Finite Group Databasebeta

← C2×#10590699 #11858801

Subgroups — C2×#10590699 #11858801

Order 1152.

897 conjugacy classes of subgroups.

The subgroup lattice has 451 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#63855C211yesmaximal, characteristic
2C2×#63642C211yesmaximal, characteristic, complemented
3C2×C3×(C2×D3)⋊C8C211yesmaximal, characteristic
4C2×C3×Dic3⋊C8C211yesmaximal, characteristic, complemented
5C2×Dic3⋊(C3⋊C8)C211yesmaximal, characteristic, complemented
6C2×(C2×D3)⋊(C3⋊C8)C211yesmaximal, characteristic
7C2×#63553C211yesmaximal, characteristic, complemented
8#10590699C218yesmaximal, direct product factor
9C2×#4840—31nomaximal
10C2×#4720—31nomaximal
11C22×C3×C4×D3C2211yescharacteristic
12C22×C32×C8C2211yescharacteristic
13C2×C4×C3⋊Dic3C2211yescharacteristic
14C22×C3⋊(C3⋊C8)C2211yescharacteristic
15C2×C3×C4×Dic3C2211yescharacteristic
16C22×C3×C3⋊C8C2211yescharacteristic
17C22×C3×C3⋊C8C2211yescharacteristic
18C2×Dic3⋊Dic3C411yescharacteristic
19C2×Dic3⋊Dic3C411yescharacteristic
20C2×(C2×D3)⋊Dic3C411yescharacteristic
21C2×(C2×D3)⋊Dic3C411yescharacteristic
22#63855C414yes—
23#63855C2214yes—
24#63642C2214yescomplemented
25C3×(C2×D3)⋊C8C2214yes—
26C3×Dic3⋊C8C2214yescomplemented
27Dic3⋊(C3⋊C8)C2214yescomplemented
28(C2×D3)⋊(C3⋊C8)C2214yes—
29#63553C2214yescomplemented
30C2×#926—31no—
31C2×#872—31no—
32C2×C3×C4⋊C8—31no—
33C2×C3×C22⋊C8—31no—
34C2×#830—31no—
35C2×(C2×D3)⋊C8—31no—
36C2×(C2×D3)⋊C8D311yescharacteristic
37C2×#815—31no—
38C2×#815—31no—
39C2×#815—61no—
40C2×Dic3⋊C8—31no—
41C2×Dic3⋊C8D311yescharacteristic, complemented
42C2×C8×Dic3—31no—
43C2×C8×Dic3—31no—
44C2×C4⋊(C3⋊C8)—31no—
45#4840—38no—
46#4720—38no—
47C23×C3×D3C2×C411yescharacteristic
48C22×C32×C4C2311yescharacteristic
49C22×C3⋊Dic3C2×C411yescharacteristic
50C22×C3⋊Dic3C2×C411yescharacteristic
51C22×C3×Dic3C2×C411yescharacteristic
52C22×C3×Dic3C2×C411yescharacteristic
53C22×C3×Dic3C2×C411yescharacteristic
54C2×C3×C4×D3—22no—
55C2×C3×C4×D3—22no—
56C2×C3×C4×D3C2×C412yes—
57C2×C3×C4×D3C2312yes—
58C2×C32×C8—22no—
59C2×C32×C8C2312yes—
60C4×C3⋊Dic3C2×C412yes—
61C4×C3⋊Dic3C2312yes—
62C2×C3⋊(C3⋊C8)—22no—
63C2×C3⋊(C3⋊C8)C2312yes—
64C3×C4×Dic3C2×C412yes—
65C3×C4×Dic3C2312yes—
66C2×C3×C3⋊C8—22no—
67C2×C3×C3⋊C8—22no—
68C2×C3×C3⋊C8C2312yes—
69C2×C3×C3⋊C8C2312yes—
70Dic3⋊Dic3C2×C414yes—
71Dic3⋊Dic3C2×C414yes—
72(C2×D3)⋊Dic3C2×C414yes—
73(C2×D3)⋊Dic3C2×C414yes—
74C2×#433—91noSylow
75C23×C3×C4—31no—
76C22×C4×D3C2×D311yescharacteristic
77C22×C3×C8—21no—
78C22×C3×C8—31no—
79C22×C3×C8—31no—
80C22×C3×C8C2×D311yescharacteristic
81C22×C3×C8C2×D311yescharacteristic
82C2×C3×C42—31no—
83C2×#217—31no—
84C2×#217—31no—
85C2×(C2×D3)⋊C4—31no—
86C2×(C2×D3)⋊C4—31no—
87#926—34no—
88#926—34no—
89C2×C4⋊Dic3—31no—
90C2×C4⋊Dic3—31no—
91C2×Dic3⋊C4—31no—
92C2×Dic3⋊C4—31no—
93C2×C4×Dic3—31no—
94C2×C4×Dic3—31no—
95C2×C4×Dic3—61no—
96C2×C4×Dic3C2×D311yescharacteristic
97C22×C3⋊C8—31no—
98C22×C3⋊C8—31no—
99C22×C3⋊C8—61no—
100C22×C3⋊C8C2×D311yescharacteristic
101C22×C3⋊C8C2×D311yescharacteristic
102#872—34no—
103#872—34no—
104C3×C4⋊C8—34no—
105C3×C22⋊C8—34no—
106#830—34no—
107(C2×D3)⋊C8—34no—
108(C2×D3)⋊C8C2×D314yes—
109#815—34no—
110#815—34no—
111#815—64no—
112Dic3⋊C8—34no—
113Dic3⋊C8C2×D314yescomplemented
114C8×Dic3—34no—
115C8×Dic3—34no—
116C4⋊(C3⋊C8)—34no—
117C23×C32C22×C411yescharacteristic
118C22×C3×D3—22no—
119C22×C3×D3—22no—
120C22×C3×D3—22no—
121C22×C3×D3C22×C412yes—
122C2×C32×C4C22×C411yescharacteristic
123C2×C32×C4#4112yes—
124C2×C32×C4#4112yes—
125C2×C32×C4C2411yescharacteristic
126C2×C3⋊Dic3—22no—
127C2×C3⋊Dic3—22no—
128C2×C3⋊Dic3C22×C412yes—
129C2×C3⋊Dic3C22×C412yes—
130C2×C3×Dic3—22no—
131C2×C3×Dic3—22no—
132C2×C3×Dic3—22no—
133C2×C3×Dic3C22×C412yes—
134C2×C3×Dic3C22×C412yes—
135C2×C3×Dic3C22×C412yes—
136C3×C4×D3—24no—
137C3×C4×D3—22no—
138C3×C4×D3—22no—
139C32×C8—22no—
140C3⋊(C3⋊C8)—22no—
141C3×C3⋊C8—22no—
142C3×C3⋊C8—22no—
143C2×#117—91no—
144#433—98no—
145C2×C4⋊C8—31no—
146C2×C4⋊C8—91no—
147C2×C22⋊C8—31no—
148C2×C22⋊C8—91no—
149C2×#97—91no—
150C2×C4×C8—91no—
151C24×C3—31no—
152C23×D3C4×D311yescharacteristic
153C22×C3×C4—21no—
154C22×C3×C4—31no—
155C22×C3×C4—31no—
156C22×C3×C4—31no—
157C22×C3×C4—32no—
158C22×C3×C4—32no—
159C22×C3×C4—62no—
160C22×C3×C4—62no—
161C22×C3×C4C22×D311yescharacteristic
162C22×C3×C4C22×D311yescharacteristic
163C22×Dic3—31no—
164C22×Dic3—31no—
165C22×Dic3—31no—
166C22×Dic3—31no—
167C22×Dic3—61no—
168C22×Dic3—61no—
169C22×Dic3C4×D311yescharacteristic
170C22×Dic3C4×D311yescharacteristic
171C22×Dic3C4×D311yescharacteristic
172C2×C4×D3—22no—
173C2×C4×D3—22no—
174C2×C4×D3C4×D312yes—
175C2×C4×D3C22×D312yes—
176C2×C3×C8—24no—
177C2×C3×C8—22no—
178C2×C3×C8—22no—
179C2×C3×C8—22no—
180C2×C3×C8—32no—
181C2×C3×C8—32no—
182C2×C3×C8—62no—
183C2×C3×C8—62no—
184C2×C3×C8C22×D312yes—
185C2×C3×C8C22×D312yes—
186C3×C42—32no—
187C3×C42—32no—
188#217—34no—
189#217—34no—
190(C2×D3)⋊C4—34no—
191(C2×D3)⋊C4—34no—
192C4⋊Dic3—34no—
193C4⋊Dic3—34no—
194Dic3⋊C4—34no—
195Dic3⋊C4—34no—
196C4×Dic3—32no—
197C4×Dic3—32no—
198C4×Dic3—32no—
199C4×Dic3—32no—
200C4×Dic3—62no—
201C4×Dic3—62no—
202C4×Dic3C4×D312yes—
203C4×Dic3C22×D312yes—
204C2×C3⋊C8—22no—
205C2×C3⋊C8—22no—
206C2×C3⋊C8—32no—
207C2×C3⋊C8—32no—
208C2×C3⋊C8—62no—
209C2×C3⋊C8—64no—
210C2×C3⋊C8—62no—
211C2×C3⋊C8—62no—
212C2×C3⋊C8C22×D312yes—
213C2×C3⋊C8C22×D312yes—
214C22×C32#11712yes—
215C22×C32#13112yes—
216C22×C32#13112yes—
217C22×C32C23×C411yescharacteristic
218C2×C3×D3—22no—
219C2×C3×D3—22no—
220C2×C3×D3—22no—
221C2×C3×D3—44no—
222C32×C4#11712yes—
223C32×C4C2×#4111yescharacteristic
224C32×C4C2×#4111yescharacteristic
225C3⋊Dic3—22no—
226C3⋊Dic3—22no—
227C3×Dic3—22no—
228C3×Dic3—22no—
229C3×Dic3—22no—
230C23×C4—31no—
231C22×C8—31no—
232C22×C8—31no—
233C22×C8—91no—
234C22×C8D3211yescharacteristic
235#117—94no—
236#117—94no—
237C2×C4⋊C4—91no—
238C2×C4⋊C4—91no—
239C2×C22⋊C4—91no—
240C2×C22⋊C4—91no—
241C2×C42—31no—
242C2×C42—91no—
243C4⋊C8—34no—
244C4⋊C8—94no—
245C22⋊C8—34no—
246C22⋊C8—94no—
247#97—94no—
248C4×C8—94no—
249C23×C3—21no—
250C23×C3—32no—
251C23×C3—62no—
252C23×C3—62no—
253C23×C3—62no—
254C23×C3C2×C4×D311yescharacteristic
255C23×C3C2×C4×D311yescharacteristic
256C22×D3—22no—
257C22×D3—22no—
258C22×D3—22no—
259C22×D3C2×C4×D312yes—
260C2×C3×C4—21no—
261C2×C3×C4—22no—
262C2×C3×C4—21no—
263C2×C3×C4—22no—
264C2×C3×C4—32no—
265C2×C3×C4—32no—
266C2×C3×C4—32no—
267C2×C3×C4—62no—
268C2×C3×C4—62no—
269C2×C3×C4—62no—
270C2×C3×C4—64no—
271C2×C3×C4—62no—
272C2×C3×C4—62no—
273C2×C3×C4C2×C4×D311yescharacteristic
274C2×C3×C4C2×C4×D311yescharacteristic
275C2×C3×C4#23712yes—
276C2×C3×C4#23712yes—
277C2×C3×C4#23712yes—
278C2×C3×C4#23912yes—
279C2×C3×C4C23×D311yescharacteristic
280C2×C3×C4C23×D311yescharacteristic
281C2×Dic3—22no—
282C2×Dic3—22no—
283C2×Dic3—22no—
284C2×Dic3—32no—
285C2×Dic3—32no—
286C2×Dic3—32no—
287C2×Dic3—32no—
288C2×Dic3—62no—
289C2×Dic3—62no—
290C2×Dic3—62no—
291C2×Dic3—62no—
292C2×Dic3—62no—
293C2×Dic3—62no—
294C2×Dic3—122no—
295C2×Dic3—122no—
296C2×Dic3C2×C4×D312yes—
297C2×Dic3C2×C4×D312yes—
298C2×Dic3C2×C4×D312yes—
299C4×D3—24no—
300C4×D3—22no—
301C4×D3—22no—
302C3×C8—24no—
303C3×C8—22no—
304C3×C8—22no—
305C3×C8—62no—
306C3×C8—62no—
307C3⋊C8—22no—
308C3⋊C8—22no—
309C3⋊C8—64no—
310C3⋊C8—62no—
311C3⋊C8—62no—
312C2×C32#43314yescomplemented
313C2×C32C2×#11711yescharacteristic
314C2×C32C2×#13111yescharacteristic
315C2×C32C2×#13111yescharacteristic
316C3×D3—42no—
317C24—31no—
318C22×C4—31no—
319C22×C4—31no—
320C22×C4—31no—
321C22×C4—32no—
322C22×C4—32no—
323C22×C4—62no—
324C22×C4—62no—
325C22×C4—91no—
326C22×C4—91no—
327C22×C4C2×D3211yescharacteristic
328C2×C8—22no—
329C2×C8—32no—
330C2×C8—32no—
331C2×C8—62no—
332C2×C8—62no—
333C2×C8—92no—
334C2×C8—182no—
335C2×C8C2×D3212yes—
336C4⋊C4—94no—
337C4⋊C4—94no—
338C22⋊C4—94no—
339C22⋊C4—94no—
340C42—32no—
341C42—32no—
342C42—92no—
343C42—92no—
344C22×C3—21no—
345C22×C3—22no—
346C22×C3—22no—
347C22×C3—22no—
348C22×C3—62no—
349C22×C3—62no—
350C22×C3—62no—
351C22×C3—124no—
352C22×C3#87712yes—
353C22×C3#89212yes—
354C22×C3#90112yes—
355C22×C3#90112yes—
356C22×C3#90712yes—
357C22×C3#90712yes—
358C22×C3C22×C4×D311yescharacteristic
359C22×C3C22×C4×D311yescharacteristic
360C2×D3—22no—
361C2×D3—22no—
362C2×D3—22no—
363C2×D3—44no—
364C3×C4—21no—
365C3×C4—21no—
366C3×C4—22no—
367C3×C4—62no—
368C3×C4—62no—
369C3×C4—62no—
370C3×C4#87712yes—
371C3×C4#89212yes—
372C3×C4C2×#23711yescharacteristic
373C3×C4C2×#23711yescharacteristic
374C3×C4C2×#23711yescharacteristic
375C3×C4C2×#23911yescharacteristic
376Dic3—22no—
377Dic3—22no—
378Dic3—22no—
379Dic3—62no—
380Dic3—62no—
381Dic3—62no—
382Dic3—62no—
383Dic3—122no—
384Dic3—122no—
385C32C2×#43311yescharacteristic, complemented, Sylow
386C23—32no—
387C23—62no—
388C23—62no—
389C23—62no—
390C23C4×D3211yescharacteristic
391C2×C4—32no—
392C2×C4—32no—
393C2×C4—32no—
394C2×C4—62no—
395C2×C4—62no—
396C2×C4—62no—
397C2×C4—62no—
398C2×C4—62no—
399C2×C4—64no—
400C2×C4—92no—
401C2×C4—92no—
402C2×C4—182no—
403C2×C4—182no—
404C2×C4#379612yes—
405C2×C4C4×D3211yescharacteristic
406C2×C4#380512yes—
407C2×C4C22×D3211yescharacteristic
408C8—22no—
409C8—62no—
410C8—62no—
411C8—182no—
412C2×C3—21no—
413C2×C3—21no—
414C2×C3—21no—
415C2×C3—24no—
416C2×C3—122no—
417C2×C3#472014yescomplemented
418C2×C3#484014yescomplemented
419C2×C3C2×#87711yescharacteristic
420C2×C3C2×#89211yescharacteristic
421C2×C3C2×#90111yescharacteristic
422C2×C3C2×#90111yescharacteristic
423C2×C3C2×#90711yescharacteristic
424C2×C3C2×#90711yescharacteristic
425D3—42no—
426C22—62no—
427C22—62no—
428C22—62no—
429C22—124no—
430C22#6380412yes—
431C22#6380412yes—
432C22#6387812yes—
433C22C2×C4×D3211yescharacteristic
434C4—62no—
435C4—62no—
436C4—62no—
437C4—182no—
438C4—182no—
439C4#6387812yes—
440C4C2×#379611yescharacteristic
441C4C2×#380511yescharacteristic
442C3—21no—
443C3C2×#472011yescharacteristic, complemented
444C3C2×#484011yescharacteristic, complemented
445C2—122no—
446C2#1059069914yesdirect product factor
447C2C2×#6380411yescharacteristic
448C2C2×#6380411yescharacteristic
449C2C2×#6387811yescharacteristic
subgroupG/H
centerC22×C4C2×D32
commutatorC22×C32C23×C4
FrattiniC2×C4C22×D32
FittingC22×C32×C8C22
socleC23×C32C22×C4
prime radicalC23×C3×D3C2×C4
cosocleC2×C32×C4C24
hypercenterC22×C8D32
hypocenterC32C2×#433
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C22×C4 ◁ C22×C8

Complements

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

NH ≅ G/Ntype
2. C2×#63642C2semidirect
4. C2×C3×Dic3⋊C8C2semidirect
5. C2×Dic3⋊(C3⋊C8)C2semidirect
7. C2×#63553C2semidirect
8. #10590699C2direct (N × H)
24. #63642C22semidirect
26. C3×Dic3⋊C8C22semidirect
27. Dic3⋊(C3⋊C8)C22semidirect
29. #63553C22semidirect
41. C2×Dic3⋊C8D3semidirect
113. Dic3⋊C8C2×D3semidirect
312. C2×C32#433semidirect
385. C32C2×#433semidirect
417. C2×C3#4720semidirect
418. C2×C3#4840semidirect
443. C3C2×#4720semidirect
444. C3C2×#4840semidirect
446. C2#10590699direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#638552
C2×#636422
C2×C3×(C2×D3)⋊C82
C2×C3×Dic3⋊C82
C2×Dic3⋊(C3⋊C8)2
C2×(C2×D3)⋊(C3⋊C8)2
C2×#635532
#105906992
C2×#48403
C2×#47203