Finite Group Databasebeta

← #11895262

Subgroups — #11895262

Order 1152.

749 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#10593960C211yesmaximal, characteristic, complemented
2#10593879C211yesmaximal, characteristic, complemented
3#10592380C211yesmaximal, characteristic, complemented
4C3×C4×D24C211yesmaximal, characteristic
5C3×C8×Dic6C211yesmaximal, characteristic, complemented
6#10590863C212yesmaximal, complemented
7#10590814C212yesmaximal, complemented
8#10590755C212yesmaximal
9#10590744C212yesmaximal, complemented
10#10590365C211yesmaximal, characteristic, complemented
11#10590268C211yesmaximal, characteristic, complemented
12#79926—31nomaximal
13#79568—31nomaximal
14#64078C2211yescharacteristic
15#64078C2211yescharacteristic
16C2×C3×D24C2211yescharacteristic
17C3×C4×D12C2211yescharacteristic
18C3×C4×D12C2211yescharacteristic
19C3×C4×Dic6C2211yescharacteristic
20#63896—22no—
21Dic3×D12C2212yes—
22D3×C4⋊Dic3—21no—
23#63869C2212yes—
24#63861—22no—
25#63860C2212yes—
26#63856—21no—
27#63856—21no—
28#63844C2212yes—
29#63841—21no—
30C2×#3716C2212yes—
31C32×C4×C8C2211yescharacteristic
32#63643C2212yes—
33#63643C2212yes—
34C3×#821C2211yescharacteristic
35C3×#821C2211yescharacteristic
36C3×#818C2211yescharacteristic
37C3×Dic3⋊C8C2212yes—
38C3×C8×Dic3C2212yes—
39C3×C4⋊(C3⋊C8)C2211yescharacteristic
40#63573C2212yes—
41#63567C2212yes—
42#63563C2212yes—
43#5584—31no—
44#5579—31no—
45#5543—31no—
46#5542—31no—
47C3×C8×Q8—31no—
48C3×C4×D8—31no—
49#5153—32no—
50#5019—31no—
51#5008—31no—
52#4877—32no—
53#4844—32no—
54#4842—31no—
55#4841—31no—
56#4829—32no—
57#4768—32no—
58#4758—32no—
59#4697—32no—
60C4×D24D311yescharacteristic
61C4×#204—32no—
62#4681—31no—
63#4681—31no—
64#4681—61no—
65C8×Dic6D311yescharacteristic, complemented
66C2×#634—21no—
67C2×#634C2312yes—
68C2×C3×D12C2311yescharacteristic
69C2×C3×D12C2311yescharacteristic
70C2×C3×C4×D3—21no—
71C2×C3×C4×D3—21no—
72C2×C3×Dic6D411yescharacteristic
73C2×D3×Dic3—22no—
74C2×C32×C8C2311yescharacteristic
75C2×C32×C8C2311yescharacteristic
76C32×C42C2311yescharacteristic
77C4⋊(C3⋊Dic3)—21no—
78C4⋊(C3⋊Dic3)—21no—
79C4⋊(C3⋊Dic3)—21no—
80C4⋊(C3⋊Dic3)C2312yes—
81C3×(C2×D3)⋊C4—21no—
82C3×(C2×D3)⋊C4—21no—
83C3×C4⋊Dic3D411yescharacteristic
84C3×C4⋊Dic3C2311yescharacteristic
85C3×C4⋊Dic3C2311yescharacteristic
86C3×Dic3⋊C4D412yes—
87C3×C4×Dic3C2312yes—
88C2×C3×C3⋊C8C2312yes—
89C3×D24—22no—
90#3724—22no—
91#3724—22no—
92Dic3⋊Dic3—22no—
93(C2×D3)⋊Dic3—22no—
94(C2×D3)⋊Dic3—22no—
95(C2×D3)⋊Dic3—22no—
96Dic32—22no—
97#3716—24no—
98#3360—91noSylow
99C2×C3×D8—31no—
100C3×C4×Q8—31no—
101C3×C4×D4—31no—
102C3×C4×D4—31no—
103#946—61no—
104#946—61no—
105#936—32no—
106D4×Dic3—32no—
107C2×#214—32no—
108#926—61no—
109C2×C4⋊Dic3—61no—
110#924—61no—
111#924—61no—
112C2×D24C2×D311yescharacteristic
113C2×#204—32no—
114#898—62no—
115#896—62no—
116#892—61no—
117D3×C4⋊C4—61no—
118#890—32no—
119#887—32no—
120#879—62no—
121#878—62no—
122#875—32no—
123C4×D12—32no—
124C4×D12C2×D311yescharacteristic
125C4×D12C2×D311yescharacteristic
126#870—32no—
127#869—31no—
128#869—31no—
129#869—31no—
130#869—31no—
131#869—61no—
132#869—61no—
133C4×Dic6—32no—
134C4×Dic6C2×D311yescharacteristic
135C3×#107—31no—
136C3×C4⋊C8—32no—
137C3×C4⋊C8—31no—
138C3×#102—31no—
139C3×#102—31no—
140C3×C4×C8—21no—
141C3×C4×C8—32no—
142C3×C4×C8C2×D311yescharacteristic
143C3×C4×C8C2×D311yescharacteristic
144#832—32no—
145#821—32no—
146#821C2×D311yescharacteristic
147#821C2×D311yescharacteristic
148#818C2×D311yescharacteristic
149#817—32no—
150#816—32no—
151#816—32no—
152#816—32no—
153#816—32no—
154#816—32no—
155#816—62no—
156#816—62no—
157Dic3⋊C8C2×D312yes—
158C8×Dic3C2×D312yes—
159#810—32no—
160#808—32no—
161C4⋊(C3⋊C8)C2×D311yescharacteristic
162C22×C3×D3—21no—
163C22×C3×D3—21no—
164C2×C32×C4C2×D411yescharacteristic
165C2×C32×C4C2×D411yescharacteristic
166C2×C32×C4C2411yescharacteristic
167C2×C3⋊Dic3—22no—
168C2×C3⋊Dic3—22no—
169#634—22no—
170#634—22no—
171#634—81no—
172C2×C3×Dic3—21no—
173C2×C3×Dic3—21no—
174C2×C3×Dic3C2×D412yes—
175C2×C3×Dic3C2×D412yes—
176C3×D12—21no—
177C3×D12—21no—
178C3×D12—21no—
179C3×D12#4112yes—
180C3×C4×D3—42no—
181C3×C4×D3—42no—
182C3×Dic6—22no—
183D3×Dic3—82no—
184C32×C8—21no—
185C32×C8—21no—
186C3×C3⋊C8—22no—
187#556—91no—
188#554—91no—
189#488—92no—
190#487—91no—
191#479—92no—
192#476—91no—
193#463—92no—
194#461—91no—
195C8×Q8—31no—
196C4×SD16—92no—
197C4×D8—31no—
198C2×C3×Q8—31no—
199C2×C3×D4—31no—
200C2×C3×D4—31no—
201C22×C3×C4—61no—
202C22×C3×C4—61no—
203C22×Dic3—62no—
204C2×D12C22×D311yescharacteristic
205C2×D12C22×D311yescharacteristic
206C2×C4×D3—21no—
207C2×C4×D3—21no—
208C2×C4×D3—62no—
209C2×Dic6—32no—
210C2×Dic6—32no—
211C2×Dic6—62no—
212C2×Dic6—61no—
213C2×Dic6—61no—
214C2×Dic6—121no—
215C2×Dic6D1211yescharacteristic
216C3×D8—62no—
217C2×C3×C8—21no—
218C2×C3×C8—21no—
219C2×C3×C8—32no—
220C2×C3×C8C22×D311yescharacteristic
221C2×C3×C8C22×D311yescharacteristic
222C2×C3×C8C22×D311yescharacteristic
223C2×C3×C8C22×D311yescharacteristic
224C3×C4⋊C4—31no—
225C3×C4⋊C4—32no—
226C3×C4⋊C4—31no—
227C3×C4⋊C4—31no—
228C3×C22⋊C4—61no—
229C3×C22⋊C4—61no—
230C3×C42—21no—
231C3×C42—32no—
232C3×C42C22×D311yescharacteristic
233C3×C42C22×D311yescharacteristic
234#217—62no—
235#217—62no—
236#217—62no—
237#214—64no—
238(C2×D3)⋊C4—21no—
239(C2×D3)⋊C4—21no—
240(C2×D3)⋊C4—62no—
241(C2×D3)⋊C4—62no—
242(C2×D3)⋊C4—62no—
243C4⋊Dic3—32no—
244C4⋊Dic3—32no—
245C4⋊Dic3—62no—
246C4⋊Dic3—61no—
247C4⋊Dic3—61no—
248C4⋊Dic3—61no—
249C4⋊Dic3—61no—
250C4⋊Dic3—61no—
251C4⋊Dic3—61no—
252C4⋊Dic3—62no—
253C4⋊Dic3—121no—
254C4⋊Dic3—121no—
255C4⋊Dic3—121no—
256C4⋊Dic3D1211yescharacteristic
257C4⋊Dic3C22×D311yescharacteristic
258C4⋊Dic3C22×D311yescharacteristic
259Dic3⋊C4—62no—
260Dic3⋊C4—62no—
261Dic3⋊C4—62no—
262Dic3⋊C4—62no—
263Dic3⋊C4—62no—
264Dic3⋊C4D1212yes—
265C4×Dic3—62no—
266C4×Dic3—62no—
267C4×Dic3C22×D312yes—
268C2×C3⋊C8C22×D312yes—
269D24—22no—
270#204—64no—
271C22×C32C22×D411yescharacteristic
272C2×C3×D3—22no—
273C2×C3×D3—41no—
274C2×C3×D3—41no—
275C2×C3×D3—41no—
276C2×C3×D3—41no—
277C2×C3×D3—41no—
278C32×C4—21no—
279C32×C4#13512yes—
280C32×C4C2×#4111yescharacteristic
281C32×C42−1+411yescharacteristic
282C3⋊Dic3—42no—
283C3⋊Dic3—42no—
284C3×Dic3—22no—
285C3×Dic3—22no—
286C3×Dic3—41no—
287C3×Dic3—41no—
288C2×SD16—92no—
289C2×D8—31no—
290C4⋊Q8—91no—
291C4⋊Q8—91no—
292#126—182no—
293#125—92no—
294#124—92no—
295C22⋊Q8—182no—
296C22⋊Q8—181no—
297C22⋊Q8—181no—
298C4×Q8—31no—
299C4×Q8—92no—
300C4×D4—31no—
301C4×D4—31no—
302C4×D4—92no—
303#117—181no—
304C2×C4⋊C4—181no—
305#107—31no—
306#106—92no—
307C4⋊C8—32no—
308C4⋊C8—31no—
309#103—92no—
310#103—92no—
311#103—92no—
312#102—31no—
313#102—31no—
314#102—92no—
315C4×C8—32no—
316C4×C8D3211yescharacteristic
317C23×C3—61no—
318C23×C3—61no—
319C22×D3—21no—
320C22×D3—21no—
321C3×Q8—62no—
322C3×D4—32no—
323C3×D4—61no—
324C3×D4—61no—
325C3×D4—61no—
326C2×C3×C4—21no—
327C2×C3×C4—21no—
328C2×C3×C4—21no—
329C2×C3×C4—32no—
330C2×C3×C4—32no—
331C2×C3×C4—61no—
332C2×C3×C4—61no—
333C2×C3×C4—122no—
334C2×C3×C4—122no—
335C2×C3×C4C2×D1211yescharacteristic
336C2×C3×C4C2×D1211yescharacteristic
337C2×C3×C4D3×D411yescharacteristic
338C2×C3×C4D3×D411yescharacteristic
339C2×C3×C4C23×D311yescharacteristic
340C2×C3×C4C23×D311yescharacteristic
341C2×Dic3—21no—
342C2×Dic3—21no—
343C2×Dic3—62no—
344C2×Dic3—62no—
345C2×Dic3—62no—
346C2×Dic3—62no—
347C2×Dic3—122no—
348C2×Dic3—122no—
349C2×Dic3—242no—
350C2×Dic3C2×D1212yes—
351C2×Dic3C2×D1212yes—
352D12—21no—
353D12—21no—
354D12—21no—
355D12#23512yes—
356C4×D3—42no—
357C4×D3—42no—
358C4×D3—242no—
359Dic6—22no—
360Dic6—62no—
361Dic6—62no—
362Dic6—62no—
363Dic6—62no—
364Dic6—122no—
365Dic6—122no—
366Dic6—241no—
367Dic6—241no—
368Dic6—242no—
369C3×C8—21no—
370C3×C8—21no—
371C3×C8—21no—
372C3×C8—21no—
373C3×C8—41no—
374C3×C8—41no—
375C3×C8—62no—
376C3⋊C8—22no—
377C2×C32#54811yescharacteristic
378C2×C32C2×#13511yescharacteristic
379C2×C32#57711yescharacteristic
380C3×D3—42no—
381C3×D3—81no—
382C2×Q8—31no—
383C2×Q8—92no—
384C2×Q8—181no—
385C2×D4—31no—
386C2×D4—31no—
387C22×C4—61no—
388C22×C4—61no—
389C22×C4—182no—
390SD16—184no—
391D8—62no—
392C2×C8—32no—
393C2×C8C2×D3211yescharacteristic
394C2×C8C2×D3211yescharacteristic
395C4⋊C4—31no—
396C4⋊C4—32no—
397C4⋊C4—31no—
398C4⋊C4—31no—
399C4⋊C4—92no—
400C4⋊C4—182no—
401C4⋊C4—182no—
402C4⋊C4—182no—
403C4⋊C4—181no—
404C4⋊C4—181no—
405C4⋊C4—181no—
406C22⋊C4—61no—
407C22⋊C4—61no—
408C22⋊C4—182no—
409C22⋊C4—182no—
410C22⋊C4—182no—
411C42—32no—
412C42—182no—
413C42C2×D3211yescharacteristic
414C22×C3—21no—
415C22×C3—62no—
416C22×C3—121no—
417C22×C3—121no—
418C22×C3—121no—
419C22×C3—121no—
420C22×C3—121no—
421C22×C3C22×D1211yescharacteristic
422C22×C3C2×D3×D411yescharacteristic
423C2×D3—22no—
424C2×D3—41no—
425C2×D3—41no—
426C2×D3—41no—
427C2×D3—41no—
428C2×D3—41no—
429C3×C4—22no—
430C3×C4—21no—
431C3×C4—21no—
432C3×C4—21no—
433C3×C4—21no—
434C3×C4—22no—
435C3×C4—62no—
436C3×C4—62no—
437C3×C4—121no—
438C3×C4—121no—
439C3×C4#90412yes—
440C3×C4#91212yes—
441C3×C4C2×#23511yescharacteristic
442C3×C4#100711yescharacteristic
443C3×C4D3×#4111yescharacteristic
444C3×C4#101011yescharacteristic
445Dic3—22no—
446Dic3—22no—
447Dic3—41no—
448Dic3—41no—
449Dic3—122no—
450Dic3—122no—
451Dic3—122no—
452Dic3—122no—
453Dic3—242no—
454Dic3—242no—
455C32#336011yescharacteristic, complemented, Sylow
456C23—61no—
457C23—61no—
458Q8—62no—
459Q8—182no—
460Q8—182no—
461Q8—721no—
462D4—32no—
463D4—61no—
464D4—61no—
465D4—61no—
466C2×C4—32no—
467C2×C4—32no—
468C2×C4—61no—
469C2×C4—61no—
470C2×C4—122no—
471C2×C4—122no—
472C2×C4—182no—
473C2×C4—182no—
474C2×C4—722no—
475C2×C4D3×D1211yescharacteristic
476C2×C4D3×D1211yescharacteristic
477C2×C4C22×D3211yescharacteristic
478C8—21no—
479C8—21no—
480C8—62no—
481C2×C3—21no—
482C2×C3—21no—
483C2×C3—21no—
484C2×C3—122no—
485C2×C3—241no—
486C2×C3#555211yescharacteristic
487C2×C3#557611yescharacteristic
488C2×C3C2×#90411yescharacteristic
489C2×C3#575111yescharacteristic
490C2×C3C2×#91211yescharacteristic
491C2×C3#577011yescharacteristic
492D3—42no—
493D3—81no—
494C22—62no—
495C22—121no—
496C22—121no—
497C22—121no—
498C22—121no—
499C22—121no—
500C22C2×D3×D1211yescharacteristic
501C4—21no—
502C4—62no—
503C4—62no—
504C4—121no—
505C4—121no—
506C4—362no—
507C4—362no—
508C4#6380712yes—
509C4#6429711yescharacteristic
510C4D3×#23511yescharacteristic
511C3—21no—
512C3#7956811yescharacteristic, complemented
513C3#7992611yescharacteristic, complemented
514C2—122no—
515C2—241no—
516C2#1059389911yescharacteristic
517C2#1059467911yescharacteristic
518C2C2×#6380711yescharacteristic
subgroupG/H
centerC22C2×D3×D12
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×C4×C8C22
socleC22×C32C22×D4
prime radicalC2×C3×D24C22
hypercenterC4×C8D32
hypocenterC32#3360
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C42 ◁ C4×C8

Complements

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

NH ≅ G/Ntype
1. #10593960C2semidirect
2. #10593879C2semidirect
3. #10592380C2semidirect
5. C3×C8×Dic6C2semidirect
6. #10590863C2semidirect
7. #10590814C2semidirect
9. #10590744C2semidirect
10. #10590365C2semidirect
11. #10590268C2semidirect
65. C8×Dic6D3semidirect
455. C32#3360semidirect
512. C3#79568semidirect
513. C3#79926semidirect

Maximal subgroups

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

subgroupindex
#105939602
#105938792
#105923802
C3×C4×D242
C3×C8×Dic62
#105908632
#105908142
#105907552
#105907442
#105903652
#105902682
#799263
#795683