Finite Group Databasebeta

← #11778415

Subgroups — #11778415

Order 1152.

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

normal subgroups only

This group has 560 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#10594977C211yesmaximal, characteristic
2C3×#4673C211yesmaximal, characteristic, complemented
3#10591186C211yesmaximal, characteristic, complemented
4#10591171C211yesmaximal, characteristic, complemented
5#10589318C211yesmaximal, characteristic, complemented
6C3×#4451C211yesmaximal, characteristic, complemented
7#10589145C211yesmaximal, characteristic, complemented
8#69700—31nomaximal
9#68287—31nomaximal
10C22×C3×Dic6C2211yescharacteristic
11#64133C2211yescharacteristic
12C3×#930C2211yescharacteristic
13C2×C3×(C2×D3)⋊C4—21no—
14C2×C3×(C2×D3)⋊C4C2211yescharacteristic
15#63976—21no—
16Dic3×#67—21no—
17#63913—21no—
18#63891—21no—
19#63885—21no—
20#63858—21no—
21C2×#3719—21no—
22C2×#3715—21no—
23C32×#95C2211yescharacteristic
24#63657C2211yescharacteristic
25C3×C3⋊#95—21no—
26C3×#830C2211yescharacteristic
27#63566—21no—
28#63565—21no—
29#5617—31no—
30#5494—31no—
31C3×#393—31no—
32#5228—31no—
33#5227—31no—
34#5040—31no—
35#4739—31no—
36#4673D311yescharacteristic, complemented
37C3×#327—31no—
38#4525—31no—
39#4468—31no—
40#4452—31no—
41#4452—31no—
42#4452—61no—
43#4451D311yescharacteristic, complemented
44C23×C3×D3D411yescharacteristic
45C22×C32×C4—21no—
46C22×C32×C4C2311yescharacteristic
47C2×#634D411yescharacteristic
48C2×C3×#67—21no—
49C22×C3×Dic3—21no—
50C22×C3×Dic3D411yescharacteristic
51C2×C3×D12D411yescharacteristic
52C2×C3×Dic6—21no—
53C2×C3×Dic6—21no—
54C2×C3×Dic6—42no—
55C2×#625—21no—
56C2×#625—21no—
57C2×D3×Dic3—21no—
58#3757—21no—
59C4⋊(C3⋊Dic3)D411yescharacteristic
60#3750—21no—
61C2×C3⋊(C3⋊C8)—21no—
62C3×(C2×D3)⋊C4—21no—
63C3×(C2×D3)⋊C4—21no—
64C3×(C2×D3)⋊C4—21no—
65C3×(C2×D3)⋊C4—42no—
66C3×C4⋊Dic3D411yescharacteristic
67C2×C3×C3⋊C8—21no—
68Dic3⋊Dic3—21no—
69(C2×D3)⋊Dic3—21no—
70(C2×D3)⋊Dic3—21no—
71(C2×D3)⋊Dic3—21no—
72Dic32—21no—
73#3719—42no—
74#3715—42no—
75#1606—91noSylow
76C22×C3×Q8—31no—
77C22×Dic6C2×D311yescharacteristic
78C3×#121—31no—
79C2×C3×C22⋊C4—31no—
80C2×C3×C22⋊C4—61no—
81#953—61no—
82C2×#216—61no—
83C2×#215—61no—
84#939—61no—
85#937—61no—
86D4×Dic3—61no—
87C2×#214—61no—
88#930C2×D311yescharacteristic
89C4×#67—61no—
90C2×(C2×D3)⋊C4—21no—
91C2×(C2×D3)⋊C4C2×D311yescharacteristic
92#924—31no—
93#924—31no—
94#924—61no—
95C2×Dic12—61no—
96#898—61no—
97#886—61no—
98#885—61no—
99#885—61no—
100#884—61no—
101#883—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
130C2×C3⋊Dic3—21no—
131C2×C3⋊Dic3—21no—
132#634—41no—
133C3×#67—41no—
134C3×#67—41no—
135C2×C3×Dic3—22no—
136C2×C3×Dic3—21no—
137C2×C3×Dic3—21no—
138C2×C3×Dic3—41no—
139C2×C3×Dic3—41no—
140C2×C3×Dic3—41no—
141C3×D12—41no—
142C3×Dic6—22no—
143C3×Dic6—22no—
144C3×Dic6—41no—
145C3×Dic6—41no—
146#625—81no—
147#625—81no—
148D3×Dic3—81no—
149C3⋊(C3⋊C8)—41no—
150C3×C3⋊C8—41no—
151#538—91no—
152#451—91no—
153#448—91no—
154#393—31no—
155#328—91no—
156#327—31no—
157#323—91no—
158C24×C3—31no—
159C23×D3#6711yescharacteristic
160C2×C3×Q8—61no—
161C2×C3×Q8—61no—
162C2×C3×Q8—122no—
163C2×C3×D4—31no—
164C2×C3×D4—61no—
165C22×C3×C4—21no—
166C22×C3×C4—21no—
167C22×C3×C4—21no—
168C22×C3×C4—31no—
169C22×C3×C4—41no—
170C22×C3×C4—61no—
171C22×C3×C4C22×D311yescharacteristic
172C22×C3×C4C22×D311yescharacteristic
173C2×#67—21no—
174C2×#67—61no—
175C2×#67—61no—
176C2×#67—61no—
177C2×#67—61no—
178C22×Dic3—21no—
179C22×Dic3—61no—
180C22×Dic3#6711yescharacteristic
181C2×D12D1211yescharacteristic
182C2×C4×D3—61no—
183C2×Dic6—21no—
184C2×Dic6—21no—
185C2×Dic6—31no—
186C2×Dic6—31no—
187C2×Dic6—42no—
188C2×Dic6—61no—
189C2×C3×C8—61no—
190C3×C4⋊C4—31no—
191C3×C22⋊C4—61no—
192C3×C22⋊C4—61no—
193C3×C22⋊C4—61no—
194C3×C22⋊C4—122no—
195#217—61no—
196#217—61no—
197#217—61no—
198#217—61no—
199#217—61no—
200#217—121no—
201#216—122no—
202#215—122no—
203#214—122no—
204(C2×D3)⋊C4—21no—
205(C2×D3)⋊C4—21no—
206(C2×D3)⋊C4—21no—
207(C2×D3)⋊C4—42no—
208(C2×D3)⋊C4—61no—
209(C2×D3)⋊C4—61no—
210(C2×D3)⋊C4—61no—
211C4⋊Dic3—31no—
212C4⋊Dic3—31no—
213C4⋊Dic3—61no—
214C4⋊Dic3—61no—
215C4⋊Dic3D1211yescharacteristic
216Dic3⋊C4—61no—
217Dic3⋊C4—61no—
218Dic3⋊C4—61no—
219Dic3⋊C4—121no—
220C4×Dic3—61no—
221C4×Dic3—61no—
222C2×C3⋊C8—21no—
223C2×C3⋊C8—61no—
224C2×C3⋊C8—61no—
225C2×C3⋊C8—121no—
226Dic12—122no—
227C22×C32—21no—
228C22×C32—21no—
229C22×C32#12011yescharacteristic
230C22×C32#13511yescharacteristic
231C22×C32#13711yescharacteristic
232C2×C3×D3—42no—
233C2×C3×D3—41no—
234C2×C3×D3—41no—
235C2×C3×D3—41no—
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—91no—
255#121—31no—
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—61no—
272C23×C3—121no—
273C23×C3—121no—
274C23×C3D3×D411yescharacteristic
275C23×C3C2×#6711yescharacteristic
276C22×D3—21no—
277C22×D3—21no—
278C22×D3—21no—
279C22×D3—21no—
280C22×D3—41no—
281C22×D3—41no—
282C3×Q8—62no—
283C3×Q8—62no—
284C3×Q8—121no—
285C3×Q8—121no—
286C3×D4—121no—
287C3×D4—121no—
288C3×D4—121no—
289C2×C3×C4—21no—
290C2×C3×C4—21no—
291C2×C3×C4—41no—
292C2×C3×C4—41no—
293C2×C3×C4—41no—
294C2×C3×C4—41no—
295C2×C3×C4—41no—
296C2×C3×C4—41no—
297C2×C3×C4—42no—
298C2×C3×C4—41no—
299C2×C3×C4—41no—
300C2×C3×C4—62no—
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—41no—
314#67—41no—
315#67—241no—
316#67—241no—
317#67—241no—
318#67—241no—
319C2×Dic3—22no—
320C2×Dic3—21no—
321C2×Dic3—21no—
322C2×Dic3—41no—
323C2×Dic3—41no—
324C2×Dic3—41no—
325C2×Dic3—61no—
326C2×Dic3—61no—
327C2×Dic3—61no—
328C2×Dic3—61no—
329C2×Dic3—121no—
330C2×Dic3—121no—
331C2×Dic3—241no—
332D12—41no—
333C4×D3—241no—
334Dic6—22no—
335Dic6—22no—
336Dic6—41no—
337Dic6—41no—
338Dic6—121no—
339Dic6—121no—
340Dic6—241no—
341C3×C8—121no—
342C3⋊C8—41no—
343C3⋊C8—121no—
344C3⋊C8—121no—
345C3⋊C8—241no—
346C2×C32—21no—
347C2×C32—21no—
348C2×C32#45211yescharacteristic
349C2×C32#45511yescharacteristic
350C2×C32B(4,𝔽2)11yescharacteristic
351C3×D3—81no—
352C3×D3—81no—
353C24—31no—
354C2×Q8—61no—
355C2×Q8—61no—
356C2×Q8—91no—
357C2×Q8—122no—
358C2×D4—31no—
359C2×D4—61no—
360C2×D4—181no—
361C2×D4—181no—
362C22×C4—21no—
363C22×C4—31no—
364C22×C4—61no—
365C22×C4—181no—
366C22×C4C2×D3211yescharacteristic
367Q16—362no—
368SD16—362no—
369C2×C8—61no—
370C2×C8—181no—
371C4⋊C4—31no—
372C4⋊C4—91no—
373C4⋊C4—181no—
374C4⋊C4—181no—
375C22⋊C4—61no—
376C22⋊C4—61no—
377C22⋊C4—61no—
378C22⋊C4—122no—
379C22⋊C4—181no—
380C22⋊C4—181no—
381C22⋊C4—181no—
382C22⋊C4—181no—
383C42—181no—
384C22×C3—21no—
385C22×C3—21no—
386C22×C3—21no—
387C22×C3—21no—
388C22×C3—21no—
389C22×C3—21no—
390C22×C3—21no—
391C22×C3—41no—
392C22×C3—41no—
393C22×C3—122no—
394C22×C3—121no—
395C22×C3—121no—
396C22×C3—121no—
397C22×C3—121no—
398C22×C3—121no—
399C22×C3—121no—
400C22×C3—241no—
401C22×C3#88211yescharacteristic
402C22×C3#91211yescharacteristic
403C22×C3#91511yescharacteristic
404C22×C3#93711yescharacteristic
405C22×C3#94211yescharacteristic
406C22×C3#95011yescharacteristic
407C2×D3—42no—
408C2×D3—41no—
409C2×D3—41no—
410C2×D3—41no—
411C2×D3—41no—
412C2×D3—41no—
413C2×D3—41no—
414C2×D3—81no—
415C3×C4—21no—
416C3×C4—21no—
417C3×C4—21no—
418C3×C4—21no—
419C3×C4—41no—
420C3×C4—41no—
421C3×C4—81no—
422C3×C4—81no—
423C3×C4—82no—
424C3×C4—122no—
425C3×C4—121no—
426C3×C4—121no—
427Dic3—42no—
428Dic3—41no—
429Dic3—41no—
430Dic3—121no—
431Dic3—121no—
432Dic3—121no—
433Dic3—121no—
434Dic3—241no—
435Dic3—241no—
436C32#160611yescharacteristic, complemented, Sylow
437C23—61no—
438C23—61no—
439C23—61no—
440C23—61no—
441C23—121no—
442C23—121no—
443C23D3×#6711yescharacteristic
444Q8—62no—
445Q8—62no—
446Q8—121no—
447Q8—121no—
448Q8—361no—
449D4—121no—
450D4—121no—
451D4—121no—
452D4—721no—
453D4—721no—
454C2×C4—41no—
455C2×C4—41no—
456C2×C4—41no—
457C2×C4—41no—
458C2×C4—62no—
459C2×C4—61no—
460C2×C4—61no—
461C2×C4—121no—
462C2×C4—121no—
463C2×C4—121no—
464C2×C4—181no—
465C2×C4—181no—
466C2×C4—721no—
467C2×C4D3×D1211yescharacteristic
468C2×C4#380211yescharacteristic
469C8—121no—
470C8—361no—
471C2×C3—21no—
472C2×C3—21no—
473C2×C3—21no—
474C2×C3—21no—
475C2×C3—21no—
476C2×C3—21no—
477C2×C3—21no—
478C2×C3—41no—
479C2×C3—41no—
480C2×C3—241no—
481C2×C3—241no—
482C2×C3#474111yescharacteristic
483C2×C3#478311yescharacteristic
484C2×C3#482511yescharacteristic
485C2×C3#503211yescharacteristic
486C2×C3#504711yescharacteristic
487C2×C3#506111yescharacteristic
488D3—81no—
489D3—81no—
490C22—21no—
491C22—21no—
492C22—122no—
493C22—121no—
494C22—121no—
495C22—121no—
496C22—121no—
497C22—121no—
498C22—121no—
499C22—241no—
500C22#6392211yescharacteristic
501C22#6393311yescharacteristic
502C22#6394611yescharacteristic
503C4—21no—
504C4—21no—
505C4—81no—
506C4—121no—
507C4—121no—
508C4—122no—
509C4—361no—
510C4—361no—
511C3—21no—
512C3#6828711yescharacteristic, complemented
513C3#6970011yescharacteristic, complemented
514C2—21no—
515C2—21no—
516C2—241no—
517C2—241no—
518C2#1059039611yescharacteristic
519C2#1059040711yescharacteristic
520C2#1059061411yescharacteristic
subgroupG/H
centerC22#63922
commutator, cosocleC22×C32×C4C23
FrattiniC22×C4C2×D32
FittingC32×#95C22
socleC22×C32#120
prime radical#10594977C2
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. #10591186C2semidirect
4. #10591171C2semidirect
5. #10589318C2semidirect
6. C3×#4451C2semidirect
7. #10589145C2semidirect
36. #4673D3semidirect
43. #4451D3semidirect
436. C32#1606semidirect
512. C3#68287semidirect
513. C3#69700semidirect

Maximal subgroups

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

subgroupindex
#105949772
C3×#46732
#105911862
#105911712
#105893182
C3×#44512
#105891452
#697003
#682873