Finite Group Databasebeta

← #11775580

Subgroups — #11775580

Order 1152.

893 conjugacy classes of subgroups; only the 102 normal subgroups are shown.

normal subgroups only

This group has 893 conjugacy classes of subgroups — too many to draw. Only its 102 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⋊D3×#121C211yesmaximal, characteristic
2#10591355C211yesmaximal, characteristic, complemented
3#10591152C211yesmaximal, characteristic, complemented
4C3×#4537C212yesmaximal, complemented
5#10589151C212yesmaximal, complemented
6#68307—32nomaximal
7C2×D4×C3⋊D3—21no—
8C2×D4×C3⋊D3C411yescharacteristic, complemented
9C22×C4×C3⋊D3C2211yescharacteristic
10C32×#121C2211yescharacteristic
11#64148—21no—
12#64147C411yescharacteristic, complemented
13#64139C2211yescharacteristic
14#64104C411yescharacteristic, complemented
15C4⋊C4×C3⋊D3C411yescharacteristic, complemented
16#64093—21no—
17C22⋊C4×C3⋊D3—21no—
18C2×#3724—21no—
19C2×#3722—21no—
20C2×#3710—21no—
21C3×C3⋊#95C2212yescomplemented
22C3×#830C2212yescomplemented
23#63557—21no—
24D3×#121—32no—
25D3×#121—61no—
26D3×C22⋊C8—32no—
27#4667—32no—
28C3×#327—32no—
29#4537D312yescomplemented
30#4470—32no—
31#4451—32no—
32C23×C3⋊D3—21no—
33C23×C3⋊D3D411yescharacteristic
34C2×C32×D4—21no—
35C2×C32×D4C2×C411yescharacteristic
36C22×C32×C4C2311yescharacteristic
37C2×#638—21no—
38C2×#638—21no—
39C2×#638—21no—
40C22×C3⋊Dic3D411yescharacteristic
41D4×C3⋊D3—42no—
42D4×C3⋊D3—42no—
43D4×C3⋊D3—42no—
44C2×C4⋊(C3⋊D3)—21no—
45C2×C4⋊(C3⋊D3)C2×C411yescharacteristic
46C2×C4×C3⋊D3—21no—
47C2×C4×C3⋊D3—42no—
48C2×C4×C3⋊D3C2×C411yescharacteristic
49C2×C4×C3⋊D3C2×C411yescharacteristic
50C2×C4×C3⋊D3D411yescharacteristic
51C2×C4×C3⋊D3D411yescharacteristic
52C22×C3×Dic3—22no—
53C32×C4⋊C4C2×C411yescharacteristic
54C32×C22⋊C4—21no—
55#3757—21no—
56#3752—21no—
57#3752—21no—
58C4⋊(C3⋊Dic3)C2×C411yescharacteristic
59#3750—21no—
60C2×C3×C3⋊C8—22no—
61#3724—42no—
62#3722—42no—
63#3710—42no—
64#1519—91noSylow
65C2×D3×D4—32no—
66C2×D3×D4—61no—
67C2×D3×D4—62no—
68C2×D3×D4—62no—
69C22×C4×D3—32no—
70C22×C4×D3—61no—
71C3×#121—21no—
72C3×#121C2×D312yes—
73#939—62no—
74#939—62no—
75#938—32no—
76#938—61no—
77#930—32no—
78#930—61no—
79C2×(C2×D3)⋊C4—62no—
80C2×Dic3⋊C4—62no—
81C2×D3×C8—62no—
82#895—32no—
83#895—61no—
84D3×C4⋊C4—32no—
85D3×C4⋊C4—61no—
86#884—62no—
87#884—62no—
88D3×C22⋊C4—62no—
89D3×C22⋊C4—62no—
90C3×C22⋊C8—32no—
91C3×#95—32no—
92C3⋊#95C2×D312yescomplemented
93#830C2×D312yescomplemented
94(C2×D3)⋊C8—62no—
95C23×C32—21no—
96C23×C32C2×D411yescharacteristic
97C22×C3⋊D3—21no—
98C22×C3⋊D3—41no—
99C22×C3⋊D3—41no—
100C22×C3⋊D3—42no—
101C22×C3⋊D3—42no—
102C22×C3⋊D3—42no—
103C22×C3⋊D3C22⋊C411yescharacteristic
104C22×C3⋊D3C22⋊C411yescharacteristic
105C22×C3⋊D3D812yes—
106C22×C3⋊D3SD1612yes—
107C32×D4—41no—
108C32×D4—41no—
109C32×D4—41no—
110C2×C32×C4—21no—
111C2×C32×C4—41no—
112C2×C32×C4C22×C411yescharacteristic
113C2×C32×C4C2×D411yescharacteristic
114#638—41no—
115#638—41no—
116#638—42no—
117#638—42no—
118C2×C3⋊Dic3—21no—
119C2×C3⋊Dic3—22no—
120C2×C3⋊Dic3C22⋊C411yescharacteristic
121C2×C3⋊Dic3C22⋊C411yescharacteristic
122C4⋊(C3⋊D3)—41no—
123C4⋊(C3⋊D3)—42no—
124C4×C3⋊D3—22no—
125C4×C3⋊D3—22no—
126C4×C3⋊D3—41no—
127C4×C3⋊D3—41no—
128C4×C3⋊D3—42no—
129C2×C3×Dic3—42no—
130C2×C3×Dic3—42no—
131C2×C3×Dic3—42no—
132C3×C3⋊C8—42no—
133C2×#121—91no—
134C2×C22⋊C8—91no—
135#380—91no—
136#327—32no—
137#327—92no—
138C23×D3—32no—
139C23×D3—61no—
140C23×D3—62no—
141C23×D3—62no—
142C2×C3×D4—22no—
143C2×C3×D4—22no—
144C2×C3×D4—21no—
145C2×C3×D4C4×D312yes—
146C22×C3×C4—21no—
147C22×C3×C4—62no—
148C22×C3×C4C22×D312yes—
149C2×#67—62no—
150C2×#67—62no—
151C2×#67—62no—
152C2×#67—62no—
153C2×#67—62no—
154C2×#67—62no—
155C22×Dic3—22no—
156C22×Dic3—32no—
157C22×Dic3—61no—
158D3×D4—124no—
159D3×D4—124no—
160D3×D4—124no—
161D3×D4—124no—
162D3×D4—124no—
163D3×D4—124no—
164C2×D12—32no—
165C2×D12—61no—
166C2×D12—62no—
167C2×D12—62no—
168C2×C4×D3—32no—
169C2×C4×D3—32no—
170C2×C4×D3—32no—
171C2×C4×D3—32no—
172C2×C4×D3—61no—
173C2×C4×D3—61no—
174C2×C4×D3—61no—
175C2×C4×D3—61no—
176C2×C4×D3—62no—
177C2×C4×D3—62no—
178C2×C4×D3—124no—
179C2×C4×D3—124no—
180C2×C3×C8—62no—
181C3×C4⋊C4—21no—
182C3×C4⋊C4C4×D312yes—
183C3×C22⋊C4—22no—
184C3×C22⋊C4—22no—
185#217—62no—
186#217—62no—
187(C2×D3)⋊C4—62no—
188(C2×D3)⋊C4—62no—
189(C2×D3)⋊C4—62no—
190(C2×D3)⋊C4—62no—
191(C2×D3)⋊C4—124no—
192C4⋊Dic3—32no—
193C4⋊Dic3—61no—
194Dic3⋊C4—62no—
195Dic3⋊C4—62no—
196Dic3⋊C4—124no—
197C2×C3⋊C8—22no—
198D3×C8—124no—
199C22×C32—21no—
200C22×C32—21no—
201C22×C32—41no—
202C22×C32—41no—
203C22×C32—41no—
204C22×C32C2×C22⋊C411yescharacteristic
205C22×C32C2×D811yescharacteristic
206C22×C32C2×SD1611yescharacteristic
207C2×C3⋊D3—21no—
208C2×C3⋊D3—21no—
209C2×C3⋊D3—21no—
210C2×C3⋊D3—21no—
211C2×C3⋊D3—42no—
212C2×C3⋊D3—42no—
213C2×C3⋊D3—41no—
214C2×C3⋊D3—41no—
215C2×C3⋊D3—41no—
216C2×C3⋊D3—84no—
217C2×C3⋊D3#10212yes—
218C2×C3⋊D3#10212yes—
219C32×C4—21no—
220C32×C4—21no—
221C32×C4—41no—
222C3⋊Dic3—21no—
223C3⋊Dic3—41no—
224C3⋊Dic3#9912yes—
225C3×Dic3—82no—
226C22×D4—91no—
227C22×D4—181no—
228C23×C4—91no—
229C22×C8—181no—
230#121—91no—
231#121—91no—
232#121—91no—
233#121—181no—
234#121—181no—
235#121D3211yescharacteristic
236C2×C4⋊C4—91no—
237C2×C4⋊C4—181no—
238C2×C22⋊C4—181no—
239C2×C22⋊C4—181no—
240C22⋊C8—32no—
241C22⋊C8—181no—
242#95—32no—
243C23×C3—22no—
244C23×C3—22no—
245C23×C3—21no—
246C23×C3D3×D412yes—
247C22×D3—32no—
248C22×D3—32no—
249C22×D3—34no—
250C22×D3—34no—
251C22×D3—61no—
252C22×D3—61no—
253C22×D3—62no—
254C22×D3—62no—
255C22×D3—62no—
256C22×D3—62no—
257C22×D3—124no—
258C22×D3—122no—
259C22×D3—122no—
260C22×D3—122no—
261C22×D3—122no—
262C22×D3—124no—
263C22×D3—124no—
264C22×D3—124no—
265C22×D3—124no—
266C22×D3—124no—
267C3×D4—42no—
268C3×D4—42no—
269C3×D4—42no—
270C3×D4—42no—
271C3×D4—42no—
272C3×D4—42no—
273C2×C3×C4—22no—
274C2×C3×C4—22no—
275C2×C3×C4—21no—
276C2×C3×C4—21no—
277C2×C3×C4—42no—
278C2×C3×C4—42no—
279C2×C3×C4—122no—
280C2×C3×C4—122no—
281C2×C3×C4—122no—
282C2×C3×C4C2×C4×D312yes—
283C2×C3×C4D3×D412yes—
284#67—124no—
285#67—124no—
286#67—124no—
287#67—124no—
288#67—122no—
289#67—122no—
290#67—122no—
291#67—122no—
292C2×Dic3—32no—
293C2×Dic3—32no—
294C2×Dic3—42no—
295C2×Dic3—42no—
296C2×Dic3—42no—
297C2×Dic3—61no—
298C2×Dic3—61no—
299C2×Dic3—64no—
300C2×Dic3—62no—
301C2×Dic3—62no—
302C2×Dic3—122no—
303D12—122no—
304D12—122no—
305D12—124no—
306D12—124no—
307C4×D3—64no—
308C4×D3—64no—
309C4×D3—64no—
310C4×D3—122no—
311C4×D3—122no—
312C4×D3—122no—
313C4×D3—122no—
314C4×D3—124no—
315C4×D3—122no—
316C4×D3—124no—
317C3×C8—122no—
318C3⋊C8—42no—
319C2×C32—21no—
320C2×C32—21no—
321C2×C32—81no—
322C2×C32C2×#9911yescharacteristic
323C2×C32C2×#10211yescharacteristic
324C2×C32#42111yescharacteristic
325C3⋊D3—22no—
326C3⋊D3—22no—
327C3⋊D3—81no—
328C24—91no—
329C24—181no—
330C2×D4—21no—
331C2×D4—91no—
332C2×D4—181no—
333C2×D4—181no—
334C2×D4—181no—
335C2×D4—181no—
336C2×D4—362no—
337C2×D4—362no—
338C2×D4—362no—
339C2×D4#62411yescharacteristic
340C22×C4—62no—
341C22×C4—91no—
342C22×C4—91no—
343C22×C4—91no—
344C22×C4—91no—
345C22×C4—91no—
346C22×C4—181no—
347C22×C4—362no—
348C22×C4C2×D3211yescharacteristic
349C2×C8—62no—
350C2×C8—362no—
351C4⋊C4—91no—
352C4⋊C4—181no—
353C4⋊C4—362no—
354C4⋊C4#62411yescharacteristic
355C22⋊C4—21no—
356C22⋊C4—181no—
357C22⋊C4—181no—
358C22⋊C4—181no—
359C22⋊C4—362no—
360C22×C3—22no—
361C22×C3—22no—
362C22×C3—21no—
363C22×C3—21no—
364C22×C3—21no—
365C22×C3—41no—
366C22×C3—41no—
367C22×C3—42no—
368C22×C3—42no—
369C22×C3—42no—
370C22×C3—42no—
371C22×C3—42no—
372C22×C3—42no—
373C22×C3D3×C22⋊C412yes—
374C22×C3D3×D812yes—
375C22×C3D3×SD1612yes—
376C2×D3—34no—
377C2×D3—34no—
378C2×D3—62no—
379C2×D3—62no—
380C2×D3—62no—
381C2×D3—62no—
382C2×D3—62no—
383C2×D3—62no—
384C2×D3—62no—
385C2×D3—62no—
386C2×D3—121no—
387C2×D3—121no—
388C2×D3—124no—
389C2×D3—124no—
390C2×D3—124no—
391C2×D3—124no—
392C2×D3—122no—
393C2×D3—122no—
394C2×D3—122no—
395C2×D3—122no—
396C2×D3—122no—
397C2×D3—122no—
398C2×D3—248no—
399C2×D3—248no—
400C3×C4—22no—
401C3×C4—22no—
402C3×C4—22no—
403C3×C4—41no—
404C3×C4—42no—
405C3×C4—42no—
406C3×C4—242no—
407Dic3—34no—
408Dic3—62no—
409Dic3—62no—
410Dic3—82no—
411Dic3—121no—
412Dic3—122no—
413Dic3—122no—
414C32#151911yescharacteristic, complemented, Sylow
415C23—21no—
416C23—91no—
417C23—91no—
418C23—92no—
419C23—92no—
420C23—181no—
421C23—361no—
422C23—361no—
423C23—362no—
424C23—362no—
425C23—362no—
426C23#381111yescharacteristic
427D4—41no—
428D4—41no—
429D4—41no—
430D4—361no—
431D4—362no—
432D4—362no—
433D4—362no—
434D4—361no—
435D4—361no—
436C2×C4—21no—
437C2×C4—41no—
438C2×C4—91no—
439C2×C4—91no—
440C2×C4—122no—
441C2×C4—122no—
442C2×C4—122no—
443C2×C4—182no—
444C2×C4—182no—
445C2×C4—182no—
446C2×C4—181no—
447C2×C4—361no—
448C2×C4—361no—
449C2×C4—362no—
450C2×C4C2×#62411yescharacteristic
451C2×C4#381111yescharacteristic
452C8—122no—
453C2×C3—22no—
454C2×C3—22no—
455C2×C3—21no—
456C2×C3—21no—
457C2×C3—21no—
458C2×C3—41no—
459C2×C3—41no—
460C2×C3—82no—
461C2×C3—82no—
462C2×C3D3×#9912yes—
463C2×C3D3×#10212yes—
464C2×C3#482112yes—
465D3—64no—
466D3—64no—
467D3—64no—
468D3—122no—
469D3—242no—
470D3—242no—
471C22—21no—
472C22—21no—
473C22—41no—
474C22—41no—
475C22—41no—
476C22—92no—
477C22—92no—
478C22—181no—
479C22—181no—
480C22—181no—
481C22—181no—
482C22—362no—
483C22—362no—
484C22—361no—
485C22—361no—
486C22—361no—
487C22—724no—
488C22#6392611yescharacteristic
489C22#6393011yescharacteristic
490C22#6397411yescharacteristic
491C4—21no—
492C4—21no—
493C4—41no—
494C4—92no—
495C4—181no—
496C4—242no—
497C4—361no—
498C3—21no—
499C3#6830712yescomplemented
500C2—21no—
501C2—21no—
502C2—81no—
503C2—182no—
504C2—182no—
505C2—721no—
506C2#1059141611yescharacteristic
507C2#1059152711yescharacteristic
508C2#1059167211yescharacteristic
subgroupG/H
centerC22#63974
commutatorC2×C32×C4C22×C4
FrattiniC22×C4C2×D32
FittingC32×#121C22
socleC22×C32C2×C22⋊C4
prime radicalC3⋊D3×#121C2
cosocleC22×C32×C4C23
hypercenter#121D32
hypocenterC32#1519
LCSG ▷ C2×C32×C4 ▷ C22×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4 ◁ #121

Complements

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

NH ≅ G/Ntype
2. #10591355C2semidirect
3. #10591152C2semidirect
4. C3×#4537C2semidirect
5. #10589151C2semidirect
8. C2×D4×C3⋊D3C4semidirect
12. #64147C4semidirect
14. #64104C4semidirect
15. C4⋊C4×C3⋊D3C4semidirect
21. C3×C3⋊#95C22semidirect
22. C3×#830C22semidirect
29. #4537D3semidirect
92. C3⋊#95C2×D3semidirect
93. #830C2×D3semidirect
414. C32#1519semidirect
499. C3#68307semidirect

Maximal subgroups

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

subgroupindex
C3⋊D3×#1212
#105913552
#105911522
C3×#45372
#105891512
#683073