Finite Group Databasebeta

← C2×#10595396 #11901693

Subgroups — C2×#10595396 #11901693

Order 1152.

2413 conjugacy classes of subgroups.

The subgroup lattice has 636 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×Q8×C3⋊Dic3C211yesmaximal, characteristic, complemented
2C2×C3×#947C211yesmaximal, characteristic, complemented
3C2×C3×#946C211yesmaximal, characteristic, complemented
4#10595396C2116yesmaximal, direct product factor
5C2×#63918C211yesmaximal, characteristic, complemented
6C2×#63915C212yesmaximal, complemented
7C2×#63908C211yesmaximal, characteristic
8C2×#63898C211yesmaximal, characteristic, complemented
9C2×#63893C212yesmaximal, complemented
10C2×#63891C212yesmaximal, complemented
11C2×#63862C212yesmaximal, complemented
12C2×#63855C211yesmaximal, characteristic, complemented
13C2×#5682—31nomaximal
14C2×#5643—31nomaximal
15C22×C32×Q8C2211yescharacteristic
16C22×C3×D12C2211yescharacteristic
17C22×C3×C4×D3C2211yescharacteristic
18C22×#627C2212yes—
19C22×#625C2212yes—
20C22×D3×Dic3C2212yes—
21Q8×C3⋊Dic3C2218yescomplemented
22C2×C4⋊(C3⋊Dic3)C2212yes—
23C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
24C2×C4×C3⋊Dic3C2211yescharacteristic
25C2×C4×C3⋊Dic3C2212yes—
26C3×#947C2218yescomplemented
27C3×#946C2218yescomplemented
28C2×C3×(C2×D3)⋊C4C2212yes—
29C2×C3×(C2×D3)⋊C4C2212yes—
30C2×C3×(C2×D3)⋊C4C2212yes—
31C2×C3×C4⋊Dic3C2211yescharacteristic
32C2×C3×Dic3⋊C4C2212yes—
33C2×C3×C4×Dic3C2211yescharacteristic
34C2×Dic3⋊Dic3C2211yescharacteristic
35C2×Dic3⋊Dic3C2211yescharacteristic
36C2×Dic3⋊Dic3C2212yes—
37C2×(C2×D3)⋊Dic3C2211yescharacteristic
38C2×(C2×D3)⋊Dic3C2211yescharacteristic
39C2×(C2×D3)⋊Dic3C2212yes—
40C2×(C2×D3)⋊Dic3C2212yes—
41#63918C2218yescomplemented
42#63915C22116yescomplemented
43#63908C2218yes—
44#63898C2218yescomplemented
45#63893C22116yescomplemented
46#63891C22116yescomplemented
47#63862C22116yescomplemented
48#63855C2218yescomplemented
49C2×C3×#124—31no—
50C2×C3×C22⋊Q8—31no—
51C2×#947D311yescharacteristic, complemented
52C2×#946D311yescharacteristic, complemented
53C2×Q8×Dic3—31no—
54C2×Q8×Dic3—31no—
55C2×Q8×Dic3—61no—
56C2×#938—31no—
57C2×D4×Dic3—31no—
58C2×#930—31no—
59C2×#926—31no—
60#5682—316no—
61#5643—316no—
62C2×#898—32no—
63C2×#897—32no—
64C2×#893—31no—
65C2×#888—31no—
66C2×#886—32no—
67C2×#885—32no—
68C2×#885—32no—
69C2×#883—32no—
70C2×#879—32no—
71C2×#878—32no—
72C2×#872—31no—
73C2×#869—31no—
74C23×C3×D3C2312yes—
75C23×C3×D3C2311yescharacteristic
76C2×C32×Q8—24no—
77C2×C32×Q8C2314yes—
78C22×C32×C4C2312yes—
79C22×C32×C4C2311yescharacteristic
80C22×C3⋊Dic3C2311yescharacteristic
81C22×C3⋊Dic3C2312yes—
82C22×C3⋊Dic3C2311yescharacteristic
83C22×C3×Dic3C2311yescharacteristic
84C22×C3×Dic3C2311yescharacteristic
85C22×C3×Dic3C2311yescharacteristic
86C22×C3×Dic3C2312yes—
87C2×C3×D12—24no—
88C2×C3×D12C2314yes—
89C2×C3×C4×D3—24no—
90C2×C3×C4×D3C2314yes—
91C2×#627—44no—
92C2×#627C2318yes—
93C2×#625—44no—
94C2×#625C2318yes—
95C2×D3×Dic3—44no—
96C2×D3×Dic3C2318yes—
97C4⋊(C3⋊Dic3)C2318yes—
98C4⋊(C3⋊Dic3)C2314yes—
99C4×C3⋊Dic3C2314yes—
100C4×C3⋊Dic3C2318yes—
101C3×(C2×D3)⋊C4C2318yes—
102C3×(C2×D3)⋊C4C2318yes—
103C3×(C2×D3)⋊C4C2318yes—
104C3×C4⋊Dic3C2314yes—
105C3×Dic3⋊C4C2318yes—
106C3×C4×Dic3C2314yes—
107Dic3⋊Dic3C2314yes—
108Dic3⋊Dic3C2314yes—
109Dic3⋊Dic3C2318yes—
110(C2×D3)⋊Dic3C2314yes—
111(C2×D3)⋊Dic3C2314yes—
112(C2×D3)⋊Dic3C2318yes—
113(C2×D3)⋊Dic3C2318yes—
114C2×#542—91noSylow
115C22×C3×Q8—21no—
116C22×C3×Q8C2×D311yescharacteristic
117C22×C3×Q8C2×D311yescharacteristic
118C22×C3×D4—31no—
119C23×C3×C4—31no—
120C22×#67—32no—
121C22×#67—32no—
122C23×Dic3—32no—
123C22×D12C2×D311yescharacteristic
124C22×C4×D3—32no—
125C22×C4×D3C2×D311yescharacteristic
126C22×Dic6—32no—
127C22×Dic6—32no—
128C3×#124—38no—
129C3×C22⋊Q8—38no—
130C2×C3×C4⋊C4—32no—
131C2×C3×C4⋊C4—31no—
132C2×C3×C22⋊C4—32no—
133C2×C3×C22⋊C4—32no—
134C2×C3×C22⋊C4—32no—
135C2×C3×C42—31no—
136C2×#217—32no—
137C2×#217—32no—
138C2×#217—31no—
139C2×#217—31no—
140#947C2×D318yescomplemented
141#946C2×D318yescomplemented
142Q8×Dic3—38no—
143Q8×Dic3—38no—
144Q8×Dic3—68no—
145#938—38no—
146D4×Dic3—38no—
147#930—38no—
148C2×(C2×D3)⋊C4—31no—
149C2×(C2×D3)⋊C4—31no—
150C2×(C2×D3)⋊C4—32no—
151C2×(C2×D3)⋊C4—32no—
152C2×(C2×D3)⋊C4C2×D312yes—
153C2×(C2×D3)⋊C4C2×D312yes—
154C2×(C2×D3)⋊C4C2×D312yes—
155#926—38no—
156C2×C4⋊Dic3—31no—
157C2×C4⋊Dic3—32no—
158C2×C4⋊Dic3—32no—
159C2×C4⋊Dic3—31no—
160C2×C4⋊Dic3—32no—
161C2×C4⋊Dic3—31no—
162C2×C4⋊Dic3—31no—
163C2×C4⋊Dic3—61no—
164C2×C4⋊Dic3—62no—
165C2×C4⋊Dic3C2×D311yescharacteristic
166C2×Dic3⋊C4—31no—
167C2×Dic3⋊C4—31no—
168C2×Dic3⋊C4—32no—
169C2×Dic3⋊C4C2×D312yes—
170C2×C4×Dic3—31no—
171C2×C4×Dic3—32no—
172C2×C4×Dic3—32no—
173C2×C4×Dic3—31no—
174C2×C4×Dic3—61no—
175C2×C4×Dic3—62no—
176C2×C4×Dic3C2×D311yescharacteristic
177#898—316no—
178#897—316no—
179#893—38no—
180#888—38no—
181#886—316no—
182#885—316no—
183#885—316no—
184#883—316no—
185#879—316no—
186#878—316no—
187#872—38no—
188#869—38no—
189C23×C32C2411yescharacteristic
190C22×C3×D3—22no—
191C22×C3×D3—24no—
192C22×C3×D3—24no—
193C22×C3×D3—22no—
194C22×C3×D3—22no—
195C22×C3×D3—24no—
196C22×C3×D3C2414yes—
197C22×C3×D3C2412yes—
198C32×Q8—28no—
199C2×C32×C4—24no—
200C2×C32×C4#4114yes—
201C2×C32×C4C2414yes—
202C2×C32×C4C2412yes—
203C2×C3⋊Dic3—22no—
204C2×C3⋊Dic3—22no—
205C2×C3⋊Dic3—24no—
206C2×C3⋊Dic3C2412yes—
207C2×C3⋊Dic3C2412yes—
208C2×C3⋊Dic3C2414yes—
209C2×C3×Dic3—22no—
210C2×C3×Dic3—24no—
211C2×C3×Dic3—22no—
212C2×C3×Dic3—22no—
213C2×C3×Dic3C2412yes—
214C2×C3×Dic3C2412yes—
215C2×C3×Dic3C2412yes—
216C2×C3×Dic3C2414yes—
217C3×D12—28no—
218C3×C4×D3—28no—
219#627—48no—
220#625—48no—
221D3×Dic3—48no—
222#542—916no—
223C2×C4⋊Q8—91no—
224C2×#126—92no—
225C2×#124—31no—
226C2×#124—92no—
227C2×#123—92no—
228C2×C22⋊Q8—31no—
229C2×C22⋊Q8—92no—
230C2×#121—91no—
231C2×C4×Q8—91no—
232C2×C4×D4—91no—
233C2×#117—91no—
234C24×C3—32no—
235C24×C3—31no—
236C23×D3C22×D312yes—
237C23×D3C22×D311yescharacteristic
238C2×C3×Q8—28no—
239C2×C3×Q8—24no—
240C2×C3×Q8—24no—
241C2×C3×Q8—24no—
242C2×C3×Q8C22×D314yes—
243C2×C3×Q8C22×D314yes—
244C2×C3×D4—34no—
245C2×C3×D4—64no—
246C22×C3×C4—22no—
247C22×C3×C4—21no—
248C22×C3×C4—31no—
249C22×C3×C4—31no—
250C22×C3×C4—32no—
251C22×C3×C4—31no—
252C22×C3×C4—34no—
253C22×C3×C4—64no—
254C22×C3×C4C22×D312yes—
255C22×C3×C4C22×D312yes—
256C22×C3×C4C22×D311yescharacteristic
257C22×C3×C4C22×D311yescharacteristic
258C2×#67—38no—
259C2×#67—38no—
260C2×#67—124no—
261C2×#67—124no—
262C22×Dic3—31no—
263C22×Dic3—31no—
264C22×Dic3—32no—
265C22×Dic3—31no—
266C22×Dic3—32no—
267C22×Dic3—31no—
268C22×Dic3—38no—
269C22×Dic3—61no—
270C22×Dic3—61no—
271C22×Dic3—62no—
272C22×Dic3—124no—
273C22×Dic3C22×D311yescharacteristic
274C22×Dic3C22×D311yescharacteristic
275C22×Dic3C22×D311yescharacteristic
276C22×Dic3C22×D312yes—
277C2×D12—24no—
278C2×D12C22×D314yes—
279C2×C4×D3—24no—
280C2×C4×D3—38no—
281C2×C4×D3—124no—
282C2×C4×D3C22×D314yes—
283C2×Dic6—38no—
284C2×Dic6—38no—
285C2×Dic6—124no—
286C2×Dic6—124no—
287C3×C4⋊C4—34no—
288C3×C4⋊C4—38no—
289C3×C22⋊C4—38no—
290C3×C22⋊C4—38no—
291C3×C22⋊C4—38no—
292C3×C42—34no—
293#217—38no—
294#217—38no—
295#217—34no—
296#217—34no—
297(C2×D3)⋊C4—34no—
298(C2×D3)⋊C4—34no—
299(C2×D3)⋊C4—38no—
300(C2×D3)⋊C4—38no—
301(C2×D3)⋊C4C22×D318yes—
302(C2×D3)⋊C4C22×D318yes—
303(C2×D3)⋊C4C22×D318yes—
304C4⋊Dic3—34no—
305C4⋊Dic3—38no—
306C4⋊Dic3—38no—
307C4⋊Dic3—34no—
308C4⋊Dic3—38no—
309C4⋊Dic3—34no—
310C4⋊Dic3—34no—
311C4⋊Dic3—64no—
312C4⋊Dic3—68no—
313C4⋊Dic3C22×D314yes—
314Dic3⋊C4—34no—
315Dic3⋊C4—34no—
316Dic3⋊C4—38no—
317Dic3⋊C4C22×D318yes—
318C4×Dic3—34no—
319C4×Dic3—38no—
320C4×Dic3—38no—
321C4×Dic3—34no—
322C4×Dic3—64no—
323C4×Dic3—68no—
324C4×Dic3C22×D314yes—
325C22×C32C2×#4112yes—
326C22×C32H(5,𝔽2)12yes—
327C22×C322−1+412yes—
328C22×C32C2511yescharacteristic
329C2×C3×D3—22no—
330C2×C3×D3—24no—
331C2×C3×D3—24no—
332C2×C3×D3—22no—
333C2×C3×D3—22no—
334C2×C3×D3—24no—
335C2×C3×D3—44no—
336C2×C3×D3—48no—
337C32×C4—24no—
338C32×C4C2×#4114yes—
339C3⋊Dic3—22no—
340C3⋊Dic3—22no—
341C3⋊Dic3—24no—
342C3×Dic3—22no—
343C3×Dic3—24no—
344C3×Dic3—22no—
345C3×Dic3—22no—
346C22×Q8—92no—
347C22×Q8D3211yescharacteristic
348C22×D4—31no—
349C22×D4—92no—
350C23×C4—31no—
351C23×C4—92no—
352C4⋊Q8—98no—
353#126—916no—
354#124—38no—
355#124—916no—
356#123—916no—
357C22⋊Q8—38no—
358C22⋊Q8—916no—
359#121—98no—
360C4×Q8—98no—
361C4×D4—98no—
362#117—98no—
363C2×C4⋊C4—31no—
364C2×C4⋊C4—32no—
365C2×C4⋊C4—91no—
366C2×C4⋊C4—91no—
367C2×C4⋊C4—92no—
368C2×C4⋊C4—91no—
369C2×C4⋊C4—92no—
370C2×C22⋊C4—32no—
371C2×C22⋊C4—32no—
372C2×C22⋊C4—32no—
373C2×C22⋊C4—91no—
374C2×C22⋊C4—91no—
375C2×C22⋊C4—92no—
376C2×C22⋊C4—92no—
377C2×C42—31no—
378C2×C42—91no—
379C2×C42—92no—
380C23×C3—21no—
381C23×C3—34no—
382C23×C3—32no—
383C23×C3—62no—
384C23×C3—64no—
385C23×C3—64no—
386C23×C3—64no—
387C23×C3—62no—
388C23×C3—62no—
389C23×C3C23×D311yescharacteristic
390C23×C3C23×D311yescharacteristic
391C22×D3—22no—
392C22×D3—24no—
393C22×D3—22no—
394C22×D3—24no—
395C22×D3—22no—
396C22×D3—24no—
397C22×D3C23×D314yes—
398C22×D3C23×D312yes—
399C3×Q8—216no—
400C3×Q8—28no—
401C3×Q8—28no—
402C3×D4—68no—
403C2×C3×C4—28no—
404C2×C3×C4—24no—
405C2×C3×C4—24no—
406C2×C3×C4—24no—
407C2×C3×C4—22no—
408C2×C3×C4—24no—
409C2×C3×C4—32no—
410C2×C3×C4—32no—
411C2×C3×C4—34no—
412C2×C3×C4—32no—
413C2×C3×C4—62no—
414C2×C3×C4—62no—
415C2×C3×C4—62no—
416C2×C3×C4—64no—
417C2×C3×C4—68no—
418C2×C3×C4#23714yes—
419C2×C3×C4#23714yes—
420C2×C3×C4C23×D314yes—
421C2×C3×C4C23×D314yes—
422C2×C3×C4C23×D312yes—
423C2×C3×C4C23×D312yes—
424#67—128no—
425#67—128no—
426C2×Dic3—22no—
427C2×Dic3—22no—
428C2×Dic3—24no—
429C2×Dic3—22no—
430C2×Dic3—32no—
431C2×Dic3—32no—
432C2×Dic3—34no—
433C2×Dic3—32no—
434C2×Dic3—34no—
435C2×Dic3—32no—
436C2×Dic3—62no—
437C2×Dic3—62no—
438C2×Dic3—64no—
439C2×Dic3—64no—
440C2×Dic3—62no—
441C2×Dic3—64no—
442C2×Dic3—64no—
443C2×Dic3—62no—
444C2×Dic3—62no—
445C2×Dic3—62no—
446C2×Dic3—122no—
447C2×Dic3—124no—
448C2×Dic3—128no—
449C2×Dic3C23×D312yes—
450C2×Dic3C23×D312yes—
451C2×Dic3C23×D312yes—
452C2×Dic3C23×D314yes—
453D12—28no—
454C4×D3—28no—
455C4×D3—128no—
456Dic6—128no—
457Dic6—128no—
458C2×C32#54214yescomplemented
459C2×C32C22×#4111yescharacteristic
460C2×C32C2×H(5,𝔽2)11yescharacteristic
461C2×C32C2×2−1+411yescharacteristic
462C3×D3—44no—
463C3×D3—42no—
464C24—31no—
465C24—32no—
466C2×Q8—24no—
467C2×Q8—98no—
468C2×Q8—364no—
469C2×Q8C2×D3214yes—
470C2×D4—34no—
471C2×D4—64no—
472C2×D4—98no—
473C2×D4—364no—
474C22×C4—31no—
475C22×C4—31no—
476C22×C4—32no—
477C22×C4—31no—
478C22×C4—34no—
479C22×C4—64no—
480C22×C4—98no—
481C22×C4—91no—
482C22×C4—91no—
483C22×C4—92no—
484C22×C4—364no—
485C22×C4C2×D3212yes—
486C22×C4C2×D3211yescharacteristic
487C4⋊C4—34no—
488C4⋊C4—38no—
489C4⋊C4—94no—
490C4⋊C4—94no—
491C4⋊C4—98no—
492C4⋊C4—94no—
493C4⋊C4—98no—
494C22⋊C4—38no—
495C22⋊C4—38no—
496C22⋊C4—38no—
497C22⋊C4—94no—
498C22⋊C4—94no—
499C22⋊C4—98no—
500C22⋊C4—98no—
501C42—34no—
502C42—94no—
503C42—98no—
504C22×C3—22no—
505C22×C3—22no—
506C22×C3—22no—
507C22×C3—21no—
508C22×C3—62no—
509C22×C3—64no—
510C22×C3—64no—
511C22×C3—64no—
512C22×C3—62no—
513C22×C3—62no—
514C22×C3—128no—
515C22×C3—124no—
516C22×C3C2×#23712yes—
517C22×C3C2×#23712yes—
518C22×C3#100712yes—
519C22×C3#100912yes—
520C22×C3#100912yes—
521C22×C3#101012yes—
522C22×C3C24×D311yescharacteristic
523C22×C3C24×D311yescharacteristic
524C2×D3—22no—
525C2×D3—24no—
526C2×D3—22no—
527C2×D3—24no—
528C2×D3—22no—
529C2×D3—24no—
530C2×D3—44no—
531C2×D3—48no—
532C3×C4—28no—
533C3×C4—24no—
534C3×C4—24no—
535C3×C4—24no—
536C3×C4—62no—
537C3×C4—62no—
538C3×C4—62no—
539C3×C4—64no—
540C3×C4C2×#23714yes—
541C3×C4C2×#23714yes—
542Dic3—22no—
543Dic3—22no—
544Dic3—24no—
545Dic3—22no—
546Dic3—64no—
547Dic3—62no—
548Dic3—64no—
549Dic3—64no—
550Dic3—62no—
551Dic3—62no—
552Dic3—62no—
553Dic3—122no—
554Dic3—124no—
555C32C2×#54211yescharacteristic, complemented, Sylow
556C23—32no—
557C23—34no—
558C23—62no—
559C23—64no—
560C23—64no—
561C23—62no—
562C23—62no—
563C23—64no—
564C23C22×D3211yescharacteristic
565Q8—28no—
566Q8—368no—
567D4—68no—
568D4—368no—
569C2×C4—24no—
570C2×C4—32no—
571C2×C4—32no—
572C2×C4—34no—
573C2×C4—32no—
574C2×C4—62no—
575C2×C4—64no—
576C2×C4—62no—
577C2×C4—62no—
578C2×C4—68no—
579C2×C4—92no—
580C2×C4—92no—
581C2×C4—94no—
582C2×C4—182no—
583C2×C4—182no—
584C2×C4—184no—
585C2×C4—368no—
586C2×C4#380514yes—
587C2×C4C22×D3214yes—
588C2×C4C22×D3212yes—
589C2×C3—24no—
590C2×C3—21no—
591C2×C3—21no—
592C2×C3—21no—
593C2×C3—122no—
594C2×C3—124no—
595C2×C3#564314yescomplemented
596C2×C3#568214yescomplemented
597C2×C3C22×#23711yescharacteristic
598C2×C3C22×#23711yescharacteristic
599C2×C3C2×#100711yescharacteristic
600C2×C3C2×#100911yescharacteristic
601C2×C3C2×#100911yescharacteristic
602C2×C3C2×#101011yescharacteristic
603D3—44no—
604D3—42no—
605C22—62no—
606C22—64no—
607C22—64no—
608C22—62no—
609C22—62no—
610C22—64no—
611C22—128no—
612C22—124no—
613C22#6431512yes—
614C22#6432012yes—
615C22C2×#380512yes—
616C22C23×D3211yescharacteristic
617C4—24no—
618C4—62no—
619C4—64no—
620C4—62no—
621C4—62no—
622C4—182no—
623C4—182no—
624C4—184no—
625C4C2×#380514yes—
626C3—21no—
627C3C2×#564311yescharacteristic, complemented
628C3C2×#568211yescharacteristic, complemented
629C2—124no—
630C2—122no—
631C2#1059539614yesdirect product factor
632C2C2×#6431511yescharacteristic
633C2C2×#6432011yescharacteristic
634C2C22×#380511yescharacteristic
subgroupG/H
centerC23C22×D32
commutator, cosocleC22×C32C25
FrattiniC22C23×D32
FittingC22×C32×Q8C22
socleC23×C32C24
prime radicalC2×#63908C2
hypercenterC22×Q8D32
hypocenterC32C2×#542
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C23 ◁ C22×Q8

Complements

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

NH ≅ G/Ntype
1. C2×Q8×C3⋊Dic3C2semidirect
2. C2×C3×#947C2semidirect
3. C2×C3×#946C2semidirect
4. #10595396C2direct (N × H)
5. C2×#63918C2semidirect
6. C2×#63915C2semidirect
8. C2×#63898C2semidirect
9. C2×#63893C2semidirect
10. C2×#63891C2semidirect
11. C2×#63862C2semidirect
12. C2×#63855C2semidirect
21. Q8×C3⋊Dic3C22semidirect
26. C3×#947C22semidirect
27. C3×#946C22semidirect
41. #63918C22semidirect
42. #63915C22semidirect
44. #63898C22semidirect
45. #63893C22semidirect
46. #63891C22semidirect
47. #63862C22semidirect
48. #63855C22semidirect
51. C2×#947D3semidirect
52. C2×#946D3semidirect
140. #947C2×D3semidirect
141. #946C2×D3semidirect
458. C2×C32#542semidirect
555. C32C2×#542semidirect
595. C2×C3#5643semidirect
596. C2×C3#5682semidirect
627. C3C2×#5643semidirect
628. C3C2×#5682semidirect
631. C2#10595396direct (N × H)

Maximal subgroups

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

subgroupindex
C2×Q8×C3⋊Dic32
C2×C3×#9472
C2×C3×#9462
#105953962
C2×#639182
C2×#639152
C2×#639082
C2×#638982
C2×#638932
C2×#638912
C2×#638622
C2×#638552
C2×#56823
C2×#56433