Finite Group Databasebeta

← #11896069

Subgroups — #11896069

Order 1152.

723 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
1C3×#5584C211yesmaximal, characteristic
2C3×Q8×Dic6C211yesmaximal, characteristic, complemented
3#10592723C211yesmaximal, characteristic, complemented
4#10590384C211yesmaximal, characteristic, complemented
5#10590381C212yesmaximal, complemented
6C4×#3715C211yesmaximal, characteristic
7#10590290C211yesmaximal, characteristic, complemented
8#10590285C212yesmaximal, complemented
9#10590280C212yesmaximal
10#10590267C212yesmaximal
11#10590266C211yesmaximal, characteristic
12#83704—31nomaximal
13#83677—31nomaximal
14C32×C4×Q8C2211yescharacteristic
15C3×#946—21no—
16C3×Q8×Dic3—21no—
17C3×#898—22no—
18C3×#892—21no—
19C3×#888—21no—
20C3×#888—22no—
21C3×#875C2212yes—
22C3×C4×D12C2211yescharacteristic
23C3×#869C2211yescharacteristic
24C3×#869C2211yescharacteristic
25C3×#869C2212yes—
26C3×C4×Dic6C2212yes—
27C3×C4×Dic6C2212yes—
28C3×C4×Dic6C2211yescharacteristic
29C2×#3718C2212yes—
30C2×#3715C2211yescharacteristic
31C4⋊(C3⋊(C3⋊C8))C2211yescharacteristic
32C4⋊(C3⋊(C3⋊C8))C2212yes—
33#63630C2212yes—
34C4×C3⋊(C3⋊C8)C2211yescharacteristic
35#63574C2212yes—
36#63574C2211yescharacteristic
37#63565C2212yes—
38#63565C2212yes—
39#63565C2212yes—
40#63565C2211yescharacteristic
41#63562C2212yes—
42#63562C2211yescharacteristic
43C3×Q82—31no—
44C3×#556—31no—
45#5584D311yescharacteristic
46Q8×Dic6D311yescharacteristic, complemented
47#5094—32no—
48#5093—31no—
49#5090—31no—
50#5089—32no—
51#5084—31no—
52#5079—31no—
53#5055—32no—
54#5054—32no—
55#5031—31no—
56#5030—32no—
57#5030—32no—
58#5028—32no—
59C4×#215—31no—
60#5024—31no—
61#5024—31no—
62#5024—61no—
63#5020—32no—
64C4×#214—31no—
65#5008—31no—
66C2×C32×Q8D411yescharacteristic
67C2×C3×D12C2311yescharacteristic
68C2×C3×C4×D3—21no—
69C2×C3×Dic6—22no—
70C2×C3×Dic6—21no—
71C2×C3×Dic6C2312yes—
72C2×C3×Dic6C2311yescharacteristic
73C32×C4⋊C4D411yescharacteristic
74C32×C4⋊C4D412yes—
75C32×C42C2311yescharacteristic
76C32×C42C2312yes—
77C2×C3⋊(C3⋊C8)C2311yescharacteristic
78C2×C3⋊(C3⋊C8)C2312yes—
79C2×C3⋊(C3⋊C8)C2311yescharacteristic
80C3×(C2×D3)⋊C4—22no—
81C3×(C2×D3)⋊C4—21no—
82C3×(C2×D3)⋊C4—22no—
83C3×C4⋊Dic3—22no—
84C3×C4⋊Dic3—21no—
85C3×C4⋊Dic3—21no—
86C3×C4⋊Dic3—21no—
87C3×C4⋊Dic3C2312yes—
88C3×C4⋊Dic3C2311yescharacteristic
89C3×C4⋊Dic3C2311yescharacteristic
90C3×Dic3⋊C4—22no—
91C3×Dic3⋊C4—21no—
92C3×Dic3⋊C4—22no—
93C3×C4×Dic3—22no—
94C3×C4×Dic3—21no—
95C3×C4×Dic3—22no—
96#3718—24no—
97#3715—22no—
98#3369—91noSylow
99C3×C4⋊Q8—31no—
100C3×C4⋊Q8—32no—
101C3×C4⋊Q8—31no—
102C3×C4⋊Q8—61no—
103C3×C4⋊Q8—62no—
104C3×#126—62no—
105C3×#124—32no—
106C3×C22⋊Q8—61no—
107C3×C4×Q8—21no—
108C3×C4×Q8—31no—
109C3×C4×Q8—32no—
110C3×C4×Q8—32no—
111C3×C4×Q8—61no—
112C3×C4×Q8C2×D311yescharacteristic
113C3×C4×Q8C2×D311yescharacteristic
114C3×C4×D4—31no—
115C3×#117—61no—
116#946—21no—
117Q8×Dic3—21no—
118C2×#216—32no—
119C2×#216—32no—
120C2×#215—31no—
121C2×#214—31no—
122#898—22no—
123#892—21no—
124#888—21no—
125#888—22no—
126#875C2×D312yes—
127C4×D12C2×D311yescharacteristic
128#869C2×D311yescharacteristic
129#869C2×D311yescharacteristic
130#869C2×D312yes—
131C4×Dic6C2×D311yescharacteristic
132C4×Dic6C2×D312yes—
133C4×Dic6C2×D312yes—
134#835—32no—
135#835—32no—
136#835—31no—
137#835—32no—
138#832—32no—
139#832—31no—
140#810—31no—
141#810—32no—
142#810—32no—
143#810—32no—
144#809—31no—
145#809—32no—
146#808—32no—
147#808—31no—
148#808—31no—
149#808—32no—
150C4⋊(C3⋊C8)—31no—
151C4⋊(C3⋊C8)—32no—
152C4⋊(C3⋊C8)—32no—
153C4⋊(C3⋊C8)—31no—
154C4⋊(C3⋊C8)—61no—
155C4⋊(C3⋊C8)—62no—
156#803—32no—
157#803—32no—
158#803—62no—
159C4×C3⋊C8—31no—
160C4×C3⋊C8—31no—
161C4×C3⋊C8—61no—
162C22×C3×D3—21no—
163C32×Q8—22no—
164C2×C32×C4C2×D412yes—
165C2×C32×C4C2×D412yes—
166C2×C32×C4C2×D411yescharacteristic
167C2×C32×C4C2×D411yescharacteristic
168C2×C32×C4C2411yescharacteristic
169C2×C3×Dic3—21no—
170C2×C3×Dic3—21no—
171C2×C3×Dic3—22no—
172C2×C3×Dic3—21no—
173C2×C3×Dic3—22no—
174C3×D12—21no—
175C3×D12—21no—
176C3×C4×D3—42no—
177C3×Dic6—21no—
178C3×Dic6—22no—
179C3×Dic6—22no—
180C3×Dic6—82no—
181C3×Dic6—81no—
182C3×Dic6#4112yes—
183C3⋊(C3⋊C8)—21no—
184C3⋊(C3⋊C8)—21no—
185C3⋊(C3⋊C8)—22no—
186Q82—31no—
187#556—31no—
188#489—92no—
189#487—91no—
190#476—91no—
191#475—92no—
192#464—92no—
193#462—91no—
194#446—91no—
195#441—92no—
196C4×SD16—91no—
197C2×C3×Q8—21no—
198C2×C3×Q8—31no—
199C2×C3×Q8—32no—
200C2×C3×Q8—62no—
201C2×C3×Q8—61no—
202C2×C3×Q8#6711yescharacteristic
203C2×C3×Q8#6711yescharacteristic
204C2×C3×D4—31no—
205C22×C3×C4—61no—
206C2×D12C22×D311yescharacteristic
207C2×C4×D3—21no—
208C2×Dic6—22no—
209C2×Dic6—21no—
210C2×Dic6C22×D312yes—
211C2×Dic6C22×D311yescharacteristic
212C3×C4⋊C4—21no—
213C3×C4⋊C4—22no—
214C3×C4⋊C4—31no—
215C3×C4⋊C4—31no—
216C3×C4⋊C4—32no—
217C3×C4⋊C4—62no—
218C3×C4⋊C4—62no—
219C3×C4⋊C4—61no—
220C3×C4⋊C4—61no—
221C3×C4⋊C4—62no—
222C3×C4⋊C4—61no—
223C3×C4⋊C4—61no—
224C3×C4⋊C4#6711yescharacteristic
225C3×C4⋊C4#6712yes—
226C3×C4⋊C4#6711yescharacteristic
227C3×C4⋊C4#6712yes—
228C3×C22⋊C4—62no—
229C3×C22⋊C4—61no—
230C3×C22⋊C4—62no—
231C3×C42—21no—
232C3×C42—22no—
233C3×C42—62no—
234C3×C42—62no—
235C3×C42—61no—
236C3×C42C22×D311yescharacteristic
237C3×C42C22×D311yescharacteristic
238C3×C42C22×D312yes—
239C3×C42C22×D312yes—
240#216—64no—
241#216—64no—
242#215—62no—
243#214—62no—
244(C2×D3)⋊C4—21no—
245(C2×D3)⋊C4—22no—
246(C2×D3)⋊C4—22no—
247C4⋊Dic3—22no—
248C4⋊Dic3—21no—
249C4⋊Dic3—21no—
250C4⋊Dic3—21no—
251C4⋊Dic3C22×D311yescharacteristic
252C4⋊Dic3C22×D312yes—
253C4⋊Dic3C22×D311yescharacteristic
254Dic3⋊C4—22no—
255Dic3⋊C4—21no—
256Dic3⋊C4—22no—
257C4×Dic3—22no—
258C4×Dic3—21no—
259C4×Dic3—22no—
260C2×C3⋊C8—31no—
261C2×C3⋊C8—31no—
262C2×C3⋊C8—31no—
263C2×C3⋊C8—31no—
264C2×C3⋊C8—32no—
265C2×C3⋊C8—32no—
266C2×C3⋊C8—61no—
267C2×C3⋊C8—61no—
268C2×C3⋊C8—62no—
269C22×C32C22×D411yescharacteristic
270C2×C3×D3—41no—
271C2×C3×D3—41no—
272C2×C3×D3—41no—
273C32×C4—22no—
274C32×C4—22no—
275C32×C4—21no—
276C32×C4#13712yes—
277C32×C4C2×#4111yescharacteristic
278C32×C42−1+411yescharacteristic
279C3×Dic3—22no—
280C3×Dic3—42no—
281C3×Dic3—41no—
282C3×Dic3—41no—
283C3×Dic3—42no—
284C2×Q16—92no—
285C2×SD16—91no—
286C4⋊Q8—32no—
287C4⋊Q8—31no—
288C4⋊Q8—31no—
289C4⋊Q8—61no—
290C4⋊Q8—62no—
291#126—62no—
292#124—32no—
293C22⋊Q8—61no—
294C4×Q8—32no—
295C4×Q8—31no—
296C4×Q8—32no—
297C4×Q8—61no—
298C4×Q8D3211yescharacteristic
299C4×D4—31no—
300#117—61no—
301#106—91no—
302#106—92no—
303C4⋊C8—91no—
304C4⋊C8—92no—
305#103—91no—
306#103—92no—
307#103—92no—
308#103—92no—
309#102—91no—
310#102—92no—
311#97—92no—
312C4×C8—91no—
313C23×C3—61no—
314C22×D3—21no—
315C3×Q8—22no—
316C3×Q8—22no—
317C3×Q8—32no—
318C3×Q8—42no—
319C3×Q8—61no—
320C3×Q8—62no—
321C3×Q8—62no—
322C3×Q8—242no—
323C3×Q8—241no—
324C3×D4—61no—
325C3×D4—61no—
326C2×C3×C4—21no—
327C2×C3×C4—21no—
328C2×C3×C4—22no—
329C2×C3×C4—21no—
330C2×C3×C4—22no—
331C2×C3×C4—61no—
332C2×C3×C4—61no—
333C2×C3×C4—62no—
334C2×C3×C4—62no—
335C2×C3×C4—61no—
336C2×C3×C4—122no—
337C2×C3×C4C2×#6712yes—
338C2×C3×C4C2×#6712yes—
339C2×C3×C4C2×#6712yes—
340C2×C3×C4C2×#6712yes—
341C2×C3×C4C2×#6711yescharacteristic
342C2×C3×C4C2×#6711yescharacteristic
343C2×C3×C4C2×#6711yescharacteristic
344C2×C3×C4C2×#6711yescharacteristic
345C2×C3×C4C23×D311yescharacteristic
346C2×C3×C4C23×D311yescharacteristic
347C2×Dic3—21no—
348C2×Dic3—21no—
349C2×Dic3—22no—
350C2×Dic3—21no—
351C2×Dic3—22no—
352D12—21no—
353D12—21no—
354C4×D3—42no—
355Dic6—21no—
356Dic6—22no—
357Dic6—22no—
358Dic6—82no—
359Dic6—81no—
360Dic6#23912yes—
361C3⋊C8—62no—
362C3⋊C8—61no—
363C3⋊C8—62no—
364C3⋊C8—61no—
365C3⋊C8—61no—
366C3⋊C8—62no—
367C3⋊C8—61no—
368C3⋊C8—121no—
369C3⋊C8—122no—
370C2×C32#54811yescharacteristic
371C2×C32C2×#13711yescharacteristic
372C2×C32#57711yescharacteristic
373C3×D3—81no—
374C2×Q8—31no—
375C2×Q8—32no—
376C2×Q8—62no—
377C2×Q8—61no—
378C2×Q8#62511yescharacteristic
379C2×D4—31no—
380C22×C4—61no—
381Q16—184no—
382SD16—182no—
383C2×C8—91no—
384C2×C8—91no—
385C2×C8—92no—
386C4⋊C4—31no—
387C4⋊C4—32no—
388C4⋊C4—31no—
389C4⋊C4—61no—
390C4⋊C4—62no—
391C4⋊C4—62no—
392C4⋊C4—61no—
393C4⋊C4—62no—
394C4⋊C4—61no—
395C4⋊C4—61no—
396C4⋊C4#62511yescharacteristic
397C4⋊C4#62512yes—
398C22⋊C4—62no—
399C22⋊C4—61no—
400C22⋊C4—62no—
401C42—62no—
402C42—62no—
403C42—61no—
404C42C2×D3211yescharacteristic
405C42C2×D3212yes—
406C22×C3—21no—
407C22×C3—121no—
408C22×C3—121no—
409C22×C3—121no—
410C22×C3C22×#6711yescharacteristic
411C22×C3C22×#6711yescharacteristic
412C2×D3—41no—
413C2×D3—41no—
414C2×D3—41no—
415C3×C4—22no—
416C3×C4—22no—
417C3×C4—22no—
418C3×C4—21no—
419C3×C4—22no—
420C3×C4—21no—
421C3×C4—21no—
422C3×C4—21no—
423C3×C4—22no—
424C3×C4—42no—
425C3×C4—42no—
426C3×C4—41no—
427C3×C4—62no—
428C3×C4—121no—
429C3×C4—122no—
430C3×C4—122no—
431C3×C4—121no—
432C3×C4#94212yes—
433C3×C4#95112yes—
434C3×C4C2×#23911yescharacteristic
435C3×C4#100711yescharacteristic
436C3×C4D3×#4111yescharacteristic
437C3×C4#101011yescharacteristic
438Dic3—22no—
439Dic3—41no—
440Dic3—42no—
441Dic3—41no—
442Dic3—42no—
443C32#336911yescharacteristic, complemented, Sylow
444C23—61no—
445Q8—22no—
446Q8—32no—
447Q8—61no—
448Q8—62no—
449Q8—62no—
450Q8—242no—
451Q8—241no—
452D4—61no—
453D4—61no—
454C2×C4—61no—
455C2×C4—61no—
456C2×C4—62no—
457C2×C4—62no—
458C2×C4—61no—
459C2×C4—122no—
460C2×C4C2×#62512yes—
461C2×C4C2×#62512yes—
462C2×C4C2×#62511yescharacteristic
463C2×C4C2×#62511yescharacteristic
464C2×C4C22×D3211yescharacteristic
465C8—181no—
466C8—181no—
467C8—182no—
468C2×C3—21no—
469C2×C3—21no—
470C2×C3—21no—
471C2×C3—241no—
472C2×C3C2×#94211yescharacteristic
473C2×C3#581711yescharacteristic
474C2×C3C2×#95111yescharacteristic
475C2×C3#583111yescharacteristic
476C2×C3#583611yescharacteristic
477C2×C3#583711yescharacteristic
478D3—81no—
479C22—121no—
480C22—121no—
481C22—121no—
482C22C22×#62511yescharacteristic
483C4—22no—
484C4—21no—
485C4—22no—
486C4—62no—
487C4—122no—
488C4—122no—
489C4—121no—
490C4—121no—
491C4#6382712yes—
492C4#6431511yescharacteristic
493C4D3×#23911yescharacteristic
494C3—21no—
495C3#8367711yescharacteristic, complemented
496C3#8370411yescharacteristic, complemented
497C2—241no—
498C2C2×#6382711yescharacteristic
499C2#1059540911yescharacteristic
500C2#1059544611yescharacteristic
subgroupG/H
centerC22C22×#625
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 ◁ C4×Q8

Complements

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

NH ≅ G/Ntype
2. C3×Q8×Dic6C2semidirect
3. #10592723C2semidirect
4. #10590384C2semidirect
5. #10590381C2semidirect
7. #10590290C2semidirect
8. #10590285C2semidirect
46. Q8×Dic6D3semidirect
443. C32#3369semidirect
495. C3#83677semidirect
496. C3#83704semidirect

Maximal subgroups

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

subgroupindex
C3×#55842
C3×Q8×Dic62
#105927232
#105903842
#105903812
C4×#37152
#105902902
#105902852
#105902802
#105902672
#105902662
#837043
#836773