Finite Group Databasebeta

← C2×#10591078 #11857650

Subgroups — C2×#10591078 #11857650

Order 1152.

1957 conjugacy classes of subgroups.

The subgroup lattice has 478 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#3828C211yesmaximal, characteristic
2C22×C3×#208C212yesmaximal, complemented
3C2×#63561C212yesmaximal, complemented
4#10591078C218yesmaximal, direct product factor
5C2×#63559C212yesmaximal, complemented
6C2×#5132—32nomaximal
7C23×C32×C4C2211yescharacteristic
8C22×#638C412yes—
9C2×#3828—22no—
10C2×#3828—22no—
11C2×#3828—24no—
12C2×#3828C414yes—
13C2×#3828C2214yes—
14C22×C4⋊(C3⋊D3)C2211yescharacteristic
15C22×C4×C3⋊D3C412yes—
16C22×#634C2211yescharacteristic
17C2×C3×#208—22no—
18C2×C3×#208—24no—
19C2×C3×#208C2214yes—
20C2×C3×#208C2218yescomplemented
21C22×C3×C3⋊C8—22no—
22#63561C2218yescomplemented
23#63559C2218yescomplemented
24C22×#235—32no—
25C22×#235—61no—
26C22×C3×M16—32no—
27C22×#208D312yescomplemented
28C2×#824—34no—
29#5132—316no—
30C2×#823—34no—
31C24×C32C2×C411yescharacteristic
32C23×C3⋊D3C2×C412yes—
33C22×C32×C4C2×C411yescharacteristic
34C22×C32×C4C2×C412yes—
35C22×C32×C4D412yes—
36C22×C32×C4D412yes—
37C22×C32×C4D414yes—
38C22×C32×C4C2311yescharacteristic
39C22×C32×C4C2312yes—
40C2×#638—24no—
41C2×#638—24no—
42C2×#638C2×C418yes—
43C22×C3⋊Dic3C2×C412yes—
44#3828—28no—
45#3828—28no—
46#3828—28no—
47#3828—28no—
48C2×C4⋊(C3⋊D3)—22no—
49C2×C4⋊(C3⋊D3)—22no—
50C2×C4⋊(C3⋊D3)C2×C412yes—
51C2×C4⋊(C3⋊D3)C2312yes—
52C2×C4×C3⋊D3—24no—
53C2×C4×C3⋊D3—22no—
54C2×C4×C3⋊D3—22no—
55C2×C4×C3⋊D3C2×C418yes—
56C2×#634—22no—
57C2×#634—22no—
58C2×#634C2×C412yes—
59C2×#634C2312yes—
60C3×#208—24no—
61C3×#208—28no—
62C3×#208C2318yes—
63C2×C3×C3⋊C8—24no—
64C2×C3×C3⋊C8—28no—
65C2×#413—91noSylow
66C23×C3×C4—21no—
67C23×C3×C4C2×D312yes—
68C22×#67—34no—
69C22×#67—62no—
70C2×#235—38no—
71C2×#235—38no—
72C2×#235—64no—
73C2×#235—64no—
74C2×#235—64no—
75C2×#235—68no—
76C2×#235—64no—
77C2×#235—62no—
78C2×#235—62no—
79C2×#235—64no—
80C2×#235—62no—
81C2×#235—62no—
82C2×#235—64no—
83C22×D12—32no—
84C22×D12—61no—
85C22×C4×D3—34no—
86C22×C4×D3—62no—
87C22×Dic6—32no—
88C22×Dic6—61no—
89C2×C3×M16—34no—
90C2×C3×M16—38no—
91C2×C3×M16—62no—
92C2×C3×M16—64no—
93C22×C3×C8—62no—
94C2×#208—22no—
95C2×#208—24no—
96C2×#208C2×D314yes—
97C2×#208C2×D318yescomplemented
98C22×C3⋊C8—22no—
99#824—316no—
100#823—316no—
101C23×C32—42no—
102C23×C32C22⋊C412yes—
103C23×C32C22⋊C412yes—
104C23×C32C22×C411yescharacteristic
105C23×C32C22×C412yes—
106C22×C3⋊D3—22no—
107C22×C3⋊D3—22no—
108C22×C3⋊D3—44no—
109C22×C3⋊D3C22×C414yes—
110C2×C32×C4C22⋊C412yes—
111C2×C32×C4C22⋊C411yescharacteristic
112C2×C32×C4C22⋊C411yescharacteristic
113C2×C32×C4C22⋊C414yes—
114C2×C32×C4C22⋊C414yes—
115C2×C32×C4C22×C411yescharacteristic
116C2×C32×C4C22×C412yes—
117C2×C32×C4C2×D412yes—
118C2×C32×C4C2×D414yes—
119C2×C32×C4C2×D412yes—
120C2×C32×C4C2×D414yes—
121C2×C32×C4C2411yescharacteristic
122#638—216no—
123C2×C3⋊Dic3—22no—
124C2×C3⋊Dic3—22no—
125C2×C3⋊Dic3C22×C414yes—
126C4⋊(C3⋊D3)—24no—
127C4⋊(C3⋊D3)—24no—
128C4×C3⋊D3—28no—
129C4×C3⋊D3—28no—
130#634—24no—
131#634—24no—
132C3×C3⋊C8—28no—
133C22×#41—91no—
134C22×M16—32no—
135#413—98no—
136C2×#101—92no—
137C2×#100—92no—
138C24×C3—21no—
139C24×C3C4×D312yes—
140C23×D3—34no—
141C23×D3—62no—
142C22×C3×C4—21no—
143C22×C3×C4—22no—
144C22×C3×C4—22no—
145C22×C3×C4—24no—
146C22×C3×C4—22no—
147C22×C3×C4—21no—
148C22×C3×C4—22no—
149C22×C3×C4C4×D312yes—
150C22×C3×C4C4×D314yes—
151C22×C3×C4D1212yes—
152C22×C3×C4D1212yes—
153C22×C3×C4D1214yes—
154C22×C3×C4#6712yes—
155C22×C3×C4#6712yes—
156C22×C3×C4#6714yes—
157C22×C3×C4C22×D312yes—
158C22×C3×C4C22×D314yes—
159C2×#67—316no—
160C2×#67—68no—
161C2×#67—68no—
162C2×#67—68no—
163C2×#67—64no—
164C2×#67—64no—
165C2×#67—68no—
166C22×Dic3—34no—
167C22×Dic3—62no—
168#235—616no—
169#235—616no—
170#235—616no—
171#235—616no—
172#235—68no—
173#235—68no—
174#235—68no—
175#235—68no—
176#235—68no—
177#235—68no—
178#235—68no—
179#235—68no—
180C2×D12—34no—
181C2×D12—34no—
182C2×D12—62no—
183C2×D12—62no—
184C2×D12—64no—
185C2×D12—64no—
186C2×D12—62no—
187C2×D12—62no—
188C2×D12—62no—
189C2×D12—62no—
190C2×C4×D3—316no—
191C2×C4×D3—68no—
192C2×C4×D3—68no—
193C2×C4×D3—64no—
194C2×C4×D3—64no—
195C2×C4×D3—68no—
196C2×C4×D3—64no—
197C2×C4×D3—64no—
198C2×Dic6—34no—
199C2×Dic6—34no—
200C2×Dic6—62no—
201C2×Dic6—62no—
202C2×Dic6—64no—
203C2×Dic6—64no—
204C2×Dic6—62no—
205C2×Dic6—62no—
206C2×Dic6—62no—
207C2×Dic6—62no—
208C3×M16—38no—
209C3×M16—64no—
210C3×M16—68no—
211C2×C3×C8—64no—
212C2×C3×C8—68no—
213#208—24no—
214#208—28no—
215#208C22×D318yes—
216C2×C3⋊C8—24no—
217C2×C3⋊C8—28no—
218C22×C32—22no—
219C22×C32—24no—
220C22×C32—42no—
221C22×C32—42no—
222C22×C32C2×C22⋊C411yescharacteristic
223C22×C32C2×C22⋊C414yes—
224C22×C32C2×C22⋊C411yescharacteristic
225C22×C32C23×C411yescharacteristic
226C2×C3⋊D3—24no—
227C2×C3⋊D3—44no—
228C2×C3⋊D3—44no—
229C2×C3⋊D3—44no—
230C32×C4C2×C22⋊C412yes—
231C32×C4C2×C22⋊C412yes—
232C32×C4C2×C22⋊C412yes—
233C32×C4C22×D412yes—
234C3⋊Dic3—24no—
235C2×#41—94no—
236C2×#41—94no—
237C2×#41—182no—
238C2×#41—184no—
239C2×#41—182no—
240C22×Q8—91no—
241C22×D4—92no—
242C22×D4—91no—
243C23×C4—92no—
244C23×C4D3211yescharacteristic
245C2×M16—34no—
246C2×M16—38no—
247C2×M16—62no—
248C2×M16—64no—
249C22×C8—62no—
250#101—98no—
251#100—98no—
252C23×C3—22no—
253C23×C3—22no—
254C23×C3—21no—
255C23×C3—22no—
256C23×C3—44no—
257C23×C3—44no—
258C23×C3(C2×D3)⋊C412yes—
259C23×C3(C2×D3)⋊C412yes—
260C23×C3(C2×D3)⋊C414yes—
261C23×C3C2×C4×D312yes—
262C23×C3C2×C4×D314yes—
263C22×D3—38no—
264C22×D3—64no—
265C22×D3—64no—
266C22×D3—64no—
267C22×D3—64no—
268C22×D3—64no—
269C22×D3—128no—
270C22×D3—128no—
271C2×C3×C4—21no—
272C2×C3×C4—21no—
273C2×C3×C4—22no—
274C2×C3×C4—24no—
275C2×C3×C4—24no—
276C2×C3×C4—21no—
277C2×C3×C4—21no—
278C2×C3×C4—22no—
279C2×C3×C4—22no—
280C2×C3×C4—22no—
281C2×C3×C4—24no—
282C2×C3×C4—24no—
283C2×C3×C4(C2×D3)⋊C414yes—
284C2×C3×C4(C2×D3)⋊C412yes—
285C2×C3×C4(C2×D3)⋊C414yes—
286C2×C3×C4(C2×D3)⋊C414yes—
287C2×C3×C4(C2×D3)⋊C414yes—
288C2×C3×C4(C2×D3)⋊C414yes—
289C2×C3×C4(C2×D3)⋊C412yes—
290C2×C3×C4C2×C4×D312yes—
291C2×C3×C4C2×C4×D314yes—
292C2×C3×C4C2×D1212yes—
293C2×C3×C4C2×D1214yes—
294C2×C3×C4C2×D1212yes—
295C2×C3×C4C2×D1214yes—
296C2×C3×C4C2×#6712yes—
297C2×C3×C4C2×#6714yes—
298C2×C3×C4C2×#6712yes—
299C2×C3×C4C2×#6714yes—
300C2×C3×C4C23×D312yes—
301#67—632no—
302#67—616no—
303#67—616no—
304C2×Dic3—38no—
305C2×Dic3—64no—
306C2×Dic3—64no—
307C2×Dic3—64no—
308C2×Dic3—64no—
309C2×Dic3—64no—
310D12—68no—
311D12—68no—
312D12—64no—
313D12—64no—
314D12—64no—
315D12—64no—
316C4×D3—616no—
317C4×D3—616no—
318C4×D3—616no—
319C4×D3—616no—
320Dic6—68no—
321Dic6—68no—
322Dic6—64no—
323Dic6—64no—
324Dic6—64no—
325Dic6—64no—
326C3×C8—68no—
327C3⋊C8—28no—
328C2×C32—21no—
329C2×C32—21no—
330C2×C32—24no—
331C2×C32#41312yescomplemented
332C2×C32C22×C22⋊C411yescharacteristic
333C3⋊D3—44no—
334C24—92no—
335C24#62411yescharacteristic
336#41—188no—
337#41—188no—
338#41—188no—
339#41—188no—
340C2×Q8—92no—
341C2×Q8—92no—
342C2×Q8—182no—
343C2×Q8—182no—
344C2×D4—98no—
345C2×D4—92no—
346C2×D4—92no—
347C2×D4—184no—
348C2×D4—184no—
349C2×D4—182no—
350C2×D4—182no—
351C22×C4—92no—
352C22×C4—98no—
353C22×C4—184no—
354C22×C4—182no—
355C22×C4—182no—
356C22×C4#62412yes—
357C22×C4#62411yescharacteristic
358C22×C4#62612yes—
359C22×C4#62614yes—
360C22×C4#62612yes—
361C22×C4C2×D3211yescharacteristic
362C22×C4C2×D3212yes—
363M16—38no—
364M16—64no—
365M16—68no—
366C2×C8—64no—
367C2×C8—68no—
368C22×C3—24no—
369C22×C3—24no—
370C22×C3—24no—
371C22×C3—24no—
372C22×C3—21no—
373C22×C3—21no—
374C22×C3—21no—
375C22×C3—24no—
376C22×C3—44no—
377C22×C3—44no—
378C22×C3—44no—
379C22×C3—44no—
380C22×C3—44no—
381C22×C3C2×(C2×D3)⋊C412yes—
382C22×C3C2×(C2×D3)⋊C414yes—
383C22×C3C2×(C2×D3)⋊C414yes—
384C22×C3C2×(C2×D3)⋊C412yes—
385C22×C3C22×C4×D312yes—
386C2×D3—68no—
387C2×D3—68no—
388C2×D3—128no—
389C2×D3—128no—
390C2×D3—128no—
391C2×D3—128no—
392C2×D3—128no—
393C2×D3—128no—
394C3×C4—22no—
395C3×C4—22no—
396C3×C4—22no—
397C3×C4—22no—
398C3×C4C2×(C2×D3)⋊C412yes—
399C3×C4C2×(C2×D3)⋊C412yes—
400C3×C4C2×(C2×D3)⋊C414yes—
401C3×C4C2×(C2×D3)⋊C414yes—
402C3×C4C22×D1212yes—
403C3×C4C22×#6712yes—
404Dic3—68no—
405Dic3—68no—
406C32C2×#41311yescharacteristic, complemented, Sylow
407C23—42no—
408C23—94no—
409C23—182no—
410C23—182no—
411C23—364no—
412C23#372212yes—
413C23#372212yes—
414C23C2×#62411yescharacteristic
415C23C2×#62412yes—
416Q8—184no—
417Q8—184no—
418D4—1816no—
419D4—184no—
420D4—184no—
421C2×C4—94no—
422C2×C4—182no—
423C2×C4—182no—
424C2×C4—188no—
425C2×C4—188no—
426C2×C4#372211yescharacteristic
427C2×C4#372212yes—
428C2×C4#372214yes—
429C2×C4#372214yes—
430C2×C4#372211yescharacteristic
431C2×C4C2×#62412yes—
432C2×C4C2×#62411yescharacteristic
433C2×C4C2×#62612yes—
434C2×C4C2×#62614yes—
435C2×C4C2×#62612yes—
436C2×C4C2×#62614yes—
437C2×C4C22×D3211yescharacteristic
438C8—68no—
439C2×C3—22no—
440C2×C3—22no—
441C2×C3—22no—
442C2×C3—22no—
443C2×C3—24no—
444C2×C3—24no—
445C2×C3—22no—
446C2×C3—21no—
447C2×C3—44no—
448C2×C3#513214yescomplemented
449C2×C3C22×(C2×D3)⋊C412yes—
450D3—128no—
451D3—128no—
452C22—22no—
453C22—24no—
454C22—42no—
455C22—42no—
456C22—184no—
457C22—364no—
458C22—364no—
459C22—364no—
460C22C2×#372211yescharacteristic
461C22C2×#372214yes—
462C22C2×#372211yescharacteristic
463C22C22×#62411yescharacteristic
464C4—184no—
465C4C2×#372212yes—
466C4C2×#372212yes—
467C4C2×#372212yes—
468C4C22×#62612yes—
469C3—21no—
470C3C2×#513212yescomplemented
471C2—21no—
472C2—21no—
473C2—24no—
474C2—364no—
475C2#1059107812yesdirect product factor
476C2C22×#372211yescharacteristic
subgroupG/H
centerC2×C4#3722
commutatorC22×C32C23×C4
FrattiniC2×C4C22×D32
FittingC23×C32×C4C22
socleC22×C32C2×C22⋊C4
prime radicalC22×#3828C2
cosocleC2×C32×C4C24
hypercenterC23×C4D32
hypocenterC32C2×#413
LCSG ▷ C22×C32 ▷ C2×C32 ▷ C32
UCSC1 ◁ C2×C4 ◁ C23×C4

Complements

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

NH ≅ G/Ntype
2. C22×C3×#208C2semidirect
3. C2×#63561C2semidirect
4. #10591078C2direct (N × H)
5. C2×#63559C2semidirect
20. C2×C3×#208C22semidirect
22. #63561C22semidirect
23. #63559C22semidirect
27. C22×#208D3semidirect
97. C2×#208C2×D3semidirect
331. C2×C32#413semidirect
406. C32C2×#413semidirect
448. C2×C3#5132semidirect
470. C3C2×#5132semidirect
475. C2#10591078direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#38282
C22×C3×#2082
C2×#635612
#105910782
C2×#635592
C2×#51323