Finite Group Databasebeta

← C2×#10590434 #11868519

Subgroups — C2×#10590434 #11868519

Order 1152.

917 conjugacy classes of subgroups.

The subgroup lattice has 439 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#64096C211yesmaximal, characteristic
2C2×#63872C211yesmaximal, characteristic
3C2×C3×#808C211yesmaximal, characteristic
4C2×C3×#807C211yesmaximal, characteristic
5C2×#63572C211yesmaximal, characteristic
6C2×#63567C211yesmaximal, characteristic
7C2×#63567C211yesmaximal, characteristic
8#10590434C218yesmaximal, direct product factor
9C2×#4877—31nomaximal
10C2×#4857—31nomaximal
11C22×#634C2211yescharacteristic
12C2×C32×C4⋊C4C2211yescharacteristic
13C2×#3750—21no—
14C2×C4×C3⋊Dic3—21no—
15C2×C4×C3⋊Dic3C2211yescharacteristic
16#64096—22no—
17#64096C2214yes—
18C2×C3×C4⋊Dic3C2211yescharacteristic
19C2×C3×C4⋊Dic3C2211yescharacteristic
20C22×C3×C3⋊C8C2211yescharacteristic
21C22×C3×C3⋊C8C2211yescharacteristic
22C2×Dic3⋊Dic3—21no—
23C2×Dic3⋊Dic3—21no—
24#63872—22no—
25#63872C2214yes—
26C3×#808C2214yes—
27C3×#807C2214yes—
28#63572C2214yes—
29#63567C2214yes—
30#63567C2214yes—
31C2×#890—31no—
32C2×#890—31no—
33C2×#887—31no—
34C2×#887—31no—
35C2×#887—61no—
36C2×C3×#107—31no—
37C2×C3×#106—31no—
38C2×#816—31no—
39C2×#816—31no—
40C2×Dic3⋊C8—31no—
41C2×Dic3⋊C8—31no—
42C2×#810—31no—
43C2×#810—31no—
44C2×#808D311yescharacteristic
45C2×#807D311yescharacteristic
46#4877—38no—
47#4857—38no—
48C22×C32×C4—21no—
49C22×C32×C4C2311yescharacteristic
50C22×C3⋊Dic3—21no—
51C22×C3⋊Dic3D411yescharacteristic
52C22×C3⋊Dic3D411yescharacteristic
53C2×#634—21no—
54C2×#634—22no—
55C2×#634Q814yes—
56C2×#634C2312yes—
57C22×C3×Dic3—21no—
58C22×C3×Dic3—21no—
59C32×C4⋊C4—21no—
60C32×C4⋊C4C2312yes—
61#3750—24no—
62C4×C3⋊Dic3—24no—
63C4×C3⋊Dic3D412yes—
64C4×C3⋊Dic3C2312yes—
65C3×C4⋊Dic3—21no—
66C3×C4⋊Dic3—21no—
67C3×C4⋊Dic3C2312yes—
68C3×C4⋊Dic3C2312yes—
69C2×C3×C3⋊C8—22no—
70C2×C3×C3⋊C8—22no—
71C2×C3×C3⋊C8C2312yes—
72C2×C3×C3⋊C8C2312yes—
73Dic3⋊Dic3—24no—
74Dic3⋊Dic3—24no—
75C2×#479—91noSylow
76C22×Dic6—31no—
77C22×Dic6—31no—
78C22×Dic6—61no—
79C22×C3×C8—31no—
80C22×C3×C8—31no—
81C2×C3×C4⋊C4—21no—
82C2×C3×C4⋊C4—31no—
83C2×C3×C4⋊C4—31no—
84C2×C3×C4⋊C4C2×D311yescharacteristic
85C2×C3×C4⋊C4C2×D311yescharacteristic
86C2×C4⋊Dic3—61no—
87C2×C4⋊Dic3—61no—
88C2×C4⋊Dic3C2×D311yescharacteristic
89C2×C4⋊Dic3C2×D311yescharacteristic
90C2×Dic3⋊C4—61no—
91C2×Dic3⋊C4—61no—
92C2×Dic3⋊C4—61no—
93C2×Dic3⋊C4—61no—
94C2×Dic3⋊C4—62no—
95C2×C4×Dic3—31no—
96C2×C4×Dic3—31no—
97C2×C4×Dic3—61no—
98C2×C4×Dic3—61no—
99C2×C4×Dic3—61no—
100C2×C4×Dic3—62no—
101C22×C3⋊C8C2×D311yescharacteristic
102C22×C3⋊C8C2×D311yescharacteristic
103#890—34no—
104#890—34no—
105#890—62no—
106#890—62no—
107#887—34no—
108#887—34no—
109#887—64no—
110#887—62no—
111#887—62no—
112#887—64no—
113C3×#107—34no—
114C3×#106—34no—
115#816—34no—
116#816—34no—
117Dic3⋊C8—34no—
118Dic3⋊C8—34no—
119#810—34no—
120#810—34no—
121#808C2×D314yes—
122#807C2×D314yes—
123C23×C32C2×D411yescharacteristic
124C2×C32×C4—22no—
125C2×C32×C4—42no—
126C2×C32×C4C2×D411yescharacteristic
127C2×C32×C4C2×Q812yes—
128C2×C32×C4#4112yes—
129C2×C32×C4C2411yescharacteristic
130C2×C3⋊Dic3—24no—
131C2×C3⋊Dic3—22no—
132C2×C3⋊Dic3—22no—
133C2×C3⋊Dic3—22no—
134C2×C3⋊Dic3C2×D412yes—
135C2×C3⋊Dic3C2×D412yes—
136#634—24no—
137#634—22no—
138#634C2×Q814yes—
139C2×C3×Dic3—22no—
140C2×C3×Dic3—22no—
141C2×C3×Dic3—42no—
142C2×C3×Dic3—42no—
143C3×C3⋊C8—22no—
144C3×C3⋊C8—22no—
145C2×#125—91no—
146C2×C4×Q8—91no—
147#479—98no—
148C2×#107—31no—
149C2×#106—31no—
150C2×C4⋊C8—91no—
151C2×#103—91no—
152C2×#103—91no—
153C22×C3×C4—22no—
154C22×C3×C4—21no—
155C22×C3×C4—21no—
156C22×C3×C4—21no—
157C22×C3×C4—61no—
158C22×C3×C4—61no—
159C22×C3×C4C22×D311yescharacteristic
160C22×C3×C4C22×D311yescharacteristic
161C22×Dic3—21no—
162C22×Dic3—21no—
163C22×Dic3—31no—
164C22×Dic3—31no—
165C22×Dic3—31no—
166C22×Dic3—31no—
167C22×Dic3—61no—
168C22×Dic3—61no—
169C22×Dic3—62no—
170C22×Dic3—61no—
171C22×Dic3—61no—
172C2×Dic6—34no—
173C2×Dic6—34no—
174C2×Dic6—32no—
175C2×Dic6—32no—
176C2×Dic6—62no—
177C2×Dic6—64no—
178C2×Dic6—62no—
179C2×Dic6—64no—
180C2×Dic6—62no—
181C2×Dic6—62no—
182C2×Dic6—61no—
183C2×Dic6—61no—
184C2×C3×C8—32no—
185C2×C3×C8—32no—
186C2×C3×C8—62no—
187C2×C3×C8—62no—
188C3×C4⋊C4—22no—
189C3×C4⋊C4—21no—
190C3×C4⋊C4—21no—
191C3×C4⋊C4—22no—
192C3×C4⋊C4—32no—
193C3×C4⋊C4—32no—
194C3×C4⋊C4—61no—
195C3×C4⋊C4—61no—
196C3×C4⋊C4C22×D312yes—
197C3×C4⋊C4C22×D312yes—
198C4⋊Dic3—21no—
199C4⋊Dic3—21no—
200C4⋊Dic3—64no—
201C4⋊Dic3—64no—
202C4⋊Dic3C22×D312yes—
203C4⋊Dic3C22×D312yes—
204Dic3⋊C4—64no—
205Dic3⋊C4—64no—
206Dic3⋊C4—64no—
207Dic3⋊C4—64no—
208Dic3⋊C4—68no—
209C4×Dic3—32no—
210C4×Dic3—32no—
211C4×Dic3—32no—
212C4×Dic3—32no—
213C4×Dic3—62no—
214C4×Dic3—62no—
215C4×Dic3—64no—
216C4×Dic3—64no—
217C4×Dic3—68no—
218C2×C3⋊C8—22no—
219C2×C3⋊C8—22no—
220C2×C3⋊C8C22×D312yes—
221C2×C3⋊C8C22×D312yes—
222C22×C32C22⋊Q812yes—
223C22×C32#13512yes—
224C22×C32#13712yes—
225C22×C32C22×D411yescharacteristic
226C32×C4—42no—
227C32×C4C22⋊Q812yes—
228C32×C4C22×Q811yescharacteristic
229C32×C4C2×#4111yescharacteristic
230C3⋊Dic3—24no—
231C3⋊Dic3—22no—
232C3⋊Dic3—22no—
233C3×Dic3—42no—
234C3×Dic3—42no—
235C22×Q8—91no—
236C22×C8—31no—
237C22×C8—31no—
238#125—94no—
239#125—182no—
240C4×Q8—94no—
241C4×Q8—182no—
242C2×C4⋊C4—31no—
243C2×C4⋊C4—31no—
244C2×C4⋊C4—181no—
245C2×C4⋊C4—181no—
246C2×C4⋊C4—181no—
247C2×C4⋊C4D3211yescharacteristic
248C2×C42—91no—
249C2×C42—181no—
250#107—34no—
251#106—34no—
252C4⋊C8—94no—
253#103—94no—
254#103—94no—
255C23×C3—21no—
256C23×C3D3×D411yescharacteristic
257C23×C3D3×D411yescharacteristic
258C2×C3×C4—24no—
259C2×C3×C4—22no—
260C2×C3×C4—22no—
261C2×C3×C4—21no—
262C2×C3×C4—22no—
263C2×C3×C4—22no—
264C2×C3×C4—21no—
265C2×C3×C4—44no—
266C2×C3×C4—42no—
267C2×C3×C4—42no—
268C2×C3×C4—62no—
269C2×C3×C4—62no—
270C2×C3×C4—122no—
271C2×C3×C4—122no—
272C2×C3×C4#23512yes—
273C2×C3×C4#23512yes—
274C2×C3×C4D3×D411yescharacteristic
275C2×C3×C4D3×D411yescharacteristic
276C2×C3×C4D3×Q812yes—
277C2×C3×C4D3×Q812yes—
278C2×C3×C4C23×D311yescharacteristic
279C2×C3×C4C23×D311yescharacteristic
280C2×Dic3—22no—
281C2×Dic3—22no—
282C2×Dic3—32no—
283C2×Dic3—32no—
284C2×Dic3—32no—
285C2×Dic3—32no—
286C2×Dic3—42no—
287C2×Dic3—42no—
288C2×Dic3—62no—
289C2×Dic3—62no—
290C2×Dic3—64no—
291C2×Dic3—68no—
292C2×Dic3—64no—
293C2×Dic3—64no—
294C2×Dic3—64no—
295C2×Dic3—62no—
296C2×Dic3—62no—
297C2×Dic3—62no—
298C2×Dic3—62no—
299C2×Dic3—62no—
300C2×Dic3—62no—
301C2×Dic3—122no—
302Dic6—34no—
303Dic6—34no—
304Dic6—64no—
305Dic6—64no—
306Dic6—68no—
307Dic6—64no—
308Dic6—64no—
309Dic6—62no—
310Dic6—62no—
311C3×C8—62no—
312C3×C8—62no—
313C3⋊C8—22no—
314C3⋊C8—22no—
315C2×C32#47914yescomplemented
316C2×C32C2×C22⋊Q811yescharacteristic
317C2×C32C2×#13511yescharacteristic
318C2×C32C2×#13711yescharacteristic
319C2×Q8—92no—
320C2×Q8—94no—
321C2×Q8—182no—
322C2×Q8—181no—
323C22×C4—21no—
324C22×C4—61no—
325C22×C4—61no—
326C22×C4—91no—
327C22×C4—91no—
328C22×C4—181no—
329C22×C4C2×D3211yescharacteristic
330C2×C8—32no—
331C2×C8—32no—
332C2×C8—62no—
333C2×C8—62no—
334C4⋊C4—21no—
335C4⋊C4—32no—
336C4⋊C4—32no—
337C4⋊C4—61no—
338C4⋊C4—61no—
339C4⋊C4—184no—
340C4⋊C4—184no—
341C4⋊C4—184no—
342C4⋊C4C2×D3212yes—
343C42—92no—
344C42—92no—
345C42—184no—
346C22×C3—21no—
347C22×C3—22no—
348C22×C3—22no—
349C22×C3—22no—
350C22×C3#89612yes—
351C22×C3#89612yes—
352C22×C3#91212yes—
353C22×C3#91512yes—
354C22×C3#91612yes—
355C22×C3#91812yes—
356C22×C3C2×D3×D411yescharacteristic
357C22×C3C2×D3×D411yescharacteristic
358C3×C4—21no—
359C3×C4—21no—
360C3×C4—22no—
361C3×C4—44no—
362C3×C4—42no—
363C3×C4—42no—
364C3×C4—122no—
365C3×C4—122no—
366C3×C4#89612yes—
367C3×C4#89612yes—
368C3×C4C2×#23511yescharacteristic
369C3×C4C2×#23511yescharacteristic
370C3×C4C2×D3×Q811yescharacteristic
371C3×C4C2×D3×Q811yescharacteristic
372Dic3—42no—
373Dic3—42no—
374Dic3—68no—
375Dic3—64no—
376Dic3—62no—
377Dic3—62no—
378Dic3—62no—
379Dic3—64no—
380Dic3—64no—
381Dic3—62no—
382Dic3—122no—
383C32C2×#47911yescharacteristic, complemented, Sylow
384C23#381111yescharacteristic
385Q8—94no—
386Q8—182no—
387Q8—184no—
388C2×C4—22no—
389C2×C4—42no—
390C2×C4—62no—
391C2×C4—62no—
392C2×C4—92no—
393C2×C4—92no—
394C2×C4—122no—
395C2×C4—122no—
396C2×C4—182no—
397C2×C4—184no—
398C2×C4—182no—
399C2×C4—182no—
400C2×C4#379712yes—
401C2×C4#379812yes—
402C2×C4#381111yescharacteristic
403C2×C4C22×D3211yescharacteristic
404C8—62no—
405C8—62no—
406C2×C3—21no—
407C2×C3—21no—
408C2×C3—21no—
409C2×C3—24no—
410C2×C3#485714yescomplemented
411C2×C3#487714yescomplemented
412C2×C3C2×#89611yescharacteristic
413C2×C3C2×#89611yescharacteristic
414C2×C3C2×#91211yescharacteristic
415C2×C3C2×#91511yescharacteristic
416C2×C3C2×#91611yescharacteristic
417C2×C3C2×#91811yescharacteristic
418C22#6386512yes—
419C22#6393612yes—
420C22#6395112yes—
421C22C2×#381111yescharacteristic
422C4—42no—
423C4—122no—
424C4—122no—
425C4—182no—
426C4—182no—
427C4—184no—
428C4#6386512yes—
429C4C2×#379711yescharacteristic
430C4C2×#379811yescharacteristic
431C3—21no—
432C3C2×#485711yescharacteristic, complemented
433C3C2×#487711yescharacteristic, complemented
434C2#1059043414yesdirect product factor
435C2C2×#6386511yescharacteristic
436C2C2×#6393611yescharacteristic
437C2C2×#6395111yescharacteristic
subgroupG/H
centerC23#3811
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC2×C32×C4⋊C4C22
socle, prime radicalC23×C32C2×D4
hypercenterC2×C4⋊C4D32
hypocenterC32C2×#479
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C23 ◁ C22×C4 ◁ C2×C4⋊C4

Complements

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

NH ≅ G/Ntype
8. #10590434C2direct (N × H)
315. C2×C32#479semidirect
383. C32C2×#479semidirect
410. C2×C3#4857semidirect
411. C2×C3#4877semidirect
432. C3C2×#4857semidirect
433. C3C2×#4877semidirect
434. C2#10590434direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#640962
C2×#638722
C2×C3×#8082
C2×C3×#8072
C2×#635722
C2×#635672
#105904342
C2×#48773
C2×#48573