Finite Group Databasebeta

← #11793949

Subgroups — #11793949

Order 1152.

605 conjugacy classes of subgroups.

The subgroup lattice has 493 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#942C211yesmaximal, characteristic
2C2×#63662C211yesmaximal, characteristic, complemented
3C2×C3×#836C211yesmaximal, characteristic, complemented
4C2×#63578C211yesmaximal, characteristic, complemented
5#10591088C211yesmaximal, characteristic
6#10591071C211yesmaximal, characteristic
7#10589168C211yesmaximal, characteristic, complemented
8#72105—31nomaximal
9#70126—31nomaximal
10C22×C32×Q8C2211yescharacteristic
11C2×C3×#235C2211yescharacteristic
12C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
13C22×C3⋊(C3⋊C8)C2211yescharacteristic
14C2×C3×#216—21no—
15C3×#942—22no—
16C3×#942—22no—
17C2×C3×#215—21no—
18C2×C3×#208C2211yescharacteristic
19C2×C3×#208C2211yescharacteristic
20C2×C3×#208C2211yescharacteristic
21#63662—22no—
22C3×#836—22no—
23#63578—22no—
24#63566—21no—
25#63563—21no—
26(C2×D3)⋊(C3⋊C8)—22no—
27C2×C3×#137—31no—
28C2×#942D311yescharacteristic
29C2×C3×#101—31no—
30#5234—31no—
31#5232—31no—
32C2×#836D311yescharacteristic, complemented
33C2×#835—31no—
34C2×#835—31no—
35C2×#835—61no—
36#5133—31no—
37#5129—31no—
38C2×#822—31no—
39C2×#822—31no—
40#4554—31no—
41#4554—31no—
42C2×C32×Q8—21no—
43C2×C32×Q8—21no—
44C2×C32×Q8—21no—
45C2×C32×Q8—21no—
46C2×C32×Q8—21no—
47C2×C32×Q8D412yes—
48C22×C32×C4—21no—
49C22×C32×C4C2311yescharacteristic
50C22×C3⋊Dic3—21no—
51C2×C3×#67—21no—
52C3×#235—21no—
53C3×#235—21no—
54C3×#235—21no—
55C3×#235—21no—
56C2×C3×D12D411yescharacteristic
57C2×C3×C4×D3—21no—
58C2×C3×Dic6D411yescharacteristic
59C4⋊(C3⋊Dic3)—21no—
60C4⋊(C3⋊Dic3)—21no—
61C2×C3⋊(C3⋊C8)—21no—
62C2×C3⋊(C3⋊C8)—21no—
63C2×C3⋊(C3⋊C8)D412yes—
64C3×#216—24no—
65C3×#215—24no—
66C3×#208—21no—
67C3×#208—21no—
68C3×#208—21no—
69C3×#208—21no—
70C3×#208—21no—
71C3×#208D412yes—
72C2×C3×C3⋊C8—21no—
73C2×C3×C3⋊C8—21no—
74C2×C3×C3⋊C8—21no—
75#2052—91noSylow
76C2×C3×#41—31no—
77C22×C3×Q8—21no—
78C22×C3×Q8C2×D311yescharacteristic
79C22×C3×Q8C2×D311yescharacteristic
80C2×#235C2×D311yescharacteristic
81C3×#137—62no—
82C3×#137—62no—
83C2×C3×Q16—61no—
84C2×C3×SD16—61no—
85C2×C3×M16—31no—
86C2×C3×M16—31no—
87C2×C3×M16—31no—
88C2×#216—21no—
89#942—22no—
90#942—22no—
91C2×#215—21no—
92C2×C4⋊Dic3—31no—
93C2×C4⋊Dic3—31no—
94C2×C4⋊Dic3—61no—
95C2×#208C2×D311yescharacteristic
96C2×#208C2×D311yescharacteristic
97C2×#208C2×D311yescharacteristic
98C22×C3⋊C8—31no—
99C22×C3⋊C8—31no—
100C22×C3⋊C8—61no—
101C3×#101—62no—
102#836—22no—
103#835—61no—
104#835—62no—
105#835—62no—
106#835—64no—
107#832—61no—
108#830—62no—
109#822—62no—
110#822—62no—
111#821—61no—
112(C2×D3)⋊C8—62no—
113#816—61no—
114C23×C32#4111yescharacteristic
115C22×C3×D3—21no—
116C32×Q8—22no—
117C32×Q8—22no—
118C32×Q8—41no—
119C32×Q8—41no—
120C2×C32×C4—22no—
121C2×C32×C4—41no—
122C2×C32×C4—41no—
123C2×C32×C4C2×D411yescharacteristic
124C2×C32×C4C2×D411yescharacteristic
125C2×C32×C4C2×D411yescharacteristic
126C2×C32×C4C2×D411yescharacteristic
127C2×C32×C4#4111yescharacteristic
128C2×C32×C4#4111yescharacteristic
129C2×C3⋊Dic3—41no—
130C2×C3⋊Dic3—81no—
131C3×#67—41no—
132C3×#67—41no—
133C2×C3×Dic3—21no—
134C3×D12—21no—
135C3×D12—21no—
136C3×C4×D3—41no—
137C3×C4×D3—41no—
138C3×Dic6—21no—
139C3×Dic6—21no—
140C3⋊(C3⋊C8)—22no—
141C3×C3⋊C8—22no—
142C3×C3⋊C8—41no—
143C3×C3⋊C8—41no—
144C2×#137—31no—
145C2×#108—91no—
146#417—91no—
147C2×#103—91no—
148C2×#101—31no—
149#408—91no—
150#343—91no—
151C3×#41—61no—
152C3×#41—61no—
153C3×#41—61no—
154C3×#41—61no—
155C2×C3×Q8—21no—
156C2×C3×Q8—21no—
157C2×C3×Q8—22no—
158C2×C3×Q8—22no—
159C2×C3×Q8—21no—
160C2×C3×Q8—21no—
161C2×C3×Q8—21no—
162C2×C3×Q8—21no—
163C2×C3×Q8—21no—
164C2×C3×Q8—21no—
165C2×C3×Q8—21no—
166C2×C3×Q8—21no—
167C2×C3×Q8—22no—
168C2×C3×Q8—31no—
169C2×C3×Q8—41no—
170C2×C3×Q8—41no—
171C2×C3×Q8—41no—
172C2×C3×Q8#6712yes—
173C2×C3×Q8#6712yes—
174C2×C3×D4—31no—
175C2×C3×D4—61no—
176C22×C3×C4—21no—
177C22×C3×C4—21no—
178C22×C3×C4—21no—
179C22×C3×C4—41no—
180C22×C3×C4—61no—
181C22×C3×C4C22×D311yescharacteristic
182C22×C3×C4C22×D311yescharacteristic
183C2×#67—21no—
184C22×Dic3—61no—
185C22×Dic3—61no—
186C22×Dic3—121no—
187#235—21no—
188#235—21no—
189#235—21no—
190#235—21no—
191C2×D12#6711yescharacteristic
192C2×C4×D3—21no—
193C2×Dic6#6711yescharacteristic
194C3×Q16—64no—
195C3×SD16—64no—
196C3×M16—32no—
197C3×M16—61no—
198C3×M16—61no—
199C3×M16—61no—
200C3×M16—61no—
201C3×M16—61no—
202C2×C3×C8—61no—
203C2×C3×C8—61no—
204C2×C3×C8—61no—
205#216—24no—
206#215—24no—
207C4⋊Dic3—62no—
208C4⋊Dic3—61no—
209C4⋊Dic3—61no—
210C4⋊Dic3—61no—
211C4⋊Dic3—61no—
212C4⋊Dic3—121no—
213#208—21no—
214#208—21no—
215#208—21no—
216#208—21no—
217#208—21no—
218#208#6712yes—
219C2×C3⋊C8—21no—
220C2×C3⋊C8—21no—
221C2×C3⋊C8—21no—
222C2×C3⋊C8—32no—
223C2×C3⋊C8—32no—
224C2×C3⋊C8—62no—
225C2×C3⋊C8—61no—
226C2×C3⋊C8—61no—
227C2×C3⋊C8—61no—
228C2×C3⋊C8—61no—
229C2×C3⋊C8—121no—
230C2×C3⋊C8—121no—
231C22×C32—21no—
232C22×C32—21no—
233C22×C32#12111yescharacteristic
234C22×C32#12311yescharacteristic
235C22×C32#12411yescharacteristic
236C2×C3×D3—41no—
237C2×C3×D3—41no—
238C2×C3×D3—41no—
239C32×C4—42no—
240C32×C4#12011yescharacteristic
241C32×C4#12111yescharacteristic
242C32×C4#12111yescharacteristic
243C32×C4#12311yescharacteristic
244C3⋊Dic3—81no—
245C3×Dic3—41no—
246C2×#41—31no—
247C22×Q8D3211yescharacteristic
248#137—62no—
249#137—62no—
250C2×Q16—61no—
251C2×SD16—61no—
252C2×M16—31no—
253C2×M16—31no—
254C2×M16—31no—
255C22×C8—91no—
256C2×C4⋊C4—91no—
257#108—182no—
258#103—181no—
259#103—182no—
260#102—181no—
261#101—62no—
262C22⋊C8—182no—
263C23×C3—21no—
264C23×C3—61no—
265C23×C3#23511yescharacteristic
266C23×C3#23711yescharacteristic
267C22×D3—21no—
268C3×Q8—24no—
269C3×Q8—22no—
270C3×Q8—22no—
271C3×Q8—22no—
272C3×Q8—22no—
273C3×Q8—42no—
274C3×Q8—42no—
275C3×Q8—42no—
276C3×Q8—41no—
277C3×Q8—41no—
278C3×Q8—41no—
279C3×Q8—41no—
280C3×Q8—61no—
281C3×Q8—61no—
282C3×D4—61no—
283C3×D4—61no—
284C3×D4—121no—
285C3×D4—121no—
286C2×C3×C4—22no—
287C2×C3×C4—22no—
288C2×C3×C4—21no—
289C2×C3×C4—21no—
290C2×C3×C4—21no—
291C2×C3×C4—21no—
292C2×C3×C4—21no—
293C2×C3×C4—21no—
294C2×C3×C4—42no—
295C2×C3×C4—42no—
296C2×C3×C4—42no—
297C2×C3×C4—41no—
298C2×C3×C4—41no—
299C2×C3×C4—41no—
300C2×C3×C4—41no—
301C2×C3×C4—61no—
302C2×C3×C4—121no—
303C2×C3×C4—121no—
304C2×C3×C4#23511yescharacteristic
305C2×C3×C4D3×D411yescharacteristic
306C2×C3×C4D3×D411yescharacteristic
307C2×C3×C4D3×D411yescharacteristic
308C2×C3×C4D3×D411yescharacteristic
309C2×C3×C4#23711yescharacteristic
310C2×C3×C4#23711yescharacteristic
311C2×C3×C4#23711yescharacteristic
312C2×C3×C4C2×#6711yescharacteristic
313C2×C3×C4C2×#6711yescharacteristic
314C2×C3×C4C2×#6711yescharacteristic
315C2×C3×C4C2×#6711yescharacteristic
316#67—41no—
317#67—41no—
318C2×Dic3—21no—
319C2×Dic3—122no—
320C2×Dic3—121no—
321C2×Dic3—121no—
322C2×Dic3—242no—
323C2×Dic3—241no—
324C2×Dic3—241no—
325D12—21no—
326D12—21no—
327C4×D3—41no—
328C4×D3—41no—
329Dic6—21no—
330Dic6—21no—
331C3×C8—62no—
332C3×C8—121no—
333C3×C8—121no—
334C3⋊C8—22no—
335C3⋊C8—41no—
336C3⋊C8—41no—
337C3⋊C8—62no—
338C3⋊C8—62no—
339C3⋊C8—122no—
340C2×C32—21no—
341C2×C32—21no—
342C2×C32#39411yescharacteristic
343C2×C32#47111yescharacteristic
344C2×C32#47311yescharacteristic
345C3×D3—81no—
346#41—61no—
347#41—61no—
348#41—61no—
349#41—61no—
350C2×Q8—21no—
351C2×Q8—21no—
352C2×Q8—21no—
353C2×Q8—21no—
354C2×Q8—21no—
355C2×Q8—31no—
356C2×Q8#62512yes—
357C2×D4—31no—
358C2×D4—61no—
359C22×C4—21no—
360C22×C4—61no—
361C22×C4—181no—
362C22×C4C2×D3211yescharacteristic
363Q16—64no—
364SD16—64no—
365M16—32no—
366M16—61no—
367M16—61no—
368M16—61no—
369M16—61no—
370M16—61no—
371C2×C8—61no—
372C2×C8—61no—
373C2×C8—61no—
374C2×C8—92no—
375C2×C8—181no—
376C2×C8—181no—
377C4⋊C4—181no—
378C4⋊C4—181no—
379C22×C3—22no—
380C22×C3—22no—
381C22×C3—21no—
382C22×C3—21no—
383C22×C3—21no—
384C22×C3—21no—
385C22×C3—21no—
386C22×C3—21no—
387C22×C3—21no—
388C22×C3—121no—
389C22×C3—121no—
390C22×C3—121no—
391C22×C3#88411yescharacteristic
392C22×C3#88511yescharacteristic
393C22×C3#92911yescharacteristic
394C22×C3#93511yescharacteristic
395C22×C3#93611yescharacteristic
396C22×C3#93911yescharacteristic
397C2×D3—41no—
398C2×D3—41no—
399C2×D3—41no—
400C3×C4—21no—
401C3×C4—21no—
402C3×C4—21no—
403C3×C4—21no—
404C3×C4—44no—
405C3×C4—42no—
406C3×C4—42no—
407C3×C4—121no—
408C3×C4#88311yescharacteristic
409C3×C4#88411yescharacteristic
410C3×C4#93511yescharacteristic
411C3×C4#93711yescharacteristic
412C3×C4#93811yescharacteristic
413C3×C4#93911yescharacteristic
414C3×C4#93911yescharacteristic
415C3×C4#95311yescharacteristic
416Dic3—41no—
417Dic3—242no—
418Dic3—241no—
419Dic3—241no—
420C32#205211yescharacteristic, complemented, Sylow
421C23—61no—
422C23#380411yescharacteristic
423Q8—22no—
424Q8—22no—
425Q8—41no—
426Q8—41no—
427Q8—61no—
428Q8—61no—
429D4—61no—
430D4—61no—
431D4—121no—
432D4—121no—
433C2×C4—22no—
434C2×C4—41no—
435C2×C4—41no—
436C2×C4—61no—
437C2×C4—121no—
438C2×C4—121no—
439C2×C4—361no—
440C2×C4—721no—
441C2×C4#380411yescharacteristic
442C2×C4#380511yescharacteristic
443C2×C4C2×#62511yescharacteristic
444C2×C4D3×#6711yescharacteristic
445C2×C4D3×#6711yescharacteristic
446C2×C4#381111yescharacteristic
447C8—62no—
448C8—121no—
449C8—121no—
450C8—182no—
451C2×C3—22no—
452C2×C3—22no—
453C2×C3—21no—
454C2×C3—21no—
455C2×C3—21no—
456C2×C3—21no—
457C2×C3—21no—
458C2×C3—21no—
459C2×C3—21no—
460C2×C3—241no—
461C2×C3#475411yescharacteristic
462C2×C3#475511yescharacteristic
463C2×C3#495911yescharacteristic
464C2×C3#520311yescharacteristic
465C2×C3#520411yescharacteristic
466C2×C3#522211yescharacteristic
467D3—81no—
468C22—21no—
469C22—21no—
470C22—121no—
471C22—121no—
472C22—121no—
473C22#6395911yescharacteristic
474C22#6396111yescharacteristic
475C22#6397111yescharacteristic
476C4—42no—
477C4—121no—
478C4—721no—
479C4#6395811yescharacteristic
480C4#6396911yescharacteristic
481C4#6397611yescharacteristic
482C4#6398011yescharacteristic
483C3—21no—
484C3#7012611yescharacteristic, complemented
485C3#7210511yescharacteristic, complemented
486C2—21no—
487C2—21no—
488C2—241no—
489C2#1059164311yescharacteristic
490C2#1059164411yescharacteristic
491C2#1059170811yescharacteristic
subgroupG/H
centerC22#63971
commutator, cosocleC22×C32×C4C23
FrattiniC22×C4C2×D32
FittingC22×C32×Q8C22
socleC22×C32#121
prime radicalC2×C3×#235C22
hypercenterC22×Q8D32
hypocenterC32#2052
LCSG ▷ C22×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×Q8

Complements

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

NH ≅ G/Ntype
2. C2×#63662C2semidirect
3. C2×C3×#836C2semidirect
4. C2×#63578C2semidirect
7. #10589168C2semidirect
32. C2×#836D3semidirect
420. C32#2052semidirect
484. C3#70126semidirect
485. C3#72105semidirect

Maximal subgroups

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

subgroupindex
C2×C3×#9422
C2×#636622
C2×C3×#8362
C2×#635782
#105910882
#105910712
#105891682
#721053
#701263