Finite Group Databasebeta

← #11778411

Subgroups — #11778411

Order 1152.

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

normal subgroups only

This group has 569 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×#4738C211yesmaximal, characteristic, complemented
3#10591310C211yesmaximal, characteristic, complemented
4#10591185C211yesmaximal, characteristic, complemented
5#10589334C211yesmaximal, characteristic, complemented
6C3×#4467C211yesmaximal, characteristic, complemented
7#10589149C211yesmaximal, characteristic, complemented
8#70973—31nomaximal
9#68319—31nomaximal
10C22×C3×Dic6C2211yescharacteristic
11C2×#3752C2211yescharacteristic
12C3×#930C2211yescharacteristic
13C3×#924C2211yescharacteristic
14C2×C3×#204—21no—
15#63981—21no—
16#67⋊Dic3—21no—
17C2×#3722—21no—
18#63907—21no—
19#63890—21no—
20#63886—21no—
21#63848—21no—
22C2×#3718—21no—
23C32×C22⋊C8C2211yescharacteristic
24#63657C2211yescharacteristic
25C3×C3⋊#95C2211yescharacteristic
26C3×#816—21no—
27#63579—21no—
28#63565—21no—
29#5644—31no—
30#5617—31no—
31C3×#448—31no—
32#5231—31no—
33#5228—31no—
34#5050—31no—
35#4738D311yescharacteristic, complemented
36#4673—31no—
37C3×#328—31no—
38#4537—31no—
39#4468—31no—
40#4468—31no—
41#4468—61no—
42#4467D311yescharacteristic, complemented
43#4451—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×Dic6—21no—
52C2×C3×Dic6—21no—
53C2×C3×Dic6—42no—
54C2×C3×Dic6D411yescharacteristic
55C2×#626—21no—
56C2×#626—21no—
57C2×D3×Dic3—21no—
58C2×C32×C8—21no—
59#3752—21no—
60#3752—21no—
61C2×C3⋊(C3⋊C8)—21no—
62C3×#217—21no—
63C3×(C2×D3)⋊C4—21no—
64C3×C4⋊Dic3D411yescharacteristic
65C3×C4⋊Dic3D411yescharacteristic
66C3×Dic3⋊C4—21no—
67C3×#204—42no—
68Dic3⋊Dic3—21no—
69#3722—21no—
70#3722—21no—
71#3722—42no—
72(C2×D3)⋊Dic3—21no—
73Dic32—21no—
74#3718—42no—
75#1606—91noSylow
76C22×C3×Q8—31no—
77C22×Dic6C2×D311yescharacteristic
78C2×C3×SD16—61no—
79C3×C22⋊Q8—31no—
80C3×#121—31no—
81#947—61no—
82C2×#216—61no—
83C2×#216—61no—
84#939—61no—
85#937—61no—
86D4×Dic3—61no—
87#930C2×D311yescharacteristic
88C2×(C2×D3)⋊C4—31no—
89C2×(C2×D3)⋊C4—31no—
90C2×(C2×D3)⋊C4—61no—
91C2×(C2×D3)⋊C4—61no—
92C2×(C2×D3)⋊C4—61no—
93#924C2×D311yescharacteristic
94C2×#204—21no—
95#898—61no—
96#898—61no—
97#895—61no—
98#894—61no—
99#886—61no—
100#885—61no—
101#882—61no—
102#67⋊C4—61no—
103C3×#103—61no—
104C3×C22⋊C8—21no—
105C3×C22⋊C8C2×D311yescharacteristic
106C3×C22⋊C8C2×D311yescharacteristic
107C3×#95—31no—
108#835—61no—
109C3⋊#95—61no—
110C3⋊#95—61no—
111C3⋊#95C2×D311yescharacteristic
112#830—31no—
113#830—31no—
114#830—61no—
115#816—21no—
116#810—61no—
117C23×C32C2×D411yescharacteristic
118C22×C3⋊D3—21no—
119C22×C3⋊D3—21no—
120C22×C3⋊D3—21no—
121C22×C3⋊D3—41no—
122C22×C3⋊D3—41no—
123C22×C3×D3—21no—
124C2×C32×C4—41no—
125C2×C32×C4C2×D411yescharacteristic
126C2×C32×C4C2×D411yescharacteristic
127C2×C3⋊Dic3—21no—
128C2×C3⋊Dic3—41no—
129C3×#67—41no—
130C3×#67—41no—
131C2×C3×Dic3—22no—
132C2×C3×Dic3—21no—
133C2×C3×Dic3—21no—
134C2×C3×Dic3—21no—
135C2×C3×Dic3—41no—
136C2×C3×Dic3—41no—
137C2×C3×Dic3—41no—
138C2×C3×Dic3—41no—
139C2×C3×Dic3—41no—
140C3×D12—41no—
141C3×Dic6—22no—
142C3×Dic6—22no—
143C3×Dic6—41no—
144C3×Dic6—41no—
145C3×Dic6—41no—
146#626—81no—
147#626—81no—
148D3×Dic3—81no—
149C32×C8—41no—
150C3⋊(C3⋊C8)—41no—
151#538—91no—
152#451—91no—
153#448—31no—
154#393—91no—
155#328—31no—
156#327—91no—
157#323—91no—
158C23×D3—31no—
159C23×D3—31no—
160C23×D3—61no—
161C2×C3×Q8—31no—
162C2×C3×Q8—61no—
163C2×C3×Q8—61no—
164C2×C3×Q8—122no—
165C2×C3×D4—31no—
166C2×C3×D4—61no—
167C22×C3×C4—21no—
168C22×C3×C4—61no—
169C22×C3×C4—61no—
170C22×C3×C4C22×D311yescharacteristic
171C22×C3×C4C22×D311yescharacteristic
172C2×#67—21no—
173C2×#67—61no—
174C2×#67—61no—
175C22×Dic3—21no—
176C22×Dic3—21no—
177C22×Dic3—31no—
178C22×Dic3—31no—
179C22×Dic3—61no—
180C22×Dic3—61no—
181C2×D12—61no—
182C2×D12—61no—
183C2×D12#6711yescharacteristic
184C2×C4×D3—61no—
185C2×Dic6—21no—
186C2×Dic6—21no—
187C2×Dic6—42no—
188C2×Dic6D1211yescharacteristic
189C3×SD16—122no—
190C2×C3×C8—21no—
191C2×C3×C8—21no—
192C2×C3×C8—41no—
193C3×C4⋊C4—31no—
194C3×C4⋊C4—31no—
195C3×C4⋊C4—61no—
196C3×C22⋊C4—61no—
197C3×C22⋊C4—61no—
198#217—21no—
199#217—61no—
200#216—122no—
201#216—122no—
202(C2×D3)⋊C4—21no—
203(C2×D3)⋊C4—61no—
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—61no—
210(C2×D3)⋊C4—61no—
211(C2×D3)⋊C4—61no—
212(C2×D3)⋊C4—121no—
213(C2×D3)⋊C4—121no—
214(C2×D3)⋊C4—122no—
215(C2×D3)⋊C4—122no—
216C4⋊Dic3—61no—
217C4⋊Dic3D1211yescharacteristic
218C4⋊Dic3#6711yescharacteristic
219Dic3⋊C4—21no—
220Dic3⋊C4—61no—
221C4×Dic3—61no—
222C4×Dic3—61no—
223C2×C3⋊C8—61no—
224C2×C3⋊C8—61no—
225C2×C3⋊C8—121no—
226#204—42no—
227C22×C32—21no—
228C22×C32—21no—
229C22×C32#12011yescharacteristic
230C22×C32#13511yescharacteristic
231C22×C32#13711yescharacteristic
232C2×C3⋊D3—41no—
233C2×C3⋊D3—42no—
234C2×C3⋊D3—41no—
235C2×C3⋊D3—41no—
236C2×C3⋊D3—81no—
237C2×C3×D3—41no—
238C2×C3×D3—41no—
239C2×C3×D3—41no—
240C32×C4—21no—
241C32×C4—21no—
242C3⋊Dic3—41no—
243C3×Dic3—41no—
244C3×Dic3—41no—
245C3×Dic3—41no—
246C3×Dic3—42no—
247C3×Dic3—81no—
248C22×Q8—31no—
249C2×Q16—181no—
250C2×SD16—61no—
251#126—181no—
252#124—181no—
253#123—181no—
254C22⋊Q8—31no—
255#121—31no—
256#121—181no—
257#120—181no—
258C4×D4—181no—
259C2×C22⋊C4—91no—
260C2×C22⋊C4—181no—
261#103—61no—
262#103—181no—
263C22⋊C8—91no—
264C22⋊C8D3211yescharacteristic
265#95—31no—
266#95—181no—
267C23×C3—21no—
268C23×C3—61no—
269C23×C3D3×D411yescharacteristic
270C23×C3D3×D411yescharacteristic
271C22×D3—21no—
272C22×D3—61no—
273C22×D3—61no—
274C22×D3—61no—
275C22×D3—61no—
276C22×D3—62no—
277C22×D3—61no—
278C22×D3—61no—
279C22×D3—121no—
280C22×D3—121no—
281C22×D3—121no—
282C22×D3—121no—
283C22×D3—121no—
284C22×D3—121no—
285C22×D3—241no—
286C22×D3—241no—
287C3×Q8—62no—
288C3×Q8—62no—
289C3×Q8—121no—
290C3×Q8—121no—
291C3×Q8—121no—
292C3×D4—121no—
293C3×D4—121no—
294C3×D4—121no—
295C2×C3×C4—21no—
296C2×C3×C4—21no—
297C2×C3×C4—41no—
298C2×C3×C4—41no—
299C2×C3×C4—62no—
300C2×C3×C4—61no—
301C2×C3×C4—61no—
302C2×C3×C4—61no—
303C2×C3×C4—81no—
304C2×C3×C4—121no—
305C2×C3×C4—121no—
306C2×C3×C4—121no—
307C2×C3×C4—121no—
308C2×C3×C4—121no—
309C2×C3×C4C2×D1211yescharacteristic
310C2×C3×C4D3×D411yescharacteristic
311C2×C3×C4D3×D411yescharacteristic
312C2×C3×C4C2×#6711yescharacteristic
313#67—41no—
314#67—41no—
315#67—241no—
316#67—241no—
317C2×Dic3—22no—
318C2×Dic3—21no—
319C2×Dic3—21no—
320C2×Dic3—21no—
321C2×Dic3—41no—
322C2×Dic3—41no—
323C2×Dic3—41no—
324C2×Dic3—41no—
325C2×Dic3—41no—
326C2×Dic3—61no—
327C2×Dic3—61no—
328C2×Dic3—121no—
329C2×Dic3—121no—
330C2×Dic3—121no—
331C2×Dic3—241no—
332C2×Dic3—241no—
333D12—41no—
334D12—241no—
335D12—241no—
336C4×D3—241no—
337Dic6—22no—
338Dic6—22no—
339Dic6—41no—
340Dic6—41no—
341Dic6—41no—
342C3×C8—41no—
343C3×C8—41no—
344C3×C8—81no—
345C3⋊C8—121no—
346C3⋊C8—121no—
347C3⋊C8—241no—
348C2×C32—21no—
349C2×C32—21no—
350C2×C32#45211yescharacteristic
351C2×C32#45511yescharacteristic
352C2×C32B(4,𝔽2)11yescharacteristic
353C3⋊D3—81no—
354C3×D3—81no—
355C24—91no—
356C2×Q8—31no—
357C2×Q8—61no—
358C2×Q8—61no—
359C2×Q8—122no—
360C2×D4—31no—
361C2×D4—61no—
362C2×D4—181no—
363C2×D4—181no—
364C22×C4—61no—
365C22×C4—61no—
366C22×C4—91no—
367C22×C4—181no—
368C22×C4C2×D3211yescharacteristic
369Q16—362no—
370SD16—122no—
371C2×C8—21no—
372C2×C8—181no—
373C4⋊C4—31no—
374C4⋊C4—31no—
375C4⋊C4—61no—
376C4⋊C4—181no—
377C22⋊C4—61no—
378C22⋊C4—61no—
379C22⋊C4—181no—
380C22⋊C4—181no—
381C22⋊C4—181no—
382C22⋊C4—181no—
383C22⋊C4—181no—
384C22⋊C4—362no—
385C42—181no—
386C22×C3—21no—
387C22×C3—21no—
388C22×C3—21no—
389C22×C3—21no—
390C22×C3—21no—
391C22×C3—21no—
392C22×C3—21no—
393C22×C3—41no—
394C22×C3—41no—
395C22×C3—121no—
396C22×C3—121no—
397C22×C3—121no—
398C22×C3#88211yescharacteristic
399C22×C3#91511yescharacteristic
400C22×C3#91611yescharacteristic
401C22×C3#91611yescharacteristic
402C22×C3#91811yescharacteristic
403C22×C3#93711yescharacteristic
404C2×D3—41no—
405C2×D3—41no—
406C2×D3—41no—
407C2×D3—122no—
408C2×D3—122no—
409C2×D3—122no—
410C2×D3—121no—
411C2×D3—121no—
412C2×D3—121no—
413C2×D3—121no—
414C2×D3—121no—
415C2×D3—121no—
416C2×D3—241no—
417C2×D3—241no—
418C2×D3—242no—
419C2×D3—241no—
420C2×D3—241no—
421C2×D3—242no—
422C3×C4—21no—
423C3×C4—21no—
424C3×C4—21no—
425C3×C4—21no—
426C3×C4—41no—
427C3×C4—41no—
428C3×C4—121no—
429C3×C4—122no—
430C3×C4—121no—
431C3×C4—121no—
432C3×C4—241no—
433Dic3—41no—
434Dic3—41no—
435Dic3—42no—
436Dic3—41no—
437Dic3—81no—
438Dic3—121no—
439Dic3—121no—
440Dic3—241no—
441C32#160611yescharacteristic, complemented, Sylow
442C23—61no—
443C23—181no—
444C23—181no—
445C23—181no—
446C23—361no—
447C23—361no—
448C23#380211yescharacteristic
449Q8—62no—
450Q8—62no—
451Q8—121no—
452Q8—121no—
453Q8—121no—
454D4—121no—
455D4—121no—
456D4—121no—
457D4—721no—
458D4—721no—
459C2×C4—41no—
460C2×C4—62no—
461C2×C4—61no—
462C2×C4—61no—
463C2×C4—61no—
464C2×C4—121no—
465C2×C4—121no—
466C2×C4—121no—
467C2×C4—121no—
468C2×C4—121no—
469C2×C4—181no—
470C2×C4—361no—
471C2×C4—721no—
472C2×C4D3×D1211yescharacteristic
473C2×C4D3×#6711yescharacteristic
474C8—41no—
475C8—361no—
476C2×C3—21no—
477C2×C3—21no—
478C2×C3—21no—
479C2×C3—21no—
480C2×C3—21no—
481C2×C3—21no—
482C2×C3—21no—
483C2×C3—41no—
484C2×C3—41no—
485C2×C3—241no—
486C2×C3#474111yescharacteristic
487C2×C3#480811yescharacteristic
488C2×C3#482511yescharacteristic
489C2×C3#503211yescharacteristic
490C2×C3#517311yescharacteristic
491C2×C3#520211yescharacteristic
492D3—81no—
493D3—242no—
494D3—241no—
495D3—241no—
496C22—21no—
497C22—21no—
498C22—121no—
499C22—121no—
500C22—121no—
501C22—362no—
502C22—361no—
503C22—361no—
504C22—361no—
505C22—721no—
506C22#6380911yescharacteristic
507C22#6381111yescharacteristic
508C22#6392211yescharacteristic
509C4—21no—
510C4—21no—
511C4—121no—
512C4—122no—
513C4—121no—
514C4—121no—
515C4—241no—
516C4—361no—
517C3—21no—
518C3#6831911yescharacteristic, complemented
519C3#7097311yescharacteristic, complemented
520C2—21no—
521C2—21no—
522C2—241no—
523C2—721no—
524C2#1059040711yescharacteristic
525C2#1059096111yescharacteristic
526C2#1059101111yescharacteristic
subgroupG/H
centerC22#63922
commutator, cosocleC22×C32×C4C23
FrattiniC22×C4C2×D32
FittingC32×C22⋊C8C22
socleC22×C32#120
prime radical#10594979C2
hypercenterC22⋊C8D32
hypocenterC32#1606
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×#4738C2semidirect
3. #10591310C2semidirect
4. #10591185C2semidirect
5. #10589334C2semidirect
6. C3×#4467C2semidirect
7. #10589149C2semidirect
35. #4738D3semidirect
42. #4467D3semidirect
441. C32#1606semidirect
518. C3#68319semidirect
519. C3#70973semidirect

Maximal subgroups

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

subgroupindex
#105949792
C3×#47382
#105913102
#105911852
#105893342
C3×#44672
#105891492
#709733
#683193