Finite Group Databasebeta

← C2×#10594346 #11901586

Subgroups — C2×#10594346 #11901586

Order 1152.

2157 conjugacy classes of subgroups.

The subgroup lattice has 588 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#64096C211yesmaximal, characteristic, complemented
2C2×C3×#897C211yesmaximal, characteristic
3C2×C3×#890C211yesmaximal, characteristic, complemented
4C2×#63872C212yesmaximal, complemented
5C2×#63866C211yesmaximal, characteristic, complemented
6C2×#63862C212yesmaximal
7C2×#63858C212yesmaximal
8C2×#63857C211yesmaximal, characteristic
9C2×#63855C211yesmaximal, characteristic
10C2×#63846C212yesmaximal, complemented
11C2×#63843C211yesmaximal, characteristic, complemented
12#10594346C2116yesmaximal, direct product factor
13C2×#5698—31nomaximal
14C2×#5625—31nomaximal
15C22×#634C2211yescharacteristic
16C22×C3×C4×D3C2211yescharacteristic
17C22×C3×Dic6C2211yescharacteristic
18C2×C32×C4⋊C4C2211yescharacteristic
19C2×#3750C2212yes—
20C2×C4×C3⋊Dic3C2211yescharacteristic
21C2×C4×C3⋊Dic3C2212yes—
22#64096C2218yescomplemented
23C2×C3×(C2×D3)⋊C4C2212yes—
24C2×C3×C4⋊Dic3C2211yescharacteristic
25C2×C3×C4⋊Dic3C2212yes—
26C2×C3×C4⋊Dic3C2212yes—
27C2×C3×Dic3⋊C4C2212yes—
28C2×C3×C4×Dic3C2211yescharacteristic
29C3×#897C2218yes—
30C3×#890C2218yescomplemented
31C2×Dic3⋊Dic3C2212yes—
32C2×Dic3⋊Dic3C2211yescharacteristic
33C2×Dic3⋊Dic3C2212yes—
34C2×Dic3⋊Dic3C2212yes—
35C2×Dic3⋊Dic3C2211yescharacteristic
36C2×Dic3⋊Dic3C2212yes—
37C2×(C2×D3)⋊Dic3C2211yescharacteristic
38C2×(C2×D3)⋊Dic3C2211yescharacteristic
39C2×(C2×D3)⋊Dic3C2212yes—
40C2×Dic32C2212yes—
41#63872C22116yescomplemented
42#63866C2218yescomplemented
43#63862C22116yes—
44#63858C22116yes—
45#63857C2218yes—
46#63855C2218yes—
47#63846C22116yescomplemented
48#63843C2218yescomplemented
49C2×C3×#125—31no—
50C2×C3×C22⋊Q8—31no—
51C2×Q8×Dic3—31no—
52C2×#944—31no—
53C2×#926—31no—
54C2×#924—31no—
55#5698—316no—
56#5625—316no—
57C2×#898—32no—
58C2×#898—32no—
59C2×#897—31no—
60C2×#897D311yescharacteristic
61C2×#890—32no—
62C2×#890—32no—
63C2×#890—32no—
64C2×#890D311yescharacteristic, complemented
65C2×#889—32no—
66C2×#887—31no—
67C2×#887—31no—
68C2×#887—31no—
69C2×#887—61no—
70C2×#879—32no—
71C2×#879—32no—
72C2×#872—31no—
73C2×#869—31no—
74C23×C3×D3C2311yescharacteristic
75C22×C32×C4C2312yes—
76C22×C32×C4C2311yescharacteristic
77C22×C3⋊Dic3C2312yes—
78C22×C3⋊Dic3C2311yescharacteristic
79C22×C3⋊Dic3C2311yescharacteristic
80C2×#634—24no—
81C2×#634C2314yes—
82C22×C3×Dic3C2311yescharacteristic
83C22×C3×Dic3C2311yescharacteristic
84C22×C3×Dic3C2312yes—
85C22×C3×Dic3C2311yescharacteristic
86C22×C3×Dic3C2312yes—
87C2×C3×C4×D3—24no—
88C2×C3×C4×D3C2314yes—
89C2×C3×Dic6—24no—
90C2×C3×Dic6C2314yes—
91C32×C4⋊C4C2314yes—
92#3750C2318yes—
93C4×C3⋊Dic3C2314yes—
94C4×C3⋊Dic3C2318yes—
95C3×(C2×D3)⋊C4C2318yes—
96C3×C4⋊Dic3C2314yes—
97C3×C4⋊Dic3C2318yes—
98C3×C4⋊Dic3C2318yes—
99C3×Dic3⋊C4C2318yes—
100C3×C4×Dic3C2314yes—
101Dic3⋊Dic3C2318yes—
102Dic3⋊Dic3C2314yes—
103Dic3⋊Dic3C2318yes—
104Dic3⋊Dic3C2318yes—
105Dic3⋊Dic3C2314yes—
106Dic3⋊Dic3C2318yes—
107(C2×D3)⋊Dic3C2314yes—
108(C2×D3)⋊Dic3C2314yes—
109(C2×D3)⋊Dic3C2318yes—
110Dic32C2318yes—
111C2×#541—91noSylow
112C22×C3×Q8—31no—
113C23×C3×C4—31no—
114C22×C4×D3C2×D311yescharacteristic
115C22×Dic6—31no—
116C22×Dic6—31no—
117C22×Dic6—61no—
118C22×Dic6C2×D311yescharacteristic
119C3×#125—38no—
120C3×C22⋊Q8—38no—
121C2×C3×C4⋊C4—21no—
122C2×C3×C4⋊C4—32no—
123C2×C3×C4⋊C4—31no—
124C2×C3×C4⋊C4—32no—
125C2×C3×C4⋊C4—32no—
126C2×C3×C4⋊C4C2×D311yescharacteristic
127C2×C3×C4⋊C4C2×D311yescharacteristic
128C2×C3×C22⋊C4—32no—
129C2×C3×C42—31no—
130C2×#217—32no—
131C2×#217—31no—
132C2×#217—31no—
133Q8×Dic3—38no—
134#944—38no—
135C2×(C2×D3)⋊C4—31no—
136C2×(C2×D3)⋊C4—31no—
137C2×(C2×D3)⋊C4—32no—
138C2×(C2×D3)⋊C4C2×D312yes—
139#926—38no—
140C2×C4⋊Dic3—32no—
141C2×C4⋊Dic3—32no—
142C2×C4⋊Dic3—32no—
143C2×C4⋊Dic3—31no—
144C2×C4⋊Dic3—32no—
145C2×C4⋊Dic3—31no—
146C2×C4⋊Dic3C2×D312yes—
147C2×C4⋊Dic3C2×D312yes—
148C2×C4⋊Dic3C2×D311yescharacteristic
149#924—38no—
150C2×Dic3⋊C4—32no—
151C2×Dic3⋊C4—32no—
152C2×Dic3⋊C4—31no—
153C2×Dic3⋊C4—31no—
154C2×Dic3⋊C4—32no—
155C2×Dic3⋊C4—32no—
156C2×Dic3⋊C4—32no—
157C2×Dic3⋊C4—32no—
158C2×Dic3⋊C4—62no—
159C2×Dic3⋊C4C2×D312yes—
160C2×C4×Dic3—31no—
161C2×C4×Dic3—32no—
162C2×C4×Dic3—32no—
163C2×C4×Dic3—31no—
164C2×C4×Dic3—32no—
165C2×C4×Dic3—32no—
166C2×C4×Dic3—61no—
167C2×C4×Dic3—62no—
168C2×C4×Dic3C2×D311yescharacteristic
169#898—316no—
170#898—316no—
171#897—38no—
172#897C2×D318yes—
173#890—316no—
174#890—316no—
175#890—316no—
176#890C2×D318yescomplemented
177#889—316no—
178#887—38no—
179#887—38no—
180#887—38no—
181#887—68no—
182#879—316no—
183#879—316no—
184#872—38no—
185#869—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⋊Dic3—22no—
198C2×C3⋊Dic3C2412yes—
199C2×C3⋊Dic3C2412yes—
200C2×C3⋊Dic3C2414yes—
201#634—28no—
202C2×C3×Dic3—24no—
203C2×C3×Dic3—22no—
204C2×C3×Dic3—22no—
205C2×C3×Dic3—24no—
206C2×C3×Dic3—22no—
207C2×C3×Dic3C2414yes—
208C2×C3×Dic3C2414yes—
209C2×C3×Dic3C2412yes—
210C2×C3×Dic3C2412yes—
211C2×C3×Dic3C2412yes—
212C3×C4×D3—28no—
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—31no—
222C2×C22⋊Q8—91no—
223C2×C4×Q8—91no—
224C2×C4×Q8—91no—
225C2×#117—91no—
226C24×C3—31no—
227C23×D3C22×D311yescharacteristic
228C2×C3×Q8—34no—
229C2×C3×Q8—64no—
230C22×C3×C4—21no—
231C22×C3×C4—22no—
232C22×C3×C4—32no—
233C22×C3×C4—32no—
234C22×C3×C4—31no—
235C22×C3×C4—31no—
236C22×C3×C4—31no—
237C22×C3×C4—34no—
238C22×C3×C4—64no—
239C22×C3×C4C22×D312yes—
240C22×C3×C4C22×D312yes—
241C22×C3×C4C22×D311yescharacteristic
242C22×C3×C4C22×D311yescharacteristic
243C22×Dic3—31no—
244C22×Dic3—31no—
245C22×Dic3—31no—
246C22×Dic3—31no—
247C22×Dic3—32no—
248C22×Dic3—32no—
249C22×Dic3—61no—
250C22×Dic3—62no—
251C22×Dic3—61no—
252C22×Dic3C22×D312yes—
253C22×Dic3C22×D312yes—
254C22×Dic3C22×D311yescharacteristic
255C22×Dic3C22×D311yescharacteristic
256C22×Dic3C22×D311yescharacteristic
257C2×C4×D3—24no—
258C2×C4×D3C22×D314yes—
259C2×Dic6—24no—
260C2×Dic6—34no—
261C2×Dic6—34no—
262C2×Dic6—64no—
263C2×Dic6—68no—
264C2×Dic6—64no—
265C2×Dic6—64no—
266C2×Dic6C22×D314yes—
267C3×C4⋊C4—24no—
268C3×C4⋊C4—34no—
269C3×C4⋊C4—38no—
270C3×C4⋊C4—38no—
271C3×C4⋊C4—38no—
272C3×C4⋊C4C22×D314yes—
273C3×C4⋊C4C22×D314yes—
274C3×C22⋊C4—38no—
275C3×C42—34no—
276#217—38no—
277#217—34no—
278#217—34no—
279(C2×D3)⋊C4—34no—
280(C2×D3)⋊C4—34no—
281(C2×D3)⋊C4—38no—
282(C2×D3)⋊C4C22×D318yes—
283C4⋊Dic3—38no—
284C4⋊Dic3—38no—
285C4⋊Dic3—38no—
286C4⋊Dic3—34no—
287C4⋊Dic3—38no—
288C4⋊Dic3—34no—
289C4⋊Dic3C22×D318yes—
290C4⋊Dic3C22×D318yes—
291C4⋊Dic3C22×D314yes—
292Dic3⋊C4—38no—
293Dic3⋊C4—38no—
294Dic3⋊C4—34no—
295Dic3⋊C4—34no—
296Dic3⋊C4—38no—
297Dic3⋊C4—38no—
298Dic3⋊C4—38no—
299Dic3⋊C4—38no—
300Dic3⋊C4—68no—
301Dic3⋊C4C22×D318yes—
302C4×Dic3—34no—
303C4×Dic3—38no—
304C4×Dic3—38no—
305C4×Dic3—34no—
306C4×Dic3—38no—
307C4×Dic3—38no—
308C4×Dic3—64no—
309C4×Dic3—68no—
310C4×Dic3C22×D314yes—
311C22×C32C2×#4112yes—
312C22×C322−1+412yes—
313C22×C322−1+412yes—
314C22×C32C2511yescharacteristic
315C2×C3×D3—22no—
316C2×C3×D3—22no—
317C2×C3×D3—22no—
318C2×C3×D3—44no—
319C32×C4—24no—
320C32×C4C2×#4114yes—
321C3⋊Dic3—24no—
322C3⋊Dic3—22no—
323C3⋊Dic3—22no—
324C3×Dic3—24no—
325C3×Dic3—22no—
326C3×Dic3—24no—
327C3×Dic3—22no—
328C3×Dic3—22no—
329C22×Q8—31no—
330C22×Q8—91no—
331C23×C4—31no—
332C4⋊Q8—98no—
333#126—916no—
334#126—916no—
335#125—38no—
336#125—916no—
337#125—916no—
338C22⋊Q8—38no—
339C22⋊Q8—98no—
340C4×Q8—98no—
341C4×Q8—98no—
342#117—98no—
343C2×C4⋊C4—31no—
344C2×C4⋊C4—32no—
345C2×C4⋊C4—32no—
346C2×C4⋊C4—32no—
347C2×C4⋊C4—91no—
348C2×C4⋊C4—91no—
349C2×C4⋊C4—92no—
350C2×C4⋊C4—92no—
351C2×C4⋊C4—92no—
352C2×C4⋊C4—92no—
353C2×C4⋊C4—92no—
354C2×C4⋊C4D3211yescharacteristic
355C2×C22⋊C4—32no—
356C2×C22⋊C4—91no—
357C2×C22⋊C4—91no—
358C2×C22⋊C4—92no—
359C2×C42—31no—
360C2×C42—92no—
361C2×C42—91no—
362C2×C42—92no—
363C23×C3—21no—
364C23×C3—32no—
365C23×C3—62no—
366C23×C3—62no—
367C23×C3—62no—
368C23×C3C23×D311yescharacteristic
369C23×C3C23×D311yescharacteristic
370C22×D3—22no—
371C22×D3—22no—
372C22×D3—22no—
373C22×D3C23×D312yes—
374C3×Q8—68no—
375C2×C3×C4—24no—
376C2×C3×C4—24no—
377C2×C3×C4—22no—
378C2×C3×C4—24no—
379C2×C3×C4—24no—
380C2×C3×C4—34no—
381C2×C3×C4—34no—
382C2×C3×C4—32no—
383C2×C3×C4—32no—
384C2×C3×C4—32no—
385C2×C3×C4—44no—
386C2×C3×C4—62no—
387C2×C3×C4—64no—
388C2×C3×C4—64no—
389C2×C3×C4—62no—
390C2×C3×C4—62no—
391C2×C3×C4—68no—
392C2×C3×C4#23714yes—
393C2×C3×C4#23914yes—
394C2×C3×C4C23×D314yes—
395C2×C3×C4C23×D314yes—
396C2×C3×C4C23×D312yes—
397C2×C3×C4C23×D312yes—
398C2×Dic3—24no—
399C2×Dic3—22no—
400C2×Dic3—22no—
401C2×Dic3—24no—
402C2×Dic3—22no—
403C2×Dic3—32no—
404C2×Dic3—32no—
405C2×Dic3—32no—
406C2×Dic3—32no—
407C2×Dic3—34no—
408C2×Dic3—34no—
409C2×Dic3—62no—
410C2×Dic3—64no—
411C2×Dic3—62no—
412C2×Dic3—68no—
413C2×Dic3—64no—
414C2×Dic3—64no—
415C2×Dic3—64no—
416C2×Dic3—62no—
417C2×Dic3—62no—
418C2×Dic3—62no—
419C2×Dic3—62no—
420C2×Dic3—122no—
421C2×Dic3C23×D314yes—
422C2×Dic3C23×D314yes—
423C2×Dic3C23×D312yes—
424C2×Dic3C23×D312yes—
425C2×Dic3C23×D312yes—
426C4×D3—28no—
427Dic6—28no—
428Dic6—616no—
429Dic6—68no—
430Dic6—68no—
431C2×C32#54114yescomplemented
432C2×C32C22×#4111yescharacteristic
433C2×C32C2×2−1+411yescharacteristic
434C2×C32C2×2−1+411yescharacteristic
435C3×D3—42no—
436C24—31no—
437C2×Q8—34no—
438C2×Q8—64no—
439C2×Q8—94no—
440C2×Q8—184no—
441C22×C4—31no—
442C22×C4—31no—
443C22×C4—32no—
444C22×C4—32no—
445C22×C4—31no—
446C22×C4—34no—
447C22×C4—64no—
448C22×C4—91no—
449C22×C4—91no—
450C22×C4—92no—
451C22×C4C2×D3212yes—
452C22×C4C2×D3211yescharacteristic
453C4⋊C4—34no—
454C4⋊C4—38no—
455C4⋊C4—38no—
456C4⋊C4—38no—
457C4⋊C4—94no—
458C4⋊C4—94no—
459C4⋊C4—98no—
460C4⋊C4—98no—
461C4⋊C4—98no—
462C4⋊C4—98no—
463C4⋊C4—98no—
464C4⋊C4C2×D3214yes—
465C22⋊C4—38no—
466C22⋊C4—94no—
467C22⋊C4—94no—
468C22⋊C4—98no—
469C42—34no—
470C42—98no—
471C42—94no—
472C42—98no—
473C22×C3—22no—
474C22×C3—22no—
475C22×C3—22no—
476C22×C3—21no—
477C22×C3—62no—
478C22×C3—62no—
479C22×C3—62no—
480C22×C3—124no—
481C22×C3C2×#23712yes—
482C22×C3C2×#23912yes—
483C22×C3#100712yes—
484C22×C3#101012yes—
485C22×C3#101012yes—
486C22×C3#101012yes—
487C22×C3C24×D311yescharacteristic
488C22×C3C24×D311yescharacteristic
489C2×D3—22no—
490C2×D3—22no—
491C2×D3—22no—
492C2×D3—44no—
493C3×C4—24no—
494C3×C4—24no—
495C3×C4—24no—
496C3×C4—44no—
497C3×C4—62no—
498C3×C4—64no—
499C3×C4—64no—
500C3×C4—62no—
501C3×C4—62no—
502C3×C4C2×#23714yes—
503C3×C4C2×#23914yes—
504Dic3—24no—
505Dic3—22no—
506Dic3—22no—
507Dic3—24no—
508Dic3—22no—
509Dic3—68no—
510Dic3—64no—
511Dic3—64no—
512Dic3—64no—
513Dic3—62no—
514Dic3—62no—
515Dic3—62no—
516Dic3—62no—
517Dic3—122no—
518C32C2×#54111yescharacteristic, complemented, Sylow
519C23—32no—
520C23—62no—
521C23—62no—
522C23—62no—
523C23C22×D3211yescharacteristic
524Q8—68no—
525Q8—188no—
526C2×C4—24no—
527C2×C4—32no—
528C2×C4—32no—
529C2×C4—34no—
530C2×C4—34no—
531C2×C4—32no—
532C2×C4—62no—
533C2×C4—64no—
534C2×C4—62no—
535C2×C4—62no—
536C2×C4—64no—
537C2×C4—68no—
538C2×C4—92no—
539C2×C4—92no—
540C2×C4—94no—
541C2×C4—184no—
542C2×C4—182no—
543C2×C4—182no—
544C2×C4#379614yes—
545C2×C4C22×D3214yes—
546C2×C4C22×D3212yes—
547C2×C3—24no—
548C2×C3—21no—
549C2×C3—21no—
550C2×C3—21no—
551C2×C3—122no—
552C2×C3#562514yescomplemented
553C2×C3#569814yescomplemented
554C2×C3C22×#23711yescharacteristic
555C2×C3C22×#23911yescharacteristic
556C2×C3C2×#100711yescharacteristic
557C2×C3C2×#101011yescharacteristic
558C2×C3C2×#101011yescharacteristic
559C2×C3C2×#101011yescharacteristic
560D3—42no—
561C22—62no—
562C22—62no—
563C22—62no—
564C22—124no—
565C22C2×#379612yes—
566C22#6430912yes—
567C22#6431512yes—
568C22C23×D3211yescharacteristic
569C4—24no—
570C4—62no—
571C4—64no—
572C4—62no—
573C4—62no—
574C4—64no—
575C4—184no—
576C4—182no—
577C4—182no—
578C4C2×#379614yes—
579C3—21no—
580C3C2×#562511yescharacteristic, complemented
581C3C2×#569811yescharacteristic, complemented
582C2—122no—
583C2#1059434614yesdirect product factor
584C2C22×#379611yescharacteristic
585C2C2×#6430911yescharacteristic
586C2C2×#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
1. C2×#64096C2semidirect
3. C2×C3×#890C2semidirect
4. C2×#63872C2semidirect
5. C2×#63866C2semidirect
10. C2×#63846C2semidirect
11. C2×#63843C2semidirect
12. #10594346C2direct (N × H)
22. #64096C22semidirect
30. C3×#890C22semidirect
41. #63872C22semidirect
42. #63866C22semidirect
47. #63846C22semidirect
48. #63843C22semidirect
64. C2×#890D3semidirect
176. #890C2×D3semidirect
431. C2×C32#541semidirect
518. C32C2×#541semidirect
552. C2×C3#5625semidirect
553. C2×C3#5698semidirect
580. C3C2×#5625semidirect
581. C3C2×#5698semidirect
583. C2#10594346direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#640962
C2×C3×#8972
C2×C3×#8902
C2×#638722
C2×#638662
C2×#638622
C2×#638582
C2×#638572
C2×#638552
C2×#638462
C2×#638432
#105943462
C2×#56983
C2×#56253