Finite Group Databasebeta

← #11793422

Subgroups — #11793422

Order 1152.

615 conjugacy classes of subgroups.

The subgroup lattice has 531 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10594855C211yesmaximal, characteristic
2#10592820C211yesmaximal, characteristic, complemented
3C2×C3×#825C211yesmaximal, characteristic
4C2×C3×#824C211yesmaximal, characteristic, complemented
5#10591220C211yesmaximal, characteristic, complemented
6#10591088C211yesmaximal, characteristic
7#10589162C211yesmaximal, characteristic, complemented
8#70360—31nomaximal
9#70100—31nomaximal
10C2×C3×#235C2211yescharacteristic
11C22×C3×Dic6C2211yescharacteristic
12C2×C32×M16C2211yescharacteristic
13#64135C2211yescharacteristic
14C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
15C2×C3×C4×Dic3C2211yescharacteristic
16C2×C3×#208C2211yescharacteristic
17#63961—22no—
18#63873—21no—
19#63863—21no—
20#63856—21no—
21#63856—21no—
22#63645—21no—
23#63644—21no—
24C3×#825—22no—
25C3×#824—22no—
26#63579—22no—
27#63566—21no—
28#63563—21no—
29#5825—31no—
30#5816—31no—
31C2×C3×#104—31no—
32C2×C3×#101—31no—
33#5232—31no—
34#5229—31no—
35C2×#825D311yescharacteristic
36C2×#824D311yescharacteristic, complemented
37#5133—31no—
38#5121—31no—
39#5121—31no—
40#5121—61no—
41#4929—31no—
42#4555—31no—
43#4523—31no—
44C22×C32×C4C2311yescharacteristic
45C22×C3⋊Dic3—21no—
46C2×C3×#67—21no—
47C22×C3×Dic3—21no—
48C22×C3×Dic3D412yes—
49C3×#235—21no—
50C3×#235—21no—
51C3×#235—21no—
52C3×#235—21no—
53C2×C3×D12D411yescharacteristic
54C2×C3×C4×D3—21no—
55C2×C3×Dic6—21no—
56C2×C3×Dic6—21no—
57C2×C3×Dic6—21no—
58C2×C3×Dic6—21no—
59C2×C3×Dic6—21no—
60C2×C3×Dic6—21no—
61C2×C3×Dic6D411yescharacteristic
62C32×M16—21no—
63C32×M16D412yes—
64C2×C32×C8—21no—
65#3757—21no—
66C4⋊(C3⋊Dic3)—21no—
67C4⋊(C3⋊Dic3)—21no—
68C4⋊(C3⋊Dic3)D411yescharacteristic
69C4⋊(C3⋊Dic3)D411yescharacteristic
70C4×C3⋊Dic3—21no—
71C3×C4×Dic3—21no—
72C3×C4×Dic3—21no—
73C3×#208—21no—
74C3×#208—21no—
75C2×C3×C3⋊C8—21no—
76#3724—22no—
77#3724—22no—
78(C2×D3)⋊Dic3—22no—
79(C2×D3)⋊Dic3—22no—
80#2038—91noSylow
81C2×C3×#41—31no—
82C22×C3×Q8—31no—
83C2×#235C2×D311yescharacteristic
84C22×Dic6C2×D311yescharacteristic
85C2×C3×M16—21no—
86C2×C3×M16—31no—
87C2×C3×M16C2×D311yescharacteristic
88C2×C3×M16C2×D311yescharacteristic
89C2×C3×C42—31no—
90#947—61no—
91#946—61no—
92#946—61no—
93#944—61no—
94#944—61no—
95#936—61no—
96#935—62no—
97#929—62no—
98#926—31no—
99#926—31no—
100#926—61no—
101C2×C4⋊Dic3—31no—
102C2×C4⋊Dic3—31no—
103C2×C4⋊Dic3—61no—
104#924—61no—
105#924—61no—
106C2×C4×Dic3C2×D311yescharacteristic
107C2×#208C2×D311yescharacteristic
108C3×#104—62no—
109C3×#101—62no—
110#835—61no—
111#832—61no—
112C3⋊#95—62no—
113C3⋊#95—62no—
114#825—22no—
115#824—22no—
116#821—61no—
117#818—61no—
118#818—61no—
119#818—62no—
120#817—61no—
121#817—61no—
122#817—62no—
123#816—61no—
124C23×C32C2×D411yescharacteristic
125C22×C3×D3—21no—
126C2×C32×C4C2×D411yescharacteristic
127C2×C32×C4C2×D411yescharacteristic
128C2×C32×C4C2×D411yescharacteristic
129C2×C32×C4#4111yescharacteristic
130C2×C32×C4#4111yescharacteristic
131C2×C32×C4#4111yescharacteristic
132C2×C3⋊Dic3—21no—
133C2×C3⋊Dic3—21no—
134C2×C3⋊Dic3—41no—
135C2×C3⋊Dic3—42no—
136C3×#67—41no—
137C3×#67—41no—
138C2×C3×Dic3—22no—
139C2×C3×Dic3—22no—
140C2×C3×Dic3—21no—
141C2×C3×Dic3—22no—
142C2×C3×Dic3—22no—
143C2×C3×Dic3—41no—
144C2×C3×Dic3—41no—
145C3×D12—21no—
146C3×D12—21no—
147C3×C4×D3—41no—
148C3×C4×D3—41no—
149C3×Dic6—21no—
150C3×Dic6—21no—
151C3×Dic6—41no—
152C3×Dic6—41no—
153C3×Dic6—41no—
154C3×Dic6—41no—
155C32×C8—22no—
156C3×C3⋊C8—41no—
157#536—91no—
158#428—91no—
159C2×#104—31no—
160#417—91no—
161C2×#101—31no—
162#391—91no—
163#339—91no—
164C3×#41—61no—
165C3×#41—61no—
166C3×#41—61no—
167C3×#41—61no—
168C2×C3×Q8—31no—
169C2×C3×Q8—61no—
170C2×C3×Q8—61no—
171C2×C3×Q8—61no—
172C2×C3×Q8—61no—
173C2×C3×Q8—61no—
174C2×C3×Q8—61no—
175C2×C3×D4—31no—
176C2×C3×D4—61no—
177C22×C3×C4—21no—
178C22×C3×C4—32no—
179C22×C3×C4—61no—
180C22×C3×C4—61no—
181C22×C3×C4C22×D311yescharacteristic
182C22×C3×C4C22×D311yescharacteristic
183C2×#67—21no—
184C22×Dic3—21no—
185C22×Dic3—61no—
186C22×Dic3—61no—
187C22×Dic3—121no—
188C22×Dic3D1212yes—
189#235—21no—
190#235—21no—
191#235—21no—
192#235—21no—
193C2×D12D1211yescharacteristic
194C2×C4×D3—21no—
195C2×Dic6—21no—
196C2×Dic6—21no—
197C2×Dic6—21no—
198C2×Dic6—21no—
199C2×Dic6—21no—
200C2×Dic6—21no—
201C2×Dic6D1211yescharacteristic
202C3×M16—22no—
203C3×M16—21no—
204C3×M16—21no—
205C3×M16—22no—
206C3×M16—61no—
207C3×M16—61no—
208C3×M16#6712yes—
209C3×M16#6712yes—
210C2×C3×C8—22no—
211C2×C3×C8—21no—
212C2×C3×C8—21no—
213C2×C3×C8—61no—
214C3×C42—61no—
215C3×C42—61no—
216#217—62no—
217#217—62no—
218#217—61no—
219#217—61no—
220#217—121no—
221(C2×D3)⋊C4—62no—
222(C2×D3)⋊C4—62no—
223C4⋊Dic3—31no—
224C4⋊Dic3—31no—
225C4⋊Dic3—31no—
226C4⋊Dic3—31no—
227C4⋊Dic3—61no—
228C4⋊Dic3—61no—
229C4⋊Dic3—62no—
230C4⋊Dic3—61no—
231C4⋊Dic3—61no—
232C4⋊Dic3—61no—
233C4⋊Dic3—61no—
234C4⋊Dic3—121no—
235Dic3⋊C4—62no—
236Dic3⋊C4—62no—
237Dic3⋊C4—62no—
238Dic3⋊C4—62no—
239C4×Dic3—21no—
240C4×Dic3—21no—
241C4×Dic3—61no—
242C4×Dic3—61no—
243C4×Dic3—121no—
244#208—21no—
245#208—21no—
246C2×C3⋊C8—21no—
247C22×C32—21no—
248C22×C32—21no—
249C22×C32#12011yescharacteristic
250C22×C32#12111yescharacteristic
251C22×C32#12311yescharacteristic
252C2×C3×D3—41no—
253C2×C3×D3—41no—
254C2×C3×D3—41no—
255C32×C4#12111yescharacteristic
256C32×C4#12111yescharacteristic
257C32×C4#12311yescharacteristic
258C32×C4#12411yescharacteristic
259C3⋊Dic3—41no—
260C3⋊Dic3—41no—
261C3⋊Dic3—81no—
262C3×Dic3—42no—
263C3×Dic3—41no—
264C3×Dic3—42no—
265C2×#41—31no—
266C22×Q8—31no—
267C2×M16—31no—
268C2×M16D3211yescharacteristic
269C4⋊Q8—181no—
270#124—181no—
271#123—182no—
272C22⋊Q8—181no—
273C22⋊Q8—181no—
274#117—91no—
275C2×C4⋊C4—91no—
276C2×C42—31no—
277#107—181no—
278#106—181no—
279#104—62no—
280#103—181no—
281#102—181no—
282#101—62no—
283#95—182no—
284C23×C3—21no—
285C23×C3—61no—
286C23×C3C2×D1211yescharacteristic
287C23×C3D3×D411yescharacteristic
288C22×D3—21no—
289C3×Q8—61no—
290C3×Q8—61no—
291C3×Q8—121no—
292C3×Q8—121no—
293C3×Q8—121no—
294C3×Q8—121no—
295C3×D4—61no—
296C3×D4—61no—
297C3×D4—121no—
298C3×D4—121no—
299C2×C3×C4—21no—
300C2×C3×C4—21no—
301C2×C3×C4—21no—
302C2×C3×C4—21no—
303C2×C3×C4—21no—
304C2×C3×C4—21no—
305C2×C3×C4—62no—
306C2×C3×C4—61no—
307C2×C3×C4—62no—
308C2×C3×C4—62no—
309C2×C3×C4—62no—
310C2×C3×C4—121no—
311C2×C3×C4—121no—
312C2×C3×C4—121no—
313C2×C3×C4—121no—
314C2×C3×C4C2×D1211yescharacteristic
315C2×C3×C4#23511yescharacteristic
316C2×C3×C4#23511yescharacteristic
317C2×C3×C4D3×D411yescharacteristic
318C2×C3×C4D3×D411yescharacteristic
319C2×C3×C4D3×D411yescharacteristic
320C2×C3×C4#23711yescharacteristic
321C2×C3×C4#23711yescharacteristic
322C2×C3×C4#23711yescharacteristic
323C2×C3×C4#23711yescharacteristic
324C2×C3×C4C2×#6711yescharacteristic
325C2×C3×C4C2×#6711yescharacteristic
326#67—41no—
327#67—41no—
328C2×Dic3—22no—
329C2×Dic3—21no—
330C2×Dic3—22no—
331C2×Dic3—22no—
332C2×Dic3—22no—
333C2×Dic3—41no—
334C2×Dic3—41no—
335C2×Dic3—61no—
336C2×Dic3—61no—
337C2×Dic3—61no—
338C2×Dic3—61no—
339C2×Dic3—121no—
340C2×Dic3—121no—
341C2×Dic3—122no—
342C2×Dic3—122no—
343C2×Dic3—122no—
344C2×Dic3—121no—
345C2×Dic3—121no—
346C2×Dic3—242no—
347D12—21no—
348D12—21no—
349C4×D3—41no—
350C4×D3—41no—
351Dic6—21no—
352Dic6—21no—
353Dic6—41no—
354Dic6—41no—
355Dic6—41no—
356Dic6—41no—
357C3×C8—24no—
358C3×C8—22no—
359C3×C8—22no—
360C3×C8—121no—
361C3⋊C8—41no—
362C2×C32—21no—
363C2×C32—21no—
364C2×C32#39411yescharacteristic
365C2×C32#45411yescharacteristic
366C2×C32#45611yescharacteristic
367C3×D3—81no—
368#41—61no—
369#41—61no—
370#41—61no—
371#41—61no—
372C2×Q8—31no—
373C2×Q8—61no—
374C2×Q8—61no—
375C2×Q8—61no—
376C2×Q8—61no—
377C2×Q8—61no—
378C2×Q8—61no—
379C2×D4—31no—
380C2×D4—61no—
381C22×C4—32no—
382C22×C4—61no—
383C22×C4—61no—
384C22×C4—181no—
385C22×C4C2×D3211yescharacteristic
386M16—21no—
387M16—61no—
388M16—61no—
389M16#62512yes—
390C2×C8—21no—
391C2×C8—61no—
392C4⋊C4—91no—
393C4⋊C4—91no—
394C4⋊C4—182no—
395C4⋊C4—182no—
396C4⋊C4—181no—
397C4⋊C4—181no—
398C22⋊C4—182no—
399C22⋊C4—182no—
400C22⋊C4—181no—
401C42—61no—
402C42—61no—
403C42—181no—
404C22×C3—21no—
405C22×C3—21no—
406C22×C3—21no—
407C22×C3—21no—
408C22×C3—21no—
409C22×C3—21no—
410C22×C3—21no—
411C22×C3—41no—
412C22×C3—41no—
413C22×C3—121no—
414C22×C3—121no—
415C22×C3—121no—
416C22×C3#88211yescharacteristic
417C22×C3#88211yescharacteristic
418C22×C3#88311yescharacteristic
419C22×C3#88611yescharacteristic
420C22×C3#93011yescharacteristic
421C22×C3#93811yescharacteristic
422C2×D3—41no—
423C2×D3—41no—
424C2×D3—41no—
425C3×C4—21no—
426C3×C4—21no—
427C3×C4—21no—
428C3×C4—21no—
429C3×C4—122no—
430C3×C4—122no—
431C3×C4—121no—
432C3×C4#88311yescharacteristic
433C3×C4#88511yescharacteristic
434C3×C4#88511yescharacteristic
435C3×C4#88611yescharacteristic
436C3×C4#93011yescharacteristic
437C3×C4#93811yescharacteristic
438C3×C4#93911yescharacteristic
439C3×C4#93911yescharacteristic
440Dic3—42no—
441Dic3—41no—
442Dic3—42no—
443Dic3—121no—
444Dic3—121no—
445Dic3—121no—
446Dic3—121no—
447Dic3—241no—
448Dic3—241no—
449Dic3—242no—
450Dic3—241no—
451Dic3—241no—
452C32#203811yescharacteristic, complemented, Sylow
453C23—61no—
454C23D3×D1211yescharacteristic
455Q8—61no—
456Q8—61no—
457Q8—121no—
458Q8—121no—
459Q8—121no—
460Q8—121no—
461D4—61no—
462D4—61no—
463D4—121no—
464D4—121no—
465C2×C4—62no—
466C2×C4—62no—
467C2×C4—62no—
468C2×C4—62no—
469C2×C4—61no—
470C2×C4—121no—
471C2×C4—121no—
472C2×C4—121no—
473C2×C4—121no—
474C2×C4—181no—
475C2×C4—181no—
476C2×C4—362no—
477C2×C4—361no—
478C2×C4#379511yescharacteristic
479C2×C4#379511yescharacteristic
480C2×C4D3×D1211yescharacteristic
481C2×C4#380511yescharacteristic
482C2×C4C2×#62511yescharacteristic
483C2×C4#381111yescharacteristic
484C8—22no—
485C8—121no—
486C2×C3—21no—
487C2×C3—21no—
488C2×C3—21no—
489C2×C3—21no—
490C2×C3—21no—
491C2×C3—21no—
492C2×C3—21no—
493C2×C3—41no—
494C2×C3—41no—
495C2×C3—241no—
496C2×C3#475211yescharacteristic
497C2×C3#475311yescharacteristic
498C2×C3#482611yescharacteristic
499C2×C3#482711yescharacteristic
500C2×C3#496111yescharacteristic
501C2×C3#496111yescharacteristic
502D3—81no—
503C22—21no—
504C22—21no—
505C22—121no—
506C22—121no—
507C22—121no—
508C22#6389111yescharacteristic
509C22#6390811yescharacteristic
510C22#6392311yescharacteristic
511C4—122no—
512C4—122no—
513C4—121no—
514C4—361no—
515C4—361no—
516C4—721no—
517C4#6389111yescharacteristic
518C4#6390811yescharacteristic
519C4#6391311yescharacteristic
520C4#6398011yescharacteristic
521C3—21no—
522C3#7010011yescharacteristic, complemented
523C3#7036011yescharacteristic, complemented
524C2—21no—
525C2—21no—
526C2—241no—
527C2#1059102111yescharacteristic
528C2#1059102211yescharacteristic
529C2#1059139411yescharacteristic
subgroupG/H
centerC22#63923
commutator, cosocleC22×C32×C4C23
FrattiniC22×C4C2×D32
FittingC2×C32×M16C22
socleC22×C32#120
prime radicalC2×C3×#235C22
hypercenterC2×M16D32
hypocenterC32#2038
LCSG ▷ C22×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×M16

Complements

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

NH ≅ G/Ntype
2. #10592820C2semidirect
4. C2×C3×#824C2semidirect
5. #10591220C2semidirect
7. #10589162C2semidirect
36. C2×#824D3semidirect
452. C32#2038semidirect
522. C3#70100semidirect
523. C3#70360semidirect

Maximal subgroups

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

subgroupindex
#105948552
#105928202
C2×C3×#8252
C2×C3×#8242
#105912202
#105910882
#105891622
#703603
#701003