Finite Group Databasebeta

← #11778413

Subgroups — #11778413

Order 1152.

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

normal subgroups only

This group has 565 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#10595038C211yesmaximal, characteristic
2C3×#4673C211yesmaximal, characteristic, complemented
3#10591185C211yesmaximal, characteristic, complemented
4#10591174C211yesmaximal, characteristic, complemented
5#10589317C211yesmaximal, characteristic, complemented
6C3×#4452C211yesmaximal, characteristic, complemented
7#10589145C211yesmaximal, characteristic, complemented
8#69700—31nomaximal
9#68319—31nomaximal
10C22×C3×Dic6C2211yescharacteristic
11#64139C2211yescharacteristic
12C2×C3×(C2×D3)⋊C4—21no—
13C2×C3×(C2×D3)⋊C4C2211yescharacteristic
14C3×#924C2211yescharacteristic
15#63977—21no—
16#63952—21no—
17#63910—21no—
18#63907—21no—
19#63861—21no—
20#63854—21no—
21C2×#3718—21no—
22C2×#3717—21no—
23C32×#95C2211yescharacteristic
24#63657C2211yescharacteristic
25C3×C3⋊#95—21no—
26C3×#830C2211yescharacteristic
27#63566—21no—
28#63565—21no—
29#5644—31no—
30#5494—31no—
31C3×#393—31no—
32#5228—31no—
33#5227—31no—
34#5050—31no—
35#4738—31no—
36#4673D311yescharacteristic, complemented
37C3×#328—31no—
38#4525—31no—
39#4468—31no—
40#4452D311yescharacteristic, complemented
41#4451—31no—
42#4451—31no—
43#4451—61no—
44C23×C3×D3D411yescharacteristic
45C22×C32×C4—21no—
46C22×C32×C4C2311yescharacteristic
47C2×#638—21no—
48C2×C4⋊(C3⋊D3)D411yescharacteristic
49C22×C3×Dic3—21no—
50C22×C3×Dic3D411yescharacteristic
51C2×C3×Dic6—21no—
52C2×C3×Dic6—21no—
53C2×C3×Dic6—42no—
54C2×C3×Dic6D411yescharacteristic
55C2×#626—21no—
56C2×#626—21no—
57C2×#624—21no—
58#3752—21no—
59C4⋊(C3⋊Dic3)D411yescharacteristic
60C2×C3⋊(C3⋊C8)—21no—
61C3×#217—21no—
62C3×(C2×D3)⋊C4—21no—
63C3×(C2×D3)⋊C4—21no—
64C3×(C2×D3)⋊C4—42no—
65C3×C4⋊Dic3D411yescharacteristic
66C3×Dic3⋊C4—21no—
67C2×C3×C3⋊C8—21no—
68#3724—21no—
69#3722—21no—
70(C2×D3)⋊Dic3—21no—
71(C2×D3)⋊Dic3—21no—
72Dic32—21no—
73#3718—42no—
74#3717—42no—
75#1606—91noSylow
76C22×C3×Q8—31no—
77C22×Dic6C2×D311yescharacteristic
78C3×C22⋊Q8—31no—
79C2×C3×C22⋊C4—31no—
80C2×C3×C22⋊C4—61no—
81#953—61no—
82#947—61no—
83C2×#216—61no—
84C2×#216—61no—
85C2×#215—61no—
86#930—31no—
87#930—31no—
88#930—61no—
89C4×#67—61no—
90C2×(C2×D3)⋊C4—21no—
91C2×(C2×D3)⋊C4C2×D311yescharacteristic
92#924C2×D311yescharacteristic
93C2×#204—61no—
94#898—61no—
95#895—61no—
96#894—61no—
97#885—61no—
98#884—61no—
99#883—61no—
100#882—61no—
101#67⋊C4—61no—
102#879—61no—
103C3×C22⋊C8—31no—
104C3×#95—21no—
105C3×#95—61no—
106C3×#95C2×D311yescharacteristic
107C3×#95C2×D311yescharacteristic
108#835—61no—
109#835—61no—
110C3⋊#95—21no—
111#830—31no—
112#830—31no—
113#830—61no—
114#830C2×D311yescharacteristic
115#816—61no—
116#810—61no—
117C23×C32C2×D411yescharacteristic
118C22×C3⋊D3—21no—
119C22×C3×D3—21no—
120C22×C3×D3—21no—
121C22×C3×D3—21no—
122C22×C3×D3—41no—
123C22×C3×D3—41no—
124C2×C32×C4—41no—
125C2×C32×C4—41no—
126C2×C32×C4—41no—
127C2×C32×C4—41no—
128C2×C32×C4C2×D411yescharacteristic
129C2×C32×C4C2×D411yescharacteristic
130#638—41no—
131#638—41no—
132C2×C3⋊Dic3—21no—
133C4⋊(C3⋊D3)—41no—
134C2×C3×Dic3—22no—
135C2×C3×Dic3—21no—
136C2×C3×Dic3—21no—
137C2×C3×Dic3—21no—
138C2×C3×Dic3—41no—
139C2×C3×Dic3—41no—
140C2×C3×Dic3—41no—
141C3×Dic6—22no—
142C3×Dic6—22no—
143C3×Dic6—41no—
144C3×Dic6—41no—
145C3×Dic6—41no—
146#626—81no—
147#626—81no—
148#624—81no—
149C3⋊(C3⋊C8)—41no—
150C3×C3⋊C8—41no—
151#538—91no—
152#451—91no—
153#448—91no—
154#393—31no—
155#328—31no—
156#327—91no—
157#323—91no—
158C24×C3—31no—
159C23×D3#6711yescharacteristic
160C2×C3×Q8—31no—
161C2×C3×Q8—61no—
162C2×C3×Q8—61no—
163C2×C3×Q8—122no—
164C22×C3×C4—21no—
165C22×C3×C4—21no—
166C22×C3×C4—21no—
167C22×C3×C4—31no—
168C22×C3×C4—41no—
169C22×C3×C4—61no—
170C22×C3×C4C22×D311yescharacteristic
171C22×C3×C4C22×D311yescharacteristic
172C2×#67—61no—
173C2×#67—61no—
174C2×#67—61no—
175C2×#67—61no—
176C2×#67—121no—
177C22×Dic3—21no—
178C22×Dic3#6711yescharacteristic
179C2×D12—31no—
180C2×D12—31no—
181C2×D12—61no—
182C2×D12—61no—
183C2×D12—61no—
184C2×C4×D3—61no—
185C2×C4×D3—61no—
186C2×Dic6—21no—
187C2×Dic6—21no—
188C2×Dic6—42no—
189C2×Dic6D1211yescharacteristic
190C2×C3×C8—61no—
191C3×C4⋊C4—31no—
192C3×C4⋊C4—61no—
193C3×C22⋊C4—61no—
194C3×C22⋊C4—61no—
195C3×C22⋊C4—61no—
196C3×C22⋊C4—122no—
197#217—21no—
198#217—61no—
199#217—61no—
200#216—122no—
201#216—122no—
202#215—122no—
203(C2×D3)⋊C4—21no—
204(C2×D3)⋊C4—21no—
205(C2×D3)⋊C4—42no—
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—
213C4⋊Dic3—31no—
214C4⋊Dic3—31no—
215C4⋊Dic3—61no—
216C4⋊Dic3D1211yescharacteristic
217Dic3⋊C4—21no—
218Dic3⋊C4—61no—
219Dic3⋊C4—61no—
220C4×Dic3—61no—
221C4×Dic3—61no—
222C2×C3⋊C8—21no—
223C2×C3⋊C8—61no—
224C2×C3⋊C8—61no—
225C2×C3⋊C8—121no—
226#204—122no—
227C22×C32—21no—
228C22×C32—21no—
229C22×C32#12011yescharacteristic
230C22×C32#13511yescharacteristic
231C22×C32#13711yescharacteristic
232C2×C3⋊D3—41no—
233C2×C3⋊D3—41no—
234C2×C3⋊D3—41no—
235C2×C3×D3—42no—
236C2×C3×D3—41no—
237C2×C3×D3—41no—
238C2×C3×D3—41no—
239C2×C3×D3—81no—
240C32×C4—21no—
241C32×C4—21no—
242C32×C4—81no—
243C3⋊Dic3—41no—
244C3×Dic3—41no—
245C3×Dic3—41no—
246C3×Dic3—41no—
247C3×Dic3—42no—
248C22×Q8—31no—
249C2×Q16—181no—
250C2×SD16—181no—
251#126—181no—
252#124—181no—
253#123—181no—
254C22⋊Q8—31no—
255#121—91no—
256#121—181no—
257#120—181no—
258C4×D4—181no—
259C2×C22⋊C4—31no—
260C2×C22⋊C4—61no—
261#103—181no—
262#103—181no—
263C22⋊C8—31no—
264C22⋊C8—91no—
265#95—61no—
266#95D3211yescharacteristic
267C23×C3—21no—
268C23×C3—61no—
269C23×C3—61no—
270C23×C3—61no—
271C23×C3—121no—
272C23×C3—121no—
273C23×C3D3×D411yescharacteristic
274C23×C3C2×#6711yescharacteristic
275C22×D3—21no—
276C22×D3—21no—
277C22×D3—21no—
278C22×D3—41no—
279C22×D3—41no—
280C22×D3—61no—
281C22×D3—61no—
282C22×D3—121no—
283C3×Q8—62no—
284C3×Q8—62no—
285C3×Q8—121no—
286C3×Q8—121no—
287C3×Q8—121no—
288C2×C3×C4—21no—
289C2×C3×C4—21no—
290C2×C3×C4—41no—
291C2×C3×C4—41no—
292C2×C3×C4—41no—
293C2×C3×C4—41no—
294C2×C3×C4—41no—
295C2×C3×C4—41no—
296C2×C3×C4—42no—
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—81no—
305C2×C3×C4—81no—
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×C4D3×D411yescharacteristic
313#67—121no—
314#67—121no—
315#67—121no—
316#67—121no—
317#67—241no—
318#67—241no—
319#67—241no—
320#67—241no—
321C2×Dic3—22no—
322C2×Dic3—21no—
323C2×Dic3—21no—
324C2×Dic3—21no—
325C2×Dic3—41no—
326C2×Dic3—41no—
327C2×Dic3—41no—
328C2×Dic3—61no—
329C2×Dic3—61no—
330C2×Dic3—121no—
331D12—121no—
332D12—121no—
333D12—241no—
334D12—241no—
335D12—241no—
336C4×D3—241no—
337C4×D3—241no—
338Dic6—22no—
339Dic6—22no—
340Dic6—41no—
341Dic6—41no—
342Dic6—41no—
343C3×C8—121no—
344C3⋊C8—41no—
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—31no—
356C2×Q8—31no—
357C2×Q8—61no—
358C2×Q8—61no—
359C2×Q8—122no—
360C2×D4—91no—
361C2×D4—181no—
362C2×D4—181no—
363C2×D4—181no—
364C22×C4—21no—
365C22×C4—31no—
366C22×C4—61no—
367C22×C4—181no—
368C22×C4C2×D3211yescharacteristic
369Q16—362no—
370SD16—362no—
371C2×C8—61no—
372C2×C8—181no—
373C4⋊C4—31no—
374C4⋊C4—61no—
375C4⋊C4—91no—
376C4⋊C4—181no—
377C22⋊C4—61no—
378C22⋊C4—61no—
379C22⋊C4—61no—
380C22⋊C4—122no—
381C22⋊C4—181no—
382C22⋊C4—181no—
383C22⋊C4—181no—
384C22⋊C4—181no—
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—122no—
396C22×C3—121no—
397C22×C3—121no—
398C22×C3—121no—
399C22×C3—241no—
400C22×C3#88211yescharacteristic
401C22×C3#91611yescharacteristic
402C22×C3#91811yescharacteristic
403C22×C3#93711yescharacteristic
404C22×C3#94211yescharacteristic
405C22×C3#95011yescharacteristic
406C2×D3—42no—
407C2×D3—41no—
408C2×D3—41no—
409C2×D3—41no—
410C2×D3—81no—
411C2×D3—121no—
412C2×D3—121no—
413C2×D3—121no—
414C2×D3—121no—
415C2×D3—121no—
416C2×D3—121no—
417C2×D3—241no—
418C2×D3—241no—
419C2×D3—241no—
420C3×C4—21no—
421C3×C4—21no—
422C3×C4—21no—
423C3×C4—21no—
424C3×C4—41no—
425C3×C4—41no—
426C3×C4—81no—
427C3×C4—81no—
428C3×C4—82no—
429C3×C4—122no—
430C3×C4—121no—
431C3×C4—121no—
432C3×C4—121no—
433Dic3—41no—
434Dic3—42no—
435Dic3—41no—
436Dic3—41no—
437Dic3—121no—
438Dic3—121no—
439Dic3—241no—
440C32#160611yescharacteristic, complemented, Sylow
441C23—61no—
442C23—61no—
443C23—61no—
444C23—121no—
445C23—121no—
446C23—181no—
447C23D3×#6711yescharacteristic
448Q8—62no—
449Q8—62no—
450Q8—121no—
451Q8—121no—
452Q8—121no—
453D4—361no—
454D4—361no—
455D4—361no—
456D4—721no—
457D4—721no—
458C2×C4—41no—
459C2×C4—41no—
460C2×C4—41no—
461C2×C4—41no—
462C2×C4—62no—
463C2×C4—61no—
464C2×C4—61no—
465C2×C4—61no—
466C2×C4—121no—
467C2×C4—121no—
468C2×C4—121no—
469C2×C4—181no—
470C2×C4—721no—
471C2×C4D3×D1211yescharacteristic
472C2×C4#380211yescharacteristic
473C8—121no—
474C8—361no—
475C2×C3—21no—
476C2×C3—21no—
477C2×C3—21no—
478C2×C3—21no—
479C2×C3—21no—
480C2×C3—21no—
481C2×C3—21no—
482C2×C3—41no—
483C2×C3—41no—
484C2×C3—241no—
485C2×C3#474111yescharacteristic
486C2×C3#480811yescharacteristic
487C2×C3#482511yescharacteristic
488C2×C3#503211yescharacteristic
489C2×C3#504711yescharacteristic
490C2×C3#506111yescharacteristic
491D3—81no—
492D3—241no—
493D3—241no—
494D3—481no—
495C22—21no—
496C22—21no—
497C22—122no—
498C22—121no—
499C22—121no—
500C22—121no—
501C22—241no—
502C22—361no—
503C22—361no—
504C22—361no—
505C22#6392211yescharacteristic
506C22#6393511yescharacteristic
507C22#6394811yescharacteristic
508C4—21no—
509C4—21no—
510C4—81no—
511C4—121no—
512C4—121no—
513C4—122no—
514C4—121no—
515C4—361no—
516C3—21no—
517C3#6831911yescharacteristic, complemented
518C3#6970011yescharacteristic, complemented
519C2—21no—
520C2—21no—
521C2—241no—
522C2—721no—
523C2#1059039611yescharacteristic
524C2#1059040711yescharacteristic
525C2#1059061611yescharacteristic
subgroupG/H
centerC22#63922
commutator, cosocleC22×C32×C4C23
FrattiniC22×C4C2×D32
FittingC32×#95C22
socleC22×C32#120
prime radical#10595038C2
hypercenter#95D32
hypocenterC32#1606
LCSG ▷ C22×C32×C4 ▷ C22×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4 ◁ #95

Complements

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

NH ≅ G/Ntype
2. C3×#4673C2semidirect
3. #10591185C2semidirect
4. #10591174C2semidirect
5. #10589317C2semidirect
6. C3×#4452C2semidirect
7. #10589145C2semidirect
36. #4673D3semidirect
40. #4452D3semidirect
440. C32#1606semidirect
517. C3#68319semidirect
518. C3#69700semidirect

Maximal subgroups

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

subgroupindex
#105950382
C3×#46732
#105911852
#105911742
#105893172
C3×#44522
#105891452
#697003
#683193