Finite Group Databasebeta

← #11778419

Subgroups — #11778419

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×#4739C211yesmaximal, characteristic, complemented
3#10591304C211yesmaximal, characteristic, complemented
4#10591174C211yesmaximal, characteristic, complemented
5#10589336C211yesmaximal, characteristic, complemented
6C3×#4468C211yesmaximal, characteristic, complemented
7#10589152C211yesmaximal, characteristic, complemented
8#70981—31nomaximal
9#68109—31nomaximal
10C22×C3×Dic6C2211yescharacteristic
11#64139C2211yescharacteristic
12C2×C3×(C2×D3)⋊C4C2211yescharacteristic
13C3×#924C2211yescharacteristic
14C2×C3×Dic12—21no—
15#63977—21no—
16C2×(C2×D3)⋊Dic3—21no—
17#63952—21no—
18#63910—21no—
19#63907—21no—
20#63861—21no—
21#63854—21no—
22C2×#3717—21no—
23C32×C22⋊C8C2211yescharacteristic
24#63658C2211yescharacteristic
25C3×#830C2211yescharacteristic
26C3×#816—21no—
27#63579—21no—
28#63566—21no—
29#5644—31no—
30#5494—31no—
31C3×#451—31no—
32#5231—31no—
33#5227—31no—
34#4947—31no—
35#4739D311yescharacteristic, complemented
36#4738—31no—
37C3×#323—31no—
38#4538—31no—
39#4470—31no—
40#4470—31no—
41#4470—61no—
42#4468D311yescharacteristic, complemented
43#4467—31no—
44C23×C3×D3D411yescharacteristic
45C22×C32×C4C2311yescharacteristic
46C2×#638—21no—
47C22×C3⋊Dic3—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—
58C2×C32×C8—21no—
59#3752—21no—
60C4⋊(C3⋊Dic3)D411yescharacteristic
61C3×#217—21no—
62C3×(C2×D3)⋊C4—21no—
63C3×(C2×D3)⋊C4—21no—
64C3×C4⋊Dic3D411yescharacteristic
65C3×Dic3⋊C4—21no—
66C2×C3×C3⋊C8—21no—
67C3×Dic12—42no—
68#3724—21no—
69#3722—21no—
70(C2×D3)⋊Dic3—21no—
71(C2×D3)⋊Dic3—21no—
72(C2×D3)⋊Dic3—42no—
73Dic32—21no—
74#3717—42no—
75#1606—91noSylow
76C22×C3×Q8—31no—
77C22×Dic6C2×D311yescharacteristic
78C2×C3×Q16—61no—
79C3×C22⋊Q8—31no—
80C2×C3×C22⋊C4—31no—
81#953—61no—
82C2×#217—61no—
83#947—61no—
84C2×#215—61no—
85#930—31no—
86#930—31no—
87#930—61no—
88C4×#67—61no—
89C2×(C2×D3)⋊C4—61no—
90C2×(C2×D3)⋊C4C2×D311yescharacteristic
91#924C2×D311yescharacteristic
92C2×Dic12—21no—
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×#103—61no—
104C3×C22⋊C8—21no—
105C3×C22⋊C8—31no—
106C3×C22⋊C8C2×D311yescharacteristic
107C3×C22⋊C8C2×D311yescharacteristic
108#835—61no—
109C3⋊#95—31no—
110C3⋊#95—31no—
111C3⋊#95—61no—
112C3⋊#95—61no—
113C3⋊#95—61no—
114#830C2×D311yescharacteristic
115#816—21no—
116#816—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×C4C2×D411yescharacteristic
126C2×C32×C4C2×D411yescharacteristic
127#638—41no—
128#638—41no—
129C2×C3⋊Dic3—21no—
130C2×C3⋊Dic3—41no—
131C2×C3⋊Dic3—41no—
132C2×C3⋊Dic3—41no—
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—
149C32×C8—41no—
150C3×C3⋊C8—41no—
151#538—91no—
152#451—31no—
153#448—91no—
154#393—91no—
155#328—91no—
156#327—91no—
157#323—31no—
158C24×C3—31no—
159C23×D3D1211yescharacteristic
160C2×C3×Q8—31no—
161C2×C3×Q8—61no—
162C2×C3×Q8—61no—
163C2×C3×Q8—122no—
164C22×C3×C4—21no—
165C22×C3×C4—31no—
166C22×C3×C4—61no—
167C22×C3×C4C22×D311yescharacteristic
168C22×C3×C4C22×D311yescharacteristic
169C2×#67—61no—
170C2×#67—61no—
171C2×#67—61no—
172C2×#67—61no—
173C2×#67—121no—
174C22×Dic3—21no—
175C22×Dic3—61no—
176C22×Dic3—61no—
177C22×Dic3—121no—
178C22×Dic3D1211yescharacteristic
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×Dic6#6711yescharacteristic
190C3×Q16—122no—
191C2×C3×C8—21no—
192C2×C3×C8—21no—
193C2×C3×C8—41no—
194C2×C3×C8—61no—
195C3×C4⋊C4—31no—
196C3×C4⋊C4—61no—
197C3×C22⋊C4—61no—
198C3×C22⋊C4—61no—
199C3×C22⋊C4—61no—
200#217—21no—
201#217—61no—
202#217—61no—
203#217—122no—
204#215—122no—
205(C2×D3)⋊C4—21no—
206(C2×D3)⋊C4—21no—
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—61no—
213(C2×D3)⋊C4—121no—
214(C2×D3)⋊C4—122no—
215C4⋊Dic3—31no—
216C4⋊Dic3—31no—
217C4⋊Dic3—61no—
218C4⋊Dic3#6711yescharacteristic
219Dic3⋊C4—21no—
220Dic3⋊C4—61no—
221Dic3⋊C4—61no—
222C4×Dic3—61no—
223C4×Dic3—61no—
224C2×C3⋊C8—21no—
225Dic12—42no—
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—
242C3⋊Dic3—41no—
243C3⋊Dic3—81no—
244C3×Dic3—41no—
245C3×Dic3—41no—
246C3×Dic3—41no—
247C3×Dic3—42no—
248C22×Q8—31no—
249C2×Q16—61no—
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—181no—
261#103—61no—
262#103—181no—
263C22⋊C8—31no—
264C22⋊C8D3211yescharacteristic
265#95—91no—
266#95—181no—
267C23×C3—21no—
268C23×C3—61no—
269C23×C3—61no—
270C23×C3—61no—
271C23×C3—121no—
272C23×C3—121no—
273C23×C3C2×D1211yescharacteristic
274C23×C3D3×D411yescharacteristic
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—62no—
293C2×C3×C4—61no—
294C2×C3×C4—61no—
295C2×C3×C4—61no—
296C2×C3×C4—81no—
297C2×C3×C4—121no—
298C2×C3×C4—121no—
299C2×C3×C4—121no—
300C2×C3×C4D3×D411yescharacteristic
301C2×C3×C4D3×D411yescharacteristic
302C2×C3×C4D3×D411yescharacteristic
303C2×C3×C4C2×#6711yescharacteristic
304#67—121no—
305#67—121no—
306#67—121no—
307#67—121no—
308#67—241no—
309#67—241no—
310#67—241no—
311#67—241no—
312C2×Dic3—22no—
313C2×Dic3—21no—
314C2×Dic3—21no—
315C2×Dic3—21no—
316C2×Dic3—41no—
317C2×Dic3—41no—
318C2×Dic3—41no—
319C2×Dic3—61no—
320C2×Dic3—61no—
321C2×Dic3—121no—
322C2×Dic3—121no—
323C2×Dic3—121no—
324C2×Dic3—121no—
325C2×Dic3—121no—
326C2×Dic3—122no—
327C2×Dic3—121no—
328C2×Dic3—121no—
329C2×Dic3—241no—
330C2×Dic3—241no—
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—41no—
344C3×C8—41no—
345C3×C8—81no—
346C3×C8—121no—
347C3⋊C8—41no—
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—31no—
365C22×C4—61no—
366C22×C4—181no—
367C22×C4—181no—
368C22×C4C2×D3211yescharacteristic
369Q16—122no—
370SD16—362no—
371C2×C8—21no—
372C2×C8—61no—
373C4⋊C4—31no—
374C4⋊C4—61no—
375C4⋊C4—91no—
376C4⋊C4—181no—
377C22⋊C4—61no—
378C22⋊C4—61no—
379C22⋊C4—61no—
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—122no—
396C22×C3—121no—
397C22×C3—121no—
398C22×C3—121no—
399C22×C3—241no—
400C22×C3#88211yescharacteristic
401C22×C3#90411yescharacteristic
402C22×C3#90911yescharacteristic
403C22×C3#91811yescharacteristic
404C22×C3#91911yescharacteristic
405C22×C3#93711yescharacteristic
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—121no—
427C3×C4—121no—
428C3×C4—122no—
429C3×C4—121no—
430Dic3—41no—
431Dic3—41no—
432Dic3—42no—
433Dic3—41no—
434Dic3—121no—
435Dic3—121no—
436Dic3—241no—
437Dic3—241no—
438Dic3—241no—
439Dic3—242no—
440C32#160611yescharacteristic, complemented, Sylow
441C23—61no—
442C23—61no—
443C23—61no—
444C23—121no—
445C23—121no—
446C23—181no—
447C23D3×D1211yescharacteristic
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—62no—
460C2×C4—61no—
461C2×C4—61no—
462C2×C4—61no—
463C2×C4—121no—
464C2×C4—121no—
465C2×C4—121no—
466C2×C4—181no—
467C2×C4—361no—
468C2×C4—361no—
469C2×C4—361no—
470C2×C4—721no—
471C2×C4#380211yescharacteristic
472C2×C4D3×#6711yescharacteristic
473C8—41no—
474C8—121no—
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#473311yescharacteristic
486C2×C3#474111yescharacteristic
487C2×C3#474611yescharacteristic
488C2×C3#503211yescharacteristic
489C2×C3#518711yescharacteristic
490C2×C3#520211yescharacteristic
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#6380111yescharacteristic
506C22#6380811yescharacteristic
507C22#6392211yescharacteristic
508C4—21no—
509C4—21no—
510C4—121no—
511C4—121no—
512C4—122no—
513C4—121no—
514C4—361no—
515C4—721no—
516C3—21no—
517C3#6810911yescharacteristic, complemented
518C3#7098111yescharacteristic, complemented
519C2—21no—
520C2—21no—
521C2—241no—
522C2—721no—
523C2#1059040711yescharacteristic
524C2#1059096611yescharacteristic
525C2#1059101211yescharacteristic
subgroupG/H
centerC22#63922
commutator, cosocleC22×C32×C4C23
FrattiniC22×C4C2×D32
FittingC32×C22⋊C8C22
socleC22×C32#120
prime radical#10595038C2
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×#4739C2semidirect
3. #10591304C2semidirect
4. #10591174C2semidirect
5. #10589336C2semidirect
6. C3×#4468C2semidirect
7. #10589152C2semidirect
35. #4739D3semidirect
42. #4468D3semidirect
440. C32#1606semidirect
517. C3#68109semidirect
518. C3#70981semidirect

Maximal subgroups

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

subgroupindex
#105950382
C3×#47392
#105913042
#105911742
#105893362
C3×#44682
#105891522
#709813
#681093