Finite Group Databasebeta

← C2×#10594092 #11902949

Subgroups — C2×#10594092 #11902949

Order 1152.

2779 conjugacy classes of subgroups.

The subgroup lattice has 948 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#64088C211yesmaximal, characteristic, complemented
2C2×C3×#885C211yesmaximal, characteristic, complemented
3C2×C3×D3×C22⋊C4C211yesmaximal, characteristic, complemented
4C2×#63976C211yesmaximal, characteristic
5C2×#63969C211yesmaximal, characteristic, complemented
6C2×D3×#217C211yesmaximal, characteristic, complemented
7C2×#63956C211yesmaximal, characteristic, complemented
8C2×#63905C211yesmaximal, characteristic, complemented
9C2×#63902C211yesmaximal, characteristic, complemented
10C2×#63891C211yesmaximal, characteristic, complemented
11C2×#63887C211yesmaximal, characteristic, complemented
12C2×#63879C211yesmaximal, characteristic, complemented
13C2×#63877C211yesmaximal, characteristic, complemented
14C2×#63856C211yesmaximal, characteristic, complemented
15C2×#63855C211yesmaximal, characteristic, complemented
16#10594092C2116yesmaximal, direct product factor
17C2×#5679—31nomaximal
18C2×#5495—31nomaximal
19C24×C3×D3C2211yescharacteristic
20C22×C3×#67C2211yescharacteristic
21C22×C3×C4×D3C2211yescharacteristic
22C22×C3×C4×D3C2211yescharacteristic
23C22×C3×Dic6C2211yescharacteristic, complemented
24C22×#625C2211yescharacteristic
25C22×#625C2211yescharacteristic
26C22×D3×Dic3C2211yescharacteristic
27C22×D3×Dic3C2211yescharacteristic
28C22×D3×Dic3C2211yescharacteristic, complemented
29C2×C32×C22⋊C4C2211yescharacteristic
30C2×#3757C2211yescharacteristic
31C2×#3757C2211yescharacteristic
32C2×C4⋊(C3⋊Dic3)C2211yescharacteristic, complemented
33C2×#3750C2211yescharacteristic, complemented
34C2×#3750C2211yescharacteristic, complemented
35C2×C4×C3⋊Dic3C2211yescharacteristic, complemented
36#64088C2218yescomplemented
37C2×C3×#217C2211yescharacteristic
38C2×C3×#217C2211yescharacteristic
39C2×C3×(C2×D3)⋊C4C2211yescharacteristic
40C2×C3×(C2×D3)⋊C4C2211yescharacteristic
41C2×C3×(C2×D3)⋊C4C2211yescharacteristic, complemented
42C2×C3×(C2×D3)⋊C4C2211yescharacteristic, complemented
43C2×C3×C4×Dic3C2211yescharacteristic, complemented
44C3×#885C2218yescomplemented
45C3×D3×C22⋊C4C2218yescomplemented
46#63976C2218yes—
47#63969C2218yescomplemented
48D3×#217C2218yescomplemented
49C2×#3724C2211yescharacteristic, complemented
50C2×#3724C2211yescharacteristic, complemented
51C2×Dic3⋊Dic3C2211yescharacteristic, complemented
52C2×Dic3⋊Dic3C2211yescharacteristic, complemented
53C2×Dic3⋊Dic3C2211yescharacteristic, complemented
54C2×(C2×D3)⋊Dic3C2211yescharacteristic
55C2×(C2×D3)⋊Dic3C2211yescharacteristic
56C2×(C2×D3)⋊Dic3C2211yescharacteristic
57C2×(C2×D3)⋊Dic3C2211yescharacteristic
58C2×(C2×D3)⋊Dic3C2211yescharacteristic, complemented
59#63956C2218yescomplemented
60C2×Dic32C2211yescharacteristic, complemented
61#63905C2218yescomplemented
62#63902C2218yescomplemented
63#63891C2218yescomplemented
64#63887C2218yescomplemented
65#63879C2218yescomplemented
66#63877C2218yescomplemented
67#63856C2218yescomplemented
68#63855C2218yescomplemented
69C2×C3×#124—31no—
70C22×C3×C22⋊C4—31no—
71C2×#953—31no—
72C22×#217—31no—
73C2×#946—31no—
74C2×#946—31no—
75C2×#937—31no—
76C2×#935—31no—
77C2×#929—31no—
78C2×C4×#67—31no—
79C2×#926—31no—
80C2×#924—31no—
81#5679—316no—
82#5495—316no—
83C2×#886—31no—
84C2×#885D311yescharacteristic, complemented
85C2×#883—31no—
86C2×#883—31no—
87C2×#883—31no—
88C2×#67⋊C4—31no—
89C2×#67⋊C4—31no—
90C2×#67⋊C4—31no—
91C2×D3×C22⋊C4—31no—
92C2×D3×C22⋊C4D311yescharacteristic, complemented
93C2×#879—31no—
94C2×#879—31no—
95C2×#879—31no—
96C2×#879—31no—
97C2×#879—61no—
98C2×#878—31no—
99C2×#877—31no—
100C2×#872—31no—
101C2×#872—31no—
102C24×C32C2311yescharacteristic
103C23×C3×D3—24no—
104C23×C3×D3—24no—
105C23×C3×D3—42no—
106C23×C3×D3C2311yescharacteristic
107C23×C3×D3C2314yes—
108C23×C3×D3C2311yescharacteristic
109C23×C3×D3C2311yescharacteristic
110C22×C32×C4C2311yescharacteristic
111C22×C32×C4C2311yescharacteristic
112C22×C3⋊Dic3C2311yescharacteristic
113C22×C3⋊Dic3C2311yescharacteristic
114C22×C3⋊Dic3C2311yescharacteristic
115C22×C3⋊Dic3C2311yescharacteristic
116C2×C3×#67—42no—
117C2×C3×#67C2314yes—
118C22×C3×Dic3C2311yescharacteristic
119C22×C3×Dic3C2311yescharacteristic
120C22×C3×Dic3C2311yescharacteristic
121C22×C3×Dic3C2311yescharacteristic
122C22×C3×Dic3C2311yescharacteristic
123C2×C3×C4×D3—24no—
124C2×C3×C4×D3—42no—
125C2×C3×C4×D3C2314yes—
126C2×C3×C4×D3C2314yes—
127C2×C3×Dic6—42no—
128C2×C3×Dic6C2314yescomplemented
129C2×#625—24no—
130C2×#625—24no—
131C2×#625C2314yes—
132C2×#625C2314yes—
133C2×D3×Dic3—24no—
134C2×D3×Dic3—42no—
135C2×D3×Dic3—42no—
136C2×D3×Dic3C2314yes—
137C2×D3×Dic3C2314yes—
138C2×D3×Dic3C2314yescomplemented
139C32×C22⋊C4C2314yes—
140#3757C2314yes—
141#3757C2314yes—
142C4⋊(C3⋊Dic3)C2314yescomplemented
143#3750C2314yescomplemented
144#3750C2314yescomplemented
145C4×C3⋊Dic3C2314yescomplemented
146C3×#217C2314yes—
147C3×#217C2314yes—
148C3×(C2×D3)⋊C4C2314yes—
149C3×(C2×D3)⋊C4C2314yes—
150C3×(C2×D3)⋊C4C2314yescomplemented
151C3×(C2×D3)⋊C4C2314yescomplemented
152C3×C4×Dic3C2314yescomplemented
153#3724C2314yescomplemented
154#3724C2314yescomplemented
155Dic3⋊Dic3C2314yescomplemented
156Dic3⋊Dic3C2314yescomplemented
157Dic3⋊Dic3C2314yescomplemented
158(C2×D3)⋊Dic3C2314yes—
159(C2×D3)⋊Dic3C2314yes—
160(C2×D3)⋊Dic3C2314yes—
161(C2×D3)⋊Dic3C2314yes—
162(C2×D3)⋊Dic3C2314yescomplemented
163Dic32C2314yescomplemented
164C2×#551—91noSylow
165C25×C3—31no—
166C24×D3C2×D311yescharacteristic
167C22×C3×Q8—31no—
168C22×C3×D4—31no—
169C23×C3×C4—31no—
170C23×C3×C4—31no—
171C22×#67—31no—
172C22×#67—31no—
173C22×#67—31no—
174C22×#67—31no—
175C22×#67C2×D311yescharacteristic
176C23×Dic3—31no—
177C23×Dic3—31no—
178C23×Dic3—31no—
179C22×C4×D3—31no—
180C22×C4×D3—31no—
181C22×C4×D3—31no—
182C22×C4×D3C2×D311yescharacteristic
183C22×C4×D3C2×D311yescharacteristic
184C22×Dic6C2×D311yescharacteristic, complemented
185C3×#124—38no—
186C2×C3×C22⋊C4—21no—
187C2×C3×C22⋊C4—31no—
188C2×C3×C22⋊C4—31no—
189C2×C3×C22⋊C4—31no—
190C2×C3×C22⋊C4—31no—
191C2×C3×C22⋊C4—31no—
192C2×C3×C22⋊C4—31no—
193C2×C3×C22⋊C4—38no—
194C2×C3×C22⋊C4C2×D311yescharacteristic
195C2×C3×C22⋊C4C2×D311yescharacteristic
196C2×C3×C42—31no—
197#953—38no—
198C2×#217—31no—
199C2×#217—31no—
200C2×#217—31no—
201C2×#217—31no—
202C2×#217—31no—
203C2×#217—31no—
204C2×#217—31no—
205C2×#217—31no—
206C2×#217—31no—
207C2×#217—38no—
208C2×#217—61no—
209C2×#217—61no—
210C2×#217C2×D311yescharacteristic
211C2×#217C2×D311yescharacteristic
212#946—38no—
213#946—38no—
214#937—38no—
215#935—38no—
216#929—38no—
217C4×#67—38no—
218C2×(C2×D3)⋊C4—31no—
219C2×(C2×D3)⋊C4—31no—
220C2×(C2×D3)⋊C4—31no—
221C2×(C2×D3)⋊C4—31no—
222C2×(C2×D3)⋊C4—31no—
223C2×(C2×D3)⋊C4C2×D311yescharacteristic
224C2×(C2×D3)⋊C4C2×D311yescharacteristic
225C2×(C2×D3)⋊C4C2×D311yescharacteristic, complemented
226C2×(C2×D3)⋊C4C2×D311yescharacteristic, complemented
227#926—38no—
228C2×C4⋊Dic3—31no—
229C2×C4⋊Dic3—31no—
230C2×C4⋊Dic3—31no—
231C2×C4⋊Dic3—31no—
232C2×C4⋊Dic3—31no—
233C2×C4⋊Dic3—61no—
234#924—38no—
235C2×Dic3⋊C4—31no—
236C2×Dic3⋊C4—31no—
237C2×Dic3⋊C4—31no—
238C2×Dic3⋊C4—31no—
239C2×Dic3⋊C4—31no—
240C2×Dic3⋊C4—31no—
241C2×Dic3⋊C4—31no—
242C2×Dic3⋊C4—31no—
243C2×Dic3⋊C4—31no—
244C2×Dic3⋊C4—31no—
245C2×Dic3⋊C4—31no—
246C2×Dic3⋊C4—61no—
247C2×Dic3⋊C4—61no—
248C2×C4×Dic3—31no—
249C2×C4×Dic3—31no—
250C2×C4×Dic3—31no—
251C2×C4×Dic3—31no—
252C2×C4×Dic3—61no—
253C2×C4×Dic3C2×D311yescharacteristic, complemented
254#886—38no—
255#885C2×D318yescomplemented
256#883—38no—
257#883—38no—
258#883—38no—
259#67⋊C4—38no—
260#67⋊C4—38no—
261#67⋊C4—38no—
262D3×C22⋊C4—38no—
263D3×C22⋊C4C2×D318yescomplemented
264#879—38no—
265#879—38no—
266#879—38no—
267#879—38no—
268#879—68no—
269#878—38no—
270#877—38no—
271#872—38no—
272#872—38no—
273C23×C32—22no—
274C23×C32—22no—
275C23×C32—22no—
276C23×C32C2412yes—
277C23×C32C2411yescharacteristic
278C22×C3×D3—22no—
279C22×C3×D3—22no—
280C22×C3×D3—22no—
281C22×C3×D3—22no—
282C22×C3×D3—22no—
283C22×C3×D3—22no—
284C22×C3×D3—22no—
285C22×C3×D3—28no—
286C22×C3×D3—28no—
287C22×C3×D3—44no—
288C22×C3×D3—416no—
289C22×C3×D3#4114yes—
290C22×C3×D3#4114yes—
291C22×C3×D3C2412yes—
292C22×C3×D3C2412yes—
293C22×C3×D3C2412yes—
294C2×C32×C4—22no—
295C2×C32×C4—22no—
296C2×C32×C4C2412yes—
297C2×C32×C4C2412yes—
298C2×C3⋊Dic3—22no—
299C2×C3⋊Dic3—22no—
300C2×C3⋊Dic3—22no—
301C2×C3⋊Dic3—22no—
302C2×C3⋊Dic3C2412yes—
303C2×C3⋊Dic3C2412yes—
304C2×C3⋊Dic3C2412yes—
305C2×C3⋊Dic3C2412yes—
306C3×#67—44no—
307C2×C3×Dic3—22no—
308C2×C3×Dic3—22no—
309C2×C3×Dic3—22no—
310C2×C3×Dic3—22no—
311C2×C3×Dic3—22no—
312C2×C3×Dic3C2412yes—
313C2×C3×Dic3C2412yes—
314C2×C3×Dic3C2412yes—
315C2×C3×Dic3C2412yes—
316C2×C3×Dic3C2412yes—
317C3×C4×D3—28no—
318C3×C4×D3—44no—
319C3×Dic6—44no—
320#625—28no—
321#625—28no—
322D3×Dic3—28no—
323D3×Dic3—44no—
324D3×Dic3—44no—
325#551—916no—
326C2×#126—91no—
327C2×#126—91no—
328C2×#124—31no—
329C2×#123—91no—
330C2×#123—91no—
331C2×#123—91no—
332C2×C22⋊Q8—91no—
333C2×C22⋊Q8—91no—
334C2×#120—91no—
335C2×C4×D4—91no—
336C2×C4×D4—91no—
337C2×#117—91no—
338C2×#117—91no—
339C22×C22⋊C4—31no—
340C22×C22⋊C4—91no—
341C24×C3—21no—
342C24×C3—31no—
343C24×C3—31no—
344C24×C3—31no—
345C24×C3—34no—
346C24×C3—64no—
347C24×C3—64no—
348C24×C3—122no—
349C24×C3C22×D311yescharacteristic
350C24×C3C22×D311yescharacteristic
351C23×D3—24no—
352C23×D3—24no—
353C23×D3—42no—
354C23×D3C22×D311yescharacteristic
355C23×D3C22×D314yes—
356C23×D3C22×D311yescharacteristic
357C23×D3C22×D311yescharacteristic
358C2×C3×Q8—34no—
359C2×C3×Q8—122no—
360C2×C3×D4—34no—
361C2×C3×D4—122no—
362C22×C3×C4—21no—
363C22×C3×C4—21no—
364C22×C3×C4—31no—
365C22×C3×C4—31no—
366C22×C3×C4—31no—
367C22×C3×C4—31no—
368C22×C3×C4—31no—
369C22×C3×C4—34no—
370C22×C3×C4—34no—
371C22×C3×C4—64no—
372C22×C3×C4—122no—
373C22×C3×C4C22×D311yescharacteristic
374C22×C3×C4C22×D311yescharacteristic
375C22×C3×C4C22×D311yescharacteristic
376C22×C3×C4C22×D311yescharacteristic
377C2×#67—34no—
378C2×#67—34no—
379C2×#67—34no—
380C2×#67—34no—
381C2×#67—42no—
382C2×#67—64no—
383C2×#67—64no—
384C2×#67—64no—
385C2×#67—64no—
386C2×#67C22×D314yes—
387C22×Dic3—31no—
388C22×Dic3—31no—
389C22×Dic3—31no—
390C22×Dic3—31no—
391C22×Dic3—31no—
392C22×Dic3—31no—
393C22×Dic3—31no—
394C22×Dic3—31no—
395C22×Dic3—34no—
396C22×Dic3—34no—
397C22×Dic3—34no—
398C22×Dic3—61no—
399C22×Dic3—61no—
400C22×Dic3—61no—
401C22×Dic3—61no—
402C22×Dic3—64no—
403C22×Dic3—122no—
404C22×Dic3—122no—
405C22×Dic3C22×D311yescharacteristic
406C22×Dic3C22×D311yescharacteristic
407C22×Dic3C22×D311yescharacteristic
408C22×Dic3C22×D311yescharacteristic
409C22×Dic3C22×D311yescharacteristic
410C2×C4×D3—24no—
411C2×C4×D3—34no—
412C2×C4×D3—34no—
413C2×C4×D3—34no—
414C2×C4×D3—42no—
415C2×C4×D3—64no—
416C2×C4×D3—122no—
417C2×C4×D3—122no—
418C2×C4×D3C22×D314yes—
419C2×C4×D3C22×D314yes—
420C2×Dic6—42no—
421C2×Dic6C22×D314yescomplemented
422C3×C22⋊C4—24no—
423C3×C22⋊C4—34no—
424C3×C22⋊C4—34no—
425C3×C22⋊C4—34no—
426C3×C22⋊C4—34no—
427C3×C22⋊C4—34no—
428C3×C22⋊C4—34no—
429C3×C22⋊C4C22×D314yes—
430C3×C22⋊C4C22×D314yes—
431C3×C42—34no—
432#217—34no—
433#217—34no—
434#217—34no—
435#217—34no—
436#217—34no—
437#217—34no—
438#217—34no—
439#217—34no—
440#217—34no—
441#217—64no—
442#217—64no—
443#217C22×D314yes—
444#217C22×D314yes—
445(C2×D3)⋊C4—34no—
446(C2×D3)⋊C4—34no—
447(C2×D3)⋊C4—34no—
448(C2×D3)⋊C4—34no—
449(C2×D3)⋊C4—34no—
450(C2×D3)⋊C4C22×D314yes—
451(C2×D3)⋊C4C22×D314yes—
452(C2×D3)⋊C4C22×D314yescomplemented
453(C2×D3)⋊C4C22×D314yescomplemented
454C4⋊Dic3—34no—
455C4⋊Dic3—34no—
456C4⋊Dic3—34no—
457C4⋊Dic3—34no—
458C4⋊Dic3—34no—
459C4⋊Dic3—64no—
460Dic3⋊C4—34no—
461Dic3⋊C4—34no—
462Dic3⋊C4—34no—
463Dic3⋊C4—34no—
464Dic3⋊C4—34no—
465Dic3⋊C4—34no—
466Dic3⋊C4—34no—
467Dic3⋊C4—34no—
468Dic3⋊C4—34no—
469Dic3⋊C4—34no—
470Dic3⋊C4—34no—
471Dic3⋊C4—64no—
472Dic3⋊C4—64no—
473C4×Dic3—34no—
474C4×Dic3—34no—
475C4×Dic3—34no—
476C4×Dic3—34no—
477C4×Dic3—64no—
478C4×Dic3C22×D314yescomplemented
479C22×C32—22no—
480C22×C32—22no—
481C22×C32—22no—
482C22×C32—44no—
483C22×C32C2×#4112yes—
484C22×C32C2×#4112yes—
485C22×C32H(5,𝔽2)12yes—
486C22×C32C2511yescharacteristic
487C2×C3×D3—28no—
488C2×C3×D3—28no—
489C2×C3×D3—22no—
490C2×C3×D3—22no—
491C2×C3×D3—22no—
492C2×C3×D3—22no—
493C2×C3×D3—22no—
494C2×C3×D3—22no—
495C2×C3×D3—22no—
496C2×C3×D3—416no—
497C2×C3×D3—44no—
498C2×C3×D3C2×#4114yes—
499C2×C3×D3C2×#4114yes—
500C32×C4—22no—
501C32×C4—22no—
502C3⋊Dic3—22no—
503C3⋊Dic3—22no—
504C3⋊Dic3—22no—
505C3⋊Dic3—22no—
506C3×Dic3—22no—
507C3×Dic3—22no—
508C3×Dic3—22no—
509C3×Dic3—22no—
510C3×Dic3—22no—
511C25—31no—
512C22×Q8—31no—
513C22×D4—31no—
514C22×D4—91no—
515C22×D4—91no—
516C23×C4—31no—
517C23×C4—31no—
518C23×C4—91no—
519C23×C4—91no—
520C23×C4—91no—
521#126—98no—
522#126—98no—
523#124—38no—
524#123—98no—
525#123—98no—
526#123—98no—
527C22⋊Q8—98no—
528C22⋊Q8—98no—
529#120—98no—
530C4×D4—98no—
531C4×D4—98no—
532#117—98no—
533#117—98no—
534C2×C4⋊C4—91no—
535C2×C4⋊C4—91no—
536C2×C4⋊C4—91no—
537C2×C4⋊C4—91no—
538C2×C4⋊C4—91no—
539C2×C4⋊C4—91no—
540C2×C4⋊C4—91no—
541C2×C4⋊C4—91no—
542C2×C22⋊C4—31no—
543C2×C22⋊C4—31no—
544C2×C22⋊C4—31no—
545C2×C22⋊C4—31no—
546C2×C22⋊C4—31no—
547C2×C22⋊C4—31no—
548C2×C22⋊C4—38no—
549C2×C22⋊C4—98no—
550C2×C22⋊C4—91no—
551C2×C22⋊C4—91no—
552C2×C22⋊C4—91no—
553C2×C22⋊C4—91no—
554C2×C22⋊C4—91no—
555C2×C22⋊C4—91no—
556C2×C22⋊C4—91no—
557C2×C22⋊C4D3211yescharacteristic
558C2×C42—31no—
559C2×C42—91no—
560C2×C42—91no—
561C23×C3—22no—
562C23×C3—22no—
563C23×C3—22no—
564C23×C3—22no—
565C23×C3—22no—
566C23×C3—22no—
567C23×C3—22no—
568C23×C3—21no—
569C23×C3—34no—
570C23×C3—34no—
571C23×C3—32no—
572C23×C3—32no—
573C23×C3—32no—
574C23×C3—42no—
575C23×C3—42no—
576C23×C3—42no—
577C23×C3—68no—
578C23×C3—68no—
579C23×C3—62no—
580C23×C3—62no—
581C23×C3—62no—
582C23×C3—62no—
583C23×C3—62no—
584C23×C3—62no—
585C23×C3—62no—
586C23×C3—124no—
587C23×C3—1216no—
588C23×C3C23×D312yes—
589C23×C3C23×D312yes—
590C23×C3C23×D311yescharacteristic
591C23×C3C23×D311yescharacteristic
592C22×D3—22no—
593C22×D3—22no—
594C22×D3—22no—
595C22×D3—22no—
596C22×D3—22no—
597C22×D3—22no—
598C22×D3—22no—
599C22×D3—28no—
600C22×D3—28no—
601C22×D3—44no—
602C22×D3—416no—
603C22×D3#23514yes—
604C22×D3#23714yes—
605C22×D3C23×D312yes—
606C22×D3C23×D312yes—
607C22×D3C23×D312yes—
608C3×Q8—124no—
609C3×D4—124no—
610C2×C3×C4—22no—
611C2×C3×C4—22no—
612C2×C3×C4—22no—
613C2×C3×C4—22no—
614C2×C3×C4—22no—
615C2×C3×C4—22no—
616C2×C3×C4—32no—
617C2×C3×C4—32no—
618C2×C3×C4—32no—
619C2×C3×C4—32no—
620C2×C3×C4—32no—
621C2×C3×C4—42no—
622C2×C3×C4—42no—
623C2×C3×C4—68no—
624C2×C3×C4—62no—
625C2×C3×C4—62no—
626C2×C3×C4—62no—
627C2×C3×C4—62no—
628C2×C3×C4—62no—
629C2×C3×C4—124no—
630C2×C3×C4C23×D312yes—
631C2×C3×C4C23×D312yes—
632C2×C3×C4C23×D312yes—
633C2×C3×C4C23×D312yes—
634#67—44no—
635#67—68no—
636#67—68no—
637#67—68no—
638#67—68no—
639C2×Dic3—22no—
640C2×Dic3—22no—
641C2×Dic3—22no—
642C2×Dic3—22no—
643C2×Dic3—22no—
644C2×Dic3—32no—
645C2×Dic3—32no—
646C2×Dic3—32no—
647C2×Dic3—32no—
648C2×Dic3—32no—
649C2×Dic3—32no—
650C2×Dic3—32no—
651C2×Dic3—32no—
652C2×Dic3—62no—
653C2×Dic3—62no—
654C2×Dic3—62no—
655C2×Dic3—62no—
656C2×Dic3—68no—
657C2×Dic3—62no—
658C2×Dic3—62no—
659C2×Dic3—62no—
660C2×Dic3—62no—
661C2×Dic3—62no—
662C2×Dic3—62no—
663C2×Dic3—62no—
664C2×Dic3—62no—
665C2×Dic3—122no—
666C2×Dic3—122no—
667C2×Dic3—122no—
668C2×Dic3—122no—
669C2×Dic3—124no—
670C2×Dic3—124no—
671C2×Dic3C23×D312yes—
672C2×Dic3C23×D312yes—
673C2×Dic3C23×D312yes—
674C2×Dic3C23×D312yes—
675C2×Dic3C23×D312yes—
676C4×D3—28no—
677C4×D3—44no—
678C4×D3—68no—
679C4×D3—124no—
680C4×D3—124no—
681Dic6—44no—
682C2×C32—42no—
683C2×C32#55114yescomplemented
684C2×C32C22×#4111yescharacteristic
685C2×C32C22×#4111yescharacteristic
686C2×C32C2×H(5,𝔽2)11yescharacteristic
687C3×D3—24no—
688C3×D3—24no—
689C3×D3—42no—
690C24—31no—
691C24—31no—
692C24—31no—
693C24—34no—
694C24—64no—
695C24—64no—
696C24—122no—
697C24C2×D3211yescharacteristic
698C2×Q8—34no—
699C2×Q8—122no—
700C2×D4—34no—
701C2×D4—94no—
702C2×D4—94no—
703C2×D4—122no—
704C2×D4—184no—
705C2×D4—184no—
706C22×C4—31no—
707C22×C4—31no—
708C22×C4—31no—
709C22×C4—31no—
710C22×C4—31no—
711C22×C4—34no—
712C22×C4—34no—
713C22×C4—64no—
714C22×C4—94no—
715C22×C4—94no—
716C22×C4—94no—
717C22×C4—91no—
718C22×C4—91no—
719C22×C4—91no—
720C22×C4—91no—
721C22×C4—122no—
722C22×C4—184no—
723C22×C4—362no—
724C22×C4—362no—
725C22×C4C2×D3211yescharacteristic
726C22×C4C2×D3211yescharacteristic
727C4⋊C4—94no—
728C4⋊C4—94no—
729C4⋊C4—94no—
730C4⋊C4—94no—
731C4⋊C4—94no—
732C4⋊C4—94no—
733C4⋊C4—94no—
734C4⋊C4—94no—
735C22⋊C4—34no—
736C22⋊C4—34no—
737C22⋊C4—34no—
738C22⋊C4—34no—
739C22⋊C4—34no—
740C22⋊C4—34no—
741C22⋊C4—94no—
742C22⋊C4—94no—
743C22⋊C4—94no—
744C22⋊C4—94no—
745C22⋊C4—94no—
746C22⋊C4—94no—
747C22⋊C4—94no—
748C22⋊C4C2×D3214yes—
749C42—34no—
750C42—94no—
751C42—94no—
752C22×C3—22no—
753C22×C3—22no—
754C22×C3—22no—
755C22×C3—22no—
756C22×C3—22no—
757C22×C3—22no—
758C22×C3—22no—
759C22×C3—22no—
760C22×C3—22no—
761C22×C3—21no—
762C22×C3—34no—
763C22×C3—34no—
764C22×C3—42no—
765C22×C3—42no—
766C22×C3—42no—
767C22×C3—44no—
768C22×C3—44no—
769C22×C3—68no—
770C22×C3—68no—
771C22×C3—62no—
772C22×C3—62no—
773C22×C3—62no—
774C22×C3—62no—
775C22×C3—62no—
776C22×C3—62no—
777C22×C3—62no—
778C22×C3—84no—
779C22×C3—1216no—
780C22×C3—124no—
781C22×C3C2×#23512yes—
782C22×C3C2×#23712yes—
783C22×C3#100412yes—
784C22×C3#100412yes—
785C22×C3D3×#4112yes—
786C22×C3D3×#4112yes—
787C22×C3C24×D311yescharacteristic
788C22×C3C24×D311yescharacteristic
789C2×D3—22no—
790C2×D3—22no—
791C2×D3—22no—
792C2×D3—22no—
793C2×D3—28no—
794C2×D3—28no—
795C2×D3—22no—
796C2×D3—22no—
797C2×D3—22no—
798C2×D3—416no—
799C2×D3—44no—
800C2×D3C2×#23514yes—
801C2×D3C2×#23714yes—
802C3×C4—22no—
803C3×C4—22no—
804C3×C4—22no—
805C3×C4—22no—
806C3×C4—42no—
807C3×C4—42no—
808C3×C4—62no—
809C3×C4—62no—
810C3×C4—62no—
811C3×C4—62no—
812C3×C4—62no—
813Dic3—22no—
814Dic3—22no—
815Dic3—22no—
816Dic3—22no—
817Dic3—22no—
818Dic3—62no—
819Dic3—62no—
820Dic3—62no—
821Dic3—62no—
822Dic3—62no—
823Dic3—62no—
824Dic3—62no—
825Dic3—62no—
826Dic3—122no—
827Dic3—122no—
828Dic3—122no—
829Dic3—122no—
830C32C2×#55111yescharacteristic, complemented, Sylow
831C23—22no—
832C23—22no—
833C23—22no—
834C23—34no—
835C23—34no—
836C23—32no—
837C23—32no—
838C23—32no—
839C23—68no—
840C23—68no—
841C23—62no—
842C23—62no—
843C23—62no—
844C23—62no—
845C23—62no—
846C23—62no—
847C23—62no—
848C23—124no—
849C23—1216no—
850C23C22×D3212yes—
851C23C22×D3211yescharacteristic
852Q8—124no—
853D4—124no—
854D4—188no—
855D4—188no—
856C2×C4—22no—
857C2×C4—22no—
858C2×C4—32no—
859C2×C4—32no—
860C2×C4—32no—
861C2×C4—32no—
862C2×C4—32no—
863C2×C4—68no—
864C2×C4—62no—
865C2×C4—62no—
866C2×C4—62no—
867C2×C4—62no—
868C2×C4—62no—
869C2×C4—92no—
870C2×C4—92no—
871C2×C4—92no—
872C2×C4—92no—
873C2×C4—124no—
874C2×C4—188no—
875C2×C4—182no—
876C2×C4—182no—
877C2×C4—182no—
878C2×C4—182no—
879C2×C4—364no—
880C2×C4—364no—
881C2×C4C22×D3212yes—
882C2×C4C22×D3212yes—
883C2×C3—24no—
884C2×C3—21no—
885C2×C3—21no—
886C2×C3—21no—
887C2×C3—42no—
888C2×C3—42no—
889C2×C3—64no—
890C2×C3—64no—
891C2×C3—82no—
892C2×C3—122no—
893C2×C3#549514yescomplemented
894C2×C3#567914yescomplemented
895C2×C3C22×#23511yescharacteristic
896C2×C3C22×#23711yescharacteristic
897C2×C3C2×#100411yescharacteristic
898C2×C3C2×#100411yescharacteristic
899C2×C3C2×D3×#4111yescharacteristic
900C2×C3C2×D3×#4111yescharacteristic
901D3—24no—
902D3—24no—
903D3—42no—
904C22—22no—
905C22—22no—
906C22—22no—
907C22—34no—
908C22—34no—
909C22—44no—
910C22—68no—
911C22—68no—
912C22—62no—
913C22—62no—
914C22—62no—
915C22—62no—
916C22—62no—
917C22—62no—
918C22—62no—
919C22—1216no—
920C22—124no—
921C22D3×#23512yes—
922C22D3×#23712yes—
923C22#6431312yes—
924C22C23×D3211yescharacteristic
925C4—22no—
926C4—22no—
927C4—62no—
928C4—62no—
929C4—62no—
930C4—62no—
931C4—62no—
932C4—182no—
933C4—182no—
934C4—182no—
935C4—182no—
936C3—21no—
937C3C2×#549511yescharacteristic, complemented
938C3C2×#567911yescharacteristic, complemented
939C2—42no—
940C2—64no—
941C2—64no—
942C2—122no—
943C2#1059409214yesdirect product factor
944C2C2×D3×#23511yescharacteristic
945C2C2×D3×#23711yescharacteristic
946C2C2×#6431311yescharacteristic
subgroupG/H
centerC23C22×D32
commutator, cosocleC22×C32C25
FrattiniC22C23×D32
FittingC2×C32×C22⋊C4C22
socleC23×C32C24
prime radicalC2×#63976C2
hypercenterC2×C22⋊C4D32
hypocenterC32C2×#551
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C23 ◁ C2×C22⋊C4

Complements

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

NH ≅ G/Ntype
1. C2×#64088C2semidirect
2. C2×C3×#885C2semidirect
3. C2×C3×D3×C22⋊C4C2semidirect
5. C2×#63969C2semidirect
6. C2×D3×#217C2semidirect
7. C2×#63956C2semidirect
8. C2×#63905C2semidirect
9. C2×#63902C2semidirect
10. C2×#63891C2semidirect
11. C2×#63887C2semidirect
12. C2×#63879C2semidirect
13. C2×#63877C2semidirect
14. C2×#63856C2semidirect
15. C2×#63855C2semidirect
16. #10594092C2direct (N × H)
23. C22×C3×Dic6C22semidirect
28. C22×D3×Dic3C22semidirect
32. C2×C4⋊(C3⋊Dic3)C22semidirect
33. C2×#3750C22semidirect
34. C2×#3750C22semidirect
35. C2×C4×C3⋊Dic3C22semidirect
36. #64088C22semidirect
41. C2×C3×(C2×D3)⋊C4C22semidirect
42. C2×C3×(C2×D3)⋊C4C22semidirect
43. C2×C3×C4×Dic3C22semidirect
44. C3×#885C22semidirect
45. C3×D3×C22⋊C4C22semidirect
47. #63969C22semidirect
48. D3×#217C22semidirect
49. C2×#3724C22semidirect
50. C2×#3724C22semidirect
51. C2×Dic3⋊Dic3C22semidirect
52. C2×Dic3⋊Dic3C22semidirect
53. C2×Dic3⋊Dic3C22semidirect
58. C2×(C2×D3)⋊Dic3C22semidirect
59. #63956C22semidirect
60. C2×Dic32C22semidirect
61. #63905C22semidirect
62. #63902C22semidirect
63. #63891C22semidirect
64. #63887C22semidirect
65. #63879C22semidirect
66. #63877C22semidirect
67. #63856C22semidirect
68. #63855C22semidirect
84. C2×#885D3semidirect
92. C2×D3×C22⋊C4D3semidirect
128. C2×C3×Dic6C23semidirect
138. C2×D3×Dic3C23semidirect
142. C4⋊(C3⋊Dic3)C23semidirect
143. #3750C23semidirect
144. #3750C23semidirect
145. C4×C3⋊Dic3C23semidirect
150. C3×(C2×D3)⋊C4C23semidirect
151. C3×(C2×D3)⋊C4C23semidirect
152. C3×C4×Dic3C23semidirect
153. #3724C23semidirect
154. #3724C23semidirect
155. Dic3⋊Dic3C23semidirect
156. Dic3⋊Dic3C23semidirect
157. Dic3⋊Dic3C23semidirect
162. (C2×D3)⋊Dic3C23semidirect
163. Dic32C23semidirect
184. C22×Dic6C2×D3semidirect
225. C2×(C2×D3)⋊C4C2×D3semidirect
226. C2×(C2×D3)⋊C4C2×D3semidirect
253. C2×C4×Dic3C2×D3semidirect
255. #885C2×D3semidirect
263. D3×C22⋊C4C2×D3semidirect
421. C2×Dic6C22×D3semidirect
452. (C2×D3)⋊C4C22×D3semidirect
453. (C2×D3)⋊C4C22×D3semidirect
478. C4×Dic3C22×D3semidirect
683. C2×C32#551semidirect
830. C32C2×#551semidirect
893. C2×C3#5495semidirect
894. C2×C3#5679semidirect
937. C3C2×#5495semidirect
938. C3C2×#5679semidirect
943. C2#10594092direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#640882
C2×C3×#8852
C2×C3×D3×C22⋊C42
C2×#639762
C2×#639692
C2×D3×#2172
C2×#639562
C2×#639052
C2×#639022
C2×#638912
C2×#638872
C2×#638792
C2×#638772
C2×#638562
C2×#638552
#105940922
C2×#56793
C2×#54953