Finite Group Databasebeta

← #11775613

Subgroups — #11775613

Order 1152.

616 conjugacy classes of subgroups.

The subgroup lattice has 534 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1D3×#924C211yesmaximal, characteristic
2C3×D3×C22⋊C8C211yesmaximal, characteristic
3#10591295C211yesmaximal, characteristic
4#10589333C211yesmaximal, characteristic, complemented
5C3×#4467C211yesmaximal, characteristic, complemented
6#10589154C211yesmaximal, characteristic, complemented
7#10589152C211yesmaximal, characteristic, complemented
8#69946—31nomaximal
9#68339—31nomaximal
10C22×C3×C4×D3C2211yescharacteristic
11C2×D3×Dic6C411yescharacteristic, complemented
12#64133C2211yescharacteristic
13C3×#924C2211yescharacteristic
14C2×C3×D3×C8—21no—
15D3×#217—21no—
16C2×Dic3⋊Dic3—21no—
17#63964—21no—
18C2×(C2×D3)⋊Dic3—21no—
19D3×C4⋊Dic3C411yescharacteristic, complemented
20D3×Dic3⋊C4—21no—
21#63857C411yescharacteristic, complemented
22#63856C411yescharacteristic, complemented
23#63851—21no—
24C32×C22⋊C8C2211yescharacteristic
25#63658C2211yescharacteristic
26C3×C3⋊#95C2211yescharacteristic
27C3×#830C2211yescharacteristic
28C3×(C2×D3)⋊C8—21no—
29C2×#924—31no—
30D3×C22⋊Q8—31no—
31C2×C3×C22⋊C8—31no—
32#5212—31no—
33D3×C22⋊C8D311yescharacteristic
34#4667—31no—
35C3×#328—31no—
36#4538—31no—
37#4467—31no—
38#4467—31no—
39#4467—31no—
40#4467—31no—
41#4467—61no—
42#4467D311yescharacteristic, complemented
43#4452—31no—
44C23×C3×D3D411yescharacteristic
45C22×C32×C4C2311yescharacteristic
46C22×C3⋊Dic3—21no—
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—
60C2×C32×C8—21no—
61#3757—21no—
62C4⋊(C3⋊Dic3)C2×C411yescharacteristic
63#3750—21no—
64C3×#217—21no—
65C3×C4⋊Dic3C2×C411yescharacteristic
66C3×Dic3⋊C4—21no—
67C2×C3×C3⋊C8—21no—
68C3×D3×C8—42no—
69#3724—21no—
70Dic3⋊Dic3—21no—
71Dic3⋊Dic3—21no—
72Dic3⋊Dic3—42no—
73(C2×D3)⋊Dic3—21no—
74(C2×D3)⋊Dic3—21no—
75(C2×D3)⋊Dic3—42no—
76#1520—91noSylow
77C23×C3×C4—31no—
78C2×D3×Q8—31no—
79C22×C4×D3C2×D311yescharacteristic
80C22×Dic6—31no—
81C22×C3×C8—61no—
82C3×C22⋊Q8—31no—
83C2×#217—61no—
84C2×#217—61no—
85#946—31no—
86C2×(C2×D3)⋊C4—61no—
87C2×C4⋊Dic3—31no—
88C2×C4⋊Dic3—61no—
89#924—31no—
90#924—31no—
91#924—31no—
92#924—31no—
93#924—61no—
94#924—61no—
95#924—61no—
96#924C2×D311yescharacteristic
97C2×Dic3⋊C4—61no—
98C2×Dic3⋊C4—61no—
99C2×D3×C8—21no—
100#897—31no—
101#896—61no—
102D3×C4⋊C4—31no—
103D3×C4⋊C4—61no—
104D3×C22⋊C4—61no—
105#878—61no—
106C3×C22⋊C8—21no—
107C3×C22⋊C8—31no—
108C3×C22⋊C8—61no—
109C3×C22⋊C8C2×D311yescharacteristic
110C3×C22⋊C8C2×D311yescharacteristic
111C3×#95—31no—
112C3⋊#95—31no—
113C3⋊#95—31no—
114C3⋊#95—61no—
115C3⋊#95C2×D311yescharacteristic
116#830C2×D311yescharacteristic
117(C2×D3)⋊C8—21no—
118C23×C32C2×D411yescharacteristic
119C22×C3×D3—41no—
120C22×C3×D3—41no—
121C22×C3×D3C22⋊C411yescharacteristic
122C22×C3×D3C22⋊C411yescharacteristic
123C22×C3×D3SD1612yes—
124C22×C3×D3Q1612yes—
125C2×C32×C4—41no—
126C2×C32×C4C22×C411yescharacteristic
127C2×C32×C4C2×D411yescharacteristic
128C2×C3⋊Dic3—21no—
129C2×C3⋊Dic3—21no—
130C2×C3⋊Dic3—41no—
131C2×C3⋊Dic3—41no—
132C2×C3⋊Dic3—41no—
133#634—41no—
134C2×C3×Dic3—22no—
135C2×C3×Dic3—21no—
136C2×C3×Dic3—21no—
137C2×C3×Dic3—41no—
138C2×C3×Dic3—41no—
139C2×C3×Dic3—41no—
140C2×C3×Dic3C22⋊C411yescharacteristic
141C2×C3×Dic3C22⋊C411yescharacteristic
142C3×C4×D3—22no—
143C3×C4×D3—22no—
144C3×C4×D3—41no—
145C3×C4×D3—41no—
146C3×Dic6—41no—
147#627—42no—
148D3×Dic3—42no—
149D3×Dic3—42no—
150C32×C8—41no—
151C3×C3⋊C8—41no—
152C2×C22⋊Q8—91no—
153C2×C22⋊C8—31no—
154#380—91no—
155#328—31no—
156#328—91no—
157#328—91no—
158#328—91no—
159C24×C3—31no—
160C23×D3D1211yescharacteristic
161C2×C3×Q8—31no—
162C22×C3×C4—21no—
163C22×C3×C4—31no—
164C22×C3×C4—31no—
165C22×C3×C4—31no—
166C22×C3×C4—31no—
167C22×C3×C4—31no—
168C22×C3×C4—61no—
169C22×C3×C4—122no—
170C22×C3×C4C22×D311yescharacteristic
171C22×C3×C4C22×D311yescharacteristic
172C22×Dic3—21no—
173C22×Dic3—61no—
174C22×Dic3—61no—
175C22×Dic3—61no—
176C22×Dic3—61no—
177C22×Dic3—121no—
178C22×Dic3D1211yescharacteristic
179D3×Q8—122no—
180C2×C4×D3—42no—
181C2×C4×D3—61no—
182C2×C4×D3—61no—
183C2×C4×D3C4×D311yescharacteristic
184C2×C4×D3C4×D311yescharacteristic
185C2×C4×D3#6711yescharacteristic
186C2×C4×D3#6711yescharacteristic
187C2×Dic6—31no—
188C2×Dic6—31no—
189C2×Dic6—61no—
190C2×Dic6—61no—
191C2×Dic6—61no—
192C2×Dic6—122no—
193C2×Dic6C4×D311yescharacteristic
194C2×C3×C8—21no—
195C2×C3×C8—21no—
196C2×C3×C8—41no—
197C2×C3×C8—61no—
198C2×C3×C8—122no—
199C3×C4⋊C4—31no—
200C3×C4⋊C4—61no—
201C3×C22⋊C4—61no—
202#217—21no—
203#217—61no—
204#217—61no—
205#217—61no—
206#217—61no—
207#217—121no—
208#217—122no—
209(C2×D3)⋊C4—61no—
210(C2×D3)⋊C4—61no—
211(C2×D3)⋊C4—122no—
212C4⋊Dic3—31no—
213C4⋊Dic3—31no—
214C4⋊Dic3—61no—
215C4⋊Dic3—61no—
216C4⋊Dic3—61no—
217C4⋊Dic3—122no—
218C4⋊Dic3C4×D311yescharacteristic
219Dic3⋊C4—21no—
220Dic3⋊C4—61no—
221Dic3⋊C4—61no—
222Dic3⋊C4—61no—
223Dic3⋊C4—61no—
224Dic3⋊C4—61no—
225Dic3⋊C4—61no—
226Dic3⋊C4—121no—
227Dic3⋊C4—122no—
228C2×C3⋊C8—21no—
229D3×C8—42no—
230C22×C32—21no—
231C22×C32—21no—
232C22×C32C2×C22⋊C411yescharacteristic
233C22×C32C2×SD1611yescharacteristic
234C22×C32C2×Q1611yescharacteristic
235C2×C3×D3—21no—
236C2×C3×D3—21no—
237C2×C3×D3—21no—
238C2×C3×D3—21no—
239C2×C3×D3—42no—
240C2×C3×D3—42no—
241C2×C3×D3#10312yes—
242C2×C3×D3#10312yes—
243C32×C4—21no—
244C32×C4—21no—
245C3⋊Dic3—41no—
246C3⋊Dic3—41no—
247C3⋊Dic3—81no—
248C3×Dic3—21no—
249C3×Dic3—41no—
250C3×Dic3—41no—
251C3×Dic3—81no—
252C3×Dic3#9912yes—
253C22×Q8—91no—
254C23×C4—31no—
255C22×C8—61no—
256C22⋊Q8—31no—
257C22⋊Q8—91no—
258C22⋊Q8—91no—
259C22⋊Q8—91no—
260C22⋊Q8—181no—
261C22⋊Q8—181no—
262C2×C4⋊C4—91no—
263C2×C4⋊C4—181no—
264C2×C4⋊C4—181no—
265C2×C22⋊C4—181no—
266C2×C22⋊C4—181no—
267C22⋊C8—31no—
268C22⋊C8—61no—
269C22⋊C8D3211yescharacteristic
270#95—31no—
271#95—91no—
272C23×C3—21no—
273C23×C3—31no—
274C23×C3—31no—
275C23×C3—32no—
276C23×C3—32no—
277C23×C3—121no—
278C23×C3—121no—
279C23×C3C2×D1211yescharacteristic
280C23×C3D3×D411yescharacteristic
281C22×D3—41no—
282C22×D3—41no—
283C22×D3#20412yes—
284C22×D3Dic1212yes—
285C22×D3(C2×D3)⋊C411yescharacteristic
286C22×D3(C2×D3)⋊C411yescharacteristic
287C3×Q8—121no—
288C2×C3×C4—21no—
289C2×C3×C4—21no—
290C2×C3×C4—31no—
291C2×C3×C4—31no—
292C2×C3×C4—41no—
293C2×C3×C4—41no—
294C2×C3×C4—62no—
295C2×C3×C4—62no—
296C2×C3×C4—62no—
297C2×C3×C4—61no—
298C2×C3×C4—61no—
299C2×C3×C4—81no—
300C2×C3×C4—121no—
301C2×C3×C4—121no—
302C2×C3×C4—121no—
303C2×C3×C4—121no—
304C2×C3×C4—121no—
305C2×C3×C4C2×C4×D311yescharacteristic
306C2×C3×C4C2×C4×D311yescharacteristic
307C2×C3×C4D3×D411yescharacteristic
308C2×C3×C4C2×#6711yescharacteristic
309C2×Dic3—22no—
310C2×Dic3—21no—
311C2×Dic3—21no—
312C2×Dic3—41no—
313C2×Dic3—41no—
314C2×Dic3—41no—
315C2×Dic3—61no—
316C2×Dic3—61no—
317C2×Dic3—61no—
318C2×Dic3—61no—
319C2×Dic3—121no—
320C2×Dic3—121no—
321C2×Dic3—122no—
322C2×Dic3—122no—
323C2×Dic3—121no—
324C2×Dic3—121no—
325C2×Dic3—121no—
326C2×Dic3—121no—
327C2×Dic3—122no—
328C2×Dic3—121no—
329C2×Dic3—121no—
330C2×Dic3—241no—
331C2×Dic3—241no—
332C2×Dic3(C2×D3)⋊C411yescharacteristic
333C2×Dic3(C2×D3)⋊C411yescharacteristic
334C4×D3—22no—
335C4×D3—22no—
336C4×D3—41no—
337C4×D3—41no—
338C4×D3—122no—
339C4×D3—122no—
340Dic6—41no—
341Dic6—122no—
342Dic6—122no—
343Dic6—121no—
344Dic6—121no—
345Dic6—241no—
346C3×C8—41no—
347C3×C8—41no—
348C3×C8—81no—
349C3×C8—121no—
350C3⋊C8—41no—
351C2×C32—21no—
352C2×C32—21no—
353C2×C32C2×#9911yescharacteristic
354C2×C32C2×#10311yescharacteristic
355C2×C32#42111yescharacteristic
356C3×D3—22no—
357C3×D3—22no—
358C24—31no—
359C2×Q8—31no—
360C2×Q8—91no—
361C2×Q8—181no—
362C2×Q8—362no—
363C22×C4—31no—
364C22×C4—31no—
365C22×C4—31no—
366C22×C4—31no—
367C22×C4—31no—
368C22×C4—61no—
369C22×C4—122no—
370C22×C4—181no—
371C22×C4—181no—
372C22×C4—181no—
373C22×C4C2×D3211yescharacteristic
374C2×C8—21no—
375C2×C8—61no—
376C2×C8—122no—
377C4⋊C4—31no—
378C4⋊C4—61no—
379C4⋊C4—91no—
380C4⋊C4—181no—
381C4⋊C4—181no—
382C4⋊C4—181no—
383C4⋊C4—181no—
384C4⋊C4—362no—
385C22⋊C4—61no—
386C22⋊C4—181no—
387C22⋊C4—181no—
388C22⋊C4—181no—
389C22⋊C4—362no—
390C22×C3—21no—
391C22×C3—21no—
392C22×C3—21no—
393C22×C3—21no—
394C22×C3—21no—
395C22×C3—21no—
396C22×C3—21no—
397C22×C3—32no—
398C22×C3—32no—
399C22×C3—41no—
400C22×C3—41no—
401C22×C3—61no—
402C22×C3—61no—
403C22×C3—61no—
404C22×C3—61no—
405C22×C3—122no—
406C22×C3—122no—
407C22×C3D3×C22⋊C411yescharacteristic
408C22×C3C2×#20411yescharacteristic
409C22×C3C2×Dic1211yescharacteristic
410C22×C3D3×SD1611yescharacteristic
411C22×C3D3×Q1611yescharacteristic
412C22×C3C2×(C2×D3)⋊C411yescharacteristic
413C2×D3—21no—
414C2×D3—21no—
415C2×D3—21no—
416C2×D3—21no—
417C2×D3—42no—
418C2×D3—42no—
419C2×D3#81612yes—
420C2×D3#81612yes—
421C3×C4—21no—
422C3×C4—21no—
423C3×C4—21no—
424C3×C4—21no—
425C3×C4—32no—
426C3×C4—41no—
427C3×C4—41no—
428C3×C4—61no—
429C3×C4—121no—
430C3×C4—121no—
431C3×C4—241no—
432Dic3—21no—
433Dic3—41no—
434Dic3—41no—
435Dic3—81no—
436Dic3—121no—
437Dic3—121no—
438Dic3—121no—
439Dic3—121no—
440Dic3—241no—
441Dic3—241no—
442Dic3—241no—
443Dic3—241no—
444Dic3—242no—
445Dic3#80612yes—
446C32#152011yescharacteristic, complemented, Sylow
447C23—31no—
448C23—31no—
449C23—32no—
450C23—32no—
451C23—121no—
452C23—121no—
453C23D3×D1211yescharacteristic
454Q8—121no—
455Q8—361no—
456Q8—362no—
457C2×C4—31no—
458C2×C4—31no—
459C2×C4—41no—
460C2×C4—62no—
461C2×C4—62no—
462C2×C4—62no—
463C2×C4—61no—
464C2×C4—61no—
465C2×C4—121no—
466C2×C4—121no—
467C2×C4—121no—
468C2×C4—121no—
469C2×C4—121no—
470C2×C4—181no—
471C2×C4—181no—
472C2×C4—362no—
473C2×C4—362no—
474C2×C4—361no—
475C2×C4—361no—
476C2×C4—361no—
477C2×C4C4×D3211yescharacteristic
478C2×C4D3×#6711yescharacteristic
479C8—41no—
480C8—121no—
481C2×C3—21no—
482C2×C3—21no—
483C2×C3—21no—
484C2×C3—21no—
485C2×C3—21no—
486C2×C3—21no—
487C2×C3—21no—
488C2×C3—41no—
489C2×C3—41no—
490C2×C3—62no—
491C2×C3—62no—
492C2×C3D3×#9911yescharacteristic
493C2×C3D3×#10311yescharacteristic
494C2×C3#482111yescharacteristic
495C2×C3C2×#80611yescharacteristic
496C2×C3C2×#81611yescharacteristic
497C2×C3#513911yescharacteristic
498D3—22no—
499D3—22no—
500C22—21no—
501C22—21no—
502C22—32no—
503C22—32no—
504C22—61no—
505C22—61no—
506C22—61no—
507C22—61no—
508C22—122no—
509C22—122no—
510C22D3×#20411yescharacteristic
511C22D3×Dic1211yescharacteristic
512C22D3×(C2×D3)⋊C411yescharacteristic
513C4—21no—
514C4—21no—
515C4—32no—
516C4—61no—
517C4—121no—
518C4—121no—
519C4—241no—
520C4—361no—
521C4—361no—
522C4—721no—
523C3—21no—
524C3#6833911yescharacteristic, complemented
525C3#6994611yescharacteristic, complemented
526C2—21no—
527C2—21no—
528C2—62no—
529C2—62no—
530C2D3×#80611yescharacteristic
531C2D3×#81611yescharacteristic
532C2#1059100511yescharacteristic
subgroupG/H
centerC22D3×(C2×D3)⋊C4
commutatorC2×C32×C4C22×C4
FrattiniC22×C4C2×D32
FittingC32×C22⋊C8C22
socleC22×C32C2×C22⋊C4
prime radicalC23×C3×D3D4
cosocleC22×C32×C4C23
hypercenterC22⋊C8D32
hypocenterC32#1520
LCSG ▷ C2×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
4. #10589333C2semidirect
5. C3×#4467C2semidirect
6. #10589154C2semidirect
7. #10589152C2semidirect
11. C2×D3×Dic6C4semidirect
19. D3×C4⋊Dic3C4semidirect
21. #63857C4semidirect
22. #63856C4semidirect
42. #4467D3semidirect
446. C32#1520semidirect
524. C3#68339semidirect
525. C3#69946semidirect

Maximal subgroups

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

subgroupindex
D3×#9242
C3×D3×C22⋊C82
#105912952
#105893332
C3×#44672
#105891542
#105891522
#699463
#683393