Finite Group Databasebeta

← #11778294

Subgroups — #11778294

Order 1152.

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

normal subgroups only

This group has 579 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×#5515C211yesmaximal, characteristic
2#10592678C211yesmaximal, characteristic, complemented
3#10591190C211yesmaximal, characteristic, complemented
4#10591181C211yesmaximal, characteristic
5C3×#4528C211yesmaximal, characteristic, complemented
6#10589152C211yesmaximal, characteristic, complemented
7#10589150C211yesmaximal, characteristic
8#71889—31nomaximal
9#68132—31nomaximal
10C22×#634C2211yescharacteristic
11C2×C32×C4⋊C4C2211yescharacteristic
12C2×#3750—21no—
13C3×#930C2211yescharacteristic
14C3×#929—21no—
15C3×C4×#67—21no—
16C3×#924C2211yescharacteristic
17C3×#898—21no—
18C3×#896—21no—
19C3×#894—21no—
20C3×#889—21no—
21C2×#3719—21no—
22C2×#3716—21no—
23#63658—21no—
24#63658C2211yescharacteristic
25C3×#830C2211yescharacteristic
26C3×#830C2211yescharacteristic
27#63567—21no—
28#63567—21no—
29C3×#539—31no—
30#5515D311yescharacteristic
31#5050—31no—
32#5040—31no—
33#4979—31no—
34#4979—31no—
35#4979—61no—
36#4739—31no—
37#4738—31no—
38C3×#324—31no—
39#4538—31no—
40#4537—31no—
41#4528D311yescharacteristic, complemented
42#4470—31no—
43#4467—31no—
44C22×C32×C4D411yescharacteristic
45C22×C32×C4D411yescharacteristic
46C22×C32×C4C2311yescharacteristic
47C22×C3⋊Dic3—21no—
48C22×C3⋊Dic3—21no—
49C2×#634—21no—
50C2×#634—21no—
51C2×#634—42no—
52C2×C3×#67—21no—
53C2×C3×D12D411yescharacteristic
54C2×C3×C4×D3—21no—
55C2×C3×Dic6D411yescharacteristic
56C32×C4⋊C4—21no—
57C32×C4⋊C4—21no—
58#3750—42no—
59C3×#217—21no—
60C3×(C2×D3)⋊C4—21no—
61C3×(C2×D3)⋊C4—21no—
62C3×(C2×D3)⋊C4—21no—
63C3×(C2×D3)⋊C4—21no—
64C3×C4⋊Dic3D411yescharacteristic
65C3×C4⋊Dic3D411yescharacteristic
66C3×Dic3⋊C4—21no—
67C3×Dic3⋊C4—21no—
68C3×Dic3⋊C4—21no—
69C3×Dic3⋊C4—21no—
70C3×C4×Dic3—21no—
71C2×C3×C3⋊C8—21no—
72C2×C3×C3⋊C8—21no—
73#3719—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—31no—
84C3×C22⋊Q8—61no—
85C3×#121—31no—
86C3×C4×D4—61no—
87C2×C3×C4⋊C4—21no—
88C2×C3×C4⋊C4C2×D311yescharacteristic
89C2×C3×C4⋊C4C2×D311yescharacteristic
90C2×#216—61no—
91C2×#214—61no—
92#930C2×D311yescharacteristic
93#929—21no—
94C4×#67—21no—
95#924C2×D311yescharacteristic
96C2×Dic3⋊C4—62no—
97C2×Dic3⋊C4—61no—
98C2×Dic3⋊C4—61no—
99C2×Dic12—61no—
100C2×#204—61no—
101#898—21no—
102#896—21no—
103#894—21no—
104#889—21no—
105C3×C22⋊C8—31no—
106C3×C22⋊C8—31no—
107C3⋊#95—31no—
108C3⋊#95—31no—
109C3⋊#95—61no—
110C3⋊#95—62no—
111C3⋊#95—61no—
112C3⋊#95—61no—
113#830C2×D311yescharacteristic
114#830C2×D311yescharacteristic
115#816—61no—
116#816—61no—
117#810—61no—
118#810—61no—
119C23×C32C2×D411yescharacteristic
120C22×C3×D3—21no—
121C2×C32×C4—21no—
122C2×C32×C4—21no—
123C2×C32×C4—21no—
124C2×C32×C4—21no—
125C2×C32×C4—41no—
126C2×C32×C4—41no—
127C2×C32×C4C2×D411yescharacteristic
128C2×C32×C4C2×D411yescharacteristic
129C2×C3⋊Dic3—22no—
130C2×C3⋊Dic3—22no—
131C2×C3⋊Dic3—41no—
132C2×C3⋊Dic3—41no—
133C2×C3⋊Dic3—41no—
134C2×C3⋊Dic3—41no—
135#634—22no—
136#634—22no—
137#634—41no—
138#634—41no—
139C3×#67—41no—
140C3×#67—41no—
141C2×C3×Dic3—21no—
142C2×C3×Dic3—21no—
143C2×C3×Dic3—21no—
144C3×D12—41no—
145C3×C4×D3—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—91no—
155#324—31no—
156C2×C3×Q8—31no—
157C2×C3×D4—31no—
158C2×C3×D4—61no—
159C22×C3×C4—21no—
160C22×C3×C4—21no—
161C22×C3×C4—21no—
162C22×C3×C4—61no—
163C22×C3×C4D1211yescharacteristic
164C22×C3×C4D1211yescharacteristic
165C22×C3×C4#6711yescharacteristic
166C22×C3×C4#6711yescharacteristic
167C22×C3×C4C22×D311yescharacteristic
168C22×C3×C4C22×D311yescharacteristic
169C2×#67—21no—
170C22×Dic3—62no—
171C22×Dic3—62no—
172C22×Dic3—61no—
173C22×Dic3—61no—
174C22×Dic3—61no—
175C22×Dic3—61no—
176C2×D12#6711yescharacteristic
177C2×C4×D3—21no—
178C2×Dic6—61no—
179C2×Dic6—61no—
180C2×Dic6—61no—
181C2×Dic6—61no—
182C2×Dic6—121no—
183C2×Dic6—121no—
184C2×Dic6—122no—
185C2×Dic6—122no—
186C2×Dic6—124no—
187C2×Dic6#6711yescharacteristic
188C2×C3×C8—61no—
189C2×C3×C8—61no—
190C3×C4⋊C4—21no—
191C3×C4⋊C4—21no—
192C3×C4⋊C4—21no—
193C3×C4⋊C4—21no—
194C3×C4⋊C4—31no—
195C3×C4⋊C4—31no—
196C3×C4⋊C4—41no—
197C3×C4⋊C4—41no—
198C3×C4⋊C4—61no—
199C3×C4⋊C4—61no—
200C3×C4⋊C4—61no—
201C3×C4⋊C4—61no—
202C3×C22⋊C4—61no—
203C3×C22⋊C4—61no—
204C3×C22⋊C4—61no—
205C3×C22⋊C4—61no—
206C3×C22⋊C4—61no—
207C3×C42—61no—
208#217—21no—
209#216—122no—
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#6711yescharacteristic
216C4⋊Dic3#6711yescharacteristic
217Dic3⋊C4—21no—
218Dic3⋊C4—21no—
219Dic3⋊C4—21no—
220Dic3⋊C4—21no—
221Dic3⋊C4—122no—
222Dic3⋊C4—122no—
223Dic3⋊C4—124no—
224C4×Dic3—21no—
225C2×C3⋊C8—21no—
226C2×C3⋊C8—21no—
227Dic12—122no—
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—31no—
254C22⋊Q8—61no—
255#121—31no—
256C4×D4—61no—
257C2×C4⋊C4—181no—
258C2×C4⋊C4D3211yescharacteristic
259#103—181no—
260#103—181no—
261C22⋊C8—31no—
262C22⋊C8—31no—
263#95—91no—
264#95—181no—
265C23×C3—21no—
266C23×C3—61no—
267C23×C3C2×D1211yescharacteristic
268C23×C3C2×#6711yescharacteristic
269C22×D3—21no—
270C3×Q8—121no—
271C3×D4—121no—
272C3×D4—121no—
273C3×D4—121no—
274C2×C3×C4—22no—
275C2×C3×C4—21no—
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—21no—
283C2×C3×C4—21no—
284C2×C3×C4—21no—
285C2×C3×C4—41no—
286C2×C3×C4—41no—
287C2×C3×C4—41no—
288C2×C3×C4—41no—
289C2×C3×C4—41no—
290C2×C3×C4—42no—
291C2×C3×C4—41no—
292C2×C3×C4—41no—
293C2×C3×C4—42no—
294C2×C3×C4—61no—
295C2×C3×C4—61no—
296C2×C3×C4—61no—
297C2×C3×C4—241no—
298C2×C3×C4D3×D411yescharacteristic
299C2×C3×C4D3×D411yescharacteristic
300C2×C3×C4C2×#6711yescharacteristic
301C2×C3×C4C2×#6711yescharacteristic
302#67—41no—
303#67—41no—
304C2×Dic3—21no—
305C2×Dic3—21no—
306C2×Dic3—21no—
307C2×Dic3—64no—
308C2×Dic3—62no—
309C2×Dic3—62no—
310C2×Dic3—64no—
311C2×Dic3—62no—
312C2×Dic3—62no—
313C2×Dic3—122no—
314C2×Dic3—121no—
315C2×Dic3—121no—
316C2×Dic3—122no—
317C2×Dic3—121no—
318C2×Dic3—121no—
319C2×Dic3—122no—
320C2×Dic3—122no—
321C2×Dic3—121no—
322C2×Dic3—121no—
323C2×Dic3—121no—
324C2×Dic3—121no—
325D12—41no—
326C4×D3—81no—
327Dic6—41no—
328Dic6—62no—
329Dic6—62no—
330Dic6—62no—
331Dic6—62no—
332Dic6—122no—
333Dic6—122no—
334Dic6—121no—
335Dic6—121no—
336Dic6—121no—
337Dic6—121no—
338Dic6—122no—
339Dic6—122no—
340C3×C8—121no—
341C3×C8—121no—
342C3⋊C8—41no—
343C3⋊C8—41no—
344C2×C32—21no—
345C2×C32—21no—
346C2×C32#45211yescharacteristic
347C2×C32#45611yescharacteristic
348C2×C32B(4,𝔽2)11yescharacteristic
349C3×D3—81no—
350C2×Q8—31no—
351C2×Q8—181no—
352C2×Q8—181no—
353C2×Q8—362no—
354C2×D4—31no—
355C2×D4—61no—
356C22×C4—61no—
357C22×C4—181no—
358C22×C4—181no—
359C22×C4#62611yescharacteristic
360C22×C4#62611yescharacteristic
361C22×C4C2×D3211yescharacteristic
362Q16—362no—
363SD16—362no—
364C2×C8—61no—
365C2×C8—61no—
366C4⋊C4—21no—
367C4⋊C4—21no—
368C4⋊C4—31no—
369C4⋊C4—31no—
370C4⋊C4—61no—
371C4⋊C4—61no—
372C4⋊C4—61no—
373C4⋊C4—61no—
374C4⋊C4—362no—
375C22⋊C4—61no—
376C22⋊C4—61no—
377C22⋊C4—61no—
378C22⋊C4—61no—
379C22⋊C4—61no—
380C42—61no—
381C22×C3—22no—
382C22×C3—22no—
383C22×C3—21no—
384C22×C3—21no—
385C22×C3—21no—
386C22×C3—21no—
387C22×C3—21no—
388C22×C3—21no—
389C22×C3—21no—
390C22×C3—121no—
391C22×C3—121no—
392C22×C3—121no—
393C22×C3#88211yescharacteristic
394C22×C3#90411yescharacteristic
395C22×C3#90911yescharacteristic
396C22×C3#95011yescharacteristic
397C22×C3#95111yescharacteristic
398C22×C3#95311yescharacteristic
399C2×D3—41no—
400C2×D3—41no—
401C2×D3—41no—
402C3×C4—21no—
403C3×C4—21no—
404C3×C4—21no—
405C3×C4—21no—
406C3×C4—41no—
407C3×C4—41no—
408C3×C4—42no—
409C3×C4—41no—
410C3×C4—41no—
411C3×C4—41no—
412C3×C4—41no—
413C3×C4—81no—
414C3×C4—121no—
415C3×C4—121no—
416C3×C4—121no—
417Dic3—41no—
418Dic3—41no—
419Dic3—41no—
420Dic3—124no—
421Dic3—124no—
422Dic3—122no—
423Dic3—122no—
424Dic3—122no—
425Dic3—122no—
426C32#160311yescharacteristic, complemented, Sylow
427C23—61no—
428C23C2×#62611yescharacteristic
429Q8—121no—
430Q8—182no—
431Q8—182no—
432Q8—361no—
433Q8—361no—
434D4—121no—
435D4—121no—
436D4—121no—
437C2×C4—21no—
438C2×C4—21no—
439C2×C4—21no—
440C2×C4—21no—
441C2×C4—41no—
442C2×C4—41no—
443C2×C4—61no—
444C2×C4—61no—
445C2×C4—61no—
446C2×C4—182no—
447C2×C4—182no—
448C2×C4—241no—
449C2×C4—361no—
450C2×C4—361no—
451C2×C4—361no—
452C2×C4—361no—
453C2×C4D3×#6711yescharacteristic
454C2×C4D3×#6711yescharacteristic
455C8—121no—
456C8—121no—
457C2×C3—22no—
458C2×C3—22no—
459C2×C3—21no—
460C2×C3—21no—
461C2×C3—21no—
462C2×C3—21no—
463C2×C3—21no—
464C2×C3—21no—
465C2×C3—21no—
466C2×C3—241no—
467C2×C3#473311yescharacteristic
468C2×C3#474111yescharacteristic
469C2×C3#475211yescharacteristic
470C2×C3#523911yescharacteristic
471C2×C3#524411yescharacteristic
472C2×C3#524611yescharacteristic
473D3—81no—
474C22—21no—
475C22—21no—
476C22—121no—
477C22—121no—
478C22—121no—
479C22#6382911yescharacteristic
480C22#6383111yescharacteristic
481C22#6397711yescharacteristic
482C4—21no—
483C4—21no—
484C4—41no—
485C4—41no—
486C4—121no—
487C4—121no—
488C4—121no—
489C4—362no—
490C4—362no—
491C3—21no—
492C3#6813211yescharacteristic, complemented
493C3#7188911yescharacteristic, complemented
494C2—21no—
495C2—21no—
496C2—241no—
497C2#1059117311yescharacteristic
498C2#1059153111yescharacteristic
499C2#1059164911yescharacteristic
subgroupG/H
centerC22#63977
commutator, cosocleC22×C32×C4C23
FrattiniC22×C4C2×D32
FittingC2×C32×C4⋊C4C22
socleC22×C32#120
prime radicalC3×#930C22
hypercenterC2×C4⋊C4D32
hypocenterC32#1603
LCSG ▷ C22×C32×C4 ▷ C22×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C4⋊C4

Complements

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

NH ≅ G/Ntype
2. #10592678C2semidirect
3. #10591190C2semidirect
5. C3×#4528C2semidirect
6. #10589152C2semidirect
41. #4528D3semidirect
426. C32#1603semidirect
492. C3#68132semidirect
493. C3#71889semidirect

Maximal subgroups

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

subgroupindex
C3×#55152
#105926782
#105911902
#105911812
C3×#45282
#105891522
#105891502
#718893
#681323