Finite Group Databasebeta

← C2×#10591627 #11874408

Subgroups — C2×#10591627 #11874408

Order 1152.

1257 conjugacy classes of subgroups.

The subgroup lattice has 500 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#3756C211yesmaximal, characteristic, complemented
2C2×C3×#947C211yesmaximal, characteristic
3C22×C3×#216C211yesmaximal, characteristic, complemented
4C2×#63866C211yesmaximal, characteristic, complemented
5C22×#3716C211yesmaximal, characteristic
6C22×#3715C211yesmaximal, characteristic
7#10591627C218yesmaximal, direct product factor
8C2×#63554C211yesmaximal, characteristic, complemented
9C2×#5190—31nomaximal
10C2×#5060—31nomaximal
11C22×C32×Q8C2211yescharacteristic
12C22×#634C2211yescharacteristic
13C22×C3×D12C2211yescharacteristic
14C22×C3×Dic6C2211yescharacteristic
15C2×#3756—24no—
16C2×#3756C2214yescomplemented
17C22×C3⋊(C3⋊C8)C2211yescharacteristic
18C3×#947—22no—
19C3×#947C2214yes—
20C2×C3×#216—24no—
21C2×C3×#216C2214yescomplemented
22C2×C3×(C2×D3)⋊C4—22no—
23C2×C3×C4×Dic3C2211yescharacteristic
24C22×C3×C3⋊C8C2211yescharacteristic
25C2×Dic3⋊Dic3—22no—
26#63866—22no—
27#63866C2214yescomplemented
28C2×#3716—24no—
29C2×#3716C2214yes—
30C2×#3715—24no—
31C2×#3715C2214yes—
32#63554C2214yescomplemented
33C22×C3×Q16—31no—
34C2×C3×#124—31no—
35C2×#947D311yescharacteristic
36C2×#944—31no—
37C22×#216—31no—
38C22×#216—31no—
39C22×#216—61no—
40C22×#216D311yescharacteristic, complemented
41C22×#215—31no—
42C22×#214—31no—
43C22×#214—31no—
44C22×#204—31no—
45C2×#869—31no—
46#5190—38no—
47C2×#815—31no—
48#5060—38no—
49C2×#803—31no—
50C23×C3×D3—21no—
51C2×C32×Q8—21no—
52C2×C32×Q8—22no—
53C2×C32×Q8—22no—
54C2×C32×Q8C2312yes—
55C22×C32×C4—21no—
56C22×C32×C4C2311yescharacteristic
57C22×C3⋊Dic3—21no—
58C2×#634—22no—
59C2×#634—22no—
60C2×#634—21no—
61C2×#634C2312yes—
62C22×C3×Dic3—21no—
63C22×C3×Dic3D412yes—
64C2×C3×D12—22no—
65C2×C3×D12—22no—
66C2×C3×D12—21no—
67C2×C3×D12C2312yes—
68C2×C3×Dic6—22no—
69C2×C3×Dic6—22no—
70C2×C3×Dic6—21no—
71C2×C3×Dic6C2312yes—
72#3756—28no—
73C2×C3⋊(C3⋊C8)D414yes—
74C2×C3⋊(C3⋊C8)C2312yes—
75C3×#216—28no—
76C3×(C2×D3)⋊C4—28no—
77C3×C4×Dic3D412yes—
78C3×C4×Dic3C2312yes—
79C2×C3×C3⋊C8D414yes—
80C2×C3×C3⋊C8C2312yes—
81Dic3⋊Dic3—28no—
82#3716—28no—
83#3715—28no—
84C2×#497—91noSylow
85C22×C3×Q8—21no—
86C22×C3×Q8—31no—
87C22×C3×Q8C2×D311yescharacteristic
88C22×C3×Q8C2×D311yescharacteristic
89C22×C3×D4—31no—
90C22×D12C2×D311yescharacteristic
91C22×Dic6—31no—
92C22×Dic6—31no—
93C22×Dic6—61no—
94C22×Dic6C2×D311yescharacteristic
95C2×C3×Q16—34no—
96C2×C3×Q16—64no—
97C22×C3×C8—31no—
98C3×#124—34no—
99C3×#124—62no—
100C2×C3×C22⋊C4—62no—
101C2×C3×C42—31no—
102#947—22no—
103#947C2×D314yes—
104#944—34no—
105#944—62no—
106C2×#216—24no—
107C2×#216—34no—
108C2×#216—34no—
109C2×#216—64no—
110C2×#216—64no—
111C2×#216—64no—
112C2×#216—68no—
113C2×#216C2×D314yescomplemented
114C2×#215—34no—
115C2×#215—64no—
116C2×#214—34no—
117C2×#214—34no—
118C2×#214—64no—
119C2×#214—64no—
120C2×(C2×D3)⋊C4—22no—
121C2×C4⋊Dic3—62no—
122C2×Dic3⋊C4—62no—
123C2×C4×Dic3C2×D311yescharacteristic
124C22×C3⋊C8—31no—
125C22×C3⋊C8—31no—
126C22×C3⋊C8—61no—
127C22×C3⋊C8C2×D311yescharacteristic
128C2×#204—34no—
129C2×#204—64no—
130#869—34no—
131#869—62no—
132#815—34no—
133#803—34no—
134C23×C32C2×D411yescharacteristic
135C22×C3×D3—22no—
136C22×C3×D3—42no—
137C22×C3×D3—44no—
138C32×Q8—22no—
139C32×Q8—22no—
140C32×Q8—42no—
141C2×C32×C4—22no—
142C2×C32×C4—42no—
143C2×C32×C4C2×D412yes—
144C2×C32×C4C2×D411yescharacteristic
145C2×C32×C4C2×D412yes—
146C2×C32×C4C2411yescharacteristic
147C2×C3⋊Dic3—22no—
148C2×C3⋊Dic3—42no—
149#634—22no—
150#634—22no—
151#634—42no—
152C2×C3×Dic3—24no—
153C2×C3×Dic3—22no—
154C2×C3×Dic3—42no—
155C2×C3×Dic3C2×D414yes—
156C3×D12—22no—
157C3×D12—22no—
158C3×D12—42no—
159C3×Dic6—22no—
160C3×Dic6—22no—
161C3×Dic6—42no—
162C3⋊(C3⋊C8)C2×D414yes—
163C3×C3⋊C8C2×D414yes—
164C22×Q16—31no—
165C22×Q16—91no—
166C22×SD16—91no—
167C22×SD16—91no—
168C2×C4⋊Q8—91no—
169C2×#124—31no—
170#497—98no—
171C2×#97—91no—
172C24×C3—61no—
173C23×D3—21no—
174C2×C3×Q8—21no—
175C2×C3×Q8—21no—
176C2×C3×Q8—24no—
177C2×C3×Q8—22no—
178C2×C3×Q8—22no—
179C2×C3×Q8—22no—
180C2×C3×Q8—22no—
181C2×C3×Q8—22no—
182C2×C3×Q8—32no—
183C2×C3×Q8—41no—
184C2×C3×Q8—42no—
185C2×C3×Q8—61no—
186C2×C3×Q8—62no—
187C2×C3×Q8—62no—
188C2×C3×Q8C22×D312yes—
189C2×C3×Q8C22×D312yes—
190C2×C3×D4—32no—
191C2×C3×D4—62no—
192C2×C3×D4—61no—
193C2×C3×D4—62no—
194C22×C3×C4—21no—
195C22×C3×C4—21no—
196C22×C3×C4—21no—
197C22×C3×C4—32no—
198C22×C3×C4—41no—
199C22×C3×C4—61no—
200C22×C3×C4C22×D311yescharacteristic
201C22×C3×C4C22×D311yescharacteristic
202C22×Dic3—21no—
203C22×Dic3—61no—
204C22×Dic3—61no—
205C22×Dic3—121no—
206C22×Dic3#6712yes—
207C2×D12—22no—
208C2×D12—22no—
209C2×D12—21no—
210C2×D12C22×D312yes—
211C2×Dic6—22no—
212C2×Dic6—22no—
213C2×Dic6—21no—
214C2×Dic6—32no—
215C2×Dic6—32no—
216C2×Dic6—62no—
217C2×Dic6—64no—
218C2×Dic6—62no—
219C2×Dic6—62no—
220C2×Dic6—62no—
221C2×Dic6—62no—
222C2×Dic6—61no—
223C2×Dic6—61no—
224C2×Dic6—121no—
225C2×Dic6—122no—
226C2×Dic6C22×D312yes—
227C3×Q16—68no—
228C2×C3×C8—34no—
229C2×C3×C8—32no—
230C3×C22⋊C4—68no—
231C3×C42—32no—
232C3×C42—32no—
233#216—28no—
234#216—68no—
235#216—68no—
236#216—616no—
237#215—68no—
238#214—68no—
239#214—68no—
240(C2×D3)⋊C4—28no—
241C4⋊Dic3—68no—
242Dic3⋊C4—68no—
243C4×Dic3#6712yes—
244C4×Dic3C22×D312yes—
245C2×C3⋊C8—34no—
246C2×C3⋊C8—34no—
247C2×C3⋊C8—32no—
248C2×C3⋊C8—32no—
249C2×C3⋊C8—64no—
250C2×C3⋊C8—62no—
251C2×C3⋊C8#6714yes—
252C2×C3⋊C8C22×D312yes—
253#204—68no—
254C22×C32#12712yes—
255C22×C32#13714yes—
256C22×C32C22×D411yescharacteristic
257C2×C3×D3—42no—
258C2×C3×D3—44no—
259C2×C3×D3—84no—
260C32×C4—42no—
261C32×C4#12712yes—
262C32×C4C22×D411yescharacteristic
263C32×C4C22×D411yescharacteristic
264C3⋊Dic3—42no—
265C3×Dic3—24no—
266C3×Dic3—42no—
267C22×Q8—31no—
268C22×Q8—91no—
269C22×Q8D3211yescharacteristic
270C22×D4—31no—
271C2×Q16—34no—
272C2×Q16—64no—
273C2×Q16—94no—
274C2×Q16—184no—
275C2×SD16—94no—
276C2×SD16—94no—
277C2×SD16—184no—
278C2×SD16—184no—
279C22×C8—31no—
280C22×C8—91no—
281C4⋊Q8—94no—
282C4⋊Q8—182no—
283#124—34no—
284#124—62no—
285C2×C4⋊C4—182no—
286C2×C22⋊C4—62no—
287C2×C42—31no—
288#97—94no—
289C23×C3—21no—
290C23×C3—62no—
291C23×C3—124no—
292C23×C3—122no—
293C23×C3D3×D411yescharacteristic
294C23×C3C2×#6711yescharacteristic
295C22×D3—22no—
296C22×D3—42no—
297C22×D3—44no—
298C3×Q8—24no—
299C3×Q8—22no—
300C3×Q8—22no—
301C3×Q8—22no—
302C3×Q8—22no—
303C3×Q8—42no—
304C3×Q8—44no—
305C3×Q8—42no—
306C3×Q8—42no—
307C3×Q8—62no—
308C3×Q8—62no—
309C3×Q8—122no—
310C3×D4—62no—
311C3×D4—62no—
312C3×D4—122no—
313C2×C3×C4—22no—
314C2×C3×C4—22no—
315C2×C3×C4—21no—
316C2×C3×C4—22no—
317C2×C3×C4—21no—
318C2×C3×C4—22no—
319C2×C3×C4—34no—
320C2×C3×C4—42no—
321C2×C3×C4—44no—
322C2×C3×C4—42no—
323C2×C3×C4—42no—
324C2×C3×C4—64no—
325C2×C3×C4—62no—
326C2×C3×C4—122no—
327C2×C3×C4D3×D411yescharacteristic
328C2×C3×C4D3×D412yes—
329C2×C3×C4D3×D412yes—
330C2×C3×C4D3×D412yes—
331C2×C3×C4C2×#6711yescharacteristic
332C2×C3×C4C2×#6712yes—
333C2×C3×C4C23×D311yescharacteristic
334C2×C3×C4C23×D311yescharacteristic
335C2×Dic3—24no—
336C2×Dic3—22no—
337C2×Dic3—42no—
338C2×Dic3—62no—
339C2×Dic3—62no—
340C2×Dic3—122no—
341C2×Dic3—124no—
342C2×Dic3—122no—
343C2×Dic3—122no—
344C2×Dic3C2×#6714yes—
345D12—22no—
346D12—22no—
347D12—42no—
348Dic6—22no—
349Dic6—22no—
350Dic6—42no—
351Dic6—64no—
352Dic6—62no—
353Dic6—62no—
354Dic6—62no—
355Dic6—62no—
356Dic6—122no—
357Dic6—124no—
358Dic6—122no—
359Dic6—122no—
360C3×C8—34no—
361C3⋊C8—34no—
362C3⋊C8—34no—
363C3⋊C8—64no—
364C3⋊C8C2×#6714yes—
365C2×C32#49714yescomplemented
366C2×C32C2×#12711yescharacteristic
367C2×C32C2×#13712yes—
368C3×D3—82no—
369C24—61no—
370C2×Q8—21no—
371C2×Q8—22no—
372C2×Q8—22no—
373C2×Q8—32no—
374C2×Q8—61no—
375C2×Q8—62no—
376C2×Q8—62no—
377C2×Q8—92no—
378C2×Q8—181no—
379C2×Q8—182no—
380C2×Q8—182no—
381C2×Q8C2×D3212yes—
382C2×D4—32no—
383C2×D4—62no—
384C2×D4—61no—
385C2×D4—62no—
386C22×C4—21no—
387C22×C4—32no—
388C22×C4—61no—
389C22×C4—181no—
390C22×C4C2×D3211yescharacteristic
391Q16—68no—
392Q16—188no—
393SD16—188no—
394SD16—188no—
395C2×C8—32no—
396C2×C8—34no—
397C2×C8—92no—
398C2×C8—94no—
399C4⋊C4—188no—
400C22⋊C4—68no—
401C42—32no—
402C42—32no—
403C22×C3—21no—
404C22×C3—24no—
405C22×C3—22no—
406C22×C3—124no—
407C22×C3—122no—
408C22×C3—244no—
409C22×C3#91814yes—
410C22×C3#94012yes—
411C22×C3#94012yes—
412C22×C3#95114yes—
413C22×C3C2×D3×D411yescharacteristic
414C22×C3C22×#6711yescharacteristic
415C2×D3—42no—
416C2×D3—44no—
417C2×D3—84no—
418C3×C4—21no—
419C3×C4—21no—
420C3×C4—22no—
421C3×C4—44no—
422C3×C4—42no—
423C3×C4—42no—
424C3×C4—64no—
425C3×C4—122no—
426C3×C4#94012yes—
427C3×C4#94012yes—
428C3×C4C2×D3×D411yescharacteristic
429C3×C4C2×D3×D411yescharacteristic
430C3×C4C2×D3×D411yescharacteristic
431C3×C4C22×#6711yescharacteristic
432Dic3—24no—
433Dic3—42no—
434Dic3—124no—
435Dic3—122no—
436Dic3—122no—
437C32C2×#49711yescharacteristic, complemented, Sylow
438C23—62no—
439C23—124no—
440C23—122no—
441C23D3×#6711yescharacteristic
442Q8—22no—
443Q8—22no—
444Q8—42no—
445Q8—62no—
446Q8—62no—
447Q8—122no—
448Q8—182no—
449Q8—182no—
450Q8—362no—
451D4—62no—
452D4—62no—
453D4—122no—
454C2×C4—22no—
455C2×C4—34no—
456C2×C4—42no—
457C2×C4—64no—
458C2×C4—62no—
459C2×C4—122no—
460C2×C4—182no—
461C2×C4—362no—
462C2×C4D3×#6712yes—
463C2×C4D3×#6711yescharacteristic
464C2×C4#381112yes—
465C2×C4C22×D3211yescharacteristic
466C8—34no—
467C8—94no—
468C2×C3—24no—
469C2×C3—21no—
470C2×C3—22no—
471C2×C3—242no—
472C2×C3#506014yescomplemented
473C2×C3#519014yescomplemented
474C2×C3C2×#91812yes—
475C2×C3C2×#94011yescharacteristic
476C2×C3C2×#94011yescharacteristic
477C2×C3C2×#95112yes—
478D3—82no—
479C22—122no—
480C22—124no—
481C22—244no—
482C22#6394314yes—
483C22#6397912yes—
484C22C2×D3×#6711yescharacteristic
485C4—42no—
486C4—64no—
487C4—122no—
488C4—362no—
489C4#6397912yes—
490C4C2×D3×#6711yescharacteristic
491C4C2×#381111yescharacteristic
492C3—21no—
493C3C2×#506011yescharacteristic, complemented
494C3C2×#519011yescharacteristic, complemented
495C2—242no—
496C2#1059162714yesdirect product factor
497C2C2×#6394312yes—
498C2C2×#6397911yescharacteristic
subgroupG/H
centerC23D3×#67
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC22×C32×Q8C22
socleC23×C32C2×D4
prime radicalC22×C3×D12C22
hypercenterC22×Q8D32
hypocenterC32C2×#497
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C23 ◁ C22×C4 ◁ C22×Q8

Complements

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

NH ≅ G/Ntype
1. C22×#3756C2semidirect
3. C22×C3×#216C2semidirect
4. C2×#63866C2semidirect
7. #10591627C2direct (N × H)
8. C2×#63554C2semidirect
16. C2×#3756C22semidirect
21. C2×C3×#216C22semidirect
27. #63866C22semidirect
32. #63554C22semidirect
40. C22×#216D3semidirect
113. C2×#216C2×D3semidirect
365. C2×C32#497semidirect
437. C32C2×#497semidirect
472. C2×C3#5060semidirect
473. C2×C3#5190semidirect
493. C3C2×#5060semidirect
494. C3C2×#5190semidirect
496. C2#10591627direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#37562
C2×C3×#9472
C22×C3×#2162
C2×#638662
C22×#37162
C22×#37152
#105916272
C2×#635542
C2×#51903
C2×#50603