C4—61no—
216(C2×D3)⋊C4—61no—
217C4⋊Dic3—31no—
218C4⋊Dic3—31no—
219C4⋊Dic3—31no—
220C4⋊Dic3—31no—
221C4⋊Dic3—61no—
222C4⋊Dic3—61no—
223Dic3⋊C4—42no—
224Dic3⋊C4—62no—
225Dic3⋊C4—62no—
226Dic3⋊C4—61no—
227Dic3⋊C4—61no—
228Dic3⋊C4—62no—
229Dic3⋊C4—61no—
230Dic3⋊C4—61no—
231Dic3⋊C4—62no—
232Dic3⋊C4—61no—
233Dic3⋊C4—61no—
234Dic3⋊C4—61no—
235Dic3⋊C4—61no—
236C4×Dic3—62no—
237C4×Dic3—61no—
238C4×Dic3—61no—
239C2×C3⋊C8—21no—
240C2×C3⋊C8—21no—
241Dic12—122no—
242#204—122no—
243C22×C32—21no—
244C22×C32—21no—
245C22×C32#12011yescharacteristic
246C22×C32#13511yescharacteristic
247C22×C32#13711yescharacteristic
248C2×C3⋊D3—41no—
249C2×C3⋊D3—41no—
250C2×C3⋊D3—41no—
251C32×C4—21no—
252C32×C4—21no—
253C32×C4—41no—
254C32×C4—41no—
255C3⋊Dic3—41no—
256C3⋊Dic3—41no—
257C3⋊Dic3—41no—
258C3×Dic3—42no—
259C3×Dic3—42no—
260C22×Q8—31no—
261C2×Q16—181no—
262C2×SD16—181no—
263#126—181no—
264#125—181no—
265#123—181no—
266#123—181no—
267C22⋊Q8—91no—
268C22⋊Q8—181no—
269#121—91no—
270C4×D4—181no—
271C2×C4⋊C4—61no—
272C2×C4⋊C4D3211yescharacteristic
273#103—181no—
274#103—181no—
275C22⋊C8—31no—
276C22⋊C8—31no—
277#95—31no—
278#95—61no—
279C23×C3—21no—
280C23×C3C2×D1211yescharacteristic
281C23×C3C2×#6711yescharacteristic
282C22×D3—62no—
283C22×D3—61no—
284C22×D3—61no—
285C3×Q8—62no—
286C3×Q8—62no—
287C3×Q8—121no—
288C3×Q8—121no—
289C2×C3×C4—22no—
290C2×C3×C4—22no—
291C2×C3×C4—21no—
292C2×C3×C4—21no—
293C2×C3×C4—21no—
294C2×C3×C4—21no—
295C2×C3×C4—21no—
296C2×C3×C4—21no—
297C2×C3×C4—21no—
298C2×C3×C4—21no—
299C2×C3×C4—21no—
300C2×C3×C4—21no—
301C2×C3×C4—41no—
302C2×C3×C4—41no—
303C2×C3×C4—41no—
304C2×C3×C4—41no—
305C2×C3×C4—41no—
306C2×C3×C4—41no—
307C2×C3×C4—62no—
308C2×C3×C4—62no—
309C2×C3×C4—81no—
310C2×C3×C4—81no—
311C2×C3×C4—121no—
312C2×C3×C4—121no—
313C2×C3×C4—121no—
314C2×C3×C4—121no—
315C2×C3×C4D3×D411yescharacteristic
316C2×C3×C4D3×D411yescharacteristic
317C2×C3×C4D3×D411yescharacteristic
318C2×C3×C4D3×D411yescharacteristic
319#67—122no—
320#67—122no—
321#67—121no—
322#67—121no—
323#67—121no—
324#67—121no—
325C2×Dic3—22no—
326C2×Dic3—22no—
327C2×Dic3—41no—
328C2×Dic3—41no—
329C2×Dic3—41no—
330C2×Dic3—41no—
331C2×Dic3—62no—
332C2×Dic3—62no—
333C2×Dic3—62no—
334C2×Dic3—61no—
335C2×Dic3—61no—
336C2×Dic3—61no—
337C2×Dic3—61no—
338C2×Dic3—61no—
339C2×Dic3—61no—
340D12—121no—
341D12—121no—
342D12—241no—
343C4×D3—242no—
344C4×D3—241no—
345C4×D3—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#45211yescharacteristic
360C2×C32#45611yescharacteristic
361C2×C32B(4,𝔽2)11yescharacteristic
362C3⋊D3—81no—
363C2×Q8—61no—
364C2×Q8—61no—
365C2×Q8—91no—
366C2×Q8—122no—
367C2×D4—91no—
368C2×D4—181no—
369C22×C4—61no—
370C22×C4—61no—
371C22×C4—181no—
372C22×C4#62611yescharacteristic
373C22×C4#62611yescharacteristic
374C22×C4C2×D3211yescharacteristic
375Q16—362no—
376SD16—362no—
377C2×C8—61no—
378C2×C8—61no—
379C4⋊C4—21no—
380C4⋊C4—21no—
381C4⋊C4—91no—
382C4⋊C4—91no—
383C4⋊C4—122no—
384C4⋊C4—181no—
385C4⋊C4—181no—
386C4⋊C4—181no—
387C4⋊C4—181no—
388C22⋊C4—181no—
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#88211yescharacteristic
404C22×C3#90411yescharacteristic
405C22×C3#90911yescharacteristic
406C22×C3#93711yescharacteristic
407C22×C3#94211yescharacteristic
408C22×C3#95011yescharacteristic
409C2×D3—122no—
410C2×D3—122no—
411C2×D3—122no—
412C2×D3—121no—
413C2×D3—121no—
414C2×D3—121no—
415C2×D3—121no—
416C2×D3—121no—
417C2×D3—121no—
418C3×C4—21no—
419C3×C4—21no—
420C3×C4—21no—
421C3×C4—21no—
422C3×C4—41no—
423C3×C4—41no—
424C3×C4—42no—
425C3×C4—42no—
426C3×C4—41no—
427C3×C4—41no—
428C3×C4—41no—
429C3×C4—41no—
430C3×C4—122no—
431C3×C4—122no—
432Dic3—42no—
433Dic3—42no—
434Dic3—122no—
435Dic3—122no—
436Dic3—122no—
437Dic3—121no—
438Dic3—121no—
439Dic3—121no—
440Dic3—121no—
441Dic3—121no—
442Dic3—121no—
443C32#160311yescharacteristic, complemented, Sylow
444C23—181no—
445C23C2×#62611yescharacteristic
446Q8—62no—
447Q8—62no—
448Q8—121no—
449Q8—121no—
450Q8—361no—
451D4—361no—
452D4—361no—
453D4—361no—
454C2×C4—21no—
455C2×C4—21no—
456C2×C4—21no—
457C2×C4—21no—
458C2×C4—41no—
459C2×C4—41no—
460C2×C4—62no—
461C2×C4—62no—
462C2×C4—121no—
463C2×C4—121no—
464C2×C4—121no—
465C2×C4—121no—
466C2×C4—181no—
467C2×C4—181no—
468C2×C4—181no—
469C2×C4—721no—
470C2×C4#381111yescharacteristic
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#473311yescharacteristic
484C2×C3#474111yescharacteristic
485C2×C3#475211yescharacteristic
486C2×C3#503211yescharacteristic
487C2×C3#504711yescharacteristic
488C2×C3#509511yescharacteristic
489D3—242no—
490D3—241no—
491D3—241no—
492C22—21no—
493C22—21no—
494C22—361no—
495C22—361no—
496C22—361no—
497C22#6382911yescharacteristic
498C22#6383311yescharacteristic
499C22#6398111yescharacteristic
500C4—21no—
501C4—21no—
502C4—41no—
503C4—41no—
504C4—122no—
505C4—122no—
506C4—361no—
507C4—361no—
508C4—361no—
509C3—21no—
510C3#6813211yescharacteristic, complemented
511C3#6970511yescharacteristic, complemented
512C2—21no—
513C2—21no—
514C2—721no—
515C2#1059118411yescharacteristic
516C2#1059153211yescharacteristic
517C2#1059165011yescharacteristic
subgroupG/H
centerC22#63981
commutator, cosocleC22×C32×C4C23
FrattiniC22×C4C2×D32
FittingC2×C32×C4⋊C4C22
socleC22×C32#120
prime radical#64139C22
hypercenterC2×C4⋊C4D32
hypocenterC32#1603
LCSG ▷ C22×C32×C4 ▷ C22×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C4⋊C4

Complements

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

NH ≅ G/Ntype
2. C3×#4979C2semidirect
3. #10591186C2semidirect
5. C3×#4528C2semidirect
6. #10589154C2semidirect
35. #4979D3semidirect
39. #4528D3semidirect
443. C32#1603semidirect
510. C3#68132semidirect
511. C3#69705semidirect

Maximal subgroups

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

subgroupindex
#105959862
C3×#49792
#105911862
#105911742
C3×#45282
#105891542
#105891512
#697053
#681323