Finite Group Databasebeta

← #11859125

Subgroups — #11859125

Order 1152.

849 conjugacy classes of subgroups.

The subgroup lattice has 548 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1Dic3×#235C211yesmaximal, characteristic
2#10592821C211yesmaximal, characteristic, complemented
3C3×#5129C211yesmaximal, characteristic
4C3×#5118C211yesmaximal, characteristic, complemented
5C2×Dic3⋊(C3⋊C8)C211yesmaximal, characteristic, complemented
6#10591071C211yesmaximal, characteristic
7#10591059C211yesmaximal, characteristic, complemented
8#10590699C212yesmaximal, complemented
9#10590698C212yesmaximal, complemented
10#10590661C212yesmaximal, complemented
11#10590656C212yesmaximal, complemented
12#79040—31nomaximal
13#78650—31nomaximal
14C2×C3×#235C2211yescharacteristic
15C2×C32×M16C2211yescharacteristic
16#64135C2211yescharacteristic
17C22×C3⋊(C3⋊C8)C2211yescharacteristic
18C2×C3×C4×Dic3C2211yescharacteristic
19C2×C3×#208C2211yescharacteristic
20C22×C3×C3⋊C8C2211yescharacteristic
21Dic3×#67C412yes—
22Dic3×#67C412yes—
23Dic3×D12C411yescharacteristic
24Dic3×D12C411yescharacteristic
25C4×D3×Dic3C2212yes—
26#63855C2212yes—
27Dic3×Dic6C411yescharacteristic
28Dic3×Dic6C411yescharacteristic
29#63642C2212yes—
30C8×C3⋊Dic3C2212yes—
31C3×(C2×D3)⋊C8C2212yes—
32C3×(C2×D3)⋊C8C2212yes—
33C3×Dic3⋊C8C2212yes—
34C3×Dic3⋊C8C2212yes—
35Dic3⋊(C3⋊C8)C2211yescharacteristic
36Dic3⋊(C3⋊C8)C2211yescharacteristic
37Dic3⋊(C3⋊C8)C2211yescharacteristic
38Dic3⋊(C3⋊C8)C2211yescharacteristic
39(C2×D3)⋊(C3⋊C8)C2212yes—
40(C2×D3)⋊(C3⋊C8)C2212yes—
41#63555C2212yes—
42#63553C2212yes—
43Dic3×#41—31no—
44C4×#235—31no—
45C3×#423—31no—
46C3×#408—31no—
47#5234—31no—
48#5129—31no—
49#5129D311yescharacteristic
50#5122—31no—
51#5122—31no—
52#5122—31no—
53#5122—61no—
54#5118D311yescharacteristic, complemented
55#5101—31no—
56C2×Dic3⋊C8—31no—
57C2×C4⋊(C3⋊C8)—31no—
58#4840—32no—
59#4840—32no—
60#4835—32no—
61#4833—32no—
62#4720—32no—
63#4720—32no—
64#4719—32no—
65#4718—32no—
66C22×C32×C4C2311yescharacteristic
67C2×C3×#67C2×C412yes—
68C22×C3×Dic3C2×C411yescharacteristic
69C22×C3×Dic3C2×C411yescharacteristic
70C3×#235—22no—
71C3×#235—22no—
72C2×C3×D12C2×C411yescharacteristic
73C2×C3×C4×D3C2312yes—
74C2×C3×Dic6C2×C411yescharacteristic
75C2×D3×Dic3C2×C412yes—
76C2×D3×Dic3C2×C412yes—
77C32×M16—22no—
78C2×C32×C8C2312yes—
79#3757C2×C412yes—
80C4⋊(C3⋊Dic3)C2×C411yescharacteristic
81C4⋊(C3⋊Dic3)C2×C411yescharacteristic
82C4×C3⋊Dic3C2312yes—
83C2×C3⋊(C3⋊C8)—22no—
84C2×C3⋊(C3⋊C8)C2311yescharacteristic
85C2×C3⋊(C3⋊C8)C2311yescharacteristic
86C3×C4×Dic3C2×C411yescharacteristic
87C3×C4×Dic3C2×C411yescharacteristic
88C3×C4×Dic3C2311yescharacteristic
89C3×C4×Dic3C2311yescharacteristic
90C3×#208—22no—
91C2×C3×C3⋊C8—22no—
92C2×C3×C3⋊C8C2311yescharacteristic
93C2×C3×C3⋊C8C2311yescharacteristic
94C2×C3×C3⋊C8C2312yes—
95Dic3⋊Dic3C2×C412yes—
96Dic3⋊Dic3C2×C412yes—
97(C2×D3)⋊Dic3C2×C412yes—
98(C2×D3)⋊Dic3C2×C412yes—
99Dic32C2×C412yes—
100Dic32C2×C412yes—
101#2925—91noSylow
102C2×C3×#41—31no—
103C2×#235C2×D311yescharacteristic
104C2×C3×M16—21no—
105C2×C3×M16—31no—
106C2×C3×M16C2×D311yescharacteristic
107C2×C3×M16C2×D311yescharacteristic
108C22×C3×C8—31no—
109C2×C3×C42—31no—
110Q8×Dic3—31no—
111Q8×Dic3—31no—
112D4×Dic3—32no—
113D4×Dic3—32no—
114D4×Dic3—31no—
115D4×Dic3—31no—
116C4×#67—32no—
117C4×#67—32no—
118#926—31no—
119#926—31no—
120#926—32no—
121#926—61no—
122C2×C4×Dic3—32no—
123C2×C4×Dic3C2×D311yescharacteristic
124C2×#208C2×D311yescharacteristic
125C22×C3⋊C8—31no—
126C22×C3⋊C8—31no—
127C22×C3⋊C8—61no—
128C22×C3⋊C8C2×D311yescharacteristic
129C4×D12—31no—
130C4×D12—31no—
131#872—32no—
132C42×D3—32no—
133C4×Dic6—31no—
134C4×Dic6—31no—
135C3×C4⋊C8—32no—
136C3×C4⋊C8—32no—
137C3×C22⋊C8—32no—
138C3×C22⋊C8—32no—
139#830—32no—
140#830—32no—
141(C2×D3)⋊C8—32no—
142(C2×D3)⋊C8—32no—
143(C2×D3)⋊C8C2×D312yes—
144(C2×D3)⋊C8C2×D312yes—
145#815—32no—
146#815—32no—
147#815—32no—
148#815—32no—
149#815—62no—
150Dic3⋊C8—31no—
151Dic3⋊C8—31no—
152Dic3⋊C8—31no—
153Dic3⋊C8—31no—
154Dic3⋊C8C2×D312yes—
155Dic3⋊C8C2×D312yes—
156C8×Dic3—32no—
157C8×Dic3—32no—
158C8×Dic3—32no—
159C8×Dic3—32no—
160C8×Dic3—62no—
161C4⋊(C3⋊C8)—31no—
162C4⋊(C3⋊C8)—31no—
163C4⋊(C3⋊C8)—31no—
164C4⋊(C3⋊C8)—31no—
165C23×C32C22×C411yescharacteristic
166C22×C3×D3C22×C412yes—
167C2×C32×C4C22×C411yescharacteristic
168C2×C32×C4#4112yes—
169C2×C32×C4#4112yes—
170C2×C32×C4C2411yescharacteristic
171C2×C3⋊Dic3C22×C412yes—
172C2×C3⋊Dic3C22×C412yes—
173C3×#67—24no—
174C2×C3×Dic3—22no—
175C2×C3×Dic3—41no—
176C2×C3×Dic3C22×C412yes—
177C2×C3×Dic3C22×C411yescharacteristic
178C2×C3×Dic3C22×C411yescharacteristic
179C2×C3×Dic3C22×C411yescharacteristic
180C2×C3×Dic3C22×C411yescharacteristic
181C3×D12—22no—
182C3×C4×D3—22no—
183C3×C4×D3—22no—
184C3×Dic6—22no—
185D3×Dic3—24no—
186D3×Dic3—42no—
187C32×C8—22no—
188C3⋊(C3⋊C8)—21no—
189C3⋊(C3⋊C8)—21no—
190C3×C3⋊C8—21no—
191C3×C3⋊C8—21no—
192C3×C3⋊C8—22no—
193C4×#41—91no—
194#433—92no—
195#433—92no—
196#432—92no—
197#431—92no—
198#423—31no—
199C2×C4⋊C8—91no—
200#408—31no—
201#408—91no—
202#405—91no—
203#405—91no—
204C3×#41—62no—
205C3×#41—62no—
206C2×C3×Q8—31no—
207C2×C3×D4—32no—
208C2×C3×D4—31no—
209C22×C3×C4—21no—
210C22×C3×C4—31no—
211C22×C3×C4—31no—
212C22×C3×C4—32no—
213C22×C3×C4C22×D311yescharacteristic
214C22×C3×C4C22×D311yescharacteristic
215C2×#67C4×D312yes—
216C22×Dic3—32no—
217C22×Dic3—32no—
218C22×Dic3C4×D311yescharacteristic
219C22×Dic3C4×D311yescharacteristic
220#235—22no—
221#235—22no—
222C2×D12C4×D311yescharacteristic
223C2×C4×D3—32no—
224C2×C4×D3—32no—
225C2×C4×D3C22×D312yes—
226C2×Dic6C4×D311yescharacteristic
227C3×M16—24no—
228C3×M16—22no—
229C3×M16—22no—
230C3×M16—62no—
231C2×C3×C8—22no—
232C2×C3×C8—31no—
233C2×C3×C8—32no—
234C2×C3×C8—31no—
235C2×C3×C8—62no—
236C2×C3×C8C22×D312yes—
237C2×C3×C8C22×D312yes—
238C3×C42—31no—
239C3×C42—31no—
240C3×C42—31no—
241C3×C42—31no—
242#217—32no—
243#217—32no—
244#217—32no—
245#217—32no—
246#217—62no—
247(C2×D3)⋊C4—32no—
248(C2×D3)⋊C4—32no—
249C4⋊Dic3—31no—
250C4⋊Dic3—31no—
251C4⋊Dic3—31no—
252C4⋊Dic3—31no—
253C4⋊Dic3—32no—
254C4⋊Dic3—32no—
255C4⋊Dic3—61no—
256C4⋊Dic3—61no—
257Dic3⋊C4—32no—
258Dic3⋊C4—32no—
259C4×Dic3—32no—
260C4×Dic3—32no—
261C4×Dic3—32no—
262C4×Dic3—32no—
263C4×Dic3—32no—
264C4×Dic3—32no—
265C4×Dic3—62no—
266C4×Dic3C4×D311yescharacteristic
267C4×Dic3C4×D311yescharacteristic
268C4×Dic3C22×D311yescharacteristic
269C4×Dic3C22×D311yescharacteristic
270#208—22no—
271C2×C3⋊C8—22no—
272C2×C3⋊C8—31no—
273C2×C3⋊C8—31no—
274C2×C3⋊C8—31no—
275C2×C3⋊C8—31no—
276C2×C3⋊C8—61no—
277C2×C3⋊C8—61no—
278C2×C3⋊C8—64no—
279C2×C3⋊C8—62no—
280C2×C3⋊C8—62no—
281C2×C3⋊C8C22×D311yescharacteristic
282C2×C3⋊C8C22×D311yescharacteristic
283C2×C3⋊C8C22×D312yes—
284C22×C32—21no—
285C22×C32—21no—
286C22×C32#11712yes—
287C22×C32C23×C411yescharacteristic
288C2×C3×D3—22no—
289C2×C3×D3—22no—
290C2×C3×D3—22no—
291C32×C4#11712yes—
292C32×C4C2×#4111yescharacteristic
293C32×C4C2×#4111yescharacteristic
294C3⋊Dic3—22no—
295C3⋊Dic3—22no—
296C3×Dic3—22no—
297C3×Dic3—21no—
298C3×Dic3—21no—
299C3×Dic3—21no—
300C3×Dic3#13112yes—
301C2×#41—31no—
302C2×M16—31no—
303C2×M16D3211yescharacteristic
304C22×C8—31no—
305C22×C8—91no—
306C4×Q8—91no—
307C4×Q8—91no—
308C4×D4—91no—
309C4×D4—91no—
310C4×D4—92no—
311C4×D4—92no—
312#117—92no—
313#117—91no—
314C2×C42—31no—
315C2×C42—92no—
316C4⋊C8—32no—
317C4⋊C8—32no—
318C4⋊C8—91no—
319C4⋊C8—91no—
320C4⋊C8—91no—
321C4⋊C8—91no—
322C22⋊C8—32no—
323C22⋊C8—32no—
324C22⋊C8—92no—
325C22⋊C8—92no—
326#97—92no—
327#97—92no—
328C4×C8—92no—
329C4×C8—92no—
330C23×C3—21no—
331C23×C3—32no—
332C23×C3C2×C4×D311yescharacteristic
333C23×C3C2×C4×D311yescharacteristic
334C22×D3C2×C4×D312yes—
335C3×Q8—62no—
336C3×D4—64no—
337C3×D4—62no—
338C2×C3×C4—21no—
339C2×C3×C4—22no—
340C2×C3×C4—21no—
341C2×C3×C4—22no—
342C2×C3×C4—31no—
343C2×C3×C4—32no—
344C2×C3×C4—31no—
345C2×C3×C4—31no—
346C2×C3×C4—31no—
347C2×C3×C4—62no—
348C2×C3×C4—62no—
349C2×C3×C4—62no—
350C2×C3×C4—121no—
351C2×C3×C4C2×C4×D311yescharacteristic
352C2×C3×C4C2×C4×D311yescharacteristic
353C2×C3×C4#23712yes—
354C2×C3×C4#23712yes—
355C2×C3×C4#23712yes—
356C2×C3×C4#23912yes—
357C2×C3×C4C23×D311yescharacteristic
358C2×C3×C4C23×D311yescharacteristic
359#67—24no—
360C2×Dic3—22no—
361C2×Dic3—32no—
362C2×Dic3—32no—
363C2×Dic3—32no—
364C2×Dic3—32no—
365C2×Dic3—41no—
366C2×Dic3—62no—
367C2×Dic3—62no—
368C2×Dic3—64no—
369C2×Dic3—122no—
370C2×Dic3C2×C4×D311yescharacteristic
371C2×Dic3C2×C4×D312yes—
372C2×Dic3C2×C4×D311yescharacteristic
373C2×Dic3C2×C4×D311yescharacteristic
374C2×Dic3C2×C4×D311yescharacteristic
375D12—22no—
376C4×D3—22no—
377C4×D3—22no—
378C4×D3—64no—
379C4×D3—122no—
380Dic6—22no—
381C3×C8—24no—
382C3×C8—22no—
383C3×C8—22no—
384C3×C8—62no—
385C3×C8—61no—
386C3×C8—61no—
387C3⋊C8—21no—
388C3⋊C8—21no—
389C3⋊C8—22no—
390C3⋊C8—62no—
391C3⋊C8—62no—
392C3⋊C8—61no—
393C3⋊C8—61no—
394C3⋊C8—61no—
395C3⋊C8—61no—
396C2×C32—22no—
397C2×C32C2×#11711yescharacteristic
398C2×C32C2×#13111yescharacteristic
399C2×C32#56811yescharacteristic
400C3×D3—42no—
401#41—62no—
402#41—62no—
403C2×Q8—31no—
404C2×D4—32no—
405C2×D4—31no—
406C22×C4—31no—
407C22×C4—31no—
408C22×C4—32no—
409C22×C4—92no—
410C22×C4—92no—
411C22×C4C2×D3211yescharacteristic
412M16—22no—
413M16—62no—
414C2×C8—31no—
415C2×C8—32no—
416C2×C8—31no—
417C2×C8—62no—
418C2×C8—91no—
419C2×C8—91no—
420C2×C8—182no—
421C2×C8C2×D3212yes—
422C4⋊C4—92no—
423C4⋊C4—92no—
424C4⋊C4—91no—
425C4⋊C4—91no—
426C22⋊C4—92no—
427C22⋊C4—92no—
428C22⋊C4—92no—
429C42—31no—
430C42—31no—
431C42—31no—
432C42—31no—
433C42—92no—
434C42—92no—
435C42—92no—
436C22×C3—21no—
437C22×C3—21no—
438C22×C3—21no—
439C22×C3—21no—
440C22×C3—21no—
441C22×C3—22no—
442C22×C3—41no—
443C22×C3—41no—
444C22×C3—62no—
445C22×C3—62no—
446C22×C3—62no—
447C22×C3#87712yes—
448C22×C3#89212yes—
449C22×C3C22×C4×D311yescharacteristic
450C22×C3C22×C4×D311yescharacteristic
451C2×D3—22no—
452C2×D3—22no—
453C2×D3—22no—
454C3×C4—21no—
455C3×C4—21no—
456C3×C4—22no—
457C3×C4—32no—
458C3×C4—61no—
459C3×C4—61no—
460C3×C4—61no—
461C3×C4—62no—
462C3×C4#87712yes—
463C3×C4#89212yes—
464C3×C4C2×#23711yescharacteristic
465C3×C4C2×#23711yescharacteristic
466C3×C4C2×#23711yescharacteristic
467C3×C4C2×#23911yescharacteristic
468Dic3—22no—
469Dic3—21no—
470Dic3—21no—
471Dic3—21no—
472Dic3—62no—
473Dic3—62no—
474Dic3—62no—
475Dic3—62no—
476Dic3—122no—
477Dic3—122no—
478Dic3#90712yes—
479C32#292511yescharacteristic, complemented, Sylow
480C23—32no—
481C23C4×D3211yescharacteristic
482Q8—62no—
483D4—64no—
484D4—62no—
485C2×C4—31no—
486C2×C4—31no—
487C2×C4—31no—
488C2×C4—31no—
489C2×C4—32no—
490C2×C4—62no—
491C2×C4—62no—
492C2×C4—62no—
493C2×C4—92no—
494C2×C4—92no—
495C2×C4—121no—
496C2×C4—184no—
497C2×C4—362no—
498C2×C4#379612yes—
499C2×C4C4×D3211yescharacteristic
500C2×C4#380512yes—
501C2×C4C22×D3211yescharacteristic
502C8—22no—
503C8—61no—
504C8—61no—
505C8—62no—
506C8—181no—
507C8—181no—
508C2×C3—22no—
509C2×C3—22no—
510C2×C3—21no—
511C2×C3—21no—
512C2×C3—21no—
513C2×C3—42no—
514C2×C3—122no—
515C2×C3C2×#87711yescharacteristic
516C2×C3C2×#89211yescharacteristic
517C2×C3C2×#90711yescharacteristic
518C2×C3#574511yescharacteristic
519C2×C3D3×#13111yescharacteristic
520C2×C3#575011yescharacteristic
521D3—42no—
522C22—21no—
523C22—21no—
524C22—62no—
525C22—62no—
526C22—62no—
527C22#6387812yes—
528C22C2×C4×D3211yescharacteristic
529C4—32no—
530C4—62no—
531C4—61no—
532C4—61no—
533C4—61no—
534C4—182no—
535C4—182no—
536C4#6387812yes—
537C4C2×#379611yescharacteristic
538C4C2×#380511yescharacteristic
539C3—21no—
540C3#7865011yescharacteristic, complemented
541C3#7904011yescharacteristic, complemented
542C2—22no—
543C2—122no—
544C2D3×#90711yescharacteristic
545C2#1059470611yescharacteristic
546C2C2×#6387811yescharacteristic
subgroupG/H
center, FrattiniC2×C4C22×D32
commutator, socleC22×C32C23×C4
FittingC2×C32×M16C22
prime radicalC2×C3×#235C22
cosocleC2×C32×C4C24
hypercenterC2×M16D32
hypocenterC32#2925
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C2×C4 ◁ C2×M16

Complements

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

NH ≅ G/Ntype
2. #10592821C2semidirect
4. C3×#5118C2semidirect
5. C2×Dic3⋊(C3⋊C8)C2semidirect
7. #10591059C2semidirect
8. #10590699C2semidirect
9. #10590698C2semidirect
10. #10590661C2semidirect
11. #10590656C2semidirect
54. #5118D3semidirect
479. C32#2925semidirect
540. C3#78650semidirect
541. C3#79040semidirect

Maximal subgroups

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

subgroupindex
Dic3×#2352
#105928212
C3×#51292
C3×#51182
C2×Dic3⋊(C3⋊C8)2
#105910712
#105910592
#105906992
#105906982
#105906612
#105906562
#790403
#786503