Finite Group Databasebeta

← #11896078

Subgroups — #11896078

Order 1152.

725 conjugacy classes of subgroups.

The subgroup lattice has 504 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10593879C211yesmaximal, characteristic
2Dic62C211yesmaximal, characteristic, complemented
3#10592380C211yesmaximal, characteristic, complemented
4C3×C4×#204C211yesmaximal, characteristic
5C3×#4679C211yesmaximal, characteristic, complemented
6#10590895C212yesmaximal
7#10590859C212yesmaximal
8#10590802C212yesmaximal, complemented
9#10590794C212yesmaximal, complemented
10#10590385C211yesmaximal, characteristic, complemented
11#10590268C211yesmaximal, characteristic
12#79981—31nomaximal
13#79626—31nomaximal
14#64078C2211yescharacteristic
15#64078C2211yescharacteristic
16C2×C3×#204C2211yescharacteristic
17C3×C4×D12C2211yescharacteristic
18C3×C4×Dic6C2211yescharacteristic
19C3×C4×Dic6C2211yescharacteristic
20#63918—21no—
21#63918C2212yes—
22#63861—22no—
23#63860C2212yes—
24#63856—21no—
25#63844C2212yes—
26Dic3×Dic6—21no—
27Dic3×Dic6C2212yes—
28#63841—21no—
29#63840—22no—
30C2×#3719C2212yes—
31C32×C4×C8C2211yescharacteristic
32#63643C2212yes—
33#63643C2212yes—
34C3×#821C2211yescharacteristic
35C3×#817C2211yescharacteristic
36C3×#816C2211yescharacteristic
37C3×#815C2212yes—
38C3×Dic3⋊C8C2212yes—
39C3×C4⋊(C3⋊C8)C2211yescharacteristic
40#63573C2212yes—
41#63567C2212yes—
42#63563C2212yes—
43#5584—31no—
44Q8×Dic6—31no—
45Q8×Dic6—31no—
46#5542—31no—
47C3×#446—31no—
48C3×C4×SD16—31no—
49#5166—32no—
50#5031—31no—
51#5008—31no—
52#4854—32no—
53#4851—32no—
54#4849—31no—
55#4845—32no—
56#4842—31no—
57#4789—32no—
58#4765—32no—
59#4716—32no—
60#4714—32no—
61C4×#204D311yescharacteristic
62#4681—31no—
63#4681—31no—
64#4681—61no—
65#4679D311yescharacteristic, complemented
66C2×#634—21no—
67C2×#634C2312yes—
68C2×C3×D12C2311yescharacteristic
69C2×C3×C4×D3—21no—
70C2×C3×Dic6D411yescharacteristic
71C2×C3×Dic6C2311yescharacteristic
72C2×#627—22no—
73C2×C32×C8C2311yescharacteristic
74C2×C32×C8C2311yescharacteristic
75C32×C42C2311yescharacteristic
76C4⋊(C3⋊Dic3)—21no—
77C4⋊(C3⋊Dic3)—21no—
78C4⋊(C3⋊Dic3)—21no—
79C4⋊(C3⋊Dic3)C2312yes—
80C3×(C2×D3)⋊C4—21no—
81C3×C4⋊Dic3D411yescharacteristic
82C3×C4⋊Dic3C2311yescharacteristic
83C3×C4⋊Dic3C2311yescharacteristic
84C3×Dic3⋊C4—21no—
85C3×Dic3⋊C4D412yes—
86C3×C4×Dic3—21no—
87C3×C4×Dic3C2312yes—
88C2×C3×C3⋊C8C2312yes—
89C3×#204—22no—
90#3724—22no—
91Dic3⋊Dic3—22no—
92Dic3⋊Dic3—22no—
93(C2×D3)⋊Dic3—22no—
94(C2×D3)⋊Dic3—22no—
95Dic32—22no—
96Dic32—22no—
97#3719—24no—
98#3369—91noSylow
99C2×C3×SD16—31no—
100C3×C4×Q8—31no—
101C3×C4×Q8—31no—
102C3×C4×D4—31no—
103#946—61no—
104Q8×Dic3—32no—
105Q8×Dic3—61no—
106C2×#216—32no—
107#936—32no—
108#926—61no—
109#924—61no—
110C2×Dic12—32no—
111C2×#204C2×D311yescharacteristic
112#898—62no—
113#892—61no—
114#888—32no—
115#888—61no—
116#888—62no—
117#888—62no—
118#887—32no—
119#879—62no—
120#875—32no—
121C4×D12C2×D311yescharacteristic
122#869—31no—
123#869—31no—
124#869—32no—
125#869—31no—
126#869—31no—
127#869—61no—
128#869—61no—
129#869—61no—
130C4×Dic6—32no—
131C4×Dic6—32no—
132C4×Dic6—61no—
133C4×Dic6C2×D311yescharacteristic
134C4×Dic6C2×D311yescharacteristic
135C3×#106—31no—
136C3×C4⋊C8—32no—
137C3×C4⋊C8—31no—
138C3×#103—31no—
139C3×#102—31no—
140C3×#97—32no—
141C3×C4×C8—21no—
142C3×C4×C8C2×D311yescharacteristic
143C3×C4×C8C2×D311yescharacteristic
144#832—32no—
145#821—32no—
146#821C2×D311yescharacteristic
147#817—32no—
148#817C2×D311yescharacteristic
149#816—32no—
150#816—32no—
151#816—32no—
152#816—32no—
153#816—32no—
154#816—62no—
155#816—62no—
156#816C2×D311yescharacteristic
157#815C2×D312yes—
158Dic3⋊C8C2×D312yes—
159#810—32no—
160#808—32no—
161C4⋊(C3⋊C8)C2×D311yescharacteristic
162C22×C3×D3—21no—
163C2×C32×C4C2×D411yescharacteristic
164C2×C32×C4C2×D411yescharacteristic
165C2×C32×C4C2411yescharacteristic
166C2×C3⋊Dic3—22no—
167C2×C3⋊Dic3—22no—
168#634—22no—
169#634—22no—
170#634—81no—
171C2×C3×Dic3—21no—
172C2×C3×Dic3—21no—
173C2×C3×Dic3—21no—
174C2×C3×Dic3C2×D412yes—
175C2×C3×Dic3C2×D412yes—
176C3×D12—21no—
177C3×D12—21no—
178C3×C4×D3—42no—
179C3×Dic6—22no—
180C3×Dic6—21no—
181C3×Dic6#4112yes—
182#627—82no—
183C32×C8—21no—
184C32×C8—21no—
185C3×C3⋊C8—22no—
186Q82—91no—
187#556—91no—
188#489—92no—
189#487—91no—
190#476—91no—
191#475—92no—
192#464—92no—
193#462—91no—
194#446—31no—
195#441—92no—
196C4×SD16—31no—
197C2×C3×Q8—31no—
198C2×C3×Q8—31no—
199C2×C3×D4—31no—
200C22×C3×C4—61no—
201C2×D12C22×D311yescharacteristic
202C2×C4×D3—21no—
203C2×Dic6—32no—
204C2×Dic6—32no—
205C2×Dic6—62no—
206C2×Dic6—62no—
207C2×Dic6—61no—
208C2×Dic6—61no—
209C2×Dic6—62no—
210C2×Dic6—121no—
211C2×Dic6D1211yescharacteristic
212C2×Dic6C22×D311yescharacteristic
213C3×SD16—62no—
214C2×C3×C8—21no—
215C2×C3×C8—21no—
216C2×C3×C8—32no—
217C2×C3×C8C22×D311yescharacteristic
218C2×C3×C8C22×D311yescharacteristic
219C2×C3×C8C22×D311yescharacteristic
220C2×C3×C8C22×D311yescharacteristic
221C3×C4⋊C4—31no—
222C3×C4⋊C4—32no—
223C3×C4⋊C4—31no—
224C3×C4⋊C4—31no—
225C3×C4⋊C4—61no—
226C3×C22⋊C4—61no—
227C3×C42—21no—
228C3×C42—32no—
229C3×C42—61no—
230C3×C42C22×D311yescharacteristic
231C3×C42C22×D311yescharacteristic
232#217—62no—
233#217—62no—
234#216—64no—
235(C2×D3)⋊C4—21no—
236(C2×D3)⋊C4—62no—
237(C2×D3)⋊C4—62no—
238C4⋊Dic3—32no—
239C4⋊Dic3—32no—
240C4⋊Dic3—62no—
241C4⋊Dic3—62no—
242C4⋊Dic3—61no—
243C4⋊Dic3—61no—
244C4⋊Dic3—61no—
245C4⋊Dic3—61no—
246C4⋊Dic3—61no—
247C4⋊Dic3—61no—
248C4⋊Dic3—62no—
249C4⋊Dic3—121no—
250C4⋊Dic3—121no—
251C4⋊Dic3—121no—
252C4⋊Dic3D1211yescharacteristic
253C4⋊Dic3C22×D311yescharacteristic
254C4⋊Dic3C22×D311yescharacteristic
255Dic3⋊C4—21no—
256Dic3⋊C4—62no—
257Dic3⋊C4—62no—
258Dic3⋊C4—62no—
259Dic3⋊C4—62no—
260Dic3⋊C4D1212yes—
261C4×Dic3—21no—
262C4×Dic3—62no—
263C4×Dic3—62no—
264C4×Dic3—62no—
265C4×Dic3—62no—
266C4×Dic3C22×D312yes—
267C2×C3⋊C8C22×D312yes—
268Dic12—64no—
269#204—22no—
270C22×C32C22×D411yescharacteristic
271C2×C3×D3—41no—
272C2×C3×D3—41no—
273C2×C3×D3—41no—
274C32×C4—21no—
275C32×C4#13712yes—
276C32×C4C2×#4111yescharacteristic
277C32×C42−1+411yescharacteristic
278C3⋊Dic3—42no—
279C3⋊Dic3—42no—
280C3×Dic3—22no—
281C3×Dic3—22no—
282C3×Dic3—22no—
283C3×Dic3—41no—
284C3×Dic3—41no—
285C2×Q16—92no—
286C2×SD16—31no—
287C4⋊Q8—92no—
288C4⋊Q8—91no—
289C4⋊Q8—91no—
290C4⋊Q8—181no—
291C4⋊Q8—182no—
292#126—182no—
293#124—92no—
294C22⋊Q8—181no—
295C4×Q8—31no—
296C4×Q8—31no—
297C4×Q8—92no—
298C4×Q8—92no—
299C4×Q8—181no—
300C4×D4—31no—
301#117—181no—
302#106—31no—
303#106—92no—
304C4⋊C8—32no—
305C4⋊C8—31no—
306#103—31no—
307#103—92no—
308#103—92no—
309#103—92no—
310#102—31no—
311#102—92no—
312#97—32no—
313C4×C8D3211yescharacteristic
314C23×C3—61no—
315C22×D3—21no—
316C3×Q8—32no—
317C3×Q8—62no—
318C3×Q8—61no—
319C3×D4—61no—
320C3×D4—61no—
321C2×C3×C4—21no—
322C2×C3×C4—21no—
323C2×C3×C4—21no—
324C2×C3×C4—32no—
325C2×C3×C4—32no—
326C2×C3×C4—61no—
327C2×C3×C4—61no—
328C2×C3×C4—61no—
329C2×C3×C4—122no—
330C2×C3×C4C2×D1211yescharacteristic
331C2×C3×C4C2×D1211yescharacteristic
332C2×C3×C4D3×D411yescharacteristic
333C2×C3×C4D3×D411yescharacteristic
334C2×C3×C4C23×D311yescharacteristic
335C2×C3×C4C23×D311yescharacteristic
336C2×Dic3—21no—
337C2×Dic3—21no—
338C2×Dic3—21no—
339C2×Dic3—62no—
340C2×Dic3—62no—
341C2×Dic3—62no—
342C2×Dic3—62no—
343C2×Dic3—122no—
344C2×Dic3—122no—
345C2×Dic3C2×D1212yes—
346C2×Dic3C2×D1212yes—
347D12—21no—
348D12—21no—
349C4×D3—42no—
350Dic6—22no—
351Dic6—21no—
352Dic6—62no—
353Dic6—62no—
354Dic6—62no—
355Dic6—62no—
356Dic6—122no—
357Dic6—122no—
358Dic6—242no—
359Dic6—242no—
360Dic6—241no—
361Dic6—241no—
362Dic6—242no—
363Dic6#23512yes—
364C3×C8—21no—
365C3×C8—21no—
366C3×C8—21no—
367C3×C8—21no—
368C3×C8—41no—
369C3×C8—41no—
370C3×C8—62no—
371C3⋊C8—22no—
372C2×C32#54811yescharacteristic
373C2×C32C2×#13711yescharacteristic
374C2×C32#57711yescharacteristic
375C3×D3—81no—
376C2×Q8—31no—
377C2×Q8—31no—
378C2×Q8—92no—
379C2×Q8—182no—
380C2×Q8—181no—
381C2×D4—31no—
382C22×C4—61no—
383Q16—184no—
384SD16—62no—
385C2×C8—32no—
386C2×C8C2×D3211yescharacteristic
387C2×C8C2×D3211yescharacteristic
388C4⋊C4—31no—
389C4⋊C4—32no—
390C4⋊C4—31no—
391C4⋊C4—31no—
392C4⋊C4—61no—
393C4⋊C4—92no—
394C4⋊C4—182no—
395C4⋊C4—182no—
396C4⋊C4—182no—
397C4⋊C4—181no—
398C4⋊C4—181no—
399C4⋊C4—181no—
400C22⋊C4—61no—
401C22⋊C4—182no—
402C22⋊C4—182no—
403C42—32no—
404C42—61no—
405C42—182no—
406C42—182no—
407C42C2×D3211yescharacteristic
408C22×C3—21no—
409C22×C3—121no—
410C22×C3—121no—
411C22×C3—121no—
412C22×C3C22×D1211yescharacteristic
413C22×C3C2×D3×D411yescharacteristic
414C2×D3—41no—
415C2×D3—41no—
416C2×D3—41no—
417C3×C4—22no—
418C3×C4—21no—
419C3×C4—21no—
420C3×C4—21no—
421C3×C4—21no—
422C3×C4—22no—
423C3×C4—62no—
424C3×C4—62no—
425C3×C4—62no—
426C3×C4—121no—
427C3×C4—121no—
428C3×C4#90912yes—
429C3×C4#91512yes—
430C3×C4C2×#23511yescharacteristic
431C3×C4#100711yescharacteristic
432C3×C4D3×#4111yescharacteristic
433C3×C4#101011yescharacteristic
434Dic3—22no—
435Dic3—22no—
436Dic3—22no—
437Dic3—41no—
438Dic3—41no—
439Dic3—122no—
440Dic3—122no—
441Dic3—122no—
442Dic3—122no—
443Dic3—242no—
444Dic3—242no—
445C32#336911yescharacteristic, complemented, Sylow
446C23—61no—
447Q8—32no—
448Q8—61no—
449Q8—62no—
450Q8—182no—
451Q8—182no—
452Q8—721no—
453Q8—722no—
454D4—61no—
455D4—61no—
456C2×C4—32no—
457C2×C4—32no—
458C2×C4—61no—
459C2×C4—61no—
460C2×C4—61no—
461C2×C4—122no—
462C2×C4—182no—
463C2×C4—182no—
464C2×C4D3×D1211yescharacteristic
465C2×C4D3×D1211yescharacteristic
466C2×C4C22×D3211yescharacteristic
467C8—21no—
468C8—21no—
469C8—62no—
470C2×C3—21no—
471C2×C3—21no—
472C2×C3—21no—
473C2×C3—241no—
474C2×C3#555211yescharacteristic
475C2×C3#557611yescharacteristic
476C2×C3C2×#90911yescharacteristic
477C2×C3#575111yescharacteristic
478C2×C3C2×#91511yescharacteristic
479C2×C3#577011yescharacteristic
480D3—81no—
481C22—121no—
482C22—121no—
483C22—121no—
484C22C2×D3×D1211yescharacteristic
485C4—21no—
486C4—62no—
487C4—62no—
488C4—62no—
489C4—121no—
490C4—121no—
491C4—362no—
492C4—362no—
493C4#6380012yes—
494C4#6429711yescharacteristic
495C4D3×#23511yescharacteristic
496C3—21no—
497C3#7962611yescharacteristic, complemented
498C3#7998111yescharacteristic, complemented
499C2—241no—
500C2#1059389911yescharacteristic
501C2#1059467911yescharacteristic
502C2C2×#6380011yescharacteristic
subgroupG/H
centerC22C2×D3×D12
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. Dic62C2semidirect
3. #10592380C2semidirect
5. C3×#4679C2semidirect
8. #10590802C2semidirect
9. #10590794C2semidirect
10. #10590385C2semidirect
65. #4679D3semidirect
445. C32#3369semidirect
497. C3#79626semidirect
498. C3#79981semidirect

Maximal subgroups

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

subgroupindex
#105938792
Dic622
#105923802
C3×C4×#2042
C3×#46792
#105908952
#105908592
#105908022
#105907942
#105903852
#105902682
#799813
#796263