Finite Group Databasebeta

← C2×#10594776 #11918506

Subgroups — C2×#10594776 #11918506

Order 1152.

3069 conjugacy classes of subgroups.

The subgroup lattice has 577 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C3×#235C211yesmaximal, characteristic
2C22×#3748C211yesmaximal, characteristic, complemented
3C22×C3×#208C211yesmaximal, characteristic, complemented
4#10594776C2116yesmaximal, direct product factor
5C2×#63815C214yesmaximal, complemented
6C2×#63814C214yesmaximal, complemented
7C2×D3×#208C214yesmaximal, complemented
8C2×#5819—31nomaximal
9C2×#5745—31nomaximal
10C23×C32×C4C2211yescharacteristic
11C22×C3×#67C412yes—
12C2×C3×#235C412yes—
13C2×C3×#235C412yes—
14C2×C3×#235C418yes—
15C2×C3×#235C2212yes—
16C2×C3×#235C2212yes—
17C2×C3×#235C2218yes—
18C22×C3×D12C411yescharacteristic
19C22×C3×C4×D3C2212yes—
20C22×C3×Dic6C411yescharacteristic
21C2×#3748C2212yes—
22C2×#3748C2212yescomplemented
23C2×#3748C2218yescomplemented
24C22×C3⋊(C3⋊C8)C2212yescomplemented
25C2×C3×#208C2212yes—
26C2×C3×#208C2212yescomplemented
27C2×C3×#208C2218yescomplemented
28C22×C3×C3⋊C8C2212yescomplemented
29C2×#3711C2218yescomplemented
30#63815C22132yescomplemented
31#63814C22132yescomplemented
32D3×#208C22132yescomplemented
33C2×D3×C3⋊C8C2218yescomplemented
34C22×C3×#41—31no—
35C22×#235D311yescharacteristic
36C22×C3×M16—31no—
37#5819—316no—
38C2×#948—34no—
39C2×#948—34no—
40C22×#208—31no—
41C22×#208—31no—
42C22×#208—34no—
43C22×#208—61no—
44C22×#208D311yescharacteristic, complemented
45#5745—316no—
46C2×#907—34no—
47C2×D3×M16—34no—
48C2×#901—34no—
49C24×C32C2×C411yescharacteristic
50C23×C3×D3C2×C412yes—
51C22×C32×C4C2×C411yescharacteristic
52C22×C32×C4C2×C411yescharacteristic
53C22×C32×C4C2×C411yescharacteristic
54C22×C32×C4C2×C414yes—
55C22×C32×C4C2311yescharacteristic
56C22×C32×C4C2311yescharacteristic
57C22×C32×C4C2311yescharacteristic
58C22×C32×C4C2314yes—
59C2×C3×#67C2×C414yes—
60C2×C3×#67C2×C414yes—
61C2×C3×#67C2×C4116yes—
62C22×C3×Dic3C2×C412yes—
63C3×#235C2×C418yes—
64C3×#235C2×C418yes—
65C3×#235C2×C4116yes—
66C3×#235C2×C4116yes—
67C3×#235C2318yes—
68C3×#235C2318yes—
69C2×C3×D12C2×C412yes—
70C2×C3×D12C2×C412yes—
71C2×C3×D12C2×C418yes—
72C2×C3×C4×D3C2×C414yes—
73C2×C3×C4×D3C2×C418yes—
74C2×C3×C4×D3C2314yes—
75C2×C3×C4×D3C2318yes—
76C2×C3×Dic6C2×C412yes—
77C2×C3×Dic6C2×C412yes—
78C2×C3×Dic6C2×C418yes—
79#3748C2318yes—
80#3748C2318yescomplemented
81C2×C3⋊(C3⋊C8)C2314yes—
82C2×C3⋊(C3⋊C8)C2318yescomplemented
83C3×#208C2318yes—
84C3×#208C2318yescomplemented
85C2×C3×C3⋊C8C2314yes—
86C2×C3×C3⋊C8C2318yescomplemented
87#3711C23132yescomplemented
88D3×C3⋊C8C23132yescomplemented
89C2×#568—91noSylow
90C2×C3×#41—32no—
91C2×C3×#41—32no—
92C2×C3×#41—38no—
93C2×C3×#41—32no—
94C2×C3×#41—32no—
95C2×C3×#41—38no—
96C22×C3×Q8—31no—
97C22×C3×D4—32no—
98C22×C3×D4—31no—
99C23×C3×C4—21no—
100C23×C3×C4—32no—
101C23×C3×C4C2×D311yescharacteristic
102C23×C3×C4C2×D311yescharacteristic
103C22×#67Dic312yes—
104C2×#235Dic312yes—
105C2×#235Dic312yes—
106C2×#235Dic318yes—
107C2×#235C2×D312yes—
108C2×#235C2×D312yes—
109C2×#235C2×D318yes—
110C22×D12Dic311yescharacteristic
111C22×C4×D3C2×D312yes—
112C22×Dic6Dic311yescharacteristic
113C2×C3×M16—32no—
114C2×C3×M16—32no—
115C2×C3×M16—38no—
116C22×C3×C8—32no—
117#948—332no—
118#948—332no—
119C2×#208—32no—
120C2×#208—32no—
121C2×#208—38no—
122C2×#208—32no—
123C2×#208—32no—
124C2×#208—38no—
125C2×#208—332no—
126C2×#208—38no—
127C2×#208—62no—
128C2×#208—62no—
129C2×#208—68no—
130C2×#208C2×D312yes—
131C2×#208C2×D312yescomplemented
132C2×#208C2×D318yescomplemented
133C22×C3⋊C8—32no—
134C22×C3⋊C8—32no—
135C22×C3⋊C8—38no—
136C22×C3⋊C8—62no—
137C22×C3⋊C8C2×D312yescomplemented
138#907—332no—
139D3×M16—332no—
140#901—332no—
141C2×ΓL(1,𝔽25)—38no—
142C2×D3×C8—38no—
143C23×C32—42no—
144C23×C32C22×C411yescharacteristic
145C23×C32C22×C411yescharacteristic
146C23×C32C22×C411yescharacteristic
147C23×C32C22×C414yes—
148C22×C3×D3—44no—
149C22×C3×D3C22×C414yes—
150C22×C3×D3C22×C418yes—
151C2×C32×C4C22×C414yes—
152C2×C32×C4C22×C411yescharacteristic
153C2×C32×C4C22×C411yescharacteristic
154C2×C32×C4C22×C412yes—
155C2×C32×C4C22×C411yescharacteristic
156C2×C32×C4C22×C412yes—
157C2×C32×C4C22×C412yes—
158C2×C32×C4C22×C414yes—
159C2×C32×C4C22×C414yes—
160C2×C32×C4C2411yescharacteristic
161C2×C32×C4C2412yes—
162C2×C32×C4C2412yes—
163C2×C32×C4C2412yes—
164C3×#67C22×C4116yes—
165C3×#67C22×C4116yes—
166C2×C3×Dic3C22×C418yes—
167C2×C3×Dic3C22×C414yes—
168C3×D12C22×C418yes—
169C3×D12C22×C418yes—
170C3×C4×D3C22×C418yes—
171C3×C4×D3C22×C4116yes—
172C3×C4×D3C2418yes—
173C3×Dic6C22×C418yes—
174C3×Dic6C22×C418yes—
175C3⋊(C3⋊C8)C2418yes—
176C3×C3⋊C8C2418yes—
177C22×#41—31no—
178#568—916no—
179C2×#131—94no—
180C2×#131—94no—
181C22×M16—31no—
182C22×M16—94no—
183C22×M16—91no—
184C24×C3—21no—
185C24×C3—32no—
186C24×C3C4×D311yescharacteristic
187C24×C3C2×Dic311yescharacteristic
188C23×D3C2×Dic312yes—
189C3×#41—38no—
190C3×#41—38no—
191C3×#41—316no—
192C3×#41—316no—
193C3×#41—38no—
194C3×#41—38no—
195C2×C3×Q8—32no—
196C2×C3×Q8—32no—
197C2×C3×Q8—38no—
198C2×C3×D4—34no—
199C2×C3×D4—34no—
200C2×C3×D4—316no—
201C2×C3×D4—32no—
202C2×C3×D4—32no—
203C2×C3×D4—38no—
204C22×C3×C4—21no—
205C22×C3×C4—21no—
206C22×C3×C4—21no—
207C22×C3×C4—24no—
208C22×C3×C4—21no—
209C22×C3×C4—24no—
210C22×C3×C4—21no—
211C22×C3×C4—21no—
212C22×C3×C4—32no—
213C22×C3×C4—34no—
214C22×C3×C4—38no—
215C22×C3×C4—34no—
216C22×C3×C4—38no—
217C22×C3×C4C4×D311yescharacteristic
218C22×C3×C4C4×D311yescharacteristic
219C22×C3×C4C4×D311yescharacteristic
220C22×C3×C4C4×D314yes—
221C22×C3×C4C2×Dic311yescharacteristic
222C22×C3×C4C2×Dic311yescharacteristic
223C22×C3×C4C2×Dic311yescharacteristic
224C22×C3×C4C2×Dic314yes—
225C22×C3×C4C22×D311yescharacteristic
226C22×C3×C4C22×D311yescharacteristic
227C22×C3×C4C22×D311yescharacteristic
228C22×C3×C4C22×D314yes—
229C22×C3×C4C22×D311yescharacteristic
230C22×C3×C4C22×D311yescharacteristic
231C22×C3×C4C22×D311yescharacteristic
232C22×C3×C4C22×D314yes—
233C2×#67C2×Dic314yes—
234C2×#67C2×Dic314yes—
235C2×#67C2×Dic3116yes—
236C22×Dic3C2×Dic312yes—
237#235C2×Dic318yes—
238#235C2×Dic318yes—
239#235C2×Dic3116yes—
240#235C2×Dic3116yes—
241#235C22×D318yes—
242#235C22×D318yes—
243C2×D12C2×Dic312yes—
244C2×D12C2×Dic312yes—
245C2×D12C2×Dic318yes—
246C2×C4×D3C2×Dic314yes—
247C2×C4×D3C2×Dic318yes—
248C2×C4×D3C22×D314yes—
249C2×C4×D3C22×D318yes—
250C2×Dic6C2×Dic312yes—
251C2×Dic6C2×Dic312yes—
252C2×Dic6C2×Dic318yes—
253C3×M16—38no—
254C3×M16—38no—
255C2×C3×C8—34no—
256C2×C3×C8—38no—
257#208—38no—
258#208—38no—
259#208—38no—
260#208—38no—
261#208—332no—
262#208—68no—
263#208—68no—
264#208C22×D318yes—
265#208C22×D318yescomplemented
266C2×C3⋊C8—34no—
267C2×C3⋊C8—38no—
268C2×C3⋊C8—34no—
269C2×C3⋊C8—38no—
270C2×C3⋊C8—332no—
271C2×C3⋊C8—64no—
272C2×C3⋊C8—68no—
273C2×C3⋊C8C22×D314yes—
274C2×C3⋊C8C22×D318yescomplemented
275ΓL(1,𝔽25)—332no—
276D3×C8—332no—
277C22×C32—22no—
278C22×C32—22no—
279C22×C32—22no—
280C22×C32—44no—
281C22×C32C23×C412yes—
282C22×C32C23×C412yes—
283C22×C32C23×C412yes—
284C22×C32C23×C411yescharacteristic
285C2×C3×D3—28no—
286C2×C3×D3—48no—
287C2×C3×D3C23×C418yes—
288C32×C4C23×C412yes—
289C32×C4C23×C412yes—
290C32×C4C23×C411yescharacteristic
291C32×C4C23×C412yes—
292C32×C4C2511yescharacteristic
293C3×Dic3C23×C418yes—
294C2×#41—32no—
295C2×#41—32no—
296C2×#41—38no—
297C2×#41—32no—
298C2×#41—32no—
299C2×#41—38no—
300C22×Q8—31no—
301C22×D4—32no—
302C22×D4—31no—
303C23×C4—32no—
304C23×C4D3211yescharacteristic
305#131—932no—
306#131—932no—
307C2×M16—32no—
308C2×M16—32no—
309C2×M16—38no—
310C2×M16—98no—
311C2×M16—932no—
312C2×M16—92no—
313C2×M16—92no—
314C2×M16—98no—
315C22×C8—32no—
316C22×C8—98no—
317C22×C8—92no—
318C23×C3—21no—
319C23×C3—21no—
320C23×C3—21no—
321C23×C3—24no—
322C23×C3—34no—
323C23×C3—38no—
324C23×C3—42no—
325C23×C3—42no—
326C23×C3—44no—
327C23×C3—124no—
328C23×C3C2×C4×D311yescharacteristic
329C23×C3C2×C4×D311yescharacteristic
330C23×C3C2×C4×D311yescharacteristic
331C23×C3C2×C4×D314yes—
332C23×C3C22×Dic311yescharacteristic
333C23×C3C22×Dic311yescharacteristic
334C23×C3C22×Dic311yescharacteristic
335C23×C3C22×Dic314yes—
336C22×D3—44no—
337C22×D3C22×Dic314yes—
338C22×D3C22×Dic318yes—
339C3×Q8—38no—
340C3×Q8—38no—
341C3×D4—316no—
342C3×D4—316no—
343C3×D4—38no—
344C3×D4—38no—
345C2×C3×C4—22no—
346C2×C3×C4—22no—
347C2×C3×C4—22no—
348C2×C3×C4—21no—
349C2×C3×C4—21no—
350C2×C3×C4—22no—
351C2×C3×C4—21no—
352C2×C3×C4—21no—
353C2×C3×C4—24no—
354C2×C3×C4—22no—
355C2×C3×C4—24no—
356C2×C3×C4—24no—
357C2×C3×C4—22no—
358C2×C3×C4—38no—
359C2×C3×C4—34no—
360C2×C3×C4—38no—
361C2×C3×C4—316no—
362C2×C3×C4—38no—
363C2×C3×C4C2×C4×D312yes—
364C2×C3×C4C2×C4×D311yescharacteristic
365C2×C3×C4C2×C4×D314yes—
366C2×C3×C4C2×C4×D311yescharacteristic
367C2×C3×C4C2×C4×D311yescharacteristic
368C2×C3×C4C2×C4×D312yes—
369C2×C3×C4C2×C4×D312yes—
370C2×C3×C4C2×C4×D314yes—
371C2×C3×C4C2×C4×D314yes—
372C2×C3×C4C22×Dic314yes—
373C2×C3×C4C22×Dic311yescharacteristic
374C2×C3×C4C22×Dic311yescharacteristic
375C2×C3×C4C22×Dic312yes—
376C2×C3×C4C22×Dic311yescharacteristic
377C2×C3×C4C22×Dic312yes—
378C2×C3×C4C22×Dic312yes—
379C2×C3×C4C22×Dic314yes—
380C2×C3×C4C22×Dic314yes—
381C2×C3×C4C23×D312yes—
382C2×C3×C4C23×D312yes—
383C2×C3×C4C23×D312yes—
384C2×C3×C4C23×D312yes—
385C2×C3×C4C23×D312yes—
386C2×C3×C4C23×D312yes—
387C2×C3×C4C23×D311yescharacteristic
388C2×C3×C4C23×D311yescharacteristic
389#67C22×Dic3116yes—
390#67C22×Dic3116yes—
391C2×Dic3C22×Dic318yes—
392C2×Dic3C22×Dic314yes—
393D12C22×Dic318yes—
394D12C22×Dic318yes—
395C4×D3C22×Dic318yes—
396C4×D3C22×Dic3116yes—
397C4×D3C23×D318yes—
398Dic6C22×Dic318yes—
399Dic6C22×Dic318yes—
400C3×C8—38no—
401C3⋊C8—38no—
402C3⋊C8—38no—
403C3⋊C8—68no—
404C3⋊C8C23×D318yes—
405C2×C32—22no—
406C2×C32—22no—
407C2×C32—22no—
408C2×C32#56812yescomplemented
409C2×C32C24×C411yescharacteristic
410C3×D3—28no—
411C24—32no—
412C24D3×Dic311yescharacteristic
413#41—38no—
414#41—38no—
415#41—38no—
416#41—38no—
417#41—316no—
418#41—316no—
419C2×Q8—32no—
420C2×Q8—32no—
421C2×Q8—38no—
422C2×D4—34no—
423C2×D4—34no—
424C2×D4—316no—
425C2×D4—32no—
426C2×D4—32no—
427C2×D4—38no—
428C22×C4—32no—
429C22×C4—38no—
430C22×C4—34no—
431C22×C4—34no—
432C22×C4—38no—
433C22×C4D3×Dic311yescharacteristic
434C22×C4D3×Dic311yescharacteristic
435C22×C4D3×Dic311yescharacteristic
436C22×C4D3×Dic314yes—
437C22×C4C2×D3214yes—
438C22×C4C2×D3211yescharacteristic
439C22×C4C2×D3211yescharacteristic
440C22×C4C2×D3211yescharacteristic
441M16—38no—
442M16—38no—
443M16—932no—
444M16—98no—
445M16—98no—
446C2×C8—38no—
447C2×C8—34no—
448C2×C8—932no—
449C2×C8—98no—
450C2×C8—94no—
451C22×C3—24no—
452C22×C3—22no—
453C22×C3—22no—
454C22×C3—22no—
455C22×C3—22no—
456C22×C3—22no—
457C22×C3—22no—
458C22×C3—22no—
459C22×C3—21no—
460C22×C3—22no—
461C22×C3—22no—
462C22×C3—38no—
463C22×C3—42no—
464C22×C3—42no—
465C22×C3—44no—
466C22×C3—44no—
467C22×C3—48no—
468C22×C3—68no—
469C22×C3—128no—
470C22×C3C22×C4×D312yes—
471C22×C3C22×C4×D312yes—
472C22×C3C22×C4×D312yes—
473C22×C3C22×C4×D311yescharacteristic
474C22×C3C23×Dic312yes—
475C22×C3C23×Dic312yes—
476C22×C3C23×Dic312yes—
477C22×C3C23×Dic311yescharacteristic
478C2×D3—28no—
479C2×D3—48no—
480C2×D3C23×Dic318yes—
481C3×C4—22no—
482C3×C4—21no—
483C3×C4—22no—
484C3×C4—22no—
485C3×C4—21no—
486C3×C4—38no—
487C3×C4C22×C4×D312yes—
488C3×C4C22×C4×D311yescharacteristic
489C3×C4C22×C4×D312yes—
490C3×C4C22×C4×D312yes—
491C3×C4C23×Dic312yes—
492C3×C4C23×Dic312yes—
493C3×C4C23×Dic312yes—
494C3×C4C23×Dic311yescharacteristic
495C3×C4C24×D311yescharacteristic
496C3×C4C24×D311yescharacteristic
497Dic3C23×Dic318yes—
498C32C2×#56811yescharacteristic, complemented, Sylow
499C23—34no—
500C23—38no—
501C23—42no—
502C23—124no—
503C23C2×D3×Dic311yescharacteristic
504C23C2×D3×Dic311yescharacteristic
505C23C2×D3×Dic311yescharacteristic
506C23C2×D3×Dic314yes—
507Q8—38no—
508Q8—38no—
509D4—316no—
510D4—316no—
511D4—38no—
512D4—38no—
513C2×C4—38no—
514C2×C4—34no—
515C2×C4—316no—
516C2×C4—38no—
517C2×C4—38no—
518C2×C4C2×D3×Dic311yescharacteristic
519C2×C4C2×D3×Dic312yes—
520C2×C4C2×D3×Dic314yes—
521C2×C4C2×D3×Dic311yescharacteristic
522C2×C4C2×D3×Dic311yescharacteristic
523C2×C4C2×D3×Dic314yes—
524C2×C4C2×D3×Dic314yes—
525C2×C4C2×D3×Dic312yes—
526C2×C4C2×D3×Dic312yes—
527C2×C4C22×D3212yes—
528C2×C4C22×D3212yes—
529C2×C4C22×D3212yes—
530C2×C4C22×D3211yescharacteristic
531C8—38no—
532C8—98no—
533C2×C3—24no—
534C2×C3—22no—
535C2×C3—22no—
536C2×C3—22no—
537C2×C3—22no—
538C2×C3—22no—
539C2×C3—22no—
540C2×C3—21no—
541C2×C3—22no—
542C2×C3—42no—
543C2×C3—42no—
544C2×C3—68no—
545C2×C3#574512yescomplemented
546C2×C3#581912yescomplemented
547C2×C3C23×C4×D311yescharacteristic
548C2×C3C24×Dic311yescharacteristic
549D3—28no—
550C22—22no—
551C22—22no—
552C22—22no—
553C22—38no—
554C22—44no—
555C22—68no—
556C22—128no—
557C22C22×D3×Dic312yes—
558C22C22×D3×Dic312yes—
559C22C22×D3×Dic312yes—
560C22C22×D3×Dic311yescharacteristic
561C4—38no—
562C4C22×D3×Dic312yes—
563C4C22×D3×Dic311yescharacteristic
564C4C22×D3×Dic312yes—
565C4C22×D3×Dic312yes—
566C4C23×D3211yescharacteristic
567C3—21no—
568C3C2×#574511yescharacteristic, complemented
569C3C2×#581911yescharacteristic, complemented
570C2—22no—
571C2—22no—
572C2—22no—
573C2—68no—
574C2#1059477612yesdirect product factor
575C2C23×D3×Dic311yescharacteristic
subgroupG/H
centerC2×C4C22×D32
commutatorC2×C32C24×C4
FrattiniC4C23×D32
FittingC23×C32×C4C22
socleC22×C32C23×C4
prime radicalC22×C3×#235C2
cosocleC32×C4C25
hypercenterC23×C4D32
hypocenterC32C2×#568
LCSG ▷ C2×C32 ▷ C32
UCSC1 ◁ C2×C4 ◁ C23×C4

Complements

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

NH ≅ G/Ntype
2. C22×#3748C2semidirect
3. C22×C3×#208C2semidirect
4. #10594776C2direct (N × H)
5. C2×#63815C2semidirect
6. C2×#63814C2semidirect
7. C2×D3×#208C2semidirect
22. C2×#3748C22semidirect
23. C2×#3748C22semidirect
24. C22×C3⋊(C3⋊C8)C22semidirect
26. C2×C3×#208C22semidirect
27. C2×C3×#208C22semidirect
28. C22×C3×C3⋊C8C22semidirect
29. C2×#3711C22semidirect
30. #63815C22semidirect
31. #63814C22semidirect
32. D3×#208C22semidirect
33. C2×D3×C3⋊C8C22semidirect
44. C22×#208D3semidirect
80. #3748C23semidirect
82. C2×C3⋊(C3⋊C8)C23semidirect
84. C3×#208C23semidirect
86. C2×C3×C3⋊C8C23semidirect
87. #3711C23semidirect
88. D3×C3⋊C8C23semidirect
131. C2×#208C2×D3semidirect
132. C2×#208C2×D3semidirect
137. C22×C3⋊C8C2×D3semidirect
265. #208C22×D3semidirect
274. C2×C3⋊C8C22×D3semidirect
408. C2×C32#568semidirect
498. C32C2×#568semidirect
545. C2×C3#5745semidirect
546. C2×C3#5819semidirect
568. C3C2×#5745semidirect
569. C3C2×#5819semidirect
574. C2#10594776direct (N × H)

Maximal subgroups

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

subgroupindex
C22×C3×#2352
C22×#37482
C22×C3×#2082
#105947762
C2×#638152
C2×#638142
C2×D3×#2082
C2×#58193
C2×#57453