Finite Group Databasebeta

← #11895258

Subgroups — #11895258

Order 1152.

760 conjugacy classes of subgroups.

The subgroup lattice has 527 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#5732C211yesmaximal, characteristic, complemented
2#10593958C211yesmaximal, characteristic, complemented
3#10592782C211yesmaximal, characteristic, complemented
4C3×#5079C211yesmaximal, characteristic, complemented
5#10591614C212yesmaximal, complemented
6#10591568C212yesmaximal
7#10591547C212yesmaximal, complemented
8#10591536C212yesmaximal, complemented
9C4×#3714C211yesmaximal, characteristic
10#10590266C211yesmaximal, characteristic, complemented
11C3⋊C8×Dic6C211yesmaximal, characteristic, complemented
12#83667—31nomaximal
13#81621—31nomaximal
14C32×C4⋊Q8C2211yescharacteristic
15C2×#3755C2212yes—
16C4×C4⋊(C3⋊D3)C2211yescharacteristic
17C3×#947C2212yes—
18C3×Q8×Dic3C2212yes—
19C3×#898—22no—
20C3×#897—21no—
21C3×#892—21no—
22C3×C4×D12C2211yescharacteristic
23C3×#869C2211yescharacteristic
24C3×C4×Dic6C2211yescharacteristic
25#63900—21no—
26#63894C2212yes—
27#63888—22no—
28#63871—21no—
29#63869C2212yes—
30C2×#3714C2211yescharacteristic
31#63662C2212yes—
32C4⋊(C3⋊(C3⋊C8))C2211yescharacteristic
33C3×#835C2212yes—
34C3×#835C2212yes—
35C3×C4×C3⋊C8C2211yescharacteristic
36#63575C2211yescharacteristic
37#63574C2212yes—
38Dic3⋊(C3⋊C8)C2212yes—
39#63564C2211yescharacteristic
40#63563C2211yescharacteristic
41#63562C2212yes—
42Dic3×C3⋊C8C2212yes—
43C3×#556—31no—
44#5732D311yescharacteristic, complemented
45#5730—31no—
46#5579—31no—
47C3×#487—31no—
48#5084—31no—
49#5083—31no—
50#5083—31no—
51#5083—61no—
52#5079D311yescharacteristic, complemented
53#5057—32no—
54#5056—32no—
55C4×#215—32no—
56Q8×C3⋊C8—31no—
57#5022—32no—
58C4×#213—31no—
59#5008—31no—
60#4819—32no—
61#4800—32no—
62#4796—32no—
63#4788—32no—
64C4×D24—31no—
65C8×Dic6—31no—
66C2×C32×Q8C2312yes—
67C2×C4⋊(C3⋊D3)C2311yescharacteristic
68C2×C4×C3⋊D3—21no—
69C2×C3×D12C2311yescharacteristic
70C2×C3×C4×D3—21no—
71C2×C3×Dic6—21no—
72C2×C3×Dic6D411yescharacteristic
73C2×#624—22no—
74C32×C4⋊C4—21no—
75C32×C4⋊C4—21no—
76C32×C42C2311yescharacteristic
77#3755—24no—
78#3752—21no—
79C4⋊(C3⋊Dic3)C2311yescharacteristic
80C2×C3⋊(C3⋊C8)C2312yes—
81C3×(C2×D3)⋊C4—21no—
82C3×(C2×D3)⋊C4—22no—
83C3×(C2×D3)⋊C4—22no—
84C3×C4⋊Dic3—21no—
85C3×C4⋊Dic3—22no—
86C3×C4⋊Dic3D411yescharacteristic
87C3×C4⋊Dic3C2311yescharacteristic
88C3×C4⋊Dic3C2312yes—
89C3×Dic3⋊C4D412yes—
90C3×C4×Dic3—22no—
91C3×C4×Dic3C2312yes—
92C2×C3×C3⋊C8C2311yescharacteristic
93C2×C3×C3⋊C8C2311yescharacteristic
94#3724—22no—
95Dic3⋊Dic3—22no—
96#3722—22no—
97#3714—22no—
98#3360—91noSylow
99C3×C4⋊Q8—21no—
100C3×C4⋊Q8—31no—
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×#117—61no—
110#947C2×D312yes—
111#946—61no—
112#946—62no—
113Q8×Dic3C2×D312yes—
114C2×#215—32no—
115C2×#215—32no—
116C2×#215—62no—
117C2×#213—31no—
118C2×D24—31no—
119#898—22no—
120#897—21no—
121#897—61no—
122#896—62no—
123#893—32no—
124#892—21no—
125D3×C4⋊C4—61no—
126D3×C4⋊C4—61no—
127#890—32no—
128C4×D12—31no—
129C4×D12—31no—
130C4×D12—32no—
131C4×D12—61no—
132C4×D12C2×D311yescharacteristic
133#870—32no—
134#869C2×D311yescharacteristic
135C4×Dic6C2×D311yescharacteristic
136C3×#103—32no—
137C3×#103—32no—
138C3×C4×C8—31no—
139#835—32no—
140#835—32no—
141#835—62no—
142#835C2×D312yes—
143#835C2×D312yes—
144#832—32no—
145#832—31no—
146#821—31no—
147#821—31no—
148#818—31no—
149Dic3⋊C8—32no—
150C8×Dic3—32no—
151#809—32no—
152#809—31no—
153#808—32no—
154#808—32no—
155#807—31no—
156C4⋊(C3⋊C8)—31no—
157C4⋊(C3⋊C8)—31no—
158C4⋊(C3⋊C8)—32no—
159C4⋊(C3⋊C8)—61no—
160C4×C3⋊C8—32no—
161C4×C3⋊C8C2×D311yescharacteristic
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—21no—
171C4⋊(C3⋊D3)—21no—
172C4⋊(C3⋊D3)#4112yes—
173C4×C3⋊D3—42no—
174C2×C3×Dic3—22no—
175C2×C3×Dic3—21no—
176C2×C3×Dic3C2×D412yes—
177C2×C3×Dic3C2×D412yes—
178C3×D12—21no—
179C3×D12—21no—
180C3×C4×D3—42no—
181C3×Dic6—22no—
182C3×Dic6—81no—
183#624—82no—
184C3⋊(C3⋊C8)—22no—
185C3×C3⋊C8—21no—
186C3×C3⋊C8—21no—
187#556—31no—
188#554—91no—
189#488—92no—
190#487—31no—
191#479—92no—
192#476—91no—
193#463—92no—
194#461—91no—
195C8×Q8—91no—
196C4×SD16—92no—
197C4×D8—91no—
198C2×C3×Q8—22no—
199C2×C3×Q8—31no—
200C2×C3×Q8—61no—
201C2×C3×Q8C22×D312yes—
202C2×C3×Q8C22×D312yes—
203C2×C3×D4—31no—
204C22×C3×C4—61no—
205C2×D12—31no—
206C2×D12—31no—
207C2×D12—61no—
208C2×D12C22×D311yescharacteristic
209C2×C4×D3—21no—
210C2×C4×D3—61no—
211C2×C4×D3—61no—
212C2×C4×D3—62no—
213C2×C4×D3—62no—
214C2×C4×D3—121no—
215C2×Dic6—21no—
216C2×Dic6#6711yescharacteristic
217C2×C3×C8—31no—
218C2×C3×C8—31no—
219C3×C4⋊C4—21no—
220C3×C4⋊C4—21no—
221C3×C4⋊C4—21no—
222C3×C4⋊C4—21no—
223C3×C4⋊C4—31no—
224C3×C4⋊C4—32no—
225C3×C4⋊C4—31no—
226C3×C4⋊C4—32no—
227C3×C4⋊C4—41no—
228C3×C4⋊C4—41no—
229C3×C4⋊C4—62no—
230C3×C4⋊C4—61no—
231C3×C22⋊C4—62no—
232C3×C22⋊C4—62no—
233C3×C22⋊C4—61no—
234C3×C42—21no—
235C3×C42—32no—
236C3×C42—62no—
237C3×C42C22×D311yescharacteristic
238C3×C42C22×D311yescharacteristic
239#215—64no—
240#215—64no—
241#215—124no—
242#213—62no—
243(C2×D3)⋊C4—21no—
244(C2×D3)⋊C4—22no—
245(C2×D3)⋊C4—22no—
246(C2×D3)⋊C4—62no—
247(C2×D3)⋊C4—61no—
248(C2×D3)⋊C4—61no—
249(C2×D3)⋊C4—62no—
250(C2×D3)⋊C4—121no—
251C4⋊Dic3—21no—
252C4⋊Dic3—22no—
253C4⋊Dic3—31no—
254C4⋊Dic3—31no—
255C4⋊Dic3—61no—
256C4⋊Dic3—62no—
257C4⋊Dic3#6711yescharacteristic
258C4⋊Dic3C22×D311yescharacteristic
259C4⋊Dic3C22×D312yes—
260Dic3⋊C4—62no—
261Dic3⋊C4—62no—
262Dic3⋊C4—62no—
263Dic3⋊C4#6712yes—
264C4×Dic3—22no—
265C4×Dic3C22×D312yes—
266C2×C3⋊C8—32no—
267C2×C3⋊C8—32no—
268C2×C3⋊C8—62no—
269C2×C3⋊C8C22×D311yescharacteristic
270C2×C3⋊C8C22×D311yescharacteristic
271D24—62no—
272C22×C32C22×D411yescharacteristic
273C2×C3⋊D3—22no—
274C2×C3⋊D3—41no—
275C2×C3⋊D3—41no—
276C2×C3×D3—41no—
277C2×C3×D3—41no—
278C2×C3×D3—41no—
279C32×C4—21no—
280C32×C4—42no—
281C32×C4#13512yes—
282C32×C4C2×#4111yescharacteristic
283C32×C42−1+411yescharacteristic
284C3⋊Dic3—41no—
285C3×Dic3—22no—
286C3×Dic3—22no—
287C3×Dic3—41no—
288C3×Dic3—42no—
289C2×SD16—92no—
290C2×D8—91no—
291C4⋊Q8—31no—
292C4⋊Q8D3211yescharacteristic
293#126—62no—
294#125—92no—
295#124—32no—
296C22⋊Q8—61no—
297C22⋊Q8—182no—
298C22⋊Q8—181no—
299C4×Q8—31no—
300C4×Q8—32no—
301C4×D4—31no—
302C4×D4—92no—
303C4×D4—91no—
304#117—61no—
305C2×C4⋊C4—181no—
306#107—91no—
307#106—92no—
308C4⋊C8—92no—
309C4⋊C8—91no—
310#103—32no—
311#103—32no—
312#103—92no—
313#102—91no—
314#102—92no—
315#102—91no—
316C4×C8—31no—
317C4×C8—92no—
318C23×C3—61no—
319C22×D3—21no—
320C22×D3—61no—
321C22×D3—61no—
322C22×D3—121no—
323C3×Q8—22no—
324C3×Q8—22no—
325C3×Q8—22no—
326C3×Q8—22no—
327C3×Q8—42no—
328C3×Q8—42no—
329C3×Q8—62no—
330C3×Q8—241no—
331C3×D4—61no—
332C3×D4—61no—
333C2×C3×C4—22no—
334C2×C3×C4—22no—
335C2×C3×C4—21no—
336C2×C3×C4—21no—
337C2×C3×C4—21no—
338C2×C3×C4—32no—
339C2×C3×C4—32no—
340C2×C3×C4—42no—
341C2×C3×C4—61no—
342C2×C3×C4—62no—
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—22no—
351C2×Dic3—21no—
352C2×Dic3—61no—
353C2×Dic3—61no—
354C2×Dic3—121no—
355C2×Dic3C2×#6712yes—
356C2×Dic3C2×#6712yes—
357D12—21no—
358D12—21no—
359D12—32no—
360D12—32no—
361D12—62no—
362D12—61no—
363D12—61no—
364D12—121no—
365C4×D3—42no—
366C4×D3—122no—
367C4×D3—122no—
368C4×D3—242no—
369C4×D3—242no—
370C4×D3—242no—
371Dic6—22no—
372Dic6—81no—
373C3×C8—61no—
374C3×C8—61no—
375C3⋊C8—21no—
376C3⋊C8—21no—
377C3⋊C8—62no—
378C3⋊C8—62no—
379C3⋊C8—122no—
380C2×C32#54811yescharacteristic
381C2×C32C2×#13511yescharacteristic
382C2×C32#57711yescharacteristic
383C3⋊D3—42no—
384C3×D3—81no—
385C2×Q8—31no—
386C2×Q8—61no—
387C2×Q8C2×D3212yes—
388C2×D4—31no—
389C2×D4—91no—
390C22×C4—61no—
391C22×C4—182no—
392C22×C4—181no—
393SD16—184no—
394D8—182no—
395C2×C8—31no—
396C2×C8—31no—
397C2×C8—92no—
398C4⋊C4—21no—
399C4⋊C4—21no—
400C4⋊C4—31no—
401C4⋊C4—32no—
402C4⋊C4—32no—
403C4⋊C4—31no—
404C4⋊C4—62no—
405C4⋊C4—61no—
406C4⋊C4—91no—
407C4⋊C4—182no—
408C4⋊C4—182no—
409C22⋊C4—62no—
410C22⋊C4—62no—
411C22⋊C4—61no—
412C22⋊C4—182no—
413C22⋊C4—181no—
414C42—32no—
415C42—62no—
416C42C2×D3211yescharacteristic
417C22×C3—21no—
418C22×C3—121no—
419C22×C3—121no—
420C22×C3—121no—
421C22×C3C2×D3×D411yescharacteristic
422C22×C3C22×#6711yescharacteristic
423C2×D3—41no—
424C2×D3—41no—
425C2×D3—41no—
426C2×D3—62no—
427C2×D3—62no—
428C2×D3—122no—
429C2×D3—121no—
430C2×D3—121no—
431C2×D3—121no—
432C2×D3—121no—
433C2×D3—241no—
434C2×D3—241no—
435C3×C4—21no—
436C3×C4—21no—
437C3×C4—21no—
438C3×C4—21no—
439C3×C4—22no—
440C3×C4—41no—
441C3×C4—42no—
442C3×C4—42no—
443C3×C4—62no—
444C3×C4—62no—
445C3×C4—82no—
446C3×C4—121no—
447C3×C4—122no—
448C3×C4#91912yes—
449C3×C4#95012yes—
450C3×C4D3×#4111yescharacteristic
451C3×C4D3×#4111yescharacteristic
452C3×C4#101011yescharacteristic
453C3×C4#101011yescharacteristic
454Dic3—22no—
455Dic3—22no—
456Dic3—42no—
457Dic3—41no—
458Dic3—121no—
459Dic3—121no—
460Dic3—241no—
461C32#336011yescharacteristic, complemented, Sylow
462C23—61no—
463C23—181no—
464Q8—22no—
465Q8—22no—
466Q8—62no—
467Q8—241no—
468D4—61no—
469D4—61no—
470D4—92no—
471D4—181no—
472C2×C4—22no—
473C2×C4—32no—
474C2×C4—32no—
475C2×C4—61no—
476C2×C4—62no—
477C2×C4—122no—
478C2×C4—181no—
479C2×C4—362no—
480C2×C4—722no—
481C2×C4D3×#6711yescharacteristic
482C2×C4D3×#6711yescharacteristic
483C2×C4C22×D3211yescharacteristic
484C8—61no—
485C8—61no—
486C8—182no—
487C2×C3—21no—
488C2×C3—21no—
489C2×C3—21no—
490C2×C3—241no—
491C2×C3#567711yescharacteristic
492C2×C3#576211yescharacteristic
493C2×C3C2×#91911yescharacteristic
494C2×C3C2×#95011yescharacteristic
495C2×C3#583111yescharacteristic
496C2×C3#583711yescharacteristic
497D3—81no—
498D3—122no—
499D3—122no—
500D3—242no—
501C22—121no—
502C22—121no—
503C22—121no—
504C22—182no—
505C22—361no—
506C22—361no—
507C22C2×D3×#6711yescharacteristic
508C4—21no—
509C4—42no—
510C4—62no—
511C4—62no—
512C4—121no—
513C4—122no—
514C4—361no—
515C4#6394912yes—
516C4#6430911yescharacteristic
517C4#6431211yescharacteristic
518C3—21no—
519C3#8162111yescharacteristic, complemented
520C3#8366711yescharacteristic, complemented
521C2—241no—
522C2—362no—
523C2#1059523711yescharacteristic
524C2#1059531811yescharacteristic
525C2C2×#6394911yescharacteristic
subgroupG/H
centerC22C2×D3×#67
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×C4⋊Q8C22
socleC22×C32C22×D4
prime radicalC2×#3714C22
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. #10593958C2semidirect
3. #10592782C2semidirect
4. C3×#5079C2semidirect
5. #10591614C2semidirect
7. #10591547C2semidirect
8. #10591536C2semidirect
10. #10590266C2semidirect
11. C3⋊C8×Dic6C2semidirect
44. #5732D3semidirect
52. #5079D3semidirect
461. C32#3360semidirect
519. C3#81621semidirect
520. C3#83667semidirect

Maximal subgroups

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

subgroupindex
C3×#57322
#105939582
#105927822
C3×#50792
#105916142
#105915682
#105915472
#105915362
C4×#37142
#105902662
C3⋊C8×Dic62
#836673
#816213