Finite Group Databasebeta

← C2×#10594355 #11901587

Subgroups — C2×#10594355 #11901587

Order 1152.

2169 conjugacy classes of subgroups.

The subgroup lattice has 596 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#64106C211yesmaximal, characteristic
2C2×C3×#890C211yesmaximal, characteristic, complemented
3C2×C3×#887C211yesmaximal, characteristic, complemented
4C2×#63874C211yesmaximal, characteristic
5C2×#63871C211yesmaximal, characteristic
6C2×#63869C212yesmaximal, complemented
7C2×#63868C212yesmaximal
8C2×#63866C211yesmaximal, characteristic, complemented
9C2×#63848C212yesmaximal
10C2×#63845C212yesmaximal, complemented
11C2×#63844C211yesmaximal, characteristic, complemented
12#10594355C2116yesmaximal, direct product factor
13C2×#5698—31nomaximal
14C2×#5583—31nomaximal
15C22×C4×C3⋊D3C2211yescharacteristic
16C22×#634C2211yescharacteristic
17C22×C3×Dic6C2211yescharacteristic
18C2×C32×C4⋊C4C2211yescharacteristic
19C2×#3752C2212yes—
20C2×C4⋊(C3⋊Dic3)C2212yes—
21#64106C2218yes—
22C2×C3×C4⋊Dic3C2211yescharacteristic
23C2×C3×C4⋊Dic3C2212yes—
24C2×C3×Dic3⋊C4C2212yes—
25C2×C3×Dic3⋊C4C2212yes—
26C2×C3×C4×Dic3C2211yescharacteristic
27C2×C3×C4×Dic3C2212yes—
28C2×C3×C4×Dic3C2211yescharacteristic
29C3×#890C2218yescomplemented
30C3×#887C2218yescomplemented
31C2×#3724C2212yes—
32C2×#3724C2211yescharacteristic
33C2×#3724C2211yescharacteristic
34C2×Dic3⋊Dic3C2212yes—
35C2×Dic3⋊Dic3C2212yes—
36C2×Dic3⋊Dic3C2212yes—
37C2×#3722C2211yescharacteristic
38C2×#3722C2212yes—
39C2×#3722C2211yescharacteristic
40C2×Dic32C2212yes—
41#63874C2218yes—
42#63871C2218yes—
43#63869C22116yescomplemented
44#63868C22116yes—
45#63866C2218yescomplemented
46#63848C22116yes—
47#63845C22116yescomplemented
48#63844C2218yescomplemented
49C2×C3×#125—31no—
50C2×C3×C4×Q8—31no—
51C2×#946—31no—
52C2×#944—31no—
53#5698—316no—
54#5583—316no—
55C2×#898—32no—
56C2×#898—32no—
57C2×#898—32no—
58C2×#897—31no—
59C2×#897—31no—
60C2×#897—31no—
61C2×#897—61no—
62C2×#890—32no—
63C2×#890—32no—
64C2×#890D311yescharacteristic, complemented
65C2×#889—32no—
66C2×#887—31no—
67C2×#887D311yescharacteristic, complemented
68C2×#876—32no—
69C2×#872—31no—
70C2×#872—31no—
71C2×#870—32no—
72C2×#869—31no—
73C2×C4×Dic6—31no—
74C23×C3⋊D3C2311yescharacteristic
75C22×C32×C4C2312yes—
76C22×C32×C4C2311yescharacteristic
77C22×C3⋊Dic3C2312yes—
78C22×C3⋊Dic3C2311yescharacteristic
79C2×C4×C3⋊D3—24no—
80C2×C4×C3⋊D3C2314yes—
81C2×#634—24no—
82C2×#634C2314yes—
83C22×C3×Dic3C2311yescharacteristic
84C22×C3×Dic3C2311yescharacteristic
85C22×C3×Dic3C2311yescharacteristic
86C22×C3×Dic3C2312yes—
87C22×C3×Dic3C2311yescharacteristic
88C22×C3×Dic3C2312yes—
89C2×C3×Dic6—24no—
90C2×C3×Dic6C2314yes—
91C32×C4⋊C4C2314yes—
92#3752C2318yes—
93C4⋊(C3⋊Dic3)C2318yes—
94C3×C4⋊Dic3C2314yes—
95C3×C4⋊Dic3C2318yes—
96C3×Dic3⋊C4C2318yes—
97C3×Dic3⋊C4C2318yes—
98C3×C4×Dic3C2314yes—
99C3×C4×Dic3C2318yes—
100C3×C4×Dic3C2314yes—
101#3724C2318yes—
102#3724C2314yes—
103#3724C2314yes—
104Dic3⋊Dic3C2318yes—
105Dic3⋊Dic3C2318yes—
106Dic3⋊Dic3C2318yes—
107#3722C2314yes—
108#3722C2318yes—
109#3722C2314yes—
110Dic32C2318yes—
111C2×#541—91noSylow
112C22×C3×Q8—31no—
113C22×C4×D3—31no—
114C22×C4×D3—31no—
115C22×C4×D3—61no—
116C22×Dic6—31no—
117C22×Dic6—31no—
118C22×Dic6—61no—
119C22×Dic6C2×D311yescharacteristic
120C3×#125—38no—
121C3×C4×Q8—38no—
122C2×C3×C4⋊C4—21no—
123C2×C3×C4⋊C4—32no—
124C2×C3×C4⋊C4—32no—
125C2×C3×C4⋊C4—31no—
126C2×C3×C4⋊C4—32no—
127C2×C3×C4⋊C4C2×D311yescharacteristic
128C2×C3×C4⋊C4C2×D311yescharacteristic
129C2×C3×C42—31no—
130C2×C3×C42—31no—
131C2×C3×C42—32no—
132#946—38no—
133#944—38no—
134C2×(C2×D3)⋊C4—32no—
135C2×(C2×D3)⋊C4—32no—
136C2×(C2×D3)⋊C4—31no—
137C2×(C2×D3)⋊C4—31no—
138C2×(C2×D3)⋊C4—31no—
139C2×(C2×D3)⋊C4—31no—
140C2×(C2×D3)⋊C4—32no—
141C2×(C2×D3)⋊C4—32no—
142C2×(C2×D3)⋊C4—62no—
143C2×C4⋊Dic3—32no—
144C2×C4⋊Dic3—32no—
145C2×C4⋊Dic3—32no—
146C2×C4⋊Dic3—32no—
147C2×C4⋊Dic3—32no—
148C2×C4⋊Dic3—62no—
149C2×C4⋊Dic3C2×D311yescharacteristic
150C2×C4⋊Dic3C2×D312yes—
151C2×Dic3⋊C4—32no—
152C2×Dic3⋊C4—31no—
153C2×Dic3⋊C4—32no—
154C2×Dic3⋊C4—32no—
155C2×Dic3⋊C4—31no—
156C2×Dic3⋊C4—31no—
157C2×Dic3⋊C4—31no—
158C2×Dic3⋊C4—32no—
159C2×Dic3⋊C4—32no—
160C2×Dic3⋊C4C2×D312yes—
161C2×Dic3⋊C4C2×D312yes—
162C2×C4×Dic3—32no—
163C2×C4×Dic3—32no—
164C2×C4×Dic3C2×D311yescharacteristic
165C2×C4×Dic3C2×D311yescharacteristic
166C2×C4×Dic3C2×D312yes—
167#898—316no—
168#898—316no—
169#898—316no—
170#897—38no—
171#897—38no—
172#897—38no—
173#897—68no—
174#890—316no—
175#890—316no—
176#890C2×D318yescomplemented
177#889—316no—
178#887—38no—
179#887C2×D318yescomplemented
180#876—316no—
181#872—38no—
182#872—38no—
183#870—316no—
184#869—38no—
185C4×Dic6—38no—
186C23×C32C2411yescharacteristic
187C22×C3⋊D3—22no—
188C22×C3⋊D3—22no—
189C22×C3⋊D3—22no—
190C22×C3⋊D3C2412yes—
191C2×C32×C4—24no—
192C2×C32×C4#4114yes—
193C2×C32×C4C2414yes—
194C2×C32×C4C2412yes—
195C2×C3⋊Dic3—24no—
196C2×C3⋊Dic3—22no—
197C2×C3⋊Dic3C2414yes—
198C2×C3⋊Dic3C2412yes—
199C4×C3⋊D3—28no—
200#634—28no—
201C2×C3×Dic3—24no—
202C2×C3×Dic3—22no—
203C2×C3×Dic3—22no—
204C2×C3×Dic3—24no—
205C2×C3×Dic3—22no—
206C2×C3×Dic3—22no—
207C2×C3×Dic3C2412yes—
208C2×C3×Dic3C2414yes—
209C2×C3×Dic3C2414yes—
210C2×C3×Dic3C2412yes—
211C2×C3×Dic3C2412yes—
212C2×C3×Dic3C2412yes—
213C3×Dic6—28no—
214#541—916no—
215C2×C4⋊Q8—91no—
216C2×#126—92no—
217C2×#126—92no—
218C2×#125—31no—
219C2×#125—92no—
220C2×#125—92no—
221C2×C22⋊Q8—91no—
222C2×C22⋊Q8—91no—
223C2×C4×Q8—31no—
224C2×C4×Q8—91no—
225C2×#117—91no—
226C23×D3—31no—
227C23×D3—31no—
228C23×D3—61no—
229C2×C3×Q8—34no—
230C2×C3×Q8—64no—
231C22×C3×C4—21no—
232C22×C3×C4—22no—
233C22×C3×C4—31no—
234C22×C3×C4—32no—
235C22×C3×C4—31no—
236C22×C3×C4—32no—
237C22×C3×C4—31no—
238C22×C3×C4—31no—
239C22×C3×C4C22×D312yes—
240C22×C3×C4C22×D312yes—
241C22×C3×C4C22×D311yescharacteristic
242C22×C3×C4C22×D311yescharacteristic
243C22×Dic3—32no—
244C22×Dic3—32no—
245C22×Dic3—31no—
246C22×Dic3—31no—
247C22×Dic3—61no—
248C22×Dic3—62no—
249C22×Dic3C22×D311yescharacteristic
250C22×Dic3C22×D312yes—
251C22×Dic3C22×D311yescharacteristic
252C22×Dic3C22×D311yescharacteristic
253C22×Dic3C22×D311yescharacteristic
254C22×Dic3C22×D312yes—
255C2×C4×D3—34no—
256C2×C4×D3—34no—
257C2×C4×D3—64no—
258C2×C4×D3—64no—
259C2×C4×D3—64no—
260C2×C4×D3—124no—
261C2×Dic6—24no—
262C2×Dic6—34no—
263C2×Dic6—34no—
264C2×Dic6—64no—
265C2×Dic6—64no—
266C2×Dic6—64no—
267C2×Dic6—124no—
268C2×Dic6C22×D314yes—
269C3×C4⋊C4—24no—
270C3×C4⋊C4—34no—
271C3×C4⋊C4—38no—
272C3×C4⋊C4—38no—
273C3×C4⋊C4—38no—
274C3×C4⋊C4C22×D314yes—
275C3×C4⋊C4C22×D314yes—
276C3×C42—34no—
277C3×C42—34no—
278C3×C42—38no—
279(C2×D3)⋊C4—38no—
280(C2×D3)⋊C4—38no—
281(C2×D3)⋊C4—34no—
282(C2×D3)⋊C4—34no—
283(C2×D3)⋊C4—34no—
284(C2×D3)⋊C4—34no—
285(C2×D3)⋊C4—38no—
286(C2×D3)⋊C4—38no—
287(C2×D3)⋊C4—68no—
288C4⋊Dic3—38no—
289C4⋊Dic3—38no—
290C4⋊Dic3—38no—
291C4⋊Dic3—38no—
292C4⋊Dic3—38no—
293C4⋊Dic3—68no—
294C4⋊Dic3C22×D314yes—
295C4⋊Dic3C22×D318yes—
296Dic3⋊C4—38no—
297Dic3⋊C4—34no—
298Dic3⋊C4—38no—
299Dic3⋊C4—38no—
300Dic3⋊C4—34no—
301Dic3⋊C4—34no—
302Dic3⋊C4—34no—
303Dic3⋊C4—38no—
304Dic3⋊C4—38no—
305Dic3⋊C4C22×D318yes—
306Dic3⋊C4C22×D318yes—
307C4×Dic3—38no—
308C4×Dic3—38no—
309C4×Dic3C22×D314yes—
310C4×Dic3C22×D314yes—
311C4×Dic3C22×D318yes—
312C22×C32C2×#4112yes—
313C22×C322−1+412yes—
314C22×C322−1+412yes—
315C22×C32C2511yescharacteristic
316C2×C3⋊D3—22no—
317C2×C3⋊D3—22no—
318C2×C3⋊D3—22no—
319C2×C3⋊D3—44no—
320C32×C4—24no—
321C32×C4C2×#4114yes—
322C3⋊Dic3—24no—
323C3⋊Dic3—22no—
324C3×Dic3—24no—
325C3×Dic3—22no—
326C3×Dic3—24no—
327C3×Dic3—22no—
328C3×Dic3—22no—
329C3×Dic3—22no—
330C22×Q8—31no—
331C22×Q8—91no—
332C23×C4—91no—
333C4⋊Q8—98no—
334#126—916no—
335#126—916no—
336#125—38no—
337#125—916no—
338#125—916no—
339C22⋊Q8—98no—
340C22⋊Q8—98no—
341C4×Q8—38no—
342C4×Q8—98no—
343#117—98no—
344C2×C4⋊C4—32no—
345C2×C4⋊C4—31no—
346C2×C4⋊C4—32no—
347C2×C4⋊C4—32no—
348C2×C4⋊C4—91no—
349C2×C4⋊C4—91no—
350C2×C4⋊C4—92no—
351C2×C4⋊C4—92no—
352C2×C4⋊C4—92no—
353C2×C4⋊C4—92no—
354C2×C4⋊C4—92no—
355C2×C4⋊C4D3211yescharacteristic
356C2×C22⋊C4—91no—
357C2×C22⋊C4—91no—
358C2×C22⋊C4—92no—
359C2×C22⋊C4—92no—
360C2×C42—31no—
361C2×C42—31no—
362C2×C42—32no—
363C2×C42—92no—
364C23×C3—21no—
365C23×C3C23×D311yescharacteristic
366C23×C3C23×D311yescharacteristic
367C22×D3—32no—
368C22×D3—32no—
369C22×D3—62no—
370C22×D3—64no—
371C22×D3—62no—
372C22×D3—62no—
373C22×D3—62no—
374C22×D3—62no—
375C22×D3—62no—
376C22×D3—62no—
377C22×D3—122no—
378C22×D3—122no—
379C3×Q8—68no—
380C2×C3×C4—24no—
381C2×C3×C4—24no—
382C2×C3×C4—22no—
383C2×C3×C4—24no—
384C2×C3×C4—24no—
385C2×C3×C4—32no—
386C2×C3×C4—34no—
387C2×C3×C4—32no—
388C2×C3×C4—34no—
389C2×C3×C4—32no—
390C2×C3×C4—32no—
391C2×C3×C4—44no—
392C2×C3×C4—64no—
393C2×C3×C4—64no—
394C2×C3×C4—62no—
395C2×C3×C4—62no—
396C2×C3×C4—62no—
397C2×C3×C4—62no—
398C2×C3×C4#23514yes—
399C2×C3×C4#23914yes—
400C2×C3×C4C23×D314yes—
401C2×C3×C4C23×D314yes—
402C2×C3×C4C23×D312yes—
403C2×C3×C4C23×D312yes—
404C2×Dic3—24no—
405C2×Dic3—22no—
406C2×Dic3—22no—
407C2×Dic3—22no—
408C2×Dic3—24no—
409C2×Dic3—22no—
410C2×Dic3—34no—
411C2×Dic3—34no—
412C2×Dic3—32no—
413C2×Dic3—32no—
414C2×Dic3—62no—
415C2×Dic3—64no—
416C2×Dic3—64no—
417C2×Dic3—62no—
418C2×Dic3—64no—
419C2×Dic3—62no—
420C2×Dic3—124no—
421C2×Dic3—122no—
422C2×Dic3C23×D312yes—
423C2×Dic3C23×D314yes—
424C2×Dic3C23×D312yes—
425C2×Dic3C23×D312yes—
426C2×Dic3C23×D312yes—
427C2×Dic3C23×D314yes—
428C4×D3—68no—
429C4×D3—68no—
430C4×D3—128no—
431Dic6—28no—
432Dic6—68no—
433Dic6—68no—
434Dic6—128no—
435C2×C32#54114yescomplemented
436C2×C32C22×#4111yescharacteristic
437C2×C32C2×2−1+411yescharacteristic
438C2×C32C2×2−1+411yescharacteristic
439C3⋊D3—42no—
440C24—91no—
441C2×Q8—34no—
442C2×Q8—64no—
443C2×Q8—94no—
444C2×Q8—184no—
445C22×C4—31no—
446C22×C4—31no—
447C22×C4—31no—
448C22×C4—31no—
449C22×C4—32no—
450C22×C4—32no—
451C22×C4—92no—
452C22×C4—91no—
453C22×C4—94no—
454C22×C4—184no—
455C22×C4C2×D3212yes—
456C22×C4C2×D3211yescharacteristic
457C4⋊C4—38no—
458C4⋊C4—34no—
459C4⋊C4—38no—
460C4⋊C4—38no—
461C4⋊C4—94no—
462C4⋊C4—94no—
463C4⋊C4—98no—
464C4⋊C4—98no—
465C4⋊C4—98no—
466C4⋊C4—98no—
467C4⋊C4—98no—
468C4⋊C4C2×D3214yes—
469C22⋊C4—94no—
470C22⋊C4—94no—
471C22⋊C4—98no—
472C22⋊C4—98no—
473C42—34no—
474C42—34no—
475C42—38no—
476C42—98no—
477C22×C3—22no—
478C22×C3—22no—
479C22×C3—22no—
480C22×C3—21no—
481C22×C3C2×#23512yes—
482C22×C3C2×#23912yes—
483C22×C3#100712yes—
484C22×C3#101012yes—
485C22×C3#101012yes—
486C22×C3#101012yes—
487C22×C3C24×D311yescharacteristic
488C22×C3C24×D311yescharacteristic
489C2×D3—64no—
490C2×D3—62no—
491C2×D3—62no—
492C2×D3—62no—
493C2×D3—62no—
494C2×D3—62no—
495C2×D3—62no—
496C2×D3—122no—
497C2×D3—122no—
498C2×D3—128no—
499C2×D3—124no—
500C2×D3—124no—
501C3×C4—24no—
502C3×C4—24no—
503C3×C4—24no—
504C3×C4—44no—
505C3×C4—64no—
506C3×C4—64no—
507C3×C4—62no—
508C3×C4—62no—
509C3×C4—62no—
510C3×C4—62no—
511C3×C4C2×#23514yes—
512C3×C4C2×#23914yes—
513Dic3—24no—
514Dic3—22no—
515Dic3—22no—
516Dic3—22no—
517Dic3—24no—
518Dic3—22no—
519Dic3—64no—
520Dic3—62no—
521Dic3—64no—
522Dic3—62no—
523Dic3—124no—
524Dic3—122no—
525C32C2×#54111yescharacteristic, complemented, Sylow
526C23—92no—
527C23—182no—
528C23—182no—
529C23—182no—
530C23C22×D3211yescharacteristic
531Q8—68no—
532Q8—188no—
533C2×C4—24no—
534C2×C4—32no—
535C2×C4—32no—
536C2×C4—32no—
537C2×C4—32no—
538C2×C4—34no—
539C2×C4—34no—
540C2×C4—64no—
541C2×C4—62no—
542C2×C4—62no—
543C2×C4—62no—
544C2×C4—62no—
545C2×C4—64no—
546C2×C4—94no—
547C2×C4—92no—
548C2×C4—182no—
549C2×C4—184no—
550C2×C4—188no—
551C2×C4#379914yes—
552C2×C4C22×D3214yes—
553C2×C4C22×D3212yes—
554C2×C3—24no—
555C2×C3—21no—
556C2×C3—21no—
557C2×C3—21no—
558C2×C3#558314yescomplemented
559C2×C3#569814yescomplemented
560C2×C3C22×#23511yescharacteristic
561C2×C3C22×#23911yescharacteristic
562C2×C3C2×#100711yescharacteristic
563C2×C3C2×#101011yescharacteristic
564C2×C3C2×#101011yescharacteristic
565C2×C3C2×#101011yescharacteristic
566D3—124no—
567D3—122no—
568D3—122no—
569C22—182no—
570C22—182no—
571C22—182no—
572C22—364no—
573C22C2×#379912yes—
574C22#6430912yes—
575C22#6431512yes—
576C22C23×D3211yescharacteristic
577C4—24no—
578C4—64no—
579C4—62no—
580C4—62no—
581C4—62no—
582C4—62no—
583C4—64no—
584C4—182no—
585C4—184no—
586C4C2×#379914yes—
587C3—21no—
588C3C2×#558311yescharacteristic, complemented
589C3C2×#569811yescharacteristic, complemented
590C2—362no—
591C2#1059435514yesdirect product factor
592C2C22×#379911yescharacteristic
593C2C2×#6430911yescharacteristic
594C2C2×#6431511yescharacteristic
subgroupG/H
centerC23C22×D32
commutator, cosocleC22×C32C25
FrattiniC22C23×D32
FittingC2×C32×C4⋊C4C22
socleC23×C32C24
prime radicalC23×C3⋊D3C23
hypercenterC2×C4⋊C4D32
hypocenterC32C2×#541
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C23 ◁ C2×C4⋊C4

Complements

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

NH ≅ G/Ntype
2. C2×C3×#890C2semidirect
3. C2×C3×#887C2semidirect
6. C2×#63869C2semidirect
8. C2×#63866C2semidirect
10. C2×#63845C2semidirect
11. C2×#63844C2semidirect
12. #10594355C2direct (N × H)
29. C3×#890C22semidirect
30. C3×#887C22semidirect
43. #63869C22semidirect
45. #63866C22semidirect
47. #63845C22semidirect
48. #63844C22semidirect
64. C2×#890D3semidirect
67. C2×#887D3semidirect
176. #890C2×D3semidirect
179. #887C2×D3semidirect
435. C2×C32#541semidirect
525. C32C2×#541semidirect
558. C2×C3#5583semidirect
559. C2×C3#5698semidirect
588. C3C2×#5583semidirect
589. C3C2×#5698semidirect
591. C2#10594355direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#641062
C2×C3×#8902
C2×C3×#8872
C2×#638742
C2×#638712
C2×#638692
C2×#638682
C2×#638662
C2×#638482
C2×#638452
C2×#638442
#105943552
C2×#56983
C2×#55833