Finite Group Databasebeta

← C2×#10594211 #11902915

Subgroups — C2×#10594211 #11902915

Order 1152.

2817 conjugacy classes of subgroups.

The subgroup lattice has 952 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#64087C211yesmaximal, characteristic, complemented
2C2×C3×#886C211yesmaximal, characteristic, complemented
3C2×C3×D3×C22⋊C4C211yesmaximal, characteristic, complemented
4C2×#63976C211yesmaximal, characteristic
5C2×#67⋊Dic3C211yesmaximal, characteristic, complemented
6C22×(C2×D3)⋊Dic3C211yesmaximal, characteristic, complemented
7C2×#63955C211yesmaximal, characteristic, complemented
8C2×#63913C211yesmaximal, characteristic, complemented
9C2×#63905C211yesmaximal, characteristic, complemented
10C2×#63891C211yesmaximal, characteristic, complemented
11C2×#63879C211yesmaximal, characteristic, complemented
12C2×#63858C211yesmaximal, characteristic, complemented
13C2×#63858C211yesmaximal, characteristic, complemented
14C2×#63857C211yesmaximal, characteristic, complemented
15C2×#63841C211yesmaximal, characteristic, complemented
16#10594211C2116yesmaximal, direct product factor
17C2×#5658—31nomaximal
18C2×#5495—31nomaximal
19C24×C3×D3C2211yescharacteristic
20C23×C3⋊Dic3C2211yescharacteristic
21C22×#634C2211yescharacteristic, complemented
22C22×C3×#67C2211yescharacteristic
23C23×C3×Dic3C2211yescharacteristic
24C22×C3×C4×D3C2211yescharacteristic
25C22×C3×C4×D3C2211yescharacteristic
26C22×#625C2211yescharacteristic
27C22×#625C2211yescharacteristic
28C22×D3×Dic3C2211yescharacteristic, complemented
29C2×C32×C22⋊C4C2211yescharacteristic
30C2×#3757C2211yescharacteristic
31C2×C4⋊(C3⋊Dic3)C2211yescharacteristic, complemented
32C2×#3750C2211yescharacteristic, complemented
33C2×#3750C2211yescharacteristic, complemented
34#64087C2218yescomplemented
35C2×C3×#217C2211yescharacteristic
36C2×C3×(C2×D3)⋊C4C2211yescharacteristic
37C2×C3×(C2×D3)⋊C4C2211yescharacteristic
38C2×C3×(C2×D3)⋊C4C2211yescharacteristic, complemented
39C2×C3×(C2×D3)⋊C4C2211yescharacteristic, complemented
40C2×C3×C4⋊Dic3C2211yescharacteristic, complemented
41C2×C3×C4⋊Dic3C2211yescharacteristic, complemented
42C3×#886C2218yescomplemented
43C3×D3×C22⋊C4C2218yescomplemented
44#63976C2218yes—
45#67⋊Dic3C2218yescomplemented
46C2×Dic3⋊Dic3C2211yescharacteristic, complemented
47C2×Dic3⋊Dic3C2211yescharacteristic, complemented
48C2×Dic3⋊Dic3C2211yescharacteristic, complemented
49C2×(C2×D3)⋊Dic3C2211yescharacteristic
50C2×(C2×D3)⋊Dic3C2211yescharacteristic
51C2×(C2×D3)⋊Dic3C2211yescharacteristic
52C2×(C2×D3)⋊Dic3C2211yescharacteristic
53C2×(C2×D3)⋊Dic3C2211yescharacteristic
54C2×(C2×D3)⋊Dic3C2211yescharacteristic
55C2×(C2×D3)⋊Dic3C2218yescomplemented
56C2×(C2×D3)⋊Dic3C2211yescharacteristic, complemented
57#63955C2218yescomplemented
58C2×Dic32C2211yescharacteristic, complemented
59C2×Dic32C2211yescharacteristic, complemented
60C2×Dic32C2211yescharacteristic, complemented
61#63913C2218yescomplemented
62#63905C2218yescomplemented
63#63891C2218yescomplemented
64#63879C2218yescomplemented
65#63858C2218yescomplemented
66#63858C2218yescomplemented
67#63857C2218yescomplemented
68#63841C2218yescomplemented
69C2×C3×#123—31no—
70C22×C3×C22⋊C4—31no—
71C2×#953—31no—
72C22×#217—31no—
73C2×#937—31no—
74C2×D4×Dic3—31no—
75C2×#929—31no—
76C2×C4×#67—31no—
77C22×(C2×D3)⋊C4—31no—
78C2×#926—31no—
79C2×#926—31no—
80C2×#924—31no—
81#5658—316no—
82C2×#898—31no—
83C2×#898—31no—
84C2×#897—31no—
85C2×#892—31no—
86#5495—316no—
87C2×#886—31no—
88C2×#886D311yescharacteristic, complemented
89C2×#885—31no—
90C2×#885—31no—
91C2×#883—31no—
92C2×#883—31no—
93C2×#67⋊C4—31no—
94C2×#67⋊C4—31no—
95C2×D3×C22⋊C4D311yescharacteristic, complemented
96C2×#879—31no—
97C2×#879—31no—
98C2×#878—31no—
99C2×#878—31no—
100C2×#878—61no—
101C2×#877—31no—
102C24×C32C2311yescharacteristic
103C23×C3×D3—24no—
104C23×C3×D3—24no—
105C23×C3×D3—42no—
106C23×C3×D3C2311yescharacteristic
107C23×C3×D3C2311yescharacteristic
108C23×C3×D3C2314yes—
109C23×C3×D3C2311yescharacteristic
110C22×C32×C4C2311yescharacteristic
111C22×C32×C4C2311yescharacteristic
112C22×C3⋊Dic3—42no—
113C22×C3⋊Dic3C2311yescharacteristic
114C22×C3⋊Dic3C2311yescharacteristic
115C22×C3⋊Dic3C2311yescharacteristic
116C22×C3⋊Dic3C2311yescharacteristic
117C22×C3⋊Dic3C2314yes—
118C2×#634—42no—
119C2×#634C2314yescomplemented
120C2×C3×#67—24no—
121C2×C3×#67C2314yes—
122C22×C3×Dic3—24no—
123C22×C3×Dic3C2314yes—
124C22×C3×Dic3C2311yescharacteristic
125C22×C3×Dic3C2311yescharacteristic
126C22×C3×Dic3C2311yescharacteristic
127C22×C3×Dic3C2311yescharacteristic
128C22×C3×Dic3C2311yescharacteristic
129C2×C3×C4×D3—24no—
130C2×C3×C4×D3—42no—
131C2×C3×C4×D3C2314yes—
132C2×C3×C4×D3C2314yes—
133C2×#625—24no—
134C2×#625—42no—
135C2×#625C2314yes—
136C2×#625C2314yes—
137C2×D3×Dic3—42no—
138C2×D3×Dic3C2314yescomplemented
139C32×C22⋊C4C2314yes—
140#3757C2314yes—
141C4⋊(C3⋊Dic3)C2314yescomplemented
142#3750C2314yescomplemented
143#3750C2314yescomplemented
144C3×#217C2314yes—
145C3×(C2×D3)⋊C4C2314yes—
146C3×(C2×D3)⋊C4C2314yes—
147C3×(C2×D3)⋊C4C2314yescomplemented
148C3×(C2×D3)⋊C4C2314yescomplemented
149C3×C4⋊Dic3C2314yescomplemented
150C3×C4⋊Dic3C2314yescomplemented
151Dic3⋊Dic3C2314yescomplemented
152Dic3⋊Dic3C2314yescomplemented
153Dic3⋊Dic3C2314yescomplemented
154(C2×D3)⋊Dic3C2314yes—
155(C2×D3)⋊Dic3C2314yes—
156(C2×D3)⋊Dic3C2314yes—
157(C2×D3)⋊Dic3C2314yes—
158(C2×D3)⋊Dic3C2314yes—
159(C2×D3)⋊Dic3C2314yes—
160(C2×D3)⋊Dic3C2314yescomplemented
161Dic32C2314yescomplemented
162Dic32C2314yescomplemented
163Dic32C2314yescomplemented
164C2×#551—91noSylow
165C25×C3—31no—
166C24×D3C2×D311yescharacteristic
167C22×C3×D4—31no—
168C23×C3×C4—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—
179C23×Dic3—61no—
180C23×Dic3C2×D311yescharacteristic
181C22×C4×D3—31no—
182C22×C4×D3C2×D311yescharacteristic
183C22×C4×D3C2×D311yescharacteristic
184C22×Dic6—31no—
185C22×Dic6—31no—
186C22×Dic6—61no—
187C3×#123—38no—
188C2×C3×C4⋊C4—31no—
189C2×C3×C4⋊C4—31no—
190C2×C3×C22⋊C4—21no—
191C2×C3×C22⋊C4—31no—
192C2×C3×C22⋊C4—31no—
193C2×C3×C22⋊C4—31no—
194C2×C3×C22⋊C4—31no—
195C2×C3×C22⋊C4—31no—
196C2×C3×C22⋊C4—38no—
197C2×C3×C22⋊C4C2×D311yescharacteristic
198C2×C3×C22⋊C4C2×D311yescharacteristic
199#953—38no—
200C2×#217—31no—
201C2×#217—31no—
202C2×#217—31no—
203C2×#217—31no—
204C2×#217—31no—
205C2×#217—31no—
206C2×#217—38no—
207C2×#217—31no—
208C2×#217—31no—
209C2×#217—31no—
210C2×#217—61no—
211C2×#217C2×D311yescharacteristic
212#937—38no—
213D4×Dic3—38no—
214#929—38no—
215C4×#67—38no—
216C2×(C2×D3)⋊C4—38no—
217C2×(C2×D3)⋊C4—31no—
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)⋊C4—31no—
224C2×(C2×D3)⋊C4C2×D311yescharacteristic
225C2×(C2×D3)⋊C4C2×D311yescharacteristic
226C2×(C2×D3)⋊C4C2×D311yescharacteristic, complemented
227C2×(C2×D3)⋊C4C2×D311yescharacteristic, complemented
228#926—38no—
229#926—38no—
230C2×C4⋊Dic3—31no—
231C2×C4⋊Dic3—31no—
232C2×C4⋊Dic3—31no—
233C2×C4⋊Dic3—31no—
234C2×C4⋊Dic3—31no—
235C2×C4⋊Dic3—61no—
236C2×C4⋊Dic3C2×D311yescharacteristic, complemented
237C2×C4⋊Dic3C2×D311yescharacteristic, complemented
238#924—38no—
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—31no—
253C2×C4×Dic3—31no—
254#898—38no—
255#898—38no—
256#897—38no—
257#892—38no—
258#886—38no—
259#886C2×D318yescomplemented
260#885—38no—
261#885—38no—
262#883—38no—
263#883—38no—
264#67⋊C4—38no—
265#67⋊C4—38no—
266D3×C22⋊C4C2×D318yescomplemented
267#879—38no—
268#879—38no—
269#878—38no—
270#878—38no—
271#878—68no—
272#877—38no—
273C23×C32—22no—
274C23×C32—22no—
275C23×C32#4114yes—
276C23×C32C2412yes—
277C23×C32C2411yescharacteristic
278C22×C3×D3—22no—
279C22×C3×D3—22no—
280C22×C3×D3—28no—
281C22×C3×D3—22no—
282C22×C3×D3—22no—
283C22×C3×D3—22no—
284C22×C3×D3—22no—
285C22×C3×D3—22no—
286C22×C3×D3—22no—
287C22×C3×D3—28no—
288C22×C3×D3—44no—
289C22×C3×D3—416no—
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⋊Dic3—44no—
303C2×C3⋊Dic3C2412yes—
304C2×C3⋊Dic3C2412yes—
305C2×C3⋊Dic3C2412yes—
306C2×C3⋊Dic3C2412yes—
307#634—44no—
308C3×#67—28no—
309C2×C3×Dic3—22no—
310C2×C3×Dic3—28no—
311C2×C3×Dic3—22no—
312C2×C3×Dic3—22no—
313C2×C3×Dic3—22no—
314C2×C3×Dic3—22no—
315C2×C3×Dic3C2412yes—
316C2×C3×Dic3C2412yes—
317C2×C3×Dic3C2412yes—
318C2×C3×Dic3C2412yes—
319C2×C3×Dic3C2412yes—
320C3×C4×D3—28no—
321C3×C4×D3—44no—
322#625—28no—
323#625—44no—
324D3×Dic3—44no—
325#551—916no—
326C2×#126—91no—
327C2×#126—91no—
328C2×#124—91no—
329C2×#123—31no—
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×D311yescharacteristic
356C23×D3C22×D314yes—
357C23×D3C22×D311yescharacteristic
358C2×C3×D4—34no—
359C2×C3×D4—64no—
360C22×C3×C4—21no—
361C22×C3×C4—21no—
362C22×C3×C4—31no—
363C22×C3×C4—31no—
364C22×C3×C4—31no—
365C22×C3×C4—31no—
366C22×C3×C4—31no—
367C22×C3×C4—34no—
368C22×C3×C4—34no—
369C22×C3×C4—34no—
370C22×C3×C4—64no—
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—24no—
378C2×#67—34no—
379C2×#67—34no—
380C2×#67—34no—
381C2×#67—34no—
382C2×#67—64no—
383C2×#67—64no—
384C2×#67—122no—
385C2×#67—122no—
386C2×#67C22×D314yes—
387C22×Dic3—24no—
388C22×Dic3—31no—
389C22×Dic3—31no—
390C22×Dic3—31no—
391C22×Dic3—31no—
392C22×Dic3—31no—
393C22×Dic3—31no—
394C22×Dic3—31no—
395C22×Dic3—31no—
396C22×Dic3—34no—
397C22×Dic3—34no—
398C22×Dic3—34no—
399C22×Dic3—61no—
400C22×Dic3—64no—
401C22×Dic3—61no—
402C22×Dic3—61no—
403C22×Dic3—61no—
404C22×Dic3—122no—
405C22×Dic3—122no—
406C22×Dic3—122no—
407C22×Dic3—124no—
408C22×Dic3C22×D314yes—
409C22×Dic3C22×D311yescharacteristic
410C22×Dic3C22×D311yescharacteristic
411C22×Dic3C22×D311yescharacteristic
412C22×Dic3C22×D311yescharacteristic
413C22×Dic3C22×D311yescharacteristic
414C2×C4×D3—24no—
415C2×C4×D3—34no—
416C2×C4×D3—42no—
417C2×C4×D3—122no—
418C2×C4×D3C22×D314yes—
419C2×C4×D3C22×D314yes—
420C2×Dic6—34no—
421C2×Dic6—34no—
422C2×Dic6—64no—
423C2×Dic6—122no—
424C2×Dic6—122no—
425C2×Dic6—124no—
426C3×C4⋊C4—34no—
427C3×C4⋊C4—34no—
428C3×C22⋊C4—24no—
429C3×C22⋊C4—34no—
430C3×C22⋊C4—34no—
431C3×C22⋊C4—34no—
432C3×C22⋊C4—34no—
433C3×C22⋊C4—34no—
434C3×C22⋊C4C22×D314yes—
435C3×C22⋊C4C22×D314yes—
436#217—34no—
437#217—34no—
438#217—34no—
439#217—34no—
440#217—34no—
441#217—34no—
442#217—34no—
443#217—34no—
444#217—34no—
445#217—64no—
446#217C22×D314yes—
447(C2×D3)⋊C4—34no—
448(C2×D3)⋊C4—34no—
449(C2×D3)⋊C4—34no—
450(C2×D3)⋊C4—34no—
451(C2×D3)⋊C4—34no—
452(C2×D3)⋊C4—34no—
453(C2×D3)⋊C4—34no—
454(C2×D3)⋊C4C22×D314yes—
455(C2×D3)⋊C4C22×D314yes—
456(C2×D3)⋊C4C22×D314yescomplemented
457(C2×D3)⋊C4C22×D314yescomplemented
458C4⋊Dic3—34no—
459C4⋊Dic3—34no—
460C4⋊Dic3—34no—
461C4⋊Dic3—34no—
462C4⋊Dic3—34no—
463C4⋊Dic3—64no—
464C4⋊Dic3C22×D314yescomplemented
465C4⋊Dic3C22×D314yescomplemented
466Dic3⋊C4—34no—
467Dic3⋊C4—34no—
468Dic3⋊C4—34no—
469Dic3⋊C4—34no—
470Dic3⋊C4—34no—
471Dic3⋊C4—34no—
472Dic3⋊C4—34no—
473Dic3⋊C4—64no—
474Dic3⋊C4—64no—
475C4×Dic3—34no—
476C4×Dic3—34no—
477C4×Dic3—34no—
478C4×Dic3—34no—
479C4×Dic3—34no—
480C4×Dic3—34no—
481C22×C32—28no—
482C22×C32—22no—
483C22×C32—22no—
484C22×C32C2×#4114yes—
485C22×C32C2×#4112yes—
486C22×C32C2×#4112yes—
487C22×C32H(5,𝔽2)12yes—
488C22×C32C2511yescharacteristic
489C2×C3×D3—28no—
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—22no—
497C2×C3×D3—22no—
498C2×C3×D3—416no—
499C2×C3×D3—44no—
500C2×C3×D3—44no—
501C2×C3×D3C2×#4114yes—
502C32×C4—22no—
503C32×C4—22no—
504C3⋊Dic3—22no—
505C3⋊Dic3—22no—
506C3⋊Dic3—22no—
507C3⋊Dic3—22no—
508C3×Dic3—22no—
509C3×Dic3—22no—
510C3×Dic3—22no—
511C3×Dic3—22no—
512C3×Dic3—22no—
513C25—31no—
514C22×Q8—91no—
515C22×D4—31no—
516C22×D4—91no—
517C22×D4—91no—
518C23×C4—31no—
519C23×C4—31no—
520C23×C4—31no—
521C23×C4—91no—
522C23×C4—91no—
523#126—98no—
524#126—98no—
525#124—98no—
526#123—38no—
527#123—98no—
528#123—98no—
529C22⋊Q8—98no—
530C22⋊Q8—98no—
531#120—98no—
532C4×D4—98no—
533C4×D4—98no—
534#117—98no—
535#117—98no—
536C2×C4⋊C4—31no—
537C2×C4⋊C4—31no—
538C2×C4⋊C4—91no—
539C2×C4⋊C4—91no—
540C2×C4⋊C4—91no—
541C2×C4⋊C4—91no—
542C2×C4⋊C4—91no—
543C2×C4⋊C4—91no—
544C2×C22⋊C4—31no—
545C2×C22⋊C4—31no—
546C2×C22⋊C4—31no—
547C2×C22⋊C4—31no—
548C2×C22⋊C4—31no—
549C2×C22⋊C4—38no—
550C2×C22⋊C4—91no—
551C2×C22⋊C4—91no—
552C2×C22⋊C4—91no—
553C2×C22⋊C4—91no—
554C2×C22⋊C4—98no—
555C2×C22⋊C4—91no—
556C2×C22⋊C4—91no—
557C2×C22⋊C4—91no—
558C2×C22⋊C4—91no—
559C2×C22⋊C4D3211yescharacteristic
560C2×C42—91no—
561C2×C42—91no—
562C2×C42—91no—
563C23×C3—22no—
564C23×C3—22no—
565C23×C3—22no—
566C23×C3—22no—
567C23×C3—22no—
568C23×C3—21no—
569C23×C3—24no—
570C23×C3—34no—
571C23×C3—32no—
572C23×C3—32no—
573C23×C3—32no—
574C23×C3—42no—
575C23×C3—42no—
576C23×C3—68no—
577C23×C3—62no—
578C23×C3—62no—
579C23×C3—62no—
580C23×C3—62no—
581C23×C3—68no—
582C23×C3—62no—
583C23×C3—62no—
584C23×C3—62no—
585C23×C3—62no—
586C23×C3—124no—
587C23×C3—1216no—
588C23×C3#23514yes—
589C23×C3#23714yes—
590C23×C3C23×D312yes—
591C23×C3C23×D312yes—
592C23×C3C23×D311yescharacteristic
593C23×C3C23×D311yescharacteristic
594C22×D3—22no—
595C22×D3—22no—
596C22×D3—28no—
597C22×D3—22no—
598C22×D3—22no—
599C22×D3—22no—
600C22×D3—22no—
601C22×D3—22no—
602C22×D3—22no—
603C22×D3—28no—
604C22×D3—44no—
605C22×D3—416no—
606C22×D3#23714yes—
607C22×D3C23×D312yes—
608C22×D3C23×D312yes—
609C22×D3C23×D312yes—
610C3×D4—68no—
611C2×C3×C4—22no—
612C2×C3×C4—22no—
613C2×C3×C4—22no—
614C2×C3×C4—22no—
615C2×C3×C4—22no—
616C2×C3×C4—22no—
617C2×C3×C4—32no—
618C2×C3×C4—32no—
619C2×C3×C4—32no—
620C2×C3×C4—32no—
621C2×C3×C4—32no—
622C2×C3×C4—42no—
623C2×C3×C4—42no—
624C2×C3×C4—68no—
625C2×C3×C4—68no—
626C2×C3×C4—62no—
627C2×C3×C4—62no—
628C2×C3×C4—62no—
629C2×C3×C4—62no—
630C2×C3×C4—62no—
631C2×C3×C4—124no—
632C2×C3×C4C23×D312yes—
633C2×C3×C4C23×D312yes—
634C2×C3×C4C23×D312yes—
635C2×C3×C4C23×D312yes—
636#67—28no—
637#67—68no—
638#67—68no—
639#67—124no—
640#67—124no—
641C2×Dic3—22no—
642C2×Dic3—28no—
643C2×Dic3—22no—
644C2×Dic3—22no—
645C2×Dic3—22no—
646C2×Dic3—22no—
647C2×Dic3—32no—
648C2×Dic3—32no—
649C2×Dic3—32no—
650C2×Dic3—32no—
651C2×Dic3—32no—
652C2×Dic3—32no—
653C2×Dic3—32no—
654C2×Dic3—32no—
655C2×Dic3—62no—
656C2×Dic3—62no—
657C2×Dic3—62no—
658C2×Dic3—62no—
659C2×Dic3—64no—
660C2×Dic3—62no—
661C2×Dic3—62no—
662C2×Dic3—62no—
663C2×Dic3—62no—
664C2×Dic3—62no—
665C2×Dic3—62no—
666C2×Dic3—62no—
667C2×Dic3—62no—
668C2×Dic3—122no—
669C2×Dic3—122no—
670C2×Dic3—122no—
671C2×Dic3—124no—
672C2×Dic3—124no—
673C2×Dic3—124no—
674C2×Dic3—128no—
675C2×Dic3C23×D312yes—
676C2×Dic3C23×D312yes—
677C2×Dic3C23×D312yes—
678C2×Dic3C23×D312yes—
679C2×Dic3C23×D312yes—
680C4×D3—28no—
681C4×D3—44no—
682C4×D3—124no—
683Dic6—124no—
684Dic6—124no—
685Dic6—128no—
686C2×C32—24no—
687C2×C32#55114yescomplemented
688C2×C32C22×#4111yescharacteristic
689C2×C32C22×#4111yescharacteristic
690C2×C32C2×H(5,𝔽2)11yescharacteristic
691C3×D3—24no—
692C3×D3—42no—
693C3×D3—42no—
694C24—31no—
695C24—31no—
696C24—31no—
697C24—34no—
698C24—64no—
699C24—64no—
700C24—122no—
701C24C2×D3211yescharacteristic
702C2×Q8—94no—
703C2×Q8—362no—
704C2×D4—34no—
705C2×D4—64no—
706C2×D4—94no—
707C2×D4—94no—
708C2×D4—184no—
709C2×D4—362no—
710C22×C4—34no—
711C22×C4—31no—
712C22×C4—31no—
713C22×C4—31no—
714C22×C4—31no—
715C22×C4—31no—
716C22×C4—34no—
717C22×C4—34no—
718C22×C4—64no—
719C22×C4—64no—
720C22×C4—94no—
721C22×C4—91no—
722C22×C4—91no—
723C22×C4—91no—
724C22×C4—91no—
725C22×C4—94no—
726C22×C4—122no—
727C22×C4—362no—
728C22×C4—362no—
729C22×C4C2×D3211yescharacteristic
730C22×C4C2×D3211yescharacteristic
731C4⋊C4—34no—
732C4⋊C4—34no—
733C4⋊C4—94no—
734C4⋊C4—94no—
735C4⋊C4—94no—
736C4⋊C4—94no—
737C4⋊C4—94no—
738C4⋊C4—94no—
739C22⋊C4—34no—
740C22⋊C4—34no—
741C22⋊C4—34no—
742C22⋊C4—34no—
743C22⋊C4—34no—
744C22⋊C4—94no—
745C22⋊C4—94no—
746C22⋊C4—94no—
747C22⋊C4—94no—
748C22⋊C4—94no—
749C22⋊C4—94no—
750C22⋊C4—94no—
751C22⋊C4—94no—
752C22⋊C4C2×D3214yes—
753C42—94no—
754C42—94no—
755C42—94no—
756C22×C3—28no—
757C22×C3—22no—
758C22×C3—22no—
759C22×C3—22no—
760C22×C3—22no—
761C22×C3—28no—
762C22×C3—22no—
763C22×C3—24no—
764C22×C3—22no—
765C22×C3—22no—
766C22×C3—21no—
767C22×C3—34no—
768C22×C3—42no—
769C22×C3—42no—
770C22×C3—48no—
771C22×C3—68no—
772C22×C3—62no—
773C22×C3—62no—
774C22×C3—62no—
775C22×C3—62no—
776C22×C3—62no—
777C22×C3—62no—
778C22×C3—62no—
779C22×C3—62no—
780C22×C3—1216no—
781C22×C3—124no—
782C22×C3—124no—
783C22×C3C2×#23514yes—
784C22×C3C2×#23512yes—
785C22×C3C2×#23714yes—
786C22×C3C2×#23712yes—
787C22×C3C2×#23712yes—
788C22×C3#100412yes—
789C22×C3D3×#4112yes—
790C22×C3#100912yes—
791C22×C3C24×D311yescharacteristic
792C22×C3C24×D311yescharacteristic
793C2×D3—22no—
794C2×D3—22no—
795C2×D3—28no—
796C2×D3—22no—
797C2×D3—22no—
798C2×D3—22no—
799C2×D3—22no—
800C2×D3—22no—
801C2×D3—22no—
802C2×D3—416no—
803C2×D3—44no—
804C2×D3—44no—
805C2×D3C2×#23714yes—
806C3×C4—22no—
807C3×C4—22no—
808C3×C4—22no—
809C3×C4—22no—
810C3×C4—42no—
811C3×C4—42no—
812C3×C4—62no—
813C3×C4—62no—
814C3×C4—62no—
815C3×C4—62no—
816C3×C4—62no—
817Dic3—22no—
818Dic3—22no—
819Dic3—22no—
820Dic3—22no—
821Dic3—22no—
822Dic3—64no—
823Dic3—62no—
824Dic3—62no—
825Dic3—62no—
826Dic3—62no—
827Dic3—62no—
828Dic3—62no—
829Dic3—62no—
830Dic3—62no—
831Dic3—122no—
832Dic3—122no—
833Dic3—122no—
834C32C2×#55111yescharacteristic, complemented, Sylow
835C23—22no—
836C23—22no—
837C23—34no—
838C23—32no—
839C23—32no—
840C23—32no—
841C23—68no—
842C23—62no—
843C23—62no—
844C23—62no—
845C23—68no—
846C23—62no—
847C23—62no—
848C23—62no—
849C23—62no—
850C23—62no—
851C23—124no—
852C23—1216no—
853C23#379514yes—
854C23C22×D3212yes—
855C23C22×D3211yescharacteristic
856Q8—364no—
857D4—68no—
858D4—188no—
859D4—364no—
860C2×C4—22no—
861C2×C4—22no—
862C2×C4—32no—
863C2×C4—32no—
864C2×C4—32no—
865C2×C4—32no—
866C2×C4—32no—
867C2×C4—68no—
868C2×C4—68no—
869C2×C4—62no—
870C2×C4—62no—
871C2×C4—62no—
872C2×C4—62no—
873C2×C4—62no—
874C2×C4—92no—
875C2×C4—92no—
876C2×C4—92no—
877C2×C4—92no—
878C2×C4—124no—
879C2×C4—182no—
880C2×C4—182no—
881C2×C4—182no—
882C2×C4—182no—
883C2×C4—364no—
884C2×C4—364no—
885C2×C4C22×D3212yes—
886C2×C4C22×D3212yes—
887C2×C3—24no—
888C2×C3—24no—
889C2×C3—21no—
890C2×C3—21no—
891C2×C3—21no—
892C2×C3—24no—
893C2×C3—44no—
894C2×C3—64no—
895C2×C3—122no—
896C2×C3—122no—
897C2×C3#549514yescomplemented
898C2×C3#565814yescomplemented
899C2×C3C22×#23511yescharacteristic
900C2×C3C22×#23711yescharacteristic
901C2×C3C22×#23711yescharacteristic
902C2×C3C2×#100411yescharacteristic
903C2×C3C2×D3×#4111yescharacteristic
904C2×C3C2×#100911yescharacteristic
905D3—24no—
906D3—42no—
907D3—42no—
908C22—22no—
909C22—22no—
910C22—28no—
911C22—34no—
912C22—62no—
913C22—62no—
914C22—68no—
915C22—62no—
916C22—62no—
917C22—62no—
918C22—62no—
919C22—62no—
920C22—62no—
921C22—1216no—
922C22—124no—
923C22—124no—
924C22C2×#379514yes—
925C22C2×#379512yes—
926C22D3×#23712yes—
927C22#6431412yes—
928C22C23×D3211yescharacteristic
929C4—22no—
930C4—22no—
931C4—62no—
932C4—62no—
933C4—62no—
934C4—62no—
935C4—62no—
936C4—182no—
937C4—182no—
938C4—182no—
939C4—182no—
940C3—21no—
941C3C2×#549511yescharacteristic, complemented
942C3C2×#565811yescharacteristic, complemented
943C2—24no—
944C2—64no—
945C2—122no—
946C2—122no—
947C2#1059421114yesdirect product factor
948C2C22×#379511yescharacteristic
949C2C2×D3×#23711yescharacteristic
950C2C2×#6431411yescharacteristic
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×#64087C2semidirect
2. C2×C3×#886C2semidirect
3. C2×C3×D3×C22⋊C4C2semidirect
5. C2×#67⋊Dic3C2semidirect
6. C22×(C2×D3)⋊Dic3C2semidirect
7. C2×#63955C2semidirect
8. C2×#63913C2semidirect
9. C2×#63905C2semidirect
10. C2×#63891C2semidirect
11. C2×#63879C2semidirect
12. C2×#63858C2semidirect
13. C2×#63858C2semidirect
14. C2×#63857C2semidirect
15. C2×#63841C2semidirect
16. #10594211C2direct (N × H)
21. C22×#634C22semidirect
28. C22×D3×Dic3C22semidirect
31. C2×C4⋊(C3⋊Dic3)C22semidirect
32. C2×#3750C22semidirect
33. C2×#3750C22semidirect
34. #64087C22semidirect
38. C2×C3×(C2×D3)⋊C4C22semidirect
39. C2×C3×(C2×D3)⋊C4C22semidirect
40. C2×C3×C4⋊Dic3C22semidirect
41. C2×C3×C4⋊Dic3C22semidirect
42. C3×#886C22semidirect
43. C3×D3×C22⋊C4C22semidirect
45. #67⋊Dic3C22semidirect
46. C2×Dic3⋊Dic3C22semidirect
47. C2×Dic3⋊Dic3C22semidirect
48. C2×Dic3⋊Dic3C22semidirect
55. C2×(C2×D3)⋊Dic3C22semidirect
56. C2×(C2×D3)⋊Dic3C22semidirect
57. #63955C22semidirect
58. C2×Dic32C22semidirect
59. C2×Dic32C22semidirect
60. C2×Dic32C22semidirect
61. #63913C22semidirect
62. #63905C22semidirect
63. #63891C22semidirect
64. #63879C22semidirect
65. #63858C22semidirect
66. #63858C22semidirect
67. #63857C22semidirect
68. #63841C22semidirect
88. C2×#886D3semidirect
95. C2×D3×C22⋊C4D3semidirect
119. C2×#634C23semidirect
138. C2×D3×Dic3C23semidirect
141. C4⋊(C3⋊Dic3)C23semidirect
142. #3750C23semidirect
143. #3750C23semidirect
147. C3×(C2×D3)⋊C4C23semidirect
148. C3×(C2×D3)⋊C4C23semidirect
149. C3×C4⋊Dic3C23semidirect
150. C3×C4⋊Dic3C23semidirect
151. Dic3⋊Dic3C23semidirect
152. Dic3⋊Dic3C23semidirect
153. Dic3⋊Dic3C23semidirect
160. (C2×D3)⋊Dic3C23semidirect
161. Dic32C23semidirect
162. Dic32C23semidirect
163. Dic32C23semidirect
226. C2×(C2×D3)⋊C4C2×D3semidirect
227. C2×(C2×D3)⋊C4C2×D3semidirect
236. C2×C4⋊Dic3C2×D3semidirect
237. C2×C4⋊Dic3C2×D3semidirect
259. #886C2×D3semidirect
266. D3×C22⋊C4C2×D3semidirect
456. (C2×D3)⋊C4C22×D3semidirect
457. (C2×D3)⋊C4C22×D3semidirect
464. C4⋊Dic3C22×D3semidirect
465. C4⋊Dic3C22×D3semidirect
687. C2×C32#551semidirect
834. C32C2×#551semidirect
897. C2×C3#5495semidirect
898. C2×C3#5658semidirect
941. C3C2×#5495semidirect
942. C3C2×#5658semidirect
947. C2#10594211direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#640872
C2×C3×#8862
C2×C3×D3×C22⋊C42
C2×#639762
C2×#67⋊Dic32
C22×(C2×D3)⋊Dic32
C2×#639552
C2×#639132
C2×#639052
C2×#638912
C2×#638792
C2×#638582
C2×#638572
C2×#638412
#105942112
C2×#56583
C2×#54953