Finite Group Databasebeta

← C2×#10596173 #11903351

Subgroups — C2×#10596173 #11903351

Order 1152.

3336 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×C32×#126C211yesmaximal, characteristic, complemented
2#10596173C2116yesmaximal, direct product factor
3C2×#64107C211yesmaximal, characteristic, complemented
4C2×#64107C211yesmaximal, characteristic, complemented
5C2×#64105C211yesmaximal, characteristic, complemented
6C2×#64097C211yesmaximal, characteristic, complemented
7C2×#64096C211yesmaximal, characteristic, complemented
8C2×#64096C211yesmaximal, characteristic, complemented
9C2×#64094C211yesmaximal, characteristic
10C2×#64094C211yesmaximal, characteristic
11C2×#64090C211yesmaximal, characteristic
12C2×#64088C211yesmaximal, characteristic, complemented
13C2×#64087C211yesmaximal, characteristic, complemented
14C2×#64086C211yesmaximal, characteristic, complemented
15C2×#64081C211yesmaximal, characteristic, complemented
16C2×C4×#634C211yesmaximal, characteristic, complemented
17C2×#5702—34nomaximal
18C22×#638C2211yescharacteristic
19C23×C3⋊Dic3C2211yescharacteristic
20C22×C4×C3⋊D3C2211yescharacteristic
21C22×#634C2211yescharacteristic
22C22×#634C2211yescharacteristic
23C22×#634C2211yescharacteristic
24C32×#126C2218yescomplemented
25C2×C32×C4⋊C4C2211yescharacteristic
26C2×C32×C4⋊C4C2211yescharacteristic
27C2×C32×C4⋊C4C2211yescharacteristic
28C2×C32×C22⋊C4C2211yescharacteristic
29C2×C32×C22⋊C4C2211yescharacteristic
30C2×C32×C22⋊C4C2211yescharacteristic
31C2×C32×C42C2211yescharacteristic
32C2×#3757C2211yescharacteristic
33C2×#3757C2211yescharacteristic
34C2×#3752C2211yescharacteristic
35C2×#3752C2211yescharacteristic
36C2×#3752C2211yescharacteristic
37C2×#3752C2211yescharacteristic
38C2×#3752C2211yescharacteristic
39C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
40C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
41C2×#3750C2211yescharacteristic
42C2×#3750C2211yescharacteristic
43C2×#3750C2211yescharacteristic
44C2×#3750C2211yescharacteristic
45C2×#3750C2211yescharacteristic
46C2×#3750C2211yescharacteristic
47C2×#3750C2211yescharacteristic
48C2×C4×C3⋊Dic3C2211yescharacteristic
49C2×C4×C3⋊Dic3C2211yescharacteristic
50C2×C4×C3⋊Dic3C2211yescharacteristic
51C2×C4×C3⋊Dic3C2211yescharacteristic
52C2×C4×C3⋊Dic3C2211yescharacteristic
53C2×C4×C3⋊Dic3C2211yescharacteristic
54#64107C2218yescomplemented
55#64107C2218yescomplemented
56#64105C2218yescomplemented
57#64097C2218yescomplemented
58#64096C2218yescomplemented
59#64096C2218yescomplemented
60#64094C2218yes—
61#64094C2218yes—
62#64090C2218yes—
63#64088C2218yescomplemented
64#64087C2218yescomplemented
65#64086C2218yescomplemented
66#64081C2218yescomplemented
67C4×#634C2218yescomplemented
68C2×C3×#126D314yescomplemented
69#5702—364no—
70C2×#898—34no—
71C2×#898—34no—
72C2×#896—34no—
73C2×#888—34no—
74C2×#887—34no—
75C2×#887—34no—
76C2×#885—34no—
77C2×#885—34no—
78C2×#67⋊C4—34no—
79C2×#879—34no—
80C2×#878—34no—
81C2×#877—34no—
82C2×#872—34no—
83C2×C4×Dic6—34no—
84C24×C32C2311yescharacteristic
85C23×C3⋊D3C2311yescharacteristic
86C22×C32×C4C2311yescharacteristic
87C22×C32×C4C2311yescharacteristic
88C22×C32×C4C2311yescharacteristic
89C22×C32×C4C2311yescharacteristic
90C22×C32×C4C2311yescharacteristic
91C22×C32×C4C2311yescharacteristic
92C2×#638—24no—
93C2×#638C2314yes—
94C22×C3⋊Dic3—24no—
95C22×C3⋊Dic3C2314yes—
96C22×C3⋊Dic3C2311yescharacteristic
97C22×C3⋊Dic3C2311yescharacteristic
98C22×C3⋊Dic3C2311yescharacteristic
99C22×C3⋊Dic3C2311yescharacteristic
100C22×C3⋊Dic3C2311yescharacteristic
101C22×C3⋊Dic3C2311yescharacteristic
102C22×C3⋊Dic3C2311yescharacteristic
103C2×C4×C3⋊D3—24no—
104C2×C4×C3⋊D3C2314yes—
105C2×#634—24no—
106C2×#634—24no—
107C2×#634—24no—
108C2×#634C2314yes—
109C2×#634C2314yes—
110C2×#634C2314yes—
111C32×C4⋊C4C2314yes—
112C32×C4⋊C4C2314yes—
113C32×C4⋊C4C2314yes—
114C32×C22⋊C4C2314yes—
115C32×C22⋊C4C2314yes—
116C32×C22⋊C4C2314yes—
117C32×C42C2314yes—
118#3757C2314yes—
119#3757C2314yes—
120#3752C2314yes—
121#3752C2314yes—
122#3752C2314yes—
123#3752C2314yes—
124#3752C2314yes—
125C4⋊(C3⋊Dic3)C2314yes—
126C4⋊(C3⋊Dic3)C2314yes—
127#3750C2314yes—
128#3750C2314yes—
129#3750C2314yes—
130#3750C2314yes—
131#3750C2314yes—
132#3750C2314yes—
133#3750C2314yes—
134C4×C3⋊Dic3C2314yes—
135C4×C3⋊Dic3C2314yes—
136C4×C3⋊Dic3C2314yes—
137C4×C3⋊Dic3C2314yes—
138C4×C3⋊Dic3C2314yes—
139C4×C3⋊Dic3C2314yes—
140C2×#556—91noSylow
141C22×#67—34no—
142C23×Dic3—34no—
143C22×C4×D3—34no—
144C22×Dic6—34no—
145C22×Dic6—34no—
146C22×Dic6—34no—
147C3×#126C2×D3132yescomplemented
148C2×C3×C4⋊C4C2×D314yes—
149C2×C3×C4⋊C4C2×D314yes—
150C2×C3×C4⋊C4C2×D314yes—
151C2×C3×C22⋊C4C2×D314yes—
152C2×C3×C22⋊C4C2×D314yes—
153C2×C3×C22⋊C4C2×D314yes—
154C2×C3×C42C2×D314yes—
155C2×#217—34no—
156C2×#217—34no—
157C2×(C2×D3)⋊C4—34no—
158C2×(C2×D3)⋊C4—34no—
159C2×(C2×D3)⋊C4—34no—
160C2×(C2×D3)⋊C4—34no—
161C2×(C2×D3)⋊C4—34no—
162C2×C4⋊Dic3—34no—
163C2×C4⋊Dic3—34no—
164C2×Dic3⋊C4—34no—
165C2×Dic3⋊C4—34no—
166C2×Dic3⋊C4—34no—
167C2×Dic3⋊C4—34no—
168C2×Dic3⋊C4—34no—
169C2×Dic3⋊C4—34no—
170C2×Dic3⋊C4—34no—
171C2×C4×Dic3—34no—
172C2×C4×Dic3—34no—
173C2×C4×Dic3—34no—
174C2×C4×Dic3—34no—
175C2×C4×Dic3—34no—
176C2×C4×Dic3—34no—
177#898—332no—
178#898—332no—
179#896—332no—
180#888—332no—
181#887—332no—
182#887—332no—
183#885—332no—
184#885—332no—
185#67⋊C4—332no—
186#879—332no—
187#878—332no—
188#877—332no—
189#872—332no—
190C4×Dic6—332no—
191C23×C32—22no—
192C23×C32—22no—
193C23×C32—22no—
194C23×C32C2412yes—
195C23×C32C2411yescharacteristic
196C22×C3⋊D3—22no—
197C22×C3⋊D3—22no—
198C22×C3⋊D3—22no—
199C22×C3⋊D3C2412yes—
200C2×C32×C4—22no—
201C2×C32×C4—22no—
202C2×C32×C4—22no—
203C2×C32×C4—22no—
204C2×C32×C4—22no—
205C2×C32×C4—22no—
206C2×C32×C4C2412yes—
207C2×C32×C4C2412yes—
208C2×C32×C4C2412yes—
209C2×C32×C4C2412yes—
210C2×C32×C4C2412yes—
211C2×C32×C4C2412yes—
212#638—28no—
213C2×C3⋊Dic3—22no—
214C2×C3⋊Dic3—22no—
215C2×C3⋊Dic3—22no—
216C2×C3⋊Dic3—22no—
217C2×C3⋊Dic3—22no—
218C2×C3⋊Dic3—28no—
219C2×C3⋊Dic3#4114yes—
220C2×C3⋊Dic3#4114yes—
221C2×C3⋊Dic3C2412yes—
222C2×C3⋊Dic3C2412yes—
223C2×C3⋊Dic3C2412yes—
224C2×C3⋊Dic3C2412yes—
225C2×C3⋊Dic3C2412yes—
226C2×C3⋊Dic3C2412yes—
227C2×C3⋊Dic3C2412yes—
228C4×C3⋊D3—28no—
229#634—28no—
230#634—28no—
231#634—28no—
232#556—916no—
233C2×C4⋊Q8—91no—
234C2×#126—91no—
235C2×#126—91no—
236C2×#126—91no—
237C2×#126C3⋊D311yescharacteristic, complemented
238C2×#124—91no—
239C2×#124—91no—
240C2×C22⋊Q8—91no—
241C2×C22⋊Q8—91no—
242C2×C4×Q8—91no—
243C2×C4×Q8—91no—
244C2×C4×Q8—91no—
245C2×C4×D4—91no—
246C2×#117—91no—
247C2×#117—91no—
248C24×C3C22×D314yes—
249C23×D3—34no—
250C22×C3×C4C22×D314yes—
251C22×C3×C4C22×D314yes—
252C22×C3×C4C22×D314yes—
253C22×C3×C4C22×D314yes—
254C22×C3×C4C22×D314yes—
255C22×C3×C4C22×D314yes—
256C2×#67—316no—
257C2×#67—616no—
258C22×Dic3—34no—
259C22×Dic3—34no—
260C22×Dic3—316no—
261C22×Dic3—34no—
262C22×Dic3—34no—
263C22×Dic3—34no—
264C22×Dic3—34no—
265C22×Dic3—34no—
266C22×Dic3—616no—
267C2×C4×D3—316no—
268C2×C4×D3—616no—
269C2×Dic6—316no—
270C2×Dic6—316no—
271C2×Dic6—316no—
272C2×Dic6—616no—
273C2×Dic6—616no—
274C2×Dic6—616no—
275C3×C4⋊C4C22×D3116yes—
276C3×C4⋊C4C22×D3116yes—
277C3×C4⋊C4C22×D3116yes—
278C3×C22⋊C4C22×D3116yes—
279C3×C22⋊C4C22×D3116yes—
280C3×C22⋊C4C22×D3116yes—
281C3×C42C22×D3116yes—
282#217—316no—
283#217—316no—
284(C2×D3)⋊C4—316no—
285(C2×D3)⋊C4—316no—
286(C2×D3)⋊C4—316no—
287(C2×D3)⋊C4—316no—
288(C2×D3)⋊C4—316no—
289C4⋊Dic3—316no—
290C4⋊Dic3—316no—
291Dic3⋊C4—316no—
292Dic3⋊C4—316no—
293Dic3⋊C4—316no—
294Dic3⋊C4—316no—
295Dic3⋊C4—316no—
296Dic3⋊C4—316no—
297Dic3⋊C4—316no—
298C4×Dic3—316no—
299C4×Dic3—316no—
300C4×Dic3—316no—
301C4×Dic3—316no—
302C4×Dic3—316no—
303C4×Dic3—316no—
304C22×C32—22no—
305C22×C32—22no—
306C22×C32—22no—
307C22×C32—44no—
308C22×C32C2×#4112yes—
309C22×C32C2×#4112yes—
310C22×C322−1+412yes—
311C22×C32C2511yescharacteristic
312C2×C3⋊D3—22no—
313C2×C3⋊D3—22no—
314C2×C3⋊D3—22no—
315C2×C3⋊D3—44no—
316C32×C4—22no—
317C32×C4—22no—
318C32×C4—22no—
319C32×C4—22no—
320C32×C4—22no—
321C32×C4—22no—
322C3⋊Dic3—22no—
323C3⋊Dic3—22no—
324C3⋊Dic3—22no—
325C3⋊Dic3—22no—
326C3⋊Dic3—22no—
327C3⋊Dic3C2×#4114yes—
328C3⋊Dic3C2×#4114yes—
329C22×Q8—91no—
330C22×Q8—91no—
331C22×Q8—91no—
332C22×D4—91no—
333C23×C4—91no—
334C23×C4—91no—
335C4⋊Q8—98no—
336#126—98no—
337#126—98no—
338#126—98no—
339#126C2×C3⋊D318yescomplemented
340#124—98no—
341#124—98no—
342C22⋊Q8—98no—
343C22⋊Q8—98no—
344C4×Q8—98no—
345C4×Q8—98no—
346C4×Q8—98no—
347C4×D4—98no—
348#117—98no—
349#117—98no—
350C2×C4⋊C4—91no—
351C2×C4⋊C4—91no—
352C2×C4⋊C4—91no—
353C2×C4⋊C4—91no—
354C2×C4⋊C4—91no—
355C2×C4⋊C4—91no—
356C2×C4⋊C4—91no—
357C2×C4⋊C4—91no—
358C2×C4⋊C4—91no—
359C2×C4⋊C4C2×C3⋊D311yescharacteristic
360C2×C4⋊C4C2×C3⋊D311yescharacteristic
361C2×C4⋊C4C2×C3⋊D311yescharacteristic
362C2×C22⋊C4—91no—
363C2×C22⋊C4—91no—
364C2×C22⋊C4—91no—
365C2×C22⋊C4—91no—
366C2×C22⋊C4—91no—
367C2×C22⋊C4—91no—
368C2×C22⋊C4—91no—
369C2×C22⋊C4C2×C3⋊D311yescharacteristic
370C2×C22⋊C4C2×C3⋊D311yescharacteristic
371C2×C22⋊C4C2×C3⋊D311yescharacteristic
372C2×C42—91no—
373C2×C42—91no—
374C2×C42—91no—
375C2×C42—91no—
376C2×C42—91no—
377C2×C42—91no—
378C2×C42C2×C3⋊D311yescharacteristic
379C23×C3—28no—
380C23×C3—28no—
381C23×C3—28no—
382C23×C3C23×D318yes—
383C23×C3C23×D314yes—
384C22×D3—38no—
385C22×D3—68no—
386C22×D3—68no—
387C22×D3—68no—
388C2×C3×C4—28no—
389C2×C3×C4—28no—
390C2×C3×C4—28no—
391C2×C3×C4—28no—
392C2×C3×C4—28no—
393C2×C3×C4—28no—
394C2×C3×C4C23×D318yes—
395C2×C3×C4C23×D318yes—
396C2×C3×C4C23×D318yes—
397C2×C3×C4C23×D318yes—
398C2×C3×C4C23×D318yes—
399C2×C3×C4C23×D318yes—
400#67—632no—
401C2×Dic3—316no—
402C2×Dic3—316no—
403C2×Dic3—38no—
404C2×Dic3—38no—
405C2×Dic3—38no—
406C2×Dic3—38no—
407C2×Dic3—38no—
408C2×Dic3—38no—
409C2×Dic3—38no—
410C2×Dic3—632no—
411C2×Dic3—68no—
412C2×Dic3—68no—
413C2×Dic3—68no—
414C2×Dic3—68no—
415C2×Dic3—68no—
416C4×D3—632no—
417Dic6—632no—
418Dic6—632no—
419Dic6—632no—
420C2×C32—42no—
421C2×C32#55614yescomplemented
422C2×C32C22×#4111yescharacteristic
423C2×C32C22×#4111yescharacteristic
424C2×C32C2×2−1+411yescharacteristic
425C3⋊D3—42no—
426C24—91no—
427C24C22×C3⋊D311yescharacteristic
428C2×Q8—94no—
429C2×Q8—94no—
430C2×Q8—94no—
431C2×Q8—184no—
432C2×Q8—184no—
433C2×Q8—184no—
434C2×D4—94no—
435C2×D4—184no—
436C22×C4—91no—
437C22×C4—91no—
438C22×C4—94no—
439C22×C4—91no—
440C22×C4—91no—
441C22×C4—91no—
442C22×C4—91no—
443C22×C4—91no—
444C22×C4—94no—
445C22×C4—184no—
446C22×C4—184no—
447C22×C4C22×C3⋊D311yescharacteristic
448C22×C4C22×C3⋊D311yescharacteristic
449C22×C4C22×C3⋊D311yescharacteristic
450C22×C4C22×C3⋊D311yescharacteristic
451C22×C4C22×C3⋊D311yescharacteristic
452C22×C4C22×C3⋊D311yescharacteristic
453C4⋊C4—94no—
454C4⋊C4—94no—
455C4⋊C4—94no—
456C4⋊C4—94no—
457C4⋊C4—94no—
458C4⋊C4—94no—
459C4⋊C4—94no—
460C4⋊C4—94no—
461C4⋊C4—94no—
462C4⋊C4C22×C3⋊D314yes—
463C4⋊C4C22×C3⋊D314yes—
464C4⋊C4C22×C3⋊D314yes—
465C22⋊C4—94no—
466C22⋊C4—94no—
467C22⋊C4—94no—
468C22⋊C4—94no—
469C22⋊C4—94no—
470C22⋊C4—94no—
471C22⋊C4—94no—
472C22⋊C4C22×C3⋊D314yes—
473C22⋊C4C22×C3⋊D314yes—
474C22⋊C4C22×C3⋊D314yes—
475C42—94no—
476C42—94no—
477C42—94no—
478C42—94no—
479C42—94no—
480C42—94no—
481C42C22×C3⋊D314yes—
482C22×C3—28no—
483C22×C3—28no—
484C22×C3—28no—
485C22×C3—416no—
486C22×C3D3×#4118yes—
487C22×C3D3×#4118yes—
488C22×C3#101018yes—
489C22×C3C24×D314yes—
490C2×D3—68no—
491C2×D3—68no—
492C2×D3—68no—
493C2×D3—1216no—
494C3×C4—28no—
495C3×C4—28no—
496C3×C4—28no—
497C3×C4—28no—
498C3×C4—28no—
499C3×C4—28no—
500Dic3—316no—
501Dic3—316no—
502Dic3—68no—
503Dic3—68no—
504Dic3—68no—
505Dic3—68no—
506Dic3—68no—
507C32C2×#55611yescharacteristic, complemented, Sylow
508C23—22no—
509C23—22no—
510C23—22no—
511C23—92no—
512C23—182no—
513C23—182no—
514C23—182no—
515C23C23×C3⋊D312yes—
516C23C23×C3⋊D311yescharacteristic
517Q8—188no—
518Q8—188no—
519Q8—188no—
520D4—188no—
521C2×C4—22no—
522C2×C4—22no—
523C2×C4—22no—
524C2×C4—22no—
525C2×C4—22no—
526C2×C4—22no—
527C2×C4—94no—
528C2×C4—94no—
529C2×C4—92no—
530C2×C4—92no—
531C2×C4—92no—
532C2×C4—92no—
533C2×C4—92no—
534C2×C4—92no—
535C2×C4—92no—
536C2×C4—188no—
537C2×C4—188no—
538C2×C4—182no—
539C2×C4—182no—
540C2×C4—182no—
541C2×C4—182no—
542C2×C4—182no—
543C2×C4C23×C3⋊D312yes—
544C2×C4C23×C3⋊D312yes—
545C2×C4C23×C3⋊D312yes—
546C2×C4C23×C3⋊D312yes—
547C2×C4C23×C3⋊D312yes—
548C2×C4C23×C3⋊D312yes—
549C2×C3—48no—
550C2×C3#5702116yescomplemented
551C2×C3C2×D3×#4114yes—
552C2×C3C2×D3×#4114yes—
553C2×C3C2×#101014yes—
554D3—128no—
555C22—22no—
556C22—22no—
557C22—22no—
558C22—44no—
559C22—182no—
560C22—182no—
561C22—182no—
562C22—364no—
563C22#41×C3⋊D312yes—
564C22#41×C3⋊D312yes—
565C22#6436712yes—
566C22C24×C3⋊D311yescharacteristic
567C4—22no—
568C4—22no—
569C4—22no—
570C4—22no—
571C4—22no—
572C4—22no—
573C4—94no—
574C4—94no—
575C4—182no—
576C4—182no—
577C4—182no—
578C4—182no—
579C4—182no—
580C3C2×#570214yescomplemented
581C2—42no—
582C2—362no—
583C2#1059617314yesdirect product factor
584C2C2×#41×C3⋊D311yescharacteristic
585C2C2×#41×C3⋊D311yescharacteristic
586C2C2×#6436711yescharacteristic
subgroupG/H
centerC23C23×C3⋊D3
commutator, cosocleC22×C32C25
FrattiniC22C24×C3⋊D3
FittingC2×C32×#126C2
socleC23×C32C24
prime radicalC22×#638C22
hypercenterC2×#126C3⋊D3
hypocenterC32C2×#556
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C23 ◁ C2×#126

Complements

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

NH ≅ G/Ntype
1. C2×C32×#126C2semidirect
2. #10596173C2direct (N × H)
3. C2×#64107C2semidirect
4. C2×#64107C2semidirect
5. C2×#64105C2semidirect
6. C2×#64097C2semidirect
7. C2×#64096C2semidirect
8. C2×#64096C2semidirect
12. C2×#64088C2semidirect
13. C2×#64087C2semidirect
14. C2×#64086C2semidirect
15. C2×#64081C2semidirect
16. C2×C4×#634C2semidirect
24. C32×#126C22semidirect
54. #64107C22semidirect
55. #64107C22semidirect
56. #64105C22semidirect
57. #64097C22semidirect
58. #64096C22semidirect
59. #64096C22semidirect
63. #64088C22semidirect
64. #64087C22semidirect
65. #64086C22semidirect
66. #64081C22semidirect
67. C4×#634C22semidirect
68. C2×C3×#126D3semidirect
147. C3×#126C2×D3semidirect
237. C2×#126C3⋊D3semidirect
339. #126C2×C3⋊D3semidirect
421. C2×C32#556semidirect
507. C32C2×#556semidirect
550. C2×C3#5702semidirect
580. C3C2×#5702semidirect
583. C2#10596173direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C32×#1262
#105961732
C2×#641072
C2×#641052
C2×#640972
C2×#640962
C2×#640942
C2×#640902
C2×#640882
C2×#640872
C2×#640862
C2×#640812
C2×C4×#6342
C2×#57023