Finite Group Databasebeta

← C2×#10594808 #11900840

Subgroups — C2×#10594808 #11900840

Order 1152.

2497 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×#64133C211yesmaximal, characteristic
2C2×C3×#924C211yesmaximal, characteristic
3C22×C3×C4×Dic3C211yesmaximal, characteristic
4C2×#63964C212yesmaximal
5C2×#63955C212yesmaximal
6C2×#63918C211yesmaximal, characteristic, complemented
7C2×#63867C212yesmaximal, complemented
8C2×#63866C211yesmaximal, characteristic, complemented
9C2×#63844C211yesmaximal, characteristic, complemented
10C2×Dic3×Dic6C211yesmaximal, characteristic, complemented
11#10594808C2116yesmaximal, direct product factor
12C2×#63837C212yesmaximal, complemented
13C2×#5622—31nomaximal
14C2×#5470—31nomaximal
15C23×C32×C4C2211yescharacteristic
16C22×#634C2211yescharacteristic
17C23×C3×Dic3C2211yescharacteristic
18C23×C3×Dic3C2211yescharacteristic
19C22×C3×Dic6C2211yescharacteristic
20C22×#627C2212yes—
21C2×#3757C2212yes—
22C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
23#64133C2218yes—
24C2×#3750C2212yes—
25C2×C3×#217C2212yes—
26C2×C3×C4⋊Dic3C2211yescharacteristic
27C3×#924C2218yes—
28C2×C3×Dic3⋊C4C2212yes—
29C2×C3×C4×Dic3C2211yescharacteristic
30C2×C3×C4×Dic3C2211yescharacteristic
31C2×C3×C4×Dic3C2211yescharacteristic
32C2×C3×C4×Dic3C2211yescharacteristic
33C2×C3×C4×Dic3C2218yes—
34C2×#3724C2212yes—
35C2×Dic3⋊Dic3C2212yes—
36C2×Dic3⋊Dic3C2212yes—
37C2×Dic3⋊Dic3C2212yes—
38C2×Dic3⋊Dic3C2212yes—
39#63964C22116yes—
40#63955C22116yes—
41C2×Dic32C2212yes—
42C2×Dic32C2212yes—
43#63918C2218yescomplemented
44#63867C22116yescomplemented
45#63866C2218yescomplemented
46#63844C2218yescomplemented
47Dic3×Dic6C2218yescomplemented
48#63837C22116yescomplemented
49C2×C3×C22⋊Q8—31no—
50C22×C3×C42—31no—
51C2×Q8×Dic3—31no—
52C2×#944—31no—
53C2×#926—32no—
54C2×#924—31no—
55C2×#924—31no—
56C2×#924—32no—
57C2×#924—61no—
58C2×#924D311yescharacteristic
59C22×C4×Dic3D311yescharacteristic
60#5622—316no—
61C2×#889—32no—
62C2×#888—31no—
63C2×#887—31no—
64C2×#887—32no—
65C2×#878—32no—
66C2×#877—32no—
67#5470—316no—
68C2×#870—32no—
69C2×#869—31no—
70C2×#869—31no—
71C2×C4×Dic6—31no—
72C2×C4×Dic6—31no—
73C2×C4×Dic6—32no—
74C24×C32C2311yescharacteristic
75C22×C32×C4—24no—
76C22×C32×C4C2311yescharacteristic
77C22×C32×C4C2314yes—
78C22×C32×C4C2311yescharacteristic
79C22×C3⋊Dic3C2312yes—
80C22×C3⋊Dic3C2312yes—
81C2×#634—24no—
82C2×#634C2314yes—
83C22×C3×Dic3—24no—
84C22×C3×Dic3Q818yescomplemented
85C22×C3×Dic3C2314yes—
86C22×C3×Dic3C2311yescharacteristic
87C22×C3×Dic3C2312yes—
88C22×C3×Dic3C2312yes—
89C22×C3×Dic3C2311yescharacteristic
90C22×C3×Dic3C2311yescharacteristic
91C22×C3×Dic3C2314yes—
92C22×C3×Dic3C2311yescharacteristic
93C2×C3×Dic6—24no—
94C2×C3×Dic6C2314yes—
95C2×#627—28no—
96C2×#627C2318yes—
97#3757C2318yes—
98C4⋊(C3⋊Dic3)C2314yes—
99#3750C2318yes—
100C3×#217C2318yes—
101C3×C4⋊Dic3C2314yes—
102C3×Dic3⋊C4C2318yes—
103C3×C4×Dic3C2314yes—
104C3×C4×Dic3C2314yes—
105C3×C4×Dic3C2314yes—
106C3×C4×Dic3C2314yes—
107#3724C2318yes—
108Dic3⋊Dic3C2318yes—
109Dic3⋊Dic3C2318yes—
110Dic3⋊Dic3C2318yes—
111Dic3⋊Dic3C2318yes—
112Dic32C2318yes—
113Dic32C2318yes—
114C2×#533—91noSylow
115C22×C3×Q8—31no—
116C23×C3×C4—21no—
117C23×C3×C4—31no—
118C23×C3×C4—31no—
119C23×C3×C4C2×D311yescharacteristic
120C23×C3×C4C2×D311yescharacteristic
121C23×Dic3C2×D311yescharacteristic
122C23×Dic3C2×D311yescharacteristic
123C22×Dic6—31no—
124C22×Dic6—31no—
125C22×Dic6—32no—
126C22×Dic6—32no—
127C22×Dic6—61no—
128C22×Dic6C2×D311yescharacteristic
129C3×C22⋊Q8—38no—
130C2×C3×C4⋊C4—32no—
131C2×C3×C4⋊C4—31no—
132C2×C3×C22⋊C4—32no—
133C2×C3×C42—31no—
134C2×C3×C42—31no—
135C2×C3×C42—31no—
136C2×C3×C42—31no—
137C2×C3×C42—38no—
138C2×#217—32no—
139C2×#217—32no—
140C2×#217—62no—
141C2×#217C2×D312yes—
142Q8×Dic3—38no—
143#944—38no—
144#926—316no—
145C2×C4⋊Dic3—31no—
146C2×C4⋊Dic3—31no—
147C2×C4⋊Dic3—32no—
148C2×C4⋊Dic3—32no—
149C2×C4⋊Dic3—32no—
150C2×C4⋊Dic3—32no—
151C2×C4⋊Dic3—61no—
152C2×C4⋊Dic3C2×D311yescharacteristic
153#924—38no—
154#924—38no—
155#924—316no—
156#924—68no—
157#924C2×D318yes—
158C2×Dic3⋊C4—32no—
159C2×Dic3⋊C4—32no—
160C2×Dic3⋊C4—32no—
161C2×Dic3⋊C4—32no—
162C2×Dic3⋊C4—32no—
163C2×Dic3⋊C4—32no—
164C2×Dic3⋊C4—32no—
165C2×Dic3⋊C4—32no—
166C2×Dic3⋊C4—62no—
167C2×Dic3⋊C4C2×D312yes—
168C2×C4×Dic3—32no—
169C2×C4×Dic3—32no—
170C2×C4×Dic3—32no—
171C2×C4×Dic3—32no—
172C2×C4×Dic3C2×D311yescharacteristic
173C2×C4×Dic3C2×D311yescharacteristic
174C2×C4×Dic3C2×D311yescharacteristic
175C2×C4×Dic3C2×D311yescharacteristic
176C2×C4×Dic3C2×D318yes—
177#889—316no—
178#888—38no—
179#887—316no—
180#887—38no—
181#878—316no—
182#877—316no—
183#870—316no—
184#869—38no—
185#869—38no—
186C4×Dic6—38no—
187C4×Dic6—38no—
188C4×Dic6—316no—
189C23×C32—22no—
190C23×C32—22no—
191C23×C32C2×Q814yes—
192C23×C32C2412yes—
193C23×C32C2411yescharacteristic
194C2×C32×C4—22no—
195C2×C32×C4—28no—
196C2×C32×C4#4114yes—
197C2×C32×C4C2412yes—
198C2×C32×C4C2412yes—
199C2×C3⋊Dic3—24no—
200C2×C3⋊Dic3—24no—
201C2×C3⋊Dic3C2414yes—
202C2×C3⋊Dic3C2414yes—
203#634—28no—
204C2×C3×Dic3—24no—
205C2×C3×Dic3—24no—
206C2×C3×Dic3—22no—
207C2×C3×Dic3—28no—
208C2×C3×Dic3C2×Q814yes—
209C2×C3×Dic3C2×Q814yes—
210C2×C3×Dic3C2×Q8116yescomplemented
211C2×C3×Dic3#4114yes—
212C2×C3×Dic3C2414yes—
213C2×C3×Dic3C2414yes—
214C2×C3×Dic3C2412yes—
215C2×C3×Dic3C2412yes—
216C2×C3×Dic3C2412yes—
217C2×C3×Dic3C2412yes—
218C3×Dic6—28no—
219#627—216no—
220#533—916no—
221C2×C4⋊Q8—91no—
222C2×C4⋊Q8—91no—
223C2×#125—92no—
224C2×C22⋊Q8—31no—
225C2×C22⋊Q8—92no—
226C2×C22⋊Q8—91no—
227C2×C4×Q8—92no—
228C2×C4×Q8—91no—
229C2×C4×Q8—91no—
230C2×#117—92no—
231C22×C42—31no—
232C24×C3—21no—
233C24×C3C22×D311yescharacteristic
234C24×C3C22×D311yescharacteristic
235C2×C3×Q8—34no—
236C2×C3×Q8—64no—
237C22×C3×C4—24no—
238C22×C3×C4—24no—
239C22×C3×C4—21no—
240C22×C3×C4—21no—
241C22×C3×C4—24no—
242C22×C3×C4—38no—
243C22×C3×C4—31no—
244C22×C3×C4—31no—
245C22×C3×C4—31no—
246C22×C3×C4—34no—
247C22×C3×C4—32no—
248C22×C3×C4—32no—
249C22×C3×C4—31no—
250C22×C3×C4—34no—
251C22×C3×C4—44no—
252C22×C3×C4—64no—
253C22×C3×C4C22×D311yescharacteristic
254C22×C3×C4C22×D314yes—
255C22×C3×C4C22×D311yescharacteristic
256C22×C3×C4C22×D314yes—
257C22×C3×C4C22×D311yescharacteristic
258C22×C3×C4C22×D311yescharacteristic
259C22×Dic3—24no—
260C22×Dic3—32no—
261C22×Dic3—32no—
262C22×Dic3—32no—
263C22×Dic3—32no—
264C22×Dic3—62no—
265C22×Dic3—62no—
266C22×Dic3Dic618yescomplemented
267C22×Dic3C22×D314yes—
268C22×Dic3C22×D312yes—
269C22×Dic3C22×D312yes—
270C22×Dic3C22×D311yescharacteristic
271C22×Dic3C22×D311yescharacteristic
272C22×Dic3C22×D311yescharacteristic
273C22×Dic3C22×D314yes—
274C22×Dic3C22×D311yescharacteristic
275C2×Dic6—24no—
276C2×Dic6—34no—
277C2×Dic6—34no—
278C2×Dic6—38no—
279C2×Dic6—38no—
280C2×Dic6—64no—
281C2×Dic6—68no—
282C2×Dic6—64no—
283C2×Dic6—64no—
284C2×Dic6—68no—
285C2×Dic6—124no—
286C2×Dic6C22×D314yes—
287C3×C4⋊C4—34no—
288C3×C4⋊C4—38no—
289C3×C22⋊C4—38no—
290C3×C42—34no—
291C3×C42—34no—
292C3×C42—34no—
293C3×C42—34no—
294#217—38no—
295#217—38no—
296#217—68no—
297#217C22×D318yes—
298C4⋊Dic3—34no—
299C4⋊Dic3—34no—
300C4⋊Dic3—38no—
301C4⋊Dic3—38no—
302C4⋊Dic3—38no—
303C4⋊Dic3—38no—
304C4⋊Dic3—64no—
305C4⋊Dic3C22×D314yes—
306Dic3⋊C4—38no—
307Dic3⋊C4—38no—
308Dic3⋊C4—38no—
309Dic3⋊C4—38no—
310Dic3⋊C4—38no—
311Dic3⋊C4—38no—
312Dic3⋊C4—38no—
313Dic3⋊C4—38no—
314Dic3⋊C4—68no—
315Dic3⋊C4C22×D318yes—
316C4×Dic3—38no—
317C4×Dic3—38no—
318C4×Dic3—38no—
319C4×Dic3—38no—
320C4×Dic3C22×D314yes—
321C4×Dic3C22×D314yes—
322C4×Dic3C22×D314yes—
323C4×Dic3C22×D314yes—
324C22×C32—28no—
325C22×C32—22no—
326C22×C32—22no—
327C22×C32C22×Q814yes—
328C22×C32C22×Q812yes—
329C22×C32C2×#4112yes—
330C22×C32C2×#4112yes—
331C22×C32C2511yescharacteristic
332C32×C4—22no—
333C32×C4C2×#4114yes—
334C3⋊Dic3—24no—
335C3⋊Dic3—24no—
336C3×Dic3—24no—
337C3×Dic3—24no—
338C3×Dic3—22no—
339C3×Dic3C22×Q814yes—
340C3×Dic3C22×Q814yes—
341C3×Dic3C2×#4114yes—
342C22×Q8—31no—
343C22×Q8—92no—
344C22×Q8—91no—
345C23×C4—31no—
346C23×C4—31no—
347C23×C4D3211yescharacteristic
348C4⋊Q8—98no—
349C4⋊Q8—98no—
350#125—916no—
351C22⋊Q8—38no—
352C22⋊Q8—916no—
353C22⋊Q8—98no—
354C4×Q8—916no—
355C4×Q8—98no—
356C4×Q8—98no—
357#117—916no—
358C2×C4⋊C4—32no—
359C2×C4⋊C4—31no—
360C2×C4⋊C4—92no—
361C2×C4⋊C4—92no—
362C2×C4⋊C4—92no—
363C2×C4⋊C4—92no—
364C2×C4⋊C4—92no—
365C2×C4⋊C4—92no—
366C2×C4⋊C4—91no—
367C2×C22⋊C4—32no—
368C2×C22⋊C4—92no—
369C2×C42—31no—
370C2×C42—31no—
371C2×C42—31no—
372C2×C42—31no—
373C2×C42—38no—
374C2×C42—92no—
375C2×C42—92no—
376C23×C3—22no—
377C23×C3—22no—
378C23×C3—22no—
379C23×C3—22no—
380C23×C3—22no—
381C23×C3—21no—
382C23×C3—24no—
383C23×C3—42no—
384C23×C3—42no—
385C23×C3C2×Dic614yes—
386C23×C3D3×Q814yes—
387C23×C3C23×D312yes—
388C23×C3C23×D312yes—
389C23×C3C23×D311yescharacteristic
390C23×C3C23×D311yescharacteristic
391C3×Q8—68no—
392C2×C3×C4—22no—
393C2×C3×C4—22no—
394C2×C3×C4—28no—
395C2×C3×C4—28no—
396C2×C3×C4—22no—
397C2×C3×C4—22no—
398C2×C3×C4—24no—
399C2×C3×C4—34no—
400C2×C3×C4—34no—
401C2×C3×C4—316no—
402C2×C3×C4—34no—
403C2×C3×C4—32no—
404C2×C3×C4—32no—
405C2×C3×C4—32no—
406C2×C3×C4—34no—
407C2×C3×C4—34no—
408C2×C3×C4—32no—
409C2×C3×C4—48no—
410C2×C3×C4—42no—
411C2×C3×C4—68no—
412C2×C3×C4—64no—
413C2×C3×C4—64no—
414C2×C3×C4—62no—
415C2×C3×C4#23514yes—
416C2×C3×C4#23714yes—
417C2×C3×C4C23×D312yes—
418C2×C3×C4C23×D312yes—
419C2×C3×C4C23×D312yes—
420C2×C3×C4C23×D312yes—
421C2×Dic3—22no—
422C2×Dic3—24no—
423C2×Dic3—24no—
424C2×Dic3—28no—
425C2×Dic3—34no—
426C2×Dic3—34no—
427C2×Dic3—34no—
428C2×Dic3—34no—
429C2×Dic3—64no—
430C2×Dic3—64no—
431C2×Dic3—64no—
432C2×Dic3—64no—
433C2×Dic3—64no—
434C2×Dic3—64no—
435C2×Dic3—124no—
436C2×Dic3—124no—
437C2×Dic3C2×Dic614yes—
438C2×Dic3C2×Dic614yes—
439C2×Dic3C2×Dic6116yescomplemented
440C2×Dic3#23514yes—
441C2×Dic3C23×D314yes—
442C2×Dic3C23×D314yes—
443C2×Dic3C23×D312yes—
444C2×Dic3C23×D312yes—
445C2×Dic3C23×D312yes—
446C2×Dic3C23×D312yes—
447Dic6—28no—
448Dic6—616no—
449Dic6—68no—
450Dic6—68no—
451Dic6—616no—
452Dic6—128no—
453C2×C32—24no—
454C2×C32#53314yescomplemented
455C2×C32C23×Q811yescharacteristic
456C2×C32C22×#4111yescharacteristic
457C2×C32C22×#4111yescharacteristic
458C24C2×D3211yescharacteristic
459C2×Q8—34no—
460C2×Q8—64no—
461C2×Q8—98no—
462C2×Q8—94no—
463C2×Q8—188no—
464C2×Q8—184no—
465C22×C4—24no—
466C22×C4—34no—
467C22×C4—31no—
468C22×C4—31no—
469C22×C4—31no—
470C22×C4—38no—
471C22×C4—34no—
472C22×C4—31no—
473C22×C4—32no—
474C22×C4—32no—
475C22×C4—64no—
476C22×C4—92no—
477C22×C4—92no—
478C22×C4C2×D3214yes—
479C22×C4C2×D3211yescharacteristic
480C22×C4C2×D3211yescharacteristic
481C4⋊C4—38no—
482C4⋊C4—34no—
483C4⋊C4—98no—
484C4⋊C4—98no—
485C4⋊C4—98no—
486C4⋊C4—98no—
487C4⋊C4—98no—
488C4⋊C4—98no—
489C4⋊C4—94no—
490C22⋊C4—38no—
491C22⋊C4—98no—
492C42—34no—
493C42—34no—
494C42—34no—
495C42—34no—
496C42—98no—
497C42—98no—
498C22×C3—22no—
499C22×C3—22no—
500C22×C3—22no—
501C22×C3—22no—
502C22×C3—28no—
503C22×C3—28no—
504C22×C3—22no—
505C22×C3—24no—
506C22×C3—22no—
507C22×C3—22no—
508C22×C3—21no—
509C22×C3—42no—
510C22×C3—42no—
511C22×C3—48no—
512C22×C3C22×Dic614yes—
513C22×C3C22×Dic612yes—
514C22×C3C2×#23512yes—
515C22×C3C2×#23512yes—
516C22×C3C2×#23712yes—
517C22×C3C2×D3×Q814yes—
518C22×C3C2×D3×Q812yes—
519C22×C3D3×#4112yes—
520C22×C3C24×D311yescharacteristic
521C22×C3C24×D311yescharacteristic
522C3×C4—22no—
523C3×C4—22no—
524C3×C4—24no—
525C3×C4—34no—
526C3×C4—34no—
527C3×C4—34no—
528C3×C4—42no—
529C3×C4—64no—
530C3×C4—64no—
531C3×C4—62no—
532C3×C4C2×#23514yes—
533C3×C4C2×#23714yes—
534Dic3—22no—
535Dic3—24no—
536Dic3—24no—
537Dic3—64no—
538Dic3—64no—
539Dic3—64no—
540Dic3—64no—
541Dic3—124no—
542Dic3—124no—
543Dic3C22×Dic614yes—
544Dic3C22×Dic614yes—
545Dic3C2×#23514yes—
546C32C2×#53311yescharacteristic, complemented, Sylow
547C23—22no—
548C23—22no—
549C23D3×Dic614yes—
550C23C22×D3212yes—
551C23C22×D3211yescharacteristic
552Q8—68no—
553Q8—1816no—
554Q8—188no—
555C2×C4—22no—
556C2×C4—28no—
557C2×C4—34no—
558C2×C4—34no—
559C2×C4—316no—
560C2×C4—34no—
561C2×C4—32no—
562C2×C4—32no—
563C2×C4—32no—
564C2×C4—32no—
565C2×C4—34no—
566C2×C4—34no—
567C2×C4—68no—
568C2×C4—62no—
569C2×C4—64no—
570C2×C4—64no—
571C2×C4—94no—
572C2×C4—94no—
573C2×C4—184no—
574C2×C4—184no—
575C2×C4#380414yes—
576C2×C4C22×D3212yes—
577C2×C4C22×D3212yes—
578C2×C3—24no—
579C2×C3—24no—
580C2×C3—21no—
581C2×C3—21no—
582C2×C3—21no—
583C2×C3—24no—
584C2×C3—44no—
585C2×C3#547014yescomplemented
586C2×C3#562214yescomplemented
587C2×C3C23×Dic611yescharacteristic
588C2×C3C22×#23511yescharacteristic
589C2×C3C22×#23511yescharacteristic
590C2×C3C22×#23711yescharacteristic
591C2×C3C22×D3×Q811yescharacteristic
592C2×C3C2×D3×#4111yescharacteristic
593C22—22no—
594C22—22no—
595C22—28no—
596C22C2×D3×Dic614yes—
597C22C2×D3×Dic612yes—
598C22D3×#23512yes—
599C22C2×#380412yes—
600C22C23×D3211yescharacteristic
601C4—22no—
602C4—34no—
603C4—34no—
604C4—34no—
605C4—62no—
606C4—64no—
607C4—64no—
608C4—184no—
609C4—184no—
610C4C2×#380414yes—
611C3—21no—
612C3C2×#547011yescharacteristic, complemented
613C3C2×#562211yescharacteristic, complemented
614C2—24no—
615C2#1059480814yesdirect product factor
616C2C22×D3×Dic611yescharacteristic
617C2C2×D3×#23511yescharacteristic
618C2C22×#380411yescharacteristic
subgroupG/H
centerC23C22×D32
commutator, cosocleC22×C32C25
FrattiniC22C23×D32
FittingC23×C32×C4C22
socleC23×C32C24
prime radicalC24×C32C23
hypercenterC23×C4D32
hypocenterC32C2×#533
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C23 ◁ C23×C4

Complements

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

NH ≅ G/Ntype
6. C2×#63918C2semidirect
7. C2×#63867C2semidirect
8. C2×#63866C2semidirect
9. C2×#63844C2semidirect
10. C2×Dic3×Dic6C2semidirect
11. #10594808C2direct (N × H)
12. C2×#63837C2semidirect
43. #63918C22semidirect
44. #63867C22semidirect
45. #63866C22semidirect
46. #63844C22semidirect
47. Dic3×Dic6C22semidirect
48. #63837C22semidirect
84. C22×C3×Dic3Q8semidirect
210. C2×C3×Dic3C2×Q8semidirect
266. C22×Dic3Dic6semidirect
439. C2×Dic3C2×Dic6semidirect
454. C2×C32#533semidirect
546. C32C2×#533semidirect
585. C2×C3#5470semidirect
586. C2×C3#5622semidirect
612. C3C2×#5470semidirect
613. C3C2×#5622semidirect
615. C2#10594808direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#641332
C2×C3×#9242
C22×C3×C4×Dic32
C2×#639642
C2×#639552
C2×#639182
C2×#638672
C2×#638662
C2×#638442
C2×Dic3×Dic62
#105948082
C2×#638372
C2×#56223
C2×#54703