Finite Group Databasebeta

← #11859349

Subgroups — #11859349

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
2C2×C3×#901C211yesmaximal, characteristic, complemented
3#10595034C211yesmaximal, characteristic
4C3×#5101C211yesmaximal, characteristic, complemented
5#10591117C211yesmaximal, characteristic, complemented
6#10591074C211yesmaximal, characteristic, complemented
7#10591071C211yesmaximal, characteristic, complemented
8#10590736C214yesmaximal, complemented
9C8×#626C214yesmaximal, complemented
10#83794—31nomaximal
11#78553—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
22C3×#901—24no—
23C2×C3×ΓL(1,𝔽25)C2212yescomplemented
24C2×C3×D3×C8C2212yescomplemented
25#63981C412yes—
26#63962C412yes—
27#63916C412yes—
28C4×#626C2214yes—
29#63871C412yes—
30C3×#815C2212yescomplemented
31C3×C8×Dic3C2212yescomplemented
32Dic3⋊(C3⋊C8)C2214yescomplemented
33#63557C2214yes—
34(C2×D3)⋊(C3⋊C8)C2214yescomplemented
35C2×C3×#131—31no—
36#5828—31no—
37C2×#901D311yescharacteristic, complemented
38C22×D3×C8—31no—
39C22×D3×C8—31no—
40C22×D3×C8—61no—
41#5524—31no—
42C3×#405—31no—
43#5234—31no—
44#5129—31no—
45#5127—34no—
46#5126—31no—
47#5126—31no—
48#5119—31no—
49C8×#67—34no—
50#5101D311yescharacteristic, complemented
51#4999—31no—
52#4706—34no—
53C8×D12—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×C8D414yescomplemented
69C2×C32×C8C2311yescharacteristic
70C2×C32×C8C2311yescharacteristic
71C2×C3⋊(C3⋊C8)—22no—
72C2×C3⋊(C3⋊C8)C2312yes—
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—
82C3×ΓL(1,𝔽25)—24no—
83C3×D3×C8—24no—
84Dic3⋊Dic3C2×C414yes—
85#3722C2×C414yes—
86(C2×D3)⋊Dic3C2×C414yes—
87#2929—91noSylow
88C2×C3×#41—31no—
89C2×#235C2×D311yescharacteristic
90C22×C4×D3—31no—
91C22×C4×D3—31no—
92C22×C4×D3—61no—
93C3×#131—64no—
94C2×C3×M16—31no—
95C2×C3×M16—31no—
96C2×C3×M16—32no—
97C22×C3×C8—21no—
98C22×C3×C8—32no—
99C22×C3×C8C2×D311yescharacteristic
100C22×C3×C8C2×D311yescharacteristic
101C3×#117—31no—
102#946—32no—
103#938—32no—
104#937—32no—
105#935—32no—
106C4×#67—34no—
107#926C2×D311yescharacteristic
108C2×#208C2×D311yescharacteristic
109C2×#208C2×D311yescharacteristic
110C22×C3⋊C8—31no—
111C22×C3⋊C8—31no—
112C22×C3⋊C8—61no—
113#901—24no—
114C2×ΓL(1,𝔽25)C2×D312yescomplemented
115C2×D3×C8—32no—
116C2×D3×C8—32no—
117C2×D3×C8—32no—
118C2×D3×C8—32no—
119C2×D3×C8—62no—
120C2×D3×C8—62no—
121C2×D3×C8—68no—
122C2×D3×C8—64no—
123C2×D3×C8—64no—
124C2×D3×C8C2×D312yescomplemented
125#897—32no—
126#895—32no—
127#886—32no—
128#882—32no—
129C4×D12—34no—
130C3×#97—32no—
131C3×C4×C8—32no—
132#830—34no—
133(C2×D3)⋊C8—34no—
134(C2×D3)⋊C8—34no—
135(C2×D3)⋊C8—34no—
136#815C2×D312yescomplemented
137Dic3⋊C8—34no—
138C8×Dic3C2×D312yescomplemented
139C4⋊(C3⋊C8)—34no—
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×C8C2×D412yes—
163C32×C8C2×D412yes—
164C3⋊(C3⋊C8)—22no—
165C3×C3⋊C8—22no—
166C3×C3⋊C8—22no—
167C2×#131—31no—
168C23×C8—91no—
169#525—91no—
170#435—94no—
171C8×D4—94no—
172#424—91no—
173#408—91no—
174#407—91no—
175#405—31no—
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—
213C3×M16—64no—
214C2×C3×C8—24no—
215C2×C3×C8—21no—
216C2×C3×C8—21no—
217C2×C3×C8—32no—
218C2×C3×C8—32no—
219C2×C3×C8—64no—
220C2×C3×C8D1214yescomplemented
221C2×C3×C8#6714yescomplemented
222C2×C3×C8C22×D311yescharacteristic
223C2×C3×C8C22×D311yescharacteristic
224C2×C3×C8C22×D311yescharacteristic
225C2×C3×C8C22×D311yescharacteristic
226C3×C4⋊C4—32no—
227C3×C22⋊C4—32no—
228C3×C42—32no—
229#217—34no—
230#217C4×D312yes—
231(C2×D3)⋊C4—34no—
232(C2×D3)⋊C4—34no—
233(C2×D3)⋊C4—34no—
234C4⋊Dic3—34no—
235C4⋊Dic3C4×D312yes—
236Dic3⋊C4—34no—
237C4×Dic3C22×D312yes—
238#208—22no—
239#208—22no—
240C2×C3⋊C8—32no—
241C2×C3⋊C8—32no—
242C2×C3⋊C8—62no—
243C2×C3⋊C8—64no—
244C2×C3⋊C8—62no—
245C2×C3⋊C8—62no—
246C2×C3⋊C8C22×D312yes—
247C2×C3⋊C8C22×D312yes—
248ΓL(1,𝔽25)—24no—
249D3×C8—24no—
250D3×C8—68no—
251D3×C8—68no—
252D3×C8—64no—
253D3×C8—64no—
254D3×C8—64no—
255D3×C8—64no—
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—64no—
274C2×M16—31no—
275C2×M16—31no—
276C2×M16—32no—
277C22×C8—32no—
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—94no—
290C22⋊C8—94no—
291C22⋊C8—94no—
292#97—32no—
293C4×C8—32no—
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×C4C2×D1212yes—
322C2×C3×C4#23512yes—
323C2×C3×C4#23512yes—
324C2×C3×C4C2×#6712yes—
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—22no—
352C3×C8—22no—
353C3×C8—62no—
354C3×C8—62no—
355C3×C8C2×D1212yes—
356C3×C8C2×D1212yes—
357C3×C8C2×#6712yes—
358C3×C8C2×#6712yes—
359C3⋊C8—22no—
360C3⋊C8—22no—
361C3⋊C8—64no—
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—64no—
386C2×C8—32no—
387C2×C8—32no—
388C2×C8—64no—
389C2×C8—92no—
390C2×C8—182no—
391C2×C8—184no—
392C2×C8—184no—
393C2×C8#62614yescomplemented
394C2×C8C2×D3211yescharacteristic
395C2×C8C2×D3211yescharacteristic
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—62no—
408C22×C3—64no—
409C22×C3C4×D1212yes—
410C22×C3C4×#6712yes—
411C22×C3C22×C4×D311yescharacteristic
412C22×C3C22×C4×D311yescharacteristic
413C2×D3—24no—
414C2×D3—22no—
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—62no—
431C3×C4—64no—
432C3×C4C4×D1212yes—
433C3×C4C4×#6712yes—
434C3×C4C22×D1211yescharacteristic
435C3×C4C2×#23511yescharacteristic
436C3×C4C2×#23511yescharacteristic
437C3×C4C22×#6711yescharacteristic
438Dic3—24no—
439Dic3—22no—
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#379812yes—
463C2×C4C4×D3211yescharacteristic
464C2×C4C2×#62612yes—
465C2×C4C22×D3211yescharacteristic
466C8—62no—
467C8—62no—
468C8—182no—
469C8C2×#62612yes—
470C8C2×#62612yes—
471C2×C3—24no—
472C2×C3—22no—
473C2×C3—22no—
474C2×C3—22no—
475C2×C3—21no—
476C2×C3—122no—
477C2×C3C2×C4×D1211yescharacteristic
478C2×C3D3×#13112yes—
479C2×C3D3×#13112yes—
480C2×C3C2×C4×#6711yescharacteristic
481D3—42no—
482D3—68no—
483D3—64no—
484D3—64no—
485C22—22no—
486C22—64no—
487C22—62no—
488C22—94no—
489C22—188no—
490C22—182no—
491C22—182no—
492C22C4×#62612yes—
493C22C2×C4×D3211yescharacteristic
494C4—64no—
495C4—62no—
496C4—182no—
497C4C4×#62612yes—
498C4C2×#379811yescharacteristic
499C4C22×#62611yescharacteristic
500C3—21no—
501C3#7855311yescharacteristic, complemented
502C3#8379411yescharacteristic, complemented
503C2—22no—
504C2—122no—
505C2—184no—
506C2#1059466912yes—
507C2C2×C4×#62611yescharacteristic
subgroupG/H
centerC2×C8C2×D32
commutator, socleC22×C32C23×C4
FrattiniC2×C4C22×D32
FittingC22×C32×C8C22
prime radical#10595034C2
cosocleC2×C32×C4C24
hypercenterC22×C8D32
hypocenterC32#2929
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C2×C8 ◁ C22×C8

Complements

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

NH ≅ G/Ntype
1. C22×C8×C3⋊D3C2semidirect
2. C2×C3×#901C2semidirect
4. C3×#5101C2semidirect
5. #10591117C2semidirect
6. #10591074C2semidirect
7. #10591071C2semidirect
8. #10590736C2semidirect
9. C8×#626C2semidirect
23. C2×C3×ΓL(1,𝔽25)C22semidirect
24. C2×C3×D3×C8C22semidirect
30. C3×#815C22semidirect
31. C3×C8×Dic3C22semidirect
32. Dic3⋊(C3⋊C8)C22semidirect
34. (C2×D3)⋊(C3⋊C8)C22semidirect
37. C2×#901D3semidirect
50. #5101D3semidirect
68. C2×C32×C8D4semidirect
114. C2×ΓL(1,𝔽25)C2×D3semidirect
124. C2×D3×C8C2×D3semidirect
136. #815C2×D3semidirect
138. C8×Dic3C2×D3semidirect
220. C2×C3×C8D12semidirect
221. C2×C3×C8#67semidirect
262. C2×C3⋊D3#131semidirect
393. C2×C8#626semidirect
443. C32#2929semidirect
501. C3#78553semidirect
502. C3#83794semidirect

Maximal subgroups

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

subgroupindex
C22×C8×C3⋊D32
C2×C3×#9012
#105950342
C3×#51012
#105911172
#105910742
#105910712
#105907362
C8×#6262
#837943
#785533