Finite Group Databasebeta

← #11895259

Subgroups — #11895259

Order 1152.

749 conjugacy classes of subgroups.

The subgroup lattice has 520 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#5732C211yesmaximal, characteristic, complemented
2#10593960C211yesmaximal, characteristic, complemented
3#10592778C211yesmaximal, characteristic, complemented
4C3×#5083C211yesmaximal, characteristic, complemented
5#10591614C212yesmaximal, complemented
6#10591567C212yesmaximal
7Dic3×#215C212yesmaximal, complemented
8#10591545C212yesmaximal, complemented
9C4×#3713C211yesmaximal, characteristic
10#10590268C211yesmaximal, characteristic, complemented
11#10590250C211yesmaximal, characteristic, complemented
12#83667—31nomaximal
13#80415—31nomaximal
14C32×C4⋊Q8C2211yescharacteristic
15#64078C2211yescharacteristic
16C3×#947C2212yes—
17C3×Q8×Dic3C2212yes—
18C2×C3×#215C2212yes—
19C3×#898—22no—
20C3×#897—21no—
21C3×#892—21no—
22C3×C4×D12C2211yescharacteristic
23C3×C4×D12C2211yescharacteristic
24C3×C4×Dic6C2211yescharacteristic
25#63896—22no—
26Dic3×D12C2212yes—
27D3×C4⋊Dic3—21no—
28#63869C2212yes—
29#63856—21no—
30C2×#3713C2211yescharacteristic
31#63662C2212yes—
32#63662C2212yes—
33C4×C3⋊(C3⋊C8)C2211yescharacteristic
34C3×#835C2212yes—
35C3×C4⋊(C3⋊C8)C2211yescharacteristic
36#63576C2211yescharacteristic
37#63573C2212yes—
38Dic3⋊(C3⋊C8)C2212yes—
39#63563C2212yes—
40#63562C2211yescharacteristic
41#63562C2211yescharacteristic
42Dic3×C3⋊C8C2212yes—
43C3×#556—31no—
44#5732D311yescharacteristic, complemented
45#5579—31no—
46#5543—31no—
47C3×#461—31no—
48#5165—32no—
49Dic3×SD16—32no—
50#5083D311yescharacteristic, complemented
51#5079—31no—
52#5079—31no—
53#5079—61no—
54#5057—32no—
55#5056—32no—
56C4×#215—32no—
57Q8×C3⋊C8—31no—
58#5022—32no—
59C4×#213—31no—
60C4×#213—31no—
61#5008—31no—
62#4842—31no—
63#4830—31no—
64#4800—32no—
65#4799—32no—
66C2×C32×Q8C2312yes—
67C2×#634—21no—
68C2×C3×D12C2311yescharacteristic
69C2×C3×D12C2311yescharacteristic
70C2×C3×C4×D3—21no—
71C2×C3×C4×D3—21no—
72C2×C3×Dic6D411yescharacteristic
73C2×D3×Dic3—22no—
74C32×C4⋊C4—21no—
75C32×C4⋊C4—21no—
76C32×C42C2311yescharacteristic
77C4⋊(C3⋊Dic3)—21no—
78C4⋊(C3⋊Dic3)C2312yes—
79C2×C3⋊(C3⋊C8)C2311yescharacteristic
80C2×C3⋊(C3⋊C8)C2311yescharacteristic
81C3×#215—24no—
82C3×(C2×D3)⋊C4—21no—
83C3×(C2×D3)⋊C4—21no—
84C3×(C2×D3)⋊C4—22no—
85C3×(C2×D3)⋊C4—22no—
86C3×C4⋊Dic3—22no—
87C3×C4⋊Dic3D411yescharacteristic
88C3×C4⋊Dic3C2311yescharacteristic
89C3×C4⋊Dic3C2311yescharacteristic
90C3×Dic3⋊C4D412yes—
91C3×C4×Dic3—22no—
92C3×C4×Dic3C2312yes—
93C2×C3×C3⋊C8C2312yes—
94#3724—22no—
95Dic3⋊Dic3—22no—
96(C2×D3)⋊Dic3—22no—
97#3713—22no—
98#3360—91noSylow
99C2×C3×SD16—32no—
100C3×C4⋊Q8—21no—
101C3×C4⋊Q8C2×D311yescharacteristic
102C3×C4⋊Q8C2×D311yescharacteristic
103C3×#126—62no—
104C3×#124—32no—
105C3×C22⋊Q8—61no—
106C3×C4×Q8—31no—
107C3×C4×Q8—32no—
108C3×C4×D4—31no—
109C3×C4×D4—31no—
110C3×#117—61no—
111#947C2×D312yes—
112#946—61no—
113Q8×Dic3C2×D312yes—
114C2×#215C2×D312yes—
115D4×Dic3—32no—
116C2×#213—31no—
117C2×#213—31no—
118C2×C4⋊Dic3—61no—
119#924—61no—
120#898—22no—
121#897—21no—
122#896—62no—
123#892—21no—
124D3×C4⋊C4—61no—
125#890—32no—
126#878—62no—
127C4×D12—32no—
128C4×D12C2×D311yescharacteristic
129C4×D12C2×D311yescharacteristic
130#870—32no—
131#869—31no—
132#869—31no—
133#869—61no—
134C4×Dic6C2×D311yescharacteristic
135C3×C4⋊C8—31no—
136C3×#103—32no—
137#835—32no—
138#835—32no—
139#835—32no—
140#835—32no—
141#835—62no—
142#835—62no—
143#835C2×D312yes—
144#832—31no—
145#832—31no—
146#832—32no—
147#821—32no—
148#817—32no—
149Dic3⋊C8—32no—
150C8×Dic3—32no—
151#809—31no—
152#809—31no—
153#808—32no—
154#807—31no—
155#807—31no—
156C4⋊(C3⋊C8)—32no—
157C4⋊(C3⋊C8)C2×D311yescharacteristic
158C4×C3⋊C8—31no—
159C4×C3⋊C8—31no—
160C4×C3⋊C8—32no—
161C4×C3⋊C8—61no—
162C22×C3×D3—21no—
163C22×C3×D3—21no—
164C32×Q8—22no—
165C32×Q8—22no—
166C2×C32×C4—22no—
167C2×C32×C4C2×D411yescharacteristic
168C2×C32×C4C2×D411yescharacteristic
169C2×C32×C4C2411yescharacteristic
170C2×C3⋊Dic3—22no—
171#634—81no—
172C2×C3×Dic3—21no—
173C2×C3×Dic3—21no—
174C2×C3×Dic3C2×D412yes—
175C2×C3×Dic3C2×D412yes—
176C3×D12—21no—
177C3×D12—21no—
178C3×D12—21no—
179C3×D12#4112yes—
180C3×C4×D3—42no—
181C3×C4×D3—42no—
182C3×Dic6—22no—
183D3×Dic3—82no—
184C3⋊(C3⋊C8)—21no—
185C3⋊(C3⋊C8)—21no—
186C3×C3⋊C8—22no—
187#556—31no—
188#554—91no—
189#488—92no—
190#487—91no—
191#479—92no—
192#476—91no—
193#463—92no—
194#461—31no—
195C8×Q8—91no—
196C4×SD16—92no—
197C4×D8—91no—
198C2×C3×Q8—22no—
199C2×C3×Q8—31no—
200C2×C3×Q8C22×D312yes—
201C2×C3×Q8C22×D312yes—
202C2×C3×D4—31no—
203C2×C3×D4—31no—
204C22×C3×C4—61no—
205C22×C3×C4—61no—
206C22×Dic3—62no—
207C2×D12C22×D311yescharacteristic
208C2×D12C22×D311yescharacteristic
209C2×C4×D3—21no—
210C2×C4×D3—21no—
211C2×C4×D3—62no—
212C2×Dic6—61no—
213C2×Dic6—61no—
214C2×Dic6—121no—
215C2×Dic6#6711yescharacteristic
216C3×SD16—64no—
217C2×C3×C8—32no—
218C3×C4⋊C4—21no—
219C3×C4⋊C4—21no—
220C3×C4⋊C4—21no—
221C3×C4⋊C4—21no—
222C3×C4⋊C4—31no—
223C3×C4⋊C4—32no—
224C3×C4⋊C4—31no—
225C3×C4⋊C4—31no—
226C3×C4⋊C4—41no—
227C3×C4⋊C4—41no—
228C3×C4⋊C4—62no—
229C3×C22⋊C4—62no—
230C3×C22⋊C4—62no—
231C3×C22⋊C4—61no—
232C3×C22⋊C4—61no—
233C3×C42—21no—
234C3×C42—32no—
235C3×C42—62no—
236C3×C42C22×D311yescharacteristic
237C3×C42C22×D311yescharacteristic
238#217—62no—
239#215—24no—
240#213—62no—
241#213—62no—
242(C2×D3)⋊C4—21no—
243(C2×D3)⋊C4—21no—
244(C2×D3)⋊C4—22no—
245(C2×D3)⋊C4—22no—
246(C2×D3)⋊C4—62no—
247C4⋊Dic3—22no—
248C4⋊Dic3—32no—
249C4⋊Dic3—32no—
250C4⋊Dic3—62no—
251C4⋊Dic3—61no—
252C4⋊Dic3—61no—
253C4⋊Dic3—62no—
254C4⋊Dic3—121no—
255C4⋊Dic3#6711yescharacteristic
256C4⋊Dic3C22×D311yescharacteristic
257C4⋊Dic3C22×D311yescharacteristic
258Dic3⋊C4—62no—
259Dic3⋊C4—62no—
260Dic3⋊C4—62no—
261Dic3⋊C4#6712yes—
262C4×Dic3—22no—
263C4×Dic3C22×D312yes—
264C2×C3⋊C8—31no—
265C2×C3⋊C8—31no—
266C2×C3⋊C8—31no—
267C2×C3⋊C8—31no—
268C2×C3⋊C8—61no—
269C2×C3⋊C8—61no—
270C2×C3⋊C8C22×D312yes—
271C22×C32C22×D411yescharacteristic
272C2×C3×D3—22no—
273C2×C3×D3—41no—
274C2×C3×D3—41no—
275C2×C3×D3—41no—
276C2×C3×D3—41no—
277C2×C3×D3—41no—
278C32×C4—21no—
279C32×C4—42no—
280C32×C4#13512yes—
281C32×C4C2×#4111yescharacteristic
282C32×C42−1+411yescharacteristic
283C3⋊Dic3—42no—
284C3×Dic3—22no—
285C3×Dic3—22no—
286C3×Dic3—41no—
287C3×Dic3—41no—
288C2×SD16—32no—
289C2×D8—91no—
290C4⋊Q8—91no—
291C4⋊Q8D3211yescharacteristic
292#126—62no—
293#125—92no—
294#124—32no—
295C22⋊Q8—61no—
296C22⋊Q8—182no—
297C22⋊Q8—181no—
298C4×Q8—31no—
299C4×Q8—32no—
300C4×D4—31no—
301C4×D4—31no—
302C4×D4—92no—
303#117—61no—
304C2×C4⋊C4—181no—
305#107—91no—
306#106—92no—
307C4⋊C8—31no—
308C4⋊C8—92no—
309#103—32no—
310#103—92no—
311#103—92no—
312#102—91no—
313#102—91no—
314#102—92no—
315C4×C8—92no—
316C4×C8—91no—
317C23×C3—61no—
318C23×C3—61no—
319C22×D3—21no—
320C22×D3—21no—
321C3×Q8—22no—
322C3×Q8—22no—
323C3×Q8—22no—
324C3×Q8—22no—
325C3×Q8—42no—
326C3×Q8—42no—
327C3×Q8—62no—
328C3×D4—32no—
329C3×D4—61no—
330C3×D4—61no—
331C3×D4—61no—
332C2×C3×C4—22no—
333C2×C3×C4—22no—
334C2×C3×C4—21no—
335C2×C3×C4—21no—
336C2×C3×C4—21no—
337C2×C3×C4—32no—
338C2×C3×C4—32no—
339C2×C3×C4—42no—
340C2×C3×C4—61no—
341C2×C3×C4—61no—
342C2×C3×C4—122no—
343C2×C3×C4—122no—
344C2×C3×C4D3×D411yescharacteristic
345C2×C3×C4D3×D411yescharacteristic
346C2×C3×C4C2×#6711yescharacteristic
347C2×C3×C4C2×#6711yescharacteristic
348C2×C3×C4C23×D311yescharacteristic
349C2×C3×C4C23×D311yescharacteristic
350C2×Dic3—21no—
351C2×Dic3—21no—
352C2×Dic3—62no—
353C2×Dic3—62no—
354C2×Dic3—122no—
355C2×Dic3—242no—
356C2×Dic3C2×#6712yes—
357C2×Dic3C2×#6712yes—
358D12—21no—
359D12—21no—
360D12—21no—
361D12#23712yes—
362C4×D3—42no—
363C4×D3—42no—
364C4×D3—242no—
365Dic6—22no—
366Dic6—241no—
367Dic6—241no—
368Dic6—242no—
369C3×C8—62no—
370C3⋊C8—22no—
371C3⋊C8—61no—
372C3⋊C8—61no—
373C3⋊C8—61no—
374C3⋊C8—61no—
375C3⋊C8—121no—
376C3⋊C8—121no—
377C2×C32#54811yescharacteristic
378C2×C32C2×#13511yescharacteristic
379C2×C32#57711yescharacteristic
380C3×D3—42no—
381C3×D3—81no—
382C2×Q8—31no—
383C2×Q8—181no—
384C2×Q8C2×D3212yes—
385C2×D4—31no—
386C2×D4—31no—
387C22×C4—61no—
388C22×C4—61no—
389C22×C4—182no—
390SD16—64no—
391D8—182no—
392C2×C8—32no—
393C2×C8—91no—
394C2×C8—91no—
395C4⋊C4—21no—
396C4⋊C4—21no—
397C4⋊C4—31no—
398C4⋊C4—32no—
399C4⋊C4—31no—
400C4⋊C4—31no—
401C4⋊C4—62no—
402C4⋊C4—92no—
403C4⋊C4—182no—
404C4⋊C4—182no—
405C4⋊C4—181no—
406C22⋊C4—62no—
407C22⋊C4—62no—
408C22⋊C4—61no—
409C22⋊C4—61no—
410C22⋊C4—182no—
411C42—32no—
412C42—62no—
413C42C2×D3211yescharacteristic
414C22×C3—21no—
415C22×C3—62no—
416C22×C3—121no—
417C22×C3—121no—
418C22×C3—121no—
419C22×C3—121no—
420C22×C3—121no—
421C22×C3C2×D3×D411yescharacteristic
422C22×C3C22×#6711yescharacteristic
423C2×D3—22no—
424C2×D3—41no—
425C2×D3—41no—
426C2×D3—41no—
427C2×D3—41no—
428C2×D3—41no—
429C3×C4—22no—
430C3×C4—21no—
431C3×C4—21no—
432C3×C4—21no—
433C3×C4—21no—
434C3×C4—22no—
435C3×C4—42no—
436C3×C4—42no—
437C3×C4—62no—
438C3×C4—62no—
439C3×C4—82no—
440C3×C4—121no—
441C3×C4—121no—
442C3×C4#91612yes—
443C3×C4#95012yes—
444C3×C4C2×#23711yescharacteristic
445C3×C4D3×#4111yescharacteristic
446C3×C4#101011yescharacteristic
447C3×C4#101011yescharacteristic
448Dic3—22no—
449Dic3—22no—
450Dic3—41no—
451Dic3—41no—
452Dic3—122no—
453Dic3—122no—
454Dic3—242no—
455C32#336011yescharacteristic, complemented, Sylow
456C23—61no—
457C23—61no—
458Q8—22no—
459Q8—22no—
460Q8—62no—
461Q8—721no—
462D4—32no—
463D4—61no—
464D4—61no—
465D4—61no—
466C2×C4—22no—
467C2×C4—32no—
468C2×C4—32no—
469C2×C4—61no—
470C2×C4—61no—
471C2×C4—122no—
472C2×C4—122no—
473C2×C4—182no—
474C2×C4—722no—
475C2×C4D3×#6711yescharacteristic
476C2×C4D3×#6711yescharacteristic
477C2×C4C22×D3211yescharacteristic
478C8—62no—
479C8—181no—
480C8—181no—
481C2×C3—21no—
482C2×C3—21no—
483C2×C3—21no—
484C2×C3—122no—
485C2×C3—241no—
486C2×C3#559811yescharacteristic
487C2×C3C2×#91611yescharacteristic
488C2×C3#577811yescharacteristic
489C2×C3C2×#95011yescharacteristic
490C2×C3#583111yescharacteristic
491C2×C3#583711yescharacteristic
492D3—42no—
493D3—81no—
494C22—62no—
495C22—121no—
496C22—121no—
497C22—121no—
498C22—121no—
499C22—121no—
500C22C2×D3×#6711yescharacteristic
501C4—21no—
502C4—42no—
503C4—62no—
504C4—62no—
505C4—121no—
506C4—121no—
507C4—362no—
508C4#6394712yes—
509C4#6430911yescharacteristic
510C4D3×#23711yescharacteristic
511C3—21no—
512C3#8041511yescharacteristic, complemented
513C3#8366711yescharacteristic, complemented
514C2—122no—
515C2—241no—
516C2#1059515711yescharacteristic
517C2#1059531911yescharacteristic
518C2C2×#6394711yescharacteristic
subgroupG/H
centerC22C2×D3×#67
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×C4⋊Q8C22
socleC22×C32C22×D4
prime radicalC2×#3713C22
hypercenterC4⋊Q8D32
hypocenterC32#3360
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C42 ◁ C4⋊Q8

Complements

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

NH ≅ G/Ntype
1. C3×#5732C2semidirect
2. #10593960C2semidirect
3. #10592778C2semidirect
4. C3×#5083C2semidirect
5. #10591614C2semidirect
7. Dic3×#215C2semidirect
8. #10591545C2semidirect
10. #10590268C2semidirect
11. #10590250C2semidirect
44. #5732D3semidirect
50. #5083D3semidirect
455. C32#3360semidirect
512. C3#80415semidirect
513. C3#83667semidirect

Maximal subgroups

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

subgroupindex
C3×#57322
#105939602
#105927782
C3×#50832
#105916142
#105915672
Dic3×#2152
#105915452
C4×#37132
#105902682
#105902502
#836673
#804153