Finite Group Databasebeta

← #11895354

Subgroups — #11895354

Order 1152.

775 conjugacy classes of subgroups.

The subgroup lattice has 526 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#5585C211yesmaximal, characteristic, complemented
2C3×#5579C211yesmaximal, characteristic, complemented
3Q8×C3⋊(C3⋊C8)C211yesmaximal, characteristic, complemented
4C4×#3715C211yesmaximal, characteristic, complemented
5#10590348C212yesmaximal, complemented
6#10590347C211yesmaximal, characteristic
7C4×#3713C212yesmaximal, complemented
8#10590310C211yesmaximal, characteristic, complemented
9#10590278C212yesmaximal, complemented
10#10590277C211yesmaximal, characteristic, complemented
11#10590270C212yesmaximal, complemented
12#83713—31nomaximal
13#83643—31nomaximal
14C32×C4×Q8C2211yescharacteristic
15C3×#947—21no—
16C3×#946—21no—
17C3×#896—22no—
18C3×#894—22no—
19C3×#893—21no—
20C3×D3×C4⋊C4—21no—
21C3×#875C2212yes—
22C3×#874C2211yescharacteristic
23C3×C4×D12C2212yes—
24C3×C4×D12C2212yes—
25C3×C4×D12C2211yescharacteristic
26C3×#870C2212yes—
27C3×#869C2211yescharacteristic
28C3×C4×Dic6C2211yescharacteristic
29C2×#3715C2211yescharacteristic
30C2×#3713C2212yes—
31C4⋊(C3⋊(C3⋊C8))C2212yes—
32C4⋊(C3⋊(C3⋊C8))C2211yescharacteristic
33C4×C3⋊(C3⋊C8)C2211yescharacteristic
34C4×C3⋊(C3⋊C8)C2212yes—
35#63576C2212yes—
36#63574C2211yescharacteristic
37#63565C2211yescharacteristic
38#63565C2212yes—
39#63562C2212yes—
40#63562C2212yes—
41#63562C2212yes—
42#63562C2211yescharacteristic
43C3×#559—31no—
44C3×#554—31no—
45#5585D311yescharacteristic, complemented
46#5579D311yescharacteristic, complemented
47#5091—31no—
48#5088—31no—
49#5072—31no—
50#5070—31no—
51#5068—32no—
52#5066—32no—
53#5057—32no—
54#5056—32no—
55C4×#215—31no—
56Q8×C3⋊C8—31no—
57Q8×C3⋊C8—31no—
58Q8×C3⋊C8—61no—
59#5021—31no—
60C4×#214—31no—
61#5016—32no—
62#5015—31no—
63C4×#213—32no—
64C4×#213—32no—
65#5009—32no—
66C2×C32×Q8D411yescharacteristic
67C2×C3×D12—21no—
68C2×C3×D12—21no—
69C2×C3×D12C2312yes—
70C2×C3×D12C2311yescharacteristic
71C2×C3×C4×D3—21no—
72C2×C3×C4×D3—22no—
73C2×C3×C4×D3—22no—
74C2×C3×Dic6—21no—
75C2×C3×Dic6C2311yescharacteristic
76C32×C4⋊C4D411yescharacteristic
77C32×C4⋊C4D412yes—
78C32×C42C2311yescharacteristic
79C32×C42C2312yes—
80C2×C3⋊(C3⋊C8)C2311yescharacteristic
81C2×C3⋊(C3⋊C8)C2311yescharacteristic
82C2×C3⋊(C3⋊C8)C2312yes—
83C3×(C2×D3)⋊C4—22no—
84C3×(C2×D3)⋊C4—22no—
85C3×(C2×D3)⋊C4—22no—
86C3×(C2×D3)⋊C4—21no—
87C3×(C2×D3)⋊C4—22no—
88C3×C4⋊Dic3—21no—
89C3×C4⋊Dic3C2311yescharacteristic
90C3×C4⋊Dic3C2312yes—
91C3×C4⋊Dic3C2311yescharacteristic
92C3×Dic3⋊C4—22no—
93C3×Dic3⋊C4—21no—
94C3×Dic3⋊C4—22no—
95C3×C4×Dic3—21no—
96#3715—22no—
97#3713—24no—
98#3361—91noSylow
99C3×C4⋊Q8—31no—
100C3×#127—31no—
101C3×#125—32no—
102C3×#124—32no—
103C3×#124—61no—
104C3×#123—62no—
105C3×C22⋊Q8—61no—
106C3×C22⋊Q8—62no—
107C3×C4×Q8—21no—
108C3×C4×Q8—31no—
109C3×C4×Q8C2×D311yescharacteristic
110C3×C4×Q8C2×D311yescharacteristic
111C3×C4×D4—32no—
112C3×C4×D4—32no—
113C3×C4×D4—31no—
114C3×C4×D4—61no—
115C2×C3×C4⋊C4—61no—
116#947—21no—
117#946—21no—
118C2×#215—31no—
119C2×#214—31no—
120C2×#213—32no—
121C2×#213—32no—
122#896—22no—
123#894—22no—
124#893—21no—
125D3×C4⋊C4—21no—
126#875C2×D312yes—
127#874C2×D311yescharacteristic
128C4×D12C2×D312yes—
129C4×D12C2×D312yes—
130C4×D12C2×D311yescharacteristic
131#870C2×D312yes—
132#869C2×D311yescharacteristic
133C4×Dic6C2×D311yescharacteristic
134#835—32no—
135#835—31no—
136#832—32no—
137#832—32no—
138#832—31no—
139#832—32no—
140#810—32no—
141#810—31no—
142#809—31no—
143#809—32no—
144#809—32no—
145#809—32no—
146#808—31no—
147#808—31no—
148#807—32no—
149#807—32no—
150C4⋊(C3⋊C8)—32no—
151C4⋊(C3⋊C8)—31no—
152C4⋊(C3⋊C8)—32no—
153C4⋊(C3⋊C8)—31no—
154C4⋊(C3⋊C8)—61no—
155C4⋊(C3⋊C8)—62no—
156C4×C3⋊C8—32no—
157C4×C3⋊C8—32no—
158C4×C3⋊C8—31no—
159C4×C3⋊C8—31no—
160C4×C3⋊C8—62no—
161C4×C3⋊C8—61no—
162C22×C3×D3—21no—
163C22×C3×D3—22no—
164C32×Q8—22no—
165C2×C32×C4C2×D412yes—
166C2×C32×C4C2×D411yescharacteristic
167C2×C32×C4C2×D412yes—
168C2×C32×C4C2×D411yescharacteristic
169C2×C32×C4C2411yescharacteristic
170C2×C3×Dic3—21no—
171C2×C3×Dic3—21no—
172C2×C3×Dic3—21no—
173C2×C3×Dic3—22no—
174C3×D12—22no—
175C3×D12—21no—
176C3×D12—22no—
177C3×D12—42no—
178C3×D12—81no—
179C3×D12#4112yes—
180C3×C4×D3—42no—
181C3×C4×D3—82no—
182C3×C4×D3—82no—
183C3×Dic6—21no—
184C3×Dic6—21no—
185C3×Dic6—81no—
186C3⋊(C3⋊C8)—21no—
187C3⋊(C3⋊C8)—22no—
188C3⋊(C3⋊C8)—21no—
189#559—31no—
190#554—31no—
191#488—92no—
192#486—91no—
193#478—92no—
194#477—91no—
195#463—92no—
196#459—91no—
197C8×Q8—91no—
198C4×SD16—91no—
199C4×D8—92no—
200C2×C3×Q8—21no—
201C2×C3×Q8—31no—
202C2×C3×Q8—61no—
203C2×C3×Q8#6711yescharacteristic
204C2×C3×Q8#6711yescharacteristic
205C2×C3×D4—31no—
206C2×C3×D4—32no—
207C2×C3×D4—61no—
208C2×C3×D4—61no—
209C22×C3×C4—61no—
210C22×C3×C4—62no—
211C22×C3×C4—62no—
212C2×D12—21no—
213C2×D12—21no—
214C2×D12C22×D312yes—
215C2×D12C22×D311yescharacteristic
216C2×C4×D3—21no—
217C2×C4×D3—22no—
218C2×C4×D3—22no—
219C2×Dic6—21no—
220C2×Dic6C22×D311yescharacteristic
221C3×C4⋊C4—21no—
222C3×C4⋊C4—22no—
223C3×C4⋊C4—31no—
224C3×C4⋊C4—32no—
225C3×C4⋊C4—31no—
226C3×C4⋊C4—62no—
227C3×C4⋊C4—61no—
228C3×C4⋊C4—62no—
229C3×C4⋊C4—61no—
230C3×C4⋊C4#6711yescharacteristic
231C3×C4⋊C4#6711yescharacteristic
232C3×C4⋊C4#6712yes—
233C3×C4⋊C4#6712yes—
234C3×C22⋊C4—61no—
235C3×C22⋊C4—62no—
236C3×C22⋊C4—62no—
237C3×C22⋊C4—62no—
238C3×C22⋊C4—62no—
239C3×C42—22no—
240C3×C42—21no—
241C3×C42—61no—
242C3×C42C22×D311yescharacteristic
243C3×C42C22×D311yescharacteristic
244C3×C42C22×D312yes—
245C3×C42C22×D312yes—
246#215—62no—
247#214—62no—
248#213—64no—
249#213—64no—
250(C2×D3)⋊C4—22no—
251(C2×D3)⋊C4—21no—
252(C2×D3)⋊C4—22no—
253(C2×D3)⋊C4—22no—
254(C2×D3)⋊C4—22no—
255C4⋊Dic3—21no—
256C4⋊Dic3C22×D311yescharacteristic
257C4⋊Dic3C22×D312yes—
258C4⋊Dic3C22×D311yescharacteristic
259Dic3⋊C4—21no—
260Dic3⋊C4—22no—
261Dic3⋊C4—22no—
262C4×Dic3—21no—
263C2×C3⋊C8—31no—
264C2×C3⋊C8—31no—
265C2×C3⋊C8—32no—
266C2×C3⋊C8—32no—
267C2×C3⋊C8—31no—
268C2×C3⋊C8—31no—
269C2×C3⋊C8—61no—
270C2×C3⋊C8—61no—
271C2×C3⋊C8—62no—
272C22×C32C22×D411yescharacteristic
273C2×C3×D3—22no—
274C2×C3×D3—41no—
275C2×C3×D3—41no—
276C2×C3×D3—42no—
277C2×C3×D3—42no—
278C2×C3×D3—42no—
279C32×C4—22no—
280C32×C4—21no—
281C32×C4—22no—
282C32×C4#13512yes—
283C32×C4C2×#4111yescharacteristic
284C32×C42−1+411yescharacteristic
285C3×Dic3—41no—
286C3×Dic3—41no—
287C3×Dic3—42no—
288C3×Dic3—41no—
289C2×SD16—91no—
290C2×D8—92no—
291C4⋊Q8—31no—
292#127—31no—
293#125—32no—
294#124—32no—
295#124—61no—
296#123—62no—
297C22⋊Q8—61no—
298C22⋊Q8—62no—
299C4×Q8—31no—
300C4×Q8D3211yescharacteristic
301C4×D4—32no—
302C4×D4—31no—
303C4×D4—32no—
304C4×D4—61no—
305C2×C4⋊C4—61no—
306#107—92no—
307#106—91no—
308C4⋊C8—91no—
309C4⋊C8—92no—
310#103—91no—
311#103—92no—
312#102—91no—
313#102—92no—
314#102—92no—
315#102—92no—
316C4×C8—92no—
317C4×C8—91no—
318C23×C3—61no—
319C23×C3—62no—
320C22×D3—21no—
321C22×D3—22no—
322C3×Q8—24no—
323C3×Q8—22no—
324C3×Q8—22no—
325C3×Q8—61no—
326C3×Q8—61no—
327C3×Q8—241no—
328C3×D4—32no—
329C3×D4—62no—
330C3×D4—62no—
331C3×D4—61no—
332C3×D4—122no—
333C3×D4—241no—
334C2×C3×C4—21no—
335C2×C3×C4—22no—
336C2×C3×C4—21no—
337C2×C3×C4—22no—
338C2×C3×C4—21no—
339C2×C3×C4—61no—
340C2×C3×C4—61no—
341C2×C3×C4—61no—
342C2×C3×C4—62no—
343C2×C3×C4—122no—
344C2×C3×C4—242no—
345C2×C3×C4—242no—
346C2×C3×C4C2×#6712yes—
347C2×C3×C4C2×#6712yes—
348C2×C3×C4C2×#6711yescharacteristic
349C2×C3×C4C2×#6712yes—
350C2×C3×C4C2×#6711yescharacteristic
351C2×C3×C4C2×#6712yes—
352C2×C3×C4C2×#6711yescharacteristic
353C2×C3×C4C2×#6711yescharacteristic
354C2×C3×C4C23×D311yescharacteristic
355C2×C3×C4C23×D311yescharacteristic
356C2×Dic3—21no—
357C2×Dic3—21no—
358C2×Dic3—21no—
359C2×Dic3—22no—
360D12—21no—
361D12—22no—
362D12—22no—
363D12—42no—
364D12—81no—
365D12#23912yes—
366C4×D3—42no—
367C4×D3—82no—
368C4×D3—82no—
369Dic6—21no—
370Dic6—21no—
371Dic6—81no—
372C3⋊C8—62no—
373C3⋊C8—62no—
374C3⋊C8—61no—
375C3⋊C8—61no—
376C3⋊C8—62no—
377C3⋊C8—61no—
378C3⋊C8—61no—
379C3⋊C8—122no—
380C3⋊C8—121no—
381C2×C32#54811yescharacteristic
382C2×C32C2×#13511yescharacteristic
383C2×C32#57611yescharacteristic
384C3×D3—42no—
385C3×D3—82no—
386C2×Q8—31no—
387C2×Q8—61no—
388C2×Q8#62511yescharacteristic
389C2×D4—31no—
390C2×D4—32no—
391C2×D4—61no—
392C2×D4—61no—
393C22×C4—61no—
394C22×C4—62no—
395C22×C4—62no—
396SD16—182no—
397D8—184no—
398C2×C8—91no—
399C2×C8—91no—
400C2×C8—92no—
401C4⋊C4—31no—
402C4⋊C4—32no—
403C4⋊C4—31no—
404C4⋊C4—62no—
405C4⋊C4—61no—
406C4⋊C4—61no—
407C4⋊C4—62no—
408C4⋊C4#62511yescharacteristic
409C4⋊C4#62512yes—
410C22⋊C4—61no—
411C22⋊C4—62no—
412C22⋊C4—62no—
413C22⋊C4—62no—
414C22⋊C4—62no—
415C42—61no—
416C42C2×D3212yes—
417C42C2×D3211yescharacteristic
418C22×C3—21no—
419C22×C3—62no—
420C22×C3—121no—
421C22×C3—121no—
422C22×C3—122no—
423C22×C3—122no—
424C22×C3—122no—
425C22×C3C22×#6711yescharacteristic
426C22×C3C22×#6711yescharacteristic
427C2×D3—22no—
428C2×D3—41no—
429C2×D3—41no—
430C2×D3—42no—
431C2×D3—42no—
432C2×D3—42no—
433C3×C4—24no—
434C3×C4—22no—
435C3×C4—22no—
436C3×C4—21no—
437C3×C4—22no—
438C3×C4—22no—
439C3×C4—21no—
440C3×C4—21no—
441C3×C4—21no—
442C3×C4—22no—
443C3×C4—42no—
444C3×C4—41no—
445C3×C4—121no—
446C3×C4—121no—
447C3×C4—121no—
448C3×C4—122no—
449C3×C4#95012yes—
450C3×C4#95012yes—
451C3×C4C2×#23911yescharacteristic
452C3×C4#100711yescharacteristic
453C3×C4D3×#4111yescharacteristic
454C3×C4#101011yescharacteristic
455Dic3—41no—
456Dic3—41no—
457Dic3—42no—
458Dic3—41no—
459C32#336111yescharacteristic, complemented, Sylow
460C23—61no—
461C23—62no—
462Q8—22no—
463Q8—61no—
464Q8—61no—
465Q8—241no—
466D4—32no—
467D4—61no—
468D4—62no—
469D4—62no—
470D4—122no—
471D4—241no—
472C2×C4—61no—
473C2×C4—61no—
474C2×C4—61no—
475C2×C4—62no—
476C2×C4—122no—
477C2×C4—242no—
478C2×C4—242no—
479C2×C4C2×#62512yes—
480C2×C4C2×#62512yes—
481C2×C4C2×#62511yescharacteristic
482C2×C4C2×#62511yescharacteristic
483C2×C4C22×D3211yescharacteristic
484C8—181no—
485C8—182no—
486C8—181no—
487C2×C3—21no—
488C2×C3—21no—
489C2×C3—21no—
490C2×C3—122no—
491C2×C3—242no—
492C2×C3#581711yescharacteristic
493C2×C3C2×#95011yescharacteristic
494C2×C3C2×#95011yescharacteristic
495C2×C3#583111yescharacteristic
496C2×C3#583511yescharacteristic
497C2×C3#583511yescharacteristic
498D3—42no—
499D3—82no—
500C22—62no—
501C22—121no—
502C22—121no—
503C22—122no—
504C22—122no—
505C22—122no—
506C22C22×#62511yescharacteristic
507C4—22no—
508C4—21no—
509C4—22no—
510C4—121no—
511C4—121no—
512C4—122no—
513C4—121no—
514C4#6382212yes—
515C4#6431511yescharacteristic
516C4D3×#23911yescharacteristic
517C3—21no—
518C3#8364311yescharacteristic, complemented
519C3#8371311yescharacteristic, complemented
520C2—122no—
521C2—242no—
522C2C2×#6382211yescharacteristic
523C2#1059540911yescharacteristic
524C2#1059544411yescharacteristic
subgroupG/H
centerC22C22×#625
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×C4×Q8C22
socleC22×C32C22×D4
prime radical#10590347C2
hypercenterC4×Q8D32
hypocenterC32#3361
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C4×Q8

Complements

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

NH ≅ G/Ntype
1. C3×#5585C2semidirect
2. C3×#5579C2semidirect
3. Q8×C3⋊(C3⋊C8)C2semidirect
4. C4×#3715C2semidirect
5. #10590348C2semidirect
7. C4×#3713C2semidirect
8. #10590310C2semidirect
9. #10590278C2semidirect
10. #10590277C2semidirect
11. #10590270C2semidirect
45. #5585D3semidirect
46. #5579D3semidirect
459. C32#3361semidirect
518. C3#83643semidirect
519. C3#83713semidirect

Maximal subgroups

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

subgroupindex
C3×#55852
C3×#55792
Q8×C3⋊(C3⋊C8)2
C4×#37152
#105903482
#105903472
C4×#37132
#105903102
#105902782
#105902772
#105902702
#837133
#836433