Finite Group Databasebeta

← #11778261

Subgroups — #11778261

Order 1152.

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

normal subgroups only

This group has 552 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#10594971C211yesmaximal, characteristic
2C3×#4673C211yesmaximal, characteristic
3#10591186C211yesmaximal, characteristic, complemented
4#10591185C211yesmaximal, characteristic, complemented
5#10589318C211yesmaximal, characteristic, complemented
6C3×#4452C211yesmaximal, characteristic, complemented
7#10589145C211yesmaximal, characteristic
8#69701—31nomaximal
9#68318—31nomaximal
10C22×C3×Dic6C2211yescharacteristic
11#64133C2211yescharacteristic
12C2×C3×(C2×D3)⋊C4—21no—
13C2×C3×(C2×D3)⋊C4C2211yescharacteristic
14C3×#924C2211yescharacteristic
15D3×#217—21no—
16#63964—21no—
17#63899—21no—
18#63896—21no—
19#63893—21no—
20#63887—21no—
21C2×#3719—21no—
22C2×#3718—21no—
23C32×#95C2211yescharacteristic
24#63657C2211yescharacteristic
25C3×C3⋊#95—21no—
26C3×#830C2211yescharacteristic
27#63566—21no—
28#63565—21no—
29#5634—31no—
30#5483—31no—
31C3×#393—31no—
32#5228—31no—
33#5228—31no—
34#5050—31no—
35#4739—31no—
36#4673D311yescharacteristic
37C3×#328—31no—
38#4525—31no—
39#4468—31no—
40#4452—31no—
41#4452—31no—
42#4452—61no—
43#4452D311yescharacteristic, complemented
44C23×C3×D3D411yescharacteristic
45C22×C32×C4—21no—
46C22×C32×C4C2311yescharacteristic
47C2×#634D411yescharacteristic
48C22×C3×Dic3—21no—
49C22×C3×Dic3D411yescharacteristic
50C2×C3×Dic6—21no—
51C2×C3×Dic6—21no—
52C2×C3×Dic6—42no—
53C2×C3×Dic6D411yescharacteristic
54C2×#627—21no—
55C2×D3×Dic3—21no—
56C2×D3×Dic3—21no—
57#3757—21no—
58C4⋊(C3⋊Dic3)D411yescharacteristic
59#3750—21no—
60C2×C3⋊(C3⋊C8)—21no—
61C3×#217—21no—
62C3×(C2×D3)⋊C4—21no—
63C3×(C2×D3)⋊C4—21no—
64C3×(C2×D3)⋊C4—42no—
65C3×C4⋊Dic3D411yescharacteristic
66C3×Dic3⋊C4—21no—
67C2×C3×C3⋊C8—21no—
68#3724—21no—
69Dic3⋊Dic3—21no—
70Dic3⋊Dic3—21no—
71(C2×D3)⋊Dic3—21no—
72(C2×D3)⋊Dic3—21no—
73#3719—42no—
74#3718—42no—
75#1602—91noSylow
76C22×C3×Q8—31no—
77C22×Dic6C2×D311yescharacteristic
78C3×C22⋊Q8—31no—
79C2×C3×C22⋊C4—31no—
80C2×C3×C22⋊C4—61no—
81C2×#217—61no—
82#946—61no—
83C2×#216—61no—
84C2×#216—61no—
85C2×#216—61no—
86C2×(C2×D3)⋊C4—21no—
87C2×(C2×D3)⋊C4C2×D311yescharacteristic
88#924—31no—
89#924—31no—
90#924—61no—
91#924—61no—
92#924C2×D311yescharacteristic
93C2×Dic12—61no—
94#897—61no—
95#896—61no—
96#896—61no—
97D3×C22⋊C4—61no—
98#878—61no—
99#878—61no—
100#878—61no—
101#878—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—
119C22×C3×D3—21no—
120C22×C3×D3—41no—
121C22×C3×D3—41no—
122C22×C3×D3Q1612yescomplemented
123C2×C32×C4—41no—
124C2×C32×C4—41no—
125C2×C32×C4—41no—
126C2×C32×C4—41no—
127C2×C32×C4C2×D411yescharacteristic
128C2×C32×C4C2×D411yescharacteristic
129C2×C3⋊Dic3—21no—
130C2×C3⋊Dic3—21no—
131#634—41no—
132C2×C3×Dic3—22no—
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#627—81no—
145D3×Dic3—81no—
146D3×Dic3—81no—
147C3⋊(C3⋊C8)—41no—
148C3×C3⋊C8—41no—
149#543—91no—
150#451—91no—
151#451—91no—
152#393—31no—
153#328—31no—
154#328—91no—
155#323—91no—
156C24×C3—31no—
157C23×D3#6711yescharacteristic
158C2×C3×Q8—31no—
159C2×C3×Q8—61no—
160C2×C3×Q8—61no—
161C2×C3×Q8—122no—
162C22×C3×C4—21no—
163C22×C3×C4—21no—
164C22×C3×C4—21no—
165C22×C3×C4—31no—
166C22×C3×C4—41no—
167C22×C3×C4—61no—
168C22×C3×C4C22×D311yescharacteristic
169C22×C3×C4C22×D311yescharacteristic
170C22×Dic3—21no—
171C22×Dic3—61no—
172C22×Dic3—61no—
173C22×Dic3#6711yescharacteristic
174C2×C4×D3—61no—
175C2×C4×D3—61no—
176C2×Dic6—21no—
177C2×Dic6—21no—
178C2×Dic6—31no—
179C2×Dic6—31no—
180C2×Dic6—42no—
181C2×Dic6—61no—
182C2×Dic6—61no—
183C2×Dic6—61no—
184C2×Dic6D1211yescharacteristic
185C2×C3×C8—61no—
186C3×C4⋊C4—31no—
187C3×C4⋊C4—61no—
188C3×C22⋊C4—61no—
189C3×C22⋊C4—61no—
190C3×C22⋊C4—61no—
191C3×C22⋊C4—122no—
192#217—21no—
193#217—61no—
194#217—61no—
195#217—61no—
196#217—61no—
197#217—121no—
198#216—122no—
199#216—122no—
200#216—122no—
201(C2×D3)⋊C4—21no—
202(C2×D3)⋊C4—21no—
203(C2×D3)⋊C4—42no—
204(C2×D3)⋊C4—61no—
205(C2×D3)⋊C4—61no—
206C4⋊Dic3—31no—
207C4⋊Dic3—31no—
208C4⋊Dic3—61no—
209C4⋊Dic3—61no—
210C4⋊Dic3—61no—
211C4⋊Dic3D1211yescharacteristic
212Dic3⋊C4—21no—
213Dic3⋊C4—61no—
214Dic3⋊C4—61no—
215Dic3⋊C4—61no—
216Dic3⋊C4—61no—
217Dic3⋊C4—61no—
218Dic3⋊C4—61no—
219Dic3⋊C4—121no—
220C2×C3⋊C8—21no—
221C2×C3⋊C8—61no—
222C2×C3⋊C8—61no—
223C2×C3⋊C8—121no—
224Dic12—122no—
225C22×C32—21no—
226C22×C32—21no—
227C22×C32#12011yescharacteristic
228C22×C32C2×Q1611yescharacteristic
229C22×C32#13711yescharacteristic
230C2×C3×D3—22no—
231C2×C3×D3—41no—
232C2×C3×D3—41no—
233C2×C3×D3—42no—
234C2×C3×D3—81no—
235C32×C4—21no—
236C32×C4—21no—
237C32×C4—81no—
238C3⋊Dic3—41no—
239C3⋊Dic3—41no—
240C3×Dic3—41no—
241C3×Dic3—41no—
242C3×Dic3—41no—
243C3×Dic3—42no—
244C22×Q8—31no—
245C2×Q16—181no—
246C2×Q16—181no—
247C22⋊Q8—31no—
248C22⋊Q8—91no—
249C22⋊Q8—181no—
250C22⋊Q8—181no—
251C22⋊Q8—181no—
252C22⋊Q8—181no—
253C22⋊Q8—181no—
254C2×C22⋊C4—31no—
255C2×C22⋊C4—61no—
256C2×C22⋊C4—181no—
257#103—181no—
258#103—181no—
259C22⋊C8—31no—
260C22⋊C8—91no—
261#95—61no—
262#95D3211yescharacteristic
263C23×C3—21no—
264C23×C3—32no—
265C23×C3—61no—
266C23×C3—61no—
267C23×C3—121no—
268C23×C3—121no—
269C23×C3D3×D411yescharacteristic
270C23×C3C2×#6711yescharacteristic
271C22×D3—21no—
272C22×D3—21no—
273C22×D3—41no—
274C22×D3—41no—
275C22×D3#21612yescomplemented
276C3×Q8—62no—
277C3×Q8—62no—
278C3×Q8—121no—
279C3×Q8—121no—
280C3×Q8—121no—
281C2×C3×C4—21no—
282C2×C3×C4—21no—
283C2×C3×C4—41no—
284C2×C3×C4—41no—
285C2×C3×C4—41no—
286C2×C3×C4—41no—
287C2×C3×C4—41no—
288C2×C3×C4—41no—
289C2×C3×C4—42no—
290C2×C3×C4—41no—
291C2×C3×C4—41no—
292C2×C3×C4—62no—
293C2×C3×C4—61no—
294C2×C3×C4—61no—
295C2×C3×C4—61no—
296C2×C3×C4—81no—
297C2×C3×C4—81no—
298C2×C3×C4—81no—
299C2×C3×C4—121no—
300C2×C3×C4—121no—
301C2×C3×C4—121no—
302C2×C3×C4C2×D1211yescharacteristic
303C2×C3×C4D3×D411yescharacteristic
304C2×C3×C4D3×D411yescharacteristic
305C2×C3×C4D3×D411yescharacteristic
306C2×Dic3—22no—
307C2×Dic3—21no—
308C2×Dic3—21no—
309C2×Dic3—21no—
310C2×Dic3—41no—
311C2×Dic3—41no—
312C2×Dic3—41no—
313C2×Dic3—61no—
314C2×Dic3—61no—
315C2×Dic3—61no—
316C2×Dic3—61no—
317C2×Dic3—121no—
318C2×Dic3—121no—
319C2×Dic3—241no—
320C2×Dic3—241no—
321C4×D3—241no—
322C4×D3—241no—
323Dic6—22no—
324Dic6—22no—
325Dic6—41no—
326Dic6—41no—
327Dic6—41no—
328Dic6—121no—
329Dic6—121no—
330Dic6—241no—
331Dic6—241no—
332Dic6—241no—
333C3×C8—121no—
334C3⋊C8—41no—
335C3⋊C8—121no—
336C3⋊C8—121no—
337C3⋊C8—241no—
338C2×C32—21no—
339C2×C32—21no—
340C2×C32#45111yescharacteristic
341C2×C32#45511yescharacteristic
342C2×C32B(4,𝔽2)11yescharacteristic
343C3×D3—42no—
344C24—31no—
345C2×Q8—31no—
346C2×Q8—61no—
347C2×Q8—61no—
348C2×Q8—91no—
349C2×Q8—122no—
350C2×Q8—181no—
351C22×C4—21no—
352C22×C4—31no—
353C22×C4—61no—
354C22×C4—181no—
355C22×C4—181no—
356C22×C4C2×D3211yescharacteristic
357Q16—362no—
358Q16—362no—
359C2×C8—61no—
360C2×C8—181no—
361C4⋊C4—31no—
362C4⋊C4—61no—
363C4⋊C4—91no—
364C4⋊C4—181no—
365C4⋊C4—181no—
366C4⋊C4—181no—
367C4⋊C4—181no—
368C22⋊C4—61no—
369C22⋊C4—61no—
370C22⋊C4—61no—
371C22⋊C4—122no—
372C22⋊C4—181no—
373C22⋊C4—181no—
374C22⋊C4—181no—
375C22×C3—21no—
376C22×C3—21no—
377C22×C3—21no—
378C22×C3—21no—
379C22×C3—21no—
380C22×C3—21no—
381C22×C3—21no—
382C22×C3—41no—
383C22×C3—41no—
384C22×C3—62no—
385C22×C3—122no—
386C22×C3—121no—
387C22×C3—121no—
388C22×C3—241no—
389C22×C3#88211yescharacteristic
390C22×C3#91511yescharacteristic
391C22×C3D3×Q1611yescharacteristic
392C22×C3#93711yescharacteristic
393C22×C3C2×#21611yescharacteristic
394C22×C3#95111yescharacteristic
395C2×D3—22no—
396C2×D3—41no—
397C2×D3—41no—
398C2×D3—42no—
399C2×D3—81no—
400C3×C4—21no—
401C3×C4—21no—
402C3×C4—21no—
403C3×C4—21no—
404C3×C4—41no—
405C3×C4—41no—
406C3×C4—81no—
407C3×C4—81no—
408C3×C4—82no—
409C3×C4—122no—
410C3×C4—121no—
411C3×C4—121no—
412C3×C4—121no—
413Dic3—41no—
414Dic3—42no—
415Dic3—41no—
416Dic3—41no—
417Dic3—121no—
418Dic3—121no—
419Dic3—121no—
420Dic3—121no—
421Dic3—241no—
422Dic3—241no—
423C32#160211yescharacteristic, complemented, Sylow
424C23—32no—
425C23—61no—
426C23—61no—
427C23—121no—
428C23—121no—
429C23D3×#6711yescharacteristic
430Q8—62no—
431Q8—62no—
432Q8—121no—
433Q8—121no—
434Q8—121no—
435Q8—361no—
436Q8—721no—
437C2×C4—41no—
438C2×C4—41no—
439C2×C4—41no—
440C2×C4—41no—
441C2×C4—62no—
442C2×C4—61no—
443C2×C4—61no—
444C2×C4—61no—
445C2×C4—121no—
446C2×C4—121no—
447C2×C4—121no—
448C2×C4—181no—
449C2×C4—181no—
450C2×C4—721no—
451C2×C4—721no—
452C2×C4D3×D1211yescharacteristic
453C2×C4#380211yescharacteristic
454C8—121no—
455C8—361no—
456C2×C3—21no—
457C2×C3—21no—
458C2×C3—21no—
459C2×C3—21no—
460C2×C3—21no—
461C2×C3—21no—
462C2×C3—21no—
463C2×C3—41no—
464C2×C3—41no—
465C2×C3—122no—
466C2×C3#474111yescharacteristic
467C2×C3#480911yescharacteristic
468C2×C3#482511yescharacteristic
469C2×C3#503211yescharacteristic
470C2×C3#505011yescharacteristic
471C2×C3#506111yescharacteristic
472D3—42no—
473C22—21no—
474C22—21no—
475C22—62no—
476C22—122no—
477C22—121no—
478C22—121no—
479C22—241no—
480C22#6392211yescharacteristic
481C22#6392911yescharacteristic
482C22D3×#21611yescharacteristic
483C4—21no—
484C4—21no—
485C4—81no—
486C4—121no—
487C4—121no—
488C4—122no—
489C4—121no—
490C4—361no—
491C4—361no—
492C3—21no—
493C3#6831811yescharacteristic, complemented
494C3#6970111yescharacteristic, complemented
495C2—21no—
496C2—21no—
497C2—122no—
498C2#1059039611yescharacteristic
499C2#1059040711yescharacteristic
500C2#1059060411yescharacteristic
subgroupG/H
centerC22#63922
commutator, cosocleC22×C32×C4C23
FrattiniC22×C4C2×D32
FittingC32×#95C22
socleC22×C32#120
prime radicalC23×C3×D3D4
hypercenter#95D32
hypocenterC32#1602
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
3. #10591186C2semidirect
4. #10591185C2semidirect
5. #10589318C2semidirect
6. C3×#4452C2semidirect
43. #4452D3semidirect
122. C22×C3×D3Q16semidirect
275. C22×D3#216semidirect
423. C32#1602semidirect
493. C3#68318semidirect
494. C3#69701semidirect

Maximal subgroups

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

subgroupindex
#105949712
C3×#46732
#105911862
#105911852
#105893182
C3×#44522
#105891452
#697013
#683183