Finite Group Databasebeta

← C2×#10595509 #11902931

Subgroups — C2×#10595509 #11902931

Order 1152.

2993 conjugacy classes of subgroups.

The subgroup lattice has 972 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#3757C211yesmaximal, characteristic, complemented
2C2×C3×#953C211yesmaximal, characteristic
3C22×C3×#217C211yesmaximal, characteristic, complemented
4C2×#63982C211yesmaximal, characteristic, complemented
5#10595509C2116yesmaximal, direct product factor
6C2×#67⋊Dic3C211yesmaximal, characteristic, complemented
7C2×Dic3×#67C211yesmaximal, characteristic, complemented
8C2×#63969C211yesmaximal, characteristic, complemented
9C2×#63964C211yesmaximal, characteristic, complemented
10C2×#63962C211yesmaximal, characteristic, complemented
11C2×#63961C211yesmaximal, characteristic, complemented
12C2×#63959C211yesmaximal, characteristic, complemented
13C2×#63957C211yesmaximal, characteristic, complemented
14C2×#63956C211yesmaximal, characteristic, complemented
15C2×#63956C211yesmaximal, characteristic, complemented
16C2×#63955C211yesmaximal, characteristic, complemented
17C2×#5587—31nomaximal
18C2×#5495—31nomaximal
19C25×C32C2211yescharacteristic
20C23×C3⋊Dic3C2211yescharacteristic
21C23×C3⋊Dic3C2211yescharacteristic
22C22×C3×#67C2211yescharacteristic
23C22×C3×#67C2211yescharacteristic
24C22×C3×#67C2211yescharacteristic
25C23×C3×Dic3C2211yescharacteristic
26C23×C3×Dic3C2211yescharacteristic
27C22×#627C2211yescharacteristic, complemented
28C22×D3×Dic3C2211yescharacteristic, complemented
29C2×#3757C2211yescharacteristic
30C2×#3757C2211yescharacteristic
31C2×#3757C2211yescharacteristic
32C2×#3757C2211yescharacteristic
33C2×#3757C2218yescomplemented
34C3×#953C2218yes—
35C2×C3×#217C2211yescharacteristic
36C2×C3×#217C2211yescharacteristic
37C2×C3×#217C2211yescharacteristic
38C2×C3×#217C2211yescharacteristic
39C2×C3×#217C2211yescharacteristic
40C2×C3×#217C2211yescharacteristic
41C2×C3×#217C2211yescharacteristic
42C2×C3×#217C2218yescomplemented
43#63982C2218yescomplemented
44#67⋊Dic3C2218yescomplemented
45Dic3×#67C2218yescomplemented
46#63969C2218yescomplemented
47C2×#3724C2211yescharacteristic, complemented
48C2×#3724C2211yescharacteristic, complemented
49C2×#3724C2211yescharacteristic, complemented
50C2×Dic3⋊Dic3C2211yescharacteristic, complemented
51C2×Dic3⋊Dic3C2211yescharacteristic, complemented
52C2×Dic3⋊Dic3C2211yescharacteristic, complemented
53C2×Dic3⋊Dic3C2211yescharacteristic, complemented
54C2×Dic3⋊Dic3C2211yescharacteristic, complemented
55#63964C2218yescomplemented
56#63962C2218yescomplemented
57#63961C2218yescomplemented
58C2×(C2×D3)⋊Dic3C2211yescharacteristic, complemented
59C2×(C2×D3)⋊Dic3C2211yescharacteristic, complemented
60C2×(C2×D3)⋊Dic3C2211yescharacteristic, complemented
61#63959C2218yescomplemented
62#63957C2218yescomplemented
63#63956C2218yescomplemented
64#63956C2218yescomplemented
65#63955C2218yescomplemented
66C2×Dic32C2211yescharacteristic, complemented
67C2×Dic32C2211yescharacteristic, complemented
68C2×Dic32C2211yescharacteristic, complemented
69C2×C3×#120—31no—
70C22×C3×C22⋊C4—31no—
71C2×#953D311yescharacteristic
72C22×#217—31no—
73C22×#217—31no—
74C22×#217—61no—
75C22×#217D311yescharacteristic, complemented
76C2×#936—31no—
77C2×#935—31no—
78C2×#935—31no—
79C2×#935—31no—
80C2×D4×Dic3—31no—
81C2×D4×Dic3—31no—
82C2×#929—31no—
83C2×C4×#67—31no—
84C2×#926—31no—
85C2×#924—31no—
86#5587—316no—
87#5495—316no—
88C2×#886—31no—
89C2×#885—31no—
90C2×#883—31no—
91C2×#67⋊C4—31no—
92C2×#879—31no—
93C2×#879—31no—
94C2×#879—31no—
95C2×#879—31no—
96C2×#878—31no—
97C2×#878—31no—
98C2×#878—31no—
99C2×#877—31no—
100C2×#877—31no—
101C2×#877—31no—
102C24×C32—24no—
103C24×C32—24no—
104C24×C32—42no—
105C24×C32C2311yescharacteristic
106C24×C32C2314yes—
107C24×C32C2311yescharacteristic
108C24×C32C2311yescharacteristic
109C23×C3×D3C2311yescharacteristic
110C22×C3⋊Dic3—24no—
111C22×C3⋊Dic3—42no—
112C22×C3⋊Dic3C2311yescharacteristic
113C22×C3⋊Dic3C2311yescharacteristic
114C22×C3⋊Dic3C2311yescharacteristic
115C22×C3⋊Dic3C2311yescharacteristic
116C22×C3⋊Dic3C2314yes—
117C22×C3⋊Dic3C2314yes—
118C2×C3×#67—24no—
119C2×C3×#67—24no—
120C2×C3×#67—42no—
121C2×C3×#67C2314yes—
122C2×C3×#67C2314yes—
123C2×C3×#67C2314yes—
124C22×C3×Dic3—24no—
125C22×C3×Dic3—42no—
126C22×C3×Dic3C2311yescharacteristic
127C22×C3×Dic3C2311yescharacteristic
128C22×C3×Dic3C2311yescharacteristic
129C22×C3×Dic3C2311yescharacteristic
130C22×C3×Dic3C2311yescharacteristic
131C22×C3×Dic3C2311yescharacteristic
132C22×C3×Dic3C2311yescharacteristic
133C22×C3×Dic3C2314yes—
134C22×C3×Dic3C2314yes—
135C2×#627—42no—
136C2×#627C2314yescomplemented
137C2×D3×Dic3—42no—
138C2×D3×Dic3C2314yescomplemented
139#3757C2314yes—
140#3757C2314yes—
141#3757C2314yes—
142#3757C2314yes—
143C3×#217C2314yes—
144C3×#217C2314yes—
145C3×#217C2314yes—
146C3×#217C2314yes—
147C3×#217C2314yes—
148C3×#217C2314yes—
149C3×#217C2314yes—
150#3724C2314yescomplemented
151#3724C2314yescomplemented
152#3724C2314yescomplemented
153Dic3⋊Dic3C2314yescomplemented
154Dic3⋊Dic3C2314yescomplemented
155Dic3⋊Dic3C2314yescomplemented
156Dic3⋊Dic3C2314yescomplemented
157Dic3⋊Dic3C2314yescomplemented
158(C2×D3)⋊Dic3C2314yescomplemented
159(C2×D3)⋊Dic3C2314yescomplemented
160(C2×D3)⋊Dic3C2314yescomplemented
161Dic32C2314yescomplemented
162Dic32C2314yescomplemented
163Dic32C2314yescomplemented
164C2×#551—91noSylow
165C25×C3—21no—
166C25×C3C2×D311yescharacteristic
167C25×C3C2×D311yescharacteristic
168C22×C3×D4—31no—
169C22×C3×D4—31no—
170C22×C3×D4—31no—
171C23×C3×C4—31no—
172C23×C3×C4—31no—
173C22×#67C2×D311yescharacteristic
174C22×#67C2×D311yescharacteristic
175C22×#67C2×D311yescharacteristic
176C23×Dic3—31no—
177C23×Dic3—31no—
178C23×Dic3—31no—
179C23×Dic3—31no—
180C23×Dic3—31no—
181C23×Dic3—61no—
182C23×Dic3—61no—
183C23×Dic3C2×D311yescharacteristic
184C23×Dic3C2×D311yescharacteristic
185C22×C4×D3—31no—
186C22×Dic6—31no—
187C22×Dic6—31no—
188C3×#120—38no—
189C2×C3×C22⋊C4—31no—
190C2×C3×C22⋊C4—31no—
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—
197#953C2×D318yes—
198C2×#217—31no—
199C2×#217—31no—
200C2×#217—31no—
201C2×#217—31no—
202C2×#217—31no—
203C2×#217—31no—
204C2×#217—38no—
205C2×#217—31no—
206C2×#217—31no—
207C2×#217—38no—
208C2×#217—31no—
209C2×#217—31no—
210C2×#217—31no—
211C2×#217—61no—
212C2×#217—61no—
213C2×#217—61no—
214C2×#217—61no—
215C2×#217—68no—
216C2×#217C2×D311yescharacteristic
217C2×#217C2×D311yescharacteristic
218C2×#217C2×D311yescharacteristic
219C2×#217C2×D311yescharacteristic
220C2×#217C2×D311yescharacteristic
221C2×#217C2×D311yescharacteristic
222C2×#217C2×D311yescharacteristic
223C2×#217C2×D318yescomplemented
224#936—38no—
225#935—38no—
226#935—38no—
227#935—38no—
228D4×Dic3—38no—
229D4×Dic3—38no—
230#929—38no—
231C4×#67—38no—
232C2×(C2×D3)⋊C4—31no—
233C2×(C2×D3)⋊C4—31no—
234C2×(C2×D3)⋊C4—31no—
235#926—38no—
236C2×C4⋊Dic3—31no—
237C2×C4⋊Dic3—31no—
238C2×C4⋊Dic3—31no—
239C2×C4⋊Dic3—31no—
240C2×C4⋊Dic3—31no—
241#924—38no—
242C2×Dic3⋊C4—31no—
243C2×Dic3⋊C4—31no—
244C2×Dic3⋊C4—31no—
245C2×Dic3⋊C4—31no—
246C2×Dic3⋊C4—31no—
247C2×Dic3⋊C4—31no—
248C2×Dic3⋊C4—31no—
249C2×Dic3⋊C4—31no—
250C2×Dic3⋊C4—31no—
251C2×Dic3⋊C4—31no—
252C2×Dic3⋊C4—31no—
253C2×C4×Dic3—31no—
254C2×C4×Dic3—31no—
255C2×C4×Dic3—31no—
256C2×C4×Dic3—31no—
257C2×C4×Dic3—31no—
258C2×C4×Dic3—31no—
259#886—38no—
260#885—38no—
261#883—38no—
262#67⋊C4—38no—
263#879—38no—
264#879—38no—
265#879—38no—
266#879—38no—
267#878—38no—
268#878—38no—
269#878—38no—
270#877—38no—
271#877—38no—
272#877—38no—
273C23×C32—22no—
274C23×C32—22no—
275C23×C32—28no—
276C23×C32—22no—
277C23×C32—22no—
278C23×C32—22no—
279C23×C32—28no—
280C23×C32—22no—
281C23×C32—22no—
282C23×C32—44no—
283C23×C32—416no—
284C23×C32#4114yes—
285C23×C32#4114yes—
286C23×C32C2412yes—
287C23×C32C2412yes—
288C23×C32C2412yes—
289C23×C32C2411yescharacteristic
290C22×C3×D3—22no—
291C22×C3×D3—22no—
292C22×C3×D3—22no—
293C22×C3×D3C2412yes—
294C2×C3⋊Dic3—28no—
295C2×C3⋊Dic3—22no—
296C2×C3⋊Dic3—22no—
297C2×C3⋊Dic3—22no—
298C2×C3⋊Dic3—22no—
299C2×C3⋊Dic3—44no—
300C2×C3⋊Dic3C2412yes—
301C2×C3⋊Dic3C2412yes—
302C2×C3⋊Dic3C2412yes—
303C2×C3⋊Dic3C2412yes—
304C3×#67—28no—
305C3×#67—28no—
306C3×#67—44no—
307C2×C3×Dic3—28no—
308C2×C3×Dic3—22no—
309C2×C3×Dic3—22no—
310C2×C3×Dic3—22no—
311C2×C3×Dic3—22no—
312C2×C3×Dic3—22no—
313C2×C3×Dic3—22no—
314C2×C3×Dic3—22no—
315C2×C3×Dic3—44no—
316C2×C3×Dic3C2412yes—
317C2×C3×Dic3C2412yes—
318C2×C3×Dic3C2412yes—
319C2×C3×Dic3C2412yes—
320C2×C3×Dic3C2412yes—
321C2×C3×Dic3C2412yes—
322C2×C3×Dic3C2412yes—
323#627—44no—
324D3×Dic3—44no—
325#551—916no—
326C2×#126—91no—
327C2×#126—91no—
328C2×#124—91no—
329C2×#123—91no—
330C2×#123—91no—
331C2×#123—91no—
332C2×C22⋊Q8—91no—
333C2×C22⋊Q8—91no—
334C2×#120—31no—
335C2×C4×D4—91no—
336C2×C4×D4—91no—
337C2×#117—91no—
338C2×#117—91no—
339C22×C22⋊C4—31no—
340C22×C22⋊C4—91no—
341C24×C3—28no—
342C24×C3—24no—
343C24×C3—24no—
344C24×C3—24no—
345C24×C3—24no—
346C24×C3—21no—
347C24×C3—21no—
348C24×C3—24no—
349C24×C3—21no—
350C24×C3—31no—
351C24×C3—44no—
352C24×C3—42no—
353C24×C3—42no—
354C24×C3—44no—
355C24×C3C22×D311yescharacteristic
356C24×C3C22×D311yescharacteristic
357C24×C3C22×D314yes—
358C24×C3C22×D314yes—
359C24×C3C22×D311yescharacteristic
360C24×C3C22×D311yescharacteristic
361C24×C3C22×D311yescharacteristic
362C24×C3C22×D311yescharacteristic
363C23×D3C22×D311yescharacteristic
364C2×C3×D4—34no—
365C2×C3×D4—34no—
366C2×C3×D4—34no—
367C2×C3×D4—64no—
368C2×C3×D4—64no—
369C2×C3×D4—122no—
370C22×C3×C4—31no—
371C22×C3×C4—31no—
372C22×C3×C4—31no—
373C22×C3×C4—31no—
374C22×C3×C4—31no—
375C22×C3×C4—31no—
376C22×C3×C4—31no—
377C22×C3×C4—34no—
378C22×C3×C4—34no—
379C22×C3×C4—64no—
380C22×C3×C4—122no—
381C2×#67—24no—
382C2×#67—24no—
383C2×#67—42no—
384C2×#67C22×D314yes—
385C2×#67C22×D314yes—
386C2×#67C22×D314yes—
387C22×Dic3—24no—
388C22×Dic3—34no—
389C22×Dic3—34no—
390C22×Dic3—31no—
391C22×Dic3—31no—
392C22×Dic3—31no—
393C22×Dic3—31no—
394C22×Dic3—31no—
395C22×Dic3—31no—
396C22×Dic3—31no—
397C22×Dic3—31no—
398C22×Dic3—34no—
399C22×Dic3—34no—
400C22×Dic3—34no—
401C22×Dic3—42no—
402C22×Dic3—64no—
403C22×Dic3—61no—
404C22×Dic3—61no—
405C22×Dic3—61no—
406C22×Dic3—61no—
407C22×Dic3—64no—
408C22×Dic3—64no—
409C22×Dic3—64no—
410C22×Dic3—124no—
411C22×Dic3—122no—
412C22×Dic3—122no—
413C22×Dic3—122no—
414C22×Dic3—124no—
415C22×Dic3C22×D314yes—
416C22×Dic3C22×D311yescharacteristic
417C22×Dic3C22×D311yescharacteristic
418C22×Dic3C22×D311yescharacteristic
419C22×Dic3C22×D311yescharacteristic
420C22×Dic3C22×D311yescharacteristic
421C22×Dic3C22×D311yescharacteristic
422C22×Dic3C22×D311yescharacteristic
423C22×Dic3C22×D314yes—
424C2×C4×D3—34no—
425C2×C4×D3—122no—
426C2×Dic6—34no—
427C2×Dic6—34no—
428C2×Dic6—122no—
429C2×Dic6—122no—
430C3×C22⋊C4—34no—
431C3×C22⋊C4—34no—
432C3×C22⋊C4—34no—
433C3×C22⋊C4—34no—
434C3×C22⋊C4—34no—
435C3×C22⋊C4—34no—
436C3×C22⋊C4—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—34no—
446#217—34no—
447#217—34no—
448#217—64no—
449#217—64no—
450#217—64no—
451#217—64no—
452#217C22×D314yes—
453#217C22×D314yes—
454#217C22×D314yes—
455#217C22×D314yes—
456#217C22×D314yes—
457#217C22×D314yes—
458#217C22×D314yes—
459(C2×D3)⋊C4—34no—
460(C2×D3)⋊C4—34no—
461(C2×D3)⋊C4—34no—
462C4⋊Dic3—34no—
463C4⋊Dic3—34no—
464C4⋊Dic3—34no—
465C4⋊Dic3—34no—
466C4⋊Dic3—34no—
467Dic3⋊C4—34no—
468Dic3⋊C4—34no—
469Dic3⋊C4—34no—
470Dic3⋊C4—34no—
471Dic3⋊C4—34no—
472Dic3⋊C4—34no—
473Dic3⋊C4—34no—
474Dic3⋊C4—34no—
475Dic3⋊C4—34no—
476Dic3⋊C4—34no—
477Dic3⋊C4—34no—
478C4×Dic3—34no—
479C4×Dic3—34no—
480C4×Dic3—34no—
481C4×Dic3—34no—
482C4×Dic3—34no—
483C4×Dic3—34no—
484C22×C32—28no—
485C22×C32—22no—
486C22×C32—22no—
487C22×C32—22no—
488C22×C32—28no—
489C22×C32—22no—
490C22×C32—22no—
491C22×C32—22no—
492C22×C32—22no—
493C22×C32—416no—
494C22×C32—44no—
495C22×C32C2×#4114yes—
496C22×C32C2×#4112yes—
497C22×C32C2×#4114yes—
498C22×C32C2×#4112yes—
499C22×C32H(5,𝔽2)12yes—
500C22×C32C2511yescharacteristic
501C2×C3×D3—22no—
502C2×C3×D3—22no—
503C2×C3×D3—22no—
504C2×C3×D3—44no—
505C3⋊Dic3—22no—
506C3⋊Dic3—22no—
507C3⋊Dic3—22no—
508C3⋊Dic3—22no—
509C3×Dic3—22no—
510C3×Dic3—22no—
511C3×Dic3—22no—
512C3×Dic3—22no—
513C3×Dic3—22no—
514C3×Dic3—22no—
515C3×Dic3—22no—
516C25D3211yescharacteristic
517C22×Q8—91no—
518C22×D4—31no—
519C22×D4—31no—
520C22×D4—31no—
521C23×C4—31no—
522C23×C4—31no—
523C23×C4—91no—
524C23×C4—91no—
525C23×C4—91no—
526#126—98no—
527#126—98no—
528#124—98no—
529#123—98no—
530#123—98no—
531#123—98no—
532C22⋊Q8—98no—
533C22⋊Q8—98no—
534#120—38no—
535C4×D4—98no—
536C4×D4—98no—
537#117—98no—
538#117—98no—
539C2×C4⋊C4—91no—
540C2×C4⋊C4—91no—
541C2×C4⋊C4—91no—
542C2×C4⋊C4—91no—
543C2×C4⋊C4—91no—
544C2×C4⋊C4—91no—
545C2×C4⋊C4—91no—
546C2×C4⋊C4—91no—
547C2×C22⋊C4—31no—
548C2×C22⋊C4—31no—
549C2×C22⋊C4—31no—
550C2×C22⋊C4—31no—
551C2×C22⋊C4—38no—
552C2×C22⋊C4—31no—
553C2×C22⋊C4—31no—
554C2×C22⋊C4—31no—
555C2×C22⋊C4—91no—
556C2×C22⋊C4—91no—
557C2×C22⋊C4—91no—
558C2×C22⋊C4—91no—
559C2×C22⋊C4—91no—
560C2×C22⋊C4—91no—
561C2×C22⋊C4—91no—
562C2×C22⋊C4—98no—
563C2×C42—91no—
564C2×C42—91no—
565C2×C42—91no—
566C23×C3—24no—
567C23×C3—24no—
568C23×C3—22no—
569C23×C3—22no—
570C23×C3—22no—
571C23×C3—22no—
572C23×C3—22no—
573C23×C3—22no—
574C23×C3—22no—
575C23×C3—22no—
576C23×C3—216no—
577C23×C3—24no—
578C23×C3—28no—
579C23×C3—22no—
580C23×C3—28no—
581C23×C3—22no—
582C23×C3—28no—
583C23×C3—28no—
584C23×C3—22no—
585C23×C3—22no—
586C23×C3—22no—
587C23×C3—22no—
588C23×C3—22no—
589C23×C3—22no—
590C23×C3—22no—
591C23×C3—21no—
592C23×C3—24no—
593C23×C3—24no—
594C23×C3—32no—
595C23×C3—42no—
596C23×C3—42no—
597C23×C3—48no—
598C23×C3—42no—
599C23×C3—42no—
600C23×C3—44no—
601C23×C3—44no—
602C23×C3—416no—
603C23×C3—416no—
604C23×C3—48no—
605C23×C3—432no—
606C23×C3—62no—
607C23×C3—62no—
608C23×C3—62no—
609C23×C3#23514yes—
610C23×C3#23714yes—
611C23×C3#23714yes—
612C23×C3#23714yes—
613C23×C3C23×D312yes—
614C23×C3C23×D312yes—
615C23×C3C23×D312yes—
616C23×C3C23×D312yes—
617C23×C3C23×D312yes—
618C23×C3C23×D312yes—
619C23×C3C23×D311yescharacteristic
620C23×C3C23×D311yescharacteristic
621C22×D3—22no—
622C22×D3—22no—
623C22×D3—22no—
624C22×D3C23×D312yes—
625C3×D4—68no—
626C3×D4—68no—
627C3×D4—124no—
628C2×C3×C4—32no—
629C2×C3×C4—32no—
630C2×C3×C4—32no—
631C2×C3×C4—32no—
632C2×C3×C4—32no—
633C2×C3×C4—32no—
634C2×C3×C4—32no—
635C2×C3×C4—62no—
636C2×C3×C4—68no—
637C2×C3×C4—62no—
638C2×C3×C4—62no—
639C2×C3×C4—62no—
640C2×C3×C4—62no—
641C2×C3×C4—62no—
642C2×C3×C4—62no—
643C2×C3×C4—124no—
644#67—28no—
645#67—28no—
646#67—44no—
647C2×Dic3—28no—
648C2×Dic3—22no—
649C2×Dic3—22no—
650C2×Dic3—22no—
651C2×Dic3—22no—
652C2×Dic3—22no—
653C2×Dic3—22no—
654C2×Dic3—22no—
655C2×Dic3—32no—
656C2×Dic3—32no—
657C2×Dic3—32no—
658C2×Dic3—32no—
659C2×Dic3—32no—
660C2×Dic3—32no—
661C2×Dic3—32no—
662C2×Dic3—32no—
663C2×Dic3—44no—
664C2×Dic3—62no—
665C2×Dic3—62no—
666C2×Dic3—62no—
667C2×Dic3—62no—
668C2×Dic3—68no—
669C2×Dic3—62no—
670C2×Dic3—62no—
671C2×Dic3—68no—
672C2×Dic3—62no—
673C2×Dic3—62no—
674C2×Dic3—62no—
675C2×Dic3—62no—
676C2×Dic3—62no—
677C2×Dic3—62no—
678C2×Dic3—128no—
679C2×Dic3—122no—
680C2×Dic3—122no—
681C2×Dic3—122no—
682C2×Dic3—122no—
683C2×Dic3—124no—
684C2×Dic3—124no—
685C2×Dic3—124no—
686C2×Dic3—128no—
687C2×Dic3C23×D312yes—
688C2×Dic3C23×D312yes—
689C2×Dic3C23×D312yes—
690C2×Dic3C23×D312yes—
691C2×Dic3C23×D312yes—
692C2×Dic3C23×D312yes—
693C2×Dic3C23×D312yes—
694C4×D3—124no—
695Dic6—124no—
696Dic6—124no—
697C2×C32—24no—
698C2×C32—24no—
699C2×C32—42no—
700C2×C32#55114yescomplemented
701C2×C32C22×#4111yescharacteristic
702C2×C32C22×#4111yescharacteristic
703C2×C32C2×H(5,𝔽2)11yescharacteristic
704C3×D3—42no—
705C24—24no—
706C24—24no—
707C24—31no—
708C24—42no—
709C24C2×D3211yescharacteristic
710C24C2×D3214yes—
711C24C2×D3211yescharacteristic
712C24C2×D3211yescharacteristic
713C2×Q8—94no—
714C2×Q8—362no—
715C2×D4—34no—
716C2×D4—34no—
717C2×D4—34no—
718C2×D4—64no—
719C2×D4—64no—
720C2×D4—122no—
721C22×C4—34no—
722C22×C4—31no—
723C22×C4—31no—
724C22×C4—31no—
725C22×C4—31no—
726C22×C4—31no—
727C22×C4—31no—
728C22×C4—31no—
729C22×C4—34no—
730C22×C4—64no—
731C22×C4—94no—
732C22×C4—94no—
733C22×C4—91no—
734C22×C4—91no—
735C22×C4—91no—
736C22×C4—91no—
737C22×C4—94no—
738C22×C4—122no—
739C22×C4—184no—
740C22×C4—362no—
741C22×C4—362no—
742C4⋊C4—94no—
743C4⋊C4—94no—
744C4⋊C4—94no—
745C4⋊C4—94no—
746C4⋊C4—94no—
747C4⋊C4—94no—
748C4⋊C4—94no—
749C4⋊C4—94no—
750C22⋊C4—34no—
751C22⋊C4—34no—
752C22⋊C4—34no—
753C22⋊C4—34no—
754C22⋊C4—34no—
755C22⋊C4—34no—
756C22⋊C4—34no—
757C22⋊C4—94no—
758C22⋊C4—94no—
759C22⋊C4—94no—
760C22⋊C4—94no—
761C22⋊C4—94no—
762C22⋊C4—94no—
763C22⋊C4—94no—
764C42—94no—
765C42—94no—
766C42—94no—
767C22×C3—24no—
768C22×C3—24no—
769C22×C3—216no—
770C22×C3—22no—
771C22×C3—22no—
772C22×C3—22no—
773C22×C3—22no—
774C22×C3—22no—
775C22×C3—22no—
776C22×C3—22no—
777C22×C3—22no—
778C22×C3—28no—
779C22×C3—28no—
780C22×C3—28no—
781C22×C3—28no—
782C22×C3—24no—
783C22×C3—22no—
784C22×C3—22no—
785C22×C3—22no—
786C22×C3—22no—
787C22×C3—22no—
788C22×C3—22no—
789C22×C3—24no—
790C22×C3—22no—
791C22×C3—22no—
792C22×C3—24no—
793C22×C3—22no—
794C22×C3—21no—
795C22×C3—42no—
796C22×C3—42no—
797C22×C3—48no—
798C22×C3—42no—
799C22×C3—42no—
800C22×C3—416no—
801C22×C3—416no—
802C22×C3—432no—
803C22×C3—48no—
804C22×C3—44no—
805C22×C3—44no—
806C22×C3—62no—
807C22×C3—62no—
808C22×C3—62no—
809C22×C3—124no—
810C22×C3C2×#23514yes—
811C22×C3C2×#23512yes—
812C22×C3C2×#23714yes—
813C22×C3C2×#23712yes—
814C22×C3C2×#23714yes—
815C22×C3C2×#23714yes—
816C22×C3C2×#23712yes—
817C22×C3C2×#23712yes—
818C22×C3#100412yes—
819C22×C3#100412yes—
820C22×C3C24×D311yescharacteristic
821C22×C3C24×D311yescharacteristic
822C2×D3—22no—
823C2×D3—22no—
824C2×D3—22no—
825C2×D3—44no—
826C3×C4—62no—
827C3×C4—62no—
828C3×C4—62no—
829C3×C4—62no—
830C3×C4—62no—
831C3×C4—62no—
832C3×C4—62no—
833Dic3—22no—
834Dic3—22no—
835Dic3—22no—
836Dic3—22no—
837Dic3—22no—
838Dic3—22no—
839Dic3—22no—
840Dic3—62no—
841Dic3—62no—
842Dic3—62no—
843Dic3—62no—
844Dic3—62no—
845Dic3—62no—
846Dic3—62no—
847Dic3—62no—
848Dic3—122no—
849Dic3—122no—
850Dic3—122no—
851Dic3—122no—
852C32C2×#55111yescharacteristic, complemented, Sylow
853C23—22no—
854C23—22no—
855C23—22no—
856C23—22no—
857C23—28no—
858C23—22no—
859C23—28no—
860C23—22no—
861C23—22no—
862C23—32no—
863C23—44no—
864C23—416no—
865C23—62no—
866C23—62no—
867C23—62no—
868C23#380414yes—
869C23#380514yes—
870C23C22×D3212yes—
871C23C22×D3212yes—
872C23C22×D3212yes—
873C23C22×D3211yescharacteristic
874Q8—364no—
875D4—68no—
876D4—68no—
877D4—124no—
878C2×C4—32no—
879C2×C4—32no—
880C2×C4—32no—
881C2×C4—32no—
882C2×C4—32no—
883C2×C4—32no—
884C2×C4—32no—
885C2×C4—62no—
886C2×C4—68no—
887C2×C4—62no—
888C2×C4—62no—
889C2×C4—62no—
890C2×C4—62no—
891C2×C4—62no—
892C2×C4—62no—
893C2×C4—92no—
894C2×C4—92no—
895C2×C4—92no—
896C2×C4—92no—
897C2×C4—124no—
898C2×C4—188no—
899C2×C4—182no—
900C2×C4—182no—
901C2×C4—182no—
902C2×C4—182no—
903C2×C4—364no—
904C2×C4—364no—
905C2×C3—28no—
906C2×C3—24no—
907C2×C3—24no—
908C2×C3—24no—
909C2×C3—24no—
910C2×C3—21no—
911C2×C3—21no—
912C2×C3—21no—
913C2×C3—24no—
914C2×C3—44no—
915C2×C3—44no—
916C2×C3—42no—
917C2×C3—42no—
918C2×C3—122no—
919C2×C3#549514yescomplemented
920C2×C3#558714yescomplemented
921C2×C3C22×#23511yescharacteristic
922C2×C3C22×#23711yescharacteristic
923C2×C3C22×#23711yescharacteristic
924C2×C3C22×#23711yescharacteristic
925C2×C3C2×#100411yescharacteristic
926C2×C3C2×#100411yescharacteristic
927D3—42no—
928C22—22no—
929C22—22no—
930C22—22no—
931C22—22no—
932C22—28no—
933C22—28no—
934C22—22no—
935C22—22no—
936C22—22no—
937C22—416no—
938C22—44no—
939C22—62no—
940C22—62no—
941C22—62no—
942C22—124no—
943C22C2×#380414yes—
944C22C2×#380412yes—
945C22C2×#380514yes—
946C22C2×#380512yes—
947C22#6433012yes—
948C22C23×D3211yescharacteristic
949C4—62no—
950C4—62no—
951C4—62no—
952C4—62no—
953C4—62no—
954C4—62no—
955C4—62no—
956C4—182no—
957C4—182no—
958C4—182no—
959C4—182no—
960C3—21no—
961C3C2×#549511yescharacteristic, complemented
962C3C2×#558711yescharacteristic, complemented
963C2—24no—
964C2—24no—
965C2—42no—
966C2—122no—
967C2#1059550914yesdirect product factor
968C2C22×#380411yescharacteristic
969C2C22×#380511yescharacteristic
970C2C2×#6433011yescharacteristic
subgroupG/H
centerC23C22×D32
commutator, cosocleC22×C32C25
FrattiniC22C23×D32
FittingC25×C32C22
socleC23×C32C24
prime radicalC2×C3×#953C2
hypercenterC25D32
hypocenterC32C2×#551
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C23 ◁ C25

Complements

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

NH ≅ G/Ntype
1. C22×#3757C2semidirect
3. C22×C3×#217C2semidirect
4. C2×#63982C2semidirect
5. #10595509C2direct (N × H)
6. C2×#67⋊Dic3C2semidirect
7. C2×Dic3×#67C2semidirect
8. C2×#63969C2semidirect
9. C2×#63964C2semidirect
10. C2×#63962C2semidirect
11. C2×#63961C2semidirect
12. C2×#63959C2semidirect
13. C2×#63957C2semidirect
14. C2×#63956C2semidirect
15. C2×#63956C2semidirect
16. C2×#63955C2semidirect
27. C22×#627C22semidirect
28. C22×D3×Dic3C22semidirect
33. C2×#3757C22semidirect
42. C2×C3×#217C22semidirect
43. #63982C22semidirect
44. #67⋊Dic3C22semidirect
45. Dic3×#67C22semidirect
46. #63969C22semidirect
47. C2×#3724C22semidirect
48. C2×#3724C22semidirect
49. C2×#3724C22semidirect
50. C2×Dic3⋊Dic3C22semidirect
51. C2×Dic3⋊Dic3C22semidirect
52. C2×Dic3⋊Dic3C22semidirect
53. C2×Dic3⋊Dic3C22semidirect
54. C2×Dic3⋊Dic3C22semidirect
55. #63964C22semidirect
56. #63962C22semidirect
57. #63961C22semidirect
58. C2×(C2×D3)⋊Dic3C22semidirect
59. C2×(C2×D3)⋊Dic3C22semidirect
60. C2×(C2×D3)⋊Dic3C22semidirect
61. #63959C22semidirect
62. #63957C22semidirect
63. #63956C22semidirect
64. #63956C22semidirect
65. #63955C22semidirect
66. C2×Dic32C22semidirect
67. C2×Dic32C22semidirect
68. C2×Dic32C22semidirect
75. C22×#217D3semidirect
136. C2×#627C23semidirect
138. C2×D3×Dic3C23semidirect
150. #3724C23semidirect
151. #3724C23semidirect
152. #3724C23semidirect
153. Dic3⋊Dic3C23semidirect
154. Dic3⋊Dic3C23semidirect
155. Dic3⋊Dic3C23semidirect
156. Dic3⋊Dic3C23semidirect
157. Dic3⋊Dic3C23semidirect
158. (C2×D3)⋊Dic3C23semidirect
159. (C2×D3)⋊Dic3C23semidirect
160. (C2×D3)⋊Dic3C23semidirect
161. Dic32C23semidirect
162. Dic32C23semidirect
163. Dic32C23semidirect
223. C2×#217C2×D3semidirect
700. C2×C32#551semidirect
852. C32C2×#551semidirect
919. C2×C3#5495semidirect
920. C2×C3#5587semidirect
961. C3C2×#5495semidirect
962. C3C2×#5587semidirect
967. C2#10595509direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#37572
C2×C3×#9532
C22×C3×#2172
C2×#639822
#105955092
C2×#67⋊Dic32
C2×Dic3×#672
C2×#639692
C2×#639642
C2×#639622
C2×#639612
C2×#639592
C2×#639572
C2×#639562
C2×#639552
C2×#55873
C2×#54953