Finite Group Databasebeta

← #11792774

Subgroups — #11792774

Order 1152.

729 conjugacy classes of subgroups.

The subgroup lattice has 529 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#909C211yesmaximal, characteristic
2C22×#3718C211yesmaximal, characteristic, complemented
3C2×#63827C211yesmaximal, characteristic
4C2×C3×#824C211yesmaximal, characteristic, complemented
5C2×#63560C211yesmaximal, characteristic, complemented
6#10591071C211yesmaximal, characteristic
7#10589424C211yesmaximal, characteristic, complemented
8#72109—31nomaximal
9#70125—31nomaximal
10C2×C3×#235C2211yescharacteristic
11C22×C3×Dic6C2211yescharacteristic
12C22×C3×Dic6C2211yescharacteristic
13C2×C32×M16C2211yescharacteristic
14C2×#3748C2211yescharacteristic
15C22×C3⋊(C3⋊C8)C2211yescharacteristic
16C2×C3×#208C2211yescharacteristic
17C3×#909—22no—
18C3×#909—22no—
19C2×C3×Dic12—21no—
20C2×C3×#204—21no—
21C2×#3718—21no—
22C2×#3718—22no—
23C2×#3718—22no—
24C2×#3718—22no—
25#63827—22no—
26#63827—22no—
27C2×#3715—21no—
28C3×#824—22no—
29#63560—22no—
30(C2×D3)⋊(C3⋊C8)—22no—
31C2×C3×#137—31no—
32C2×#951—31no—
33C22×#216—31no—
34C22×#216—31no—
35C2×#942—31no—
36C2×#909D311yescharacteristic
37C2×C3×#101—31no—
38#5234—31no—
39C2×#836—31no—
40C2×#824—31no—
41C2×#824D311yescharacteristic, complemented
42#5129—31no—
43#4558—31no—
44#4558—31no—
45#4558—61no—
46C22×C32×C4C2311yescharacteristic
47C2×C3×#67—21no—
48C22×C3×Dic3—21no—
49C22×C3×Dic3—21no—
50C3×#235—21no—
51C3×#235—21no—
52C3×#235—21no—
53C3×#235—21no—
54C2×C3×D12D411yescharacteristic
55C2×C3×C4×D3—21no—
56C2×C3×Dic6—21no—
57C2×C3×Dic6—21no—
58C2×C3×Dic6—21no—
59C2×C3×Dic6—21no—
60C2×C3×Dic6—21no—
61C2×C3×Dic6—21no—
62C2×C3×Dic6—21no—
63C2×C3×Dic6—21no—
64C2×C3×Dic6—21no—
65C2×C3×Dic6—21no—
66C2×C3×Dic6D412yes—
67C2×C3×Dic6D411yescharacteristic
68C2×C3×Dic6D412yes—
69C32×M16—21no—
70C32×M16D412yes—
71C2×C32×C8—21no—
72#3748—21no—
73#3748D412yes—
74C2×C3⋊(C3⋊C8)—21no—
75C2×C3⋊(C3⋊C8)—21no—
76C2×C3⋊(C3⋊C8)—21no—
77C2×C3⋊(C3⋊C8)D412yes—
78C3×#208—21no—
79C3×#208—21no—
80C2×C3×C3⋊C8—21no—
81C3×Dic12—24no—
82C3×#204—24no—
83#3718—24no—
84#3718—28no—
85#3715—24no—
86#2020—91noSylow
87C2×C3×#41—31no—
88C22×C3×Q8—31no—
89C22×C3×Q8—31no—
90C2×#235C2×D311yescharacteristic
91C22×Dic6C2×D311yescharacteristic
92C22×Dic6C2×D311yescharacteristic
93C3×#137—62no—
94C3×#137—62no—
95C2×C3×Q16—61no—
96C2×C3×SD16—61no—
97C2×C3×M16—21no—
98C2×C3×M16—31no—
99C2×C3×M16C2×D311yescharacteristic
100C2×C3×M16C2×D311yescharacteristic
101#951—62no—
102#951—62no—
103C2×#216—62no—
104C2×#216—62no—
105C2×#216—62no—
106C2×#216—62no—
107C2×#216—61no—
108C2×#216—62no—
109C2×#216—61no—
110C2×#216—62no—
111#942—62no—
112#942—62no—
113C2×#215—61no—
114C2×#214—61no—
115C2×#208—31no—
116C2×#208—31no—
117C2×#208—61no—
118C2×#208C2×D311yescharacteristic
119C22×C3⋊C8—31no—
120C22×C3⋊C8—31no—
121C22×C3⋊C8—61no—
122#909—22no—
123#909—22no—
124C2×Dic12—21no—
125C2×#204—21no—
126C3×#101—62no—
127#836—62no—
128#830—62no—
129#824—22no—
130#824—62no—
131(C2×D3)⋊C8—62no—
132C23×C32#4111yescharacteristic
133C22×C3×D3—21no—
134C2×C32×C4C2×D411yescharacteristic
135C2×C32×C4C2×D411yescharacteristic
136C2×C32×C4C2×D411yescharacteristic
137C2×C32×C4C2×D411yescharacteristic
138C2×C32×C4C2×D411yescharacteristic
139C2×C32×C4C2×D411yescharacteristic
140C3×#67—41no—
141C3×#67—41no—
142C2×C3×Dic3—22no—
143C2×C3×Dic3—22no—
144C2×C3×Dic3—21no—
145C2×C3×Dic3—41no—
146C2×C3×Dic3—41no—
147C2×C3×Dic3—41no—
148C2×C3×Dic3—41no—
149C3×D12—21no—
150C3×D12—21no—
151C3×C4×D3—41no—
152C3×C4×D3—41no—
153C3×Dic6—22no—
154C3×Dic6—22no—
155C3×Dic6—22no—
156C3×Dic6—21no—
157C3×Dic6—22no—
158C3×Dic6—21no—
159C3×Dic6—41no—
160C3×Dic6—41no—
161C3×Dic6—41no—
162C3×Dic6—41no—
163C32×C8—22no—
164C3⋊(C3⋊C8)—22no—
165C3⋊(C3⋊C8)—22no—
166C3×C3⋊C8—41no—
167C2×#137—31no—
168C2×#137—91no—
169C22×Q16—91no—
170C2×#101—31no—
171C2×#101—91no—
172#408—91no—
173#341—91no—
174C3×#41—61no—
175C3×#41—61no—
176C3×#41—61no—
177C3×#41—61no—
178C2×C3×Q8—32no—
179C2×C3×Q8—31no—
180C2×C3×Q8—32no—
181C2×C3×Q8—61no—
182C2×C3×Q8—61no—
183C2×C3×Q8—61no—
184C2×C3×Q8—61no—
185C2×C3×Q8—61no—
186C2×C3×Q8—61no—
187C2×C3×Q8—61no—
188C2×C3×Q8—61no—
189C2×C3×Q8—61no—
190C2×C3×Q8—61no—
191C2×C3×D4—31no—
192C2×C3×D4—61no—
193C22×C3×C4—21no—
194C22×C3×C4—61no—
195C22×C3×C4—61no—
196C22×C3×C4—61no—
197C22×C3×C4C22×D311yescharacteristic
198C22×C3×C4C22×D311yescharacteristic
199C2×#67—21no—
200C22×Dic3—21no—
201C22×Dic3—21no—
202#235—21no—
203#235—21no—
204#235—21no—
205#235—21no—
206C2×D12#6711yescharacteristic
207C2×C4×D3—21no—
208C2×Dic6—21no—
209C2×Dic6—21no—
210C2×Dic6—21no—
211C2×Dic6—21no—
212C2×Dic6—21no—
213C2×Dic6—21no—
214C2×Dic6—21no—
215C2×Dic6—21no—
216C2×Dic6—21no—
217C2×Dic6—21no—
218C2×Dic6D1212yes—
219C2×Dic6#6711yescharacteristic
220C2×Dic6#6712yes—
221C3×Q16—64no—
222C3×SD16—64no—
223C3×M16—21no—
224C3×M16—21no—
225C3×M16—22no—
226C3×M16—41no—
227C3×M16—61no—
228C3×M16—61no—
229C3×M16#6712yes—
230C3×M16#6712yes—
231C2×C3×C8—21no—
232C2×C3×C8—21no—
233C2×C3×C8—41no—
234C2×C3×C8—61no—
235#216—64no—
236#216—68no—
237#216—68no—
238#216—64no—
239#215—64no—
240#214—64no—
241#208—21no—
242#208—21no—
243#208—32no—
244#208—32no—
245#208—62no—
246#208—61no—
247#208—61no—
248#208—121no—
249C2×C3⋊C8—21no—
250C2×C3⋊C8—32no—
251C2×C3⋊C8—32no—
252C2×C3⋊C8—62no—
253C2×C3⋊C8—61no—
254C2×C3⋊C8—61no—
255C2×C3⋊C8—61no—
256C2×C3⋊C8—61no—
257C2×C3⋊C8—61no—
258C2×C3⋊C8—61no—
259C2×C3⋊C8—121no—
260C2×C3⋊C8—121no—
261C2×C3⋊C8—121no—
262Dic12—24no—
263#204—24no—
264C22×C32—22no—
265C22×C32#12111yescharacteristic
266C22×C32#12111yescharacteristic
267C22×C32#12111yescharacteristic
268C2×C3×D3—41no—
269C2×C3×D3—42no—
270C32×C4#12011yescharacteristic
271C32×C4#12011yescharacteristic
272C32×C4#12011yescharacteristic
273C32×C4#12711yescharacteristic
274C3×Dic3—42no—
275C3×Dic3—42no—
276C3×Dic3—41no—
277C2×#41—31no—
278C22×Q8—31no—
279C22×Q8—31no—
280#137—62no—
281#137—62no—
282#137—182no—
283#137—182no—
284C2×Q16—61no—
285C2×Q16—182no—
286C2×Q16—182no—
287C2×Q16—182no—
288C2×Q16—181no—
289C2×SD16—61no—
290C2×SD16—181no—
291C2×M16—31no—
292C2×M16—91no—
293C2×M16D3211yescharacteristic
294C22×C8—91no—
295#101—62no—
296#101—182no—
297C22⋊C8—182no—
298C23×C3—21no—
299C23×C3—61no—
300C23×C3#23511yescharacteristic
301C23×C3#23711yescharacteristic
302C22×D3—21no—
303C3×Q8—62no—
304C3×Q8—61no—
305C3×Q8—62no—
306C3×Q8—62no—
307C3×Q8—62no—
308C3×Q8—61no—
309C3×Q8—121no—
310C3×Q8—121no—
311C3×Q8—121no—
312C3×Q8—121no—
313C3×D4—61no—
314C3×D4—61no—
315C3×D4—121no—
316C3×D4—121no—
317C2×C3×C4—21no—
318C2×C3×C4—21no—
319C2×C3×C4—21no—
320C2×C3×C4—21no—
321C2×C3×C4—21no—
322C2×C3×C4—21no—
323C2×C3×C4—61no—
324C2×C3×C4—62no—
325C2×C3×C4—62no—
326C2×C3×C4—121no—
327C2×C3×C4—121no—
328C2×C3×C4—121no—
329C2×C3×C4—121no—
330C2×C3×C4—121no—
331C2×C3×C4—121no—
332C2×C3×C4C2×D1211yescharacteristic
333C2×C3×C4D3×D411yescharacteristic
334C2×C3×C4D3×D411yescharacteristic
335C2×C3×C4D3×D411yescharacteristic
336C2×C3×C4D3×D411yescharacteristic
337C2×C3×C4D3×D411yescharacteristic
338C2×C3×C4D3×D411yescharacteristic
339C2×C3×C4D3×D411yescharacteristic
340C2×C3×C4C2×#6711yescharacteristic
341C2×C3×C4C2×#6711yescharacteristic
342C2×C3×C4C2×#6711yescharacteristic
343C2×C3×C4C2×#6711yescharacteristic
344#67—41no—
345#67—41no—
346C2×Dic3—22no—
347C2×Dic3—22no—
348C2×Dic3—21no—
349C2×Dic3—41no—
350C2×Dic3—41no—
351C2×Dic3—41no—
352C2×Dic3—41no—
353D12—21no—
354D12—21no—
355C4×D3—41no—
356C4×D3—41no—
357Dic6—22no—
358Dic6—22no—
359Dic6—22no—
360Dic6—21no—
361Dic6—22no—
362Dic6—21no—
363Dic6—41no—
364Dic6—41no—
365Dic6—41no—
366Dic6—41no—
367C3×C8—22no—
368C3×C8—22no—
369C3×C8—42no—
370C3×C8—121no—
371C3⋊C8—41no—
372C3⋊C8—62no—
373C3⋊C8—62no—
374C3⋊C8—62no—
375C3⋊C8—62no—
376C3⋊C8—122no—
377C3⋊C8—122no—
378C2×C32—21no—
379C2×C32—21no—
380C2×C32#39211yescharacteristic
381C2×C32#47312yes—
382C3×D3—81no—
383#41—61no—
384#41—61no—
385#41—61no—
386#41—61no—
387C2×Q8—32no—
388C2×Q8—31no—
389C2×Q8—32no—
390C2×Q8—61no—
391C2×Q8—61no—
392C2×Q8—61no—
393C2×Q8—61no—
394C2×Q8—61no—
395C2×Q8—61no—
396C2×Q8—61no—
397C2×Q8—61no—
398C2×Q8—61no—
399C2×Q8—61no—
400C2×D4—31no—
401C2×D4—61no—
402C22×C4—61no—
403C22×C4—61no—
404C22×C4—61no—
405C22×C4C2×D3211yescharacteristic
406Q16—64no—
407Q16—188no—
408Q16—184no—
409SD16—64no—
410SD16—184no—
411M16—21no—
412M16—61no—
413M16—61no—
414M16—92no—
415M16—181no—
416M16#62512yes—
417C2×C8—21no—
418C2×C8—61no—
419C2×C8—92no—
420C2×C8—181no—
421C2×C8—181no—
422C2×C8—181no—
423C22×C3—22no—
424C22×C3—22no—
425C22×C3—21no—
426C22×C3—21no—
427C22×C3—21no—
428C22×C3—42no—
429C22×C3—121no—
430C22×C3—122no—
431C22×C3#88411yescharacteristic
432C22×C3#88411yescharacteristic
433C22×C3#93011yescharacteristic
434C22×C3#93811yescharacteristic
435C22×C3#93911yescharacteristic
436C22×C3#93911yescharacteristic
437C2×D3—42no—
438C2×D3—41no—
439C3×C4—21no—
440C3×C4—21no—
441C3×C4—21no—
442C3×C4—21no—
443C3×C4—121no—
444C3×C4—122no—
445C3×C4—122no—
446C3×C4#88211yescharacteristic
447C3×C4#88211yescharacteristic
448C3×C4#93711yescharacteristic
449C3×C4#93711yescharacteristic
450C3×C4#93711yescharacteristic
451C3×C4#94011yescharacteristic
452C3×C4#94011yescharacteristic
453C3×C4#95311yescharacteristic
454Dic3—42no—
455Dic3—42no—
456Dic3—41no—
457C32#202011yescharacteristic, complemented, Sylow
458C23—61no—
459C23#379511yescharacteristic
460Q8—62no—
461Q8—62no—
462Q8—62no—
463Q8—61no—
464Q8—62no—
465Q8—61no—
466Q8—121no—
467Q8—121no—
468Q8—121no—
469Q8—121no—
470D4—61no—
471D4—61no—
472D4—121no—
473D4—121no—
474C2×C4—62no—
475C2×C4—61no—
476C2×C4—62no—
477C2×C4—121no—
478C2×C4—121no—
479C2×C4—121no—
480C2×C4—121no—
481C2×C4—121no—
482C2×C4—121no—
483C2×C4D3×D1211yescharacteristic
484C2×C4#380211yescharacteristic
485C2×C4#380211yescharacteristic
486C2×C4C2×#62511yescharacteristic
487C2×C4D3×#6711yescharacteristic
488C2×C4D3×#6711yescharacteristic
489C8—22no—
490C8—121no—
491C8—182no—
492C8—182no—
493C2×C3—21no—
494C2×C3—21no—
495C2×C3—21no—
496C2×C3—21no—
497C2×C3—22no—
498C2×C3—21no—
499C2×C3—41no—
500C2×C3—41no—
501C2×C3—241no—
502C2×C3#475512yes—
503C2×C3#496011yescharacteristic
504C2×C3#520412yes—
505C2×C3#522311yescharacteristic
506D3—81no—
507C22—22no—
508C22—122no—
509C22—121no—
510C22#6388511yescharacteristic
511C22#6388511yescharacteristic
512C22#6390811yescharacteristic
513C4—121no—
514C4—122no—
515C4—122no—
516C4#6391411yescharacteristic
517C4#6392211yescharacteristic
518C4#6392211yescharacteristic
519C4#6397611yescharacteristic
520C3—21no—
521C3#7012511yescharacteristic, complemented
522C3#7210911yescharacteristic, complemented
523C2—21no—
524C2—21no—
525C2—241no—
526C2#1059098112yes—
527C2#1059138911yescharacteristic
subgroupG/H
centerC22#63885
commutator, cosocleC22×C32×C4C23
FrattiniC22×C4C2×D32
FittingC2×C32×M16C22
socleC22×C32#121
prime radicalC2×C3×#235C22
hypercenterC2×M16D32
hypocenterC32#2020
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. C22×#3718C2semidirect
4. C2×C3×#824C2semidirect
5. C2×#63560C2semidirect
7. #10589424C2semidirect
41. C2×#824D3semidirect
457. C32#2020semidirect
521. C3#70125semidirect
522. C3#72109semidirect

Maximal subgroups

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

subgroupindex
C2×C3×#9092
C22×#37182
C2×#638272
C2×C3×#8242
C2×#635602
#105910712
#105894242
#721093
#701253