Finite Group Databasebeta

← #11778303

Subgroups — #11778303

Order 1152.

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

normal subgroups only

This group has 562 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×#5645C211yesmaximal, characteristic
2#10592749C211yesmaximal, characteristic, complemented
3#10591354C211yesmaximal, characteristic, complemented
4#10591181C211yesmaximal, characteristic
5C3×#4538C211yesmaximal, characteristic, complemented
6#10589149C211yesmaximal, characteristic
7#10589147C211yesmaximal, characteristic, complemented
8#71889—31nomaximal
9#68326—31nomaximal
10C22×#634C2211yescharacteristic
11C32×C22⋊Q8C2211yescharacteristic
12C2×#3756—21no—
13C3×#946—21no—
14C3×#930C2211yescharacteristic
15C2×C3×Dic3⋊C4C2211yescharacteristic
16C3×#898—21no—
17C3×#894—21no—
18C3×#890—21no—
19C3×#886—21no—
20C3×#67⋊C4—21no—
21C2×Dic3⋊Dic3—21no—
22C2×#3716—21no—
23#63657C2211yescharacteristic
24#63637—21no—
25C3×C3⋊#95C2211yescharacteristic
26C3×#830C2211yescharacteristic
27#63579—21no—
28#63567—21no—
29C3×#539—31no—
30#5645D311yescharacteristic
31#5050—31no—
32#5050—31no—
33#5050—61no—
34#5040—31no—
35#4979—31no—
36#4738—31no—
37#4656—31no—
38C3×#328—31no—
39#4538D311yescharacteristic, complemented
40#4537—31no—
41#4528—31no—
42#4469—31no—
43#4451—31no—
44C2×C32×Q8D411yescharacteristic
45C22×C32×C4C2311yescharacteristic
46C22×C3⋊Dic3—21no—
47C2×#634—21no—
48C2×#634—21no—
49C2×#634—42no—
50C2×C3×#67—21no—
51C22×C3×Dic3—21no—
52C22×C3×Dic3D411yescharacteristic
53C22×C3×Dic3D411yescharacteristic
54C2×C3×D12D411yescharacteristic
55C2×C3×C4×D3—21no—
56C32×C4⋊C4—21no—
57C32×C4⋊C4D411yescharacteristic
58C32×C22⋊C4—21no—
59#3756—42no—
60C2×C3⋊(C3⋊C8)—21no—
61C3×(C2×D3)⋊C4—21no—
62C3×(C2×D3)⋊C4—21no—
63C3×(C2×D3)⋊C4—21no—
64C3×(C2×D3)⋊C4—21no—
65C3×C4⋊Dic3—21no—
66C3×C4⋊Dic3—21no—
67C3×C4⋊Dic3D411yescharacteristic
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#3716—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—21no—
84C3×C22⋊Q8—61no—
85C3×C22⋊Q8C2×D311yescharacteristic
86C3×C22⋊Q8C2×D311yescharacteristic
87C3×#121—31no—
88C3×C4×D4—61no—
89C2×C3×C4⋊C4—31no—
90#946—21no—
91C2×#216—62no—
92C2×#216—61no—
93C2×#216—61no—
94C2×#214—61no—
95#930C2×D311yescharacteristic
96C2×C4⋊Dic3—61no—
97C2×Dic3⋊C4—61no—
98C2×Dic3⋊C4C2×D311yescharacteristic
99C2×#204—61no—
100#898—21no—
101#894—21no—
102#890—21no—
103#886—21no—
104#67⋊C4—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×C32C2×D411yescharacteristic
120C22×C3×D3—21no—
121C32×Q8—41no—
122C2×C32×C4—21no—
123C2×C32×C4—21no—
124C2×C32×C4—41no—
125C2×C32×C4C2×D411yescharacteristic
126C2×C32×C4C2×D411yescharacteristic
127C2×C3⋊Dic3—22no—
128C2×C3⋊Dic3—41no—
129C2×C3⋊Dic3—41no—
130#634—22no—
131#634—22no—
132#634—41no—
133#634—41no—
134C3×#67—41no—
135C3×#67—41no—
136C2×C3×Dic3—22no—
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—
145C3×D12—41no—
146C3×C4×D3—81no—
147C3⋊(C3⋊C8)—41no—
148C3×C3⋊C8—41no—
149#539—31no—
150#451—91no—
151#448—91no—
152#395—91no—
153#328—31no—
154#327—91no—
155#324—91no—
156C2×C3×Q8—21no—
157C2×C3×Q8D1211yescharacteristic
158C2×C3×Q8#6711yescharacteristic
159C2×C3×D4—31no—
160C2×C3×D4—61no—
161C22×C3×C4—21no—
162C22×C3×C4—31no—
163C22×C3×C4—31no—
164C22×C3×C4—61no—
165C22×C3×C4—61no—
166C22×C3×C4C22×D311yescharacteristic
167C22×C3×C4C22×D311yescharacteristic
168C2×#67—21no—
169C22×Dic3—21no—
170C22×Dic3—61no—
171C22×Dic3—61no—
172C22×Dic3—121no—
173C22×Dic3#6711yescharacteristic
174C22×Dic3#6711yescharacteristic
175C2×D12#6711yescharacteristic
176C2×C4×D3—21no—
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×C3×C8—61no—
187C3×C4⋊C4—21no—
188C3×C4⋊C4—21no—
189C3×C4⋊C4—21no—
190C3×C4⋊C4—31no—
191C3×C4⋊C4—41no—
192C3×C4⋊C4—61no—
193C3×C4⋊C4—61no—
194C3×C4⋊C4—61no—
195C3×C4⋊C4—61no—
196C3×C4⋊C4—61no—
197C3×C4⋊C4D1211yescharacteristic
198C3×C4⋊C4#6711yescharacteristic
199C3×C22⋊C4—21no—
200C3×C22⋊C4—21no—
201C3×C22⋊C4—41no—
202C3×C22⋊C4—61no—
203C3×C22⋊C4—61no—
204C3×C22⋊C4—61no—
205C3×C22⋊C4—61no—
206C3×C42—61no—
207#216—122no—
208#216—122no—
209#216—124no—
210#214—122no—
211(C2×D3)⋊C4—21no—
212(C2×D3)⋊C4—21no—
213(C2×D3)⋊C4—21no—
214(C2×D3)⋊C4—21no—
215C4⋊Dic3—21no—
216C4⋊Dic3—21no—
217C4⋊Dic3—122no—
218C4⋊Dic3#6711yescharacteristic
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—
228#204—122no—
229C22×C32—21no—
230C22×C32—21no—
231C22×C32#12011yescharacteristic
232C22×C32#13511yescharacteristic
233C22×C32#13711yescharacteristic
234C2×C3×D3—41no—
235C2×C3×D3—41no—
236C2×C3×D3—41no—
237C32×C4—21no—
238C32×C4—21no—
239C32×C4—41no—
240C32×C4—41no—
241C3⋊Dic3—42no—
242C3×Dic3—42no—
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—61no—
254C22⋊Q8D3211yescharacteristic
255#121—31no—
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—61no—
267C23×C3D3×D411yescharacteristic
268C23×C3C2×#6711yescharacteristic
269C22×D3—21no—
270C3×Q8—41no—
271C3×Q8—41no—
272C3×Q8—42no—
273C3×D4—121no—
274C3×D4—121no—
275C3×D4—121no—
276C2×C3×C4—21no—
277C2×C3×C4—21no—
278C2×C3×C4—21no—
279C2×C3×C4—21no—
280C2×C3×C4—21no—
281C2×C3×C4—21no—
282C2×C3×C4—41no—
283C2×C3×C4—41no—
284C2×C3×C4—41no—
285C2×C3×C4—41no—
286C2×C3×C4—42no—
287C2×C3×C4—62no—
288C2×C3×C4—61no—
289C2×C3×C4—61no—
290C2×C3×C4—61no—
291C2×C3×C4—61no—
292C2×C3×C4—61no—
293C2×C3×C4—121no—
294C2×C3×C4—121no—
295C2×C3×C4—121no—
296C2×C3×C4—241no—
297C2×C3×C4C2×D1211yescharacteristic
298C2×C3×C4D3×D411yescharacteristic
299C2×C3×C4C2×#6711yescharacteristic
300C2×C3×C4C2×#6711yescharacteristic
301#67—41no—
302#67—41no—
303C2×Dic3—22no—
304C2×Dic3—21no—
305C2×Dic3—21no—
306C2×Dic3—21no—
307C2×Dic3—21no—
308C2×Dic3—21no—
309C2×Dic3—41no—
310C2×Dic3—41no—
311C2×Dic3—41no—
312C2×Dic3—62no—
313C2×Dic3—62no—
314C2×Dic3—122no—
315C2×Dic3—122no—
316C2×Dic3—121no—
317C2×Dic3—121no—
318C2×Dic3—122no—
319C2×Dic3—121no—
320C2×Dic3—121no—
321D12—41no—
322C4×D3—81no—
323Dic6—62no—
324Dic6—62no—
325Dic6—64no—
326Dic6—62no—
327Dic6—62no—
328Dic6—122no—
329Dic6—122no—
330Dic6—121no—
331Dic6—121no—
332Dic6—121no—
333Dic6—121no—
334Dic6—122no—
335C3×C8—121no—
336C3⋊C8—41no—
337C3⋊C8—122no—
338C3⋊C8—121no—
339C3⋊C8—121no—
340C2×C32—21no—
341C2×C32—21no—
342C2×C32#45211yescharacteristic
343C2×C32#45611yescharacteristic
344C2×C32B(4,𝔽2)11yescharacteristic
345C3×D3—81no—
346C2×Q8—181no—
347C2×Q8—181no—
348C2×Q8—362no—
349C2×Q8#62611yescharacteristic
350C2×D4—31no—
351C2×D4—61no—
352C22×C4—31no—
353C22×C4—31no—
354C22×C4—61no—
355C22×C4—61no—
356C22×C4—181no—
357C22×C4C2×D3211yescharacteristic
358Q16—362no—
359SD16—362no—
360C2×C8—61no—
361C2×C8—181no—
362C4⋊C4—21no—
363C4⋊C4—31no—
364C4⋊C4—61no—
365C4⋊C4—61no—
366C4⋊C4—61no—
367C4⋊C4—61no—
368C4⋊C4—61no—
369C4⋊C4—362no—
370C4⋊C4#62611yescharacteristic
371C22⋊C4—21no—
372C22⋊C4—61no—
373C22⋊C4—61no—
374C22⋊C4—61no—
375C22⋊C4—61no—
376C42—61no—
377C22×C3—21no—
378C22×C3—21no—
379C22×C3—21no—
380C22×C3—21no—
381C22×C3—21no—
382C22×C3—21no—
383C22×C3—21no—
384C22×C3—41no—
385C22×C3—41no—
386C22×C3—121no—
387C22×C3—121no—
388C22×C3—121no—
389C22×C3#88211yescharacteristic
390C22×C3#91611yescharacteristic
391C22×C3#91811yescharacteristic
392C22×C3#95011yescharacteristic
393C22×C3#95111yescharacteristic
394C22×C3#95311yescharacteristic
395C2×D3—41no—
396C2×D3—41no—
397C2×D3—41no—
398C3×C4—22no—
399C3×C4—21no—
400C3×C4—21no—
401C3×C4—21no—
402C3×C4—21no—
403C3×C4—41no—
404C3×C4—41no—
405C3×C4—41no—
406C3×C4—41no—
407C3×C4—41no—
408C3×C4—81no—
409C3×C4—81no—
410C3×C4—122no—
411C3×C4—121no—
412C3×C4—121no—
413C3×C4—121no—
414Dic3—42no—
415Dic3—41no—
416Dic3—41no—
417Dic3—41no—
418Dic3—124no—
419Dic3—122no—
420Dic3—122no—
421C32#160311yescharacteristic, complemented, Sylow
422C23—61no—
423C23D3×#6711yescharacteristic
424Q8—41no—
425Q8—182no—
426Q8—182no—
427Q8—361no—
428Q8—361no—
429D4—121no—
430D4—121no—
431D4—121no—
432C2×C4—21no—
433C2×C4—21no—
434C2×C4—41no—
435C2×C4—62no—
436C2×C4—61no—
437C2×C4—61no—
438C2×C4—61no—
439C2×C4—61no—
440C2×C4—61no—
441C2×C4—121no—
442C2×C4—121no—
443C2×C4—121no—
444C2×C4—182no—
445C2×C4—241no—
446C2×C4—361no—
447C2×C4—361no—
448C2×C4C2×#62611yescharacteristic
449C2×C4D3×#6711yescharacteristic
450C8—121no—
451C8—361no—
452C2×C3—21no—
453C2×C3—21no—
454C2×C3—21no—
455C2×C3—21no—
456C2×C3—21no—
457C2×C3—21no—
458C2×C3—21no—
459C2×C3—41no—
460C2×C3—41no—
461C2×C3—241no—
462C2×C3#474111yescharacteristic
463C2×C3#480811yescharacteristic
464C2×C3#482611yescharacteristic
465C2×C3#523911yescharacteristic
466C2×C3#524411yescharacteristic
467C2×C3#524611yescharacteristic
468D3—81no—
469C22—21no—
470C22—21no—
471C22—121no—
472C22—121no—
473C22—121no—
474C22#6394311yescharacteristic
475C22#6394711yescharacteristic
476C22#6397711yescharacteristic
477C4—21no—
478C4—21no—
479C4—41no—
480C4—41no—
481C4—122no—
482C4—121no—
483C4—121no—
484C4—121no—
485C4—362no—
486C3—21no—
487C3#6832611yescharacteristic, complemented
488C3#7188911yescharacteristic, complemented
489C2—21no—
490C2—21no—
491C2—241no—
492C2#1059153111yescharacteristic
493C2#1059159911yescharacteristic
494C2#1059168911yescharacteristic
subgroupG/H
centerC22#63977
commutator, cosocleC22×C32×C4C23
FrattiniC22×C4C2×D32
FittingC32×C22⋊Q8C22
socleC22×C32#120
prime radicalC3×#930C22
hypercenterC22⋊Q8D32
hypocenterC32#1603
LCSG ▷ C22×C32×C4 ▷ C22×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22⋊Q8

Complements

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

NH ≅ G/Ntype
2. #10592749C2semidirect
3. #10591354C2semidirect
5. C3×#4538C2semidirect
7. #10589147C2semidirect
39. #4538D3semidirect
421. C32#1603semidirect
487. C3#68326semidirect
488. C3#71889semidirect

Maximal subgroups

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

subgroupindex
C3×#56452
#105927492
#105913542
#105911812
C3×#45382
#105891492
#105891472
#718893
#683263