Finite Group Databasebeta

← #11804897

Subgroups — #11804897

Order 1152.

1757 conjugacy classes of subgroups.

The subgroup lattice has 502 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#3797C211yesmaximal, characteristic
2C2×#63837C212yesmaximal, complemented
3#10592366C211yesmaximal, characteristic
4C3×#4646C212yesmaximal, complemented
5#10591367C212yesmaximal
6#10591261C212yesmaximal, complemented
7#10591260C211yesmaximal, characteristic
8#10591236C212yesmaximal, complemented
9#10591233C212yesmaximal
10#76614—32nomaximal
11C22×C4×C3⋊D3C2211yescharacteristic
12C22×C3×Dic6C2212yes—
13C22×#627C2211yescharacteristic
14C22×#627C2211yescharacteristic
15C22×#624C2212yes—
16C2×#3797—28no—
17C2×#3797C418yescomplemented
18C2×#3752C2212yes—
19C2×#3750C2212yes—
20C2×C3×Dic3⋊C4C2212yes—
21C2×C3×C4×Dic3C2212yes—
22C2×Dic3⋊Dic3C2212yes—
23C2×#3722C2211yescharacteristic
24C2×#3722C2211yescharacteristic
25C2×Dic32C2212yes—
26C2×Dic32C2212yes—
27#63837—28no—
28C32×#95C2211yescharacteristic
29#63658C2211yescharacteristic
30C3×C3⋊#95C2212yes—
31C3×C3⋊#95C2212yes—
32C3×C3⋊#95C2212yes—
33#63579C2212yes—
34#63579C2212yes—
35C22×D3×Q8—32no—
36C2×#887—32no—
37C2×C4×Dic6—32no—
38C3×#391—32no—
39#5229—32no—
40#4987—32no—
41C4×(C2×D3)⋊C4—32no—
42#4667—32no—
43#4667—32no—
44#4667—61no—
45#4666—32no—
46#4666—32no—
47#4646—32no—
48#4646—32no—
49#4646—32no—
50#4646D312yescomplemented
51C23×C3⋊D3C2311yescharacteristic
52C22×C32×C4C2312yes—
53C22×C32×C4C2311yescharacteristic
54C22×C3⋊Dic3C2312yes—
55C22×C3⋊Dic3C2311yescharacteristic
56C2×C4×C3⋊D3—24no—
57C2×C4×C3⋊D3C2×C414yes—
58C22×C3×Dic3C2312yes—
59C22×C3×Dic3C2312yes—
60C22×C3×Dic3C2312yes—
61C22×C3×Dic3C2312yes—
62C2×C3×Dic6—24no—
63C2×C3×Dic6—24no—
64C2×C3×Dic6C2×C418yes—
65C2×#627—24no—
66C2×#627C2×C414yes—
67C2×#627C2×C414yes—
68C2×#627D418yes—
69C2×#624—24no—
70C2×#624—24no—
71C2×#624C2×C418yes—
72#3797—232no—
73#3752—24no—
74#3750—24no—
75C3×Dic3⋊C4—24no—
76C3×C4×Dic3—24no—
77Dic3⋊Dic3—24no—
78#3722—22no—
79#3722Q814yescomplemented
80Dic32—24no—
81Dic32—24no—
82Q8×C22⋊C4—91noSylow
83C22×C3×Q8—32no—
84C2×D3×Q8—316no—
85C2×D3×Q8—68no—
86C2×D3×Q8—68no—
87C22×C4×D3—32no—
88C22×C4×D3—32no—
89C22×C4×D3—32no—
90C22×C4×D3—61no—
91C22×Dic6—32no—
92C22×Dic6—32no—
93C22×Dic6C2×D312yes—
94C2×C3×C4⋊C4—32no—
95C2×C3×C42—32no—
96C2×(C2×D3)⋊C4—32no—
97C2×(C2×D3)⋊C4—32no—
98C2×(C2×D3)⋊C4—32no—
99C2×(C2×D3)⋊C4—32no—
100C2×(C2×D3)⋊C4—62no—
101C2×C4⋊Dic3—32no—
102C2×Dic3⋊C4—32no—
103C2×Dic3⋊C4—32no—
104C2×Dic3⋊C4—32no—
105C2×Dic3⋊C4—62no—
106C2×Dic3⋊C4C2×D312yes—
107C2×C4×Dic3—32no—
108C2×C4×Dic3—32no—
109C2×C4×Dic3—32no—
110C2×C4×Dic3—32no—
111C2×C4×Dic3C2×D312yes—
112#887—68no—
113C4×Dic6—68no—
114C3×#95—21no—
115C3×#95—32no—
116C3×#95—32no—
117C3×#95—32no—
118C3×#95C2×D312yes—
119C3⋊#95—32no—
120C3⋊#95—32no—
121C3⋊#95—32no—
122C3⋊#95—32no—
123C3⋊#95—32no—
124C3⋊#95—61no—
125C3⋊#95C2×D312yes—
126C3⋊#95C2×D312yes—
127C3⋊#95C2×D312yes—
128C23×C32C2411yescharacteristic
129C22×C3⋊D3—22no—
130C22×C3⋊D3—22no—
131C22×C3⋊D3C22×C412yes—
132C22×C3⋊D3C2×Q812yes—
133C22×C3⋊D3#4112yes—
134C2×C32×C4—22no—
135C2×C32×C4—22no—
136C2×C32×C4—22no—
137C2×C32×C4—22no—
138C2×C32×C4C22×C412yes—
139C2×C3⋊Dic3—22no—
140C2×C3⋊Dic3—22no—
141C2×C3⋊Dic3—22no—
142C2×C3⋊Dic3C22×C412yes—
143C2×C3⋊Dic3C2×D414yes—
144C4×C3⋊D3—28no—
145C2×C3×Dic3—22no—
146C2×C3×Dic3—22no—
147C2×C3×Dic3—22no—
148C2×C3×Dic3—22no—
149C2×C3×Dic3—22no—
150C2×C3×Dic3—22no—
151C2×C3×Dic3—22no—
152C2×C3×Dic3C22×C414yes—
153C2×C3×Dic3C22×C414yes—
154C2×C3×Dic3C2×D414yes—
155C2×C3×Dic3C2×D414yes—
156C2×C3×Dic3C2×Q814yescomplemented
157C3×Dic6—216no—
158#627—28no—
159#627C22⋊C4116yescomplemented
160#624—216no—
161C23×Q8—91no—
162C2×C4×Q8—92no—
163#391—32no—
164#391—92no—
165#391—92no—
166#380—92no—
167#380—91no—
168C4×C22⋊C4—91no—
169C4×C22⋊C4—92no—
170C23×D3—32no—
171C23×D3—61no—
172C2×C3×Q8—38no—
173C2×C3×Q8—64no—
174C2×C3×Q8—64no—
175C22×C3×C4—21no—
176C22×C3×C4—22no—
177C22×C3×C4—32no—
178C22×C3×C4—32no—
179C22×C3×C4—32no—
180C22×C3×C4—32no—
181C22×C3×C4C22×D312yes—
182C22×C3×C4C22×D312yes—
183C22×C3×C4C22×D312yes—
184C22×Dic3—32no—
185C22×Dic3—32no—
186C22×Dic3—32no—
187C22×Dic3—61no—
188C22×Dic3—62no—
189C22×Dic3C22×D312yes—
190C22×Dic3C22×D312yes—
191C22×Dic3C22×D312yes—
192C22×Dic3C22×D312yes—
193D3×Q8—664no—
194C2×C4×D3—38no—
195C2×C4×D3—38no—
196C2×C4×D3—38no—
197C2×C4×D3—64no—
198C2×C4×D3—64no—
199C2×C4×D3—64no—
200C2×C4×D3—64no—
201C2×C4×D3—64no—
202C2×C4×D3—64no—
203C2×C4×D3—64no—
204C2×C4×D3—124no—
205C2×Dic6—24no—
206C2×Dic6—24no—
207C2×Dic6—38no—
208C2×Dic6—38no—
209C2×Dic6—38no—
210C2×Dic6—38no—
211C2×Dic6—64no—
212C2×Dic6—64no—
213C2×Dic6C4×D318yes—
214C3×C4⋊C4—64no—
215C3×C42—64no—
216(C2×D3)⋊C4—38no—
217(C2×D3)⋊C4—64no—
218(C2×D3)⋊C4—64no—
219(C2×D3)⋊C4—64no—
220(C2×D3)⋊C4—124no—
221C4⋊Dic3—64no—
222Dic3⋊C4—24no—
223Dic3⋊C4—64no—
224Dic3⋊C4—64no—
225Dic3⋊C4—64no—
226Dic3⋊C4—124no—
227C4×Dic3—24no—
228C4×Dic3—64no—
229C4×Dic3—64no—
230C4×Dic3—64no—
231C4×Dic3—64no—
232C22×C32C23×C411yescharacteristic
233C22×C32C22×D412yes—
234C22×C32C22×Q811yescharacteristic
235C22×C32C2×#4111yescharacteristic
236C22×C322−1+412yes—
237C2×C3⋊D3—22no—
238C2×C3⋊D3—22no—
239C2×C3⋊D3—24no—
240C2×C3⋊D3—24no—
241C2×C3⋊D3C4×Q814yescomplemented
242C32×C4—22no—
243C32×C4—42no—
244C3⋊Dic3—42no—
245C3⋊Dic3C2×C22⋊C414yes—
246C3×Dic3—24no—
247C3×Dic3—24no—
248C3×Dic3—42no—
249C3×Dic3C2×C22⋊C418yes—
250C22×Q8—32no—
251C22×Q8—91no—
252C22×Q8—91no—
253C22×Q8—98no—
254C22×Q8—188no—
255C23×C4—92no—
256C23×C4—91no—
257C4×Q8—188no—
258C2×C4⋊C4—32no—
259C2×C4⋊C4—92no—
260C2×C4⋊C4—92no—
261C2×C22⋊C4—91no—
262C2×C22⋊C4—91no—
263C2×C22⋊C4—92no—
264C2×C42—32no—
265C2×C42—92no—
266C2×C42—92no—
267#95—32no—
268#95—32no—
269#95—32no—
270#95—92no—
271#95—92no—
272#95—91no—
273#95D3211yescharacteristic
274C23×C3—21no—
275C23×C3C23×D312yes—
276C22×D3—34no—
277C22×D3—34no—
278C22×D3—34no—
279C22×D3—62no—
280C22×D3—62no—
281C22×D3—62no—
282C22×D3—62no—
283C22×D3—62no—
284C22×D3—62no—
285C22×D3—62no—
286C22×D3—122no—
287C22×D3—122no—
288C3×Q8—616no—
289C2×C3×C4—22no—
290C2×C3×C4—22no—
291C2×C3×C4—22no—
292C2×C3×C4—22no—
293C2×C3×C4—22no—
294C2×C3×C4—22no—
295C2×C3×C4—22no—
296C2×C3×C4—22no—
297C2×C3×C4—22no—
298C2×C3×C4—34no—
299C2×C3×C4—34no—
300C2×C3×C4—34no—
301C2×C3×C4—34no—
302C2×C3×C4—34no—
303C2×C3×C4—42no—
304C2×C3×C4—42no—
305C2×C3×C4—42no—
306C2×C3×C4—42no—
307C2×C3×C4—62no—
308C2×C3×C4—62no—
309C2×C3×C4—62no—
310C2×C3×C4—62no—
311C2×C3×C4—62no—
312C2×C3×C4—62no—
313C2×C3×C4—62no—
314C2×C3×C4C2×C4×D314yes—
315C2×Dic3—22no—
316C2×Dic3—22no—
317C2×Dic3—22no—
318C2×Dic3—22no—
319C2×Dic3—22no—
320C2×Dic3—22no—
321C2×Dic3—22no—
322C2×Dic3—34no—
323C2×Dic3—34no—
324C2×Dic3—34no—
325C2×Dic3—62no—
326C2×Dic3—64no—
327C2×Dic3—62no—
328C2×Dic3—62no—
329C2×Dic3—62no—
330C2×Dic3—62no—
331C2×Dic3—62no—
332C2×Dic3—62no—
333C2×Dic3—122no—
334C2×Dic3—122no—
335C2×Dic3—122no—
336C2×Dic3C2×C4×D314yes—
337C2×Dic3C2×C4×D314yes—
338C2×Dic3D3×D414yes—
339C2×Dic3D3×D414yes—
340C2×Dic3D3×Q814yescomplemented
341C4×D3—616no—
342C4×D3—616no—
343C4×D3—616no—
344C4×D3—128no—
345Dic6—216no—
346Dic6—332no—
347Dic6—616no—
348C2×C32C22×C22⋊C411yescharacteristic
349C2×C32C2×C4×Q811yescharacteristic
350C2×C32#51911yescharacteristic
351C2×C32#54812yes—
352C2×C32D4×Q812yes—
353C3⋊D3—24no—
354C24—91no—
355C2×Q8—38no—
356C2×Q8—64no—
357C2×Q8—64no—
358C2×Q8—98no—
359C2×Q8—94no—
360C2×Q8—94no—
361C2×Q8—184no—
362C2×Q8—1832no—
363C22×C4—32no—
364C22×C4—32no—
365C22×C4—32no—
366C22×C4—32no—
367C22×C4—98no—
368C22×C4—91no—
369C22×C4—94no—
370C22×C4—92no—
371C22×C4—184no—
372C22×C4—184no—
373C22×C4—184no—
374C22×C4C2×D3212yes—
375C22×C4C2×D3211yescharacteristic
376C4⋊C4—64no—
377C4⋊C4—184no—
378C4⋊C4—184no—
379C22⋊C4—94no—
380C22⋊C4—184no—
381C22⋊C4—182no—
382C42—64no—
383C42—184no—
384C42—184no—
385C22×C3—22no—
386C22×C3—21no—
387C22×C3—22no—
388C22×C3—21no—
389C22×C3—21no—
390C22×C3C22×C4×D312yes—
391C22×C3C2×D3×D412yes—
392C22×C3C2×D3×D412yes—
393C22×C3C2×D3×Q812yes—
394C22×C3#100712yes—
395C22×C3D3×#4112yes—
396C22×C3#101012yes—
397C2×D3—38no—
398C2×D3—64no—
399C2×D3—64no—
400C2×D3—64no—
401C2×D3—64no—
402C2×D3—64no—
403C2×D3—64no—
404C2×D3—64no—
405C2×D3—122no—
406C2×D3—124no—
407C2×D3—122no—
408C2×D3—124no—
409C3×C4—24no—
410C3×C4—38no—
411C3×C4—42no—
412C3×C4—42no—
413C3×C4—42no—
414C3×C4—64no—
415C3×C4—64no—
416C3×C4—82no—
417C3×C4—122no—
418Dic3—24no—
419Dic3—24no—
420Dic3—38no—
421Dic3—42no—
422Dic3—64no—
423Dic3—122no—
424Dic3—122no—
425Dic3—242no—
426Dic3D3×C22⋊C418yes—
427C32Q8×C22⋊C411yescharacteristic, complemented, Sylow
428C23—92no—
429C23—92no—
430C23—92no—
431C23—182no—
432C23—182no—
433C23C22×D3211yescharacteristic
434Q8—616no—
435Q8—916no—
436Q8—188no—
437C2×C4—22no—
438C2×C4—22no—
439C2×C4—22no—
440C2×C4—22no—
441C2×C4—34no—
442C2×C4—34no—
443C2×C4—34no—
444C2×C4—34no—
445C2×C4—34no—
446C2×C4—62no—
447C2×C4—62no—
448C2×C4—62no—
449C2×C4—62no—
450C2×C4—62no—
451C2×C4—62no—
452C2×C4—62no—
453C2×C4—92no—
454C2×C4—94no—
455C2×C4—188no—
456C2×C4—1816no—
457C2×C4—182no—
458C2×C4—182no—
459C2×C4—182no—
460C2×C4C4×D3212yes—
461C2×C3—22no—
462C2×C3—21no—
463C2×C3—21no—
464C2×C3—22no—
465C2×C3—21no—
466C2×C3C2×D3×C22⋊C412yes—
467C2×C3C4×D3×Q812yes—
468C2×C3#557212yes—
469C2×C3#563212yes—
470C2×C3#563312yes—
471C2×C3#567712yes—
472C2×C3#572712yes—
473D3—68no—
474D3—124no—
475C22—94no—
476C22—184no—
477C22—182no—
478C22—184no—
479C22—182no—
480C22#6429712yes—
481C22C2×C4×D3211yescharacteristic
482C22D32×D412yes—
483C22#6431211yescharacteristic
484C22D32×Q811yescharacteristic
485C4—22no—
486C4—38no—
487C4—42no—
488C4—64no—
489C4—64no—
490C4—94no—
491C4—122no—
492C4—362no—
493C3—21no—
494C3#7661412yescomplemented
495C2—184no—
496C2#1059384811yescharacteristic
497C2#1059407512yes—
498C2D32×C22⋊C411yescharacteristic
499C2#1059436311yescharacteristic
500C2#1059437812yes—
subgroupG/H
center, FrattiniC23C22×D32
commutatorC22×C32C23×C4
FittingC32×#95C22
socle, cosocleC23×C32C24
prime radicalC23×C3⋊D3C23
hypercenter#95D32
hypocenterC32Q8×C22⋊C4
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C23 ◁ #95

Complements

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

NH ≅ G/Ntype
2. C2×#63837C2semidirect
4. C3×#4646C2semidirect
6. #10591261C2semidirect
8. #10591236C2semidirect
17. C2×#3797C4semidirect
50. #4646D3semidirect
79. #3722Q8semidirect
156. C2×C3×Dic3C2×Q8semidirect
159. #627C22⋊C4semidirect
241. C2×C3⋊D3C4×Q8semidirect
340. C2×Dic3D3×Q8semidirect
427. C32Q8×C22⋊C4semidirect
494. C3#76614semidirect

Maximal subgroups

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

subgroupindex
C22×#37972
C2×#638372
#105923662
C3×#46462
#105913672
#105912612
#105912602
#105912362
#105912332
#766143