Finite Group Databasebeta

← #11859358

Subgroups — #11859358

Order 1152.

1209 conjugacy classes of subgroups.

The subgroup lattice has 509 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C8×C3⋊D3C211yesmaximal, characteristic, complemented
2#10595034C211yesmaximal, characteristic
3C2×#63815C211yesmaximal, characteristic, complemented
4C3×#5110C211yesmaximal, characteristic, complemented
5C3×#5102C211yesmaximal, characteristic, complemented
6#10591074C211yesmaximal, characteristic, complemented
7#10591057C211yesmaximal, characteristic, complemented
8#10590906C214yesmaximal, complemented
9#10590737C214yesmaximal, complemented
10#79073—31nomaximal
11#78655—31nomaximal
12C22×C4×C3⋊D3C2211yescharacteristic
13C2×C3×#235C2211yescharacteristic
14C22×C32×C8C2211yescharacteristic
15C22×C3⋊(C3⋊C8)C2211yescharacteristic
16C2×C8×C3⋊D3—24no—
17C2×C8×C3⋊D3C2212yes—
18C2×C8×C3⋊D3C2212yes—
19C3×#926C2211yescharacteristic
20C2×C3×#208C2211yescharacteristic
21C2×C3×#208C2211yescharacteristic
22#63981C412yes—
23#63962C412yes—
24#63916C412yes—
25C4×#626C2214yes—
26#63871C412yes—
27C2×#3711C2212yescomplemented
28#63815—24no—
29C2×D3×C3⋊C8C2212yescomplemented
30C3×(C2×D3)⋊C8C2214yescomplemented
31C3×Dic3⋊C8C2214yescomplemented
32#63557C2214yes—
33#63554C2212yescomplemented
34Dic3×C3⋊C8C2212yescomplemented
35#5828—31no—
36C2×#948—31no—
37C2×#907—31no—
38C22×D3×C8—31no—
39C22×D3×C8—31no—
40C22×D3×C8—61no—
41#5524—31no—
42C3×#424—31no—
43C3×#408—31no—
44#5126—31no—
45#5126—31no—
46#5122—31no—
47#5110D311yescharacteristic, complemented
48#5102D311yescharacteristic, complemented
49#4997—31no—
50#4836—34no—
51#4834—34no—
52#4728—34no—
53#67⋊C8—34no—
54C23×C3⋊D3C2×C411yescharacteristic
55C22×C32×C4C2311yescharacteristic
56C22×C3⋊Dic3C2×C411yescharacteristic
57C2×C4×C3⋊D3—22no—
58C2×C4×C3⋊D3—22no—
59C2×C4×C3⋊D3C2×C412yes—
60C2×C4×C3⋊D3C2312yes—
61C2×C3×#67C2×C412yes—
62C3×#235—22no—
63C3×#235—22no—
64C2×C3×D12C2×C411yescharacteristic
65C2×C3×C4×D3C2312yes—
66C2×C3×Dic6C2×C411yescharacteristic
67C2×#626C2×C414yes—
68C2×C32×C8—22no—
69C2×C32×C8C2312yes—
70C2×C3⋊(C3⋊C8)D414yescomplemented
71C2×C3⋊(C3⋊C8)C2311yescharacteristic
72C2×C3⋊(C3⋊C8)C2311yescharacteristic
73C8×C3⋊D3—24no—
74C8×C3⋊D3—24no—
75C3×#217C2×C412yes—
76C3×C4⋊Dic3C2×C412yes—
77C3×C4×Dic3C2312yes—
78C3×#208—22no—
79C3×#208—22no—
80C2×C3×C3⋊C8C2312yes—
81C2×C3×C3⋊C8C2312yes—
82Dic3⋊Dic3C2×C414yes—
83#3722C2×C414yes—
84(C2×D3)⋊Dic3C2×C414yes—
85#3711—24no—
86D3×C3⋊C8—24no—
87#2929—91noSylow
88C2×C3×#41—31no—
89C2×#235C2×D311yescharacteristic
90C22×C4×D3—31no—
91C22×C4×D3—31no—
92C22×C4×D3—61no—
93C2×C3×M16—31no—
94C2×C3×M16—31no—
95C22×C3×C8—21no—
96C22×C3×C8C2×D311yescharacteristic
97C22×C3×C8C2×D311yescharacteristic
98C3×#117—31no—
99#948—64no—
100#946—32no—
101#938—32no—
102#937—32no—
103#935—32no—
104C4×#67—34no—
105#926C2×D311yescharacteristic
106C2×#208—32no—
107C2×#208C2×D311yescharacteristic
108C2×#208C2×D311yescharacteristic
109C22×C3⋊C8—31no—
110C22×C3⋊C8—31no—
111C22×C3⋊C8—32no—
112C22×C3⋊C8—61no—
113#907—64no—
114C2×ΓL(1,𝔽25)—32no—
115C2×D3×C8—32no—
116C2×D3×C8—32no—
117C2×D3×C8—32no—
118C2×D3×C8—32no—
119C2×D3×C8—32no—
120C2×D3×C8—62no—
121C2×D3×C8—62no—
122C2×D3×C8—64no—
123C2×D3×C8—64no—
124C2×D3×C8—68no—
125#897—32no—
126#895—32no—
127#886—32no—
128#882—32no—
129C4×D12—34no—
130C3×C4⋊C8—34no—
131C3×C22⋊C8—34no—
132(C2×D3)⋊C8—34no—
133(C2×D3)⋊C8—34no—
134(C2×D3)⋊C8C2×D314yescomplemented
135#815—32no—
136Dic3⋊C8C2×D314yescomplemented
137C8×Dic3—32no—
138#803—32no—
139C4×C3⋊C8—32no—
140C23×C32C22×C411yescharacteristic
141C22×C3⋊D3—22no—
142C22×C3⋊D3—24no—
143C22×C3⋊D3C22×C412yes—
144C22×C3×D3C22×C412yes—
145C2×C32×C4C22×C411yescharacteristic
146C2×C32×C4C2×D412yes—
147C2×C32×C4#4112yes—
148C2×C32×C4C2411yescharacteristic
149C2×C3⋊Dic3—22no—
150C2×C3⋊Dic3C22×C412yes—
151C4×C3⋊D3—24no—
152C4×C3⋊D3—22no—
153C4×C3⋊D3—22no—
154C3×#67—24no—
155C2×C3×Dic3C22×C414yes—
156C2×C3×Dic3C22×C412yes—
157C3×D12—22no—
158C3×C4×D3—22no—
159C3×C4×D3—22no—
160C3×Dic6—22no—
161#626—28no—
162C32×C8—22no—
163C3⋊(C3⋊C8)C2×D412yes—
164C3⋊(C3⋊C8)C2×D412yes—
165C3×C3⋊C8—22no—
166C3×C3⋊C8—22no—
167C2×#131—91no—
168C23×C8—91no—
169#525—91no—
170#435—94no—
171C8×D4—94no—
172#424—31no—
173#408—31no—
174#407—91no—
175#405—91no—
176C23×D3—31no—
177C23×D3—31no—
178C23×D3—61no—
179C3×#41—62no—
180C3×#41—62no—
181C2×C3×Q8—31no—
182C2×C3×D4—32no—
183C2×C3×D4—31no—
184C22×C3×C4—21no—
185C22×C3×C4—32no—
186C22×C3×C4C22×D311yescharacteristic
187C22×C3×C4C22×D311yescharacteristic
188C2×#67—34no—
189C2×#67C4×D312yes—
190C22×Dic3—31no—
191C22×Dic3—31no—
192C22×Dic3—61no—
193#235—22no—
194#235—22no—
195C2×D12—34no—
196C2×D12C4×D311yescharacteristic
197C2×C4×D3—32no—
198C2×C4×D3—32no—
199C2×C4×D3—32no—
200C2×C4×D3—32no—
201C2×C4×D3—62no—
202C2×C4×D3—62no—
203C2×C4×D3—64no—
204C2×C4×D3—64no—
205C2×C4×D3—62no—
206C2×C4×D3—62no—
207C2×C4×D3—62no—
208C2×C4×D3—62no—
209C2×C4×D3C22×D312yes—
210C2×Dic6C4×D311yescharacteristic
211C3×M16—62no—
212C3×M16—62no—
213C2×C3×C8—24no—
214C2×C3×C8—22no—
215C2×C3×C8—22no—
216C2×C3×C8—22no—
217C2×C3×C8—32no—
218C2×C3×C8—32no—
219C2×C3×C8C22×D312yes—
220C2×C3×C8C22×D312yes—
221C3×C4⋊C4—32no—
222C3×C22⋊C4—32no—
223C3×C42—32no—
224#217—34no—
225#217C4×D312yes—
226(C2×D3)⋊C4—34no—
227(C2×D3)⋊C4—34no—
228(C2×D3)⋊C4—34no—
229C4⋊Dic3—34no—
230C4⋊Dic3C4×D312yes—
231Dic3⋊C4—34no—
232C4×Dic3C22×D312yes—
233#208—22no—
234#208—22no—
235#208—64no—
236C2×C3⋊C8—34no—
237C2×C3⋊C8—34no—
238C2×C3⋊C8—31no—
239C2×C3⋊C8—31no—
240C2×C3⋊C8—31no—
241C2×C3⋊C8—31no—
242C2×C3⋊C8—64no—
243C2×C3⋊C8—61no—
244C2×C3⋊C8—61no—
245C2×C3⋊C8—64no—
246C2×C3⋊C8C22×D312yes—
247C2×C3⋊C8C22×D312yes—
248ΓL(1,𝔽25)—64no—
249D3×C8—64no—
250D3×C8—64no—
251D3×C8—64no—
252D3×C8—64no—
253D3×C8—64no—
254D3×C8—68no—
255D3×C8—68no—
256C22×C32—22no—
257C22×C32C4×D412yes—
258C22×C32C23×C411yescharacteristic
259C2×C3⋊D3—28no—
260C2×C3⋊D3—22no—
261C2×C3⋊D3—22no—
262C2×C3⋊D3#13114yescomplemented
263C2×C3×D3—22no—
264C2×C3×D3—24no—
265C32×C4C4×D412yes—
266C32×C4C22×D411yescharacteristic
267C32×C4C2×#4111yescharacteristic
268C3⋊Dic3—22no—
269C3×Dic3—22no—
270C3×Dic3—24no—
271C2×#41—31no—
272C23×C4—91no—
273#131—184no—
274C2×M16—31no—
275C2×M16—31no—
276C2×M16—92no—
277C22×C8—92no—
278C22×C8—91no—
279C22×C8—92no—
280C22×C8—92no—
281C22×C8—184no—
282C22×C8D3211yescharacteristic
283#123—92no—
284C22⋊Q8—92no—
285#121—92no—
286#120—92no—
287C4×D4—94no—
288#117—31no—
289C4⋊C8—34no—
290C22⋊C8—34no—
291C22⋊C8—94no—
292#97—92no—
293C4×C8—92no—
294C23×C3—21no—
295C23×C3—32no—
296C23×C3C2×C4×D311yescharacteristic
297C23×C3C2×C4×D311yescharacteristic
298C22×D3—32no—
299C22×D3—32no—
300C22×D3—62no—
301C22×D3—64no—
302C22×D3—64no—
303C22×D3—64no—
304C22×D3—68no—
305C22×D3—62no—
306C22×D3—62no—
307C22×D3C2×C4×D312yes—
308C3×Q8—62no—
309C3×D4—64no—
310C3×D4—62no—
311C2×C3×C4—21no—
312C2×C3×C4—22no—
313C2×C3×C4—21no—
314C2×C3×C4—22no—
315C2×C3×C4—32no—
316C2×C3×C4—34no—
317C2×C3×C4—62no—
318C2×C3×C4—62no—
319C2×C3×C4C2×C4×D311yescharacteristic
320C2×C3×C4C2×C4×D311yescharacteristic
321C2×C3×C4D3×D412yes—
322C2×C3×C4D3×D412yes—
323C2×C3×C4#23712yes—
324C2×C3×C4#23912yes—
325C2×C3×C4C23×D311yescharacteristic
326C2×C3×C4C23×D311yescharacteristic
327#67—24no—
328#67—68no—
329C2×Dic3—32no—
330C2×Dic3—32no—
331C2×Dic3—62no—
332C2×Dic3—64no—
333C2×Dic3—62no—
334C2×Dic3—62no—
335C2×Dic3C2×C4×D314yes—
336C2×Dic3C2×C4×D312yes—
337D12—22no—
338D12—68no—
339C4×D3—22no—
340C4×D3—22no—
341C4×D3—64no—
342C4×D3—64no—
343C4×D3—68no—
344C4×D3—64no—
345C4×D3—64no—
346C4×D3—62no—
347C4×D3—62no—
348C4×D3—62no—
349C4×D3—62no—
350Dic6—22no—
351C3×C8—24no—
352C3×C8—22no—
353C3×C8—22no—
354C3×C8—62no—
355C3×C8—62no—
356C3⋊C8—22no—
357C3⋊C8—22no—
358C3⋊C8—32no—
359C3⋊C8—32no—
360C3⋊C8—32no—
361C3⋊C8—32no—
362C3⋊C8—62no—
363C3⋊C8—62no—
364C2×C32—22no—
365C2×C32C2×C4×D411yescharacteristic
366C2×C32C2×#13112yes—
367C3⋊D3—24no—
368C3×D3—42no—
369C24—91no—
370#41—62no—
371#41—62no—
372C2×Q8—31no—
373C2×D4—32no—
374C2×D4—31no—
375C2×D4—94no—
376C22×C4—32no—
377C22×C4—91no—
378C22×C4—92no—
379C22×C4—92no—
380C22×C4—182no—
381C22×C4—182no—
382C22×C4C2×D3211yescharacteristic
383M16—62no—
384M16—62no—
385M16—184no—
386C2×C8—22no—
387C2×C8—32no—
388C2×C8—32no—
389C2×C8—91no—
390C2×C8—91no—
391C2×C8—94no—
392C2×C8—184no—
393C2×C8—184no—
394C2×C8—184no—
395C2×C8C2×D3212yes—
396C4⋊C4—32no—
397C4⋊C4—94no—
398C22⋊C4—32no—
399C22⋊C4—94no—
400C22⋊C4—94no—
401C42—32no—
402C22×C3—24no—
403C22×C3—22no—
404C22×C3—22no—
405C22×C3—21no—
406C22×C3—22no—
407C22×C3—64no—
408C22×C3—62no—
409C22×C3#67⋊C412yes—
410C22×C3#89312yes—
411C22×C3C22×C4×D311yescharacteristic
412C22×C3C22×C4×D311yescharacteristic
413C2×D3—22no—
414C2×D3—24no—
415C2×D3—34no—
416C2×D3—34no—
417C2×D3—64no—
418C2×D3—64no—
419C2×D3—616no—
420C2×D3—68no—
421C2×D3—68no—
422C2×D3—64no—
423C2×D3—62no—
424C2×D3—62no—
425C2×D3—62no—
426C2×D3—62no—
427C3×C4—21no—
428C3×C4—21no—
429C3×C4—22no—
430C3×C4—64no—
431C3×C4—62no—
432C3×C4#67⋊C412yes—
433C3×C4#89312yes—
434C3×C4C2×D3×D411yescharacteristic
435C3×C4C2×D3×D411yescharacteristic
436C3×C4C2×#23711yescharacteristic
437C3×C4C2×#23911yescharacteristic
438Dic3—22no—
439Dic3—24no—
440Dic3—64no—
441Dic3—62no—
442Dic3—62no—
443C32#292911yescharacteristic, complemented, Sylow
444C23—32no—
445C23—92no—
446C23—184no—
447C23—182no—
448C23C4×D3211yescharacteristic
449Q8—62no—
450D4—64no—
451D4—62no—
452D4—188no—
453C2×C4—34no—
454C2×C4—32no—
455C2×C4—62no—
456C2×C4—62no—
457C2×C4—92no—
458C2×C4—182no—
459C2×C4—182no—
460C2×C4—182no—
461C2×C4—184no—
462C2×C4#379612yes—
463C2×C4C4×D3211yescharacteristic
464C2×C4#381112yes—
465C2×C4C22×D3211yescharacteristic
466C8—22no—
467C8—62no—
468C8—62no—
469C8—92no—
470C8—92no—
471C2×C3—24no—
472C2×C3—22no—
473C2×C3—22no—
474C2×C3—21no—
475C2×C3—22no—
476C2×C3—122no—
477C2×C3C2×#67⋊C411yescharacteristic
478C2×C3C2×#89311yescharacteristic
479C2×C3D3×#13112yes—
480C2×C3D3×#13112yes—
481D3—42no—
482D3—68no—
483D3—64no—
484D3—64no—
485C22—22no—
486C22—62no—
487C22—64no—
488C22—94no—
489C22—188no—
490C22—182no—
491C22—182no—
492C22#6388112yes—
493C22C2×C4×D3211yescharacteristic
494C4—62no—
495C4—64no—
496C4—182no—
497C4#6388112yes—
498C4C2×#379611yescharacteristic
499C4C2×#381111yescharacteristic
500C3—21no—
501C3#7865511yescharacteristic, complemented
502C3#7907311yescharacteristic, complemented
503C2—22no—
504C2—122no—
505C2—184no—
506C2#1059466912yes—
507C2C2×#6388111yescharacteristic
subgroupG/H
center, FrattiniC2×C4C22×D32
commutator, socleC22×C32C23×C4
FittingC22×C32×C8C22
prime radical#10595034C2
cosocleC2×C32×C4C24
hypercenterC22×C8D32
hypocenterC32#2929
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C2×C4 ◁ C22×C8

Complements

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

NH ≅ G/Ntype
1. C22×C8×C3⋊D3C2semidirect
3. C2×#63815C2semidirect
4. C3×#5110C2semidirect
5. C3×#5102C2semidirect
6. #10591074C2semidirect
7. #10591057C2semidirect
8. #10590906C2semidirect
9. #10590737C2semidirect
27. C2×#3711C22semidirect
29. C2×D3×C3⋊C8C22semidirect
30. C3×(C2×D3)⋊C8C22semidirect
31. C3×Dic3⋊C8C22semidirect
33. #63554C22semidirect
34. Dic3×C3⋊C8C22semidirect
47. #5110D3semidirect
48. #5102D3semidirect
70. C2×C3⋊(C3⋊C8)D4semidirect
134. (C2×D3)⋊C8C2×D3semidirect
136. Dic3⋊C8C2×D3semidirect
262. C2×C3⋊D3#131semidirect
443. C32#2929semidirect
501. C3#78655semidirect
502. C3#79073semidirect

Maximal subgroups

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

subgroupindex
C22×C8×C3⋊D32
#105950342
C2×#638152
C3×#51102
C3×#51022
#105910742
#105910572
#105909062
#105907372
#790733
#786553