Finite Group Databasebeta

← #11897677

Subgroups — #11897677

Order 1152.

727 conjugacy classes of subgroups.

The subgroup lattice has 498 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10593956C211yesmaximal, characteristic
2#10593856C211yesmaximal, characteristic, complemented
3#10592530C211yesmaximal, characteristic, complemented
4C3×#4850C211yesmaximal, characteristic, complemented
5C3×#4842C211yesmaximal, characteristic
6#10590903C212yesmaximal, complemented
7#10590820C212yesmaximal, complemented
8#10590778C212yesmaximal
9#10590743C212yesmaximal
10C4×#3715C211yesmaximal, characteristic
11#10590312C211yesmaximal, characteristic, complemented
12#81137—31nomaximal
13#81056—31nomaximal
14C4×#634C2211yescharacteristic
15C3×C4×D12C2211yescharacteristic
16C3×#869C2211yescharacteristic
17C3×#869C2211yescharacteristic
18C3×C4×Dic6C2211yescharacteristic
19#63919C2212yes—
20#63918—21no—
21#63898C2212yes—
22D3×C4⋊Dic3—21no—
23#63887—22no—
24#63872C2212yes—
25#63857—21no—
26#63844—21no—
27#63843C2212yes—
28#63839—22no—
29C2×#3715C2211yescharacteristic
30C32×C4⋊C8C2211yescharacteristic
31#63642C2212yes—
32#63641C2212yes—
33C4×C3⋊(C3⋊C8)C2211yescharacteristic
34C3×#821C2212yes—
35C3×#818C2212yes—
36C3×#817C2212yes—
37C3×#816C2212yes—
38#63576C2212yes—
39#63576C2212yes—
40#63574C2211yescharacteristic
41#63565C2211yescharacteristic
42#63562C2211yescharacteristic
43#5730—31no—
44#5722—31no—
45Q8×Dic6—31no—
46#5543—31no—
47C3×#477—31no—
48C3×#476—31no—
49#5078—31no—
50#5078—31no—
51C4×#215—31no—
52C4×#214—31no—
53#4890—32no—
54#4876—32no—
55#4857—32no—
56#4856—32no—
57#4850D311yescharacteristic, complemented
58#4842D311yescharacteristic
59#4831—31no—
60#4831—31no—
61#4831—61no—
62#4817—32no—
63#4799—32no—
64#4759—32no—
65#4757—32no—
66C2×#634D411yescharacteristic
67C2×C3×D12C2311yescharacteristic
68C2×C3×C4×D3—21no—
69C2×C3×Dic6—21no—
70C2×C3×Dic6—21no—
71C2×C3×Dic6C2311yescharacteristic
72C2×#627—22no—
73C2×D3×Dic3—22no—
74C2×C32×C8C2312yes—
75C32×C42C2311yescharacteristic
76C4⋊(C3⋊Dic3)D411yescharacteristic
77#3750D412yes—
78C4×C3⋊Dic3C2312yes—
79C2×C3⋊(C3⋊C8)C2311yescharacteristic
80C2×C3⋊(C3⋊C8)C2311yescharacteristic
81C3×(C2×D3)⋊C4—21no—
82C3×C4⋊Dic3—21no—
83C3×C4⋊Dic3—21no—
84C3×C4⋊Dic3C2311yescharacteristic
85C3×C4⋊Dic3C2311yescharacteristic
86C3×C4⋊Dic3C2312yes—
87C3×C4⋊Dic3C2312yes—
88C3×Dic3⋊C4—21no—
89C3×C4×Dic3—21no—
90#3724—22no—
91Dic3⋊Dic3—22no—
92Dic3⋊Dic3—22no—
93Dic3⋊Dic3—22no—
94(C2×D3)⋊Dic3—22no—
95Dic32—22no—
96#3715Q814yescomplemented
97#3385—91noSylow
98C3×C4⋊Q8—31no—
99C3×C4⋊Q8—31no—
100C3×C4×Q8—31no—
101C3×C4×D4—31no—
102#946—62no—
103Q8×Dic3—32no—
104#944—62no—
105C2×#215—31no—
106D4×Dic3—32no—
107C2×#214—31no—
108C2×C4⋊Dic3—61no—
109#924—61no—
110#897—61no—
111#893—32no—
112D3×C4⋊C4—61no—
113#890—32no—
114#890—32no—
115#888—32no—
116#888—32no—
117#888—61no—
118#888—62no—
119#887—32no—
120#887—61no—
121#878—62no—
122C4×D12C2×D311yescharacteristic
123#869—61no—
124#869C2×D311yescharacteristic
125#869C2×D311yescharacteristic
126C4×Dic6—31no—
127C4×Dic6—31no—
128C4×Dic6—61no—
129C4×Dic6—61no—
130C4×Dic6C2×D311yescharacteristic
131C3×#107—32no—
132C3×#106—32no—
133C3×C4⋊C8—21no—
134C3×C4⋊C8C2×D311yescharacteristic
135C3×C4⋊C8C2×D311yescharacteristic
136C3×#103—32no—
137C3×#102—32no—
138#835—31no—
139#832—31no—
140#821C2×D312yes—
141#818C2×D312yes—
142#817C2×D312yes—
143#816C2×D312yes—
144#815—32no—
145#815—32no—
146#815—62no—
147Dic3⋊C8—32no—
148Dic3⋊C8—32no—
149Dic3⋊C8—62no—
150#810—31no—
151#809—31no—
152#808—31no—
153#808—31no—
154#807—32no—
155#807—32no—
156#807—32no—
157#807—32no—
158C4×C3⋊C8—31no—
159C4×C3⋊C8—31no—
160C4×C3⋊C8—61no—
161C22×C3×D3—21no—
162C2×C32×C4C2×D411yescharacteristic
163C2×C32×C4C2×D411yescharacteristic
164C2×C32×C4C2411yescharacteristic
165C2×C3⋊Dic3C2×D412yes—
166C2×C3⋊Dic3C2×D412yes—
167#634—22no—
168C2×C3×Dic3—21no—
169C2×C3×Dic3—22no—
170C2×C3×Dic3—22no—
171C2×C3×Dic3—21no—
172C2×C3×Dic3—21no—
173C3×D12—21no—
174C3×D12C2×Q812yes—
175C3×C4×D3—42no—
176C3×Dic6—21no—
177C3×Dic6—81no—
178C3×Dic6—81no—
179C3×Dic6C2×Q812yes—
180#627—82no—
181D3×Dic3—82no—
182C32×C8—22no—
183C3⋊(C3⋊C8)—21no—
184C3⋊(C3⋊C8)C2×Q812yes—
185Q82—91no—
186#554—91no—
187#501—92no—
188#500—91no—
189#479—92no—
190#477—31no—
191#476—31no—
192#474—92no—
193#446—91no—
194#440—92no—
195C4×SD16—91no—
196C2×C3×Q8—31no—
197C2×C3×Q8—61no—
198C2×C3×Q8—61no—
199C2×C3×D4—31no—
200C22×C3×C4—61no—
201C22×Dic3—62no—
202C2×D12C22×D311yescharacteristic
203C2×C4×D3—21no—
204C2×C4×D3—62no—
205C2×Dic6—21no—
206C2×Dic6—21no—
207C2×Dic6—31no—
208C2×Dic6—31no—
209C2×Dic6—61no—
210C2×Dic6—62no—
211C2×Dic6—62no—
212C2×Dic6C22×D311yescharacteristic
213C2×C3×C8—22no—
214C2×C3×C8C22×D312yes—
215C2×C3×C8C22×D312yes—
216C3×C4⋊C4—32no—
217C3×C4⋊C4—32no—
218C3×C4⋊C4—31no—
219C3×C4⋊C4—31no—
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#215—34no—
230#214—34no—
231(C2×D3)⋊C4—21no—
232(C2×D3)⋊C4—62no—
233C4⋊Dic3—21no—
234C4⋊Dic3—21no—
235C4⋊Dic3—31no—
236C4⋊Dic3—31no—
237C4⋊Dic3—61no—
238C4⋊Dic3—62no—
239C4⋊Dic3—62no—
240C4⋊Dic3—62no—
241C4⋊Dic3C22×D312yes—
242C4⋊Dic3C22×D312yes—
243C4⋊Dic3C22×D311yescharacteristic
244C4⋊Dic3C22×D311yescharacteristic
245Dic3⋊C4—21no—
246Dic3⋊C4—32no—
247Dic3⋊C4—32no—
248Dic3⋊C4—62no—
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—
260C2×C3⋊C8—31no—
261C2×C3⋊C8—31no—
262C2×C3⋊C8—31no—
263C2×C3⋊C8—31no—
264C2×C3⋊C8—61no—
265C2×C3⋊C8—61no—
266C22×C32C22×D411yescharacteristic
267C2×C3×D3—22no—
268C2×C3×D3—41no—
269C2×C3×D3—41no—
270C32×C4—21no—
271C32×C4#13712yes—
272C32×C4C22×Q811yescharacteristic
273C32×C42−1+411yescharacteristic
274C3⋊Dic3—22no—
275C3⋊Dic3—22no—
276C3×Dic3—22no—
277C3×Dic3—41no—
278C3×Dic3—42no—
279C3×Dic3—41no—
280C3×Dic3—42no—
281C2×SD16—91no—
282C4⋊Q8—31no—
283C4⋊Q8—31no—
284C4⋊Q8—92no—
285C4⋊Q8—181no—
286C4⋊Q8—182no—
287#125—92no—
288C22⋊Q8—182no—
289C22⋊Q8—181no—
290C4×Q8—31no—
291C4×Q8—91no—
292C4×Q8—92no—
293C4×Q8—181no—
294C4×D4—31no—
295C4×D4—92no—
296C2×C4⋊C4—181no—
297#107—32no—
298#107—92no—
299#107—92no—
300#106—32no—
301#106—91no—
302C4⋊C8—92no—
303C4⋊C8D3211yescharacteristic
304#103—32no—
305#103—91no—
306#102—32no—
307#102—91no—
308#97—92no—
309C4×C8—91no—
310C23×C3—61no—
311C22×D3—21no—
312C3×Q8—32no—
313C3×Q8—61no—
314C3×Q8—241no—
315C3×Q8—241no—
316C3×D4—32no—
317C3×D4—61no—
318C2×C3×C4—21no—
319C2×C3×C4—21no—
320C2×C3×C4—21no—
321C2×C3×C4—61no—
322C2×C3×C4—62no—
323C2×C3×C4—61no—
324C2×C3×C4—61no—
325C2×C3×C4—62no—
326C2×C3×C4—122no—
327C2×C3×C4D3×D411yescharacteristic
328C2×C3×C4D3×D411yescharacteristic
329C2×C3×C4D3×D411yescharacteristic
330C2×C3×C4D3×D411yescharacteristic
331C2×C3×C4C23×D311yescharacteristic
332C2×C3×C4C23×D311yescharacteristic
333C2×Dic3—21no—
334C2×Dic3—21no—
335C2×Dic3—22no—
336C2×Dic3—21no—
337C2×Dic3—22no—
338C2×Dic3—32no—
339C2×Dic3—32no—
340C2×Dic3—32no—
341C2×Dic3—32no—
342C2×Dic3—62no—
343C2×Dic3—62no—
344C2×Dic3—242no—
345D12—21no—
346D12D3×Q812yes—
347C4×D3—42no—
348C4×D3—242no—
349Dic6—21no—
350Dic6—62no—
351Dic6—62no—
352Dic6—81no—
353Dic6—81no—
354Dic6—122no—
355Dic6—242no—
356Dic6—242no—
357Dic6D3×Q812yes—
358C3×C8—22no—
359C3×C8—22no—
360C3×C8—42no—
361C3⋊C8—32no—
362C3⋊C8—32no—
363C3⋊C8—62no—
364C3⋊C8—61no—
365C3⋊C8—61no—
366C3⋊C8—121no—
367C2×C32D4×Q811yescharacteristic
368C2×C32C2×#13711yescharacteristic
369C2×C32#57611yescharacteristic
370C3×D3—42no—
371C2×Q8—31no—
372C2×Q8—61no—
373C2×Q8—61no—
374C2×Q8—91no—
375C2×Q8—182no—
376C2×D4—31no—
377C22×C4—61no—
378C22×C4—182no—
379SD16—94no—
380C2×C8—91no—
381C2×C8—91no—
382C2×C8C2×D3212yes—
383C4⋊C4—32no—
384C4⋊C4—31no—
385C4⋊C4—32no—
386C4⋊C4—31no—
387C4⋊C4—61no—
388C4⋊C4—61no—
389C4⋊C4—61no—
390C4⋊C4—91no—
391C4⋊C4—92no—
392C4⋊C4—182no—
393C4⋊C4—182no—
394C4⋊C4—182no—
395C4⋊C4—182no—
396C22⋊C4—61no—
397C22⋊C4—182no—
398C42—61no—
399C42—92no—
400C42—182no—
401C42C2×D3211yescharacteristic
402C22×C3—21no—
403C22×C3—62no—
404C22×C3—121no—
405C22×C3—121no—
406C22×C3C2×D3×D411yescharacteristic
407C22×C3C2×D3×D411yescharacteristic
408C2×D3—22no—
409C2×D3—41no—
410C2×D3—41no—
411C3×C4—21no—
412C3×C4—21no—
413C3×C4—21no—
414C3×C4—21no—
415C3×C4—22no—
416C3×C4—41no—
417C3×C4—62no—
418C3×C4—121no—
419C3×C4—121no—
420C3×C4—122no—
421C3×C4—122no—
422C3×C4#91512yes—
423C3×C4#91812yes—
424C3×C4C2×D3×Q811yescharacteristic
425C3×C4C2×D3×Q811yescharacteristic
426C3×C4#101011yescharacteristic
427C3×C4#101011yescharacteristic
428Dic3—22no—
429Dic3—41no—
430Dic3—42no—
431Dic3—42no—
432Dic3—41no—
433Dic3—62no—
434Dic3—62no—
435Dic3—62no—
436Dic3—62no—
437Dic3—122no—
438Dic3—122no—
439C32#338511yescharacteristic, complemented, Sylow
440C23—61no—
441Q8—32no—
442Q8—61no—
443Q8—182no—
444Q8—241no—
445Q8—241no—
446Q8—722no—
447D4—32no—
448D4—61no—
449C2×C4—61no—
450C2×C4—61no—
451C2×C4—62no—
452C2×C4—61no—
453C2×C4—62no—
454C2×C4—92no—
455C2×C4—92no—
456C2×C4—122no—
457C2×C4—722no—
458C2×C4#380211yescharacteristic
459C2×C4#380211yescharacteristic
460C2×C4C22×D3211yescharacteristic
461C8—22no—
462C8—92no—
463C8—181no—
464C2×C3—21no—
465C2×C3—21no—
466C2×C3—21no—
467C2×C3—122no—
468C2×C3#563211yescharacteristic
469C2×C3#563211yescharacteristic
470C2×C3C2×#91511yescharacteristic
471C2×C3C2×#91811yescharacteristic
472C2×C3#577411yescharacteristic
473C2×C3#577411yescharacteristic
474D3—42no—
475C22—62no—
476C22—121no—
477C22—121no—
478C22C2×#380211yescharacteristic
479C4—21no—
480C4—62no—
481C4—121no—
482C4—122no—
483C4—122no—
484C4—121no—
485C4—182no—
486C4—182no—
487C4#6381112yes—
488C4#6430911yescharacteristic
489C4D32×Q811yescharacteristic
490C3—21no—
491C3#8105611yescharacteristic, complemented
492C3#8113711yescharacteristic, complemented
493C2—122no—
494C2#1059452611yescharacteristic
495C2C2×#6381111yescharacteristic
496C2#1059472011yescharacteristic
subgroupG/H
centerC22C2×#3802
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×C4⋊C8C22
socleC22×C32C22×D4
prime radicalC2×C3×D12C23
hypercenterC4⋊C8D32
hypocenterC32#3385
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×#4850C2semidirect
6. #10590903C2semidirect
7. #10590820C2semidirect
11. #10590312C2semidirect
57. #4850D3semidirect
96. #3715Q8semidirect
439. C32#3385semidirect
491. C3#81056semidirect
492. C3#81137semidirect

Maximal subgroups

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

subgroupindex
#105939562
#105938562
#105925302
C3×#48502
C3×#48422
#105909032
#105908202
#105907782
#105907432
C4×#37152
#105903122
#811373
#810563