Finite Group Databasebeta

← #11896074

Subgroups — #11896074

Order 1152.

730 conjugacy classes of subgroups.

The subgroup lattice has 507 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#5732C211yesmaximal, characteristic
2#10593856C211yesmaximal, characteristic, complemented
3#10592789C211yesmaximal, characteristic, complemented
4C3×#5079C211yesmaximal, characteristic, complemented
5#10591624C212yesmaximal
6#10591577C212yesmaximal
7#10591544C212yesmaximal, complemented
8#10591541C212yesmaximal, complemented
9C4×#3716C211yesmaximal, characteristic
10#10590266C211yesmaximal, characteristic
11#10590258C211yesmaximal, characteristic, complemented
12#83677—31nomaximal
13#81626—31nomaximal
14C32×C4⋊Q8C2211yescharacteristic
15C2×#3756C2212yes—
16C4×#634C2211yescharacteristic
17C3×#947C2212yes—
18C3×Q8×Dic3C2212yes—
19C3×#898—22no—
20C3×#897—21no—
21C3×#892—21no—
22C3×C4×D12C2211yescharacteristic
23C3×#869C2211yescharacteristic
24C3×C4×Dic6C2211yescharacteristic
25#63919—21no—
26#63918C2212yes—
27#63844C2212yes—
28#63843—21no—
29#63839—22no—
30C2×#3716C2211yescharacteristic
31#63662C2212yes—
32C4⋊(C3⋊(C3⋊C8))C2211yescharacteristic
33C3×#835C2212yes—
34C3×#835C2212yes—
35C3×C4×C3⋊C8C2211yescharacteristic
36#63574C2212yes—
37#63573C2211yescharacteristic
38Dic3⋊(C3⋊C8)C2212yes—
39#63567C2211yescharacteristic
40#63563C2211yescharacteristic
41#63562C2212yes—
42#63554C2212yes—
43C3×#556—31no—
44#5732D311yescharacteristic
45#5722—31no—
46Q8×Dic6—31no—
47C3×#487—31no—
48#5090—31no—
49#5090—31no—
50#5090—61no—
51#5084—31no—
52#5079D311yescharacteristic, complemented
53#5055—32no—
54#5054—32no—
55#5030—32no—
56#5024—31no—
57#5020—32no—
58C4×#214—31no—
59#5008—31no—
60#4798—32no—
61#4794—32no—
62#4791—32no—
63#4789—32no—
64C4×#204—31no—
65#4679—31no—
66C2×C32×Q8C2312yes—
67C2×#634C2311yescharacteristic
68C2×C3×D12C2311yescharacteristic
69C2×C3×C4×D3—21no—
70C2×C3×Dic6—21no—
71C2×C3×Dic6D411yescharacteristic
72C2×#627—22no—
73C32×C4⋊C4—21no—
74C32×C4⋊C4—21no—
75C32×C42C2311yescharacteristic
76#3756—24no—
77C4⋊(C3⋊Dic3)C2311yescharacteristic
78#3750—21no—
79C4×C3⋊Dic3—21no—
80C2×C3⋊(C3⋊C8)C2312yes—
81C3×(C2×D3)⋊C4—21no—
82C3×(C2×D3)⋊C4—22no—
83C3×(C2×D3)⋊C4—22no—
84C3×C4⋊Dic3—21no—
85C3×C4⋊Dic3—22no—
86C3×C4⋊Dic3D411yescharacteristic
87C3×C4⋊Dic3C2311yescharacteristic
88C3×C4⋊Dic3C2312yes—
89C3×Dic3⋊C4D412yes—
90C3×C4×Dic3—22no—
91C3×C4×Dic3C2312yes—
92C2×C3×C3⋊C8C2311yescharacteristic
93C2×C3×C3⋊C8C2311yescharacteristic
94#3724—22no—
95Dic3⋊Dic3—22no—
96Dic32—22no—
97#3716—22no—
98#3369—91noSylow
99C3×C4⋊Q8—21no—
100C3×C4⋊Q8—31no—
101C3×C4⋊Q8C2×D311yescharacteristic
102C3×C4⋊Q8C2×D311yescharacteristic
103C3×#126—62no—
104C3×#124—32no—
105C3×C22⋊Q8—61no—
106C3×C4×Q8—31no—
107C3×C4×Q8—32no—
108C3×C4×D4—31no—
109C3×#117—61no—
110#947C2×D312yes—
111Q8×Dic3—61no—
112Q8×Dic3C2×D312yes—
113#944—62no—
114C2×#216—32no—
115C2×#216—32no—
116C2×#216—62no—
117C2×#214—31no—
118C2×#204—31no—
119#898—22no—
120#897—21no—
121#892—21no—
122#888—32no—
123#888—61no—
124#888—62no—
125#888—61no—
126#887—32no—
127#887—61no—
128C4×D12C2×D311yescharacteristic
129#869—32no—
130#869C2×D311yescharacteristic
131C4×Dic6—31no—
132C4×Dic6—31no—
133C4×Dic6—32no—
134C4×Dic6—61no—
135C4×Dic6C2×D311yescharacteristic
136C3×#103—32no—
137C3×#103—32no—
138C3×C4×C8—31no—
139#835—32no—
140#835—32no—
141#835—62no—
142#835C2×D312yes—
143#835C2×D312yes—
144#832—32no—
145#832—31no—
146#821—31no—
147#817—31no—
148#816—31no—
149#815—32no—
150Dic3⋊C8—32no—
151#810—31no—
152#809—32no—
153#808—32no—
154#808—32no—
155#808—31no—
156C4⋊(C3⋊C8)—31no—
157C4⋊(C3⋊C8)—31no—
158C4⋊(C3⋊C8)—32no—
159C4⋊(C3⋊C8)—61no—
160#803—32no—
161C4×C3⋊C8C2×D311yescharacteristic
162C22×C3×D3—21no—
163C32×Q8—22no—
164C32×Q8—22no—
165C2×C32×C4—22no—
166C2×C32×C4C2×D411yescharacteristic
167C2×C32×C4C2×D411yescharacteristic
168C2×C32×C4C2411yescharacteristic
169C2×C3⋊Dic3—21no—
170C2×C3⋊Dic3—21no—
171#634—21no—
172#634#4112yes—
173C2×C3×Dic3—22no—
174C2×C3×Dic3—21no—
175C2×C3×Dic3C2×D412yes—
176C2×C3×Dic3C2×D412yes—
177C3×D12—21no—
178C3×D12—21no—
179C3×C4×D3—42no—
180C3×Dic6—22no—
181C3×Dic6—81no—
182#627—82no—
183C3⋊(C3⋊C8)—22no—
184C3×C3⋊C8—21no—
185C3×C3⋊C8—21no—
186Q82—91no—
187#556—31no—
188#489—92no—
189#487—31no—
190#476—91no—
191#475—92no—
192#464—92no—
193#462—91no—
194#446—91no—
195#441—92no—
196C4×SD16—91no—
197C2×C3×Q8—22no—
198C2×C3×Q8—31no—
199C2×C3×Q8—61no—
200C2×C3×Q8C22×D312yes—
201C2×C3×Q8C22×D312yes—
202C2×C3×D4—31no—
203C22×C3×C4—61no—
204C2×D12C22×D311yescharacteristic
205C2×C4×D3—21no—
206C2×Dic6—21no—
207C2×Dic6—31no—
208C2×Dic6—31no—
209C2×Dic6—61no—
210C2×Dic6—62no—
211C2×Dic6—62no—
212C2×Dic6#6711yescharacteristic
213C2×C3×C8—31no—
214C2×C3×C8—31no—
215C3×C4⋊C4—21no—
216C3×C4⋊C4—21no—
217C3×C4⋊C4—21no—
218C3×C4⋊C4—21no—
219C3×C4⋊C4—32no—
220C3×C4⋊C4—31no—
221C3×C4⋊C4—31no—
222C3×C4⋊C4—32no—
223C3×C4⋊C4—41no—
224C3×C4⋊C4—41no—
225C3×C4⋊C4—62no—
226C3×C4⋊C4—61no—
227C3×C22⋊C4—62no—
228C3×C22⋊C4—62no—
229C3×C22⋊C4—61no—
230C3×C42—21no—
231C3×C42—32no—
232C3×C42—62no—
233C3×C42C22×D311yescharacteristic
234C3×C42C22×D311yescharacteristic
235#216—64no—
236#216—64no—
237#216—124no—
238#214—62no—
239(C2×D3)⋊C4—21no—
240(C2×D3)⋊C4—22no—
241(C2×D3)⋊C4—22no—
242C4⋊Dic3—21no—
243C4⋊Dic3—22no—
244C4⋊Dic3—31no—
245C4⋊Dic3—31no—
246C4⋊Dic3—61no—
247C4⋊Dic3—62no—
248C4⋊Dic3#6711yescharacteristic
249C4⋊Dic3C22×D311yescharacteristic
250C4⋊Dic3C22×D312yes—
251Dic3⋊C4—62no—
252Dic3⋊C4—61no—
253Dic3⋊C4—61no—
254Dic3⋊C4—62no—
255Dic3⋊C4—62no—
256Dic3⋊C4—121no—
257Dic3⋊C4#6712yes—
258C4×Dic3—22no—
259C4×Dic3—62no—
260C4×Dic3—61no—
261C4×Dic3—61no—
262C4×Dic3—62no—
263C4×Dic3—121no—
264C4×Dic3C22×D312yes—
265C2×C3⋊C8—32no—
266C2×C3⋊C8—32no—
267C2×C3⋊C8—62no—
268C2×C3⋊C8C22×D311yescharacteristic
269C2×C3⋊C8C22×D311yescharacteristic
270#204—62no—
271C22×C32C22×D411yescharacteristic
272C2×C3×D3—41no—
273C2×C3×D3—41no—
274C2×C3×D3—41no—
275C32×C4—21no—
276C32×C4—42no—
277C32×C4#13712yes—
278C32×C4C2×#4111yescharacteristic
279C32×C42−1+411yescharacteristic
280C3⋊Dic3—22no—
281C3⋊Dic3—41no—
282C3×Dic3—22no—
283C3×Dic3—22no—
284C3×Dic3—41no—
285C3×Dic3—42no—
286C2×Q16—92no—
287C2×SD16—91no—
288C4⋊Q8—31no—
289C4⋊Q8—92no—
290C4⋊Q8—181no—
291C4⋊Q8—182no—
292C4⋊Q8D3211yescharacteristic
293#126—62no—
294#124—32no—
295C22⋊Q8—61no—
296C4×Q8—31no—
297C4×Q8—32no—
298C4×Q8—92no—
299C4×Q8—91no—
300C4×Q8—181no—
301C4×D4—31no—
302#117—61no—
303#106—92no—
304#106—91no—
305C4⋊C8—92no—
306C4⋊C8—91no—
307#103—32no—
308#103—32no—
309#103—91no—
310#103—92no—
311#102—92no—
312#102—91no—
313#97—92no—
314C4×C8—31no—
315C23×C3—61no—
316C22×D3—21no—
317C3×Q8—22no—
318C3×Q8—22no—
319C3×Q8—22no—
320C3×Q8—22no—
321C3×Q8—42no—
322C3×Q8—42no—
323C3×Q8—62no—
324C3×Q8—241no—
325C3×D4—61no—
326C3×D4—61no—
327C2×C3×C4—22no—
328C2×C3×C4—22no—
329C2×C3×C4—21no—
330C2×C3×C4—21no—
331C2×C3×C4—21no—
332C2×C3×C4—32no—
333C2×C3×C4—32no—
334C2×C3×C4—42no—
335C2×C3×C4—61no—
336C2×C3×C4—62no—
337C2×C3×C4—122no—
338C2×C3×C4D3×D411yescharacteristic
339C2×C3×C4D3×D411yescharacteristic
340C2×C3×C4C2×#6711yescharacteristic
341C2×C3×C4C2×#6711yescharacteristic
342C2×C3×C4C23×D311yescharacteristic
343C2×C3×C4C23×D311yescharacteristic
344C2×Dic3—22no—
345C2×Dic3—21no—
346C2×Dic3—61no—
347C2×Dic3—61no—
348C2×Dic3—61no—
349C2×Dic3—61no—
350C2×Dic3—121no—
351C2×Dic3—121no—
352C2×Dic3C2×#6712yes—
353C2×Dic3C2×#6712yes—
354D12—21no—
355D12—21no—
356C4×D3—42no—
357Dic6—22no—
358Dic6—32no—
359Dic6—32no—
360Dic6—62no—
361Dic6—61no—
362Dic6—61no—
363Dic6—81no—
364Dic6—121no—
365Dic6—242no—
366Dic6—242no—
367C3×C8—61no—
368C3×C8—61no—
369C3⋊C8—21no—
370C3⋊C8—21no—
371C3⋊C8—62no—
372C3⋊C8—62no—
373C3⋊C8—122no—
374C2×C32#54811yescharacteristic
375C2×C32C2×#13711yescharacteristic
376C2×C32#57711yescharacteristic
377C3×D3—81no—
378C2×Q8—31no—
379C2×Q8—61no—
380C2×Q8—91no—
381C2×Q8—182no—
382C2×Q8C2×D3212yes—
383C2×D4—31no—
384C22×C4—61no—
385Q16—184no—
386SD16—182no—
387C2×C8—31no—
388C2×C8—31no—
389C2×C8—92no—
390C4⋊C4—21no—
391C4⋊C4—21no—
392C4⋊C4—31no—
393C4⋊C4—32no—
394C4⋊C4—32no—
395C4⋊C4—31no—
396C4⋊C4—62no—
397C4⋊C4—61no—
398C4⋊C4—91no—
399C4⋊C4—182no—
400C4⋊C4—182no—
401C4⋊C4—181no—
402C22⋊C4—62no—
403C22⋊C4—62no—
404C22⋊C4—61no—
405C42—32no—
406C42—62no—
407C42—182no—
408C42—181no—
409C42C2×D3211yescharacteristic
410C22×C3—21no—
411C22×C3—121no—
412C22×C3—121no—
413C22×C3—121no—
414C22×C3C2×D3×D411yescharacteristic
415C22×C3C22×#6711yescharacteristic
416C2×D3—41no—
417C2×D3—41no—
418C2×D3—41no—
419C3×C4—21no—
420C3×C4—21no—
421C3×C4—21no—
422C3×C4—21no—
423C3×C4—22no—
424C3×C4—41no—
425C3×C4—42no—
426C3×C4—42no—
427C3×C4—62no—
428C3×C4—62no—
429C3×C4—82no—
430C3×C4—121no—
431C3×C4—122no—
432C3×C4#91812yes—
433C3×C4#95112yes—
434C3×C4D3×#4111yescharacteristic
435C3×C4D3×#4111yescharacteristic
436C3×C4#101011yescharacteristic
437C3×C4#101011yescharacteristic
438Dic3—22no—
439Dic3—22no—
440Dic3—42no—
441Dic3—41no—
442Dic3—62no—
443Dic3—62no—
444Dic3—122no—
445Dic3—121no—
446Dic3—121no—
447Dic3—241no—
448C32#336911yescharacteristic, complemented, Sylow
449C23—61no—
450Q8—22no—
451Q8—22no—
452Q8—62no—
453Q8—92no—
454Q8—181no—
455Q8—241no—
456Q8—722no—
457D4—61no—
458D4—61no—
459C2×C4—22no—
460C2×C4—32no—
461C2×C4—32no—
462C2×C4—61no—
463C2×C4—62no—
464C2×C4—122no—
465C2×C4—181no—
466C2×C4—181no—
467C2×C4D3×#6711yescharacteristic
468C2×C4D3×#6711yescharacteristic
469C2×C4C22×D3211yescharacteristic
470C8—61no—
471C8—61no—
472C8—182no—
473C2×C3—21no—
474C2×C3—21no—
475C2×C3—21no—
476C2×C3—241no—
477C2×C3#567711yescharacteristic
478C2×C3#576211yescharacteristic
479C2×C3C2×#91811yescharacteristic
480C2×C3C2×#95111yescharacteristic
481C2×C3#583111yescharacteristic
482C2×C3#583711yescharacteristic
483D3—81no—
484C22—121no—
485C22—121no—
486C22—121no—
487C22C2×D3×#6711yescharacteristic
488C4—21no—
489C4—42no—
490C4—62no—
491C4—62no—
492C4—122no—
493C4—121no—
494C4—182no—
495C4—361no—
496C4#6394312yes—
497C4#6430911yescharacteristic
498C4#6431211yescharacteristic
499C3—21no—
500C3#8162611yescharacteristic, complemented
501C3#8367711yescharacteristic, complemented
502C2—241no—
503C2#1059523711yescharacteristic
504C2#1059531811yescharacteristic
505C2C2×#6394311yescharacteristic
subgroupG/H
centerC22C2×D3×#67
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×C4⋊Q8C22
socleC22×C32C22×D4
prime radicalC2×C3×D12C23
hypercenterC4⋊Q8D32
hypocenterC32#3369
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C42 ◁ C4⋊Q8

Complements

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

NH ≅ G/Ntype
2. #10593856C2semidirect
3. #10592789C2semidirect
4. C3×#5079C2semidirect
7. #10591544C2semidirect
8. #10591541C2semidirect
11. #10590258C2semidirect
52. #5079D3semidirect
448. C32#3369semidirect
500. C3#81626semidirect
501. C3#83677semidirect

Maximal subgroups

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

subgroupindex
C3×#57322
#105938562
#105927892
C3×#50792
#105916242
#105915772
#105915442
#105915412
C4×#37162
#105902662
#105902582
#836773
#816263