Finite Group Databasebeta

← #11778300

Subgroups — #11778300

Order 1152.

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

normal subgroups only

This group has 533 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#10594980C211yesmaximal, characteristic
2C3×#4656C211yesmaximal, characteristic, complemented
3#10591185C211yesmaximal, characteristic, complemented
4#10591174C211yesmaximal, characteristic
5#10589317C211yesmaximal, characteristic
6C3×#4452C211yesmaximal, characteristic, complemented
7#10589147C211yesmaximal, characteristic, complemented
8#69705—31nomaximal
9#68326—31nomaximal
10C22×C3×Dic6C2211yescharacteristic
11#64139C2211yescharacteristic
12C2×C3×C4⋊Dic3—21no—
13C3×#924C2211yescharacteristic
14C2×C3×Dic3⋊C4C2211yescharacteristic
15#63966—21no—
16#63952—21no—
17#63897—21no—
18#63888—21no—
19#63848—21no—
20#63845—21no—
21C2×#3718—21no—
22C2×#3717—21no—
23C32×#95C2211yescharacteristic
24#63657C2211yescharacteristic
25C3×C3⋊#95—21no—
26C3×#830C2211yescharacteristic
27#63566—21no—
28#63565—21no—
29#5645—31no—
30#5515—31no—
31C3×#395—31no—
32#5228—31no—
33#5227—31no—
34#5050—31no—
35#4738—31no—
36#4656D311yescharacteristic, complemented
37C3×#328—31no—
38#4528—31no—
39#4469—31no—
40#4452D311yescharacteristic, complemented
41#4451—31no—
42#4451—31no—
43#4451—61no—
44C22×C32×C4—21no—
45C22×C32×C4C2311yescharacteristic
46C2×#638—21no—
47C2×C4⋊(C3⋊D3)D411yescharacteristic
48C22×C3×Dic3—21no—
49C22×C3×Dic3D411yescharacteristic
50C22×C3×Dic3D411yescharacteristic
51C2×C3×Dic6—21no—
52C2×C3×Dic6—21no—
53C2×C3×Dic6—42no—
54C2×C3×Dic6D411yescharacteristic
55C2×#624—21no—
56#3752—21no—
57C4⋊(C3⋊Dic3)D411yescharacteristic
58C2×C3⋊(C3⋊C8)—21no—
59C3×#217—21no—
60C3×C4⋊Dic3—42no—
61C3×C4⋊Dic3D411yescharacteristic
62C3×Dic3⋊C4—21no—
63C3×Dic3⋊C4—21no—
64C3×Dic3⋊C4—21no—
65C2×C3×C3⋊C8—21no—
66#3724—21no—
67Dic3⋊Dic3—21no—
68Dic3⋊Dic3—21no—
69#3722—21no—
70#3722—21no—
71#3722—21no—
72Dic32—21no—
73#3718—42no—
74#3717—42no—
75#1603—91noSylow
76C22×C3×Q8—31no—
77C22×Dic6C2×D311yescharacteristic
78C3×C22⋊Q8—31no—
79C2×C3×C4⋊C4—31no—
80C2×C3×C4⋊C4—61no—
81#946—61no—
82C2×#216—61no—
83C2×#216—61no—
84C2×#215—61no—
85#930—31no—
86#930—31no—
87#930—61no—
88#929—61no—
89C4×#67—61no—
90C2×C4⋊Dic3—21no—
91#924C2×D311yescharacteristic
92C2×Dic3⋊C4C2×D311yescharacteristic
93C2×#204—61no—
94#898—61no—
95#898—61no—
96#896—61no—
97#894—61no—
98#894—61no—
99#890—61no—
100#889—61no—
101#886—61no—
102#67⋊C4—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
125#638—41no—
126#638—41no—
127C2×C3⋊Dic3—21no—
128C4⋊(C3⋊D3)—41no—
129C2×C3×Dic3—22no—
130C2×C3×Dic3—21no—
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×Dic6—22no—
140C3×Dic6—22no—
141C3×Dic6—41no—
142C3×Dic6—41no—
143C3×Dic6—41no—
144#624—81no—
145C3⋊(C3⋊C8)—41no—
146C3×C3⋊C8—41no—
147#539—91no—
148#451—91no—
149#448—91no—
150#395—31no—
151#328—31no—
152#327—91no—
153#324—91no—
154C2×C3×Q8—31no—
155C2×C3×Q8—61no—
156C2×C3×Q8—61no—
157C2×C3×Q8—122no—
158C22×C3×C4—21no—
159C22×C3×C4—21no—
160C22×C3×C4—21no—
161C22×C3×C4—31no—
162C22×C3×C4—31no—
163C22×C3×C4—41no—
164C22×C3×C4—61no—
165C22×C3×C4C22×D311yescharacteristic
166C22×C3×C4C22×D311yescharacteristic
167C2×#67—61no—
168C2×#67—61no—
169C2×#67—121no—
170C22×Dic3—21no—
171C22×Dic3#6711yescharacteristic
172C22×Dic3#6711yescharacteristic
173C2×D12—31no—
174C2×D12—31no—
175C2×D12—61no—
176C2×C4×D3—61no—
177C2×C4×D3—61no—
178C2×Dic6—21no—
179C2×Dic6—21no—
180C2×Dic6—42no—
181C2×Dic6D1211yescharacteristic
182C2×C3×C8—61no—
183C3×C4⋊C4—31no—
184C3×C4⋊C4—61no—
185C3×C4⋊C4—61no—
186C3×C4⋊C4—61no—
187C3×C4⋊C4—122no—
188C3×C22⋊C4—61no—
189#217—21no—
190#216—122no—
191#216—122no—
192#215—122no—
193(C2×D3)⋊C4—61no—
194(C2×D3)⋊C4—61no—
195(C2×D3)⋊C4—61no—
196(C2×D3)⋊C4—61no—
197(C2×D3)⋊C4—61no—
198(C2×D3)⋊C4—61no—
199(C2×D3)⋊C4—61no—
200(C2×D3)⋊C4—61no—
201(C2×D3)⋊C4—121no—
202C4⋊Dic3—31no—
203C4⋊Dic3—31no—
204C4⋊Dic3—42no—
205C4⋊Dic3—61no—
206C4⋊Dic3—61no—
207C4⋊Dic3—61no—
208C4⋊Dic3D1211yescharacteristic
209Dic3⋊C4—21no—
210Dic3⋊C4—21no—
211Dic3⋊C4—21no—
212Dic3⋊C4—61no—
213Dic3⋊C4—61no—
214Dic3⋊C4—61no—
215Dic3⋊C4—61no—
216C4×Dic3—61no—
217C4×Dic3—61no—
218C2×C3⋊C8—21no—
219C2×C3⋊C8—61no—
220C2×C3⋊C8—61no—
221C2×C3⋊C8—121no—
222#204—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—31no—
248C22⋊Q8—181no—
249#121—91no—
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×C3D3×D411yescharacteristic
261C23×C3C2×#6711yescharacteristic
262C22×D3—61no—
263C22×D3—61no—
264C22×D3—121no—
265C3×Q8—62no—
266C3×Q8—62no—
267C3×Q8—121no—
268C3×Q8—121no—
269C3×Q8—121no—
270C2×C3×C4—22no—
271C2×C3×C4—22no—
272C2×C3×C4—21no—
273C2×C3×C4—21no—
274C2×C3×C4—42no—
275C2×C3×C4—41no—
276C2×C3×C4—41no—
277C2×C3×C4—41no—
278C2×C3×C4—41no—
279C2×C3×C4—41no—
280C2×C3×C4—41no—
281C2×C3×C4—62no—
282C2×C3×C4—61no—
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—121no—
299#67—121no—
300#67—121no—
301#67—121no—
302#67—241no—
303#67—241no—
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—61no—
315C2×Dic3—61no—
316C2×Dic3—121no—
317D12—121no—
318D12—121no—
319D12—241no—
320C4×D3—241no—
321C4×D3—241no—
322Dic6—22no—
323Dic6—22no—
324Dic6—41no—
325Dic6—41no—
326Dic6—41no—
327C3×C8—121no—
328C3⋊C8—41no—
329C3⋊C8—121no—
330C3⋊C8—121no—
331C3⋊C8—241no—
332C2×C32—21no—
333C2×C32—21no—
334C2×C32#45211yescharacteristic
335C2×C32#45611yescharacteristic
336C2×C32B(4,𝔽2)11yescharacteristic
337C3⋊D3—81no—
338C2×Q8—31no—
339C2×Q8—61no—
340C2×Q8—61no—
341C2×Q8—122no—
342C2×D4—91no—
343C2×D4—181no—
344C22×C4—21no—
345C22×C4—31no—
346C22×C4—31no—
347C22×C4—61no—
348C22×C4—181no—
349C22×C4C2×D3211yescharacteristic
350Q16—362no—
351SD16—362no—
352C2×C8—61no—
353C2×C8—181no—
354C4⋊C4—31no—
355C4⋊C4—61no—
356C4⋊C4—61no—
357C4⋊C4—61no—
358C4⋊C4—91no—
359C4⋊C4—122no—
360C4⋊C4—181no—
361C4⋊C4—181no—
362C4⋊C4—181no—
363C22⋊C4—61no—
364C22⋊C4—181no—
365C22⋊C4—181no—
366C22⋊C4—181no—
367C22⋊C4—181no—
368C42—181no—
369C22×C3—21no—
370C22×C3—21no—
371C22×C3—21no—
372C22×C3—21no—
373C22×C3—21no—
374C22×C3—21no—
375C22×C3—21no—
376C22×C3—41no—
377C22×C3—41no—
378C22×C3#88211yescharacteristic
379C22×C3#91611yescharacteristic
380C22×C3#91811yescharacteristic
381C22×C3#93711yescharacteristic
382C22×C3#94211yescharacteristic
383C22×C3#95011yescharacteristic
384C2×D3—121no—
385C2×D3—121no—
386C2×D3—121no—
387C2×D3—121no—
388C2×D3—121no—
389C2×D3—121no—
390C2×D3—241no—
391C2×D3—241no—
392C2×D3—241no—
393C3×C4—21no—
394C3×C4—21no—
395C3×C4—21no—
396C3×C4—21no—
397C3×C4—41no—
398C3×C4—41no—
399C3×C4—42no—
400C3×C4—42no—
401C3×C4—82no—
402C3×C4—121no—
403C3×C4—122no—
404C3×C4—121no—
405C3×C4—121no—
406C3×C4—121no—
407Dic3—41no—
408Dic3—42no—
409Dic3—41no—
410Dic3—41no—
411Dic3—41no—
412Dic3—121no—
413Dic3—121no—
414Dic3—241no—
415C32#160311yescharacteristic, complemented, Sylow
416C23—181no—
417C23D3×#6711yescharacteristic
418Q8—62no—
419Q8—62no—
420Q8—121no—
421Q8—121no—
422Q8—121no—
423D4—361no—
424D4—361no—
425D4—361no—
426C2×C4—22no—
427C2×C4—41no—
428C2×C4—41no—
429C2×C4—41no—
430C2×C4—62no—
431C2×C4—61no—
432C2×C4—61no—
433C2×C4—61no—
434C2×C4—61no—
435C2×C4—61no—
436C2×C4—61no—
437C2×C4—121no—
438C2×C4—121no—
439C2×C4—121no—
440C2×C4—181no—
441C2×C4—721no—
442C2×C4D3×D1211yescharacteristic
443C2×C4#380211yescharacteristic
444C8—121no—
445C8—361no—
446C2×C3—21no—
447C2×C3—21no—
448C2×C3—21no—
449C2×C3—21no—
450C2×C3—21no—
451C2×C3—21no—
452C2×C3—21no—
453C2×C3—41no—
454C2×C3—41no—
455C2×C3#474111yescharacteristic
456C2×C3#480811yescharacteristic
457C2×C3#482611yescharacteristic
458C2×C3#503211yescharacteristic
459C2×C3#504711yescharacteristic
460C2×C3#509511yescharacteristic
461D3—241no—
462D3—241no—
463D3—481no—
464C22—21no—
465C22—21no—
466C22—361no—
467C22—361no—
468C22—361no—
469C22#6392211yescharacteristic
470C22#6393511yescharacteristic
471C22#6394811yescharacteristic
472C4—21no—
473C4—21no—
474C4—42no—
475C4—121no—
476C4—121no—
477C4—122no—
478C4—121no—
479C4—121no—
480C4—361no—
481C3—21no—
482C3#6832611yescharacteristic, complemented
483C3#6970511yescharacteristic, complemented
484C2—21no—
485C2—21no—
486C2—721no—
487C2#1059039911yescharacteristic
488C2#1059040711yescharacteristic
489C2#1059061611yescharacteristic
subgroupG/H
centerC22#63922
commutator, cosocleC22×C32×C4C23
FrattiniC22×C4C2×D32
FittingC32×#95C22
socleC22×C32#120
prime radical#64139C22
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. #10591185C2semidirect
6. C3×#4452C2semidirect
7. #10589147C2semidirect
36. #4656D3semidirect
40. #4452D3semidirect
415. C32#1603semidirect
482. C3#68326semidirect
483. C3#69705semidirect

Maximal subgroups

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

subgroupindex
#105949802
C3×#46562
#105911852
#105911742
#105893172
C3×#44522
#105891472
#697053
#683263