Finite Group Databasebeta

← C2×#10590762 #11868260

Subgroups — C2×#10590762 #11868260

Order 1152.

1025 conjugacy classes of subgroups.

The subgroup lattice has 462 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#63918C211yesmaximal, characteristic, complemented
2C2×Dic3×D12C211yesmaximal, characteristic
3C2×#63645C211yesmaximal, characteristic, complemented
4C2×C3×#821C211yesmaximal, characteristic
5C2×C3×Dic3⋊C8C211yesmaximal, characteristic, complemented
6C2×#63575C211yesmaximal, characteristic, complemented
7C2×#63563C211yesmaximal, characteristic
8#10590762C218yesmaximal, direct product factor
9C2×#4846—31nomaximal
10C2×#4759—31nomaximal
11C22×C3×D12C2211yescharacteristic
12C22×#627—21no—
13C22×D3×Dic3—21no—
14C22×C32×C8C2211yescharacteristic
15C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
16C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
17C2×C3×C4⋊Dic3C2211yescharacteristic
18C2×C3×C4×Dic3C2211yescharacteristic
19C22×C3×C3⋊C8C2211yescharacteristic
20C2×Dic3⋊Dic3—21no—
21C2×(C2×D3)⋊Dic3—21no—
22#63918—22no—
23#63918C2214yescomplemented
24Dic3×D12—22no—
25Dic3×D12C2214yes—
26#63645C2214yescomplemented
27C3×#821C2214yes—
28C3×Dic3⋊C8C2214yescomplemented
29#63575C2214yescomplemented
30#63563C2214yes—
31C2×D4×Dic3—31no—
32C2×#888—31no—
33C2×C4×D12—31no—
34C2×#869—31no—
35C2×C3×C4⋊C8—31no—
36C2×C3×#102—31no—
37C2×#832—31no—
38C2×#821—31no—
39C2×#821D311yescharacteristic
40C2×#818—31no—
41C2×#818—31no—
42C2×#818—31no—
43C2×#818—61no—
44C2×Dic3⋊C8D311yescharacteristic, complemented
45C2×#807—31no—
46#4846—38no—
47#4759—38no—
48C23×C3×D3—21no—
49C22×C32×C4C2311yescharacteristic
50C22×C3⋊Dic3—21no—
51C22×C3⋊Dic3—21no—
52C22×C3×Dic3—21no—
53C22×C3×Dic3D411yescharacteristic
54C22×C3×Dic3D411yescharacteristic
55C2×C3×D12—21no—
56C2×C3×D12—22no—
57C2×C3×D12Q814yescomplemented
58C2×C3×D12C2312yes—
59C2×#627—24no—
60C2×#627—44no—
61C2×D3×Dic3—24no—
62C2×D3×Dic3—44no—
63C2×C32×C8—22no—
64C2×C32×C8C2312yes—
65C4⋊(C3⋊Dic3)—21no—
66C4⋊(C3⋊Dic3)—21no—
67C4⋊(C3⋊Dic3)C2312yes—
68C4⋊(C3⋊Dic3)C2312yes—
69C3×C4⋊Dic3—21no—
70C3×C4⋊Dic3C2312yes—
71C3×C4×Dic3D412yes—
72C3×C4×Dic3C2312yes—
73C2×C3×C3⋊C8—22no—
74C2×C3×C3⋊C8C2312yes—
75Dic3⋊Dic3—24no—
76(C2×D3)⋊Dic3—24no—
77C2×#474—91noSylow
78C22×C3×D4—31no—
79C23×Dic3—61no—
80C22×D12C2×D311yescharacteristic
81C22×C4×D3—61no—
82C22×Dic6—61no—
83C22×Dic6—61no—
84C22×C3×C8—21no—
85C22×C3×C8—31no—
86C22×C3×C8C2×D311yescharacteristic
87C22×C3×C8C2×D311yescharacteristic
88C2×C3×C4⋊C4—31no—
89C2×C3×C42—31no—
90C2×#217—61no—
91D4×Dic3—34no—
92D4×Dic3—62no—
93C2×(C2×D3)⋊C4—61no—
94C2×C4⋊Dic3—31no—
95C2×C4⋊Dic3—31no—
96C2×C4⋊Dic3—31no—
97C2×C4⋊Dic3—31no—
98C2×C4⋊Dic3—61no—
99C2×C4⋊Dic3—61no—
100C2×C4⋊Dic3—61no—
101C2×C4⋊Dic3C2×D311yescharacteristic
102C2×Dic3⋊C4—61no—
103C2×C4×Dic3C2×D311yescharacteristic
104C22×C3⋊C8C2×D311yescharacteristic
105#888—34no—
106#888—62no—
107C4×D12—34no—
108C4×D12—62no—
109#869—34no—
110#869—62no—
111C3×C4⋊C8—34no—
112C3×#102—34no—
113#832—34no—
114#821—34no—
115#821C2×D314yes—
116#818—34no—
117#818—34no—
118#818—34no—
119#818—64no—
120Dic3⋊C8C2×D314yescomplemented
121#807—34no—
122C23×C32C2×D411yescharacteristic
123C22×C3×D3—24no—
124C22×C3×D3—22no—
125C22×C3×D3—42no—
126C22×C3×D3—42no—
127C2×C32×C4C2×D411yescharacteristic
128C2×C32×C4C2×Q812yes—
129C2×C32×C4#4112yes—
130C2×C32×C4C2411yescharacteristic
131C2×C3⋊Dic3—22no—
132C2×C3⋊Dic3—22no—
133C2×C3⋊Dic3—42no—
134C2×C3⋊Dic3—42no—
135C2×C3×Dic3—22no—
136C2×C3×Dic3—22no—
137C2×C3×Dic3—42no—
138C2×C3×Dic3D814yes—
139C2×C3×Dic3C2×D412yes—
140C2×C3×Dic3C2×D412yes—
141C3×D12—24no—
142C3×D12—22no—
143C3×D12C2×Q814yescomplemented
144#627—48no—
145D3×Dic3—48no—
146C32×C8—22no—
147C3×C3⋊C8—22no—
148C2×C4⋊Q8—91no—
149C2×C4×D4—91no—
150#474—98no—
151C2×#107—91no—
152C2×#107—91no—
153C2×C4⋊C8—31no—
154C2×#102—31no—
155C2×#102—91no—
156C24×C3—61no—
157C23×D3—21no—
158C2×C3×D4—34no—
159C2×C3×D4—32no—
160C2×C3×D4—61no—
161C2×C3×D4—62no—
162C22×C3×C4—21no—
163C22×C3×C4—31no—
164C22×C3×C4—31no—
165C22×C3×C4—61no—
166C22×C3×C4C22×D311yescharacteristic
167C22×C3×C4C22×D311yescharacteristic
168C22×Dic3—21no—
169C22×Dic3—61no—
170C22×Dic3—61no—
171C22×Dic3—61no—
172C22×Dic3—61no—
173C22×Dic3—64no—
174C22×Dic3—121no—
175C22×Dic3—121no—
176C22×Dic3—124no—
177C22×Dic3D1211yescharacteristic
178C22×Dic3D1211yescharacteristic
179C2×D12—21no—
180C2×D12—22no—
181C2×D12Dic614yescomplemented
182C2×D12C22×D312yes—
183C2×C4×D3—64no—
184C2×C4×D3—124no—
185C2×Dic6—64no—
186C2×Dic6—64no—
187C2×Dic6—124no—
188C2×Dic6—124no—
189C2×C3×C8—24no—
190C2×C3×C8—22no—
191C2×C3×C8—22no—
192C2×C3×C8—22no—
193C2×C3×C8—32no—
194C2×C3×C8—62no—
195C2×C3×C8C22×D312yes—
196C2×C3×C8C22×D312yes—
197C3×C4⋊C4—32no—
198C3×C4⋊C4—61no—
199C3×C42—32no—
200C3×C42—32no—
201#217—64no—
202(C2×D3)⋊C4—64no—
203C4⋊Dic3—21no—
204C4⋊Dic3—32no—
205C4⋊Dic3—32no—
206C4⋊Dic3—32no—
207C4⋊Dic3—32no—
208C4⋊Dic3—62no—
209C4⋊Dic3—62no—
210C4⋊Dic3—64no—
211C4⋊Dic3—61no—
212C4⋊Dic3—61no—
213C4⋊Dic3—61no—
214C4⋊Dic3—61no—
215C4⋊Dic3—121no—
216C4⋊Dic3—121no—
217C4⋊Dic3C22×D312yes—
218Dic3⋊C4—64no—
219C4×Dic3D1212yes—
220C4×Dic3C22×D312yes—
221C2×C3⋊C8—22no—
222C2×C3⋊C8C22×D312yes—
223C22×C32C22⋊Q812yes—
224C22×C32C2×D812yes—
225C22×C32#13712yes—
226C22×C32C22×D411yescharacteristic
227C2×C3×D3—24no—
228C2×C3×D3—42no—
229C2×C3×D3—42no—
230C2×C3×D3—48no—
231C32×C4C22⋊Q812yes—
232C32×C4C22×Q811yescharacteristic
233C32×C4C2×#4111yescharacteristic
234C3⋊Dic3—42no—
235C3⋊Dic3—42no—
236C3×Dic3—22no—
237C3×Dic3—42no—
238C3×Dic3C2×D814yes—
239C22×Q8—181no—
240C22×D4—31no—
241C23×C4—181no—
242C22×C8—31no—
243C22×C8D3211yescharacteristic
244C4⋊Q8—94no—
245C4⋊Q8—182no—
246C4×D4—94no—
247C4×D4—182no—
248C2×C4⋊C4—31no—
249C2×C4⋊C4—91no—
250C2×C4⋊C4—91no—
251C2×C4⋊C4—181no—
252C2×C22⋊C4—181no—
253C2×C42—31no—
254#107—94no—
255#107—94no—
256C4⋊C8—34no—
257#102—34no—
258#102—94no—
259C23×C3—21no—
260C23×C3—64no—
261C23×C3—62no—
262C23×C3—122no—
263C23×C3—122no—
264C23×C3C2×D1211yescharacteristic
265C23×C3D3×D411yescharacteristic
266C22×D3—24no—
267C22×D3—22no—
268C22×D3—42no—
269C22×D3—42no—
270C3×D4—34no—
271C3×D4—64no—
272C3×D4—62no—
273C2×C3×C4—21no—
274C2×C3×C4—22no—
275C2×C3×C4—21no—
276C2×C3×C4—22no—
277C2×C3×C4—34no—
278C2×C3×C4—32no—
279C2×C3×C4—32no—
280C2×C3×C4—62no—
281C2×C3×C4—62no—
282C2×C3×C4—122no—
283C2×C3×C4C2×Dic612yes—
284C2×C3×C4C2×D1211yescharacteristic
285C2×C3×C4D3×D411yescharacteristic
286C2×C3×C4#23712yes—
287C2×C3×C4#23712yes—
288C2×C3×C4D3×Q812yes—
289C2×C3×C4C23×D311yescharacteristic
290C2×C3×C4C23×D311yescharacteristic
291C2×Dic3—22no—
292C2×Dic3—22no—
293C2×Dic3—42no—
294C2×Dic3—62no—
295C2×Dic3—62no—
296C2×Dic3—62no—
297C2×Dic3—62no—
298C2×Dic3—122no—
299C2×Dic3—122no—
300C2×Dic3—122no—
301C2×Dic3—122no—
302C2×Dic3—122no—
303C2×Dic3—122no—
304C2×Dic3—128no—
305C2×Dic3—242no—
306C2×Dic3—242no—
307C2×Dic3D2414yes—
308C2×Dic3C2×D1212yes—
309C2×Dic3C2×D1212yes—
310D12—24no—
311D12—22no—
312D12C2×Dic614yescomplemented
313C4×D3—128no—
314Dic6—128no—
315Dic6—128no—
316C3×C8—24no—
317C3×C8—22no—
318C3×C8—22no—
319C3×C8—62no—
320C3⋊C8—22no—
321C2×C32#47414yescomplemented
322C2×C32C2×C22⋊Q811yescharacteristic
323C2×C32C22×D811yescharacteristic
324C2×C32C2×#13711yescharacteristic
325C3×D3—44no—
326C24—61no—
327C2×Q8—184no—
328C2×Q8—364no—
329C2×D4—32no—
330C2×D4—34no—
331C2×D4—61no—
332C2×D4—62no—
333C22×C4—31no—
334C22×C4—31no—
335C22×C4—61no—
336C22×C4—184no—
337C22×C4—181no—
338C22×C4—181no—
339C22×C4—364no—
340C22×C4C2×D3211yescharacteristic
341C2×C8—22no—
342C2×C8—32no—
343C2×C8—62no—
344C2×C8C2×D3212yes—
345C4⋊C4—32no—
346C4⋊C4—61no—
347C4⋊C4—92no—
348C4⋊C4—92no—
349C4⋊C4—184no—
350C4⋊C4—181no—
351C4⋊C4—181no—
352C22⋊C4—184no—
353C42—32no—
354C42—32no—
355C22×C3—21no—
356C22×C3—22no—
357C22×C3—22no—
358C22×C3—22no—
359C22×C3—64no—
360C22×C3—122no—
361C22×C3—122no—
362C22×C3—128no—
363C22×C3#87812yes—
364C22×C3#89712yes—
365C22×C3C2×D2412yes—
366C22×C3#90912yes—
367C22×C3D3×D812yes—
368C22×C3#91512yes—
369C22×C3C22×D1211yescharacteristic
370C22×C3C2×D3×D411yescharacteristic
371C2×D3—24no—
372C2×D3—42no—
373C2×D3—42no—
374C2×D3—48no—
375C3×C4—21no—
376C3×C4—21no—
377C3×C4—22no—
378C3×C4—34no—
379C3×C4—62no—
380C3×C4—122no—
381C3×C4#87812yes—
382C3×C4#89712yes—
383C3×C4C22×Dic611yescharacteristic
384C3×C4C2×#23711yescharacteristic
385C3×C4C2×#23711yescharacteristic
386C3×C4C2×D3×Q811yescharacteristic
387Dic3—22no—
388Dic3—42no—
389Dic3—122no—
390Dic3—122no—
391Dic3—122no—
392Dic3—122no—
393Dic3—242no—
394Dic3—242no—
395Dic3C2×D2414yes—
396C32C2×#47411yescharacteristic, complemented, Sylow
397C23—62no—
398C23—64no—
399C23—122no—
400C23—122no—
401C23D3×D1211yescharacteristic
402Q8—368no—
403D4—34no—
404D4—62no—
405D4—64no—
406C2×C4—32no—
407C2×C4—34no—
408C2×C4—32no—
409C2×C4—62no—
410C2×C4—62no—
411C2×C4—122no—
412C2×C4—182no—
413C2×C4—182no—
414C2×C4—368no—
415C2×C4—362no—
416C2×C4—362no—
417C2×C4D3×Dic612yes—
418C2×C4D3×D1211yescharacteristic
419C2×C4#380512yes—
420C2×C4C22×D3211yescharacteristic
421C8—22no—
422C8—62no—
423C2×C3—24no—
424C2×C3—21no—
425C2×C3—21no—
426C2×C3—21no—
427C2×C3—124no—
428C2×C3#475914yescomplemented
429C2×C3#484614yescomplemented
430C2×C3C2×#87811yescharacteristic
431C2×C3C2×#89711yescharacteristic
432C2×C3C22×D2411yescharacteristic
433C2×C3C2×#90911yescharacteristic
434C2×C3C2×D3×D811yescharacteristic
435C2×C3C2×#91511yescharacteristic
436D3—44no—
437C22—64no—
438C22—128no—
439C22—122no—
440C22—122no—
441C22D3×D2412yes—
442C22#6380012yes—
443C22#6389312yes—
444C22C2×D3×D1211yescharacteristic
445C4—34no—
446C4—62no—
447C4—122no—
448C4—362no—
449C4—362no—
450C4#6389312yes—
451C4C2×D3×Dic611yescharacteristic
452C4C2×#380511yescharacteristic
453C3—21no—
454C3C2×#475911yescharacteristic, complemented
455C3C2×#484611yescharacteristic, complemented
456C2—124no—
457C2#1059076214yesdirect product factor
458C2C2×D3×D2411yescharacteristic
459C2C2×#6380011yescharacteristic
460C2C2×#6389311yescharacteristic
subgroupG/H
centerC23D3×D12
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC22×C32×C8C22
socleC23×C32C2×D4
prime radicalC22×C3×D12C22
hypercenterC22×C8D32
hypocenterC32C2×#474
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C23 ◁ C22×C4 ◁ C22×C8

Complements

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

NH ≅ G/Ntype
1. C2×#63918C2semidirect
3. C2×#63645C2semidirect
5. C2×C3×Dic3⋊C8C2semidirect
6. C2×#63575C2semidirect
8. #10590762C2direct (N × H)
23. #63918C22semidirect
26. #63645C22semidirect
28. C3×Dic3⋊C8C22semidirect
29. #63575C22semidirect
44. C2×Dic3⋊C8D3semidirect
57. C2×C3×D12Q8semidirect
120. Dic3⋊C8C2×D3semidirect
143. C3×D12C2×Q8semidirect
181. C2×D12Dic6semidirect
312. D12C2×Dic6semidirect
321. C2×C32#474semidirect
396. C32C2×#474semidirect
428. C2×C3#4759semidirect
429. C2×C3#4846semidirect
454. C3C2×#4759semidirect
455. C3C2×#4846semidirect
457. C2#10590762direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#639182
C2×Dic3×D122
C2×#636452
C2×C3×#8212
C2×C3×Dic3⋊C82
C2×#635752
C2×#635632
#105907622
C2×#48463
C2×#47593