Finite Group Databasebeta

← #11778338

Subgroups — #11778338

Order 1152.

643 conjugacy classes of subgroups; only the 82 normal subgroups are shown.

normal subgroups only

This group has 643 conjugacy classes of subgroups — too many to draw. Only its 82 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10594911C211yesmaximal, characteristic
2#10592437C211yesmaximal, characteristic, complemented
3#10591354C211yesmaximal, characteristic, complemented
4#10591181C211yesmaximal, characteristic, complemented
5C3×#4470C211yesmaximal, characteristic, complemented
6C3×#4469C211yesmaximal, characteristic, complemented
7#10589151C211yesmaximal, characteristic, complemented
8#68295—31nomaximal
9#68133—31nomaximal
10C22×#634C2211yescharacteristic
11C2×#3804—21no—
12#64139C2211yescharacteristic
13C2×#3744—21no—
14C3×#930C2211yescharacteristic
15C2×C3×Dic3⋊C4C2211yescharacteristic
16#63978—21no—
17C2×Dic3⋊Dic3—21no—
18#63910—21no—
19#63895—21no—
20#63893—21no—
21#63886—21no—
22C2×#3716—21no—
23C32×C22⋊C8C2211yescharacteristic
24#63643—21no—
25C3×C3⋊#95C2211yescharacteristic
26C3×#830C2211yescharacteristic
27#63579—21no—
28#63567—21no—
29#5597—31no—
30#5510—31no—
31#5040—31no—
32#4979—31no—
33#4738—31no—
34#4738—31no—
35#4738—31no—
36#4738—61no—
37#4656—31no—
38C3×#327—31no—
39C3×#324—31no—
40#4470—31no—
41#4470D311yescharacteristic, complemented
42#4469D311yescharacteristic, complemented
43#4451—31no—
44C22×C32×C4C2311yescharacteristic
45C2×#638—21no—
46C22×C3⋊Dic3—21no—
47C2×C4⋊(C3⋊D3)D411yescharacteristic
48C2×#634—21no—
49C2×#634—21no—
50C2×#634—42no—
51C2×C3×#67—21no—
52C22×C3×Dic3—21no—
53C22×C3×Dic3D411yescharacteristic
54C22×C3×Dic3D411yescharacteristic
55C2×C3×D12D411yescharacteristic
56C2×#627—21no—
57C2×#626—21no—
58C2×#626—21no—
59C2×#624—21no—
60#3804—42no—
61#3804—42no—
62C2×D3×Dic3—21no—
63C2×C32×C8—21no—
64#3752—21no—
65C4⋊(C3⋊Dic3)D411yescharacteristic
66#3744—42no—
67C3×(C2×D3)⋊C4—21no—
68C3×C4⋊Dic3D411yescharacteristic
69C3×Dic3⋊C4—21no—
70C3×Dic3⋊C4—21no—
71C2×C3×C3⋊C8—21no—
72Dic3⋊Dic3—21no—
73Dic3⋊Dic3—42no—
74#3722—21no—
75(C2×D3)⋊Dic3—21no—
76#3716—42no—
77#1604—91noSylow
78C2×#237—61no—
79C2×#235—61no—
80C22×Dic6—31no—
81C22×Dic6—31no—
82C22×Dic6—61no—
83C3×#121—31no—
84C2×C3×C4⋊C4—31no—
85#939—61no—
86#939—61no—
87C2×#214—61no—
88#930—31no—
89#930—31no—
90#930—61no—
91#930—61no—
92#930C2×D311yescharacteristic
93C2×C4⋊Dic3—61no—
94C2×Dic3⋊C4—61no—
95C2×Dic3⋊C4C2×D311yescharacteristic
96C2×#204—61no—
97C2×#204—61no—
98C2×#204—62no—
99C2×#204—61no—
100#897—61no—
101#897—61no—
102#896—61no—
103#895—61no—
104#895—61no—
105#884—61no—
106#878—61no—
107C3×C22⋊C8—21no—
108C3×C22⋊C8—31no—
109C3×C22⋊C8C2×D311yescharacteristic
110C3×C22⋊C8C2×D311yescharacteristic
111C3×#95—31no—
112C3⋊#95—61no—
113C3⋊#95—61no—
114C3⋊#95C2×D311yescharacteristic
115#830C2×D311yescharacteristic
116#816—61no—
117#816—61no—
118#816—62no—
119#816—61no—
120#810—61no—
121C23×C32C2×D411yescharacteristic
122C22×C3⋊D3—21no—
123C22×C3×D3—21no—
124C2×C32×C4—41no—
125C2×C32×C4C2×D411yescharacteristic
126C2×C32×C4C2×D411yescharacteristic
127#638—41no—
128#638—41no—
129C2×C3⋊Dic3—22no—
130C2×C3⋊Dic3—21no—
131C2×C3⋊Dic3—41no—
132C2×C3⋊Dic3—41no—
133C4⋊(C3⋊D3)—41no—
134#634—22no—
135#634—22no—
136#634—41no—
137#634—41no—
138C3×#67—41no—
139C3×#67—41no—
140C2×C3×Dic3—21no—
141C2×C3×Dic3—21no—
142C2×C3×Dic3—22no—
143C2×C3×Dic3—21no—
144C2×C3×Dic3—21no—
145C2×C3×Dic3—41no—
146C2×C3×Dic3—41no—
147C2×C3×Dic3—41no—
148C2×C3×Dic3SD1612yescomplemented
149C3×D12—41no—
150#627—42no—
151#626—42no—
152#626—81no—
153#624—42no—
154D3×Dic3—42no—
155C32×C8—41no—
156C3×C3⋊C8—41no—
157#537—91no—
158#448—91no—
159#448—91no—
160#395—91no—
161#327—31no—
162#327—91no—
163#324—31no—
164C2×C3×D4—31no—
165C2×C3×D4—61no—
166C22×C3×C4—21no—
167C22×C3×C4—31no—
168C22×C3×C4—31no—
169C22×C3×C4—61no—
170C22×C3×C4C22×D311yescharacteristic
171C22×C3×C4C22×D311yescharacteristic
172C2×#67—21no—
173C2×#67—61no—
174C2×#67—61no—
175C2×#67—61no—
176C2×#67—61no—
177C2×#67—121no—
178C22×Dic3—21no—
179C22×Dic3—61no—
180C22×Dic3—61no—
181C22×Dic3—61no—
182C22×Dic3—121no—
183C22×Dic3D1211yescharacteristic
184C22×Dic3D1211yescharacteristic
185#237—122no—
186#237—122no—
187#235—122no—
188#235—122no—
189C2×D12—31no—
190C2×D12—31no—
191C2×D12—61no—
192C2×D12—61no—
193C2×D12—61no—
194C2×D12D1211yescharacteristic
195C2×C4×D3—61no—
196C2×C4×D3—61no—
197C2×C4×D3—61no—
198C2×Dic6—62no—
199C2×Dic6—61no—
200C2×Dic6—61no—
201C2×Dic6—61no—
202C2×Dic6—61no—
203C2×Dic6—61no—
204C2×Dic6—61no—
205C2×Dic6—121no—
206C2×Dic6—122no—
207C2×Dic6—122no—
208C2×Dic6—124no—
209C2×C3×C8—22no—
210C2×C3×C8—21no—
211C2×C3×C8—21no—
212C2×C3×C8—61no—
213C3×C4⋊C4—31no—
214C3×C4⋊C4—61no—
215C3×C4⋊C4—61no—
216C3×C22⋊C4—61no—
217#217—61no—
218#214—122no—
219(C2×D3)⋊C4—21no—
220(C2×D3)⋊C4—61no—
221(C2×D3)⋊C4—61no—
222(C2×D3)⋊C4—61no—
223(C2×D3)⋊C4—61no—
224(C2×D3)⋊C4—61no—
225(C2×D3)⋊C4—121no—
226C4⋊Dic3—31no—
227C4⋊Dic3—31no—
228C4⋊Dic3—61no—
229C4⋊Dic3—61no—
230C4⋊Dic3—122no—
231C4⋊Dic3D1211yescharacteristic
232Dic3⋊C4—21no—
233Dic3⋊C4—21no—
234Dic3⋊C4—61no—
235Dic3⋊C4—122no—
236C2×C3⋊C8—21no—
237#204—122no—
238#204—122no—
239#204—124no—
240#204—122no—
241C22×C32—21no—
242C22×C32—21no—
243C22×C32#12011yescharacteristic
244C22×C32C2×SD1611yescharacteristic
245C22×C32AGL(1,ℤ/8)11yescharacteristic
246C2×C3⋊D3—41no—
247C2×C3⋊D3—41no—
248C2×C3⋊D3—41no—
249C2×C3×D3—41no—
250C2×C3×D3—41no—
251C2×C3×D3—41no—
252C32×C4—21no—
253C32×C4—21no—
254C3⋊Dic3—42no—
255C3⋊Dic3—41no—
256C3×Dic3—22no—
257C3×Dic3—42no—
258C3×Dic3—41no—
259C3×Dic3—41no—
260C2×#41—181no—
261C22×Q8—91no—
262C2×SD16—181no—
263C2×SD16—181no—
264C22⋊Q8—181no—
265C22⋊Q8—181no—
266#121—31no—
267#121—91no—
268#121—181no—
269#121—181no—
270#121—181no—
271C2×C4⋊C4—31no—
272C2×C4⋊C4—181no—
273#103—181no—
274#103—181no—
275C22⋊C8—31no—
276C22⋊C8D3211yescharacteristic
277#95—31no—
278#95—181no—
279C23×C3—21no—
280C23×C3—61no—
281C23×C3C2×D1211yescharacteristic
282C23×C3D3×D411yescharacteristic
283C22×D3—21no—
284C22×D3—61no—
285C22×D3—61no—
286C22×D3—121no—
287C3×D4—121no—
288C3×D4—121no—
289C3×D4—121no—
290C2×C3×C4—21no—
291C2×C3×C4—21no—
292C2×C3×C4—32no—
293C2×C3×C4—41no—
294C2×C3×C4—41no—
295C2×C3×C4—42no—
296C2×C3×C4—61no—
297C2×C3×C4—61no—
298C2×C3×C4—62no—
299C2×C3×C4—61no—
300C2×C3×C4—61no—
301C2×C3×C4—121no—
302C2×C3×C4—121no—
303C2×C3×C4—121no—
304C2×C3×C4C2×D1211yescharacteristic
305C2×C3×C4D3×D411yescharacteristic
306C2×C3×C4D3×D411yescharacteristic
307C2×C3×C4D3×D411yescharacteristic
308#67—41no—
309#67—41no—
310#67—122no—
311#67—121no—
312#67—121no—
313#67—121no—
314#67—121no—
315#67—241no—
316#67—241no—
317#67—241no—
318C2×Dic3—21no—
319C2×Dic3—21no—
320C2×Dic3—22no—
321C2×Dic3—21no—
322C2×Dic3—21no—
323C2×Dic3—41no—
324C2×Dic3—41no—
325C2×Dic3—41no—
326C2×Dic3—62no—
327C2×Dic3—62no—
328C2×Dic3—61no—
329C2×Dic3—61no—
330C2×Dic3—122no—
331C2×Dic3—121no—
332C2×Dic3—122no—
333C2×Dic3—122no—
334C2×Dic3—121no—
335C2×Dic3—121no—
336C2×Dic3—122no—
337C2×Dic3—121no—
338C2×Dic3—121no—
339C2×Dic3#20412yescomplemented
340D12—41no—
341D12—121no—
342D12—121no—
343D12—122no—
344D12—122no—
345D12—241no—
346C4×D3—122no—
347C4×D3—122no—
348C4×D3—122no—
349Dic6—64no—
350Dic6—62no—
351Dic6—62no—
352Dic6—62no—
353Dic6—62no—
354Dic6—122no—
355Dic6—122no—
356Dic6—122no—
357Dic6—122no—
358Dic6—121no—
359Dic6—121no—
360Dic6—121no—
361Dic6—121no—
362Dic6—122no—
363C3×C8—42no—
364C3×C8—41no—
365C3×C8—41no—
366C3×C8—121no—
367C3⋊C8—41no—
368C2×C32—21no—
369C2×C32—21no—
370C2×C32#45011yescharacteristic
371C2×C32#45611yescharacteristic
372C2×C32B(4,𝔽2)11yescharacteristic
373C3⋊D3—81no—
374C3×D3—81no—
375#41—362no—
376#41—362no—
377C2×Q8—181no—
378C2×Q8—181no—
379C2×Q8—181no—
380C2×Q8—362no—
381C2×D4—31no—
382C2×D4—61no—
383C2×D4—91no—
384C2×D4—181no—
385C2×D4—181no—
386C2×D4—181no—
387C22×C4—31no—
388C22×C4—31no—
389C22×C4—61no—
390C22×C4—181no—
391C22×C4—181no—
392C22×C4—181no—
393C22×C4C2×D3211yescharacteristic
394SD16—362no—
395SD16—362no—
396C2×C8—21no—
397C2×C8—61no—
398C4⋊C4—31no—
399C4⋊C4—61no—
400C4⋊C4—61no—
401C4⋊C4—91no—
402C4⋊C4—181no—
403C4⋊C4—362no—
404C22⋊C4—61no—
405C22⋊C4—181no—
406C22⋊C4—181no—
407C22⋊C4—181no—
408C22×C3—21no—
409C22×C3—21no—
410C22×C3—21no—
411C22×C3—21no—
412C22×C3—21no—
413C22×C3—21no—
414C22×C3—21no—
415C22×C3—41no—
416C22×C3—41no—
417C22×C3—121no—
418C22×C3—121no—
419C22×C3—121no—
420C22×C3#88211yescharacteristic
421C22×C3#88211yescharacteristic
422C22×C3C2×#20411yescharacteristic
423C22×C3#90811yescharacteristic
424C22×C3#91111yescharacteristic
425C22×C3D3×SD1611yescharacteristic
426C2×D3—41no—
427C2×D3—41no—
428C2×D3—41no—
429C2×D3—121no—
430C2×D3—121no—
431C2×D3—121no—
432C2×D3—121no—
433C2×D3—121no—
434C2×D3—121no—
435C2×D3—241no—
436C2×D3—241no—
437C2×D3—241no—
438C3×C4—22no—
439C3×C4—21no—
440C3×C4—21no—
441C3×C4—21no—
442C3×C4—21no—
443C3×C4—41no—
444C3×C4—62no—
445C3×C4—122no—
446C3×C4—121no—
447C3×C4—121no—
448Dic3—22no—
449Dic3—42no—
450Dic3—41no—
451Dic3—41no—
452Dic3—124no—
453Dic3—121no—
454Dic3—122no—
455Dic3—122no—
456Dic3—121no—
457Dic3—241no—
458C32#160411yescharacteristic, complemented, Sylow
459C23—61no—
460C23—181no—
461C23D3×D1211yescharacteristic
462Q8—182no—
463Q8—182no—
464Q8—361no—
465Q8—361no—
466Q8—362no—
467D4—121no—
468D4—121no—
469D4—121no—
470D4—361no—
471D4—362no—
472D4—361no—
473D4—361no—
474D4—721no—
475C2×C4—32no—
476C2×C4—41no—
477C2×C4—61no—
478C2×C4—61no—
479C2×C4—62no—
480C2×C4—61no—
481C2×C4—61no—
482C2×C4—121no—
483C2×C4—121no—
484C2×C4—121no—
485C2×C4—182no—
486C2×C4—181no—
487C2×C4—362no—
488C2×C4—362no—
489C2×C4—361no—
490C2×C4—361no—
491C2×C4D3×D1211yescharacteristic
492C2×C4#381111yescharacteristic
493C8—41no—
494C8—121no—
495C2×C3—21no—
496C2×C3—21no—
497C2×C3—21no—
498C2×C3—21no—
499C2×C3—21no—
500C2×C3—21no—
501C2×C3—21no—
502C2×C3—41no—
503C2×C3—41no—
504C2×C3—241no—
505C2×C3#473111yescharacteristic
506C2×C3#474111yescharacteristic
507C2×C3#474111yescharacteristic
508C2×C3#475211yescharacteristic
509C2×C3#477611yescharacteristic
510C2×C3#482611yescharacteristic
511D3—81no—
512D3—241no—
513D3—241no—
514D3—481no—
515C22—21no—
516C22—21no—
517C22—121no—
518C22—121no—
519C22—121no—
520C22—361no—
521C22—361no—
522C22—361no—
523C22D3×#20411yescharacteristic
524C22#6379511yescharacteristic
525C22#6392311yescharacteristic
526C4—21no—
527C4—21no—
528C4—62no—
529C4—122no—
530C4—121no—
531C4—121no—
532C4—362no—
533C4—361no—
534C3—21no—
535C3#6813311yescharacteristic, complemented
536C3#6829511yescharacteristic, complemented
537C2—21no—
538C2—21no—
539C2—241no—
540C2—721no—
541C2#1059041011yescharacteristic
542C2#1059094611yescharacteristic
543C2#1059102111yescharacteristic
subgroupG/H
centerC22#63923
commutator, cosocleC22×C32×C4C23
FrattiniC22×C4C2×D32
FittingC32×C22⋊C8C22
socleC22×C32#120
prime radical#10594911C2
hypercenterC22⋊C8D32
hypocenterC32#1604
LCSG ▷ C22×C32×C4 ▷ C22×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22⋊C8

Complements

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

NH ≅ G/Ntype
2. #10592437C2semidirect
3. #10591354C2semidirect
4. #10591181C2semidirect
5. C3×#4470C2semidirect
6. C3×#4469C2semidirect
7. #10589151C2semidirect
41. #4470D3semidirect
42. #4469D3semidirect
148. C2×C3×Dic3SD16semidirect
339. C2×Dic3#204semidirect
458. C32#1604semidirect
535. C3#68133semidirect
536. C3#68295semidirect

Maximal subgroups

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

subgroupindex
#105949112
#105924372
#105913542
#105911812
C3×#44702
C3×#44692
#105891512
#682953
#681333