Finite Group Databasebeta

← #11778373

Subgroups — #11778373

Order 1152.

516 conjugacy classes of subgroups; only the 82 normal subgroups are shown.

normal subgroups only

This group has 516 conjugacy classes of subgroups — too many to draw. Only its 82 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#10594812C211yesmaximal, characteristic
2C3×#4739C211yesmaximal, characteristic
3#10591344C211yesmaximal, characteristic
4#10591186C211yesmaximal, characteristic
5#10589333C211yesmaximal, characteristic
6C3×#4469C211yesmaximal, characteristic
7#10589152C211yesmaximal, characteristic
8#70983—31nomaximal
9#68139—31nomaximal
10C22×C3×Dic6C2211yescharacteristic
11#64133C2211yescharacteristic
12C3×#924C2211yescharacteristic
13C2×C3×Dic3⋊C4C2211yescharacteristic
14C2×C3×Dic12—21no—
15C2×#3724—21no—
16#63964—21no—
17#63955—21no—
18#63846—21no—
19#63845—21no—
20#63840—21no—
21#63839—21no—
22C2×#3719—21no—
23C32×C22⋊C8C2211yescharacteristic
24#63658C2211yescharacteristic
25C3×#830C2211yescharacteristic
26C3×#816—21no—
27#63579—21no—
28#63566—21no—
29#5623—31no—
30#5500—31no—
31C3×#451—31no—
32#5230—31no—
33#5228—31no—
34#4979—31no—
35#4739—31no—
36#4739D311yescharacteristic
37C3×#324—31no—
38#4538—31no—
39#4469D311yescharacteristic
40#4467—31no—
41#4467—31no—
42#4467—31no—
43#4467—61no—
44C22×C32×C4C2311yescharacteristic
45C22×C3⋊Dic3—21no—
46C2×#634D411yescharacteristic
47C22×C3×Dic3—21no—
48C22×C3×Dic3D411yescharacteristic
49C22×C3×Dic3D411yescharacteristic
50C2×C3×Dic6—21no—
51C2×C3×Dic6—21no—
52C2×C3×Dic6—42no—
53C2×C3×Dic6D411yescharacteristic
54C2×#627—21no—
55C2×C32×C8—21no—
56#3757—21no—
57C4⋊(C3⋊Dic3)D411yescharacteristic
58#3750—21no—
59C3×#217—21no—
60C3×C4⋊Dic3D411yescharacteristic
61C3×Dic3⋊C4—21no—
62C3×Dic3⋊C4—21no—
63C3×Dic3⋊C4—21no—
64C2×C3×C3⋊C8—21no—
65C3×Dic12—42no—
66#3724—21no—
67#3724—42no—
68Dic3⋊Dic3—21no—
69Dic3⋊Dic3—21no—
70Dic3⋊Dic3—21no—
71Dic3⋊Dic3—21no—
72Dic32—21no—
73Dic32—21no—
74#3719—42no—
75#1605—91noSylow
76C22×C3×Q8—31no—
77C22×Dic6C2×D311yescharacteristic
78C2×C3×Q16—61no—
79C3×C22⋊Q8—31no—
80C2×C3×C4⋊C4—31no—
81#944—61no—
82C2×#216—61no—
83#926—61no—
84#924—31no—
85#924—31no—
86#924—61no—
87#924—61no—
88#924C2×D311yescharacteristic
89C2×Dic3⋊C4—61no—
90C2×Dic3⋊C4—61no—
91C2×Dic3⋊C4C2×D311yescharacteristic
92C2×Dic12—21no—
93C2×Dic12—61no—
94#890—61no—
95#890—61no—
96#889—61no—
97#889—61no—
98#888—61no—
99#888—61no—
100#888—61no—
101#878—61no—
102#877—61no—
103C3×#103—61no—
104C3×C22⋊C8—21no—
105C3×C22⋊C8—31no—
106C3×C22⋊C8C2×D311yescharacteristic
107C3×C22⋊C8C2×D311yescharacteristic
108#835—61no—
109C3⋊#95—31no—
110C3⋊#95—31no—
111C3⋊#95—61no—
112C3⋊#95—61no—
113C3⋊#95—61no—
114#830C2×D311yescharacteristic
115#816—21no—
116#816—61no—
117C23×C32C2×D411yescharacteristic
118C2×C32×C4—41no—
119C2×C32×C4C2×D411yescharacteristic
120C2×C32×C4C2×D411yescharacteristic
121C2×C3⋊Dic3—22no—
122C2×C3⋊Dic3—21no—
123C2×C3⋊Dic3—21no—
124C2×C3⋊Dic3—41no—
125C2×C3⋊Dic3—41no—
126#634—41no—
127C2×C3×Dic3—21no—
128C2×C3×Dic3—21no—
129C2×C3×Dic3—22no—
130C2×C3×Dic3—21no—
131C2×C3×Dic3—21no—
132C2×C3×Dic3—21no—
133C2×C3×Dic3—41no—
134C2×C3×Dic3—41no—
135C2×C3×Dic3—41no—
136C2×C3×Dic3Q1612yescomplemented
137C3×Dic6—22no—
138C3×Dic6—22no—
139C3×Dic6—41no—
140C3×Dic6—41no—
141C3×Dic6—41no—
142#627—81no—
143C32×C8—41no—
144C3×C3⋊C8—41no—
145#544—91no—
146#451—31no—
147#451—91no—
148#395—91no—
149#328—91no—
150#328—91no—
151#324—31no—
152C2×C3×Q8—31no—
153C2×C3×Q8—61no—
154C2×C3×Q8—61no—
155C2×C3×Q8—122no—
156C22×C3×C4—21no—
157C22×C3×C4—31no—
158C22×C3×C4—31no—
159C22×C3×C4—61no—
160C22×C3×C4C22×D311yescharacteristic
161C22×C3×C4C22×D311yescharacteristic
162C22×Dic3—21no—
163C22×Dic3—61no—
164C22×Dic3—61no—
165C22×Dic3—121no—
166C22×Dic3D1211yescharacteristic
167C22×Dic3D1211yescharacteristic
168C2×Dic6—21no—
169C2×Dic6—21no—
170C2×Dic6—31no—
171C2×Dic6—31no—
172C2×Dic6—42no—
173C2×Dic6—61no—
174C2×Dic6—61no—
175C2×Dic6—61no—
176C2×Dic6#6711yescharacteristic
177C3×Q16—122no—
178C2×C3×C8—21no—
179C2×C3×C8—21no—
180C2×C3×C8—41no—
181C2×C3×C8—61no—
182C3×C4⋊C4—31no—
183C3×C4⋊C4—61no—
184C3×C4⋊C4—61no—
185C3×C4⋊C4—61no—
186C3×C22⋊C4—61no—
187#217—21no—
188#217—61no—
189#217—61no—
190#217—121no—
191#216—122no—
192C4⋊Dic3—31no—
193C4⋊Dic3—31no—
194C4⋊Dic3—61no—
195C4⋊Dic3—61no—
196C4⋊Dic3—61no—
197C4⋊Dic3—61no—
198C4⋊Dic3—61no—
199C4⋊Dic3#6711yescharacteristic
200Dic3⋊C4—21no—
201Dic3⋊C4—21no—
202Dic3⋊C4—21no—
203Dic3⋊C4—61no—
204Dic3⋊C4—61no—
205Dic3⋊C4—61no—
206Dic3⋊C4—61no—
207Dic3⋊C4—61no—
208Dic3⋊C4—61no—
209Dic3⋊C4—61no—
210Dic3⋊C4—61no—
211Dic3⋊C4—121no—
212Dic3⋊C4—122no—
213Dic3⋊C4—122no—
214C4×Dic3—61no—
215C4×Dic3—61no—
216C4×Dic3—61no—
217C4×Dic3—61no—
218C2×C3⋊C8—21no—
219Dic12—42no—
220Dic12—122no—
221C22×C32—21no—
222C22×C32—21no—
223C22×C32#12011yescharacteristic
224C22×C32C2×Q1611yescharacteristic
225C22×C32#13711yescharacteristic
226C32×C4—21no—
227C32×C4—21no—
228C3⋊Dic3—42no—
229C3⋊Dic3—41no—
230C3⋊Dic3—41no—
231C3×Dic3—22no—
232C3×Dic3—41no—
233C3×Dic3—41no—
234C3×Dic3—41no—
235C3×Dic3—42no—
236C22×Q8—31no—
237C2×Q16—61no—
238C2×Q16—181no—
239C4⋊Q8—181no—
240C4⋊Q8—181no—
241#125—181no—
242#125—181no—
243C22⋊Q8—31no—
244C22⋊Q8—91no—
245C22⋊Q8—181no—
246#117—181no—
247C2×C4⋊C4—31no—
248C2×C4⋊C4—181no—
249#103—61no—
250#103—181no—
251C22⋊C8—31no—
252C22⋊C8D3211yescharacteristic
253#95—91no—
254#95—181no—
255C23×C3—21no—
256C23×C3C2×D1211yescharacteristic
257C23×C3D3×D411yescharacteristic
258C3×Q8—62no—
259C3×Q8—62no—
260C3×Q8—121no—
261C3×Q8—121no—
262C3×Q8—121no—
263C2×C3×C4—21no—
264C2×C3×C4—21no—
265C2×C3×C4—32no—
266C2×C3×C4—41no—
267C2×C3×C4—41no—
268C2×C3×C4—61no—
269C2×C3×C4—61no—
270C2×C3×C4—62no—
271C2×C3×C4—61no—
272C2×C3×C4—61no—
273C2×C3×C4—61no—
274C2×C3×C4—81no—
275C2×C3×C4—121no—
276C2×C3×C4—121no—
277C2×C3×C4—121no—
278C2×C3×C4D3×D411yescharacteristic
279C2×C3×C4D3×D411yescharacteristic
280C2×C3×C4D3×D411yescharacteristic
281C2×C3×C4C2×#6711yescharacteristic
282C2×Dic3—21no—
283C2×Dic3—21no—
284C2×Dic3—22no—
285C2×Dic3—21no—
286C2×Dic3—21no—
287C2×Dic3—21no—
288C2×Dic3—41no—
289C2×Dic3—41no—
290C2×Dic3—41no—
291C2×Dic3—62no—
292C2×Dic3—62no—
293C2×Dic3—61no—
294C2×Dic3—61no—
295C2×Dic3—61no—
296C2×Dic3—61no—
297C2×Dic3—121no—
298C2×Dic3—121no—
299C2×Dic3—122no—
300C2×Dic3—121no—
301C2×Dic3—121no—
302C2×Dic3—121no—
303C2×Dic3—121no—
304C2×Dic3—241no—
305C2×Dic3—241no—
306C2×Dic3Dic1212yescomplemented
307Dic6—22no—
308Dic6—22no—
309Dic6—41no—
310Dic6—41no—
311Dic6—41no—
312Dic6—121no—
313Dic6—121no—
314Dic6—241no—
315Dic6—241no—
316Dic6—241no—
317C3×C8—41no—
318C3×C8—41no—
319C3×C8—81no—
320C3×C8—121no—
321C3⋊C8—41no—
322C2×C32—21no—
323C2×C32—21no—
324C2×C32#45111yescharacteristic
325C2×C32#45611yescharacteristic
326C2×C32B(4,𝔽2)11yescharacteristic
327C2×Q8—31no—
328C2×Q8—61no—
329C2×Q8—61no—
330C2×Q8—91no—
331C2×Q8—122no—
332C2×Q8—181no—
333C22×C4—31no—
334C22×C4—31no—
335C22×C4—61no—
336C22×C4—181no—
337C22×C4C2×D3211yescharacteristic
338Q16—122no—
339Q16—362no—
340C2×C8—21no—
341C2×C8—61no—
342C4⋊C4—31no—
343C4⋊C4—61no—
344C4⋊C4—61no—
345C4⋊C4—61no—
346C4⋊C4—91no—
347C4⋊C4—181no—
348C4⋊C4—181no—
349C4⋊C4—181no—
350C4⋊C4—181no—
351C4⋊C4—181no—
352C4⋊C4—181no—
353C4⋊C4—362no—
354C22⋊C4—61no—
355C22⋊C4—181no—
356C42—181no—
357C42—181no—
358C22×C3—21no—
359C22×C3—21no—
360C22×C3—21no—
361C22×C3—21no—
362C22×C3—21no—
363C22×C3—21no—
364C22×C3—21no—
365C22×C3—41no—
366C22×C3—41no—
367C22×C3#88211yescharacteristic
368C22×C3C2×Dic1211yescharacteristic
369C22×C3#90911yescharacteristic
370C22×C3D3×Q1611yescharacteristic
371C22×C3#91811yescharacteristic
372C22×C3#93711yescharacteristic
373C3×C4—21no—
374C3×C4—21no—
375C3×C4—21no—
376C3×C4—21no—
377C3×C4—41no—
378C3×C4—41no—
379C3×C4—62no—
380C3×C4—121no—
381C3×C4—122no—
382C3×C4—121no—
383C3×C4—121no—
384Dic3—22no—
385Dic3—41no—
386Dic3—41no—
387Dic3—42no—
388Dic3—41no—
389Dic3—122no—
390Dic3—122no—
391Dic3—121no—
392Dic3—121no—
393Dic3—121no—
394Dic3—121no—
395Dic3—241no—
396Dic3—241no—
397Dic3—242no—
398C32#160511yescharacteristic, complemented, Sylow
399C23D3×D1211yescharacteristic
400Q8—62no—
401Q8—62no—
402Q8—121no—
403Q8—121no—
404Q8—121no—
405Q8—361no—
406Q8—721no—
407C2×C4—32no—
408C2×C4—41no—
409C2×C4—61no—
410C2×C4—61no—
411C2×C4—62no—
412C2×C4—61no—
413C2×C4—61no—
414C2×C4—61no—
415C2×C4—121no—
416C2×C4—121no—
417C2×C4—121no—
418C2×C4—182no—
419C2×C4—181no—
420C2×C4—181no—
421C2×C4—361no—
422C2×C4—361no—
423C2×C4#380211yescharacteristic
424C2×C4D3×#6711yescharacteristic
425C8—41no—
426C8—121no—
427C2×C3—21no—
428C2×C3—21no—
429C2×C3—21no—
430C2×C3—21no—
431C2×C3—21no—
432C2×C3—21no—
433C2×C3—21no—
434C2×C3—41no—
435C2×C3—41no—
436C2×C3#473911yescharacteristic
437C2×C3#474111yescharacteristic
438C2×C3#475211yescharacteristic
439C2×C3#503211yescharacteristic
440C2×C3#518611yescharacteristic
441C2×C3#520511yescharacteristic
442C22—21no—
443C22—21no—
444C22D3×Dic1211yescharacteristic
445C22#6380111yescharacteristic
446C22#6392211yescharacteristic
447C4—21no—
448C4—21no—
449C4—62no—
450C4—121no—
451C4—122no—
452C4—121no—
453C4—121no—
454C4—362no—
455C4—361no—
456C4—361no—
457C3—21no—
458C3#6813911yescharacteristic, complemented
459C3#7098311yescharacteristic, complemented
460C2—21no—
461C2—21no—
462C2#1059040711yescharacteristic
463C2#1059094911yescharacteristic
464C2#1059101811yescharacteristic
subgroupG/H
centerC22#63922
commutator, cosocleC22×C32×C4C23
FrattiniC22×C4C2×D32
FittingC32×C22⋊C8C22
socleC22×C32#120
prime radicalC23×C32C2×D4
hypercenterC22⋊C8D32
hypocenterC32#1605
LCSG ▷ C22×C32×C4 ▷ C22×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22⋊C8

Complements

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

NH ≅ G/Ntype
136. C2×C3×Dic3Q16semidirect
306. C2×Dic3Dic12semidirect
398. C32#1605semidirect
458. C3#68139semidirect
459. C3#70983semidirect

Maximal subgroups

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

subgroupindex
#105948122
C3×#47392
#105913442
#105911862
#105893332
C3×#44692
#105891522
#709833
#681393