Finite Group Databasebeta

← #11778409

Subgroups — #11778409

Order 1152.

569 conjugacy classes of subgroups; only the 84 normal subgroups are shown.

normal subgroups only

This group has 569 conjugacy classes of subgroups — too many to draw. Only its 84 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
1C3×#5494C211yesmaximal, characteristic
2C3×#4947C211yesmaximal, characteristic, complemented
3#10591185C211yesmaximal, characteristic, complemented
4#10591171C211yesmaximal, characteristic, complemented
5#10589391C211yesmaximal, characteristic, complemented
6#10589153C211yesmaximal, characteristic, complemented
7#10589149C211yesmaximal, characteristic, complemented
8#71885—31nomaximal
9#69700—31nomaximal
10C22×C3×Dic6C2211yescharacteristic
11C2×C32×C22⋊C4C2211yescharacteristic
12C3×#953—21no—
13C2×C3×#217—21no—
14C3×#930C2211yescharacteristic
15C3×C4×#67—21no—
16C3×#924C2211yescharacteristic
17C3×#885—21no—
18C3×#884—21no—
19C3×#883—21no—
20C3×#879—21no—
21C2×#3718—21no—
22C2×#3715—21no—
23#63657C2211yescharacteristic
24#63657C2211yescharacteristic
25C3×C3⋊#95—21no—
26C3×C3⋊#95C2211yescharacteristic
27#63565—21no—
28#63565—21no—
29C3×#538—31no—
30#5494D311yescharacteristic
31C3×#393—31no—
32#5228—31no—
33#5227—31no—
34#5050—31no—
35#5040—31no—
36#4947D311yescharacteristic, complemented
37#4538—31no—
38#4537—31no—
39#4525—31no—
40#4525—31no—
41#4525—61no—
42#4452—31no—
43#4451—31no—
44C24×C32D411yescharacteristic
45C22×C32×C4D411yescharacteristic
46C22×C32×C4C2311yescharacteristic
47C2×C3×#67—21no—
48C2×C3×#67—21no—
49C2×C3×#67—21no—
50C22×C3×Dic3—21no—
51C22×C3×Dic3—21no—
52C2×C3×D12D411yescharacteristic
53C2×C3×C4×D3—21no—
54C2×C3×Dic6—21no—
55C2×C3×Dic6—21no—
56C2×C3×Dic6—42no—
57C2×C3×Dic6D411yescharacteristic
58C32×C22⋊C4—21no—
59C32×C22⋊C4—21no—
60C2×C3⋊(C3⋊C8)—21no—
61C2×C3⋊(C3⋊C8)—21no—
62C3×#217—21no—
63C3×#217—21no—
64C3×#217—21no—
65C3×#217—42no—
66C3×(C2×D3)⋊C4—21no—
67C3×(C2×D3)⋊C4—21no—
68C3×C4⋊Dic3D411yescharacteristic
69C3×C4⋊Dic3D411yescharacteristic
70C3×Dic3⋊C4—21no—
71C3×Dic3⋊C4—21no—
72C3×C4×Dic3—21no—
73#3718—42no—
74#3715—42no—
75#1606—91noSylow
76C22×C3×Q8—31no—
77C22×Dic6C2×D311yescharacteristic
78C3×#126—61no—
79C3×#124—61no—
80C3×#123—61no—
81C3×C22⋊Q8—31no—
82C3×#121—31no—
83C3×#121—61no—
84C3×#120—61no—
85C3×C4×D4—61no—
86C2×C3×C22⋊C4—21no—
87C2×C3×C22⋊C4—61no—
88C2×C3×C22⋊C4C2×D311yescharacteristic
89C2×C3×C22⋊C4C2×D311yescharacteristic
90#953—21no—
91C2×#217—21no—
92C2×#216—61no—
93C2×#216—61no—
94C2×#215—61no—
95C2×#214—61no—
96#930C2×D311yescharacteristic
97C4×#67—21no—
98#924C2×D311yescharacteristic
99#885—21no—
100#884—21no—
101#883—21no—
102#879—21no—
103C3×#95—31no—
104C3×#95—61no—
105#835—61no—
106#835—61no—
107C3⋊#95—21no—
108C3⋊#95C2×D311yescharacteristic
109#830—31no—
110#830—31no—
111#830—31no—
112#830—31no—
113#830—61no—
114#830—61no—
115#810—61no—
116#810—61no—
117C23×C32—21no—
118C23×C32—21no—
119C23×C32—21no—
120C23×C32—41no—
121C23×C32—41no—
122C23×C32C2×D411yescharacteristic
123C22×C3×D3—21no—
124C2×C32×C4—21no—
125C2×C32×C4—41no—
126C2×C32×C4—41no—
127C2×C32×C4C2×D411yescharacteristic
128C2×C32×C4C2×D411yescharacteristic
129C3×#67—41no—
130C3×#67—41no—
131C3×#67—81no—
132C3×#67—81no—
133C2×C3×Dic3—22no—
134C2×C3×Dic3—21no—
135C2×C3×Dic3—21no—
136C2×C3×Dic3—21no—
137C2×C3×Dic3—41no—
138C2×C3×Dic3—41no—
139C2×C3×Dic3—41no—
140C2×C3×Dic3—41no—
141C2×C3×Dic3—41no—
142C3×D12—41no—
143C3×C4×D3—81no—
144C3×Dic6—22no—
145C3×Dic6—22no—
146C3×Dic6—41no—
147C3×Dic6—41no—
148C3×Dic6—41no—
149C3⋊(C3⋊C8)—41no—
150C3⋊(C3⋊C8)—41no—
151#538—31no—
152#451—91no—
153#448—91no—
154#393—31no—
155#328—91no—
156#327—91no—
157#323—91no—
158C24×C3—21no—
159C24×C3#6711yescharacteristic
160C24×C3#6711yescharacteristic
161C2×C3×Q8—31no—
162C2×C3×Q8—61no—
163C2×C3×Q8—61no—
164C2×C3×Q8—122no—
165C2×C3×D4—31no—
166C2×C3×D4—61no—
167C2×C3×D4—61no—
168C2×C3×D4—61no—
169C22×C3×C4—21no—
170C22×C3×C4—21no—
171C22×C3×C4—61no—
172C22×C3×C4—61no—
173C22×C3×C4—61no—
174C22×C3×C4#6711yescharacteristic
175C22×C3×C4#6711yescharacteristic
176C22×C3×C4C22×D311yescharacteristic
177C22×C3×C4C22×D311yescharacteristic
178C2×#67—21no—
179C2×#67—21no—
180C2×#67—21no—
181C22×Dic3—21no—
182C22×Dic3—21no—
183C2×D12#6711yescharacteristic
184C2×C4×D3—21no—
185C2×Dic6—21no—
186C2×Dic6—21no—
187C2×Dic6—42no—
188C2×Dic6#6711yescharacteristic
189C3×C4⋊C4—31no—
190C3×C4⋊C4—31no—
191C3×C4⋊C4—61no—
192C3×C4⋊C4—61no—
193C3×C22⋊C4—21no—
194C3×C22⋊C4—21no—
195C3×C22⋊C4—21no—
196C3×C22⋊C4—21no—
197C3×C22⋊C4—41no—
198C3×C22⋊C4—41no—
199C3×C22⋊C4—61no—
200C3×C22⋊C4—61no—
201C3×C22⋊C4—61no—
202C3×C22⋊C4—61no—
203C3×C22⋊C4—61no—
204C3×C22⋊C4—122no—
205C3×C42—61no—
206#217—21no—
207#217—21no—
208#217—21no—
209#217—42no—
210#216—122no—
211#216—122no—
212#215—122no—
213#214—122no—
214(C2×D3)⋊C4—21no—
215(C2×D3)⋊C4—21no—
216C4⋊Dic3#6711yescharacteristic
217C4⋊Dic3#6711yescharacteristic
218Dic3⋊C4—21no—
219Dic3⋊C4—21no—
220C4×Dic3—21no—
221C2×C3⋊C8—61no—
222C2×C3⋊C8—61no—
223C2×C3⋊C8—61no—
224C2×C3⋊C8—61no—
225C2×C3⋊C8—121no—
226C2×C3⋊C8—121no—
227C22×C32—21no—
228C22×C32—21no—
229C22×C32—41no—
230C22×C32—42no—
231C22×C32—41no—
232C22×C32—41no—
233C22×C32—81no—
234C22×C32#12011yescharacteristic
235C22×C32#13511yescharacteristic
236C22×C32#13711yescharacteristic
237C2×C3×D3—41no—
238C2×C3×D3—41no—
239C2×C3×D3—41no—
240C32×C4—21no—
241C32×C4—21no—
242C32×C4—41no—
243C3×Dic3—41no—
244C3×Dic3—41no—
245C3×Dic3—42no—
246C3×Dic3—41no—
247C3×Dic3—81no—
248C22×Q8—31no—
249C2×Q16—181no—
250C2×SD16—181no—
251#126—61no—
252#124—61no—
253#123—61no—
254C22⋊Q8—31no—
255#121—31no—
256#121—61no—
257#120—61no—
258C4×D4—61no—
259C2×C22⋊C4—61no—
260C2×C22⋊C4D3211yescharacteristic
261#103—181no—
262#103—181no—
263C22⋊C8—91no—
264C22⋊C8—91no—
265#95—31no—
266#95—61no—
267C23×C3—22no—
268C23×C3—21no—
269C23×C3—21no—
270C23×C3—21no—
271C23×C3—21no—
272C23×C3—21no—
273C23×C3—21no—
274C23×C3—21no—
275C23×C3—41no—
276C23×C3—41no—
277C23×C3—41no—
278C23×C3—41no—
279C23×C3—41no—
280C23×C3—41no—
281C23×C3—61no—
282C23×C3—81no—
283C23×C3—81no—
284C23×C3C2×#6711yescharacteristic
285C23×C3C2×#6711yescharacteristic
286C22×D3—21no—
287C3×Q8—62no—
288C3×Q8—62no—
289C3×Q8—121no—
290C3×Q8—121no—
291C3×Q8—121no—
292C3×D4—121no—
293C3×D4—121no—
294C3×D4—121no—
295C3×D4—241no—
296C3×D4—241no—
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—62no—
307C2×C3×C4—61no—
308C2×C3×C4—61no—
309C2×C3×C4—61no—
310C2×C3×C4—81no—
311C2×C3×C4—81no—
312C2×C3×C4—121no—
313C2×C3×C4—121no—
314C2×C3×C4—121no—
315C2×C3×C4—121no—
316C2×C3×C4—121no—
317C2×C3×C4—241no—
318C2×C3×C4D3×D411yescharacteristic
319C2×C3×C4D3×D411yescharacteristic
320C2×C3×C4C2×#6711yescharacteristic
321C2×C3×C4C2×#6711yescharacteristic
322#67—41no—
323#67—41no—
324#67—81no—
325#67—81no—
326C2×Dic3—22no—
327C2×Dic3—21no—
328C2×Dic3—21no—
329C2×Dic3—21no—
330C2×Dic3—41no—
331C2×Dic3—41no—
332C2×Dic3—41no—
333C2×Dic3—41no—
334C2×Dic3—41no—
335D12—41no—
336C4×D3—81no—
337Dic6—22no—
338Dic6—22no—
339Dic6—41no—
340Dic6—41no—
341Dic6—41no—
342C3⋊C8—121no—
343C3⋊C8—121no—
344C3⋊C8—121no—
345C3⋊C8—121no—
346C3⋊C8—241no—
347C3⋊C8—241no—
348C2×C32—21no—
349C2×C32—21no—
350C2×C32—81no—
351C2×C32#45211yescharacteristic
352C2×C32#45511yescharacteristic
353C2×C32B(4,𝔽2)11yescharacteristic
354C3×D3—81no—
355C24#62511yescharacteristic
356C2×Q8—31no—
357C2×Q8—61no—
358C2×Q8—61no—
359C2×Q8—122no—
360C2×D4—31no—
361C2×D4—61no—
362C2×D4—61no—
363C2×D4—61no—
364C22×C4—61no—
365C22×C4—61no—
366C22×C4—61no—
367C22×C4#62511yescharacteristic
368C22×C4C2×D3211yescharacteristic
369Q16—362no—
370SD16—362no—
371C2×C8—181no—
372C2×C8—181no—
373C4⋊C4—31no—
374C4⋊C4—31no—
375C4⋊C4—61no—
376C4⋊C4—61no—
377C22⋊C4—21no—
378C22⋊C4—21no—
379C22⋊C4—61no—
380C22⋊C4—61no—
381C22⋊C4—61no—
382C22⋊C4—61no—
383C22⋊C4—61no—
384C22⋊C4—122no—
385C42—61no—
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—42no—
396C22×C3—42no—
397C22×C3—42no—
398C22×C3—41no—
399C22×C3—41no—
400C22×C3—41no—
401C22×C3—41no—
402C22×C3—41no—
403C22×C3—41no—
404C22×C3—81no—
405C22×C3—81no—
406C22×C3—82no—
407C22×C3—81no—
408C22×C3—81no—
409C22×C3—82no—
410C22×C3—121no—
411C22×C3—121no—
412C22×C3—121no—
413C22×C3#93711yescharacteristic
414C22×C3#94211yescharacteristic
415C22×C3#95011yescharacteristic
416C22×C3#95011yescharacteristic
417C22×C3#95111yescharacteristic
418C22×C3#95311yescharacteristic
419C2×D3—41no—
420C2×D3—41no—
421C2×D3—41no—
422C3×C4—21no—
423C3×C4—21no—
424C3×C4—21no—
425C3×C4—21no—
426C3×C4—41no—
427C3×C4—41no—
428C3×C4—41no—
429C3×C4—41no—
430C3×C4—81no—
431C3×C4—122no—
432C3×C4—121no—
433C3×C4—121no—
434C3×C4—121no—
435C3×C4—241no—
436Dic3—41no—
437Dic3—41no—
438Dic3—41no—
439Dic3—42no—
440Dic3—81no—
441C32#160611yescharacteristic, complemented, Sylow
442C23—21no—
443C23—21no—
444C23—21no—
445C23—41no—
446C23—41no—
447C23—61no—
448C23C2×#62511yescharacteristic
449Q8—62no—
450Q8—62no—
451Q8—121no—
452Q8—121no—
453Q8—121no—
454D4—121no—
455D4—121no—
456D4—121no—
457D4—241no—
458D4—241no—
459C2×C4—21no—
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—121no—
470C2×C4—121no—
471C2×C4—241no—
472C2×C4D3×#6711yescharacteristic
473C2×C4D3×#6711yescharacteristic
474C8—361no—
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—82no—
486C2×C3—81no—
487C2×C3—81no—
488C2×C3—241no—
489C2×C3#503211yescharacteristic
490C2×C3#504711yescharacteristic
491C2×C3#506111yescharacteristic
492C2×C3#523911yescharacteristic
493C2×C3#524211yescharacteristic
494C2×C3#524411yescharacteristic
495D3—81no—
496C22—21no—
497C22—21no—
498C22—42no—
499C22—41no—
500C22—41no—
501C22—41no—
502C22—81no—
503C22—121no—
504C22—121no—
505C22—121no—
506C22#6382211yescharacteristic
507C22#6382711yescharacteristic
508C22#6397611yescharacteristic
509C4—21no—
510C4—21no—
511C4—41no—
512C4—121no—
513C4—122no—
514C4—121no—
515C4—121no—
516C4—241no—
517C3—21no—
518C3#6970011yescharacteristic, complemented
519C3#7188511yescharacteristic, complemented
520C2—21no—
521C2—21no—
522C2—81no—
523C2—241no—
524C2#1059117011yescharacteristic
525C2#1059151211yescharacteristic
526C2#1059153011yescharacteristic
subgroupG/H
centerC22#63976
commutator, cosocleC22×C32×C4C23
FrattiniC22×C4C2×D32
FittingC2×C32×C22⋊C4C22
socleC22×C32#120
prime radicalC3×#5494C2
hypercenterC2×C22⋊C4D32
hypocenterC32#1606
LCSG ▷ C22×C32×C4 ▷ C22×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C22⋊C4

Complements

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

NH ≅ G/Ntype
2. C3×#4947C2semidirect
3. #10591185C2semidirect
4. #10591171C2semidirect
5. #10589391C2semidirect
6. #10589153C2semidirect
7. #10589149C2semidirect
36. #4947D3semidirect
441. C32#1606semidirect
518. C3#69700semidirect
519. C3#71885semidirect

Maximal subgroups

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

subgroupindex
C3×#54942
C3×#49472
#105911852
#105911712
#105893912
#105891532
#105891492
#718853
#697003