Finite Group Databasebeta

← #11896064

Subgroups — #11896064

Order 1152.

782 conjugacy classes of subgroups.

The subgroup lattice has 524 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10596013C211yesmaximal, characteristic
2#10593856C211yesmaximal, characteristic, complemented
3C3×C4×#214C211yesmaximal, characteristic
4C3×#5008C211yesmaximal, characteristic
5#10591496C212yesmaximal
6#10591443C212yesmaximal
7#10590485C212yesmaximal, complemented
8#10590431C212yesmaximal, complemented
9#10590385C211yesmaximal, characteristic, complemented
10#10590296C211yesmaximal, characteristic, complemented
11#10590288C211yesmaximal, characteristic, complemented
12#81091—31nomaximal
13#79626—31nomaximal
14C32×C4×D4C2211yescharacteristic
15#64145C2212yes—
16#64135—21no—
17#64133—21no—
18#64096C2212yes—
19#64088—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—
30C2×#3719C2212yes—
31C3×#832C2211yescharacteristic
32C3×#832C2212yes—
33C3×#810C2211yescharacteristic
34C3×#808C2212yes—
35C3×#808C2211yescharacteristic
36C3×C4⋊(C3⋊C8)C2211yescharacteristic
37C3×C4×C3⋊C8C2211yescharacteristic
38#63572C2212yes—
39#63567C2212yes—
40#63567C2212yes—
41#63567C2212yes—
42#63555C2212yes—
43#5722—31no—
44Q8×Dic6—31no—
45#5542—31no—
46#5542—31no—
47#5542—61no—
48C3×#476—31no—
49C3×C4×SD16—31no—
50#5166—32no—
51#5093—31no—
52#5031—31no—
53C4×#214D311yescharacteristic
54#5008D311yescharacteristic
55#4854—32no—
56#4854—32no—
57#4853—32no—
58#4849—31no—
59#4831—31no—
60#4789—32no—
61#4767—32no—
62#4765—32no—
63#4765—32no—
64#4681—31no—
65#4679—31no—
66C2×C32×D4C2311yescharacteristic
67C22×C32×C4—21no—
68C2×#634D411yescharacteristic
69C2×#634C2312yes—
70C2×C3×Dic6—21no—
71C2×C3×Dic6C2311yescharacteristic
72C2×#627—22no—
73C32×C4⋊C4C2311yescharacteristic
74C32×C22⋊C4—21no—
75C32×C42C2311yescharacteristic
76#3757—22no—
77#3757—22no—
78C4⋊(C3⋊Dic3)—21no—
79C4⋊(C3⋊Dic3)—21no—
80C4⋊(C3⋊Dic3)D411yescharacteristic
81#3750—22no—
82#3750D412yes—
83C4×C3⋊Dic3—22no—
84C4×C3⋊Dic3C2312yes—
85C3×#214—22no—
86C3×C4⋊Dic3—21no—
87C3×C4⋊Dic3C2312yes—
88C3×C4⋊Dic3C2311yescharacteristic
89C3×Dic3⋊C4—21no—
90C3×C4×Dic3—21no—
91C2×C3×C3⋊C8C2311yescharacteristic
92C2×C3×C3⋊C8C2311yescharacteristic
93C2×C3×C3⋊C8C2312yes—
94#3724—22no—
95Dic3⋊Dic3—22no—
96Dic32—22no—
97#3719—24no—
98#3369—91noSylow
99C2×C3×SD16—31no—
100C3×C4⋊Q8—31no—
101C3×C4×Q8—31no—
102C3×C4×D4—21no—
103C3×C4×D4C2×D311yescharacteristic
104C3×C4×D4C2×D311yescharacteristic
105Q8×Dic3—32no—
106#944—62no—
107C2×#216—32no—
108#936—32no—
109#936—32no—
110#936—62no—
111C2×#214C2×D311yescharacteristic
112#926—61no—
113#926—61no—
114#926—62no—
115#924—61no—
116#924—61no—
117#924—62no—
118C2×Dic12—32no—
119#888—32no—
120#888—32no—
121#888—61no—
122#888—62no—
123#887—32no—
124#887—32no—
125#887—32no—
126#887—62no—
127#887—61no—
128#879—62no—
129#879—62no—
130#879—64no—
131#869—31no—
132#869—31no—
133#869—61no—
134#869—61no—
135#869C2×D311yescharacteristic
136C4×Dic6—31no—
137C4×Dic6—31no—
138C4×Dic6—61no—
139C4×Dic6—61no—
140C4×Dic6C2×D311yescharacteristic
141C3×#106—31no—
142C3×#106—32no—
143C3×C4⋊C8—31no—
144C3×#103—31no—
145C3×#102—31no—
146C3×#102—32no—
147C3×C4×C8—31no—
148#832C2×D312yes—
149#832C2×D311yescharacteristic
150#816—32no—
151#816—32no—
152#816—32no—
153#815—32no—
154#815—32no—
155Dic3⋊C8—32no—
156Dic3⋊C8—32no—
157#810—32no—
158#810—32no—
159#810—32no—
160#810C2×D311yescharacteristic
161#808C2×D312yes—
162#808C2×D311yescharacteristic
163C4⋊(C3⋊C8)C2×D311yescharacteristic
164C4×C3⋊C8C2×D311yescharacteristic
165C23×C32—21no—
166C32×D4—21no—
167C32×D4—21no—
168C2×C32×C4—21no—
169C2×C32×C4—42no—
170C2×C32×C4C2×D411yescharacteristic
171C2×C32×C4C2×D411yescharacteristic
172C2×C32×C4C2411yescharacteristic
173C2×C3⋊Dic3—22no—
174C2×C3⋊Dic3C2×D412yes—
175C2×C3⋊Dic3C2×D412yes—
176#634—22no—
177#634—22no—
178#634—22no—
179C2×C3×Dic3—21no—
180C2×C3×Dic3—22no—
181C2×C3×Dic3—21no—
182C3×Dic6—21no—
183C3×Dic6—81no—
184C3×Dic6#4112yes—
185#627—82no—
186C3×C3⋊C8—22no—
187C3×C3⋊C8—21no—
188C3×C3⋊C8—21no—
189Q82—91no—
190#556—91no—
191#489—92no—
192#487—91no—
193#476—31no—
194#475—92no—
195#464—92no—
196#462—91no—
197#446—91no—
198#441—92no—
199C4×SD16—31no—
200C2×C3×Q8—31no—
201C2×C3×Q8—61no—
202C2×C3×D4—21no—
203C2×C3×D4C22×D311yescharacteristic
204C2×C3×D4C22×D311yescharacteristic
205C22×C3×C4—22no—
206C22×C3×C4—21no—
207C22×C3×C4—21no—
208C2×Dic6—21no—
209C2×Dic6—31no—
210C2×Dic6—31no—
211C2×Dic6—32no—
212C2×Dic6—32no—
213C2×Dic6—61no—
214C2×Dic6—62no—
215C2×Dic6—62no—
216C2×Dic6—62no—
217C2×Dic6C22×D311yescharacteristic
218C3×SD16—62no—
219C2×C3×C8—31no—
220C2×C3×C8—32no—
221C2×C3×C8—31no—
222C3×C4⋊C4—21no—
223C3×C4⋊C4—32no—
224C3×C4⋊C4—31no—
225C3×C4⋊C4—61no—
226C3×C4⋊C4—61no—
227C3×C4⋊C4C22×D311yescharacteristic
228C3×C4⋊C4C22×D311yescharacteristic
229C3×C22⋊C4—22no—
230C3×C22⋊C4—21no—
231C3×C22⋊C4—21no—
232C3×C42—21no—
233C3×C42—61no—
234C3×C42C22×D311yescharacteristic
235C3×C42C22×D311yescharacteristic
236#217—62no—
237#217—62no—
238#217—62no—
239#217—62no—
240#217—64no—
241#217—64no—
242#216—64no—
243#214—22no—
244C4⋊Dic3—21no—
245C4⋊Dic3—31no—
246C4⋊Dic3—31no—
247C4⋊Dic3—61no—
248C4⋊Dic3—62no—
249C4⋊Dic3—62no—
250C4⋊Dic3—62no—
251C4⋊Dic3—61no—
252C4⋊Dic3—61no—
253C4⋊Dic3—61no—
254C4⋊Dic3—61no—
255C4⋊Dic3C22×D311yescharacteristic
256C4⋊Dic3C22×D312yes—
257Dic3⋊C4—21no—
258Dic3⋊C4—32no—
259Dic3⋊C4—32no—
260Dic3⋊C4—62no—
261Dic3⋊C4—62no—
262Dic3⋊C4—62no—
263Dic3⋊C4—62no—
264Dic3⋊C4—62no—
265Dic3⋊C4—62no—
266Dic3⋊C4—64no—
267C4×Dic3—21no—
268C4×Dic3—32no—
269C4×Dic3—32no—
270C4×Dic3—62no—
271C4×Dic3—62no—
272C4×Dic3—62no—
273C4×Dic3—62no—
274C4×Dic3—62no—
275C4×Dic3—64no—
276C2×C3⋊C8C22×D311yescharacteristic
277C2×C3⋊C8C22×D311yescharacteristic
278C2×C3⋊C8C22×D312yes—
279Dic12—64no—
280C22×C32—41no—
281C22×C32—41no—
282C22×C32—41no—
283C22×C32C22×D411yescharacteristic
284C32×C4—21no—
285C32×C4—41no—
286C32×C4#13712yes—
287C32×C4C2×#4111yescharacteristic
288C32×C42−1+411yescharacteristic
289C3⋊Dic3—22no—
290C3⋊Dic3—22no—
291C3⋊Dic3—42no—
292C3×Dic3—22no—
293C3×Dic3—41no—
294C3×Dic3—42no—
295C2×Q16—92no—
296C2×SD16—31no—
297C4⋊Q8—31no—
298C4⋊Q8—92no—
299C4⋊Q8—91no—
300C4⋊Q8—181no—
301C4⋊Q8—182no—
302#126—182no—
303#124—92no—
304C22⋊Q8—181no—
305C4×Q8—31no—
306C4×Q8—91no—
307C4×Q8—92no—
308C4×Q8—92no—
309C4×Q8—181no—
310C4×D4D3211yescharacteristic
311#117—181no—
312#106—31no—
313#106—32no—
314C4⋊C8—31no—
315C4⋊C8—92no—
316#103—31no—
317#103—92no—
318#103—92no—
319#103—92no—
320#102—31no—
321#102—32no—
322#97—92no—
323C4×C8—31no—
324C23×C3—22no—
325C23×C3—21no—
326C23×C3—21no—
327C3×Q8—32no—
328C3×Q8—61no—
329C3×Q8—241no—
330C3×D4—21no—
331C3×D4—21no—
332C3×D4—21no—
333C3×D4—21no—
334C3×D4—41no—
335C3×D4—41no—
336C2×C3×C4—22no—
337C2×C3×C4—21no—
338C2×C3×C4—21no—
339C2×C3×C4—21no—
340C2×C3×C4—21no—
341C2×C3×C4—21no—
342C2×C3×C4—44no—
343C2×C3×C4—42no—
344C2×C3×C4—42no—
345C2×C3×C4—61no—
346C2×C3×C4—62no—
347C2×C3×C4—61no—
348C2×C3×C4D3×D411yescharacteristic
349C2×C3×C4D3×D411yescharacteristic
350C2×C3×C4D3×D411yescharacteristic
351C2×C3×C4D3×D411yescharacteristic
352C2×C3×C4C23×D311yescharacteristic
353C2×C3×C4C23×D311yescharacteristic
354C2×Dic3—21no—
355C2×Dic3—21no—
356C2×Dic3—22no—
357C2×Dic3—32no—
358C2×Dic3—32no—
359C2×Dic3—32no—
360C2×Dic3—32no—
361C2×Dic3—62no—
362C2×Dic3—62no—
363C2×Dic3—64no—
364C2×Dic3—62no—
365C2×Dic3—62no—
366Dic6—21no—
367Dic6—62no—
368Dic6—62no—
369Dic6—62no—
370Dic6—62no—
371Dic6—62no—
372Dic6—62no—
373Dic6—81no—
374Dic6—122no—
375Dic6—122no—
376Dic6—122no—
377Dic6—242no—
378Dic6—242no—
379Dic6#23512yes—
380C3×C8—62no—
381C3×C8—61no—
382C3×C8—61no—
383C3⋊C8—21no—
384C3⋊C8—22no—
385C3⋊C8—21no—
386C2×C32—81no—
387C2×C32#54811yescharacteristic
388C2×C32C2×#13711yescharacteristic
389C2×C32#57711yescharacteristic
390C2×Q8—31no—
391C2×Q8—61no—
392C2×Q8—91no—
393C2×Q8—92no—
394C2×Q8—182no—
395C2×D4C2×D3211yescharacteristic
396C22×C4—21no—
397Q16—184no—
398SD16—62no—
399C2×C8—31no—
400C2×C8—31no—
401C2×C8—32no—
402C4⋊C4—31no—
403C4⋊C4—32no—
404C4⋊C4—61no—
405C4⋊C4—61no—
406C4⋊C4—91no—
407C4⋊C4—92no—
408C4⋊C4—182no—
409C4⋊C4—182no—
410C4⋊C4—182no—
411C4⋊C4—181no—
412C4⋊C4—181no—
413C4⋊C4C2×D3211yescharacteristic
414C22⋊C4—21no—
415C22⋊C4—182no—
416C22⋊C4—182no—
417C42—61no—
418C42—92no—
419C42—182no—
420C42—182no—
421C42C2×D3211yescharacteristic
422C22×C3—21no—
423C22×C3—42no—
424C22×C3—42no—
425C22×C3—42no—
426C22×C3—41no—
427C22×C3—41no—
428C22×C3—41no—
429C22×C3—41no—
430C22×C3—41no—
431C22×C3—41no—
432C22×C3C2×D3×D411yescharacteristic
433C22×C3C2×D3×D411yescharacteristic
434C3×C4—21no—
435C3×C4—21no—
436C3×C4—21no—
437C3×C4—21no—
438C3×C4—22no—
439C3×C4—41no—
440C3×C4—42no—
441C3×C4—41no—
442C3×C4—41no—
443C3×C4—62no—
444C3×C4—122no—
445C3×C4—121no—
446C3×C4#91512yes—
447C3×C4#91512yes—
448C3×C4C2×#23511yescharacteristic
449C3×C4#100711yescharacteristic
450C3×C4D3×#4111yescharacteristic
451C3×C4#101011yescharacteristic
452Dic3—22no—
453Dic3—41no—
454Dic3—42no—
455Dic3—62no—
456Dic3—62no—
457Dic3—62no—
458Dic3—62no—
459Dic3—122no—
460Dic3—122no—
461Dic3—124no—
462Dic3—122no—
463Dic3—122no—
464C32#336911yescharacteristic, complemented, Sylow
465C23—21no—
466Q8—32no—
467Q8—61no—
468Q8—182no—
469Q8—182no—
470Q8—182no—
471Q8—241no—
472Q8—722no—
473D4—21no—
474D4—21no—
475C2×C4—21no—
476C2×C4—42no—
477C2×C4—61no—
478C2×C4—61no—
479C2×C4—62no—
480C2×C4—92no—
481C2×C4—92no—
482C2×C4—182no—
483C2×C4#381111yescharacteristic
484C2×C4#381111yescharacteristic
485C2×C4C22×D3211yescharacteristic
486C8—61no—
487C8—61no—
488C8—62no—
489C2×C3—21no—
490C2×C3—21no—
491C2×C3—21no—
492C2×C3—82no—
493C2×C3—81no—
494C2×C3—81no—
495C2×C3#555211yescharacteristic
496C2×C3#563311yescharacteristic
497C2×C3C2×#91511yescharacteristic
498C2×C3C2×#91511yescharacteristic
499C2×C3#577011yescharacteristic
500C2×C3#577511yescharacteristic
501C22—41no—
502C22—41no—
503C22—41no—
504C22C2×#381111yescharacteristic
505C4—21no—
506C4—41no—
507C4—62no—
508C4—122no—
509C4—121no—
510C4—182no—
511C4—182no—
512C4—362no—
513C4#6393112yes—
514C4#6429711yescharacteristic
515C4D3×#23511yescharacteristic
516C3—21no—
517C3#7962611yescharacteristic, complemented
518C3#8109111yescharacteristic, complemented
519C2—81no—
520C2#1059491611yescharacteristic
521C2C2×#6393111yescharacteristic
522C2#1059546211yescharacteristic
subgroupG/H
centerC22C2×#3811
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×C4×D4C22
socleC22×C32C22×D4
prime radicalC2×C32×D4C23
hypercenterC4×D4D32
hypocenterC32#3369
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. #10590485C2semidirect
8. #10590431C2semidirect
9. #10590385C2semidirect
10. #10590296C2semidirect
11. #10590288C2semidirect
464. C32#3369semidirect
517. C3#79626semidirect
518. C3#81091semidirect

Maximal subgroups

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

subgroupindex
#105960132
#105938562
C3×C4×#2142
C3×#50082
#105914962
#105914432
#105904852
#105904312
#105903852
#105902962
#105902882
#810913
#796263