Finite Group Databasebeta

← #11808842

Subgroups — #11808842

Order 1152.

1099 conjugacy classes of subgroups.

The subgroup lattice has 530 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×Q8×Dic3C211yesmaximal, characteristic
2C2×#63837C211yesmaximal, characteristic
3#10592929C211yesmaximal, characteristic
4C3×#5230C211yesmaximal, characteristic
5#10591358C211yesmaximal, characteristic
6#10591342C212yesmaximal
7#10591338C212yesmaximal
8#10591243C212yesmaximal
9Dic3×Dic3⋊C4C212yesmaximal
10#10591239C211yesmaximal, characteristic
11#10591214C211yesmaximal, characteristic
12#82467—31nomaximal
13#77171—31nomaximal
14C22×C32×Q8C2211yescharacteristic
15C22×#627C2211yescharacteristic
16C2×#3750C2212yes—
17C2×#3750C2211yescharacteristic
18C3×Q8×Dic3—24no—
19C2×C3×C4⋊Dic3C2212yes—
20C2×C3×C4⋊Dic3C2211yescharacteristic
21C2×C3×Dic3⋊C4C2212yes—
22C2×C3×Dic3⋊C4C2211yescharacteristic
23C2×C3×C4×Dic3C2212yes—
24C2×C3×C4×Dic3C2211yescharacteristic
25C2×#3724C2212yes—
26C2×Dic3⋊Dic3C2212yes—
27C2×Dic3⋊Dic3C2211yescharacteristic
28C2×Dic32C2211yescharacteristic
29C2×Dic32C2211yescharacteristic
30C2×Dic32C2212yes—
31#63837—24no—
32#63658C2211yescharacteristic
33#63658C2212yes—
34C3×C3⋊#95C2211yescharacteristic
35C3×C3⋊#95C2212yes—
36#63579C2212yes—
37#63579C2212yes—
38#63579C2212yes—
39C2×C3×C4×Q8—31no—
40C2×Q8×Dic3D311yescharacteristic
41C2×#887—31no—
42C2×C4×Dic6—31no—
43C3×#395—31no—
44#5230—31no—
45#5230—31no—
46#5230—61no—
47#5230D311yescharacteristic
48#4983—31no—
49#4983—31no—
50#4982—32no—
51#4981—31no—
52#4981—32no—
53#4979—32no—
54Dic3×C4⋊C4—32no—
55#4932—31no—
56C4×Dic3⋊C4—32no—
57C4×Dic3⋊C4—32no—
58#4661—31no—
59#4656—32no—
60#4649—32no—
61#4648—31no—
62C2×C32×Q8—22no—
63C2×C32×Q8—24no—
64C22×C32×C4C2311yescharacteristic
65C22×C32×C4C2312yes—
66C22×C3⋊Dic3C2311yescharacteristic
67C22×C3⋊Dic3C2312yes—
68C22×C3⋊Dic3C2311yescharacteristic
69C22×C3×Dic3C2312yes—
70C22×C3×Dic3C2311yescharacteristic
71C22×C3×Dic3C2311yescharacteristic
72C22×C3×Dic3C2312yes—
73C22×C3×Dic3C2311yescharacteristic
74C22×C3×Dic3C2311yescharacteristic
75C2×#627—22no—
76C2×#627—22no—
77C2×#627—22no—
78#3750—22no—
79#3750—24no—
80C3×C4⋊Dic3—22no—
81C3×C4⋊Dic3—24no—
82C3×Dic3⋊C4—22no—
83C3×Dic3⋊C4—24no—
84C3×C4×Dic3—24no—
85C3×C4×Dic3D414yes—
86#3724—24no—
87Dic3⋊Dic3—24no—
88Dic3⋊Dic3—22no—
89Dic32—22no—
90Dic32—22no—
91Dic32Q818yescomplemented
92#2399—91noSylow
93C22×C3×Q8—21no—
94C22×C3×Q8C2×D311yescharacteristic
95C22×C3×Q8C2×D311yescharacteristic
96C22×Dic6—31no—
97C22×Dic6—31no—
98C3×C4×Q8—64no—
99C2×C3×C4⋊C4—32no—
100C2×C3×C4⋊C4—31no—
101C2×C3×C4⋊C4—32no—
102C2×C3×C4⋊C4—31no—
103C2×C3×C42—31no—
104C2×C3×C42—32no—
105Q8×Dic3—24no—
106C2×C4⋊Dic3—32no—
107C2×C4⋊Dic3—31no—
108C2×C4⋊Dic3C2×D312yes—
109C2×C4⋊Dic3C2×D311yescharacteristic
110C2×Dic3⋊C4—32no—
111C2×Dic3⋊C4—31no—
112C2×Dic3⋊C4—32no—
113C2×Dic3⋊C4—31no—
114C2×Dic3⋊C4—32no—
115C2×Dic3⋊C4—32no—
116C2×Dic3⋊C4—32no—
117C2×Dic3⋊C4—31no—
118C2×Dic3⋊C4—61no—
119C2×Dic3⋊C4—62no—
120C2×Dic3⋊C4C2×D312yes—
121C2×Dic3⋊C4C2×D311yescharacteristic
122C2×C4×Dic3—32no—
123C2×C4×Dic3—32no—
124C2×C4×Dic3—31no—
125C2×C4×Dic3—31no—
126C2×C4×Dic3—31no—
127C2×C4×Dic3—31no—
128C2×C4×Dic3C2×D312yes—
129C2×C4×Dic3C2×D311yescharacteristic
130#887—64no—
131C4×Dic6—64no—
132C3×#95—31no—
133C3×#95—32no—
134C3⋊#95—31no—
135C3⋊#95—32no—
136C3⋊#95—32no—
137C3⋊#95—31no—
138C3⋊#95—32no—
139C3⋊#95—32no—
140C3⋊#95—32no—
141C3⋊#95—32no—
142C3⋊#95—32no—
143C3⋊#95—32no—
144C3⋊#95—61no—
145C3⋊#95—62no—
146C3⋊#95C2×D312yes—
147C3⋊#95C2×D311yescharacteristic
148C23×C32C2411yescharacteristic
149C32×Q8—28no—
150C2×C32×C4—22no—
151C2×C32×C4—22no—
152C2×C32×C4—22no—
153C2×C32×C4C2×D412yes—
154C2×C32×C4#4114yes—
155C2×C3⋊Dic3—21no—
156C2×C3⋊Dic3—22no—
157C2×C3⋊Dic3—22no—
158C2×C3⋊Dic3—21no—
159C2×C3⋊Dic3—21no—
160C2×C3⋊Dic3—22no—
161C2×C3⋊Dic3C2×Q814yes—
162C2×C3⋊Dic3#4112yes—
163C2×C3×Dic3—21no—
164C2×C3×Dic3—22no—
165C2×C3×Dic3—22no—
166C2×C3×Dic3—21no—
167C2×C3×Dic3—21no—
168C2×C3×Dic3—21no—
169C2×C3×Dic3—21no—
170C2×C3×Dic3—22no—
171C2×C3×Dic3—22no—
172C2×C3×Dic3—22no—
173C2×C3×Dic3—22no—
174C2×C3×Dic3C2×D412yes—
175C2×C3×Dic3C2×D412yes—
176C2×C3×Dic3C2×Q814yes—
177C2×C3×Dic3C2×Q814yes—
178C2×C3×Dic3#4112yes—
179#627—28no—
180C2×C4×Q8—31no—
181C2×C4×Q8—91no—
182#398—91no—
183#398—92no—
184#398—91no—
185#395—31no—
186#395—92no—
187#395—91no—
188C4×C4⋊C4—92no—
189C4×C4⋊C4—92no—
190#376—91no—
191C2×C3×Q8—24no—
192C2×C3×Q8—22no—
193C2×C3×Q8—24no—
194C2×C3×Q8—22no—
195C2×C3×Q8—44no—
196C2×C3×Q8—42no—
197C22×C3×C4—22no—
198C22×C3×C4—21no—
199C22×C3×C4—31no—
200C22×C3×C4—32no—
201C22×C3×C4—31no—
202C22×C3×C4—31no—
203C22×C3×C4—31no—
204C22×C3×C4—32no—
205C22×C3×C4C22×D312yes—
206C22×C3×C4C22×D311yescharacteristic
207C22×C3×C4C22×D312yes—
208C22×C3×C4C22×D311yescharacteristic
209C22×Dic3—32no—
210C22×Dic3—32no—
211C22×Dic3—31no—
212C22×Dic3—31no—
213C22×Dic3—31no—
214C22×Dic3—31no—
215C22×Dic3—62no—
216C22×Dic3—61no—
217C22×Dic3—61no—
218C22×Dic3C22×D311yescharacteristic
219C22×Dic3C22×D312yes—
220C22×Dic3C22×D312yes—
221C22×Dic3C22×D311yescharacteristic
222C22×Dic3C22×D311yescharacteristic
223C22×Dic3C22×D311yescharacteristic
224C2×Dic6—62no—
225C2×Dic6—62no—
226C2×Dic6—62no—
227C2×Dic6—62no—
228C2×Dic6—62no—
229C2×Dic6—62no—
230C3×C4⋊C4—64no—
231C3×C4⋊C4—64no—
232C3×C4⋊C4—62no—
233C3×C4⋊C4—62no—
234C3×C42—34no—
235C3×C42—64no—
236C4⋊Dic3—22no—
237C4⋊Dic3—24no—
238C4⋊Dic3—64no—
239C4⋊Dic3—62no—
240Dic3⋊C4—22no—
241Dic3⋊C4—24no—
242Dic3⋊C4—64no—
243Dic3⋊C4—64no—
244Dic3⋊C4—64no—
245Dic3⋊C4—62no—
246Dic3⋊C4—64no—
247Dic3⋊C4—62no—
248Dic3⋊C4—64no—
249Dic3⋊C4—62no—
250Dic3⋊C4—124no—
251Dic3⋊C4—122no—
252C4×Dic3—24no—
253C4×Dic3—38no—
254C4×Dic3—38no—
255C4×Dic3—62no—
256C4×Dic3—62no—
257C4×Dic3—62no—
258C4×Dic3—62no—
259C4×Dic3#6714yes—
260C22×C32C22×D411yescharacteristic
261C22×C32C22×Q812yes—
262C22×C32C2×#4112yes—
263C22×C32C2×#4111yescharacteristic
264C22×C32C2×#4111yescharacteristic
265C32×C4—22no—
266C32×C4—24no—
267C3⋊Dic3—22no—
268C3⋊Dic3—24no—
269C3⋊Dic3—41no—
270C3×Dic3—22no—
271C3×Dic3—22no—
272C3×Dic3—24no—
273C3×Dic3—42no—
274C3×Dic3—41no—
275C3×Dic3C4⋊Q814yes—
276C22×Q8—91no—
277C22×Q8D3211yescharacteristic
278C4×Q8—64no—
279C4×Q8—184no—
280C2×C4⋊C4—32no—
281C2×C4⋊C4—31no—
282C2×C4⋊C4—31no—
283C2×C4⋊C4—32no—
284C2×C4⋊C4—91no—
285C2×C4⋊C4—92no—
286C2×C4⋊C4—92no—
287C2×C4⋊C4—91no—
288C2×C4⋊C4—92no—
289C2×C42—31no—
290C2×C42—32no—
291C2×C42—92no—
292C2×C42—91no—
293C2×C42—91no—
294#95—31no—
295#95—32no—
296#95—92no—
297#95—92no—
298#95—92no—
299#95—91no—
300#95—92no—
301C23×C3—21no—
302C23×C3C23×D311yescharacteristic
303C23×C3C23×D311yescharacteristic
304C3×Q8—28no—
305C3×Q8—28no—
306C3×Q8—48no—
307C2×C3×C4—22no—
308C2×C3×C4—22no—
309C2×C3×C4—22no—
310C2×C3×C4—22no—
311C2×C3×C4—22no—
312C2×C3×C4—22no—
313C2×C3×C4—24no—
314C2×C3×C4—22no—
315C2×C3×C4—32no—
316C2×C3×C4—34no—
317C2×C3×C4—32no—
318C2×C3×C4—34no—
319C2×C3×C4—32no—
320C2×C3×C4—42no—
321C2×C3×C4—42no—
322C2×C3×C4—42no—
323C2×C3×C4—62no—
324C2×C3×C4—61no—
325C2×C3×C4—62no—
326C2×C3×C4—61no—
327C2×C3×C4—61no—
328C2×C3×C4—61no—
329C2×C3×C4—62no—
330C2×C3×C4—62no—
331C2×C3×C4—62no—
332C2×C3×C4—62no—
333C2×C3×C4—61no—
334C2×C3×C4#23514yes—
335C2×C3×C4D3×D412yes—
336C2×C3×C4#23714yes—
337C2×C3×C4C2×#6712yes—
338C2×Dic3—21no—
339C2×Dic3—22no—
340C2×Dic3—22no—
341C2×Dic3—21no—
342C2×Dic3—21no—
343C2×Dic3—21no—
344C2×Dic3—21no—
345C2×Dic3—22no—
346C2×Dic3—22no—
347C2×Dic3—22no—
348C2×Dic3—22no—
349C2×Dic3—34no—
350C2×Dic3—34no—
351C2×Dic3—32no—
352C2×Dic3—32no—
353C2×Dic3—64no—
354C2×Dic3—62no—
355C2×Dic3—62no—
356C2×Dic3—61no—
357C2×Dic3—62no—
358C2×Dic3—62no—
359C2×Dic3—61no—
360C2×Dic3—62no—
361C2×Dic3—61no—
362C2×Dic3—61no—
363C2×Dic3—62no—
364C2×Dic3—61no—
365C2×Dic3—62no—
366C2×Dic3—61no—
367C2×Dic3—122no—
368C2×Dic3—121no—
369C2×Dic3—122no—
370C2×Dic3—121no—
371C2×Dic3—122no—
372C2×Dic3—121no—
373C2×Dic3D3×Q814yes—
374C2×Dic3D3×Q814yes—
375C2×Dic3#23912yes—
376C2×Dic3C2×#6712yes—
377C2×Dic3C2×#6712yes—
378Dic6—68no—
379Dic6—68no—
380C2×C32#52511yescharacteristic
381C2×C32#52511yescharacteristic
382C2×C32C2×C4⋊Q811yescharacteristic
383C2×C32#53312yes—
384C2×C32#53312yes—
385C2×Q8—24no—
386C2×Q8—22no—
387C2×Q8—182no—
388C2×Q8—182no—
389C2×Q8—182no—
390C22×C4—31no—
391C22×C4—32no—
392C22×C4—31no—
393C22×C4—31no—
394C22×C4—32no—
395C22×C4—31no—
396C22×C4—92no—
397C22×C4—91no—
398C22×C4—91no—
399C22×C4C2×D3212yes—
400C22×C4C2×D3211yescharacteristic
401C4⋊C4—64no—
402C4⋊C4—64no—
403C4⋊C4—62no—
404C4⋊C4—62no—
405C4⋊C4—182no—
406C4⋊C4—184no—
407C4⋊C4—184no—
408C4⋊C4—184no—
409C4⋊C4—182no—
410C42—34no—
411C42—64no—
412C42—98no—
413C42—182no—
414C42—182no—
415C22×C3—22no—
416C22×C3—21no—
417C22×C3—21no—
418C22×C3—22no—
419C22×C3—21no—
420C22×C3C2×#23512yes—
421C22×C3C2×D3×D411yescharacteristic
422C22×C3C2×#23712yes—
423C22×C3C2×D3×Q812yes—
424C22×C3C2×D3×Q812yes—
425C22×C3C2×#23911yescharacteristic
426C22×C3D3×#4111yescharacteristic
427C22×C3D3×#4111yescharacteristic
428C22×C3D3×#4111yescharacteristic
429C22×C3C22×#6711yescharacteristic
430C3×C4—24no—
431C3×C4—22no—
432C3×C4—22no—
433C3×C4—24no—
434C3×C4—34no—
435C3×C4—44no—
436C3×C4—42no—
437C3×C4—62no—
438C3×C4—64no—
439C3×C4—62no—
440C3×C4—121no—
441C3×C4—122no—
442Dic3—22no—
443Dic3—24no—
444Dic3—22no—
445Dic3—42no—
446Dic3—41no—
447Dic3—64no—
448Dic3—62no—
449Dic3—64no—
450Dic3—62no—
451Dic3—124no—
452Dic3—122no—
453Dic3—121no—
454Dic3—121no—
455Dic3—241no—
456Dic3#94414yes—
457C32#239911yescharacteristic, complemented, Sylow
458C23C22×D3211yescharacteristic
459Q8—28no—
460Q8—188no—
461C2×C4—22no—
462C2×C4—22no—
463C2×C4—22no—
464C2×C4—34no—
465C2×C4—32no—
466C2×C4—34no—
467C2×C4—32no—
468C2×C4—32no—
469C2×C4—61no—
470C2×C4—62no—
471C2×C4—61no—
472C2×C4—61no—
473C2×C4—62no—
474C2×C4—61no—
475C2×C4—62no—
476C2×C4—62no—
477C2×C4—62no—
478C2×C4—62no—
479C2×C4—61no—
480C2×C4—94no—
481C2×C4—92no—
482C2×C4—182no—
483C2×C4—181no—
484C2×C4—182no—
485C2×C4—181no—
486C2×C4—182no—
487C2×C4—181no—
488C2×C4#380414yes—
489C2×C4D3×#6712yes—
490C2×C3—21no—
491C2×C3—22no—
492C2×C3—22no—
493C2×C3—21no—
494C2×C3—21no—
495C2×C3#557812yes—
496C2×C3#557812yes—
497C2×C3#558611yescharacteristic
498C2×C3#562212yes—
499C2×C3#562711yescharacteristic
500C2×C3D3×C4⋊Q811yescharacteristic
501C2×C3#572812yes—
502C2×C3#579111yescharacteristic
503C2×C3C2×#94411yescharacteristic
504C2×C3#582811yescharacteristic
505C22D32×Q812yes—
506C22D3×#23911yescharacteristic
507C22#6431911yescharacteristic
508C22C2×#380412yes—
509C22C2×D3×#6711yescharacteristic
510C4—24no—
511C4—22no—
512C4—34no—
513C4—64no—
514C4—62no—
515C4—62no—
516C4—122no—
517C4—121no—
518C4—184no—
519C4—182no—
520C4—361no—
521C3—21no—
522C3#7717111yescharacteristic, complemented
523C3#8246711yescharacteristic, complemented
524C2D3×#94411yescharacteristic
525C2#1059536712yes—
526C2#1059537412yes—
527C2#1059542411yescharacteristic
528C2#1059549811yescharacteristic
subgroupG/H
center, FrattiniC23C22×D32
commutator, socle, prime radical, cosocleC23×C32C24
FittingC22×C32×Q8C22
hypercenterC22×Q8D32
hypocenterC32#2399
LCSG ▷ C23×C32 ▷ C32
UCSC1 ◁ C23 ◁ C22×Q8

Complements

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

NH ≅ G/Ntype
91. Dic32Q8semidirect
457. C32#2399semidirect
522. C3#77171semidirect
523. C3#82467semidirect

Maximal subgroups

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

subgroupindex
C2×C3×Q8×Dic32
C2×#638372
#105929292
C3×#52302
#105913582
#105913422
#105913382
#105912432
Dic3×Dic3⋊C42
#105912392
#105912142
#824673
#771713