Finite Group Databasebeta

← #11793945

Subgroups — #11793945

Order 1152.

605 conjugacy classes of subgroups.

The subgroup lattice has 502 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#951C211yesmaximal, characteristic
2#10592931C211yesmaximal, characteristic
3C3×#5234C211yesmaximal, characteristic
4C2×#63577C211yesmaximal, characteristic, complemented
5C2×#63566C211yesmaximal, characteristic, complemented
6C2×#63560C211yesmaximal, characteristic, complemented
7#10589168C211yesmaximal, characteristic, complemented
8#72105—31nomaximal
9#70004—31nomaximal
10C2×C32×#41C2211yescharacteristic
11C22×C3×Dic6C2211yescharacteristic
12C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
13C2×#3748C2211yescharacteristic
14C3×#951—22no—
15C3×#951—22no—
16C2×C3×#216—21no—
17C2×C3×#214—21no—
18C2×C3×#208C2211yescharacteristic
19C2×C3×#208C2211yescharacteristic
20C22×C3×C3⋊C8C2211yescharacteristic
21#63662—21no—
22#63659—21no—
23C3×#830—22no—
24#63577—22no—
25#63566—22no—
26#63560—22no—
27C2×C3×#137—31no—
28C2×#951D311yescharacteristic
29C3×#408—31no—
30#5234D311yescharacteristic
31#5232—31no—
32#5232—31no—
33#5232—61no—
34C2×#836—31no—
35C2×#835—31no—
36C2×#824—31no—
37C2×#822—31no—
38C2×#819—31no—
39C2×#816—31no—
40#4554—31no—
41#4554—31no—
42C32×#41—21no—
43C32×#41—21no—
44C32×#41—21no—
45C32×#41—21no—
46C2×C32×Q8D411yescharacteristic
47C2×C32×D4—21no—
48C2×C32×D4D411yescharacteristic
49C22×C32×C4—21no—
50C22×C32×C4C2311yescharacteristic
51C22×C3⋊Dic3—21no—
52C22×C3×Dic3—21no—
53C2×C3×Dic6—21no—
54C2×C3×Dic6—21no—
55C2×C3×Dic6—21no—
56C2×C3×Dic6—21no—
57C2×C3×Dic6—21no—
58C2×C3×Dic6D412yes—
59C4⋊(C3⋊Dic3)—21no—
60C4⋊(C3⋊Dic3)—21no—
61#3748—21no—
62#3748—21no—
63C2×C3⋊(C3⋊C8)—21no—
64C3×#216—24no—
65C3×#214—24no—
66C3×#208—21no—
67C3×#208—21no—
68C3×#208—21no—
69C3×#208D412yes—
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×C3×#41—21no—
77C2×C3×#41C2×D311yescharacteristic
78C2×C3×#41C2×D311yescharacteristic
79C22×C3×Q8—31no—
80C22×Dic6C2×D311yescharacteristic
81C3×#137—62no—
82C3×#137—62no—
83C2×C3×Q16—61no—
84C2×C3×SD16—61no—
85C2×C3×M16—31no—
86C2×C3×M16—31no—
87C22×C3×C8—31no—
88#951—22no—
89#951—22no—
90C2×#216—21no—
91C2×#214—21no—
92C2×C4⋊Dic3—31no—
93C2×C4⋊Dic3—31no—
94C2×C4⋊Dic3—61no—
95C2×#208—31no—
96C2×#208—31no—
97C2×#208—61no—
98C2×#208C2×D311yescharacteristic
99C2×#208C2×D311yescharacteristic
100C22×C3⋊C8C2×D311yescharacteristic
101C3×C22⋊C8—62no—
102#836—62no—
103#835—62no—
104#835—61no—
105#835—61no—
106#835—62no—
107#832—62no—
108#832—61no—
109#832—61no—
110#830—22no—
111#824—62no—
112#822—62no—
113#819—62no—
114#816—62no—
115C23×C32—21no—
116C23×C32#4111yescharacteristic
117C32×Q8—21no—
118C32×Q8—21no—
119C32×D4—21no—
120C32×D4—21no—
121C32×D4—41no—
122C32×D4—41no—
123C2×C32×C4—21no—
124C2×C32×C4—41no—
125C2×C32×C4—41no—
126C2×C32×C4C2×D411yescharacteristic
127C2×C32×C4C2×D411yescharacteristic
128C2×C32×C4C2×D411yescharacteristic
129C2×C32×C4C2×D411yescharacteristic
130C2×C32×C4#4111yescharacteristic
131C2×C32×C4#4111yescharacteristic
132C2×C3⋊Dic3—41no—
133C2×C3⋊Dic3—81no—
134C2×C3×Dic3—22no—
135C2×C3×Dic3—41no—
136C2×C3×Dic3—41no—
137C3×Dic6—22no—
138C3×Dic6—22no—
139C3×Dic6—41no—
140C3×Dic6—41no—
141C3⋊(C3⋊C8)—41no—
142C3×C3⋊C8—22no—
143C3×C3⋊C8—22no—
144C3×C3⋊C8—41no—
145C2×#137—31no—
146C2×#108—91no—
147#417—91no—
148C2×#103—91no—
149C2×#101—91no—
150#408—31no—
151#343—91no—
152C3×#41—22no—
153C3×#41—22no—
154C3×#41—21no—
155C3×#41—21no—
156C3×#41—21no—
157C3×#41—21no—
158C3×#41—21no—
159C3×#41—21no—
160C3×#41—21no—
161C3×#41—21no—
162C3×#41—41no—
163C3×#41—41no—
164C2×C3×Q8—21no—
165C2×C3×Q8—32no—
166C2×C3×Q8—61no—
167C2×C3×Q8—61no—
168C2×C3×Q8—61no—
169C2×C3×Q8—61no—
170C2×C3×Q8—61no—
171C2×C3×Q8D1211yescharacteristic
172C2×C3×Q8#6711yescharacteristic
173C2×C3×D4—21no—
174C2×C3×D4—21no—
175C2×C3×D4—21no—
176C2×C3×D4—41no—
177C2×C3×D4D1211yescharacteristic
178C2×C3×D4#6711yescharacteristic
179C22×C3×C4—21no—
180C22×C3×C4—21no—
181C22×C3×C4—21no—
182C22×C3×C4—41no—
183C22×C3×C4—61no—
184C22×C3×C4C22×D311yescharacteristic
185C22×C3×C4C22×D311yescharacteristic
186C22×Dic3—21no—
187C22×Dic3—61no—
188C22×Dic3—61no—
189C22×Dic3—121no—
190C2×Dic6—21no—
191C2×Dic6—21no—
192C2×Dic6—21no—
193C2×Dic6—21no—
194C2×Dic6—21no—
195C2×Dic6#6712yes—
196C3×Q16—64no—
197C3×SD16—64no—
198C3×M16—32no—
199C3×M16—61no—
200C3×M16—61no—
201C3×M16—61no—
202C2×C3×C8—32no—
203C2×C3×C8—61no—
204C2×C3×C8—61no—
205C2×C3×C8—61no—
206C2×C3×C8—61no—
207#216—24no—
208#214—24no—
209C4⋊Dic3—62no—
210C4⋊Dic3—61no—
211C4⋊Dic3—61no—
212C4⋊Dic3—61no—
213C4⋊Dic3—61no—
214C4⋊Dic3—121no—
215#208—21no—
216#208—21no—
217#208—21no—
218#208—61no—
219#208—61no—
220#208—61no—
221#208—61no—
222#208—121no—
223#208—121no—
224#208#6712yes—
225C2×C3⋊C8—21no—
226C2×C3⋊C8—21no—
227C2×C3⋊C8—21no—
228C2×C3⋊C8—21no—
229C2×C3⋊C8—62no—
230C2×C3⋊C8—61no—
231C2×C3⋊C8—61no—
232C2×C3⋊C8#6712yes—
233C22×C32—21no—
234C22×C32—21no—
235C22×C32—41no—
236C22×C32—41no—
237C22×C32—41no—
238C22×C32#12111yescharacteristic
239C22×C32#12311yescharacteristic
240C22×C32#12411yescharacteristic
241C32×C4—41no—
242C32×C4#12011yescharacteristic
243C32×C4#12111yescharacteristic
244C32×C4#12111yescharacteristic
245C32×C4#12311yescharacteristic
246C3⋊Dic3—81no—
247C3×Dic3—42no—
248C2×#41D3211yescharacteristic
249C22×Q8—31no—
250#137—62no—
251#137—62no—
252C2×Q16—61no—
253C2×SD16—61no—
254C2×M16—31no—
255C2×M16—31no—
256C2×M16—91no—
257C22×C8—31no—
258C2×C4⋊C4—91no—
259#108—182no—
260#103—182no—
261#103—181no—
262#102—181no—
263#101—182no—
264C22⋊C8—62no—
265C23×C3—21no—
266C23×C3—21no—
267C23×C3—21no—
268C23×C3—41no—
269C23×C3#23511yescharacteristic
270C23×C3#23711yescharacteristic
271C3×Q8—22no—
272C3×Q8—21no—
273C3×Q8—21no—
274C3×Q8—21no—
275C3×Q8—21no—
276C3×Q8—41no—
277C3×Q8—62no—
278C3×Q8—62no—
279C3×Q8—121no—
280C3×Q8—121no—
281C3×D4—22no—
282C3×D4—21no—
283C3×D4—21no—
284C3×D4—21no—
285C3×D4—21no—
286C3×D4—41no—
287C3×D4—42no—
288C3×D4—42no—
289C3×D4—41no—
290C3×D4—41no—
291C3×D4—41no—
292C3×D4—41no—
293C2×C3×C4—21no—
294C2×C3×C4—21no—
295C2×C3×C4—21no—
296C2×C3×C4—21no—
297C2×C3×C4—21no—
298C2×C3×C4—21no—
299C2×C3×C4—21no—
300C2×C3×C4—21no—
301C2×C3×C4—41no—
302C2×C3×C4—42no—
303C2×C3×C4—42no—
304C2×C3×C4—41no—
305C2×C3×C4—41no—
306C2×C3×C4—41no—
307C2×C3×C4—41no—
308C2×C3×C4—62no—
309C2×C3×C4—121no—
310C2×C3×C4—121no—
311C2×C3×C4C2×D1211yescharacteristic
312C2×C3×C4D3×D411yescharacteristic
313C2×C3×C4D3×D411yescharacteristic
314C2×C3×C4D3×D411yescharacteristic
315C2×C3×C4#23711yescharacteristic
316C2×C3×C4#23711yescharacteristic
317C2×C3×C4#23711yescharacteristic
318C2×C3×C4#23711yescharacteristic
319C2×C3×C4C2×#6711yescharacteristic
320C2×C3×C4C2×#6711yescharacteristic
321C2×C3×C4C2×#6711yescharacteristic
322C2×C3×C4C2×#6711yescharacteristic
323C2×Dic3—22no—
324C2×Dic3—41no—
325C2×Dic3—41no—
326C2×Dic3—122no—
327C2×Dic3—121no—
328C2×Dic3—121no—
329C2×Dic3—242no—
330C2×Dic3—241no—
331C2×Dic3—241no—
332Dic6—22no—
333Dic6—22no—
334Dic6—41no—
335Dic6—41no—
336C3×C8—62no—
337C3×C8—62no—
338C3×C8—121no—
339C3⋊C8—22no—
340C3⋊C8—22no—
341C3⋊C8—41no—
342C3⋊C8—122no—
343C3⋊C8—121no—
344C3⋊C8—121no—
345C2×C32—21no—
346C2×C32—21no—
347C2×C32—81no—
348C2×C32#39411yescharacteristic
349C2×C32#47111yescharacteristic
350C2×C32#47311yescharacteristic
351#41—21no—
352#41—21no—
353#41—21no—
354#41—21no—
355C2×Q8—32no—
356C2×Q8—61no—
357C2×Q8—61no—
358C2×Q8—61no—
359C2×Q8—61no—
360C2×Q8—61no—
361C2×Q8#62611yescharacteristic
362C2×D4—21no—
363C2×D4#62611yescharacteristic
364C22×C4—21no—
365C22×C4—61no—
366C22×C4—181no—
367C22×C4C2×D3211yescharacteristic
368Q16—64no—
369SD16—64no—
370M16—32no—
371M16—61no—
372M16—61no—
373M16—61no—
374M16—181no—
375M16—181no—
376C2×C8—32no—
377C2×C8—61no—
378C2×C8—61no—
379C2×C8—61no—
380C2×C8—61no—
381C2×C8—181no—
382C4⋊C4—181no—
383C4⋊C4—181no—
384C22×C3—21no—
385C22×C3—21no—
386C22×C3—21no—
387C22×C3—21no—
388C22×C3—21no—
389C22×C3—21no—
390C22×C3—21no—
391C22×C3—41no—
392C22×C3—41no—
393C22×C3—42no—
394C22×C3—41no—
395C22×C3—41no—
396C22×C3—41no—
397C22×C3—41no—
398C22×C3—41no—
399C22×C3—41no—
400C22×C3—81no—
401C22×C3—81no—
402C22×C3#88311yescharacteristic
403C22×C3#88511yescharacteristic
404C22×C3#93011yescharacteristic
405C22×C3#93511yescharacteristic
406C22×C3#93611yescharacteristic
407C22×C3#93911yescharacteristic
408C3×C4—21no—
409C3×C4—21no—
410C3×C4—21no—
411C3×C4—21no—
412C3×C4—42no—
413C3×C4—41no—
414C3×C4—41no—
415C3×C4—122no—
416C3×C4#88211yescharacteristic
417C3×C4#88611yescharacteristic
418C3×C4#93511yescharacteristic
419C3×C4#93811yescharacteristic
420C3×C4#93811yescharacteristic
421C3×C4#93911yescharacteristic
422C3×C4#93911yescharacteristic
423C3×C4#95311yescharacteristic
424Dic3—42no—
425Dic3—242no—
426Dic3—241no—
427Dic3—241no—
428C32#205211yescharacteristic, complemented, Sylow
429C23—21no—
430C23#380411yescharacteristic
431Q8—21no—
432Q8—21no—
433Q8—62no—
434Q8—62no—
435Q8—121no—
436Q8—121no—
437D4—21no—
438D4—21no—
439D4—41no—
440D4—41no—
441C2×C4—21no—
442C2×C4—41no—
443C2×C4—41no—
444C2×C4—62no—
445C2×C4—121no—
446C2×C4—121no—
447C2×C4—361no—
448C2×C4—721no—
449C2×C4#380511yescharacteristic
450C2×C4#380511yescharacteristic
451C2×C4C2×#62611yescharacteristic
452C2×C4D3×#6711yescharacteristic
453C2×C4D3×#6711yescharacteristic
454C2×C4D3×#6711yescharacteristic
455C8—62no—
456C8—62no—
457C8—121no—
458C8—361no—
459C2×C3—21no—
460C2×C3—21no—
461C2×C3—21no—
462C2×C3—21no—
463C2×C3—21no—
464C2×C3—21no—
465C2×C3—21no—
466C2×C3—41no—
467C2×C3—41no—
468C2×C3—82no—
469C2×C3—81no—
470C2×C3—81no—
471C2×C3#496111yescharacteristic
472C2×C3#514111yescharacteristic
473C2×C3#514311yescharacteristic
474C2×C3#520311yescharacteristic
475C2×C3#520411yescharacteristic
476C2×C3#522211yescharacteristic
477C22—21no—
478C22—21no—
479C22—41no—
480C22—41no—
481C22—41no—
482C22#6395911yescharacteristic
483C22#6396911yescharacteristic
484C22#6397811yescharacteristic
485C4—41no—
486C4—122no—
487C4—721no—
488C4#6396211yescharacteristic
489C4#6397011yescharacteristic
490C4#6397011yescharacteristic
491C4#6397711yescharacteristic
492C3—21no—
493C3#7000411yescharacteristic, complemented
494C3#7210511yescharacteristic, complemented
495C2—21no—
496C2—21no—
497C2—81no—
498C2#1059168011yescharacteristic
499C2#1059168211yescharacteristic
500C2#1059170911yescharacteristic
subgroupG/H
centerC22#63978
commutator, cosocleC22×C32×C4C23
FrattiniC22×C4C2×D32
Fitting, prime radicalC2×C32×#41C22
socleC22×C32#121
hypercenterC2×#41D32
hypocenterC32#2052
LCSG ▷ C22×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×#41

Complements

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

NH ≅ G/Ntype
4. C2×#63577C2semidirect
5. C2×#63566C2semidirect
6. C2×#63560C2semidirect
7. #10589168C2semidirect
428. C32#2052semidirect
493. C3#70004semidirect
494. C3#72105semidirect

Maximal subgroups

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

subgroupindex
C2×C3×#9512
#105929312
C3×#52342
C2×#635772
C2×#635662
C2×#635602
#105891682
#721053
#700043