Finite Group Databasebeta

← C2×#10593938 #11903260

Subgroups — C2×#10593938 #11903260

Order 1152.

2613 conjugacy classes of subgroups.

The subgroup lattice has 620 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C4×C4⋊(C3⋊D3)C211yesmaximal, characteristic
2C2×C3×#870C211yesmaximal, characteristic, complemented
3C2×C3×C4×Dic6C211yesmaximal, characteristic, complemented
4C2×#63918C211yesmaximal, characteristic, complemented
5C2×#63895C212yesmaximal, complemented
6C2×#63894C211yesmaximal, characteristic
7C2×#63894C211yesmaximal, characteristic
8C2×#63888C212yesmaximal, complemented
9C2×#63883C212yesmaximal, complemented
10C2×#63869C211yesmaximal, characteristic, complemented
11C2×#63865C212yesmaximal, complemented
12#10593938C2116yesmaximal, direct product factor
13C2×#5690—31nomaximal
14C2×#5579—31nomaximal
15C22×C4⋊(C3⋊D3)C2211yescharacteristic
16C22×C4×C3⋊D3C2212yes—
17C22×C3×Dic6C2211yescharacteristic
18C22×#627C2212yes—
19C22×#624C2212yes—
20C22×#624C2212yes—
21C2×C32×C42C2211yescharacteristic
22C2×#3752C2212yes—
23C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
24C4×C4⋊(C3⋊D3)C2218yes—
25C2×C3×C4⋊Dic3C2211yescharacteristic
26C2×C3×C4⋊Dic3C2211yescharacteristic
27C2×C3×C4⋊Dic3C2211yescharacteristic
28C2×C3×Dic3⋊C4C2211yescharacteristic
29C2×C3×Dic3⋊C4C2212yes—
30C2×C3×Dic3⋊C4C2211yescharacteristic
31C2×C3×Dic3⋊C4C2212yes—
32C2×C3×C4×Dic3C2211yescharacteristic
33C2×C3×C4×Dic3C2211yescharacteristic
34C3×#870C2218yescomplemented
35C3×C4×Dic6C2218yescomplemented
36C2×#3724C2212yes—
37C2×Dic3⋊Dic3C2212yes—
38C2×Dic3⋊Dic3C2212yes—
39C2×#3722C2212yes—
40C2×#3722C2212yes—
41#63918C2218yescomplemented
42#63895C22116yescomplemented
43#63894C2218yes—
44#63894C2218yes—
45#63888C22116yescomplemented
46#63883C22116yescomplemented
47#63869C2218yescomplemented
48#63865C22116yescomplemented
49C2×C3×#125—31no—
50C2×C3×C4×Q8—31no—
51C2×#946—32no—
52#5690—316no—
53#5579—316no—
54C2×#897—32no—
55C2×#896—32no—
56C2×#896—32no—
57C2×#896—32no—
58C2×#896—32no—
59C2×#893—31no—
60C2×#893—31no—
61C2×D3×C4⋊C4—32no—
62C2×D3×C4⋊C4—32no—
63C2×#890—31no—
64C2×#888—31no—
65C2×C4×D12—31no—
66C2×C4×D12—31no—
67C2×C4×D12—31no—
68C2×C4×D12—31no—
69C2×C4×D12—61no—
70C2×#870—31no—
71C2×#870D311yescharacteristic, complemented
72C2×#869—31no—
73C2×C4×Dic6D311yescharacteristic, complemented
74C23×C3⋊D3C2312yes—
75C22×C32×C4C2311yescharacteristic
76C22×C32×C4C2311yescharacteristic
77C22×C32×C4C2311yescharacteristic
78C22×C3⋊Dic3C2312yes—
79C2×C4⋊(C3⋊D3)Q818yescomplemented
80C2×C4⋊(C3⋊D3)C2314yes—
81C2×C4×C3⋊D3—44no—
82C2×C4×C3⋊D3C2318yes—
83C22×C3×Dic3C2311yescharacteristic
84C22×C3×Dic3C2311yescharacteristic
85C22×C3×Dic3C2311yescharacteristic
86C22×C3×Dic3C2312yes—
87C22×C3×Dic3C2312yes—
88C22×C3×Dic3C2311yescharacteristic
89C2×C3×Dic6—24no—
90C2×C3×Dic6C2314yes—
91C2×#627—44no—
92C2×#627C2318yes—
93C2×#624—28no—
94C2×#624—44no—
95C2×#624C2318yes—
96C2×#624C2318yes—
97C32×C42C2314yes—
98#3752C2318yes—
99C4⋊(C3⋊Dic3)C2314yes—
100C3×C4⋊Dic3C2314yes—
101C3×C4⋊Dic3C2314yes—
102C3×C4⋊Dic3C2314yes—
103C3×Dic3⋊C4C2314yes—
104C3×Dic3⋊C4C2318yes—
105C3×Dic3⋊C4C2314yes—
106C3×Dic3⋊C4C2318yes—
107C3×C4×Dic3C2314yes—
108C3×C4×Dic3C2314yes—
109#3724C2318yes—
110Dic3⋊Dic3C2318yes—
111Dic3⋊Dic3C2318yes—
112#3722C2318yes—
113#3722C2318yes—
114C2×#554—91noSylow
115C22×C3×Q8—31no—
116C22×D12—31no—
117C22×D12—31no—
118C22×D12—61no—
119C22×C4×D3—32no—
120C22×C4×D3—32no—
121C22×C4×D3—32no—
122C22×C4×D3—32no—
123C22×C4×D3—32no—
124C22×C4×D3—32no—
125C22×C4×D3—62no—
126C22×Dic6—32no—
127C22×Dic6—32no—
128C22×Dic6C2×D311yescharacteristic
129C3×#125—38no—
130C3×C4×Q8—38no—
131C2×C3×C4⋊C4—31no—
132C2×C3×C4⋊C4—32no—
133C2×C3×C4⋊C4—31no—
134C2×C3×C4⋊C4—32no—
135C2×C3×C4⋊C4—31no—
136C2×C3×C4⋊C4—31no—
137C2×C3×C4⋊C4—31no—
138C2×C3×C42—21no—
139C2×C3×C42—31no—
140C2×C3×C42—31no—
141C2×C3×C42C2×D311yescharacteristic
142C2×C3×C42C2×D311yescharacteristic
143#946—316no—
144C2×(C2×D3)⋊C4—32no—
145C2×(C2×D3)⋊C4—32no—
146C2×(C2×D3)⋊C4—32no—
147C2×(C2×D3)⋊C4—32no—
148C2×(C2×D3)⋊C4—32no—
149C2×(C2×D3)⋊C4—32no—
150C2×(C2×D3)⋊C4—62no—
151C2×C4⋊Dic3—31no—
152C2×C4⋊Dic3—31no—
153C2×C4⋊Dic3—32no—
154C2×C4⋊Dic3—32no—
155C2×C4⋊Dic3—61no—
156C2×C4⋊Dic3C2×D311yescharacteristic
157C2×C4⋊Dic3C2×D311yescharacteristic
158C2×C4⋊Dic3C2×D311yescharacteristic
159C2×Dic3⋊C4—32no—
160C2×Dic3⋊C4—32no—
161C2×Dic3⋊C4—32no—
162C2×Dic3⋊C4—32no—
163C2×Dic3⋊C4C2×D311yescharacteristic
164C2×Dic3⋊C4C2×D311yescharacteristic
165C2×Dic3⋊C4C2×D312yes—
166C2×Dic3⋊C4C2×D312yes—
167C2×C4×Dic3C2×D311yescharacteristic
168C2×C4×Dic3C2×D311yescharacteristic
169#897—316no—
170#896—316no—
171#896—316no—
172#896—316no—
173#896—316no—
174#893—38no—
175#893—38no—
176D3×C4⋊C4—316no—
177D3×C4⋊C4—316no—
178#890—38no—
179#888—38no—
180C4×D12—38no—
181C4×D12—38no—
182C4×D12—38no—
183C4×D12—38no—
184C4×D12—68no—
185#870—38no—
186#870C2×D318yescomplemented
187#869—38no—
188C4×Dic6C2×D318yescomplemented
189C23×C32C2411yescharacteristic
190C22×C3⋊D3—24no—
191C22×C3⋊D3—24no—
192C22×C3⋊D3C2×Q818yes—
193C22×C3⋊D3C2414yes—
194C2×C32×C4—22no—
195C2×C32×C4—22no—
196C2×C32×C4C2×Q814yes—
197C2×C32×C4C2412yes—
198C2×C32×C4C2412yes—
199C2×C32×C4C2412yes—
200C2×C3⋊Dic3—24no—
201C2×C3⋊Dic3C2414yes—
202C4⋊(C3⋊D3)C2×Q8116yescomplemented
203C4×C3⋊D3—48no—
204C2×C3×Dic3—24no—
205C2×C3×Dic3—22no—
206C2×C3×Dic3—22no—
207C2×C3×Dic3—24no—
208C2×C3×Dic3—22no—
209C2×C3×Dic3#4114yes—
210C2×C3×Dic3C2412yes—
211C2×C3×Dic3C2412yes—
212C2×C3×Dic3C2414yes—
213C2×C3×Dic3C2414yes—
214C2×C3×Dic3C2412yes—
215C2×C3×Dic3C2412yes—
216C3×Dic6—28no—
217#627—48no—
218#624—216no—
219#624—48no—
220#554—916no—
221C2×C4⋊Q8—91no—
222C2×#125—31no—
223C2×#125—91no—
224C2×C22⋊Q8—92no—
225C2×C22⋊Q8—92no—
226C2×C22⋊Q8—92no—
227C2×C4×Q8—31no—
228C2×C4×D4—91no—
229C2×C4×D4—91no—
230C2×C4×D4—91no—
231C22×C4⋊C4—92no—
232C23×D3—32no—
233C23×D3—32no—
234C23×D3—62no—
235C2×C3×Q8—34no—
236C2×C3×Q8—64no—
237C22×C3×C4—21no—
238C22×C3×C4—21no—
239C22×C3×C4—21no—
240C22×C3×C4—31no—
241C22×C3×C4—31no—
242C22×C3×C4—31no—
243C22×C3×C4—32no—
244C22×C3×C4—32no—
245C22×C3×C4—31no—
246C22×C3×C4C22×D311yescharacteristic
247C22×C3×C4C22×D311yescharacteristic
248C22×C3×C4C22×D311yescharacteristic
249C22×C3×C4C22×D311yescharacteristic
250C22×C3×C4C22×D311yescharacteristic
251C22×C3×C4C22×D311yescharacteristic
252C22×Dic3—32no—
253C22×Dic3—32no—
254C22×Dic3—62no—
255C22×Dic3C22×D311yescharacteristic
256C22×Dic3C22×D311yescharacteristic
257C22×Dic3C22×D311yescharacteristic
258C22×Dic3C22×D312yes—
259C22×Dic3C22×D312yes—
260C22×Dic3C22×D311yescharacteristic
261C2×D12—38no—
262C2×D12—38no—
263C2×D12—34no—
264C2×D12—34no—
265C2×D12—64no—
266C2×D12—68no—
267C2×C4×D3—38no—
268C2×C4×D3—38no—
269C2×C4×D3—38no—
270C2×C4×D3—38no—
271C2×C4×D3—38no—
272C2×C4×D3—38no—
273C2×C4×D3—68no—
274C2×C4×D3—68no—
275C2×C4×D3—68no—
276C2×C4×D3—124no—
277C2×C4×D3—124no—
278C2×C4×D3—124no—
279C2×C4×D3—124no—
280C2×C4×D3—128no—
281C2×Dic6—24no—
282C2×Dic6—38no—
283C2×Dic6—38no—
284C2×Dic6—124no—
285C2×Dic6—124no—
286C2×Dic6C22×D314yes—
287C3×C4⋊C4—34no—
288C3×C4⋊C4—34no—
289C3×C4⋊C4—34no—
290C3×C4⋊C4—38no—
291C3×C4⋊C4—34no—
292C3×C4⋊C4—34no—
293C3×C4⋊C4—38no—
294C3×C42—24no—
295C3×C42—34no—
296C3×C42—34no—
297C3×C42C22×D314yes—
298C3×C42C22×D314yes—
299(C2×D3)⋊C4—38no—
300(C2×D3)⋊C4—38no—
301(C2×D3)⋊C4—38no—
302(C2×D3)⋊C4—38no—
303(C2×D3)⋊C4—38no—
304(C2×D3)⋊C4—38no—
305(C2×D3)⋊C4—68no—
306C4⋊Dic3—34no—
307C4⋊Dic3—34no—
308C4⋊Dic3—38no—
309C4⋊Dic3—38no—
310C4⋊Dic3—64no—
311C4⋊Dic3C22×D314yes—
312C4⋊Dic3C22×D314yes—
313C4⋊Dic3C22×D314yes—
314Dic3⋊C4—38no—
315Dic3⋊C4—38no—
316Dic3⋊C4—38no—
317Dic3⋊C4—38no—
318Dic3⋊C4C22×D314yes—
319Dic3⋊C4C22×D314yes—
320Dic3⋊C4C22×D318yes—
321Dic3⋊C4C22×D318yes—
322C4×Dic3C22×D314yes—
323C4×Dic3C22×D314yes—
324C22×C32C22×Q812yes—
325C22×C32C2×#4112yes—
326C22×C32H(5,𝔽2)12yes—
327C22×C32C2511yescharacteristic
328C2×C3⋊D3—216no—
329C2×C3⋊D3—24no—
330C2×C3⋊D3—24no—
331C2×C3⋊D3C22×Q818yes—
332C32×C4—22no—
333C32×C4—22no—
334C32×C4C22×Q814yes—
335C3⋊Dic3—24no—
336C3×Dic3—24no—
337C3×Dic3—22no—
338C3×Dic3—22no—
339C3×Dic3—24no—
340C3×Dic3—22no—
341C3×Dic3C2×#4114yes—
342C22×Q8—31no—
343C22×Q8—92no—
344C22×D4—91no—
345C23×C4—92no—
346C23×C4—92no—
347C23×C4—92no—
348C4⋊Q8—98no—
349#125—38no—
350#125—98no—
351C22⋊Q8—916no—
352C22⋊Q8—916no—
353C22⋊Q8—916no—
354C4×Q8—38no—
355C4×D4—98no—
356C4×D4—98no—
357C4×D4—98no—
358C2×C4⋊C4—31no—
359C2×C4⋊C4—32no—
360C2×C4⋊C4—31no—
361C2×C4⋊C4—31no—
362C2×C4⋊C4—31no—
363C2×C4⋊C4—31no—
364C2×C4⋊C4—32no—
365C2×C4⋊C4—916no—
366C2×C4⋊C4—92no—
367C2×C4⋊C4—92no—
368C2×C4⋊C4—92no—
369C2×C4⋊C4—91no—
370C2×C22⋊C4—92no—
371C2×C22⋊C4—92no—
372C2×C22⋊C4—92no—
373C2×C42—31no—
374C2×C42—31no—
375C2×C42D3211yescharacteristic
376C23×C3—21no—
377C23×C3C23×D311yescharacteristic
378C23×C3C23×D311yescharacteristic
379C22×D3—38no—
380C22×D3—38no—
381C22×D3—34no—
382C22×D3—34no—
383C22×D3—68no—
384C22×D3—64no—
385C22×D3—64no—
386C22×D3—64no—
387C22×D3—64no—
388C22×D3—64no—
389C22×D3—124no—
390C22×D3—124no—
391C3×Q8—68no—
392C2×C3×C4—24no—
393C2×C3×C4—22no—
394C2×C3×C4—22no—
395C2×C3×C4—22no—
396C2×C3×C4—22no—
397C2×C3×C4—22no—
398C2×C3×C4—22no—
399C2×C3×C4—22no—
400C2×C3×C4—24no—
401C2×C3×C4—34no—
402C2×C3×C4—32no—
403C2×C3×C4—32no—
404C2×C3×C4—32no—
405C2×C3×C4—34no—
406C2×C3×C4—34no—
407C2×C3×C4—32no—
408C2×C3×C4—42no—
409C2×C3×C4—64no—
410C2×C3×C4—62no—
411C2×C3×C4—62no—
412C2×C3×C4—64no—
413C2×C3×C4—62no—
414C2×C3×C4D3×Q814yes—
415C2×C3×C4D3×Q814yes—
416C2×C3×C4C23×D312yes—
417C2×C3×C4C23×D312yes—
418C2×C3×C4C23×D312yes—
419C2×C3×C4C23×D312yes—
420C2×C3×C4C23×D312yes—
421C2×C3×C4C23×D312yes—
422C2×Dic3—22no—
423C2×Dic3—24no—
424C2×Dic3—22no—
425C2×Dic3—24no—
426C2×Dic3—22no—
427C2×Dic3—34no—
428C2×Dic3—34no—
429C2×Dic3—64no—
430C2×Dic3—64no—
431C2×Dic3—64no—
432C2×Dic3—124no—
433C2×Dic3#23514yes—
434C2×Dic3C23×D312yes—
435C2×Dic3C23×D312yes—
436C2×Dic3C23×D312yes—
437C2×Dic3C23×D314yes—
438C2×Dic3C23×D314yes—
439C2×Dic3C23×D312yes—
440D12—316no—
441D12—316no—
442D12—616no—
443C4×D3—616no—
444C4×D3—616no—
445C4×D3—128no—
446C4×D3—128no—
447C4×D3—128no—
448C4×D3—128no—
449C4×D3—1216no—
450Dic6—28no—
451Dic6—128no—
452Dic6—128no—
453C2×C32#55414yescomplemented
454C2×C32C23×Q811yescharacteristic
455C2×C32C22×#4111yescharacteristic
456C2×C32C2×H(5,𝔽2)11yescharacteristic
457C3⋊D3—28no—
458C24—92no—
459C2×Q8—34no—
460C2×Q8—64no—
461C2×Q8—98no—
462C2×Q8—364no—
463C2×D4—94no—
464C2×D4—98no—
465C22×C4—31no—
466C22×C4—31no—
467C22×C4—31no—
468C22×C4—31no—
469C22×C4—32no—
470C22×C4—32no—
471C22×C4—98no—
472C22×C4—98no—
473C22×C4—92no—
474C22×C4—98no—
475C22×C4—188no—
476C22×C4—364no—
477C22×C4—364no—
478C22×C4C2×D3211yescharacteristic
479C22×C4C2×D3211yescharacteristic
480C22×C4C2×D3211yescharacteristic
481C4⋊C4—34no—
482C4⋊C4—38no—
483C4⋊C4—34no—
484C4⋊C4—34no—
485C4⋊C4—34no—
486C4⋊C4—34no—
487C4⋊C4—38no—
488C4⋊C4—98no—
489C4⋊C4—98no—
490C4⋊C4—98no—
491C4⋊C4—94no—
492C22⋊C4—98no—
493C22⋊C4—98no—
494C22⋊C4—98no—
495C42—34no—
496C42—34no—
497C42C2×D3214yes—
498C22×C3—22no—
499C22×C3—22no—
500C22×C3—22no—
501C22×C3—21no—
502C22×C3C2×#23512yes—
503C22×C3C2×D3×Q812yes—
504C22×C3C2×D3×Q812yes—
505C22×C3D3×#4112yes—
506C22×C3#100912yes—
507C22×C3#100912yes—
508C22×C3C24×D311yescharacteristic
509C22×C3C24×D311yescharacteristic
510C2×D3—38no—
511C2×D3—38no—
512C2×D3—68no—
513C2×D3—616no—
514C2×D3—64no—
515C2×D3—64no—
516C2×D3—64no—
517C2×D3—64no—
518C2×D3—616no—
519C2×D3—124no—
520C2×D3—124no—
521C2×D3—1216no—
522C3×C4—24no—
523C3×C4—22no—
524C3×C4—22no—
525C3×C4—22no—
526C3×C4—22no—
527C3×C4—24no—
528C3×C4—34no—
529C3×C4—42no—
530C3×C4—64no—
531C3×C4—62no—
532C3×C4—62no—
533C3×C4—64no—
534C3×C4—62no—
535C3×C4C2×D3×Q814yes—
536C3×C4C2×D3×Q814yes—
537Dic3—22no—
538Dic3—24no—
539Dic3—22no—
540Dic3—24no—
541Dic3—22no—
542Dic3—64no—
543Dic3—64no—
544Dic3—124no—
545Dic3C2×#23514yes—
546C32C2×#55411yescharacteristic, complemented, Sylow
547C23—98no—
548C23—94no—
549C23—184no—
550C23—184no—
551C23C22×D3211yescharacteristic
552Q8—68no—
553Q8—368no—
554D4—916no—
555C2×C4—22no—
556C2×C4—22no—
557C2×C4—34no—
558C2×C4—32no—
559C2×C4—32no—
560C2×C4—32no—
561C2×C4—32no—
562C2×C4—34no—
563C2×C4—34no—
564C2×C4—64no—
565C2×C4—62no—
566C2×C4—62no—
567C2×C4—64no—
568C2×C4—62no—
569C2×C4—94no—
570C2×C4—1816no—
571C2×C4—184no—
572C2×C4—368no—
573C2×C4—368no—
574C2×C4#379714yes—
575C2×C4C22×D3212yes—
576C2×C4C22×D3212yes—
577C2×C4C22×D3212yes—
578C2×C3—21no—
579C2×C3—21no—
580C2×C3—21no—
581C2×C3—24no—
582C2×C3#557914yescomplemented
583C2×C3#569014yescomplemented
584C2×C3C22×#23511yescharacteristic
585C2×C3C22×D3×Q811yescharacteristic
586C2×C3C22×D3×Q811yescharacteristic
587C2×C3C2×D3×#4111yescharacteristic
588C2×C3C2×#100911yescharacteristic
589C2×C3C2×#100911yescharacteristic
590D3—68no—
591D3—68no—
592D3—128no—
593C22—98no—
594C22—184no—
595C22—184no—
596C22—1816no—
597C22C2×#379712yes—
598C22D3×#23512yes—
599C22#6430812yes—
600C22C23×D3211yescharacteristic
601C4—22no—
602C4—22no—
603C4—34no—
604C4—64no—
605C4—62no—
606C4—62no—
607C4—64no—
608C4—62no—
609C4—184no—
610C4C2×#379714yes—
611C3—21no—
612C3C2×#557911yescharacteristic, complemented
613C3C2×#569011yescharacteristic, complemented
614C2—188no—
615C2#1059393814yesdirect product factor
616C2C22×#379711yescharacteristic
617C2C2×D3×#23511yescharacteristic
618C2C2×#6430811yescharacteristic
subgroupG/H
centerC23C22×D32
commutator, cosocleC22×C32C25
FrattiniC22C23×D32
FittingC2×C32×C42C22
socleC23×C32C24
prime radicalC22×C4⋊(C3⋊D3)C22
hypercenterC2×C42D32
hypocenterC32C2×#554
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C23 ◁ C2×C42

Complements

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

NH ≅ G/Ntype
2. C2×C3×#870C2semidirect
3. C2×C3×C4×Dic6C2semidirect
4. C2×#63918C2semidirect
5. C2×#63895C2semidirect
8. C2×#63888C2semidirect
9. C2×#63883C2semidirect
10. C2×#63869C2semidirect
11. C2×#63865C2semidirect
12. #10593938C2direct (N × H)
34. C3×#870C22semidirect
35. C3×C4×Dic6C22semidirect
41. #63918C22semidirect
42. #63895C22semidirect
45. #63888C22semidirect
46. #63883C22semidirect
47. #63869C22semidirect
48. #63865C22semidirect
71. C2×#870D3semidirect
73. C2×C4×Dic6D3semidirect
79. C2×C4⋊(C3⋊D3)Q8semidirect
186. #870C2×D3semidirect
188. C4×Dic6C2×D3semidirect
202. C4⋊(C3⋊D3)C2×Q8semidirect
453. C2×C32#554semidirect
546. C32C2×#554semidirect
582. C2×C3#5579semidirect
583. C2×C3#5690semidirect
612. C3C2×#5579semidirect
613. C3C2×#5690semidirect
615. C2#10593938direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C4×C4⋊(C3⋊D3)2
C2×C3×#8702
C2×C3×C4×Dic62
C2×#639182
C2×#638952
C2×#638942
C2×#638882
C2×#638832
C2×#638692
C2×#638652
#105939382
C2×#56903
C2×#55793