Finite Group Databasebeta

← C2×#10591210 #11808522

Subgroups — C2×#10591210 #11808522

Order 1152.

1417 conjugacy classes of subgroups.

The subgroup lattice has 554 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#3750C211yesmaximal, characteristic
2C22×Dic3⋊Dic3C211yesmaximal, characteristic
3C2×C3×C3⋊#95C211yesmaximal, characteristic
4C2×C3×C3⋊#95C211yesmaximal, characteristic
5C2×#63579C211yesmaximal, characteristic
6C2×#63579C211yesmaximal, characteristic
7C2×#63579C211yesmaximal, characteristic
8#10591210C218yesmaximal, direct product factor
9C2×#4660—31nomaximal
10C2×#4658—31nomaximal
11C23×C32×C4C2211yescharacteristic
12C23×C3⋊Dic3C2211yescharacteristic
13C23×C3⋊Dic3C2211yescharacteristic
14C23×C3×Dic3C2211yescharacteristic
15C23×C3×Dic3C2211yescharacteristic
16C23×C3×Dic3C2211yescharacteristic
17C23×C3×Dic3C2211yescharacteristic
18C2×#3750—24no—
19C2×#3750C2214yes—
20C2×Dic3⋊Dic3—24no—
21C2×Dic3⋊Dic3C2214yes—
22C3×C3⋊#95C2214yes—
23C3×C3⋊#95C2214yes—
24#63579C2214yes—
25#63579C2214yes—
26#63579C2214yes—
27C22×C4⋊Dic3—31no—
28C22×Dic3⋊C4—31no—
29C22×Dic3⋊C4—31no—
30C22×Dic3⋊C4—31no—
31C22×Dic3⋊C4—61no—
32C2×C3×#95—31no—
33C2×C3×#95—31no—
34C2×C3⋊#95—31no—
35C2×C3⋊#95—31no—
36C2×C3⋊#95—31no—
37C2×C3⋊#95—31no—
38C2×C3⋊#95—31no—
39C2×C3⋊#95—31no—
40C2×C3⋊#95D311yescharacteristic
41C2×C3⋊#95D311yescharacteristic
42#4660—38no—
43#4658—38no—
44C24×C32C2311yescharacteristic
45C22×C32×C4—22no—
46C22×C32×C4—22no—
47C22×C32×C4—22no—
48C22×C32×C4C2312yes—
49C22×C3⋊Dic3—22no—
50C22×C3⋊Dic3—22no—
51C22×C3⋊Dic3—22no—
52C22×C3⋊Dic3—22no—
53C22×C3⋊Dic3—22no—
54C22×C3⋊Dic3D414yes—
55C22×C3⋊Dic3C2312yes—
56C22×C3⋊Dic3C2312yes—
57C22×C3×Dic3—22no—
58C22×C3×Dic3—22no—
59C22×C3×Dic3—22no—
60C22×C3×Dic3—22no—
61C22×C3×Dic3—22no—
62C22×C3×Dic3—22no—
63C22×C3×Dic3—22no—
64C22×C3×Dic3—22no—
65C22×C3×Dic3—22no—
66C22×C3×Dic3—22no—
67C22×C3×Dic3—22no—
68C22×C3×Dic3Q814yes—
69C22×C3×Dic3C2312yes—
70C22×C3×Dic3C2312yes—
71C22×C3×Dic3C2312yes—
72C22×C3×Dic3C2312yes—
73#3750—28no—
74Dic3⋊Dic3—28no—
75C2×#400—91noSylow
76C23×C3×C4—21no—
77C23×C3×C4—31no—
78C23×C3×C4—31no—
79C23×C3×C4—31no—
80C23×C3×C4—31no—
81C23×C3×C4C2×D311yescharacteristic
82C23×C3×C4C2×D311yescharacteristic
83C23×Dic3—31no—
84C23×Dic3—31no—
85C23×Dic3—31no—
86C23×Dic3—31no—
87C23×Dic3—61no—
88C23×Dic3—61no—
89C23×Dic3C2×D311yescharacteristic
90C23×Dic3C2×D311yescharacteristic
91C23×Dic3C2×D311yescharacteristic
92C23×Dic3C2×D311yescharacteristic
93C2×C4⋊Dic3—34no—
94C2×C4⋊Dic3—64no—
95C2×Dic3⋊C4—34no—
96C2×Dic3⋊C4—34no—
97C2×Dic3⋊C4—34no—
98C2×Dic3⋊C4—64no—
99C2×Dic3⋊C4—64no—
100C2×Dic3⋊C4—64no—
101C2×Dic3⋊C4—64no—
102C2×Dic3⋊C4—68no—
103C3×#95—34no—
104C3×#95—34no—
105C3⋊#95—34no—
106C3⋊#95—34no—
107C3⋊#95—34no—
108C3⋊#95—34no—
109C3⋊#95—34no—
110C3⋊#95—34no—
111C3⋊#95C2×D314yes—
112C3⋊#95C2×D314yes—
113C23×C32C2×D412yes—
114C23×C32C2×Q812yes—
115C23×C32#4112yes—
116C23×C32#4112yes—
117C23×C32#4112yes—
118C23×C32#4112yes—
119C23×C32#4112yes—
120C23×C32C2411yescharacteristic
121C2×C32×C4—22no—
122C2×C32×C4—22no—
123C2×C32×C4—22no—
124C2×C32×C4—44no—
125C2×C3⋊Dic3—28no—
126C2×C3⋊Dic3—22no—
127C2×C3⋊Dic3—22no—
128C2×C3⋊Dic3—22no—
129C2×C3⋊Dic3—22no—
130C2×C3⋊Dic3—22no—
131C2×C3⋊Dic3—44no—
132C2×C3⋊Dic3C2×D414yes—
133C2×C3×Dic3—28no—
134C2×C3×Dic3—22no—
135C2×C3×Dic3—22no—
136C2×C3×Dic3—22no—
137C2×C3×Dic3—22no—
138C2×C3×Dic3—22no—
139C2×C3×Dic3—22no—
140C2×C3×Dic3—22no—
141C2×C3×Dic3—22no—
142C2×C3×Dic3—22no—
143C2×C3×Dic3—22no—
144C2×C3×Dic3—22no—
145C2×C3×Dic3—44no—
146C2×C3×Dic3—44no—
147C2×C3×Dic3—44no—
148C2×C3×Dic3C2×Q814yes—
149C22×C4⋊C4—91no—
150C22×C4⋊C4—91no—
151#400—98no—
152C2×#95—31no—
153C2×#95—31no—
154C2×#95—91no—
155C2×#95—91no—
156C2×#95—91no—
157C24×C3—21no—
158C24×C3C22×D311yescharacteristic
159C24×C3C22×D311yescharacteristic
160C22×C3×C4—24no—
161C22×C3×C4—22no—
162C22×C3×C4—22no—
163C22×C3×C4—22no—
164C22×C3×C4—22no—
165C22×C3×C4—22no—
166C22×C3×C4—22no—
167C22×C3×C4—22no—
168C22×C3×C4—34no—
169C22×C3×C4—32no—
170C22×C3×C4—32no—
171C22×C3×C4—32no—
172C22×C3×C4—32no—
173C22×C3×C4—42no—
174C22×C3×C4—42no—
175C22×C3×C4—62no—
176C22×C3×C4—62no—
177C22×C3×C4—62no—
178C22×C3×C4—62no—
179C22×C3×C4—62no—
180C22×C3×C4—62no—
181C22×C3×C4—62no—
182C22×C3×C4—62no—
183C22×C3×C4—62no—
184C22×C3×C4—62no—
185C22×C3×C4—62no—
186C22×C3×C4C22×D312yes—
187C22×C3×C4C22×D312yes—
188C22×Dic3—22no—
189C22×Dic3—22no—
190C22×Dic3—22no—
191C22×Dic3—22no—
192C22×Dic3—22no—
193C22×Dic3—22no—
194C22×Dic3—22no—
195C22×Dic3—22no—
196C22×Dic3—22no—
197C22×Dic3—22no—
198C22×Dic3—22no—
199C22×Dic3—34no—
200C22×Dic3—34no—
201C22×Dic3—32no—
202C22×Dic3—32no—
203C22×Dic3—32no—
204C22×Dic3—32no—
205C22×Dic3—64no—
206C22×Dic3—62no—
207C22×Dic3—62no—
208C22×Dic3—64no—
209C22×Dic3—64no—
210C22×Dic3—62no—
211C22×Dic3—62no—
212C22×Dic3—62no—
213C22×Dic3—62no—
214C22×Dic3—64no—
215C22×Dic3—62no—
216C22×Dic3—62no—
217C22×Dic3—62no—
218C22×Dic3—62no—
219C22×Dic3—62no—
220C22×Dic3—62no—
221C22×Dic3—122no—
222C22×Dic3—122no—
223C22×Dic3Dic614yes—
224C22×Dic3C22×D312yes—
225C22×Dic3C22×D312yes—
226C22×Dic3C22×D312yes—
227C22×Dic3C22×D312yes—
228C4⋊Dic3—68no—
229Dic3⋊C4—68no—
230Dic3⋊C4—68no—
231Dic3⋊C4—68no—
232Dic3⋊C4—616no—
233C22×C32C22⋊Q814yes—
234C22×C32#12314yes—
235C22×C32#12414yes—
236C22×C32#12514yes—
237C22×C32#12514yes—
238C22×C32#12614yes—
239C22×C32#12614yes—
240C22×C32C22×D411yescharacteristic
241C22×C32C22×Q811yescharacteristic
242C22×C32C2×#4111yescharacteristic
243C22×C32C2×#4111yescharacteristic
244C22×C32C2×#4111yescharacteristic
245C22×C32C2×#4111yescharacteristic
246C22×C32C2×#4111yescharacteristic
247C32×C4—42no—
248C3⋊Dic3—24no—
249C3⋊Dic3—42no—
250C3×Dic3—24no—
251C3×Dic3—42no—
252C3×Dic3—42no—
253C3×Dic3—42no—
254C23×C4—31no—
255C23×C4—31no—
256C23×C4—31no—
257C23×C4—31no—
258C23×C4—91no—
259C23×C4—91no—
260C23×C4D3211yescharacteristic
261C2×C4⋊C4—94no—
262C2×C4⋊C4—94no—
263C2×C4⋊C4—184no—
264C2×C4⋊C4—184no—
265#95—34no—
266#95—34no—
267#95—94no—
268#95—94no—
269#95—94no—
270C23×C3—21no—
271C23×C3—22no—
272C23×C3—22no—
273C23×C3—22no—
274C23×C3—22no—
275C23×C3—22no—
276C23×C3—22no—
277C23×C3—22no—
278C23×C3C2×Dic612yes—
279C23×C3#23512yes—
280C23×C3#23512yes—
281C23×C3#23512yes—
282C23×C3#23512yes—
283C23×C3#23512yes—
284C23×C3D3×D412yes—
285C23×C3D3×D412yes—
286C23×C3#23712yes—
287C23×C3#23712yes—
288C23×C3#23712yes—
289C23×C3#23712yes—
290C23×C3D3×Q812yes—
291C23×C3#23912yes—
292C23×C3C23×D311yescharacteristic
293C23×C3C23×D311yescharacteristic
294C2×C3×C4—24no—
295C2×C3×C4—22no—
296C2×C3×C4—22no—
297C2×C3×C4—22no—
298C2×C3×C4—22no—
299C2×C3×C4—22no—
300C2×C3×C4—22no—
301C2×C3×C4—34no—
302C2×C3×C4—42no—
303C2×C3×C4—42no—
304C2×C3×C4—48no—
305C2×C3×C4—44no—
306C2×C3×C4—44no—
307C2×C3×C4—68no—
308C2×C3×C4—62no—
309C2×C3×C4—62no—
310C2×C3×C4—62no—
311C2×C3×C4—62no—
312C2×C3×C4—62no—
313C2×C3×C4—62no—
314C2×C3×C4—62no—
315C2×C3×C4—62no—
316C2×C3×C4—62no—
317C2×C3×C4—62no—
318C2×C3×C4—62no—
319C2×C3×C4—124no—
320C2×C3×C4—124no—
321C2×C3×C4—124no—
322C2×Dic3—28no—
323C2×Dic3—22no—
324C2×Dic3—22no—
325C2×Dic3—22no—
326C2×Dic3—22no—
327C2×Dic3—22no—
328C2×Dic3—22no—
329C2×Dic3—22no—
330C2×Dic3—22no—
331C2×Dic3—22no—
332C2×Dic3—22no—
333C2×Dic3—22no—
334C2×Dic3—34no—
335C2×Dic3—34no—
336C2×Dic3—44no—
337C2×Dic3—44no—
338C2×Dic3—44no—
339C2×Dic3—64no—
340C2×Dic3—64no—
341C2×Dic3—64no—
342C2×Dic3—616no—
343C2×Dic3—68no—
344C2×Dic3—68no—
345C2×Dic3—62no—
346C2×Dic3—62no—
347C2×Dic3—62no—
348C2×Dic3—62no—
349C2×Dic3—64no—
350C2×Dic3—62no—
351C2×Dic3—62no—
352C2×Dic3—62no—
353C2×Dic3—62no—
354C2×Dic3—62no—
355C2×Dic3—62no—
356C2×Dic3—122no—
357C2×Dic3—122no—
358C2×Dic3—128no—
359C2×Dic3—124no—
360C2×Dic3—124no—
361C2×Dic3C2×Dic614yes—
362C2×C32#40018yescomplemented
363C2×C32C2×C22⋊Q811yescharacteristic
364C2×C32C2×#12311yescharacteristic
365C2×C32C2×#12411yescharacteristic
366C2×C32C2×#12511yescharacteristic
367C2×C32C2×#12511yescharacteristic
368C2×C32C2×#12611yescharacteristic
369C2×C32C2×#12611yescharacteristic
370C24C2×D3211yescharacteristic
371C22×C4—22no—
372C22×C4—22no—
373C22×C4—22no—
374C22×C4—32no—
375C22×C4—34no—
376C22×C4—32no—
377C22×C4—32no—
378C22×C4—32no—
379C22×C4—62no—
380C22×C4—62no—
381C22×C4—62no—
382C22×C4—62no—
383C22×C4—62no—
384C22×C4—62no—
385C22×C4—62no—
386C22×C4—62no—
387C22×C4—62no—
388C22×C4—62no—
389C22×C4—62no—
390C22×C4—92no—
391C22×C4—94no—
392C22×C4—92no—
393C22×C4—182no—
394C22×C4—182no—
395C22×C4—182no—
396C22×C4—182no—
397C22×C4—182no—
398C22×C4C2×D3212yes—
399C4⋊C4—188no—
400C4⋊C4—188no—
401C22×C3—21no—
402C22×C3—21no—
403C22×C3—21no—
404C22×C3—21no—
405C22×C3—21no—
406C22×C3—21no—
407C22×C3—21no—
408C22×C3—24no—
409C22×C3—24no—
410C22×C3—24no—
411C22×C3—24no—
412C22×C3—24no—
413C22×C3—24no—
414C22×C3—24no—
415C22×C3#87014yes—
416C22×C3#87614yes—
417C22×C3#87814yes—
418C22×C3#87914yes—
419C22×C3#87914yes—
420C22×C3#88314yes—
421C22×C3#88514yes—
422C22×C3#88514yes—
423C22×C3#88914yes—
424C22×C3#88914yes—
425C22×C3#89014yes—
426C22×C3#89414yes—
427C22×C3#89614yes—
428C22×C3#89814yes—
429C22×C3C22×Dic611yescharacteristic
430C22×C3C2×#23511yescharacteristic
431C22×C3C2×#23511yescharacteristic
432C22×C3C2×#23511yescharacteristic
433C22×C3C2×#23511yescharacteristic
434C22×C3C2×#23511yescharacteristic
435C22×C3C2×D3×D411yescharacteristic
436C22×C3C2×D3×D411yescharacteristic
437C22×C3C2×#23711yescharacteristic
438C22×C3C2×#23711yescharacteristic
439C22×C3C2×#23711yescharacteristic
440C22×C3C2×#23711yescharacteristic
441C22×C3C2×D3×Q811yescharacteristic
442C22×C3C2×#23911yescharacteristic
443C3×C4—44no—
444C3×C4—42no—
445C3×C4—42no—
446C3×C4—64no—
447C3×C4—122no—
448C3×C4—122no—
449C3×C4—122no—
450Dic3—24no—
451Dic3—42no—
452Dic3—42no—
453Dic3—42no—
454Dic3—68no—
455Dic3—64no—
456Dic3—64no—
457Dic3—124no—
458Dic3—122no—
459Dic3—122no—
460C32C2×#40011yescharacteristic, complemented, Sylow
461C23D3×Dic612yes—
462C23#379512yes—
463C23#379612yes—
464C23#379812yes—
465C23#380412yes—
466C23#380412yes—
467C23#381112yes—
468C23C22×D3211yescharacteristic
469C2×C4—22no—
470C2×C4—22no—
471C2×C4—22no—
472C2×C4—34no—
473C2×C4—44no—
474C2×C4—62no—
475C2×C4—62no—
476C2×C4—68no—
477C2×C4—62no—
478C2×C4—62no—
479C2×C4—62no—
480C2×C4—62no—
481C2×C4—62no—
482C2×C4—62no—
483C2×C4—62no—
484C2×C4—62no—
485C2×C4—62no—
486C2×C4—94no—
487C2×C4—124no—
488C2×C4—124no—
489C2×C4—124no—
490C2×C4—182no—
491C2×C4—182no—
492C2×C4—188no—
493C2×C4—182no—
494C2×C4—182no—
495C2×C4—182no—
496C2×C4—364no—
497C2×C3—21no—
498C2×C3—21no—
499C2×C3—21no—
500C2×C3—21no—
501C2×C3—21no—
502C2×C3—21no—
503C2×C3—21no—
504C2×C3—28no—
505C2×C3#465818yescomplemented
506C2×C3#466018yescomplemented
507C2×C3C2×#87011yescharacteristic
508C2×C3C2×#87611yescharacteristic
509C2×C3C2×#87811yescharacteristic
510C2×C3C2×#87911yescharacteristic
511C2×C3C2×#87911yescharacteristic
512C2×C3C2×#88311yescharacteristic
513C2×C3C2×#88511yescharacteristic
514C2×C3C2×#88511yescharacteristic
515C2×C3C2×#88911yescharacteristic
516C2×C3C2×#88911yescharacteristic
517C2×C3C2×#89011yescharacteristic
518C2×C3C2×#89411yescharacteristic
519C2×C3C2×#89611yescharacteristic
520C2×C3C2×#89811yescharacteristic
521C22#6384614yes—
522C22#6385314yes—
523C22#6385814yes—
524C22#6385914yes—
525C22#6386714yes—
526C22#6389614yes—
527C22#6395314yes—
528C22C2×D3×Dic611yescharacteristic
529C22C2×#379511yescharacteristic
530C22C2×#379611yescharacteristic
531C22C2×#379811yescharacteristic
532C22C2×#380411yescharacteristic
533C22C2×#380411yescharacteristic
534C22C2×#381111yescharacteristic
535C4—42no—
536C4—64no—
537C4—122no—
538C4—122no—
539C4—122no—
540C4—184no—
541C4—362no—
542C3—21no—
543C3C2×#465811yescharacteristic, complemented
544C3C2×#466011yescharacteristic, complemented
545C2#1059121018yesdirect product factor
546C2C2×#6384611yescharacteristic
547C2C2×#6385311yescharacteristic
548C2C2×#6385811yescharacteristic
549C2C2×#6385911yescharacteristic
550C2C2×#6386711yescharacteristic
551C2C2×#6389611yescharacteristic
552C2C2×#6395311yescharacteristic
subgroupG/H
centerC24C2×D32
commutator, cosocleC23×C32C24
FrattiniC23C22×D32
FittingC23×C32×C4C22
socle, prime radicalC24×C32C23
hypercenterC23×C4D32
hypocenterC32C2×#400
LCSG ▷ C23×C32 ▷ C32
UCSC1 ◁ C24 ◁ C23×C4

Complements

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

NH ≅ G/Ntype
8. #10591210C2direct (N × H)
362. C2×C32#400semidirect
460. C32C2×#400semidirect
505. C2×C3#4658semidirect
506. C2×C3#4660semidirect
543. C3C2×#4658semidirect
544. C3C2×#4660semidirect
545. C2#10591210direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#37502
C22×Dic3⋊Dic32
C2×C3×C3⋊#952
C2×#635792
#105912102
C2×#46603
C2×#46583