Finite Group Databasebeta

← #11778291

Subgroups — #11778291

Order 1152.

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

normal subgroups only

This group has 567 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×#5602C211yesmaximal, characteristic
2#10592739C211yesmaximal, characteristic
3#10591354C211yesmaximal, characteristic, complemented
4#10591190C211yesmaximal, characteristic, complemented
5C3×#4537C211yesmaximal, characteristic
6#10589153C211yesmaximal, characteristic, complemented
7#10589147C211yesmaximal, characteristic, complemented
8#71889—31nomaximal
9#68294—31nomaximal
10C22×#634C2211yescharacteristic
11C32×#121C2211yescharacteristic
12C2×#3754—21no—
13C3×#935—21no—
14C3×#935—21no—
15C3×D4×Dic3—21no—
16C3×#924C2211yescharacteristic
17C2×C3×Dic3⋊C4C2211yescharacteristic
18C3×#889—21no—
19C3×#879—21no—
20C3×#878—21no—
21C2×Dic3⋊Dic3—21no—
22C2×#3719—21no—
23#63657C2211yescharacteristic
24#63637—21no—
25C3×C3⋊#95C2211yescharacteristic
26C3×#830C2211yescharacteristic
27#63579—21no—
28#63567—21no—
29C3×#539—31no—
30#5602D311yescharacteristic
31#5050—31no—
32#5040—31no—
33#5040—31no—
34#5040—61no—
35#4979—31no—
36#4739—31no—
37#4656—31no—
38C3×#327—31no—
39#4538—31no—
40#4537D311yescharacteristic
41#4528—31no—
42#4469—31no—
43#4452—31no—
44C2×C32×D4—21no—
45C2×C32×D4D411yescharacteristic
46C22×C32×C4C2311yescharacteristic
47C22×C3⋊Dic3—21no—
48C2×#634—21no—
49C2×#634—21no—
50C2×#634—42no—
51C22×C3×Dic3—21no—
52C22×C3×Dic3—21no—
53C22×C3×Dic3D411yescharacteristic
54C22×C3×Dic3D411yescharacteristic
55C2×C3×Dic6D411yescharacteristic
56C32×C4⋊C4D411yescharacteristic
57C32×C22⋊C4—21no—
58#3754—42no—
59C2×C3⋊(C3⋊C8)—21no—
60C3×#217—21no—
61C3×#217—21no—
62C3×#217—21no—
63C3×#217—21no—
64C3×C4⋊Dic3—21no—
65C3×C4⋊Dic3D411yescharacteristic
66C3×Dic3⋊C4—21no—
67C3×Dic3⋊C4—21no—
68C3×Dic3⋊C4—21no—
69C3×Dic3⋊C4—21no—
70C3×Dic3⋊C4—21no—
71C3×C4×Dic3—21no—
72C2×C3×C3⋊C8—21no—
73Dic3⋊Dic3—42no—
74#3719—42no—
75#1603—91noSylow
76C22×Dic6—31no—
77C22×Dic6—31no—
78C22×Dic6—61no—
79C3×#126—61no—
80C3×#125—61no—
81C3×#123—61no—
82C3×#123—61no—
83C3×C22⋊Q8—31no—
84C3×C22⋊Q8—61no—
85C3×#121—21no—
86C3×#121C2×D311yescharacteristic
87C3×#121C2×D311yescharacteristic
88C3×C4×D4—61no—
89C2×C3×C4⋊C4—31no—
90C2×#216—61no—
91#935—21no—
92#935—21no—
93D4×Dic3—21no—
94C2×#214—62no—
95C2×#214—61no—
96C2×#214—61no—
97C2×C4⋊Dic3—61no—
98#924C2×D311yescharacteristic
99C2×Dic3⋊C4—61no—
100C2×Dic3⋊C4C2×D311yescharacteristic
101C2×Dic12—61no—
102#889—21no—
103#879—21no—
104#878—21no—
105C3×C22⋊C8—31no—
106C3×#95—31no—
107C3⋊#95—61no—
108C3⋊#95—61no—
109C3⋊#95C2×D311yescharacteristic
110#830—31no—
111#830—31no—
112#830—61no—
113#830C2×D311yescharacteristic
114#816—61no—
115#810—61no—
116#810—62no—
117#810—61no—
118#810—61no—
119C23×C32—21no—
120C23×C32C2×D411yescharacteristic
121C32×D4—41no—
122C32×D4—41no—
123C32×D4—41no—
124C2×C32×C4—21no—
125C2×C32×C4—41no—
126C2×C32×C4C2×D411yescharacteristic
127C2×C32×C4C2×D411yescharacteristic
128C2×C3⋊Dic3—22no—
129C2×C3⋊Dic3—41no—
130C2×C3⋊Dic3—41no—
131#634—22no—
132#634—22no—
133#634—41no—
134#634—41no—
135C2×C3×Dic3—22no—
136C2×C3×Dic3—21no—
137C2×C3×Dic3—21no—
138C2×C3×Dic3—21no—
139C2×C3×Dic3—21no—
140C2×C3×Dic3—21no—
141C2×C3×Dic3—21no—
142C2×C3×Dic3—41no—
143C2×C3×Dic3—41no—
144C2×C3×Dic3—41no—
145C2×C3×Dic3—81no—
146C3×Dic6—41no—
147C3⋊(C3⋊C8)—41no—
148C3×C3⋊C8—41no—
149#539—31no—
150#451—91no—
151#448—91no—
152#395—91no—
153#328—91no—
154#327—31no—
155#324—91no—
156C2×C3×Q8—31no—
157C2×C3×D4—21no—
158C2×C3×D4—21no—
159C2×C3×D4—21no—
160C2×C3×D4—41no—
161C2×C3×D4D1211yescharacteristic
162C2×C3×D4#6711yescharacteristic
163C22×C3×C4—21no—
164C22×C3×C4—31no—
165C22×C3×C4—31no—
166C22×C3×C4—61no—
167C22×C3×C4—61no—
168C22×C3×C4C22×D311yescharacteristic
169C22×C3×C4C22×D311yescharacteristic
170C22×Dic3—21no—
171C22×Dic3—21no—
172C22×Dic3—61no—
173C22×Dic3—61no—
174C22×Dic3—121no—
175C22×Dic3#6711yescharacteristic
176C22×Dic3#6711yescharacteristic
177C2×Dic6—62no—
178C2×Dic6—61no—
179C2×Dic6—61no—
180C2×Dic6—61no—
181C2×Dic6—61no—
182C2×Dic6—121no—
183C2×Dic6—122no—
184C2×Dic6—122no—
185C2×Dic6—124no—
186C2×Dic6#6711yescharacteristic
187C2×C3×C8—61no—
188C3×C4⋊C4—21no—
189C3×C4⋊C4—31no—
190C3×C4⋊C4—61no—
191C3×C4⋊C4—61no—
192C3×C4⋊C4—61no—
193C3×C4⋊C4—61no—
194C3×C4⋊C4—61no—
195C3×C4⋊C4—61no—
196C3×C4⋊C4D1211yescharacteristic
197C3×C4⋊C4#6711yescharacteristic
198C3×C22⋊C4—21no—
199C3×C22⋊C4—21no—
200C3×C22⋊C4—41no—
201C3×C22⋊C4—61no—
202C3×C22⋊C4—61no—
203C3×C22⋊C4—61no—
204C3×C22⋊C4—61no—
205C3×C42—61no—
206#217—21no—
207#217—21no—
208#217—21no—
209#217—21no—
210#216—122no—
211#214—122no—
212#214—122no—
213#214—124no—
214C4⋊Dic3—21no—
215C4⋊Dic3—122no—
216C4⋊Dic3#6711yescharacteristic
217Dic3⋊C4—21no—
218Dic3⋊C4—21no—
219Dic3⋊C4—21no—
220Dic3⋊C4—21no—
221Dic3⋊C4—21no—
222Dic3⋊C4—122no—
223C4×Dic3—21no—
224C2×C3⋊C8—21no—
225C2×C3⋊C8—62no—
226C2×C3⋊C8—61no—
227C2×C3⋊C8—61no—
228Dic12—122no—
229C22×C32—21no—
230C22×C32—21no—
231C22×C32—41no—
232C22×C32—41no—
233C22×C32—41no—
234C22×C32#12011yescharacteristic
235C22×C32#13511yescharacteristic
236C22×C32#13711yescharacteristic
237C32×C4—21no—
238C32×C4—21no—
239C32×C4—41no—
240C3⋊Dic3—42no—
241C3×Dic3—42no—
242C3×Dic3—41no—
243C3×Dic3—41no—
244C3×Dic3—41no—
245C3×Dic3—41no—
246C22×Q8—91no—
247C2×Q16—181no—
248C2×SD16—181no—
249#126—61no—
250#125—61no—
251#123—61no—
252#123—61no—
253C22⋊Q8—31no—
254C22⋊Q8—61no—
255#121D3211yescharacteristic
256C4×D4—61no—
257C2×C4⋊C4—31no—
258C2×C4⋊C4—181no—
259#103—181no—
260#103—181no—
261C22⋊C8—31no—
262C22⋊C8—91no—
263#95—31no—
264#95—181no—
265C23×C3—21no—
266C23×C3—21no—
267C23×C3—21no—
268C23×C3—41no—
269C23×C3D3×D411yescharacteristic
270C23×C3C2×#6711yescharacteristic
271C3×Q8—121no—
272C3×D4—41no—
273C3×D4—41no—
274C3×D4—42no—
275C3×D4—41no—
276C3×D4—41no—
277C3×D4—41no—
278C3×D4—41no—
279C3×D4—81no—
280C3×D4—81no—
281C2×C3×C4—21no—
282C2×C3×C4—21no—
283C2×C3×C4—21no—
284C2×C3×C4—21no—
285C2×C3×C4—41no—
286C2×C3×C4—41no—
287C2×C3×C4—41no—
288C2×C3×C4—42no—
289C2×C3×C4—62no—
290C2×C3×C4—61no—
291C2×C3×C4—61no—
292C2×C3×C4—61no—
293C2×C3×C4—61no—
294C2×C3×C4—61no—
295C2×C3×C4—61no—
296C2×C3×C4—121no—
297C2×C3×C4—121no—
298C2×C3×C4—121no—
299C2×C3×C4—241no—
300C2×C3×C4C2×D1211yescharacteristic
301C2×C3×C4D3×D411yescharacteristic
302C2×C3×C4C2×#6711yescharacteristic
303C2×C3×C4C2×#6711yescharacteristic
304C2×Dic3—22no—
305C2×Dic3—21no—
306C2×Dic3—21no—
307C2×Dic3—21no—
308C2×Dic3—21no—
309C2×Dic3—21no—
310C2×Dic3—21no—
311C2×Dic3—41no—
312C2×Dic3—41no—
313C2×Dic3—41no—
314C2×Dic3—62no—
315C2×Dic3—62no—
316C2×Dic3—81no—
317C2×Dic3—122no—
318C2×Dic3—122no—
319C2×Dic3—121no—
320C2×Dic3—121no—
321C2×Dic3—122no—
322C2×Dic3—121no—
323C2×Dic3—121no—
324Dic6—41no—
325Dic6—62no—
326Dic6—64no—
327Dic6—62no—
328Dic6—62no—
329Dic6—62no—
330Dic6—122no—
331Dic6—122no—
332Dic6—121no—
333Dic6—121no—
334Dic6—121no—
335Dic6—121no—
336Dic6—122no—
337C3×C8—121no—
338C3⋊C8—41no—
339C3⋊C8—122no—
340C3⋊C8—121no—
341C3⋊C8—121no—
342C2×C32—21no—
343C2×C32—21no—
344C2×C32—81no—
345C2×C32#45211yescharacteristic
346C2×C32#45611yescharacteristic
347C2×C32B(4,𝔽2)11yescharacteristic
348C2×Q8—31no—
349C2×Q8—181no—
350C2×Q8—181no—
351C2×Q8—362no—
352C2×D4—21no—
353C2×D4#62611yescharacteristic
354C22×C4—31no—
355C22×C4—31no—
356C22×C4—61no—
357C22×C4—61no—
358C22×C4—181no—
359C22×C4C2×D3211yescharacteristic
360Q16—362no—
361SD16—362no—
362C2×C8—61no—
363C2×C8—181no—
364C4⋊C4—31no—
365C4⋊C4—61no—
366C4⋊C4—61no—
367C4⋊C4—61no—
368C4⋊C4—61no—
369C4⋊C4—61no—
370C4⋊C4—61no—
371C4⋊C4—362no—
372C4⋊C4#62611yescharacteristic
373C22⋊C4—21no—
374C22⋊C4—61no—
375C22⋊C4—61no—
376C22⋊C4—61no—
377C22⋊C4—61no—
378C42—61no—
379C22×C3—21no—
380C22×C3—21no—
381C22×C3—21no—
382C22×C3—21no—
383C22×C3—21no—
384C22×C3—21no—
385C22×C3—21no—
386C22×C3—41no—
387C22×C3—41no—
388C22×C3—41no—
389C22×C3—41no—
390C22×C3—41no—
391C22×C3—41no—
392C22×C3—41no—
393C22×C3—41no—
394C22×C3—81no—
395C22×C3—81no—
396C22×C3—81no—
397C22×C3#88211yescharacteristic
398C22×C3#91211yescharacteristic
399C22×C3#91511yescharacteristic
400C22×C3#95011yescharacteristic
401C22×C3#95111yescharacteristic
402C22×C3#95311yescharacteristic
403C3×C4—22no—
404C3×C4—21no—
405C3×C4—21no—
406C3×C4—21no—
407C3×C4—21no—
408C3×C4—41no—
409C3×C4—41no—
410C3×C4—41no—
411C3×C4—81no—
412C3×C4—122no—
413C3×C4—121no—
414C3×C4—121no—
415C3×C4—121no—
416C3×C4—121no—
417Dic3—42no—
418Dic3—41no—
419Dic3—41no—
420Dic3—41no—
421Dic3—41no—
422Dic3—124no—
423Dic3—122no—
424Dic3—122no—
425C32#160311yescharacteristic, complemented, Sylow
426C23—21no—
427C23D3×#6711yescharacteristic
428Q8—121no—
429Q8—182no—
430Q8—182no—
431Q8—361no—
432Q8—361no—
433D4—41no—
434D4—41no—
435D4—41no—
436C2×C4—21no—
437C2×C4—41no—
438C2×C4—62no—
439C2×C4—61no—
440C2×C4—61no—
441C2×C4—61no—
442C2×C4—61no—
443C2×C4—61no—
444C2×C4—61no—
445C2×C4—121no—
446C2×C4—121no—
447C2×C4—121no—
448C2×C4—182no—
449C2×C4—241no—
450C2×C4—361no—
451C2×C4—361no—
452C2×C4C2×#62611yescharacteristic
453C2×C4D3×#6711yescharacteristic
454C8—121no—
455C8—361no—
456C2×C3—21no—
457C2×C3—21no—
458C2×C3—21no—
459C2×C3—21no—
460C2×C3—21no—
461C2×C3—21no—
462C2×C3—21no—
463C2×C3—41no—
464C2×C3—41no—
465C2×C3—81no—
466C2×C3—81no—
467C2×C3—161no—
468C2×C3#474111yescharacteristic
469C2×C3#478311yescharacteristic
470C2×C3#482611yescharacteristic
471C2×C3#523911yescharacteristic
472C2×C3#524411yescharacteristic
473C2×C3#524611yescharacteristic
474C22—21no—
475C22—21no—
476C22—41no—
477C22—41no—
478C22—41no—
479C22#6392911yescharacteristic
480C22#6393311yescharacteristic
481C22#6397711yescharacteristic
482C4—21no—
483C4—21no—
484C4—41no—
485C4—122no—
486C4—121no—
487C4—121no—
488C4—121no—
489C4—121no—
490C4—362no—
491C3—21no—
492C3#6829411yescharacteristic, complemented
493C3#7188911yescharacteristic, complemented
494C2—21no—
495C2—21no—
496C2—81no—
497C2#1059146311yescharacteristic
498C2#1059153111yescharacteristic
499C2#1059168911yescharacteristic
subgroupG/H
centerC22#63977
commutator, cosocleC22×C32×C4C23
FrattiniC22×C4C2×D32
Fitting, prime radicalC32×#121C22
socleC22×C32#120
hypercenter#121D32
hypocenterC32#1603
LCSG ▷ C22×C32×C4 ▷ C22×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4 ◁ #121

Complements

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

NH ≅ G/Ntype
3. #10591354C2semidirect
4. #10591190C2semidirect
6. #10589153C2semidirect
7. #10589147C2semidirect
425. C32#1603semidirect
492. C3#68294semidirect
493. C3#71889semidirect

Maximal subgroups

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

subgroupindex
C3×#56022
#105927392
#105913542
#105911902
C3×#45372
#105891532
#105891472
#718893
#682943