Finite Group Databasebeta

← #11874983

Subgroups — #11874983

Order 1152.

823 conjugacy classes of subgroups.

The subgroup lattice has 474 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10596199C211yesmaximal, characteristic
2#10593866C211yesmaximal, characteristic
3C3×#5080C211yesmaximal, characteristic, complemented
4C3×#5078C211yesmaximal, characteristic, complemented
5#10590574C214yesmaximal
6#10590417C214yesmaximal, complemented
7C4×#3710C211yesmaximal, characteristic
8#10590311C211yesmaximal, characteristic, complemented
9#10590303C211yesmaximal, characteristic, complemented
10#81938—31nomaximal
11#81891—31nomaximal
12C32×C4⋊Q8C2211yescharacteristic
13#64155—21no—
14Q8×C3⋊Dic3—21no—
15#64106—21no—
16#64101C2212yes—
17#64099C2212yes—
18#64096—21no—
19C42×C3⋊D3C2211yescharacteristic
20#64078C2211yescharacteristic
21C3×#869C2211yescharacteristic
22C3×#869C2211yescharacteristic
23#63872C2212yes—
24#63871—21no—
25#63871—21no—
26#63849C2212yes—
27#63843—21no—
28#63843—21no—
29C2×#3710C2212yes—
30C3×#808C2214yes—
31C3×#807C2214yes—
32C3×C4×C3⋊C8C2211yescharacteristic
33C3×C4×C3⋊C8C2211yescharacteristic
34#63575C2214yes—
35#63573C2214yes—
36#63553C2212yes—
37#5728—31no—
38#5728—31no—
39#5728—31no—
40#5728—31no—
41#5728—61no—
42C3×#500—31no—
43C3×#498—31no—
44#5080—31no—
45#5080D311yescharacteristic, complemented
46#5078—31no—
47#5078D311yescharacteristic, complemented
48#4880—34no—
49#4878—34no—
50#4860—34no—
51#4858—34no—
52C4×D3×C8—31no—
53C4×D3×C8—31no—
54#4682—31no—
55#4680—31no—
56C2×C32×Q8—21no—
57C2×C4×C3⋊D3D411yescharacteristic
58C2×C4×C3⋊D3D411yescharacteristic
59C2×C4×C3⋊D3C2311yescharacteristic
60C2×#634—21no—
61C2×C3×Dic6—21no—
62C2×C3×Dic6—21no—
63C32×C4⋊C4—21no—
64C32×C4⋊C4C2312yes—
65C32×C42C2311yescharacteristic
66#3752—22no—
67C4⋊(C3⋊Dic3)—21no—
68C4⋊(C3⋊Dic3)—22no—
69C4⋊(C3⋊Dic3)C2312yes—
70#3750—22no—
71C4×C3⋊Dic3—22no—
72C4×C3⋊Dic3D411yescharacteristic
73C4×C3⋊Dic3D411yescharacteristic
74C4×C3⋊Dic3C2311yescharacteristic
75C3×C4⋊Dic3—21no—
76C3×C4⋊Dic3—21no—
77C3×C4⋊Dic3C2312yes—
78C3×C4⋊Dic3C2312yes—
79C2×C3×C3⋊C8C2312yes—
80C2×C3×C3⋊C8C2312yes—
81Dic3⋊Dic3—22no—
82Dic3⋊Dic3—22no—
83#3722—22no—
84Dic32—22no—
85#3710Q818yescomplemented
86#3160—91noSylow
87C3×C4⋊Q8—21no—
88C3×C4⋊Q8—31no—
89C3×C4⋊Q8—31no—
90C3×C4⋊Q8C2×D311yescharacteristic
91C3×C4⋊Q8C2×D311yescharacteristic
92#946—61no—
93#946—61no—
94#946—61no—
95#946—61no—
96#946—62no—
97Q8×Dic3—61no—
98Q8×Dic3—61no—
99Q8×Dic3—61no—
100Q8×Dic3—61no—
101Q8×Dic3—62no—
102C2×D3×C8—32no—
103C2×D3×C8—32no—
104#897—61no—
105#897—61no—
106#897—62no—
107#897—61no—
108#897—61no—
109#892—32no—
110#892—32no—
111#892—32no—
112#892—32no—
113#892—62no—
114#890—32no—
115#890—32no—
116#890—32no—
117#890—32no—
118#890—62no—
119#887—61no—
120#887—61no—
121#887—61no—
122#887—61no—
123#887—62no—
124C42×D3—31no—
125C42×D3—31no—
126C42×D3—61no—
127#869—31no—
128#869—31no—
129#869—61no—
130#869C2×D311yescharacteristic
131#869C2×D311yescharacteristic
132C3×#107—34no—
133C3×#106—34no—
134C3×C4×C8—31no—
135C3×C4×C8—31no—
136#818—34no—
137#817—34no—
138C8×Dic3—32no—
139C8×Dic3—32no—
140#808—34no—
141#808C2×D314yes—
142#807—34no—
143#807C2×D314yes—
144C4×C3⋊C8C2×D311yescharacteristic
145C4×C3⋊C8C2×D311yescharacteristic
146C22×C3⋊D3C2×D411yescharacteristic
147C32×Q8—42no—
148C2×C32×C4—22no—
149C2×C32×C4C2×D411yescharacteristic
150C2×C32×C4C2×D411yescharacteristic
151C2×C32×C4C2411yescharacteristic
152C2×C3⋊Dic3—22no—
153C2×C3⋊Dic3C2×D411yescharacteristic
154C2×C3⋊Dic3C2×D411yescharacteristic
155C2×C3⋊Dic3C2×D411yescharacteristic
156C4×C3⋊D3—22no—
157C4×C3⋊D3—22no—
158C4×C3⋊D3C2×Q814yes—
159#634—42no—
160C2×C3×Dic3—22no—
161C2×C3×Dic3—22no—
162C3×Dic6—42no—
163C3×Dic6—42no—
164C3×C3⋊C8C2×Q814yes—
165C3×C3⋊C8C2×Q814yes—
166#533—91no—
167#533—91no—
168#500—31no—
169#500—91no—
170#499—94no—
171#498—31no—
172#498—91no—
173#427—94no—
174C2×C4×C8—91no—
175C2×C3×Q8—22no—
176C2×C3×Q8—21no—
177C2×C3×Q8—21no—
178C2×C3×Q8—61no—
179C2×C3×Q8—61no—
180C2×C4×D3—31no—
181C2×C4×D3—31no—
182C2×C4×D3—31no—
183C2×C4×D3—31no—
184C2×C4×D3—31no—
185C2×C4×D3—31no—
186C2×C4×D3—61no—
187C2×C4×D3—61no—
188C2×C4×D3—61no—
189C2×Dic6—21no—
190C2×Dic6—21no—
191C2×Dic6—62no—
192C2×Dic6—61no—
193C2×Dic6—61no—
194C2×C3×C8—32no—
195C2×C3×C8—32no—
196C3×C4⋊C4—22no—
197C3×C4⋊C4—21no—
198C3×C4⋊C4—21no—
199C3×C4⋊C4—22no—
200C3×C4⋊C4—32no—
201C3×C4⋊C4—32no—
202C3×C4⋊C4—61no—
203C3×C4⋊C4—61no—
204C3×C4⋊C4C22×D312yes—
205C3×C4⋊C4C22×D312yes—
206C3×C42—21no—
207C3×C42C22×D311yescharacteristic
208C3×C42C22×D311yescharacteristic
209(C2×D3)⋊C4—62no—
210(C2×D3)⋊C4—62no—
211(C2×D3)⋊C4—62no—
212(C2×D3)⋊C4—62no—
213(C2×D3)⋊C4—64no—
214C4⋊Dic3—21no—
215C4⋊Dic3—21no—
216C4⋊Dic3—32no—
217C4⋊Dic3—32no—
218C4⋊Dic3—62no—
219C4⋊Dic3—62no—
220C4⋊Dic3—62no—
221C4⋊Dic3—62no—
222C4⋊Dic3—62no—
223C4⋊Dic3—62no—
224C4⋊Dic3—64no—
225C4⋊Dic3—61no—
226C4⋊Dic3—61no—
227C4⋊Dic3C22×D312yes—
228C4⋊Dic3C22×D312yes—
229Dic3⋊C4—62no—
230Dic3⋊C4—62no—
231Dic3⋊C4—62no—
232Dic3⋊C4—62no—
233Dic3⋊C4—64no—
234C4×Dic3—31no—
235C4×Dic3—31no—
236C4×Dic3—31no—
237C4×Dic3—31no—
238C4×Dic3—31no—
239C4×Dic3—31no—
240C4×Dic3—61no—
241C4×Dic3—61no—
242C4×Dic3—61no—
243C4×Dic3—62no—
244C4×Dic3—62no—
245C4×Dic3—62no—
246C4×Dic3—62no—
247C4×Dic3—64no—
248C2×C3⋊C8C22×D312yes—
249C2×C3⋊C8C22×D312yes—
250D3×C8—38no—
251D3×C8—38no—
252C22×C32C22×D411yescharacteristic
253C2×C3⋊D3—21no—
254C2×C3⋊D3—21no—
255C2×C3⋊D3C4⋊Q812yes—
256C32×C4—42no—
257C32×C4#13512yes—
258C32×C4#13512yes—
259C32×C4C22×Q812yes—
260C3⋊Dic3—21no—
261C3⋊Dic3—21no—
262C3⋊Dic3—42no—
263C3⋊Dic3C4⋊Q812yes—
264C3×Dic3—42no—
265C3×Dic3—42no—
266C22×C8—92no—
267C4⋊Q8—31no—
268C4⋊Q8—31no—
269C4⋊Q8—91no—
270C4⋊Q8D3211yescharacteristic
271#125—92no—
272#125—92no—
273C22⋊Q8—181no—
274C22⋊Q8—181no—
275C22⋊Q8—181no—
276C22⋊Q8—181no—
277C4×Q8—181no—
278C4×Q8—181no—
279C4×Q8—181no—
280C4×Q8—181no—
281#117—92no—
282#117—92no—
283C2×C42—91no—
284#107—34no—
285#107—94no—
286#106—34no—
287#106—94no—
288C4×C8—31no—
289C4×C8—31no—
290C4×C8—92no—
291C22×D3—31no—
292C22×D3—31no—
293C22×D3—61no—
294C3×Q8—44no—
295C3×Q8—42no—
296C3×Q8—42no—
297C3×Q8—122no—
298C3×Q8—122no—
299C2×C3×C4—24no—
300C2×C3×C4—22no—
301C2×C3×C4—22no—
302C2×C3×C4—21no—
303C2×C3×C4—21no—
304C2×C3×C4—21no—
305C2×C3×C4—62no—
306C2×C3×C4—62no—
307C2×C3×C4D3×D411yescharacteristic
308C2×C3×C4D3×D411yescharacteristic
309C2×C3×C4D3×D411yescharacteristic
310C2×C3×C4D3×D411yescharacteristic
311C2×C3×C4C23×D311yescharacteristic
312C2×C3×C4C23×D311yescharacteristic
313C2×Dic3—22no—
314C2×Dic3—22no—
315C2×Dic3—31no—
316C2×Dic3—31no—
317C2×Dic3—31no—
318C2×Dic3—31no—
319C2×Dic3—31no—
320C2×Dic3—31no—
321C2×Dic3—61no—
322C2×Dic3—61no—
323C2×Dic3—61no—
324C2×Dic3—64no—
325C2×Dic3—62no—
326C2×Dic3—62no—
327C4×D3—34no—
328C4×D3—34no—
329C4×D3—64no—
330C4×D3—62no—
331C4×D3—62no—
332C4×D3—62no—
333C4×D3—62no—
334C4×D3—122no—
335C4×D3—122no—
336Dic6—42no—
337Dic6—42no—
338Dic6—124no—
339Dic6—122no—
340Dic6—122no—
341C3×C8—34no—
342C3×C8—34no—
343C3⋊C8D3×Q814yes—
344C3⋊C8D3×Q814yes—
345C2×C32C2×C4⋊Q811yescharacteristic
346C2×C32C2×#13511yescharacteristic
347C2×C32C2×#13511yescharacteristic
348C3⋊D3—22no—
349C2×Q8—21no—
350C2×Q8—61no—
351C2×Q8—61no—
352C2×Q8—181no—
353C22×C4—91no—
354C22×C4—91no—
355C22×C4—91no—
356C2×C8—32no—
357C2×C8—32no—
358C2×C8—98no—
359C4⋊C4—21no—
360C4⋊C4—32no—
361C4⋊C4—32no—
362C4⋊C4—61no—
363C4⋊C4—61no—
364C4⋊C4—92no—
365C4⋊C4—182no—
366C4⋊C4—182no—
367C4⋊C4—182no—
368C4⋊C4—182no—
369C4⋊C4—181no—
370C4⋊C4C2×D3212yes—
371C22⋊C4—182no—
372C22⋊C4—182no—
373C42—91no—
374C42—91no—
375C42—91no—
376C42—182no—
377C42—182no—
378C42C2×D3211yescharacteristic
379C22×C3—21no—
380C22×C3C2×D3×D411yescharacteristic
381C22×C3C2×D3×D411yescharacteristic
382C2×D3—32no—
383C2×D3—32no—
384C2×D3—62no—
385C2×D3—61no—
386C2×D3—61no—
387C2×D3—61no—
388C2×D3—61no—
389C2×D3—121no—
390C2×D3—121no—
391C3×C4—22no—
392C3×C4—22no—
393C3×C4—22no—
394C3×C4—44no—
395C3×C4—42no—
396C3×C4—42no—
397C3×C4—122no—
398C3×C4—122no—
399C3×C4#91212yes—
400C3×C4#91612yes—
401C3×C4#91612yes—
402C3×C4#91912yes—
403C3×C4C2×D3×Q812yes—
404C3×C4C2×D3×Q812yes—
405Dic3—32no—
406Dic3—32no—
407Dic3—42no—
408Dic3—42no—
409Dic3—62no—
410Dic3—61no—
411Dic3—61no—
412Dic3—61no—
413Dic3—61no—
414Dic3—121no—
415Dic3—121no—
416Dic3—124no—
417Dic3—122no—
418Dic3—122no—
419C32#316011yescharacteristic, complemented, Sylow
420C23—91no—
421Q8—42no—
422Q8—122no—
423Q8—122no—
424Q8—362no—
425C2×C4—22no—
426C2×C4—62no—
427C2×C4—62no—
428C2×C4—91no—
429C2×C4—94no—
430C2×C4—91no—
431C2×C4—91no—
432C2×C4—182no—
433C2×C4—182no—
434C2×C4—182no—
435C2×C4#381111yescharacteristic
436C2×C4#381111yescharacteristic
437C2×C4C22×D3211yescharacteristic
438C8—34no—
439C8—34no—
440C2×C3—21no—
441C2×C3—21no—
442C2×C3—21no—
443C2×C3D3×C4⋊Q811yescharacteristic
444C2×C3D3×C4⋊Q811yescharacteristic
445C2×C3C2×#91211yescharacteristic
446C2×C3C2×#91611yescharacteristic
447C2×C3C2×#91611yescharacteristic
448C2×C3C2×#91911yescharacteristic
449D3—62no—
450D3—62no—
451D3—122no—
452C22—92no—
453C22—181no—
454C22—181no—
455C22C2×#381111yescharacteristic
456C4—42no—
457C4—92no—
458C4—122no—
459C4—122no—
460C4—181no—
461C4—181no—
462C4—362no—
463C4#6393612yes—
464C4#6395012yes—
465C4D32×Q812yes—
466C3—21no—
467C3#8189111yescharacteristic, complemented
468C3#8193811yescharacteristic, complemented
469C2—182no—
470C2C2×#6393611yescharacteristic
471C2C2×#6395011yescharacteristic
472C2#1059536511yescharacteristic
subgroupG/H
centerC22C2×#3811
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×C4⋊Q8C22
socleC22×C32C22×D4
prime radicalC22×C3⋊D3C2×D4
hypercenterC4⋊Q8D32
hypocenterC32#3160
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
3. C3×#5080C2semidirect
4. C3×#5078C2semidirect
6. #10590417C2semidirect
8. #10590311C2semidirect
9. #10590303C2semidirect
45. #5080D3semidirect
47. #5078D3semidirect
85. #3710Q8semidirect
419. C32#3160semidirect
467. C3#81891semidirect
468. C3#81938semidirect

Maximal subgroups

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

subgroupindex
#105961992
#105938662
C3×#50802
C3×#50782
#105905742
#105904172
C4×#37102
#105903112
#105903032
#819383
#818913