Finite Group Databasebeta

← #11793953

Subgroups — #11793953

Order 1152.

653 conjugacy classes of subgroups.

The subgroup lattice has 515 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#64118C211yesmaximal, characteristic
2C2×C3×#822C211yesmaximal, characteristic, complemented
3#10591106C211yesmaximal, characteristic
4C2×#63567C211yesmaximal, characteristic, complemented
5C2×#63561C211yesmaximal, characteristic, complemented
6#10591073C211yesmaximal, characteristic
7C3×#4554C211yesmaximal, characteristic, complemented
8#70716—31nomaximal
9#68987—31nomaximal
10C2×#3828C2211yescharacteristic
11C22×#634C2211yescharacteristic
12C2×C32×M16C2211yescharacteristic
13#64118—22no—
14#64118—22no—
15C2×#3746—21no—
16C2×#3744—21no—
17C2×C3×C4⋊Dic3C2211yescharacteristic
18C2×C3×#208C2211yescharacteristic
19C2×C3×#208C2211yescharacteristic
20C22×C3×C3⋊C8C2211yescharacteristic
21C3×#822—22no—
22#63567—21no—
23#63567—22no—
24#63564—21no—
25#63561—22no—
26#63557—22no—
27C2×#909—31no—
28C2×#909—31no—
29C2×#909—61no—
30C2×C3×#108—31no—
31C2×#824—31no—
32C2×#824—31no—
33#5133—31no—
34#5129—31no—
35C2×#822D311yescharacteristic, complemented
36#5110—31no—
37C2×#816—31no—
38C2×#810—31no—
39#4966—31no—
40C3×#343—31no—
41#4554D311yescharacteristic, complemented
42C22×C32×C4C2311yescharacteristic
43C2×#638—21no—
44C22×C3⋊Dic3—21no—
45#3828—21no—
46#3828—21no—
47#3828—21no—
48#3828—21no—
49C2×C4⋊(C3⋊D3)D411yescharacteristic
50C2×C4×C3⋊D3—21no—
51C2×#634—21no—
52C2×#634—21no—
53C2×#634—21no—
54C2×#634—21no—
55C2×#634—21no—
56C2×#634D412yes—
57C2×#634D411yescharacteristic
58C22×C3×Dic3—21no—
59C32×M16—21no—
60C32×M16D412yes—
61C2×C32×C8—21no—
62#3746—24no—
63#3744—24no—
64C3×C4⋊Dic3—21no—
65C3×C4⋊Dic3—21no—
66C3×#208—21no—
67C3×#208—21no—
68C3×#208—21no—
69C3×#208—21no—
70C2×C3×C3⋊C8—21no—
71C2×C3×C3⋊C8—21no—
72C2×C3×C3⋊C8—21no—
73C2×C3×C3⋊C8—21no—
74C2×C3×C3⋊C8D412yes—
75#2052—91noSylow
76C2×#235—31no—
77C2×#235—31no—
78C2×#235—61no—
79C22×Dic6—31no—
80C22×Dic6—31no—
81C22×Dic6—61no—
82C2×C3×M16—21no—
83C2×C3×M16—31no—
84C2×C3×M16—31no—
85C2×C3×M16C2×D311yescharacteristic
86C2×C3×M16C2×D311yescharacteristic
87C22×C3×C8—31no—
88C2×C3×C4⋊C4—31no—
89C2×C4⋊Dic3C2×D311yescharacteristic
90C2×#208C2×D311yescharacteristic
91C2×#208C2×D311yescharacteristic
92C22×C3⋊C8C2×D311yescharacteristic
93#909—62no—
94#909—62no—
95#909—64no—
96#909—64no—
97#909—62no—
98#909—62no—
99C2×Dic12—61no—
100C2×Dic12—61no—
101C2×Dic12—62no—
102C2×#204—61no—
103C2×#204—61no—
104C2×#204—62no—
105C3×#108—62no—
106#824—62no—
107#824—62no—
108#822—22no—
109#821—61no—
110(C2×D3)⋊C8—62no—
111(C2×D3)⋊C8—62no—
112#816—62no—
113#816—61no—
114#810—61no—
115#810—62no—
116#809—61no—
117C23×C32#4111yescharacteristic
118C22×C3⋊D3—21no—
119C2×C32×C4C2×D411yescharacteristic
120C2×C32×C4C2×D411yescharacteristic
121C2×C32×C4C2×D411yescharacteristic
122C2×C32×C4C2×D411yescharacteristic
123C2×C32×C4#4111yescharacteristic
124C2×C32×C4#4111yescharacteristic
125#638—41no—
126#638—41no—
127C2×C3⋊Dic3—21no—
128C2×C3⋊Dic3—22no—
129C2×C3⋊Dic3—41no—
130C2×C3⋊Dic3—41no—
131C4⋊(C3⋊D3)—21no—
132C4⋊(C3⋊D3)—21no—
133C4×C3⋊D3—41no—
134C4×C3⋊D3—41no—
135#634—22no—
136#634—21no—
137#634—22no—
138#634—21no—
139#634—41no—
140#634—41no—
141C2×C3×Dic3—41no—
142C2×C3×Dic3—81no—
143C32×C8—22no—
144C3×C3⋊C8—22no—
145C3×C3⋊C8—41no—
146C3×C3⋊C8—41no—
147C2×#137—91no—
148C2×#108—31no—
149#417—91no—
150C2×#103—91no—
151C2×#101—91no—
152#408—91no—
153#343—31no—
154C22×C3×C4—21no—
155C22×C3×C4—61no—
156C22×C3×C4C22×D311yescharacteristic
157C22×C3×C4C22×D311yescharacteristic
158C2×#67—61no—
159C2×#67—61no—
160C2×#67—121no—
161C22×Dic3—21no—
162C22×Dic3—61no—
163C22×Dic3—61no—
164C22×Dic3—121no—
165#235—62no—
166#235—62no—
167#235—61no—
168#235—61no—
169#235—61no—
170#235—61no—
171#235—61no—
172#235—61no—
173#235—61no—
174#235—61no—
175#235—121no—
176#235—121no—
177C2×D12—31no—
178C2×D12—31no—
179C2×D12—61no—
180C2×C4×D3—61no—
181C2×C4×D3—61no—
182C2×C4×D3—121no—
183C2×Dic6—31no—
184C2×Dic6—31no—
185C2×Dic6—32no—
186C2×Dic6—32no—
187C2×Dic6—61no—
188C2×Dic6—62no—
189C2×Dic6—62no—
190C2×Dic6—62no—
191C2×Dic6—61no—
192C2×Dic6—61no—
193C2×Dic6—61no—
194C2×Dic6—61no—
195C2×Dic6—61no—
196C2×Dic6—61no—
197C2×Dic6—61no—
198C2×Dic6—61no—
199C2×Dic6—61no—
200C2×Dic6—61no—
201C2×Dic6—121no—
202C2×Dic6—121no—
203C2×Dic6—121no—
204C3×M16—22no—
205C3×M16—21no—
206C3×M16—21no—
207C3×M16—22no—
208C3×M16—61no—
209C3×M16—61no—
210C3×M16—61no—
211C3×M16—61no—
212C3×M16D1212yes—
213C3×M16#6712yes—
214C2×C3×C8—22no—
215C2×C3×C8—21no—
216C2×C3×C8—21no—
217C2×C3×C8—32no—
218C2×C3×C8—61no—
219C2×C3×C8—61no—
220C2×C3×C8—61no—
221C2×C3×C8—61no—
222C3×C4⋊C4—61no—
223C3×C4⋊C4—61no—
224C4⋊Dic3—21no—
225C4⋊Dic3—21no—
226#208—21no—
227#208—21no—
228#208—21no—
229#208—21no—
230C2×C3⋊C8—21no—
231C2×C3⋊C8—21no—
232C2×C3⋊C8—21no—
233C2×C3⋊C8—21no—
234C2×C3⋊C8D1212yes—
235Dic12—68no—
236Dic12—64no—
237Dic12—64no—
238#204—68no—
239#204—64no—
240#204—64no—
241C22×C32—21no—
242C22×C32—21no—
243C22×C32#12111yescharacteristic
244C22×C32#12311yescharacteristic
245C22×C32#12411yescharacteristic
246C2×C3⋊D3—41no—
247C2×C3⋊D3—41no—
248C2×C3⋊D3—41no—
249C32×C4#12011yescharacteristic
250C32×C4#12111yescharacteristic
251C32×C4#12111yescharacteristic
252C32×C4#12311yescharacteristic
253C3⋊Dic3—42no—
254C3⋊Dic3—41no—
255C3×Dic3—81no—
256C2×#41—91no—
257C22×Q8—91no—
258#137—182no—
259#137—182no—
260C2×Q16—181no—
261C2×SD16—181no—
262C2×M16—31no—
263C2×M16—31no—
264C2×M16D3211yescharacteristic
265C22×C8—31no—
266C2×C4⋊C4—31no—
267#108—62no—
268#103—182no—
269#103—181no—
270#102—181no—
271#101—182no—
272C22⋊C8—182no—
273C23×C3—21no—
274C23×C3#23511yescharacteristic
275C23×C3#23911yescharacteristic
276C22×D3—61no—
277C22×D3—61no—
278C22×D3—121no—
279C2×C3×C4—21no—
280C2×C3×C4—21no—
281C2×C3×C4—21no—
282C2×C3×C4—21no—
283C2×C3×C4—21no—
284C2×C3×C4—21no—
285C2×C3×C4—121no—
286C2×C3×C4—241no—
287C2×C3×C4C2×D1211yescharacteristic
288C2×C3×C4C2×D1211yescharacteristic
289C2×C3×C4#23511yescharacteristic
290C2×C3×C4#23511yescharacteristic
291C2×C3×C4D3×D411yescharacteristic
292C2×C3×C4D3×D411yescharacteristic
293C2×C3×C4D3×D411yescharacteristic
294C2×C3×C4D3×D411yescharacteristic
295C2×C3×C4D3×D411yescharacteristic
296C2×C3×C4#23911yescharacteristic
297C2×C3×C4#23911yescharacteristic
298C2×C3×C4C2×#6711yescharacteristic
299#67—122no—
300#67—122no—
301#67—121no—
302#67—121no—
303#67—121no—
304#67—121no—
305C2×Dic3—41no—
306C2×Dic3—61no—
307C2×Dic3—62no—
308C2×Dic3—62no—
309C2×Dic3—61no—
310C2×Dic3—81no—
311C2×Dic3—122no—
312C2×Dic3—121no—
313C2×Dic3—122no—
314C2×Dic3—122no—
315C2×Dic3—121no—
316C2×Dic3—121no—
317C2×Dic3—121no—
318C2×Dic3—121no—
319D12—62no—
320D12—61no—
321D12—61no—
322D12—61no—
323D12—61no—
324D12—121no—
325C4×D3—122no—
326C4×D3—122no—
327C4×D3—121no—
328C4×D3—121no—
329C4×D3—121no—
330C4×D3—121no—
331Dic6—64no—
332Dic6—62no—
333Dic6—62no—
334Dic6—61no—
335Dic6—62no—
336Dic6—61no—
337Dic6—61no—
338Dic6—62no—
339Dic6—62no—
340Dic6—61no—
341Dic6—122no—
342Dic6—121no—
343Dic6—122no—
344Dic6—122no—
345Dic6—121no—
346Dic6—121no—
347Dic6—121no—
348Dic6—121no—
349C3×C8—24no—
350C3×C8—22no—
351C3×C8—22no—
352C3×C8—62no—
353C3×C8—121no—
354C3×C8—121no—
355C3⋊C8—22no—
356C3⋊C8—41no—
357C3⋊C8—41no—
358C2×C32—21no—
359C2×C32—21no—
360C2×C32#39411yescharacteristic
361C2×C32#47111yescharacteristic
362C2×C32#47311yescharacteristic
363C3⋊D3—81no—
364#41—181no—
365#41—181no—
366#41—181no—
367#41—181no—
368C2×Q8—92no—
369C2×Q8—91no—
370C2×Q8—181no—
371C2×Q8—181no—
372C2×Q8—181no—
373C2×Q8—181no—
374C2×Q8—181no—
375C2×D4—91no—
376C2×D4—181no—
377C22×C4—61no—
378C22×C4—181no—
379C22×C4—181no—
380C22×C4C2×D3211yescharacteristic
381Q16—184no—
382SD16—184no—
383M16—21no—
384M16—61no—
385M16—61no—
386M16—61no—
387M16—61no—
388M16#62612yes—
389C2×C8—21no—
390C2×C8—32no—
391C2×C8—61no—
392C2×C8—61no—
393C2×C8—61no—
394C2×C8—61no—
395C4⋊C4—61no—
396C4⋊C4—61no—
397C22×C3—21no—
398C22×C3—21no—
399C22×C3—21no—
400C22×C3—21no—
401C22×C3—21no—
402C22×C3—21no—
403C22×C3—21no—
404C22×C3—41no—
405C22×C3—41no—
406C22×C3#87511yescharacteristic
407C22×C3#88411yescharacteristic
408C22×C3#89411yescharacteristic
409C22×C3#89411yescharacteristic
410C22×C3#89511yescharacteristic
411C22×C3#94711yescharacteristic
412C2×D3—122no—
413C2×D3—121no—
414C2×D3—121no—
415C2×D3—121no—
416C2×D3—121no—
417C2×D3—121no—
418C2×D3—121no—
419C2×D3—241no—
420C2×D3—241no—
421C3×C4—21no—
422C3×C4—21no—
423C3×C4—21no—
424C3×C4—21no—
425C3×C4—241no—
426C3×C4#88211yescharacteristic
427C3×C4#88411yescharacteristic
428C3×C4#89411yescharacteristic
429C3×C4#89411yescharacteristic
430C3×C4#89511yescharacteristic
431C3×C4#89511yescharacteristic
432C3×C4#93011yescharacteristic
433C3×C4#93711yescharacteristic
434Dic3—81no—
435Dic3—124no—
436Dic3—122no—
437Dic3—122no—
438Dic3—121no—
439Dic3—122no—
440Dic3—121no—
441C32#205211yescharacteristic, complemented, Sylow
442C23—181no—
443C23#379911yescharacteristic
444Q8—181no—
445Q8—182no—
446Q8—182no—
447Q8—181no—
448Q8—361no—
449Q8—361no—
450D4—181no—
451D4—181no—
452D4—361no—
453D4—361no—
454C2×C4—121no—
455C2×C4—182no—
456C2×C4—181no—
457C2×C4—241no—
458C2×C4—361no—
459C2×C4—361no—
460C2×C4—361no—
461C2×C4—361no—
462C2×C4#379911yescharacteristic
463C2×C4#379911yescharacteristic
464C2×C4D3×D1211yescharacteristic
465C2×C4C2×#62611yescharacteristic
466C2×C4#381111yescharacteristic
467C2×C4#381111yescharacteristic
468C8—22no—
469C8—62no—
470C8—121no—
471C8—121no—
472C2×C3—21no—
473C2×C3—21no—
474C2×C3—21no—
475C2×C3—21no—
476C2×C3—21no—
477C2×C3—21no—
478C2×C3—21no—
479C2×C3—41no—
480C2×C3—41no—
481C2×C3#467211yescharacteristic
482C2×C3#474811yescharacteristic
483C2×C3#475511yescharacteristic
484C2×C3#489611yescharacteristic
485C2×C3#489811yescharacteristic
486C2×C3#499111yescharacteristic
487D3—242no—
488D3—241no—
489D3—241no—
490C22—21no—
491C22—21no—
492C22—361no—
493C22—361no—
494C22—361no—
495C22#6386411yescharacteristic
496C22#6389711yescharacteristic
497C22#6391011yescharacteristic
498C4—241no—
499C4—361no—
500C4—362no—
501C4#6389711yescharacteristic
502C4#6390911yescharacteristic
503C4#6391011yescharacteristic
504C4#6398111yescharacteristic
505C3—21no—
506C3#6898711yescharacteristic, complemented
507C3#7071611yescharacteristic, complemented
508C2—21no—
509C2—21no—
510C2—721no—
511C2#1059098911yescharacteristic
512C2#1059099211yescharacteristic
513C2#1059132111yescharacteristic
subgroupG/H
centerC22#63910
commutator, cosocleC22×C32×C4C23
FrattiniC22×C4C2×D32
FittingC2×C32×M16C22
socleC22×C32#121
prime radicalC2×#3828C22
hypercenterC2×M16D32
hypocenterC32#2052
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. C2×C3×#822C2semidirect
4. C2×#63567C2semidirect
5. C2×#63561C2semidirect
7. C3×#4554C2semidirect
35. C2×#822D3semidirect
41. #4554D3semidirect
441. C32#2052semidirect
506. C3#68987semidirect
507. C3#70716semidirect

Maximal subgroups

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

subgroupindex
C2×#641182
C2×C3×#8222
#105911062
C2×#635672
C2×#635612
#105910732
C3×#45542
#707163
#689873