Finite Group Databasebeta

← #11778302

Subgroups — #11778302

Order 1152.

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

normal subgroups only

This group has 528 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#10594973C211yesmaximal, characteristic
2C3×#4656C211yesmaximal, characteristic, complemented
3#10591186C211yesmaximal, characteristic, complemented
4#10591171C211yesmaximal, characteristic
5#10589318C211yesmaximal, characteristic, complemented
6C3×#4451C211yesmaximal, characteristic
7#10589147C211yesmaximal, characteristic, complemented
8#69705—31nomaximal
9#68294—31nomaximal
10C22×C3×Dic6C2211yescharacteristic
11#64133C2211yescharacteristic
12C3×#930C2211yescharacteristic
13C2×C3×C4⋊Dic3—21no—
14C2×C3×Dic3⋊C4C2211yescharacteristic
15Dic3×#67—21no—
16#63961—21no—
17#63896—21no—
18#63884—21no—
19#63861—21no—
20#63847—21no—
21C2×#3719—21no—
22C2×#3715—21no—
23C32×#95C2211yescharacteristic
24#63657C2211yescharacteristic
25C3×C3⋊#95—21no—
26C3×#830C2211yescharacteristic
27#63566—21no—
28#63565—21no—
29#5602—31no—
30#5515—31no—
31C3×#395—31no—
32#5228—31no—
33#5227—31no—
34#5040—31no—
35#4739—31no—
36#4656D311yescharacteristic, complemented
37C3×#327—31no—
38#4528—31no—
39#4469—31no—
40#4452—31no—
41#4452—31no—
42#4452—61no—
43#4451D311yescharacteristic
44C22×C32×C4—21no—
45C22×C32×C4C2311yescharacteristic
46C2×#634D411yescharacteristic
47C2×C3×#67—21no—
48C22×C3×Dic3—21no—
49C22×C3×Dic3D411yescharacteristic
50C22×C3×Dic3D411yescharacteristic
51C2×C3×D12D411yescharacteristic
52C2×C3×Dic6—21no—
53C2×C3×Dic6—21no—
54C2×C3×Dic6—42no—
55C2×D3×Dic3—21no—
56#3757—21no—
57C4⋊(C3⋊Dic3)D411yescharacteristic
58#3750—21no—
59C2×C3⋊(C3⋊C8)—21no—
60C3×(C2×D3)⋊C4—21no—
61C3×C4⋊Dic3—42no—
62C3×C4⋊Dic3D411yescharacteristic
63C3×Dic3⋊C4—21no—
64C3×Dic3⋊C4—21no—
65C2×C3×C3⋊C8—21no—
66#3724—21no—
67#3724—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#1603—91noSylow
76C22×C3×Q8—31no—
77C22×Dic6C2×D311yescharacteristic
78C3×#121—31no—
79C2×C3×C4⋊C4—31no—
80C2×C3×C4⋊C4—61no—
81C2×#216—61no—
82C2×#215—61no—
83#935—61no—
84#935—61no—
85D4×Dic3—61no—
86C2×#214—61no—
87#930C2×D311yescharacteristic
88#929—61no—
89C4×#67—61no—
90C2×C4⋊Dic3—21no—
91#924—31no—
92#924—31no—
93#924—61no—
94C2×Dic3⋊C4C2×D311yescharacteristic
95C2×Dic12—61no—
96#898—61no—
97#896—61no—
98#894—61no—
99#889—61no—
100#889—61no—
101#879—61no—
102#878—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—
119C2×C32×C4—22no—
120C2×C32×C4—41no—
121C2×C32×C4—41no—
122C2×C32×C4—41no—
123C2×C32×C4C2×D411yescharacteristic
124C2×C32×C4C2×D411yescharacteristic
125C2×C3⋊Dic3—21no—
126C2×C3⋊Dic3—21no—
127#634—41no—
128C3×#67—41no—
129C3×#67—41no—
130C2×C3×Dic3—22no—
131C2×C3×Dic3—21no—
132C2×C3×Dic3—21no—
133C2×C3×Dic3—21no—
134C2×C3×Dic3—21no—
135C2×C3×Dic3—21no—
136C2×C3×Dic3—41no—
137C2×C3×Dic3—41no—
138C2×C3×Dic3—41no—
139C3×D12—41no—
140C3×Dic6—22no—
141C3×Dic6—22no—
142C3×Dic6—41no—
143C3×Dic6—41no—
144D3×Dic3—81no—
145C3⋊(C3⋊C8)—41no—
146C3×C3⋊C8—41no—
147#539—91no—
148#451—91no—
149#448—91no—
150#395—31no—
151#328—91no—
152#327—31no—
153#324—91no—
154C2×C3×Q8—61no—
155C2×C3×Q8—61no—
156C2×C3×Q8—122no—
157C2×C3×D4—31no—
158C2×C3×D4—61no—
159C22×C3×C4—21no—
160C22×C3×C4—21no—
161C22×C3×C4—21no—
162C22×C3×C4—31no—
163C22×C3×C4—31no—
164C22×C3×C4—41no—
165C22×C3×C4—61no—
166C22×C3×C4C22×D311yescharacteristic
167C22×C3×C4C22×D311yescharacteristic
168C2×#67—21no—
169C22×Dic3—21no—
170C22×Dic3—61no—
171C22×Dic3#6711yescharacteristic
172C22×Dic3#6711yescharacteristic
173C2×D12D1211yescharacteristic
174C2×C4×D3—61no—
175C2×Dic6—21no—
176C2×Dic6—21no—
177C2×Dic6—31no—
178C2×Dic6—31no—
179C2×Dic6—42no—
180C2×Dic6—61no—
181C2×C3×C8—61no—
182C3×C4⋊C4—31no—
183C3×C4⋊C4—61no—
184C3×C4⋊C4—61no—
185C3×C4⋊C4—122no—
186C3×C22⋊C4—61no—
187#217—61no—
188#217—61no—
189#217—61no—
190#217—61no—
191#217—61no—
192#217—121no—
193#216—122no—
194#215—122no—
195#214—122no—
196(C2×D3)⋊C4—21no—
197(C2×D3)⋊C4—61no—
198(C2×D3)⋊C4—61no—
199(C2×D3)⋊C4—61no—
200C4⋊Dic3—31no—
201C4⋊Dic3—31no—
202C4⋊Dic3—42no—
203C4⋊Dic3—61no—
204C4⋊Dic3—61no—
205C4⋊Dic3D1211yescharacteristic
206Dic3⋊C4—21no—
207Dic3⋊C4—21no—
208Dic3⋊C4—61no—
209Dic3⋊C4—61no—
210Dic3⋊C4—61no—
211Dic3⋊C4—61no—
212Dic3⋊C4—61no—
213Dic3⋊C4—61no—
214Dic3⋊C4—61no—
215Dic3⋊C4—121no—
216C4×Dic3—61no—
217C4×Dic3—61no—
218C2×C3⋊C8—21no—
219C2×C3⋊C8—61no—
220C2×C3⋊C8—61no—
221C2×C3⋊C8—121no—
222Dic12—122no—
223C22×C32—21no—
224C22×C32—21no—
225C22×C32#12011yescharacteristic
226C22×C32#13511yescharacteristic
227C22×C32#13711yescharacteristic
228C2×C3×D3—41no—
229C2×C3×D3—41no—
230C2×C3×D3—41no—
231C32×C4—21no—
232C32×C4—21no—
233C32×C4—42no—
234C3⋊Dic3—41no—
235C3⋊Dic3—41no—
236C3×Dic3—41no—
237C3×Dic3—41no—
238C3×Dic3—41no—
239C3×Dic3—42no—
240C22×Q8—31no—
241C2×Q16—181no—
242C2×SD16—181no—
243#126—181no—
244#125—181no—
245#123—181no—
246#123—181no—
247C22⋊Q8—91no—
248C22⋊Q8—181no—
249#121—31no—
250C4×D4—181no—
251C2×C4⋊C4—31no—
252C2×C4⋊C4—61no—
253#103—181no—
254#103—181no—
255C22⋊C8—31no—
256C22⋊C8—91no—
257#95—61no—
258#95D3211yescharacteristic
259C23×C3—21no—
260C23×C3—61no—
261C23×C3D3×D411yescharacteristic
262C23×C3C2×#6711yescharacteristic
263C22×D3—21no—
264C3×Q8—62no—
265C3×Q8—62no—
266C3×Q8—121no—
267C3×Q8—121no—
268C3×D4—121no—
269C3×D4—121no—
270C3×D4—121no—
271C2×C3×C4—22no—
272C2×C3×C4—22no—
273C2×C3×C4—21no—
274C2×C3×C4—21no—
275C2×C3×C4—42no—
276C2×C3×C4—41no—
277C2×C3×C4—41no—
278C2×C3×C4—41no—
279C2×C3×C4—41no—
280C2×C3×C4—41no—
281C2×C3×C4—41no—
282C2×C3×C4—62no—
283C2×C3×C4—61no—
284C2×C3×C4—61no—
285C2×C3×C4—61no—
286C2×C3×C4—61no—
287C2×C3×C4—61no—
288C2×C3×C4—81no—
289C2×C3×C4—81no—
290C2×C3×C4—81no—
291C2×C3×C4—121no—
292C2×C3×C4—121no—
293C2×C3×C4—121no—
294C2×C3×C4C2×D1211yescharacteristic
295C2×C3×C4D3×D411yescharacteristic
296C2×C3×C4D3×D411yescharacteristic
297C2×C3×C4D3×D411yescharacteristic
298#67—41no—
299#67—41no—
300C2×Dic3—22no—
301C2×Dic3—21no—
302C2×Dic3—21no—
303C2×Dic3—21no—
304C2×Dic3—21no—
305C2×Dic3—21no—
306C2×Dic3—41no—
307C2×Dic3—41no—
308C2×Dic3—41no—
309C2×Dic3—61no—
310C2×Dic3—61no—
311C2×Dic3—61no—
312C2×Dic3—61no—
313C2×Dic3—121no—
314C2×Dic3—121no—
315C2×Dic3—241no—
316D12—41no—
317C4×D3—241no—
318Dic6—22no—
319Dic6—22no—
320Dic6—41no—
321Dic6—41no—
322Dic6—121no—
323Dic6—121no—
324Dic6—241no—
325C3×C8—121no—
326C3⋊C8—41no—
327C3⋊C8—121no—
328C3⋊C8—121no—
329C3⋊C8—241no—
330C2×C32—21no—
331C2×C32—21no—
332C2×C32#45211yescharacteristic
333C2×C32#45611yescharacteristic
334C2×C32B(4,𝔽2)11yescharacteristic
335C3×D3—81no—
336C2×Q8—61no—
337C2×Q8—61no—
338C2×Q8—91no—
339C2×Q8—122no—
340C2×D4—31no—
341C2×D4—61no—
342C22×C4—21no—
343C22×C4—31no—
344C22×C4—31no—
345C22×C4—61no—
346C22×C4—181no—
347C22×C4C2×D3211yescharacteristic
348Q16—362no—
349SD16—362no—
350C2×C8—61no—
351C2×C8—181no—
352C4⋊C4—31no—
353C4⋊C4—61no—
354C4⋊C4—61no—
355C4⋊C4—91no—
356C4⋊C4—122no—
357C4⋊C4—181no—
358C4⋊C4—181no—
359C4⋊C4—181no—
360C4⋊C4—181no—
361C22⋊C4—61no—
362C22⋊C4—181no—
363C22⋊C4—181no—
364C22⋊C4—181no—
365C22⋊C4—181no—
366C42—181no—
367C22×C3—21no—
368C22×C3—21no—
369C22×C3—21no—
370C22×C3—21no—
371C22×C3—21no—
372C22×C3—21no—
373C22×C3—21no—
374C22×C3—41no—
375C22×C3—41no—
376C22×C3—121no—
377C22×C3—121no—
378C22×C3—121no—
379C22×C3#88211yescharacteristic
380C22×C3#91211yescharacteristic
381C22×C3#91511yescharacteristic
382C22×C3#93711yescharacteristic
383C22×C3#94211yescharacteristic
384C22×C3#95011yescharacteristic
385C2×D3—41no—
386C2×D3—41no—
387C2×D3—41no—
388C3×C4—21no—
389C3×C4—21no—
390C3×C4—21no—
391C3×C4—21no—
392C3×C4—41no—
393C3×C4—41no—
394C3×C4—42no—
395C3×C4—42no—
396C3×C4—82no—
397C3×C4—121no—
398C3×C4—122no—
399C3×C4—121no—
400C3×C4—121no—
401Dic3—42no—
402Dic3—41no—
403Dic3—41no—
404Dic3—41no—
405Dic3—121no—
406Dic3—121no—
407Dic3—121no—
408Dic3—121no—
409Dic3—241no—
410Dic3—241no—
411C32#160311yescharacteristic, complemented, Sylow
412C23—61no—
413C23D3×#6711yescharacteristic
414Q8—62no—
415Q8—62no—
416Q8—121no—
417Q8—121no—
418Q8—361no—
419D4—121no—
420D4—121no—
421D4—121no—
422C2×C4—22no—
423C2×C4—41no—
424C2×C4—41no—
425C2×C4—41no—
426C2×C4—62no—
427C2×C4—61no—
428C2×C4—61no—
429C2×C4—61no—
430C2×C4—61no—
431C2×C4—61no—
432C2×C4—121no—
433C2×C4—121no—
434C2×C4—121no—
435C2×C4—181no—
436C2×C4—181no—
437C2×C4—721no—
438C2×C4D3×D1211yescharacteristic
439C2×C4#380211yescharacteristic
440C8—121no—
441C8—361no—
442C2×C3—21no—
443C2×C3—21no—
444C2×C3—21no—
445C2×C3—21no—
446C2×C3—21no—
447C2×C3—21no—
448C2×C3—21no—
449C2×C3—41no—
450C2×C3—41no—
451C2×C3—241no—
452C2×C3#474111yescharacteristic
453C2×C3#478311yescharacteristic
454C2×C3#482611yescharacteristic
455C2×C3#503211yescharacteristic
456C2×C3#504711yescharacteristic
457C2×C3#509511yescharacteristic
458D3—81no—
459C22—21no—
460C22—21no—
461C22—121no—
462C22—121no—
463C22—121no—
464C22#6392211yescharacteristic
465C22#6393311yescharacteristic
466C22#6394611yescharacteristic
467C4—21no—
468C4—21no—
469C4—42no—
470C4—121no—
471C4—121no—
472C4—122no—
473C4—121no—
474C4—361no—
475C4—361no—
476C3—21no—
477C3#6829411yescharacteristic, complemented
478C3#6970511yescharacteristic, complemented
479C2—21no—
480C2—21no—
481C2—241no—
482C2#1059039911yescharacteristic
483C2#1059040711yescharacteristic
484C2#1059061411yescharacteristic
subgroupG/H
centerC22#63922
commutator, cosocleC22×C32×C4C23
FrattiniC22×C4C2×D32
FittingC32×#95C22
socleC22×C32#120
prime radicalC3×#930C22
hypercenter#95D32
hypocenterC32#1603
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×#4656C2semidirect
3. #10591186C2semidirect
5. #10589318C2semidirect
7. #10589147C2semidirect
36. #4656D3semidirect
411. C32#1603semidirect
477. C3#68294semidirect
478. C3#69705semidirect

Maximal subgroups

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

subgroupindex
#105949732
C3×#46562
#105911862
#105911712
#105893182
C3×#44512
#105891472
#697053
#682943