Finite Group Databasebeta

← #11859485

Subgroups — #11859485

Order 1152.

1133 conjugacy classes of subgroups.

The subgroup lattice has 562 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#64110C211yesmaximal, characteristic, complemented
2#10595017C211yesmaximal, characteristic
3C2×#63803C211yesmaximal, characteristic, complemented
4C3×C8×#67C212yesmaximal, complemented
5#10591153C211yesmaximal, characteristic, complemented
6#10591067C212yesmaximal, complemented
7#10590959C211yesmaximal, characteristic, complemented
8#10590732C212yesmaximal, complemented
9C8×#626C212yesmaximal, complemented
10#10590666C211yesmaximal, characteristic, complemented
11C8×#624C211yesmaximal, characteristic, complemented
12#79422—32nomaximal
13C2×#3828C2211yescharacteristic
14C2×#3798C2211yescharacteristic
15C22×C32×C8C2211yescharacteristic
16C2×#3748C2211yescharacteristic
17#64110—24no—
18C2×#3743C2211yescharacteristic
19C2×#3743C2211yescharacteristic
20C2×C8×C3⋊D3C2211yescharacteristic
21C2×C8×C3⋊D3C2211yescharacteristic
22C3×C4×#67C2212yes—
23C2×C3×D3×C8C2212yes—
24#63979C411yescharacteristic
25#63958C412yes—
26#63953C411yescharacteristic
27#63913C411yescharacteristic
28#63910C412yes—
29C4×#626C2212yes—
30C4×#624C2211yescharacteristic
31#63840C411yescharacteristic
32C2×#3712C2211yescharacteristic
33C2×#3711C2212yes—
34C2×#3710C2211yescharacteristic
35#63803—24no—
36C3×#830C2212yes—
37C3×(C2×D3)⋊C8C2212yes—
38C3×Dic3⋊C8C2212yes—
39C3×C8×Dic3C2212yes—
40Dic3⋊(C3⋊C8)C2212yes—
41#63557C2212yes—
42(C2×D3)⋊(C3⋊C8)C2212yes—
43Dic3×C3⋊C8C2212yes—
44C2×#901—32no—
45C2×#901—32no—
46C2×#901—61no—
47#5548—32no—
48C3×C8×D4—32no—
49C8×#67—32no—
50C8×#67D312yescomplemented
51#5012—32no—
52#4838—32no—
53#4837—32no—
54#4729—32no—
55#4729—32no—
56#4727—32no—
57#4727—32no—
58C8×D12—32no—
59C4×D3×C8—32no—
60C22×C32×C4C2311yescharacteristic
61C2×#638C2×C411yescharacteristic
62C2×#638C2×C411yescharacteristic
63#3828—22no—
64#3828—22no—
65C2×C4⋊(C3⋊D3)C2×C411yescharacteristic
66C2×C4×C3⋊D3C2311yescharacteristic
67C2×C4×C3⋊D3C2311yescharacteristic
68C2×#634C2×C411yescharacteristic
69C2×C3×#67C2×C412yes—
70C2×C3×C4×D3C2312yes—
71C2×#627C2×C411yescharacteristic
72C2×#626C2×C412yes—
73C2×#626C2×C412yes—
74C2×#625C2×C411yescharacteristic
75C2×#624C2×C412yes—
76#3798—22no—
77#3798—22no—
78C2×C32×C8—22no—
79C2×C32×C8C2311yescharacteristic
80C2×C32×C8C2311yescharacteristic
81#3748—22no—
82C2×C3⋊(C3⋊C8)C2311yescharacteristic
83C2×C3⋊(C3⋊C8)C2311yescharacteristic
84#3743—22no—
85#3743—22no—
86C8×C3⋊D3—22no—
87C8×C3⋊D3D414yescomplemented
88C3×#217C2×C412yes—
89C3×(C2×D3)⋊C4C2×C412yes—
90C3×Dic3⋊C4C2×C412yes—
91C3×C4×Dic3C2312yes—
92C2×C3×C3⋊C8C2312yes—
93C2×C3×C3⋊C8C2312yes—
94C3×D3×C8—24no—
95Dic3⋊Dic3C2×C412yes—
96#3722C2×C412yes—
97(C2×D3)⋊Dic3C2×C412yes—
98Dic32C2×C411yescharacteristic
99Dic32C2×C411yescharacteristic
100#3712—22no—
101#3711—24no—
102#3710—22no—
103#2931—91noSylow
104C2×#235—32no—
105C2×#235—32no—
106C2×#235—61no—
107C22×C3×C8—21no—
108C22×C3×C8—32no—
109C22×C3×C8C2×D312yes—
110C3×C4×D4—32no—
111#940—32no—
112#938—32no—
113C4×#67—32no—
114C4×#67C2×D312yes—
115C2×#208—32no—
116C2×#208—32no—
117C2×#208—61no—
118#901—68no—
119#901—68no—
120#901—68no—
121C2×ΓL(1,𝔽25)—32no—
122C2×ΓL(1,𝔽25)—32no—
123C2×ΓL(1,𝔽25)—32no—
124C2×ΓL(1,𝔽25)—32no—
125C2×ΓL(1,𝔽25)—61no—
126C2×ΓL(1,𝔽25)—61no—
127C2×D3×C8—32no—
128C2×D3×C8—32no—
129C2×D3×C8—32no—
130C2×D3×C8—61no—
131C2×D3×C8—61no—
132C2×D3×C8C2×D312yes—
133#895—32no—
134#888—32no—
135#885—32no—
136#885—32no—
137#884—32no—
138#884—32no—
139C4×D12—32no—
140C42×D3—32no—
141C3×C4⋊C8—32no—
142C3×C22⋊C8—32no—
143C3×C22⋊C8—32no—
144C3×C4×C8—32no—
145#830—32no—
146#830C2×D312yes—
147(C2×D3)⋊C8—32no—
148(C2×D3)⋊C8—32no—
149(C2×D3)⋊C8—32no—
150(C2×D3)⋊C8C2×D312yes—
151Dic3⋊C8—32no—
152Dic3⋊C8C2×D312yes—
153C8×Dic3—32no—
154C8×Dic3C2×D312yes—
155C4⋊(C3⋊C8)—32no—
156C4×C3⋊C8—32no—
157C23×C32C22×C411yescharacteristic
158C22×C3⋊D3C22×C411yescharacteristic
159C22×C3⋊D3C22×C411yescharacteristic
160C22×C3×D3C22×C412yes—
161C2×C32×C4—21no—
162C2×C32×C4—21no—
163C2×C32×C4C22×C411yescharacteristic
164C2×C32×C4C2411yescharacteristic
165#638—22no—
166#638—22no—
167C2×C3⋊Dic3C22×C411yescharacteristic
168C2×C3⋊Dic3C22×C411yescharacteristic
169C4⋊(C3⋊D3)—22no—
170C4×C3⋊D3—21no—
171C4×C3⋊D3—21no—
172C4×C3⋊D3C2×D412yes—
173C4×C3⋊D3#4112yes—
174#634—22no—
175C3×#67—24no—
176C2×C3×Dic3C22×C412yes—
177C2×C3×Dic3C22×C412yes—
178C2×C3×Dic3C22×C412yes—
179C3×C4×D3—22no—
180C3×C4×D3—22no—
181#627—22no—
182#626—24no—
183#626—24no—
184#625—22no—
185#624—24no—
186C32×C8—21no—
187C32×C8C2×D412yes—
188C3⋊(C3⋊C8)—21no—
189C3⋊(C3⋊C8)C2×D412yes—
190C3×C3⋊C8—22no—
191C3×C3⋊C8—22no—
192C2×#131—91no—
193C2×#131—91no—
194#532—91no—
195#436—92no—
196#436—92no—
197C8×D4—32no—
198C8×D4—92no—
199#423—91no—
200#408—91no—
201#408—91no—
202C2×C4×C8—91no—
203C2×C3×D4—32no—
204C22×C3×C4—21no—
205C22×C3×C4—32no—
206C22×C3×C4C22×D312yes—
207C2×#67—32no—
208C2×#67—32no—
209C2×#67—32no—
210C2×#67—32no—
211C2×#67—32no—
212C2×#67—61no—
213C2×#67—61no—
214C2×#67C4×D312yes—
215#235—64no—
216#235—64no—
217#235—64no—
218#235—64no—
219#235—64no—
220#235—64no—
221C2×D12—32no—
222C2×D12—32no—
223C2×D12—32no—
224C2×D12—61no—
225C2×C4×D3—32no—
226C2×C4×D3—32no—
227C2×C4×D3—32no—
228C2×C4×D3—32no—
229C2×C4×D3—61no—
230C2×C4×D3—61no—
231C2×C4×D3C22×D312yes—
232C2×Dic6—32no—
233C2×Dic6—32no—
234C2×Dic6—61no—
235C2×C3×C8—24no—
236C2×C3×C8—24no—
237C2×C3×C8—21no—
238C2×C3×C8—21no—
239C2×C3×C8—32no—
240C2×C3×C8—32no—
241C2×C3×C8—64no—
242C2×C3×C8C22×D312yes—
243C2×C3×C8C22×D312yes—
244C3×C4⋊C4—32no—
245C3×C22⋊C4—32no—
246C3×C22⋊C4—32no—
247C3×C42—32no—
248#217—32no—
249#217C4×D312yes—
250(C2×D3)⋊C4—32no—
251(C2×D3)⋊C4—32no—
252(C2×D3)⋊C4—32no—
253(C2×D3)⋊C4C4×D312yes—
254C4⋊Dic3—32no—
255Dic3⋊C4—32no—
256Dic3⋊C4C4×D312yes—
257C4×Dic3—32no—
258C4×Dic3—32no—
259C4×Dic3C22×D312yes—
260#208—64no—
261#208—64no—
262#208—64no—
263C2×C3⋊C8—32no—
264C2×C3⋊C8—32no—
265C2×C3⋊C8—61no—
266C2×C3⋊C8—61no—
267C2×C3⋊C8C22×D312yes—
268C2×C3⋊C8C22×D312yes—
269ΓL(1,𝔽25)—64no—
270ΓL(1,𝔽25)—64no—
271ΓL(1,𝔽25)—64no—
272ΓL(1,𝔽25)—64no—
273ΓL(1,𝔽25)—64no—
274ΓL(1,𝔽25)—64no—
275D3×C8—24no—
276D3×C8—38no—
277D3×C8—64no—
278D3×C8—64no—
279D3×C8—64no—
280D3×C8—64no—
281C22×C32—21no—
282C22×C32—22no—
283C22×C32C23×C411yescharacteristic
284C2×C3⋊D3—21no—
285C2×C3⋊D3—22no—
286C2×C3⋊D3—22no—
287C2×C3⋊D3C4×D412yes—
288C2×C3×D3—22no—
289C2×C3×D3—22no—
290C2×C3×D3—22no—
291C32×C4—21no—
292C32×C4C22×D411yescharacteristic
293C32×C4C2×#4111yescharacteristic
294C3⋊Dic3—21no—
295C3⋊Dic3C4×D412yes—
296C3×Dic3—22no—
297C3×Dic3—22no—
298C3×Dic3#13114yescomplemented
299C2×#41—91no—
300C2×#41—91no—
301#131—184no—
302#131—184no—
303C2×M16—91no—
304C2×M16—92no—
305C2×M16—91no—
306C2×M16—91no—
307C2×M16—91no—
308C22×C8—32no—
309C22×C8—91no—
310C22×C8—91no—
311C22×C8—91no—
312C22×C8D3211yescharacteristic
313C4⋊Q8—91no—
314#127—91no—
315#124—91no—
316#124—91no—
317#121—92no—
318#121—92no—
319C4×D4—32no—
320C4×D4—92no—
321C2×C42—91no—
322C4⋊C8—32no—
323C4⋊C8—92no—
324C22⋊C8—32no—
325C22⋊C8—32no—
326C22⋊C8—92no—
327C22⋊C8—92no—
328C4×C8—32no—
329C4×C8—92no—
330C23×C3—21no—
331C23×C3—32no—
332C23×C3C2×C4×D312yes—
333C22×D3—32no—
334C22×D3—32no—
335C22×D3—61no—
336C22×D3—61no—
337C22×D3C2×C4×D312yes—
338C3×D4—64no—
339C2×C3×C4—22no—
340C2×C3×C4—22no—
341C2×C3×C4—22no—
342C2×C3×C4—22no—
343C2×C3×C4—21no—
344C2×C3×C4—21no—
345C2×C3×C4—32no—
346C2×C3×C4—32no—
347C2×C3×C4—32no—
348C2×C3×C4—62no—
349C2×C3×C4—62no—
350C2×C3×C4C2×C4×D312yes—
351C2×C3×C4C23×D312yes—
352#67—24no—
353#67—64no—
354#67—64no—
355#67—64no—
356#67—64no—
357#67—64no—
358#67—64no—
359#67—64no—
360C2×Dic3—32no—
361C2×Dic3—32no—
362C2×Dic3—61no—
363C2×Dic3—61no—
364C2×Dic3C2×C4×D312yes—
365C2×Dic3C2×C4×D312yes—
366C2×Dic3C2×C4×D312yes—
367D12—64no—
368D12—64no—
369D12—64no—
370D12—64no—
371C4×D3—22no—
372C4×D3—22no—
373C4×D3—34no—
374C4×D3—34no—
375C4×D3—62no—
376C4×D3—62no—
377C4×D3—64no—
378C4×D3—62no—
379C4×D3—62no—
380C4×D3—62no—
381C4×D3—62no—
382C4×D3—64no—
383Dic6—64no—
384Dic6—64no—
385Dic6—64no—
386C3×C8—22no—
387C3×C8—22no—
388C3×C8—22no—
389C3×C8—62no—
390C3×C8—62no—
391C3×C8D3×D414yes—
392C3⋊C8—22no—
393C3⋊C8—22no—
394C3⋊C8—34no—
395C3⋊C8—62no—
396C3⋊C8—62no—
397C3⋊C8—62no—
398C2×C32—41no—
399C2×C32C2×C4×D411yescharacteristic
400C2×C32C2×#13112yes—
401C3⋊D3—22no—
402C3⋊D3—41no—
403C3×D3—42no—
404#41—182no—
405#41—182no—
406#41—182no—
407#41—182no—
408C2×Q8—91no—
409C2×Q8—91no—
410C2×D4—32no—
411C2×D4—92no—
412C2×D4—92no—
413C2×D4—91no—
414C2×D4—91no—
415C2×D4—91no—
416C2×D4—91no—
417C22×C4—32no—
418C22×C4—92no—
419C22×C4—91no—
420C22×C4—91no—
421C22×C4C2×D3211yescharacteristic
422M16—182no—
423M16—182no—
424M16—182no—
425M16—184no—
426M16—182no—
427C2×C8—22no—
428C2×C8—32no—
429C2×C8—32no—
430C2×C8—64no—
431C2×C8—91no—
432C2×C8—94no—
433C2×C8—91no—
434C2×C8—182no—
435C2×C8—182no—
436C2×C8C2×D3211yescharacteristic
437C2×C8C2×D3211yescharacteristic
438C4⋊C4—32no—
439C4⋊C4—92no—
440C22⋊C4—32no—
441C22⋊C4—32no—
442C22⋊C4—92no—
443C22⋊C4—92no—
444C42—32no—
445C42—91no—
446C42—91no—
447C22×C3—22no—
448C22×C3—22no—
449C22×C3—22no—
450C22×C3—22no—
451C22×C3—21no—
452C22×C3—42no—
453C22×C3—62no—
454C22×C3—62no—
455C22×C3—62no—
456C22×C3C22×C4×D312yes—
457C2×D3—22no—
458C2×D3—22no—
459C2×D3—22no—
460C2×D3—34no—
461C2×D3—62no—
462C2×D3—62no—
463C2×D3—62no—
464C2×D3—62no—
465C2×D3—62no—
466C2×D3—62no—
467C2×D3—62no—
468C2×D3—122no—
469C2×D3—122no—
470C3×C4—22no—
471C3×C4—22no—
472C3×C4—21no—
473C3×C4—21no—
474C3×C4—34no—
475C3×C4—62no—
476C3×C4—62no—
477C3×C4C2×D3×D412yes—
478C3×C4D3×#4112yes—
479Dic3—22no—
480Dic3—22no—
481Dic3—34no—
482Dic3—62no—
483Dic3—62no—
484Dic3—62no—
485Dic3#90114yescomplemented
486C32#293111yescharacteristic, complemented, Sylow
487C23—32no—
488C23—91no—
489C23—91no—
490C23C4×D3211yescharacteristic
491Q8—182no—
492Q8—182no—
493D4—64no—
494D4—182no—
495D4—184no—
496D4—184no—
497D4—182no—
498D4—182no—
499D4—182no—
500C2×C4—21no—
501C2×C4—21no—
502C2×C4—32no—
503C2×C4—32no—
504C2×C4—32no—
505C2×C4—62no—
506C2×C4—62no—
507C2×C4—91no—
508C2×C4—92no—
509C2×C4—92no—
510C2×C4—91no—
511C2×C4—184no—
512C2×C4—181no—
513C2×C4—181no—
514C2×C4C4×D3211yescharacteristic
515C2×C4C22×D3211yescharacteristic
516C8—21no—
517C8—62no—
518C8—62no—
519C8—92no—
520C8—181no—
521C8#381112yes—
522C2×C3—22no—
523C2×C3—21no—
524C2×C3—42no—
525C2×C3—42no—
526C2×C3—122no—
527C2×C3C4×D3×D412yes—
528C2×C3C2×#90112yes—
529C2×C3D3×#13112yes—
530D3—42no—
531D3—64no—
532D3—122no—
533D3—122no—
534D3—122no—
535C22—22no—
536C22—21no—
537C22—62no—
538C22—62no—
539C22—62no—
540C22—92no—
541C22—182no—
542C22—182no—
543C22—181no—
544C22C2×C4×D3211yescharacteristic
545C4—21no—
546C4—34no—
547C4—62no—
548C4—62no—
549C4—92no—
550C4—181no—
551C4#6430611yescharacteristic
552C4C2×#381111yescharacteristic
553C3—21no—
554C3#7942212yescomplemented
555C2—41no—
556C2—122no—
557C2—182no—
558C2—361no—
559C2D3×#90112yes—
560C2C4×#381111yescharacteristic
subgroupG/H
centerC2×C8C2×D32
commutator, socleC22×C32C23×C4
FrattiniC2×C4C22×D32
FittingC22×C32×C8C22
prime radical#10595017C2
cosocleC2×C32×C4C24
hypercenterC22×C8D32
hypocenterC32#2931
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C2×C8 ◁ C22×C8

Complements

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

NH ≅ G/Ntype
1. C2×#64110C2semidirect
3. C2×#63803C2semidirect
4. C3×C8×#67C2semidirect
5. #10591153C2semidirect
6. #10591067C2semidirect
7. #10590959C2semidirect
8. #10590732C2semidirect
9. C8×#626C2semidirect
10. #10590666C2semidirect
11. C8×#624C2semidirect
50. C8×#67D3semidirect
87. C8×C3⋊D3D4semidirect
298. C3×Dic3#131semidirect
485. Dic3#901semidirect
486. C32#2931semidirect
554. C3#79422semidirect

Maximal subgroups

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

subgroupindex
C2×#641102
#105950172
C2×#638032
C3×C8×#672
#105911532
#105910672
#105909592
#105907322
C8×#6262
#105906662
C8×#6242
#794223