Finite Group Databasebeta

← #11785321

Subgroups — #11785321

Order 1152.

779 conjugacy classes of subgroups.

The subgroup lattice has 556 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C4×#3828C211yesmaximal, characteristic
2C3×C4×C4⋊Dic3C211yesmaximal, characteristic, complemented
3C3×#4924C211yesmaximal, characteristic, complemented
4C2×#63570C212yesmaximal
5#10589162C212yesmaximal, complemented
6#70529—31nomaximal
7#69494—31nomaximal
8C2×#3828C2211yescharacteristic
9C2×C32×C42C2211yescharacteristic
10C4×#638—21no—
11C4×#638—21no—
12#64135C2211yescharacteristic
13C4×C4⋊(C3⋊D3)C411yescharacteristic, complemented
14C4×C4⋊(C3⋊D3)C411yescharacteristic, complemented
15#64081—21no—
16C42×C3⋊D3—21no—
17C4×#634C411yescharacteristic, complemented
18C4×#634C411yescharacteristic, complemented
19C2×C3×C4⋊Dic3—21no—
20C2×C3×C4×Dic3C2212yes—
21C2×C3×#208C2212yes—
22C3×C3⋊#95—21no—
23C3×C4⋊(C3⋊C8)—21no—
24C3×C4⋊(C3⋊C8)—21no—
25#63570—24no—
26C4×#235—31no—
27C4×#235—31no—
28C4×#235—61no—
29C3×#423—31no—
30C3×C4×C4⋊C4—31no—
31C2×#825—32no—
32C4×C4⋊Dic3D311yescharacteristic, complemented
33C2×#805—32no—
34#4924D311yescharacteristic, complemented
35#4555—32no—
36#4523—32no—
37C22×C32×C4D411yescharacteristic
38C22×C32×C4D411yescharacteristic
39C22×C32×C4C2311yescharacteristic
40C2×#638—21no—
41#3828—21no—
42#3828—21no—
43#3828D412yes—
44#3828Q812yes—
45C2×C4⋊(C3⋊D3)C2×C411yescharacteristic
46C2×C4×C3⋊D3—21no—
47C2×C4×C3⋊D3—21no—
48C2×C4×C3⋊D3—21no—
49C2×#634C2×C411yescharacteristic
50C22×C3×Dic3—22no—
51C32×C42C2×C411yescharacteristic
52C32×C42C2×C411yescharacteristic
53C32×C42D411yescharacteristic
54C32×C42D411yescharacteristic
55#3757—21no—
56#3752—21no—
57#3752—21no—
58C4⋊(C3⋊Dic3)C2×C411yescharacteristic
59C4⋊(C3⋊Dic3)C2×C411yescharacteristic
60#3750—21no—
61#3750—21no—
62C4×C3⋊Dic3—21no—
63C4×C3⋊Dic3—21no—
64C4×C3⋊Dic3—21no—
65C3×C4⋊Dic3—24no—
66C3×C4×Dic3—22no—
67C3×C4×Dic3—22no—
68C3×#208—22no—
69C3×#208—22no—
70C2×C3×C3⋊C8—22no—
71#1806—91noSylow
72C2×#235—31no—
73C2×#235—31no—
74C2×#235—61no—
75C2×C3×M16—32no—
76C2×C3×C4⋊C4—61no—
77C2×C3×C42—21no—
78C2×C3×C42—32no—
79C2×C3×C42C2×D311yescharacteristic
80C2×C3×C42C2×D311yescharacteristic
81C4×#67—62no—
82C4×#67—62no—
83C4×#67—61no—
84C4×#67—61no—
85C4×#67—61no—
86C4×#67—61no—
87#926—31no—
88#926—31no—
89#926—61no—
90C2×C4⋊Dic3—21no—
91C2×C4×Dic3C2×D312yes—
92C2×#208C2×D312yes—
93C4×D12—31no—
94C4×D12—31no—
95C4×D12—31no—
96C4×D12—31no—
97C4×D12—61no—
98C4×D12—61no—
99#872—62no—
100#872—61no—
101#872—61no—
102C42×D3—62no—
103C42×D3—61no—
104C42×D3—61no—
105C4×Dic6—31no—
106C4×Dic6—31no—
107C4×Dic6—31no—
108C4×Dic6—31no—
109C4×Dic6—61no—
110C4×Dic6—61no—
111C3×C4⋊C8—61no—
112C3×C4⋊C8—61no—
113C3×#95—61no—
114C3⋊#95—21no—
115#825—64no—
116#805—64no—
117C4⋊(C3⋊C8)—21no—
118C4⋊(C3⋊C8)—21no—
119C23×C32C2×D411yescharacteristic
120C22×C3⋊D3—21no—
121C2×C32×C4—22no—
122C2×C32×C4—41no—
123C2×C32×C4C22⋊C411yescharacteristic
124C2×C32×C4C22⋊C411yescharacteristic
125C2×C32×C4C22⋊C411yescharacteristic
126C2×C32×C4C22⋊C411yescharacteristic
127C2×C32×C4C22×C411yescharacteristic
128C2×C32×C4C2×D411yescharacteristic
129C2×C32×C4C2×D411yescharacteristic
130C2×C32×C4C2×Q811yescharacteristic
131C2×C32×C4#4111yescharacteristic
132C2×C32×C4#4111yescharacteristic
133#638—22no—
134#638—22no—
135C2×C3⋊Dic3—21no—
136C2×C3⋊Dic3—21no—
137C2×C3⋊Dic3—21no—
138C4⋊(C3⋊D3)—21no—
139C4⋊(C3⋊D3)C4⋊C412yescomplemented
140C4×C3⋊D3—22no—
141C4×C3⋊D3—22no—
142C4×C3⋊D3—42no—
143C4×C3⋊D3—42no—
144#634—21no—
145#634C4⋊C412yescomplemented
146C2×C3×Dic3—24no—
147C2×C3×Dic3—42no—
148C2×C3×Dic3—42no—
149C3×C3⋊C8—42no—
150C4×#41—91no—
151#423—31no—
152C2×#104—92no—
153C4×C4⋊C4—31no—
154#339—92no—
155C22×C3×C4—21no—
156C22×C3×C4—21no—
157C22×C3×C4—21no—
158C22×C3×C4—62no—
159C22×C3×C4D1211yescharacteristic
160C22×C3×C4D1211yescharacteristic
161C22×C3×C4#6711yescharacteristic
162C22×C3×C4#6711yescharacteristic
163C22×C3×C4C22×D311yescharacteristic
164C22×C3×C4C22×D311yescharacteristic
165C2×#67—62no—
166C2×#67—61no—
167C2×#67—61no—
168C22×Dic3—22no—
169#235—32no—
170#235—32no—
171#235—32no—
172#235—32no—
173#235—62no—
174#235—62no—
175#235—62no—
176#235—62no—
177#235—61no—
178#235—61no—
179#235—61no—
180#235—61no—
181C2×D12—31no—
182C2×D12—31no—
183C2×D12—61no—
184C2×C4×D3—62no—
185C2×C4×D3—61no—
186C2×C4×D3—61no—
187C2×C4×D3—62no—
188C2×C4×D3—62no—
189C2×C4×D3—61no—
190C2×C4×D3—61no—
191C2×C4×D3—61no—
192C2×C4×D3—61no—
193C2×Dic6—31no—
194C2×Dic6—31no—
195C2×Dic6—61no—
196C3×M16—62no—
197C3×M16—62no—
198C2×C3×C8—62no—
199C3×C4⋊C4—64no—
200C3×C42—21no—
201C3×C42—21no—
202C3×C42—21no—
203C3×C42—21no—
204C3×C42—62no—
205C3×C42—62no—
206C3×C42C4×D311yescharacteristic
207C3×C42C4×D311yescharacteristic
208C3×C42C4×D311yescharacteristic
209C3×C42C4×D311yescharacteristic
210C3×C42D1211yescharacteristic
211C3×C42D1211yescharacteristic
212C3×C42#6711yescharacteristic
213C3×C42#6711yescharacteristic
214#217—62no—
215#217—61no—
216#217—61no—
217(C2×D3)⋊C4—62no—
218(C2×D3)⋊C4—62no—
219(C2×D3)⋊C4—61no—
220(C2×D3)⋊C4—61no—
221(C2×D3)⋊C4—61no—
222(C2×D3)⋊C4—61no—
223C4⋊Dic3—24no—
224C4⋊Dic3—31no—
225C4⋊Dic3—31no—
226C4⋊Dic3—31no—
227C4⋊Dic3—31no—
228C4⋊Dic3—61no—
229C4⋊Dic3—61no—
230Dic3⋊C4—62no—
231Dic3⋊C4—62no—
232Dic3⋊C4—61no—
233Dic3⋊C4—61no—
234Dic3⋊C4—61no—
235Dic3⋊C4—61no—
236C4×Dic3—22no—
237C4×Dic3—22no—
238C4×Dic3—62no—
239C4×Dic3—62no—
240C4×Dic3—62no—
241C4×Dic3—61no—
242C4×Dic3—61no—
243C4×Dic3—61no—
244C4×Dic3—61no—
245C4×Dic3—61no—
246C4×Dic3—61no—
247#208—22no—
248#208—22no—
249C2×C3⋊C8—22no—
250C22×C32—21no—
251C22×C32—21no—
252C22×C32C2×C22⋊C411yescharacteristic
253C22×C32#12111yescharacteristic
254C22×C32C22⋊Q811yescharacteristic
255C2×C3⋊D3—22no—
256C2×C3⋊D3—41no—
257C2×C3⋊D3—41no—
258C32×C4—21no—
259C32×C4—21no—
260C32×C4—21no—
261C32×C4#10412yescomplemented
262C32×C4C2×C4⋊C411yescharacteristic
263C32×C4#11711yescharacteristic
264C32×C4#12111yescharacteristic
265C32×C4C22⋊Q811yescharacteristic
266C3⋊Dic3—22no—
267C3⋊Dic3—41no—
268C3⋊Dic3—41no—
269C3×Dic3—44no—
270C2×#41—91no—
271C2×M16—32no—
272C4×Q8—91no—
273C4×Q8—91no—
274C4×D4—91no—
275C4×D4—91no—
276C4×D4—181no—
277C4×D4—181no—
278#117—91no—
279#117—181no—
280C2×C4⋊C4—61no—
281C2×C42—32no—
282C2×C42—181no—
283C2×C42D3211yescharacteristic
284C4⋊C8—61no—
285C4⋊C8—61no—
286#104—184no—
287#95—61no—
288C23×C3—21no—
289C23×C3C2×D1211yescharacteristic
290C23×C3C2×#6711yescharacteristic
291C22×D3—62no—
292C22×D3—61no—
293C22×D3—61no—
294C2×C3×C4—22no—
295C2×C3×C4—22no—
296C2×C3×C4—21no—
297C2×C3×C4—21no—
298C2×C3×C4—21no—
299C2×C3×C4—21no—
300C2×C3×C4—21no—
301C2×C3×C4—21no—
302C2×C3×C4—21no—
303C2×C3×C4—21no—
304C2×C3×C4—21no—
305C2×C3×C4—21no—
306C2×C3×C4—42no—
307C2×C3×C4—41no—
308C2×C3×C4—41no—
309C2×C3×C4—42no—
310C2×C3×C4—64no—
311C2×C3×C4—122no—
312C2×C3×C4—122no—
313C2×C3×C4(C2×D3)⋊C411yescharacteristic
314C2×C3×C4(C2×D3)⋊C411yescharacteristic
315C2×C3×C4(C2×D3)⋊C411yescharacteristic
316C2×C3×C4(C2×D3)⋊C411yescharacteristic
317C2×C3×C4(C2×D3)⋊C411yescharacteristic
318C2×C3×C4(C2×D3)⋊C411yescharacteristic
319C2×C3×C4(C2×D3)⋊C411yescharacteristic
320C2×C3×C4(C2×D3)⋊C411yescharacteristic
321C2×C3×C4C2×C4×D311yescharacteristic
322C2×C3×C4C2×C4×D311yescharacteristic
323C2×C3×C4C2×D1211yescharacteristic
324C2×C3×C4D3×D411yescharacteristic
325C2×C3×C4D3×D411yescharacteristic
326C2×C3×C4#23711yescharacteristic
327C2×C3×C4#23711yescharacteristic
328C2×C3×C4D3×Q811yescharacteristic
329C2×C3×C4D3×Q811yescharacteristic
330C2×C3×C4#23911yescharacteristic
331C2×C3×C4#23911yescharacteristic
332C2×C3×C4C2×#6711yescharacteristic
333#67—64no—
334#67—64no—
335#67—62no—
336#67—62no—
337#67—62no—
338#67—62no—
339C2×Dic3—24no—
340C2×Dic3—42no—
341C2×Dic3—42no—
342C2×Dic3—62no—
343C2×Dic3—61no—
344C2×Dic3—61no—
345C2×Dic3—62no—
346C2×Dic3—62no—
347C2×Dic3—61no—
348C2×Dic3—61no—
349C2×Dic3—61no—
350C2×Dic3—61no—
351D12—32no—
352D12—32no—
353D12—62no—
354D12—62no—
355D12—61no—
356D12—61no—
357C4×D3—64no—
358C4×D3—64no—
359C4×D3—62no—
360C4×D3—62no—
361C4×D3—62no—
362C4×D3—62no—
363C4×D3—124no—
364C4×D3—122no—
365C4×D3—122no—
366C4×D3—124no—
367C4×D3—122no—
368C4×D3—122no—
369Dic6—32no—
370Dic6—32no—
371Dic6—62no—
372Dic6—62no—
373Dic6—61no—
374Dic6—61no—
375C3×C8—122no—
376C3⋊C8—42no—
377C2×C32—21no—
378C2×C32—21no—
379C2×C32#38011yescharacteristic
380C2×C32C2×#10411yescharacteristic
381C2×C32#42111yescharacteristic
382C3⋊D3—42no—
383#41—92no—
384#41—92no—
385#41—181no—
386#41—181no—
387C2×Q8—91no—
388C2×D4—91no—
389C2×D4—181no—
390C22×C4—62no—
391C22×C4—181no—
392C22×C4—181no—
393C22×C4—181no—
394C22×C4#62611yescharacteristic
395C22×C4#62611yescharacteristic
396C22×C4C2×D3211yescharacteristic
397M16—62no—
398M16—62no—
399C2×C8—62no—
400C4⋊C4—64no—
401C4⋊C4—91no—
402C4⋊C4—91no—
403C4⋊C4—181no—
404C4⋊C4—181no—
405C22⋊C4—181no—
406C22⋊C4—181no—
407C22⋊C4—181no—
408C42—62no—
409C42—62no—
410C42—181no—
411C42—181no—
412C42—181no—
413C42#62411yescharacteristic
414C42#62411yescharacteristic
415C42#62611yescharacteristic
416C42#62611yescharacteristic
417C22×C3—21no—
418C22×C3—21no—
419C22×C3—21no—
420C22×C3—21no—
421C22×C3—21no—
422C22×C3—21no—
423C22×C3—21no—
424C22×C3—41no—
425C22×C3—41no—
426C22×C3#89511yescharacteristic
427C22×C3#89711yescharacteristic
428C22×C3C2×(C2×D3)⋊C411yescharacteristic
429C22×C3C2×(C2×D3)⋊C411yescharacteristic
430C22×C3#93811yescharacteristic
431C22×C3#94611yescharacteristic
432C2×D3—64no—
433C2×D3—62no—
434C2×D3—62no—
435C2×D3—122no—
436C2×D3—122no—
437C2×D3—121no—
438C2×D3—121no—
439C2×D3—121no—
440C2×D3—121no—
441C3×C4—22no—
442C3×C4—21no—
443C3×C4—21no—
444C3×C4—21no—
445C3×C4—21no—
446C3×C4—21no—
447C3×C4—21no—
448C3×C4—22no—
449C3×C4—21no—
450C3×C4—21no—
451C3×C4—21no—
452C3×C4—21no—
453C3×C4—41no—
454C3×C4—41no—
455C3×C4—124no—
456C3×C4#80512yescomplemented
457C3×C4#82512yescomplemented
458C3×C4D3×C4⋊C411yescharacteristic
459C3×C4D3×C4⋊C411yescharacteristic
460C3×C4#89211yescharacteristic
461C3×C4#89211yescharacteristic
462C3×C4#89511yescharacteristic
463C3×C4#89711yescharacteristic
464C3×C4#93811yescharacteristic
465C3×C4#94611yescharacteristic
466Dic3—44no—
467Dic3—64no—
468Dic3—62no—
469Dic3—62no—
470Dic3—122no—
471Dic3—122no—
472Dic3—121no—
473Dic3—121no—
474Dic3—121no—
475Dic3—121no—
476C32#180611yescharacteristic, complemented, Sylow
477C23—181no—
478C23C2×#62611yescharacteristic
479Q8—92no—
480Q8—181no—
481D4—92no—
482D4—182no—
483D4—182no—
484D4—181no—
485C2×C4—22no—
486C2×C4—41no—
487C2×C4—64no—
488C2×C4—122no—
489C2×C4—122no—
490C2×C4—181no—
491C2×C4—182no—
492C2×C4—182no—
493C2×C4—181no—
494C2×C4—181no—
495C2×C4—362no—
496C2×C4—362no—
497C2×C4#372211yescharacteristic
498C2×C4#372211yescharacteristic
499C2×C4#372211yescharacteristic
500C2×C4#372211yescharacteristic
501C2×C4#379611yescharacteristic
502C2×C4#379611yescharacteristic
503C2×C4#379711yescharacteristic
504C2×C4#380211yescharacteristic
505C2×C4C2×#62411yescharacteristic
506C2×C4C2×#62611yescharacteristic
507C8—122no—
508C2×C3—21no—
509C2×C3—21no—
510C2×C3—21no—
511C2×C3—21no—
512C2×C3—21no—
513C2×C3—21no—
514C2×C3—21no—
515C2×C3—41no—
516C2×C3—41no—
517C2×C3C2×#80511yescharacteristic
518C2×C3#498711yescharacteristic
519C2×C3#498711yescharacteristic
520C2×C3#500511yescharacteristic
521C2×C3C2×#82511yescharacteristic
522C2×C3#513911yescharacteristic
523D3—124no—
524D3—122no—
525D3—122no—
526C22—21no—
527C22—21no—
528C22—182no—
529C22—361no—
530C22—361no—
531C22#6387111yescharacteristic
532C22#6391611yescharacteristic
533C22C2×#372211yescharacteristic
534C4—21no—
535C4—21no—
536C4—21no—
537C4—124no—
538C4—182no—
539C4—361no—
540C4—361no—
541C4#6357012yescomplemented
542C4#6384911yescharacteristic
543C4#6387111yescharacteristic
544C4#6390011yescharacteristic
545C4#6391611yescharacteristic
546C3—21no—
547C3#6949411yescharacteristic, complemented
548C3#7052911yescharacteristic, complemented
549C2—21no—
550C2—21no—
551C2—362no—
552C2C2×#6357011yescharacteristic
553C2#1059111311yescharacteristic
554C2#1059132511yescharacteristic
subgroupG/H
centerC2×C4C2×#626
commutatorC2×C32×C4C22×C4
FrattiniC22×C4C2×D32
FittingC2×C32×C42C22
socleC22×C32C2×C22⋊C4
prime radicalC2×#3828C22
cosocleC22×C32×C4C23
hypercenterC2×C42D32
hypocenterC32#1806
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C2×C4 ◁ C2×C42

Complements

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

NH ≅ G/Ntype
2. C3×C4×C4⋊Dic3C2semidirect
3. C3×#4924C2semidirect
5. #10589162C2semidirect
13. C4×C4⋊(C3⋊D3)C4semidirect
14. C4×C4⋊(C3⋊D3)C4semidirect
17. C4×#634C4semidirect
18. C4×#634C4semidirect
32. C4×C4⋊Dic3D3semidirect
34. #4924D3semidirect
139. C4⋊(C3⋊D3)C4⋊C4semidirect
145. #634C4⋊C4semidirect
261. C32×C4#104semidirect
456. C3×C4#805semidirect
457. C3×C4#825semidirect
476. C32#1806semidirect
541. C4#63570semidirect
547. C3#69494semidirect
548. C3#70529semidirect

Maximal subgroups

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

subgroupindex
C4×#38282
C3×C4×C4⋊Dic32
C3×#49242
C2×#635702
#105891622
#705293
#694943