Finite Group Databasebeta

← #11897666

Subgroups — #11897666

Order 1152.

794 conjugacy classes of subgroups.

The subgroup lattice has 520 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10596014C211yesmaximal, characteristic
2#10593856C211yesmaximal, characteristic, complemented
3C3×C4×#214C211yesmaximal, characteristic
4C3×#5008C211yesmaximal, characteristic
5#10591494C212yesmaximal
6#10591446C212yesmaximal
7#10590564C212yesmaximal, complemented
8#10590495C212yesmaximal, complemented
9#10590311C211yesmaximal, characteristic, complemented
10#10590296C211yesmaximal, characteristic, complemented
11#10590283C211yesmaximal, characteristic, complemented
12#81056—31nomaximal
13#79634—31nomaximal
14C32×C4×D4C2211yescharacteristic
15D4×C3⋊Dic3C2212yes—
16C2×C4⋊(C3⋊Dic3)—21no—
17#64133—21no—
18#64099C2212yes—
19#64087—22no—
20#64078C2211yescharacteristic
21C4×#634C2211yescharacteristic
22C2×C3×#214C2211yescharacteristic
23C3×#869C2211yescharacteristic
24C3×C4×Dic6C2211yescharacteristic
25#63919C2212yes—
26#63918—21no—
27#63844—21no—
28#63843C2212yes—
29#63839—22no—
30C3×#832C2211yescharacteristic
31C3×#832C2212yes—
32C3×#810C2211yescharacteristic
33C3×#808C2212yes—
34C3×#808C2211yescharacteristic
35C3×C4⋊(C3⋊C8)C2211yescharacteristic
36C3×C4×C3⋊C8C2211yescharacteristic
37#63575C2212yes—
38#63575C2212yes—
39#63575C2212yes—
40#63572C2212yes—
41#63566C2212yes—
42#63555C2212yes—
43#5722—31no—
44Q8×Dic6—31no—
45#5543—31no—
46#5543—31no—
47#5543—61no—
48C3×#476—31no—
49C3×C4×SD16—31no—
50#5164—32no—
51#5078—31no—
52#5021—31no—
53C4×#214D311yescharacteristic
54#5008D311yescharacteristic
55#4857—32no—
56#4856—32no—
57#4856—32no—
58#4850—31no—
59#4831—31no—
60#4796—32no—
61#4759—32no—
62#4759—32no—
63#4757—32no—
64#4682—31no—
65#4679—31no—
66C2×C32×D4C2311yescharacteristic
67C22×C32×C4—21no—
68C22×C3⋊Dic3—22no—
69C2×#634—21no—
70C2×#634D411yescharacteristic
71C2×C3×Dic6—21no—
72C2×C3×Dic6C2311yescharacteristic
73C2×#627—22no—
74C32×C4⋊C4C2311yescharacteristic
75C32×C22⋊C4—21no—
76C32×C42C2311yescharacteristic
77#3757—22no—
78C4⋊(C3⋊Dic3)—21no—
79C4⋊(C3⋊Dic3)—22no—
80C4⋊(C3⋊Dic3)D411yescharacteristic
81C4⋊(C3⋊Dic3)C2312yes—
82#3750—22no—
83#3750D412yes—
84C4×C3⋊Dic3C2312yes—
85C3×#214Q814yescomplemented
86C3×C4⋊Dic3—21no—
87C3×C4⋊Dic3C2312yes—
88C3×C4⋊Dic3C2311yescharacteristic
89C3×Dic3⋊C4—21no—
90C3×C4×Dic3—21no—
91C2×C3×C3⋊C8C2312yes—
92C2×C3×C3⋊C8C2311yescharacteristic
93C2×C3×C3⋊C8C2311yescharacteristic
94#3724—22no—
95Dic3⋊Dic3—22no—
96Dic32—22no—
97#3385—91noSylow
98C2×C3×SD16—31no—
99C3×C4⋊Q8—31no—
100C3×C4×Q8—31no—
101C3×C4×D4—21no—
102C3×C4×D4C2×D311yescharacteristic
103C3×C4×D4C2×D311yescharacteristic
104Q8×Dic3—32no—
105#944—62no—
106D4×Dic3—32no—
107D4×Dic3—32no—
108D4×Dic3—62no—
109C2×#214C2×D311yescharacteristic
110C2×C4⋊Dic3—61no—
111C2×C4⋊Dic3—61no—
112C2×C4⋊Dic3—62no—
113#924—61no—
114#924—61no—
115#924—62no—
116#890—32no—
117#890—32no—
118#890—62no—
119#888—32no—
120#888—32no—
121#888—61no—
122#888—62no—
123#887—32no—
124#887—61no—
125#878—62no—
126#878—62no—
127#878—64no—
128#869—31no—
129#869—31no—
130#869—61no—
131#869—61no—
132#869C2×D311yescharacteristic
133C4×Dic6—31no—
134C4×Dic6—31no—
135C4×Dic6—61no—
136C4×Dic6—61no—
137C4×Dic6C2×D311yescharacteristic
138C3×#106—31no—
139C3×#106—32no—
140C3×C4⋊C8—31no—
141C3×#103—31no—
142C3×#102—32no—
143C3×#102—31no—
144C3×C4×C8—31no—
145#835—32no—
146#832C2×D312yes—
147#832C2×D311yescharacteristic
148#818—32no—
149#818—32no—
150#818—32no—
151#816—32no—
152#815—32no—
153#815—32no—
154Dic3⋊C8—32no—
155Dic3⋊C8—32no—
156#810C2×D311yescharacteristic
157#808C2×D312yes—
158#808C2×D311yescharacteristic
159#807—32no—
160#807—32no—
161#807—32no—
162C4⋊(C3⋊C8)C2×D311yescharacteristic
163C4×C3⋊C8C2×D311yescharacteristic
164C23×C32—21no—
165C32×D4—21no—
166C32×D4C2×Q812yes—
167C2×C32×C4—21no—
168C2×C32×C4—42no—
169C2×C32×C4C2×D411yescharacteristic
170C2×C32×C4C2×D411yescharacteristic
171C2×C32×C4C2411yescharacteristic
172C2×C3⋊Dic3—22no—
173C2×C3⋊Dic3—82no—
174C2×C3⋊Dic3C2×D412yes—
175C2×C3⋊Dic3C2×D412yes—
176#634—22no—
177#634—81no—
178C2×C3×Dic3—21no—
179C2×C3×Dic3—22no—
180C2×C3×Dic3—21no—
181C3×Dic6—21no—
182C3×Dic6—81no—
183C3×Dic6C2×Q812yes—
184#627—82no—
185C3×C3⋊C8—22no—
186C3×C3⋊C8—21no—
187C3×C3⋊C8C2×Q812yes—
188Q82—91no—
189#554—91no—
190#501—92no—
191#500—91no—
192#479—92no—
193#477—91no—
194#476—31no—
195#474—92no—
196#446—91no—
197#440—92no—
198C4×SD16—31no—
199C2×C3×Q8—31no—
200C2×C3×Q8—61no—
201C2×C3×D4—21no—
202C2×C3×D4C22×D311yescharacteristic
203C2×C3×D4C22×D311yescharacteristic
204C22×C3×C4—22no—
205C22×C3×C4—21no—
206C22×C3×C4—21no—
207C22×Dic3—62no—
208C22×Dic3—62no—
209C22×Dic3—64no—
210C2×Dic6—21no—
211C2×Dic6—31no—
212C2×Dic6—31no—
213C2×Dic6—61no—
214C2×Dic6—62no—
215C2×Dic6—62no—
216C2×Dic6—62no—
217C2×Dic6—61no—
218C2×Dic6—61no—
219C2×Dic6C22×D311yescharacteristic
220C3×SD16—34no—
221C2×C3×C8—31no—
222C2×C3×C8—31no—
223C2×C3×C8—32no—
224C3×C4⋊C4—21no—
225C3×C4⋊C4—32no—
226C3×C4⋊C4—31no—
227C3×C4⋊C4—61no—
228C3×C4⋊C4—61no—
229C3×C4⋊C4C22×D311yescharacteristic
230C3×C4⋊C4C22×D311yescharacteristic
231C3×C22⋊C4—22no—
232C3×C22⋊C4—21no—
233C3×C22⋊C4—21no—
234C3×C42—21no—
235C3×C42—61no—
236C3×C42C22×D311yescharacteristic
237C3×C42C22×D311yescharacteristic
238#217—62no—
239#217—62no—
240#217—64no—
241#214Dic614yescomplemented
242C4⋊Dic3—21no—
243C4⋊Dic3—31no—
244C4⋊Dic3—31no—
245C4⋊Dic3—32no—
246C4⋊Dic3—32no—
247C4⋊Dic3—61no—
248C4⋊Dic3—62no—
249C4⋊Dic3—62no—
250C4⋊Dic3—62no—
251C4⋊Dic3—62no—
252C4⋊Dic3—62no—
253C4⋊Dic3—64no—
254C4⋊Dic3—61no—
255C4⋊Dic3—61no—
256C4⋊Dic3C22×D311yescharacteristic
257C4⋊Dic3C22×D312yes—
258Dic3⋊C4—21no—
259Dic3⋊C4—32no—
260Dic3⋊C4—32no—
261Dic3⋊C4—62no—
262Dic3⋊C4—62no—
263Dic3⋊C4—62no—
264Dic3⋊C4—62no—
265Dic3⋊C4—62no—
266Dic3⋊C4—62no—
267Dic3⋊C4—64no—
268C4×Dic3—21no—
269C4×Dic3—32no—
270C4×Dic3—32no—
271C4×Dic3—62no—
272C4×Dic3—62no—
273C4×Dic3—62no—
274C2×C3⋊C8C22×D311yescharacteristic
275C2×C3⋊C8C22×D312yes—
276C2×C3⋊C8C22×D311yescharacteristic
277C22×C32—22no—
278C22×C32—41no—
279C22×C32—41no—
280C22×C32C22×D411yescharacteristic
281C32×C4—21no—
282C32×C4—41no—
283C32×C4#13712yes—
284C32×C4C22×Q811yescharacteristic
285C32×C42−1+411yescharacteristic
286C3⋊Dic3—22no—
287C3⋊Dic3—22no—
288C3⋊Dic3—42no—
289C3×Dic3—22no—
290C3×Dic3—41no—
291C3×Dic3—42no—
292C2×SD16—31no—
293C4⋊Q8—31no—
294C4⋊Q8—92no—
295C4⋊Q8—91no—
296C4⋊Q8—181no—
297C4⋊Q8—182no—
298#125—92no—
299C22⋊Q8—182no—
300C22⋊Q8—181no—
301C4×Q8—31no—
302C4×Q8—91no—
303C4×Q8—92no—
304C4×Q8—181no—
305C4×D4—92no—
306C4×D4D3211yescharacteristic
307C2×C4⋊C4—181no—
308#107—92no—
309#107—92no—
310#107—92no—
311#106—31no—
312#106—32no—
313C4⋊C8—31no—
314C4⋊C8—92no—
315#103—31no—
316#103—92no—
317#102—31no—
318#102—32no—
319#97—92no—
320C4×C8—31no—
321C23×C3—22no—
322C23×C3—21no—
323C23×C3—21no—
324C3×Q8—32no—
325C3×Q8—61no—
326C3×Q8—241no—
327C3×D4—22no—
328C3×D4—21no—
329C3×D4—21no—
330C3×D4—22no—
331C3×D4C2×Dic612yes—
332C3×D4D3×Q812yes—
333C2×C3×C4—22no—
334C2×C3×C4—21no—
335C2×C3×C4—21no—
336C2×C3×C4—21no—
337C2×C3×C4—21no—
338C2×C3×C4—21no—
339C2×C3×C4—44no—
340C2×C3×C4—42no—
341C2×C3×C4—42no—
342C2×C3×C4—61no—
343C2×C3×C4—62no—
344C2×C3×C4—61no—
345C2×C3×C4D3×D411yescharacteristic
346C2×C3×C4D3×D411yescharacteristic
347C2×C3×C4D3×D411yescharacteristic
348C2×C3×C4D3×D411yescharacteristic
349C2×C3×C4C23×D311yescharacteristic
350C2×C3×C4C23×D311yescharacteristic
351C2×Dic3—21no—
352C2×Dic3—21no—
353C2×Dic3—22no—
354C2×Dic3—32no—
355C2×Dic3—32no—
356C2×Dic3—32no—
357C2×Dic3—32no—
358C2×Dic3—62no—
359C2×Dic3—62no—
360C2×Dic3—64no—
361C2×Dic3—62no—
362C2×Dic3—62no—
363C2×Dic3—242no—
364C2×Dic3—242no—
365C2×Dic3—244no—
366Dic6—21no—
367Dic6—62no—
368Dic6—62no—
369Dic6—81no—
370Dic6—122no—
371Dic6—242no—
372Dic6—242no—
373Dic6—241no—
374Dic6—241no—
375Dic6—242no—
376Dic6C2×Dic612yes—
377C3×C8—32no—
378C3×C8—61no—
379C3×C8—62no—
380C3⋊C8—22no—
381C3⋊C8—21no—
382C3⋊C8C2×Dic612yes—
383C2×C32—42no—
384C2×C32D4×Q811yescharacteristic
385C2×C32C2×#13711yescharacteristic
386C2×C32#57611yescharacteristic
387C2×Q8—31no—
388C2×Q8—61no—
389C2×Q8—91no—
390C2×Q8—182no—
391C2×Q8—181no—
392C2×D4C2×D3211yescharacteristic
393C22×C4—21no—
394C22×C4—182no—
395SD16—34no—
396C2×C8—31no—
397C2×C8—31no—
398C2×C8—32no—
399C4⋊C4—31no—
400C4⋊C4—32no—
401C4⋊C4—61no—
402C4⋊C4—61no—
403C4⋊C4—91no—
404C4⋊C4—92no—
405C4⋊C4—92no—
406C4⋊C4—182no—
407C4⋊C4—182no—
408C4⋊C4—182no—
409C4⋊C4—182no—
410C4⋊C4—181no—
411C4⋊C4C2×D3211yescharacteristic
412C22⋊C4—21no—
413C22⋊C4—182no—
414C42—61no—
415C42—92no—
416C42—182no—
417C42C2×D3211yescharacteristic
418C22×C3—24no—
419C22×C3—22no—
420C22×C3—22no—
421C22×C3—21no—
422C22×C3—42no—
423C22×C3—42no—
424C22×C3—41no—
425C22×C3—41no—
426C22×C3—41no—
427C22×C3—41no—
428C22×C3C2×D3×D411yescharacteristic
429C22×C3C2×D3×D411yescharacteristic
430C3×C4—21no—
431C3×C4—21no—
432C3×C4—21no—
433C3×C4—21no—
434C3×C4—22no—
435C3×C4—41no—
436C3×C4—42no—
437C3×C4—41no—
438C3×C4—41no—
439C3×C4—62no—
440C3×C4—122no—
441C3×C4—121no—
442C3×C4#91512yes—
443C3×C4#91512yes—
444C3×C4C22×Dic611yescharacteristic
445C3×C4C2×D3×Q811yescharacteristic
446C3×C4#101011yescharacteristic
447C3×C4#101011yescharacteristic
448Dic3—22no—
449Dic3—41no—
450Dic3—42no—
451Dic3—62no—
452Dic3—62no—
453Dic3—62no—
454Dic3—62no—
455Dic3—122no—
456Dic3—122no—
457Dic3—124no—
458Dic3—122no—
459Dic3—122no—
460C32#338511yescharacteristic, complemented, Sylow
461C23—21no—
462Q8—32no—
463Q8—61no—
464Q8—182no—
465Q8—241no—
466Q8—721no—
467Q8—722no—
468D4—21no—
469D4D3×Dic612yes—
470C2×C4—21no—
471C2×C4—42no—
472C2×C4—61no—
473C2×C4—61no—
474C2×C4—62no—
475C2×C4—92no—
476C2×C4—92no—
477C2×C4—182no—
478C2×C4—722no—
479C2×C4#381111yescharacteristic
480C2×C4#381111yescharacteristic
481C2×C4C22×D3211yescharacteristic
482C8—32no—
483C8—61no—
484C8—62no—
485C2×C3—21no—
486C2×C3—21no—
487C2×C3—21no—
488C2×C3—44no—
489C2×C3—42no—
490C2×C3—42no—
491C2×C3D4×Dic611yescharacteristic
492C2×C3#563211yescharacteristic
493C2×C3C2×#91511yescharacteristic
494C2×C3C2×#91511yescharacteristic
495C2×C3#576911yescharacteristic
496C2×C3#577411yescharacteristic
497C22—22no—
498C22—41no—
499C22—41no—
500C22C2×#381111yescharacteristic
501C4—21no—
502C4—41no—
503C4—62no—
504C4—122no—
505C4—121no—
506C4—182no—
507C4—182no—
508C4—362no—
509C4#6393112yes—
510C4C2×D3×Dic611yescharacteristic
511C4#6429811yescharacteristic
512C3—21no—
513C3#7963411yescharacteristic, complemented
514C3#8105611yescharacteristic, complemented
515C2—42no—
516C2#1059491511yescharacteristic
517C2C2×#6393111yescharacteristic
518C2#1059546111yescharacteristic
subgroupG/H
centerC22C2×#3811
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×C4×D4C22
socleC22×C32C22×D4
prime radicalC2×C32×D4C23
hypercenterC4×D4D32
hypocenterC32#3385
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C42 ◁ C4×D4

Complements

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

NH ≅ G/Ntype
2. #10593856C2semidirect
7. #10590564C2semidirect
8. #10590495C2semidirect
9. #10590311C2semidirect
10. #10590296C2semidirect
11. #10590283C2semidirect
85. C3×#214Q8semidirect
241. #214Dic6semidirect
460. C32#3385semidirect
513. C3#79634semidirect
514. C3#81056semidirect

Maximal subgroups

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

subgroupindex
#105960142
#105938562
C3×C4×#2142
C3×#50082
#105914942
#105914462
#105905642
#105904952
#105903112
#105902962
#105902832
#810563
#796343