Finite Group Databasebeta

← #11896082

Subgroups — #11896082

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
1#10593863C211yesmaximal, characteristic
2#10593856C211yesmaximal, characteristic, complemented
3#10592530C211yesmaximal, characteristic, complemented
4C3×#4849C211yesmaximal, characteristic, complemented
5C3×#4842C211yesmaximal, characteristic
6#10590866C212yesmaximal
7#10590819C212yesmaximal, complemented
8#10590816C212yesmaximal, complemented
9#10590797C212yesmaximal
10C4×#3715C211yesmaximal, characteristic
11#10590290C211yesmaximal, characteristic, complemented
12#81091—31nomaximal
13#80464—31nomaximal
14C4×#634C2211yescharacteristic
15C2×C3×Dic12C2212yes—
16C3×C4×D12C2211yescharacteristic
17C3×#869C2211yescharacteristic
18C3×#869C2211yescharacteristic
19C3×C4×Dic6C2211yescharacteristic
20#63919C2212yes—
21#63918—21no—
22#63863C2212yes—
23#63858—22no—
24#63857—21no—
25#63844—21no—
26#63843C2212yes—
27#63843C2212yes—
28#63841—21no—
29#63839—22no—
30C2×#3715C2211yescharacteristic
31C32×C4⋊C8C2211yescharacteristic
32#63642C2212yes—
33#63641C2212yes—
34C4×C3⋊(C3⋊C8)C2211yescharacteristic
35C3×#821C2212yes—
36C3×#817C2212yes—
37C3×#816C2212yes—
38#63574C2211yescharacteristic
39#63565C2212yes—
40#63565C2212yes—
41#63565C2211yescharacteristic
42#63562C2211yescharacteristic
43#5732—31no—
44#5722—31no—
45Q8×Dic6—31no—
46#5542—31no—
47C3×#476—31no—
48C3×#462—31no—
49#5185—32no—
50#5184—32no—
51#5093—31no—
52#5079—31no—
53C4×#215—31no—
54C4×#214—31no—
55#4854—32no—
56#4853—32no—
57#4849D311yescharacteristic, complemented
58#4842D311yescharacteristic
59#4831—31no—
60#4831—31no—
61#4831—61no—
62#4794—32no—
63#4791—32no—
64#4767—32no—
65#4765—32no—
66C2×#634D411yescharacteristic
67C2×C3×D12C2311yescharacteristic
68C2×C3×C4×D3—21no—
69C2×C3×Dic6—21no—
70C2×C3×Dic6C2312yes—
71C2×C3×Dic6C2311yescharacteristic
72C2×#627—22no—
73C2×C32×C8C2312yes—
74C32×C42C2311yescharacteristic
75C4⋊(C3⋊Dic3)D411yescharacteristic
76#3750D412yes—
77C4×C3⋊Dic3C2312yes—
78C2×C3⋊(C3⋊C8)C2311yescharacteristic
79C2×C3⋊(C3⋊C8)C2311yescharacteristic
80C3×(C2×D3)⋊C4—21no—
81C3×C4⋊Dic3—21no—
82C3×C4⋊Dic3—21no—
83C3×C4⋊Dic3—21no—
84C3×C4⋊Dic3C2311yescharacteristic
85C3×C4⋊Dic3C2312yes—
86C3×C4⋊Dic3C2311yescharacteristic
87C3×Dic3⋊C4—21no—
88C3×C4×Dic3—21no—
89C3×Dic12—24no—
90#3724—22no—
91Dic3⋊Dic3—22no—
92Dic3⋊Dic3—22no—
93(C2×D3)⋊Dic3—22no—
94(C2×D3)⋊Dic3—22no—
95Dic32—22no—
96Dic32—22no—
97#3715—22no—
98#3369—91noSylow
99C2×C3×Q16—32no—
100C3×C4⋊Q8—31no—
101C3×C4⋊Q8—31no—
102C3×C4×Q8—31no—
103C3×C4×D4—31no—
104#947—32no—
105Q8×Dic3—32no—
106Q8×Dic3—32no—
107#944—62no—
108C2×#215—31no—
109#936—32no—
110C2×#214—31no—
111#926—61no—
112#924—61no—
113C2×Dic12C2×D312yes—
114#898—62no—
115#897—61no—
116#892—61no—
117#888—32no—
118#888—32no—
119#888—61no—
120#888—62no—
121#887—32no—
122#887—32no—
123#887—61no—
124#879—62no—
125C4×D12C2×D311yescharacteristic
126#869—61no—
127#869C2×D311yescharacteristic
128#869C2×D311yescharacteristic
129C4×Dic6—31no—
130C4×Dic6—31no—
131C4×Dic6—61no—
132C4×Dic6—61no—
133C4×Dic6C2×D311yescharacteristic
134C3×#106—32no—
135C3×C4⋊C8—21no—
136C3×C4⋊C8C2×D311yescharacteristic
137C3×C4⋊C8C2×D311yescharacteristic
138C3×#103—32no—
139C3×#102—32no—
140#835—31no—
141#835—32no—
142#835—32no—
143#832—31no—
144#821C2×D312yes—
145#817C2×D312yes—
146#816C2×D312yes—
147#815—32no—
148#815—32no—
149#815—62no—
150Dic3⋊C8—32no—
151Dic3⋊C8—32no—
152Dic3⋊C8—62no—
153#810—31no—
154#810—32no—
155#810—32no—
156#809—31no—
157#808—31no—
158#808—31no—
159C4×C3⋊C8—31no—
160C4×C3⋊C8—31no—
161C4×C3⋊C8—61no—
162C22×C3×D3—21no—
163C2×C32×C4C2×D411yescharacteristic
164C2×C32×C4C2×D411yescharacteristic
165C2×C32×C4C2411yescharacteristic
166C2×C3⋊Dic3C2×D412yes—
167C2×C3⋊Dic3C2×D412yes—
168#634—22no—
169C2×C3×Dic3—21no—
170C2×C3×Dic3—21no—
171C2×C3×Dic3—22no—
172C2×C3×Dic3—22no—
173C2×C3×Dic3—21no—
174C3×D12—21no—
175C3×D12—21no—
176C3×C4×D3—42no—
177C3×Dic6—21no—
178C3×Dic6—22no—
179C3×Dic6—22no—
180C3×Dic6—81no—
181C3×Dic6#4112yes—
182#627—82no—
183C32×C8—22no—
184C3⋊(C3⋊C8)—21no—
185C3⋊(C3⋊C8)—21no—
186Q82—91no—
187#556—91no—
188#489—92no—
189#487—91no—
190#476—31no—
191#475—92no—
192#464—92no—
193#462—31no—
194#446—91no—
195#441—92no—
196C4×SD16—91no—
197C2×C3×Q8—31no—
198C2×C3×Q8—32no—
199C2×C3×Q8—61no—
200C2×C3×D4—31no—
201C22×C3×C4—61no—
202C2×D12C22×D311yescharacteristic
203C2×C4×D3—21no—
204C2×Dic6—21no—
205C2×Dic6—31no—
206C2×Dic6—31no—
207C2×Dic6—61no—
208C2×Dic6—62no—
209C2×Dic6—62no—
210C2×Dic6C22×D312yes—
211C2×Dic6C22×D311yescharacteristic
212C3×Q16—64no—
213C2×C3×C8—22no—
214C2×C3×C8C22×D312yes—
215C2×C3×C8C22×D312yes—
216C3×C4⋊C4—31no—
217C3×C4⋊C4—31no—
218C3×C4⋊C4—32no—
219C3×C4⋊C4—61no—
220C3×C4⋊C4—61no—
221C3×C4⋊C4—61no—
222C3×C4⋊C4—61no—
223C3×C22⋊C4—61no—
224C3×C42—21no—
225C3×C42—61no—
226C3×C42C22×D311yescharacteristic
227C3×C42C22×D311yescharacteristic
228#217—62no—
229#217—62no—
230#215—62no—
231#214—62no—
232(C2×D3)⋊C4—21no—
233(C2×D3)⋊C4—62no—
234(C2×D3)⋊C4—62no—
235C4⋊Dic3—21no—
236C4⋊Dic3—21no—
237C4⋊Dic3—21no—
238C4⋊Dic3—31no—
239C4⋊Dic3—31no—
240C4⋊Dic3—61no—
241C4⋊Dic3—62no—
242C4⋊Dic3—62no—
243C4⋊Dic3C22×D311yescharacteristic
244C4⋊Dic3C22×D311yescharacteristic
245C4⋊Dic3C22×D312yes—
246Dic3⋊C4—21no—
247Dic3⋊C4—32no—
248Dic3⋊C4—32no—
249Dic3⋊C4—62no—
250Dic3⋊C4—62no—
251Dic3⋊C4—62no—
252Dic3⋊C4—62no—
253Dic3⋊C4—62no—
254C4×Dic3—21no—
255C4×Dic3—32no—
256C4×Dic3—32no—
257C4×Dic3—62no—
258C4×Dic3—62no—
259C4×Dic3—62no—
260C4×Dic3—62no—
261C4×Dic3—62no—
262C2×C3⋊C8—31no—
263C2×C3⋊C8—31no—
264C2×C3⋊C8—31no—
265C2×C3⋊C8—31no—
266C2×C3⋊C8—61no—
267C2×C3⋊C8—61no—
268Dic12—24no—
269C22×C32C22×D411yescharacteristic
270C2×C3×D3—41no—
271C2×C3×D3—41no—
272C2×C3×D3—41no—
273C32×C4—21no—
274C32×C4#13712yes—
275C32×C4C2×#4111yescharacteristic
276C32×C42−1+411yescharacteristic
277C3⋊Dic3—22no—
278C3⋊Dic3—22no—
279C3×Dic3—22no—
280C3×Dic3—42no—
281C3×Dic3—41no—
282C3×Dic3—41no—
283C3×Dic3—42no—
284C2×Q16—32no—
285C2×SD16—91no—
286C4⋊Q8—31no—
287C4⋊Q8—31no—
288C4⋊Q8—92no—
289C4⋊Q8—181no—
290C4⋊Q8—182no—
291#126—182no—
292#124—92no—
293C22⋊Q8—181no—
294C4×Q8—31no—
295C4×Q8—91no—
296C4×Q8—92no—
297C4×Q8—92no—
298C4×Q8—181no—
299C4×D4—31no—
300#117—181no—
301#106—32no—
302#106—91no—
303C4⋊C8—92no—
304C4⋊C8D3211yescharacteristic
305#103—32no—
306#103—91no—
307#103—92no—
308#103—92no—
309#102—32no—
310#102—91no—
311#97—92no—
312C4×C8—91no—
313C23×C3—61no—
314C22×D3—21no—
315C3×Q8—32no—
316C3×Q8—61no—
317C3×Q8—62no—
318C3×Q8—62no—
319C3×Q8—241no—
320C3×D4—61no—
321C3×D4—61no—
322C2×C3×C4—21no—
323C2×C3×C4—21no—
324C2×C3×C4—21no—
325C2×C3×C4—61no—
326C2×C3×C4—61no—
327C2×C3×C4—62no—
328C2×C3×C4—62no—
329C2×C3×C4—61no—
330C2×C3×C4—122no—
331C2×C3×C4D3×D411yescharacteristic
332C2×C3×C4D3×D411yescharacteristic
333C2×C3×C4D3×D411yescharacteristic
334C2×C3×C4D3×D411yescharacteristic
335C2×C3×C4C23×D311yescharacteristic
336C2×C3×C4C23×D311yescharacteristic
337C2×Dic3—21no—
338C2×Dic3—21no—
339C2×Dic3—21no—
340C2×Dic3—22no—
341C2×Dic3—22no—
342C2×Dic3—32no—
343C2×Dic3—32no—
344C2×Dic3—32no—
345C2×Dic3—32no—
346C2×Dic3—62no—
347C2×Dic3—62no—
348D12—21no—
349D12—21no—
350C4×D3—42no—
351Dic6—21no—
352Dic6—22no—
353Dic6—22no—
354Dic6—62no—
355Dic6—62no—
356Dic6—81no—
357Dic6—122no—
358Dic6—242no—
359Dic6—242no—
360Dic6#23712yes—
361C3×C8—22no—
362C3×C8—22no—
363C3×C8—42no—
364C3⋊C8—62no—
365C3⋊C8—61no—
366C3⋊C8—61no—
367C3⋊C8—61no—
368C3⋊C8—61no—
369C3⋊C8—121no—
370C2×C32#54811yescharacteristic
371C2×C32C2×#13711yescharacteristic
372C2×C32#57711yescharacteristic
373C3×D3—81no—
374C2×Q8—31no—
375C2×Q8—32no—
376C2×Q8—61no—
377C2×Q8—91no—
378C2×Q8—182no—
379C2×D4—31no—
380C22×C4—61no—
381Q16—64no—
382SD16—182no—
383C2×C8—91no—
384C2×C8—91no—
385C2×C8C2×D3212yes—
386C4⋊C4—32no—
387C4⋊C4—31no—
388C4⋊C4—31no—
389C4⋊C4—61no—
390C4⋊C4—61no—
391C4⋊C4—61no—
392C4⋊C4—61no—
393C4⋊C4—91no—
394C4⋊C4—92no—
395C4⋊C4—182no—
396C4⋊C4—182no—
397C4⋊C4—182no—
398C22⋊C4—61no—
399C22⋊C4—182no—
400C22⋊C4—182no—
401C42—61no—
402C42—92no—
403C42—182no—
404C42—182no—
405C42C2×D3211yescharacteristic
406C22×C3—21no—
407C22×C3—121no—
408C22×C3—121no—
409C22×C3—121no—
410C22×C3C2×D3×D411yescharacteristic
411C22×C3C2×D3×D411yescharacteristic
412C2×D3—41no—
413C2×D3—41no—
414C2×D3—41no—
415C3×C4—21no—
416C3×C4—21no—
417C3×C4—21no—
418C3×C4—21no—
419C3×C4—22no—
420C3×C4—41no—
421C3×C4—62no—
422C3×C4—122no—
423C3×C4—121no—
424C3×C4—121no—
425C3×C4—122no—
426C3×C4#91512yes—
427C3×C4#91812yes—
428C3×C4C2×#23711yescharacteristic
429C3×C4#100711yescharacteristic
430C3×C4D3×#4111yescharacteristic
431C3×C4#101011yescharacteristic
432Dic3—22no—
433Dic3—41no—
434Dic3—42no—
435Dic3—41no—
436Dic3—42no—
437Dic3—62no—
438Dic3—62no—
439Dic3—62no—
440Dic3—62no—
441Dic3—122no—
442Dic3—122no—
443C32#336911yescharacteristic, complemented, Sylow
444C23—61no—
445Q8—32no—
446Q8—61no—
447Q8—62no—
448Q8—62no—
449Q8—182no—
450Q8—241no—
451Q8—722no—
452D4—61no—
453D4—61no—
454C2×C4—61no—
455C2×C4—61no—
456C2×C4—61no—
457C2×C4—62no—
458C2×C4—62no—
459C2×C4—92no—
460C2×C4—92no—
461C2×C4—122no—
462C2×C4#380211yescharacteristic
463C2×C4#380211yescharacteristic
464C2×C4C22×D3211yescharacteristic
465C8—22no—
466C8—181no—
467C8—181no—
468C2×C3—21no—
469C2×C3—21no—
470C2×C3—21no—
471C2×C3—241no—
472C2×C3#559811yescharacteristic
473C2×C3#563311yescharacteristic
474C2×C3C2×#91511yescharacteristic
475C2×C3C2×#91811yescharacteristic
476C2×C3#577511yescharacteristic
477C2×C3#577811yescharacteristic
478D3—81no—
479C22—121no—
480C22—121no—
481C22—121no—
482C22C2×#380211yescharacteristic
483C4—21no—
484C4—62no—
485C4—121no—
486C4—122no—
487C4—121no—
488C4—122no—
489C4—182no—
490C4—182no—
491C4#6381112yes—
492C4D3×#23711yescharacteristic
493C4#6431511yescharacteristic
494C3—21no—
495C3#8046411yescharacteristic, complemented
496C3#8109111yescharacteristic, complemented
497C2—241no—
498C2#1059452511yescharacteristic
499C2C2×#6381111yescharacteristic
500C2#1059471911yescharacteristic
subgroupG/H
centerC22C2×#3802
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×C4⋊C8C22
socleC22×C32C22×D4
prime radicalC2×C3×D12C23
hypercenterC4⋊C8D32
hypocenterC32#3369
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C42 ◁ C4⋊C8

Complements

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

NH ≅ G/Ntype
2. #10593856C2semidirect
3. #10592530C2semidirect
4. C3×#4849C2semidirect
7. #10590819C2semidirect
8. #10590816C2semidirect
11. #10590290C2semidirect
57. #4849D3semidirect
443. C32#3369semidirect
495. C3#80464semidirect
496. C3#81091semidirect

Maximal subgroups

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

subgroupindex
#105938632
#105938562
#105925302
C3×#48492
C3×#48422
#105908662
#105908192
#105908162
#105907972
C4×#37152
#105902902
#810913
#804643