Finite Group Databasebeta

← #11775327

Subgroups — #11775327

Order 1152.

588 conjugacy classes of subgroups.

The subgroup lattice has 530 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1D3×#924C211yesmaximal, characteristic
2C3×#4664C211yesmaximal, characteristic
3#10591154C211yesmaximal, characteristic
4#10589318C211yesmaximal, characteristic, complemented
5C3×#4452C211yesmaximal, characteristic, complemented
6#10589154C211yesmaximal, characteristic, complemented
7#10589153C211yesmaximal, characteristic, complemented
8#69533—31nomaximal
9#68336—31nomaximal
10C22×C3×C4×D3C2211yescharacteristic
11C2×D3×Dic6C411yescharacteristic, complemented
12#64133C2211yescharacteristic
13C2×C3×(C2×D3)⋊C4—21no—
14C3×#924C2211yescharacteristic
15D3×#217—21no—
16#63964—21no—
17D3×C4⋊Dic3C411yescharacteristic, complemented
18D3×Dic3⋊C4—21no—
19#63857C411yescharacteristic, complemented
20#63856C411yescharacteristic, complemented
21#63851—21no—
22C2×#3711—21no—
23C32×#95C2211yescharacteristic
24#63657C2211yescharacteristic
25C3×C3⋊#95—21no—
26C3×C3⋊#95C2211yescharacteristic
27C3×#830C2211yescharacteristic
28(C2×D3)⋊(C3⋊C8)—21no—
29C2×#924—31no—
30D3×C22⋊Q8—31no—
31C3×#381—31no—
32#5207—31no—
33#4726—31no—
34#4664D311yescharacteristic
35C3×#328—31no—
36#4538—31no—
37#4467—31no—
38#4452—31no—
39#4452—31no—
40#4452—31no—
41#4452—31no—
42#4452—61no—
43#4452D311yescharacteristic, complemented
44C23×C3×D3D411yescharacteristic
45C22×C32×C4—21no—
46C22×C32×C4C2311yescharacteristic
47C2×#634C2×C411yescharacteristic
48C22×C3×Dic3—21no—
49C22×C3×Dic3D411yescharacteristic
50C2×C3×C4×D3—42no—
51C2×C3×C4×D3C2×C411yescharacteristic
52C2×C3×C4×D3C2×C411yescharacteristic
53C2×C3×C4×D3D411yescharacteristic
54C2×C3×C4×D3D411yescharacteristic
55C2×C3×Dic6C2×C411yescharacteristic
56C2×#627—21no—
57C2×D3×Dic3—21no—
58C2×D3×Dic3—21no—
59D3×Dic6—42no—
60#3757—21no—
61C4⋊(C3⋊Dic3)C2×C411yescharacteristic
62#3750—21no—
63C2×C3⋊(C3⋊C8)—21no—
64C3×#217—21no—
65C3×(C2×D3)⋊C4—42no—
66C3×C4⋊Dic3C2×C411yescharacteristic
67C3×Dic3⋊C4—21no—
68C2×C3×C3⋊C8—21no—
69#3724—21no—
70Dic3⋊Dic3—21no—
71Dic3⋊Dic3—21no—
72(C2×D3)⋊Dic3—21no—
73(C2×D3)⋊Dic3—21no—
74#3711—42no—
75#1511—91noSylow
76C23×C3×C4—31no—
77C2×D3×Q8—31no—
78C22×C4×D3C2×D311yescharacteristic
79C22×Dic6—31no—
80C3×C22⋊Q8—31no—
81C2×C3×C22⋊C4—61no—
82C2×#217—61no—
83#946—31no—
84C2×(C2×D3)⋊C4—21no—
85C2×C4⋊Dic3—31no—
86#924—31no—
87#924—31no—
88#924—31no—
89#924—31no—
90#924—61no—
91#924—61no—
92#924—61no—
93#924C2×D311yescharacteristic
94C2×Dic3⋊C4—61no—
95C2×#208—61no—
96C2×ΓL(1,𝔽25)—61no—
97#897—31no—
98#896—61no—
99D3×C4⋊C4—31no—
100D3×C4⋊C4—61no—
101D3×C22⋊C4—61no—
102#878—61no—
103C3×C22⋊C8—31no—
104C3×#95—21no—
105C3×#95—31no—
106C3×#95—61no—
107C3×#95C2×D311yescharacteristic
108C3×#95C2×D311yescharacteristic
109C3⋊#95—21no—
110C3⋊#95C2×D311yescharacteristic
111#830—31no—
112#830—31no—
113#830—61no—
114#830—61no—
115#830C2×D311yescharacteristic
116(C2×D3)⋊C8—61no—
117C23×C32C2×D411yescharacteristic
118C22×C3×D3—21no—
119C22×C3×D3—21no—
120C22×C3×D3—22no—
121C22×C3×D3—41no—
122C22×C3×D3C22⋊C411yescharacteristic
123C22×C3×D3C22⋊C411yescharacteristic
124C2×C32×C4—41no—
125C2×C32×C4—41no—
126C2×C32×C4—41no—
127C2×C32×C4—41no—
128C2×C32×C4C22×C411yescharacteristic
129C2×C32×C4C2×D411yescharacteristic
130C2×C3⋊Dic3—21no—
131C2×C3⋊Dic3—21no—
132#634—41no—
133C2×C3×Dic3—21no—
134C2×C3×Dic3—21no—
135C2×C3×Dic3—41no—
136C2×C3×Dic3—41no—
137C2×C3×Dic3—41no—
138C2×C3×Dic3—41no—
139C2×C3×Dic3C22⋊C411yescharacteristic
140C2×C3×Dic3C22⋊C411yescharacteristic
141C3×C4×D3—22no—
142C3×C4×D3—22no—
143C3×C4×D3—41no—
144C3×C4×D3—41no—
145C3×Dic6—41no—
146#627—42no—
147D3×Dic3—42no—
148D3×Dic3—42no—
149C3⋊(C3⋊C8)—41no—
150C3×C3⋊C8—41no—
151C2×C22⋊Q8—91no—
152#407—91no—
153#381—31no—
154#328—31no—
155#328—91no—
156#328—91no—
157#328—91no—
158C24×C3—31no—
159C23×D3#6711yescharacteristic
160C2×C3×Q8—31no—
161C22×C3×C4—21no—
162C22×C3×C4—21no—
163C22×C3×C4—21no—
164C22×C3×C4—31no—
165C22×C3×C4—31no—
166C22×C3×C4—31no—
167C22×C3×C4—31no—
168C22×C3×C4—31no—
169C22×C3×C4—41no—
170C22×C3×C4—61no—
171C22×C3×C4—122no—
172C22×C3×C4C22×D311yescharacteristic
173C22×C3×C4C22×D311yescharacteristic
174C22×Dic3—21no—
175C22×Dic3—61no—
176C22×Dic3—61no—
177C22×Dic3#6711yescharacteristic
178D3×Q8—122no—
179C2×C4×D3—42no—
180C2×C4×D3—61no—
181C2×C4×D3—61no—
182C2×C4×D3C4×D311yescharacteristic
183C2×C4×D3C4×D311yescharacteristic
184C2×C4×D3D1211yescharacteristic
185C2×C4×D3D1211yescharacteristic
186C2×Dic6—31no—
187C2×Dic6—31no—
188C2×Dic6—61no—
189C2×Dic6—61no—
190C2×Dic6—61no—
191C2×Dic6—122no—
192C2×Dic6C4×D311yescharacteristic
193C2×C3×C8—61no—
194C3×C4⋊C4—31no—
195C3×C4⋊C4—61no—
196C3×C22⋊C4—61no—
197C3×C22⋊C4—122no—
198#217—21no—
199#217—61no—
200#217—61no—
201#217—61no—
202#217—61no—
203#217—121no—
204(C2×D3)⋊C4—42no—
205(C2×D3)⋊C4—61no—
206(C2×D3)⋊C4—61no—
207C4⋊Dic3—31no—
208C4⋊Dic3—31no—
209C4⋊Dic3—61no—
210C4⋊Dic3—61no—
211C4⋊Dic3—61no—
212C4⋊Dic3C4×D311yescharacteristic
213Dic3⋊C4—21no—
214Dic3⋊C4—61no—
215Dic3⋊C4—61no—
216Dic3⋊C4—61no—
217Dic3⋊C4—61no—
218Dic3⋊C4—61no—
219Dic3⋊C4—61no—
220Dic3⋊C4—121no—
221#208—122no—
222C2×C3⋊C8—21no—
223C2×C3⋊C8—61no—
224C2×C3⋊C8—61no—
225C2×C3⋊C8—121no—
226ΓL(1,𝔽25)—122no—
227C22×C32—21no—
228C22×C32—21no—
229C22×C32C2×C22⋊C411yescharacteristic
230C22×C32#13711yescharacteristic
231C22×C32#13711yescharacteristic
232C2×C3×D3—21no—
233C2×C3×D3—21no—
234C2×C3×D3—21no—
235C2×C3×D3—21no—
236C2×C3×D3—21no—
237C2×C3×D3—42no—
238C2×C3×D3—42no—
239C2×C3×D3#9912yes—
240C32×C4—21no—
241C32×C4—21no—
242C32×C4—81no—
243C3⋊Dic3—41no—
244C3⋊Dic3—41no—
245C3×Dic3—21no—
246C3×Dic3—21no—
247C3×Dic3—41no—
248C3×Dic3—41no—
249C3×Dic3—81no—
250C22×Q8—91no—
251C23×C4—31no—
252C2×M16—181no—
253C22⋊Q8—31no—
254C22⋊Q8—91no—
255C22⋊Q8—91no—
256C22⋊Q8—91no—
257C22⋊Q8—181no—
258C22⋊Q8—181no—
259C2×C4⋊C4—91no—
260C2×C4⋊C4—181no—
261C2×C22⋊C4—61no—
262C2×C22⋊C4—181no—
263C22⋊C8—31no—
264C22⋊C8—91no—
265C22⋊C8—181no—
266#95—31no—
267#95—61no—
268#95D3211yescharacteristic
269C23×C3—21no—
270C23×C3—31no—
271C23×C3—31no—
272C23×C3—62no—
273C23×C3—61no—
274C23×C3—61no—
275C23×C3—121no—
276C23×C3D3×D411yescharacteristic
277C23×C3C2×#6711yescharacteristic
278C22×D3—21no—
279C22×D3—21no—
280C22×D3—22no—
281C22×D3—41no—
282C22×D3(C2×D3)⋊C411yescharacteristic
283C22×D3(C2×D3)⋊C411yescharacteristic
284C3×Q8—121no—
285C2×C3×C4—21no—
286C2×C3×C4—21no—
287C2×C3×C4—31no—
288C2×C3×C4—31no—
289C2×C3×C4—41no—
290C2×C3×C4—41no—
291C2×C3×C4—41no—
292C2×C3×C4—41no—
293C2×C3×C4—41no—
294C2×C3×C4—41no—
295C2×C3×C4—42no—
296C2×C3×C4—41no—
297C2×C3×C4—41no—
298C2×C3×C4—62no—
299C2×C3×C4—62no—
300C2×C3×C4—61no—
301C2×C3×C4—61no—
302C2×C3×C4—81no—
303C2×C3×C4—81no—
304C2×C3×C4—81no—
305C2×C3×C4—121no—
306C2×C3×C4—121no—
307C2×C3×C4—121no—
308C2×C3×C4—121no—
309C2×C3×C4—121no—
310C2×C3×C4—121no—
311C2×C3×C4C2×C4×D311yescharacteristic
312C2×C3×C4C2×C4×D311yescharacteristic
313C2×C3×C4C2×D1211yescharacteristic
314C2×C3×C4D3×D411yescharacteristic
315C2×Dic3—21no—
316C2×Dic3—21no—
317C2×Dic3—41no—
318C2×Dic3—41no—
319C2×Dic3—41no—
320C2×Dic3—41no—
321C2×Dic3—61no—
322C2×Dic3—61no—
323C2×Dic3—61no—
324C2×Dic3—61no—
325C2×Dic3—121no—
326C2×Dic3—121no—
327C2×Dic3—122no—
328C2×Dic3—122no—
329C2×Dic3(C2×D3)⋊C411yescharacteristic
330C2×Dic3(C2×D3)⋊C411yescharacteristic
331C4×D3—22no—
332C4×D3—22no—
333C4×D3—41no—
334C4×D3—41no—
335C4×D3—122no—
336C4×D3—122no—
337Dic6—41no—
338Dic6—122no—
339Dic6—122no—
340Dic6—121no—
341Dic6—121no—
342Dic6—241no—
343C3×C8—121no—
344C3⋊C8—41no—
345C3⋊C8—121no—
346C3⋊C8—121no—
347C3⋊C8—241no—
348C2×C32—21no—
349C2×C32—21no—
350C2×C32C2×#9911yescharacteristic
351C2×C32#41911yescharacteristic
352C2×C32#42111yescharacteristic
353C3×D3—22no—
354C3×D3—41no—
355C24—31no—
356C2×Q8—31no—
357C2×Q8—91no—
358C2×Q8—181no—
359C2×Q8—362no—
360C22×C4—21no—
361C22×C4—31no—
362C22×C4—31no—
363C22×C4—31no—
364C22×C4—31no—
365C22×C4—31no—
366C22×C4—61no—
367C22×C4—122no—
368C22×C4—181no—
369C22×C4—181no—
370C22×C4C2×D3211yescharacteristic
371M16—362no—
372C2×C8—61no—
373C2×C8—181no—
374C4⋊C4—31no—
375C4⋊C4—61no—
376C4⋊C4—91no—
377C4⋊C4—181no—
378C4⋊C4—181no—
379C4⋊C4—181no—
380C4⋊C4—181no—
381C22⋊C4—61no—
382C22⋊C4—122no—
383C22⋊C4—181no—
384C22⋊C4—181no—
385C22⋊C4—181no—
386C22×C3—21no—
387C22×C3—21no—
388C22×C3—21no—
389C22×C3—21no—
390C22×C3—21no—
391C22×C3—21no—
392C22×C3—21no—
393C22×C3—32no—
394C22×C3—41no—
395C22×C3—41no—
396C22×C3—61no—
397C22×C3—61no—
398C22×C3—61no—
399C22×C3—61no—
400C22×C3—61no—
401C22×C3—122no—
402C22×C3—122no—
403C22×C3D3×C22⋊C411yescharacteristic
404C22×C3#91511yescharacteristic
405C22×C3#91811yescharacteristic
406C22×C3C2×(C2×D3)⋊C411yescharacteristic
407C22×C3#95111yescharacteristic
408C22×C3#95111yescharacteristic
409C2×D3—21no—
410C2×D3—21no—
411C2×D3—21no—
412C2×D3—21no—
413C2×D3—21no—
414C2×D3—42no—
415C2×D3—42no—
416C2×D3#80612yes—
417C3×C4—21no—
418C3×C4—21no—
419C3×C4—21no—
420C3×C4—21no—
421C3×C4—41no—
422C3×C4—41no—
423C3×C4—61no—
424C3×C4—61no—
425C3×C4—81no—
426C3×C4—81no—
427C3×C4—82no—
428C3×C4—121no—
429C3×C4—121no—
430C3×C4—241no—
431Dic3—21no—
432Dic3—21no—
433Dic3—41no—
434Dic3—41no—
435Dic3—81no—
436Dic3—121no—
437Dic3—121no—
438Dic3—121no—
439Dic3—121no—
440Dic3—241no—
441Dic3—241no—
442C32#151111yescharacteristic, complemented, Sylow
443C23—31no—
444C23—31no—
445C23—62no—
446C23—61no—
447C23—61no—
448C23—121no—
449C23D3×#6711yescharacteristic
450Q8—121no—
451Q8—361no—
452Q8—362no—
453C2×C4—31no—
454C2×C4—31no—
455C2×C4—41no—
456C2×C4—41no—
457C2×C4—41no—
458C2×C4—41no—
459C2×C4—62no—
460C2×C4—62no—
461C2×C4—61no—
462C2×C4—61no—
463C2×C4—121no—
464C2×C4—121no—
465C2×C4—121no—
466C2×C4—121no—
467C2×C4—121no—
468C2×C4—121no—
469C2×C4—181no—
470C2×C4—181no—
471C2×C4—362no—
472C2×C4—362no—
473C2×C4C4×D3211yescharacteristic
474C2×C4D3×D1211yescharacteristic
475C8—121no—
476C8—361no—
477C2×C3—21no—
478C2×C3—21no—
479C2×C3—21no—
480C2×C3—21no—
481C2×C3—21no—
482C2×C3—21no—
483C2×C3—21no—
484C2×C3—41no—
485C2×C3—41no—
486C2×C3—62no—
487C2×C3—121no—
488C2×C3D3×#9911yescharacteristic
489C2×C3#480211yescharacteristic
490C2×C3#482111yescharacteristic
491C2×C3C2×#80611yescharacteristic
492C2×C3#500411yescharacteristic
493C2×C3#500511yescharacteristic
494D3—22no—
495D3—41no—
496C22—21no—
497C22—21no—
498C22—32no—
499C22—61no—
500C22—61no—
501C22—61no—
502C22—61no—
503C22—61no—
504C22—122no—
505C22—122no—
506C22D3×(C2×D3)⋊C411yescharacteristic
507C22#6392911yescharacteristic
508C22#6394311yescharacteristic
509C4—21no—
510C4—21no—
511C4—61no—
512C4—61no—
513C4—81no—
514C4—121no—
515C4—121no—
516C4—241no—
517C4—361no—
518C4—361no—
519C3—21no—
520C3#6833611yescharacteristic, complemented
521C3#6953311yescharacteristic, complemented
522C2—21no—
523C2—21no—
524C2—62no—
525C2—121no—
526C2#1059039211yescharacteristic
527C2D3×#80611yescharacteristic
528C2#1059060011yescharacteristic
subgroupG/H
centerC22D3×(C2×D3)⋊C4
commutatorC2×C32×C4C22×C4
FrattiniC22×C4C2×D32
FittingC32×#95C22
socleC22×C32C2×C22⋊C4
prime radicalC23×C3×D3D4
cosocleC22×C32×C4C23
hypercenter#95D32
hypocenterC32#1511
LCSG ▷ C2×C32×C4 ▷ C22×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4 ◁ #95

Complements

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

NH ≅ G/Ntype
4. #10589318C2semidirect
5. C3×#4452C2semidirect
6. #10589154C2semidirect
7. #10589153C2semidirect
11. C2×D3×Dic6C4semidirect
17. D3×C4⋊Dic3C4semidirect
19. #63857C4semidirect
20. #63856C4semidirect
43. #4452D3semidirect
442. C32#1511semidirect
520. C3#68336semidirect
521. C3#69533semidirect

Maximal subgroups

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

subgroupindex
D3×#9242
C3×#46642
#105911542
#105893182
C3×#44522
#105891542
#105891532
#695333
#683363