Finite Group Databasebeta

← #11874447

Subgroups — #11874447

Order 1152.

1261 conjugacy classes of subgroups.

The subgroup lattice has 517 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#64113C211yesmaximal, characteristic, complemented
2C2×C3×#904C211yesmaximal, characteristic, complemented
3#10595029C212yesmaximal, complemented
4C2×#63829C212yesmaximal, complemented
5C2×C3×#815C211yesmaximal, characteristic, complemented
6#10590899C212yesmaximal, complemented
7#10590897C212yesmaximal, complemented
8#10590883C212yesmaximal, complemented
9#10590881C212yesmaximal, complemented
10#83904—31nomaximal
11#78499—31nomaximal
12C2×#3828C2212yes—
13C2×C3×#235C2212yes—
14C22×C32×C8C2211yescharacteristic
15C2×#3746C2211yescharacteristic
16#64113—24no—
17C2×#3745C2211yescharacteristic
18C2×#3744C2212yes—
19C2×C3×C4×Dic3C2211yescharacteristic
20C22×C3×C3⋊C8C2211yescharacteristic
21C2×C3×Dic12C2211yescharacteristic
22C3×#904—24no—
23C2×C3×D24C2211yescharacteristic
24C2×C3×#204C2212yes—
25#63978—24no—
26#63911C2212yes—
27C4×#626—24no—
28#63866C2212yes—
29#63864C2212yes—
30#63860C2212yes—
31C2×#3719C2212yes—
32C2×#3717C2212yes—
33#63829—28no—
34C2×#3716C2212yes—
35C2×#3714C2212yes—
36C3×#815C2212yes—
37C3×#815C2212yes—
38C2×C3×#135—31no—
39#5832—32no—
40C2×#950—32no—
41C2×#904—32no—
42C2×#904—31no—
43C2×#904—31no—
44C2×#904—61no—
45C2×#904D311yescharacteristic, complemented
46#5477—32no—
47C2×C3×#97—31no—
48#5190—32no—
49#5176—32no—
50#5167—32no—
51#5154—32no—
52C2×#815D311yescharacteristic, complemented
53#4715—32no—
54#4715—32no—
55#4712—32no—
56#4712—32no—
57C22×C32×C4C2311yescharacteristic
58C2×#638—22no—
59#3828—24no—
60#3828—24no—
61C2×C4⋊(C3⋊D3)C2312yes—
62C2×C4×C3⋊D3—22no—
63C2×#634C2312yes—
64C2×C3×#67—22no—
65C22×C3×Dic3D412yes—
66C3×#235—24no—
67C3×#235—24no—
68C2×C3×D12C2312yes—
69C2×C3×C4×D3—22no—
70C2×C3×Dic6C2312yes—
71C2×#626—24no—
72C2×C32×C8D414yescomplemented
73C2×C32×C8C2311yescharacteristic
74C2×C32×C8C2311yescharacteristic
75#3746—22no—
76#3745—22no—
77#3744—24no—
78C3×C4×Dic3D412yes—
79C3×C4×Dic3C2312yes—
80C2×C3×C3⋊C8D414yescomplemented
81C2×C3×C3⋊C8C2312yes—
82C3×Dic12—22no—
83C3×D24—22no—
84C3×#204—24no—
85Dic3⋊Dic3—24no—
86#3722—24no—
87(C2×D3)⋊Dic3—24no—
88#3719—24no—
89#3717—24no—
90#3716—24no—
91#3714—24no—
92#3150—91noSylow
93C2×C3×#41—32no—
94C2×#235—32no—
95C2×#235—32no—
96C2×#235—62no—
97C2×#235C2×D312yes—
98C3×#135—64no—
99C2×C3×Q16—31no—
100C2×C3×SD16—32no—
101C2×C3×D8—31no—
102C22×C3×C8—21no—
103C22×C3×C8—31no—
104C22×C3×C8C2×D311yescharacteristic
105C22×C3×C8C2×D311yescharacteristic
106C2×C3×C42—31no—
107#950—68no—
108#947—32no—
109#944—32no—
110C2×#216—32no—
111C2×#215—32no—
112#940—32no—
113#939—64no—
114#936—32no—
115C2×#214—32no—
116C2×#213—32no—
117#930—64no—
118C4×#67—64no—
119C2×C4×Dic3C2×D311yescharacteristic
120C22×C3⋊C8C2×D311yescharacteristic
121C2×Dic12—32no—
122C2×Dic12—31no—
123C2×Dic12—31no—
124C2×Dic12—61no—
125C2×Dic12C2×D311yescharacteristic
126#904—24no—
127#904—68no—
128#904—68no—
129#904—64no—
130#904—64no—
131C2×D24—32no—
132C2×D24—31no—
133C2×D24—31no—
134C2×D24—61no—
135C2×D24C2×D311yescharacteristic
136C2×#204—32no—
137C2×#204—32no—
138C2×#204—32no—
139C2×#204—32no—
140C2×#204—62no—
141C2×#204C2×D312yes—
142#875—32no—
143#875—32no—
144#874—32no—
145C4×D12—64no—
146#869—32no—
147C3×#97—32no—
148C3×#97—32no—
149#815C2×D312yes—
150#815C2×D312yes—
151C23×C32C2×D411yescharacteristic
152C22×C3⋊D3—22no—
153C22×C3×D3—22no—
154C2×C32×C4C2×D411yescharacteristic
155C2×C32×C4C2×D412yes—
156C2×C32×C4C2×D412yes—
157C2×C32×C4C2411yescharacteristic
158#638—44no—
159C2×C3⋊Dic3—22no—
160C4⋊(C3⋊D3)—22no—
161C4⋊(C3⋊D3)—22no—
162C4×C3⋊D3—44no—
163#634—22no—
164#634—22no—
165C3×#67—44no—
166C2×C3×Dic3—22no—
167C2×C3×Dic3—42no—
168C2×C3×Dic3C2×D414yes—
169C3×D12—22no—
170C3×D12—22no—
171C3×C4×D3—44no—
172C3×Dic6—22no—
173C3×Dic6—22no—
174#626—48no—
175C32×C8C2×D412yes—
176C32×C8C2×D412yes—
177C3×C3⋊C8C2×D414yes—
178C2×#135—31no—
179C2×#135—92no—
180C2×#135—91no—
181#532—92no—
182#497—92no—
183#497—92no—
184#496—92no—
185#496—92no—
186C2×#97—31no—
187C3×#41—64no—
188C3×#41—64no—
189C2×C3×Q8—32no—
190C2×C3×D4—32no—
191C2×C3×D4—62no—
192C22×C3×C4—21no—
193C22×C3×C4—32no—
194C22×C3×C4—62no—
195C22×C3×C4C22×D311yescharacteristic
196C22×C3×C4C22×D311yescharacteristic
197C2×#67—22no—
198C2×#67—62no—
199C2×#67—62no—
200C2×#67—64no—
201C2×#67—122no—
202C22×Dic3D1212yes—
203#235—24no—
204#235—24no—
205#235—68no—
206#235—64no—
207#235—64no—
208#235—64no—
209#235—64no—
210#235—124no—
211C2×D12—32no—
212C2×D12—32no—
213C2×D12—62no—
214C2×D12—64no—
215C2×D12C22×D312yes—
216C2×C4×D3—22no—
217C2×C4×D3—62no—
218C2×C4×D3—62no—
219C2×C4×D3—122no—
220C2×Dic6—32no—
221C2×Dic6—32no—
222C2×Dic6—62no—
223C2×Dic6C22×D312yes—
224C3×Q16—62no—
225C3×SD16—64no—
226C3×D8—62no—
227C2×C3×C8—24no—
228C2×C3×C8—21no—
229C2×C3×C8—21no—
230C2×C3×C8—34no—
231C2×C3×C8—32no—
232C2×C3×C8D1214yescomplemented
233C2×C3×C8#6714yescomplemented
234C2×C3×C8C22×D311yescharacteristic
235C2×C3×C8C22×D311yescharacteristic
236C2×C3×C8C22×D311yescharacteristic
237C2×C3×C8C22×D311yescharacteristic
238C3×C42—32no—
239C3×C42—32no—
240#217—64no—
241#216—64no—
242#215—64no—
243#214—64no—
244#213—64no—
245(C2×D3)⋊C4—64no—
246(C2×D3)⋊C4—64no—
247(C2×D3)⋊C4—64no—
248C4⋊Dic3—64no—
249Dic3⋊C4—64no—
250C4×Dic3D1212yes—
251C4×Dic3C22×D312yes—
252C2×C3⋊C8D1214yescomplemented
253C2×C3⋊C8C22×D312yes—
254Dic12—22no—
255Dic12—64no—
256Dic12—64no—
257Dic12—62no—
258Dic12—62no—
259D24—22no—
260D24—64no—
261D24—64no—
262D24—62no—
263D24—62no—
264#204—24no—
265#204—68no—
266#204—64no—
267#204—64no—
268#204—64no—
269#204—64no—
270C22×C32—22no—
271C22×C32#12712yes—
272C22×C32C22×D411yescharacteristic
273C2×C3⋊D3—42no—
274C2×C3⋊D3—44no—
275C2×C3×D3—42no—
276C2×C3×D3—44no—
277C32×C4#12712yes—
278C32×C4C22×D411yescharacteristic
279C32×C4C22×D411yescharacteristic
280C3⋊Dic3—42no—
281C3×Dic3—24no—
282C3×Dic3—42no—
283C2×#41—32no—
284C2×#41—92no—
285#135—64no—
286#135—188no—
287#135—184no—
288C2×Q16—31no—
289C2×Q16—92no—
290C2×Q16—91no—
291C2×SD16—32no—
292C2×SD16—92no—
293C2×SD16—92no—
294C2×SD16—92no—
295C2×D8—31no—
296C2×D8—92no—
297C2×D8—91no—
298C22×C8—31no—
299C22×C8D3211yescharacteristic
300C4⋊Q8—92no—
301#127—92no—
302#124—92no—
303#124—92no—
304#121—184no—
305C4×D4—184no—
306C2×C42—31no—
307#97—32no—
308#97—32no—
309C23×C3—21no—
310C23×C3—62no—
311C23×C3C2×D1211yescharacteristic
312C23×C3D3×D411yescharacteristic
313C22×D3—22no—
314C22×D3—62no—
315C22×D3—62no—
316C22×D3—122no—
317C3×Q8—62no—
318C3×Q8—62no—
319C3×D4—62no—
320C3×D4—62no—
321C3×D4—124no—
322C2×C3×C4—21no—
323C2×C3×C4—22no—
324C2×C3×C4—21no—
325C2×C3×C4—22no—
326C2×C3×C4—34no—
327C2×C3×C4—62no—
328C2×C3×C4—122no—
329C2×C3×C4—124no—
330C2×C3×C4C2×D1212yes—
331C2×C3×C4C2×D1211yescharacteristic
332C2×C3×C4C2×D1212yes—
333C2×C3×C4D3×D412yes—
334C2×C3×C4D3×D411yescharacteristic
335C2×C3×C4C2×#6712yes—
336C2×C3×C4C23×D311yescharacteristic
337C2×C3×C4C23×D311yescharacteristic
338#67—44no—
339#67—128no—
340#67—128no—
341#67—124no—
342#67—124no—
343C2×Dic3—22no—
344C2×Dic3—42no—
345C2×Dic3—62no—
346C2×Dic3—62no—
347C2×Dic3—122no—
348C2×Dic3C2×D1214yes—
349D12—22no—
350D12—22no—
351D12—64no—
352D12—62no—
353D12—62no—
354D12—62no—
355D12—62no—
356D12—122no—
357D12—128no—
358C4×D3—44no—
359C4×D3—128no—
360C4×D3—124no—
361C4×D3—124no—
362Dic6—22no—
363Dic6—22no—
364Dic6—64no—
365Dic6—62no—
366Dic6—62no—
367Dic6—62no—
368Dic6—62no—
369Dic6—122no—
370C3×C8—22no—
371C3×C8—22no—
372C3×C8—34no—
373C3×C8C2×D1212yes—
374C3×C8C2×D1212yes—
375C3×C8C2×#6712yes—
376C3×C8C2×#6712yes—
377C3⋊C8C2×D1214yes—
378C2×C32—22no—
379C2×C32C2×#12711yescharacteristic
380C2×C32#57512yes—
381C3⋊D3—82no—
382C3×D3—82no—
383#41—64no—
384#41—64no—
385#41—184no—
386#41—184no—
387C2×Q8—32no—
388C2×Q8—92no—
389C2×D4—32no—
390C2×D4—62no—
391C2×D4—92no—
392C2×D4—184no—
393C2×D4—182no—
394C22×C4—32no—
395C22×C4—62no—
396C22×C4—182no—
397C22×C4C2×D3211yescharacteristic
398Q16—62no—
399Q16—184no—
400Q16—182no—
401SD16—64no—
402SD16—184no—
403SD16—184no—
404SD16—184no—
405D8—62no—
406D8—184no—
407D8—182no—
408C2×C8—32no—
409C2×C8—34no—
410C2×C8#62614yescomplemented
411C2×C8C2×D3211yescharacteristic
412C2×C8C2×D3211yescharacteristic
413C4⋊C4—184no—
414C22⋊C4—184no—
415C22⋊C4—184no—
416C42—32no—
417C42—32no—
418C22×C3—22no—
419C22×C3—22no—
420C22×C3—21no—
421C22×C3—22no—
422C22×C3—42no—
423C22×C3—122no—
424C22×C3—124no—
425C22×C3#87412yes—
426C22×C3#94012yes—
427C22×C3C22×D1211yescharacteristic
428C22×C3C2×D3×D411yescharacteristic
429C2×D3—44no—
430C2×D3—42no—
431C2×D3—124no—
432C2×D3—122no—
433C2×D3—124no—
434C2×D3—124no—
435C2×D3—122no—
436C2×D3—244no—
437C3×C4—21no—
438C3×C4—21no—
439C3×C4—22no—
440C3×C4—64no—
441C3×C4—122no—
442C3×C4#87412yes—
443C3×C4#94012yes—
444C3×C4C22×D1211yescharacteristic
445C3×C4C22×D1211yescharacteristic
446C3×C4C2×D3×D411yescharacteristic
447C3×C4C22×#6711yescharacteristic
448Dic3—24no—
449Dic3—42no—
450Dic3—124no—
451Dic3—122no—
452Dic3—122no—
453C32#315011yescharacteristic, complemented, Sylow
454C23—62no—
455C23—182no—
456C23D3×D1211yescharacteristic
457Q8—62no—
458Q8—62no—
459Q8—182no—
460Q8—182no—
461D4—62no—
462D4—62no—
463D4—124no—
464D4—182no—
465D4—182no—
466D4—368no—
467D4—364no—
468C2×C4—34no—
469C2×C4—62no—
470C2×C4—122no—
471C2×C4—124no—
472C2×C4—182no—
473C2×C4—364no—
474C2×C4D3×D1212yes—
475C2×C4D3×D1211yescharacteristic
476C2×C4C2×#62612yes—
477C2×C4C22×D3211yescharacteristic
478C8—34no—
479C8C2×#62612yes—
480C8C2×#62612yes—
481C2×C3—22no—
482C2×C3—22no—
483C2×C3—22no—
484C2×C3—21no—
485C2×C3—42no—
486C2×C3—242no—
487C2×C3C2×#87411yescharacteristic
488C2×C3#574812yes—
489C2×C3#576812yes—
490C2×C3C2×#94011yescharacteristic
491D3—82no—
492D3—244no—
493D3—242no—
494D3—242no—
495C22—22no—
496C22—124no—
497C22—122no—
498C22—364no—
499C22—362no—
500C22#6391112yes—
501C22C2×D3×D1211yescharacteristic
502C4—64no—
503C4—122no—
504C4—362no—
505C4#6391112yes—
506C4C2×D3×D1211yescharacteristic
507C4C22×#62611yescharacteristic
508C3—21no—
509C3#7849911yescharacteristic, complemented
510C3#8390411yescharacteristic, complemented
511C2—22no—
512C2—242no—
513C2—722no—
514C2#1059467612yes—
515C2C2×#6391111yescharacteristic
subgroupG/H
centerC2×C4D3×D12
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC22×C32×C8C22
socleC22×C32C22×D4
hypercenterC22×C8D32
hypocenterC32#3150
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C2×C4 ◁ C22×C4 ◁ C22×C8

Complements

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

NH ≅ G/Ntype
1. C2×#64113C2semidirect
2. C2×C3×#904C2semidirect
3. #10595029C2semidirect
4. C2×#63829C2semidirect
5. C2×C3×#815C2semidirect
6. #10590899C2semidirect
7. #10590897C2semidirect
8. #10590883C2semidirect
9. #10590881C2semidirect
45. C2×#904D3semidirect
52. C2×#815D3semidirect
72. C2×C32×C8D4semidirect
80. C2×C3×C3⋊C8D4semidirect
232. C2×C3×C8D12semidirect
233. C2×C3×C8#67semidirect
252. C2×C3⋊C8D12semidirect
410. C2×C8#626semidirect
453. C32#3150semidirect
509. C3#78499semidirect
510. C3#83904semidirect

Maximal subgroups

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

subgroupindex
C2×#641132
C2×C3×#9042
#105950292
C2×#638292
C2×C3×#8152
#105908992
#105908972
#105908832
#105908812
#839043
#784993