Finite Group Databasebeta

← C2×#10590632 #11899517

Subgroups — C2×#10590632 #11899517

Order 1152.

869 conjugacy classes of subgroups.

The subgroup lattice has 454 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#64113C211yesmaximal, characteristic, complemented
2C2×C3×#904C211yesmaximal, characteristic, complemented
3C22×C3×C3⋊C16C211yesmaximal, characteristic, complemented
4C2×#63551C211yesmaximal, characteristic, complemented
5C2×#63549C211yesmaximal, characteristic, complemented
6C2×#63548C211yesmaximal, characteristic, complemented
7#10590632C218yesmaximal, direct product factor
8C2×#63546C211yesmaximal, characteristic, complemented
9C2×#5194—31nomaximal
10C2×#4904—31nomaximal
11C2×#3828—21no—
12C2×C3×#235—21no—
13C22×C32×C8C2211yescharacteristic
14C2×#3746C2211yescharacteristic
15#64113—22no—
16#64113C2214yescomplemented
17C2×#3745C2211yescharacteristic
18C2×#3744—21no—
19C2×C3×Dic12C2211yescharacteristic
20C3×#904—22no—
21C3×#904C2214yescomplemented
22C2×C3×D24C2211yescharacteristic
23C2×C3×#204—21no—
24C2×C3×C3⋊C16C2211yescharacteristic
25C2×C3×C3⋊C16C2211yescharacteristic
26C2×C3×C3⋊C16C2214yescomplemented
27#63551C2214yescomplemented
28#63549C2214yescomplemented
29#63548C2214yescomplemented
30#63546C2214yescomplemented
31C2×C3×#135—31no—
32C2×#904—31no—
33C2×#904—31no—
34C2×#904—61no—
35C2×#904D311yescharacteristic, complemented
36C22×C3×C16—31no—
37#5194—38no—
38C2×#829—31no—
39C2×#828—31no—
40C2×#827—31no—
41C2×#826—31no—
42C22×C3⋊C16D311yescharacteristic, complemented
43C2×Dic24—31no—
44#4904—38no—
45C2×#800—31no—
46C2×#800—31no—
47C2×D48—31no—
48C22×C32×C4D411yescharacteristic
49C2×#638—41no—
50#3828—24no—
51#3828—42no—
52C2×C4⋊(C3⋊D3)—21no—
53C2×C4×C3⋊D3—41no—
54C2×#634—21no—
55C2×C3×#67—41no—
56C3×#235—24no—
57C3×#235—42no—
58C2×C3×D12—21no—
59C2×C3×C4×D3—41no—
60C2×C3×Dic6—21no—
61C2×C32×C8D411yescharacteristic
62C2×C32×C8D412yes—
63C2×C32×C8C2311yescharacteristic
64C2×C32×C8C2312yes—
65#3746—21no—
66#3746C2312yes—
67#3745—21no—
68#3745C2312yes—
69#3744—24no—
70C3×Dic12—21no—
71C3×Dic12C2312yes—
72C3×D24—21no—
73C3×D24C2312yes—
74C3×#204—24no—
75C3×C3⋊C16C2312yes—
76C3×C3⋊C16C2312yes—
77C2×#508—91noSylow
78C2×C3×#41—61no—
79C2×#235—21no—
80C2×#235—62no—
81C2×#235—61no—
82C2×#235—61no—
83C3×#135—34no—
84C3×#135—62no—
85C2×C3×Q16—31no—
86C2×C3×SD16—61no—
87C2×C3×D8—31no—
88C22×C3×C8—21no—
89C22×C3×C8C2×D311yescharacteristic
90C22×C3×C8C2×D311yescharacteristic
91C2×Dic12—31no—
92C2×Dic12—31no—
93C2×Dic12—61no—
94C2×Dic12C2×D311yescharacteristic
95#904—22no—
96#904—34no—
97#904—34no—
98#904—64no—
99#904—64no—
100#904—62no—
101#904—62no—
102#904C2×D314yescomplemented
103C2×D24—31no—
104C2×D24—31no—
105C2×D24—61no—
106C2×D24C2×D311yescharacteristic
107C2×#204—21no—
108C2×#204—62no—
109C2×#204—61no—
110C2×#204—61no—
111C2×C3×C16—31no—
112C2×C3×C16—31no—
113C2×C3×C16—34no—
114#829—34no—
115#828—34no—
116#827—34no—
117#826—34no—
118C2×C3⋊C16C2×D311yescharacteristic
119C2×C3⋊C16C2×D311yescharacteristic
120C2×C3⋊C16C2×D314yescomplemented
121Dic24—34no—
122#800—34no—
123#800—34no—
124D48—34no—
125C23×C32D811yescharacteristic
126C22×C3⋊D3—41no—
127C22×C3×D3—41no—
128C2×C32×C4D811yescharacteristic
129C2×C32×C4D812yes—
130C2×C32×C4C2×D411yescharacteristic
131C2×C32×C4C2×D412yes—
132#638—44no—
133C2×C3⋊Dic3—41no—
134C4⋊(C3⋊D3)—22no—
135C4⋊(C3⋊D3)—41no—
136C4×C3⋊D3—44no—
137#634—22no—
138#634—41no—
139C3×#67—44no—
140C2×C3×Dic3—41no—
141C3×D12—22no—
142C3×D12—41no—
143C3×C4×D3—44no—
144C3×Dic6—22no—
145C3×Dic6—41no—
146C32×C8C2×D412yes—
147C32×C8C2×D411yescharacteristic
148C32×C8C2411yescharacteristic
149C2×#135—31no—
150C2×#135—91no—
151#508—98no—
152C2×Q32—91no—
153C2×SD32—91no—
154C2×SD32—91no—
155C2×D16—91no—
156C22×C16—31no—
157C3×#41—64no—
158C3×#41—122no—
159C2×C3×Q8—61no—
160C2×C3×D4—61no—
161C2×C3×D4—121no—
162C22×C3×C4—21no—
163C22×C3×C4—121no—
164C22×C3×C4D1211yescharacteristic
165C22×C3×C4#6711yescharacteristic
166C2×#67—41no—
167C2×#67—122no—
168C2×#67—121no—
169C2×#67—121no—
170#235—24no—
171#235—42no—
172#235—68no—
173#235—64no—
174#235—64no—
175#235—124no—
176#235—122no—
177#235—122no—
178C2×D12—21no—
179C2×D12—62no—
180C2×D12—61no—
181C2×D12—61no—
182C2×C4×D3—41no—
183C2×C4×D3—122no—
184C2×C4×D3—121no—
185C2×C4×D3—121no—
186C2×Dic6—21no—
187C2×Dic6—62no—
188C2×Dic6—61no—
189C2×Dic6—61no—
190C3×Q16—32no—
191C3×Q16—61no—
192C3×SD16—64no—
193C3×D8—32no—
194C3×D8—61no—
195C2×C3×C8—21no—
196C2×C3×C8—22no—
197C2×C3×C8—21no—
198C2×C3×C8—22no—
199C2×C3×C8D1211yescharacteristic
200C2×C3×C8D1212yes—
201C2×C3×C8#6711yescharacteristic
202C2×C3×C8#6712yes—
203C2×C3×C8C22×D311yescharacteristic
204C2×C3×C8C22×D312yes—
205C2×C3×C8C22×D311yescharacteristic
206C2×C3×C8C22×D312yes—
207Dic12—21no—
208Dic12—32no—
209Dic12—32no—
210Dic12—62no—
211Dic12—62no—
212Dic12—61no—
213Dic12—61no—
214Dic12C22×D312yes—
215D24—21no—
216D24—32no—
217D24—32no—
218D24—62no—
219D24—62no—
220D24—61no—
221D24—61no—
222D24C22×D312yes—
223#204—24no—
224#204—68no—
225#204—64no—
226#204—64no—
227C3×C16—32no—
228C3×C16—32no—
229C3⋊C16C22×D312yes—
230C3⋊C16C22×D312yes—
231C22×C32—22no—
232C22×C32C2×D812yes—
233C22×C32C2×D811yescharacteristic
234C2×C3⋊D3—42no—
235C2×C3⋊D3—82no—
236C2×C3×D3—42no—
237C2×C3×D3—82no—
238C32×C4C2×D811yescharacteristic
239C32×C4C2×D812yes—
240C32×C4C22×D411yescharacteristic
241C3⋊Dic3—42no—
242C3×Dic3—42no—
243C2×#41—61no—
244C2×#41—181no—
245#135—34no—
246#135—62no—
247#135—94no—
248#135—182no—
249C2×Q16—31no—
250C2×Q16—91no—
251C2×SD16—61no—
252C2×SD16—181no—
253C2×D8—31no—
254C2×D8—91no—
255C22×C8D3211yescharacteristic
256Q32—94no—
257SD32—94no—
258SD32—94no—
259D16—94no—
260C2×C16—31no—
261C2×C16—31no—
262C2×C16—34no—
263C23×C3—21no—
264C23×C3—121no—
265C23×C3D2411yescharacteristic
266C23×C3#21311yescharacteristic
267C22×D3—41no—
268C22×D3—122no—
269C22×D3—121no—
270C22×D3—121no—
271C3×Q8—62no—
272C3×Q8—121no—
273C3×D4—62no—
274C3×D4—124no—
275C3×D4—121no—
276C2×C3×C4—22no—
277C2×C3×C4—21no—
278C2×C3×C4—21no—
279C2×C3×C4—22no—
280C2×C3×C4—121no—
281C2×C3×C4—124no—
282C2×C3×C4D2412yes—
283C2×C3×C4D2411yescharacteristic
284C2×C3×C4#21312yes—
285C2×C3×C4#21311yescharacteristic
286C2×C3×C4C2×D1211yescharacteristic
287C2×C3×C4C2×D1212yes—
288C2×C3×C4C2×#6711yescharacteristic
289C2×C3×C4C2×#6712yes—
290#67—44no—
291#67—128no—
292#67—124no—
293#67—124no—
294C2×Dic3—41no—
295C2×Dic3—122no—
296C2×Dic3—121no—
297C2×Dic3—121no—
298D12—22no—
299D12—41no—
300D12—64no—
301D12—62no—
302D12—62no—
303D12—122no—
304D12—121no—
305D12—121no—
306C4×D3—44no—
307C4×D3—128no—
308C4×D3—124no—
309C4×D3—124no—
310Dic6—22no—
311Dic6—41no—
312Dic6—64no—
313Dic6—62no—
314Dic6—62no—
315Dic6—122no—
316Dic6—121no—
317Dic6—121no—
318C3×C8—21no—
319C3×C8—22no—
320C3×C8—21no—
321C3×C8C2×D1212yes—
322C3×C8C2×D1211yescharacteristic
323C3×C8C2×#6712yes—
324C3×C8C2×#6711yescharacteristic
325C3×C8C23×D311yescharacteristic
326C3×C8C23×D311yescharacteristic
327C2×C32—22no—
328C2×C32#50812yescomplemented
329C2×C32C22×D811yescharacteristic
330C3⋊D3—82no—
331C3×D3—82no—
332#41—64no—
333#41—122no—
334#41—184no—
335#41—362no—
336C2×Q8—61no—
337C2×Q8—181no—
338C2×D4—61no—
339C2×D4—121no—
340C2×D4—181no—
341C2×D4—361no—
342C22×C4—121no—
343C22×C4—361no—
344C22×C4#62611yescharacteristic
345Q16—32no—
346Q16—61no—
347Q16—92no—
348Q16—181no—
349SD16—64no—
350SD16—184no—
351D8—32no—
352D8—61no—
353D8—92no—
354D8—181no—
355C2×C8#62611yescharacteristic
356C2×C8#62612yes—
357C2×C8C2×D3211yescharacteristic
358C2×C8C2×D3212yes—
359C16—32no—
360C16—32no—
361C22×C3—22no—
362C22×C3—22no—
363C22×C3—21no—
364C22×C3—22no—
365C22×C3—42no—
366C22×C3—122no—
367C22×C3—242no—
368C22×C3C2×D2412yes—
369C22×C3C2×D2411yescharacteristic
370C22×C3C2×#21312yes—
371C22×C3C2×#21311yescharacteristic
372C2×D3—42no—
373C2×D3—82no—
374C2×D3—124no—
375C2×D3—122no—
376C2×D3—122no—
377C2×D3—244no—
378C2×D3—242no—
379C2×D3—242no—
380C3×C4—21no—
381C3×C4—21no—
382C3×C4—22no—
383C3×C4—122no—
384C3×C4C2×D2411yescharacteristic
385C3×C4C2×D2412yes—
386C3×C4C2×#21311yescharacteristic
387C3×C4C2×#21312yes—
388C3×C4C22×D1211yescharacteristic
389C3×C4C22×#6711yescharacteristic
390Dic3—42no—
391Dic3—124no—
392Dic3—122no—
393Dic3—122no—
394C32C2×#50811yescharacteristic, complemented, Sylow
395C23—121no—
396C23—361no—
397C23#371411yescharacteristic
398Q8—62no—
399Q8—121no—
400Q8—182no—
401Q8—361no—
402D4—62no—
403D4—124no—
404D4—121no—
405D4—182no—
406D4—364no—
407D4—361no—
408C2×C4—121no—
409C2×C4—124no—
410C2×C4—361no—
411C2×C4—364no—
412C2×C4#371412yes—
413C2×C4#371411yescharacteristic
414C2×C4C2×#62611yescharacteristic
415C2×C4C2×#62612yes—
416C8C2×#62611yescharacteristic
417C8C2×#62612yes—
418C8C22×D3211yescharacteristic
419C2×C3—22no—
420C2×C3—22no—
421C2×C3—22no—
422C2×C3—21no—
423C2×C3—42no—
424C2×C3—242no—
425C2×C3#490412yescomplemented
426C2×C3#519412yescomplemented
427C2×C3C22×D2411yescharacteristic
428C2×C3C22×#21311yescharacteristic
429D3—82no—
430D3—244no—
431D3—242no—
432D3—242no—
433C22—22no—
434C22—122no—
435C22—242no—
436C22—362no—
437C22—722no—
438C22C2×#371412yes—
439C22C2×#371411yescharacteristic
440C4—122no—
441C4—362no—
442C4C2×#371412yes—
443C4C2×#371411yescharacteristic
444C4C22×#62611yescharacteristic
445C3—21no—
446C3C2×#490411yescharacteristic, complemented
447C3C2×#519411yescharacteristic, complemented
448C2—22no—
449C2—242no—
450C2—722no—
451C2#1059063212yesdirect product factor
452C2C22×#371411yescharacteristic
subgroupG/H
centerC2×C4#3714
commutator, cosocleC32×C8C24
FrattiniC8C22×D32
FittingC22×C32×C8C22
socleC22×C32C2×D8
hypercenterC22×C8D32
hypocenterC32C2×#508
LCSG ▷ C32×C8 ▷ C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C2×C4 ◁ C22×C4 ◁ C22×C8

Complements

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

NH ≅ G/Ntype
1. C2×#64113C2semidirect
2. C2×C3×#904C2semidirect
3. C22×C3×C3⋊C16C2semidirect
4. C2×#63551C2semidirect
5. C2×#63549C2semidirect
6. C2×#63548C2semidirect
7. #10590632C2direct (N × H)
8. C2×#63546C2semidirect
16. #64113C22semidirect
21. C3×#904C22semidirect
26. C2×C3×C3⋊C16C22semidirect
27. #63551C22semidirect
28. #63549C22semidirect
29. #63548C22semidirect
30. #63546C22semidirect
35. C2×#904D3semidirect
42. C22×C3⋊C16D3semidirect
102. #904C2×D3semidirect
120. C2×C3⋊C16C2×D3semidirect
328. C2×C32#508semidirect
394. C32C2×#508semidirect
425. C2×C3#4904semidirect
426. C2×C3#5194semidirect
446. C3C2×#4904semidirect
447. C3C2×#5194semidirect
451. C2#10590632direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#641132
C2×C3×#9042
C22×C3×C3⋊C162
C2×#635512
C2×#635492
C2×#635482
#105906322
C2×#635462
C2×#51943
C2×#49043