Finite Group Databasebeta

← C2×D3×#548 #11702117

Subgroups — C2×D3×#548 #11702117

Order 768.

12142 conjugacy classes of subgroups.

The subgroup lattice has 860 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×D3×#41C211yesmaximal, characteristic, complemented
2C23×D3×Q8C211yesmaximal, characteristic, complemented
3C2×C3×#548C211yesmaximal, characteristic, complemented
4C2×#5831C211yesmaximal, characteristic, complemented
5C2×#5817C211yesmaximal, characteristic, complemented
6D3×#548C2132yesmaximal, direct product factor
7C2×#5677C213yesmaximal, complemented
8C2×D3×#124C213yesmaximal, complemented
9C2×#5633C213yesmaximal, complemented
10C2×D3×C22⋊Q8C213yesmaximal, complemented
11C2×D3×#121C213yesmaximal, complemented
12C2×#5598C213yesmaximal, complemented
13C2×#5576C211yesmaximal, characteristic, complemented
14C2×C4×D3×Q8C211yesmaximal, characteristic, complemented
15C2×C4×D3×D4C213yesmaximal, complemented
16C2×#5552C213yesmaximal, complemented
17C22×#548—31nomaximal, Sylow
18C22×C3×#41C2211yescharacteristic, complemented
19C23×C3×Q8C2211yescharacteristic, complemented
20C2×D3×#41—216no—
21C2×D3×#41C22116yescomplemented
22C22×#239C2211yescharacteristic, complemented
23C22×D3×Q8—216no—
24C22×D3×Q8C2213yes—
25C22×D3×Q8C2211yescharacteristic
26C22×D3×Q8C2211yescharacteristic, complemented
27C22×D3×Q8C2213yescomplemented
28C22×D3×Q8C22116yescomplemented
29C22×#237C2213yescomplemented
30C22×D3×D4C2213yes—
31C22×D3×D4C2213yes—
32C22×#235C2213yescomplemented
33C23×C4×D3C2213yes—
34C23×C4×D3C2213yes—
35C23×Dic6C2213yescomplemented
36C3×#548C22116yescomplemented
37C2×C3×#124C2213yescomplemented
38C2×C3×C22⋊Q8C2213yescomplemented
39C2×C3×#121C2213yescomplemented
40C2×C3×C4×Q8C2211yescharacteristic, complemented
41C2×C3×C4×D4C2213yescomplemented
42#5831C22116yescomplemented
43#5817C22116yescomplemented
44C2×#947C2213yescomplemented
45C2×#946C2213yescomplemented
46C2×Q8×Dic3C2211yescharacteristic, complemented
47C2×#939C2216yescomplemented
48C2×#938C2213yescomplemented
49C2×#936C2213yescomplemented
50C2×D4×Dic3C2213yescomplemented
51C2×#930C2213yescomplemented
52C2×C4×#67C2213yescomplemented
53C2×C4×#67C2213yescomplemented
54C2×#924C2213yescomplemented
55#5677C22148yescomplemented
56D3×#124C22148yescomplemented
57#5633C22148yescomplemented
58D3×C22⋊Q8C22148yescomplemented
59D3×#121C22148yescomplemented
60#5598C22148yescomplemented
61#5576C22116yescomplemented
62C4×D3×Q8C22116yescomplemented
63#5552C22148yescomplemented
64C4×D3×D4C22148yescomplemented
65C2×#897C2213yescomplemented
66C2×#896C2216yescomplemented
67C2×#895C2213yescomplemented
68C2×#893C2213yescomplemented
69C2×D3×C4⋊C4C2213yes—
70C2×D3×C4⋊C4C2213yes—
71C2×#887C2213yescomplemented
72C2×#885C2216yescomplemented
73C2×#885C2216yescomplemented
74C2×#884C2216yescomplemented
75C2×#67⋊C4C2213yescomplemented
76C2×#67⋊C4C2213yescomplemented
77C2×D3×C22⋊C4C2211yescharacteristic
78C2×D3×C22⋊C4C2213yes—
79C2×D3×C22⋊C4C2216yes—
80C2×#878C2216yescomplemented
81C2×#875C2213yescomplemented
82C2×C4×D12C2213yescomplemented
83C2×C42×D3C2213yes—
84C2×C4×Dic6C2213yescomplemented
85C23×#41—31no—
86C24×Q8—31no—
87C2×#548—31no—
88C2×#548—31no—
89C2×#548—332no—
90C2×#548—33no—
91C2×#548—33no—
92C2×#548—33no—
93C2×#548—31no—
94C2×#548—33no—
95C2×#548D311yescharacteristic, direct product factor
96C22×#124—33no—
97C22×C22⋊Q8—33no—
98C22×#121—33no—
99C22×C4×Q8—31no—
100C22×C4×D4—33no—
101C24×D3C2313yes—
102C24×D3C2311yescharacteristic
103C2×C3×#41—28no—
104C2×C3×#41C2318yescomplemented
105C22×C3×Q8—28no—
106C22×C3×Q8C2313yes—
107C22×C3×Q8C2311yescharacteristic
108C22×C3×Q8C2318yescomplemented
109C22×C3×D4C2313yes—
110C22×C3×D4C2313yes—
111C23×C3×C4C2313yes—
112C23×C3×C4C2313yes—
113C22×#67C2316yes—
114C22×#67C2313yes—
115C22×#67C2313yes—
116C23×Dic3C2313yes—
117C23×Dic3C2313yes—
118D3×#41—2128no—
119C2×#239—28no—
120C2×#239C2318yescomplemented
121C2×D3×Q8—28no—
122C2×D3×Q8—2128no—
123C2×D3×Q8—224no—
124C2×D3×Q8—224no—
125C2×D3×Q8D4116yescomplemented
126C2×D3×Q8C23124yes—
127C2×D3×Q8C2318yes—
128C2×D3×Q8C23124yescomplemented
129C2×D3×Q8C2318yescomplemented
130C2×#237—224no—
131C2×#237C23124yescomplemented
132C2×D3×D4—224no—
133C2×D3×D4—224no—
134C2×D3×D4C23124yes—
135C2×D3×D4C23124yes—
136C2×#235—224no—
137C2×#235C23124yescomplemented
138C22×D12C2313yes—
139C22×D12C2313yes—
140C22×C4×D3—224no—
141C22×C4×D3—224no—
142C22×C4×D3C2311yescharacteristic
143C22×C4×D3C2313yes—
144C22×C4×D3C2313yes—
145C22×C4×D3C2313yes—
146C22×C4×D3C2313yes—
147C22×C4×D3C2313yes—
148C22×C4×D3C23124yes—
149C22×C4×D3C23124yes—
150C22×C4×D3C2313yes—
151C22×C4×D3C2311yescharacteristic
152C22×C4×D3C2313yes—
153C22×Dic6—224no—
154C22×Dic6C2313yes—
155C22×Dic6C2316yes—
156C22×Dic6C2313yes—
157C22×Dic6C23124yescomplemented
158C3×#124C23124yescomplemented
159C3×C22⋊Q8C23124yescomplemented
160C3×#121C23124yescomplemented
161C3×C4×Q8C2318yescomplemented
162C3×C4×D4C23124yescomplemented
163C2×C3×C4⋊C4C2313yes—
164C2×C3×C4⋊C4C2313yes—
165C2×C3×C22⋊C4C2316yes—
166C2×C3×C22⋊C4C2311yescharacteristic
167C2×C3×C22⋊C4C2313yes—
168C2×C3×C42C2313yes—
169C2×#217C2316yes—
170C2×#217C2313yes—
171C2×#217C2311yescharacteristic
172#947C23124yescomplemented
173#946C23124yescomplemented
174Q8×Dic3C2318yescomplemented
175#939C23148yescomplemented
176#938C23124yescomplemented
177#936C23124yescomplemented
178D4×Dic3C23124yescomplemented
179#930C23124yescomplemented
180C4×#67C23124yescomplemented
181C4×#67C23124yescomplemented
182C2×(C2×D3)⋊C4C2311yescharacteristic
183C2×(C2×D3)⋊C4C2313yes—
184C2×(C2×D3)⋊C4C2316yes—
185C2×(C2×D3)⋊C4C2316yes—
186C2×(C2×D3)⋊C4C2313yes—
187C2×(C2×D3)⋊C4C2311yescharacteristic
188C2×C4⋊Dic3C2313yes—
189C2×C4⋊Dic3C2313yes—
190#924C23124yescomplemented
191C2×Dic3⋊C4C2316yes—
192C2×Dic3⋊C4C2313yes—
193C2×Dic3⋊C4C2313yes—
194C2×C4×Dic3C2313yes—
195C2×C4×Dic3C2313yes—
196C2×C4×Dic3C2313yes—
197#897C23124yescomplemented
198#896C23148yescomplemented
199#895C23124yescomplemented
200#893C23124yescomplemented
201D3×C4⋊C4C23124yes—
202D3×C4⋊C4C23124yes—
203#887C23124yescomplemented
204#885C23148yescomplemented
205#885C23148yescomplemented
206#884C23148yescomplemented
207#67⋊C4C23124yescomplemented
208#67⋊C4C23124yescomplemented
209D3×C22⋊C4C23124yes—
210D3×C22⋊C4C23148yes—
211D3×C22⋊C4C2318yes—
212#878C23148yescomplemented
213#875C23124yescomplemented
214C4×D12C23124yescomplemented
215C42×D3C23124yes—
216C4×Dic6C23124yescomplemented
217C22×#41—316no—
218C22×#41—31no—
219C22×#41—33no—
220C22×#41—33no—
221C22×#41—616no—
222C22×#41C2×D311yescharacteristic, complemented
223C23×Q8—31no—
224C23×Q8—33no—
225C23×Q8—33no—
226C23×Q8—31no—
227C23×Q8—316no—
228C23×Q8—33no—
229C23×Q8—616no—
230C23×Q8C2×D311yescharacteristic, complemented
231C23×D4—33no—
232C23×D4—33no—
233C24×C4—33no—
234C24×C4—33no—
235#548—316no—
236#548—316no—
237#548—348no—
238#548—348no—
239#548—348no—
240#548—316no—
241#548—348no—
242#548C2×D3116yesdirect product factor
243C2×#124—33no—
244C2×#124—33no—
245C2×#124—348no—
246C2×#124—36no—
247C2×#124—36no—
248C2×#124—33no—
249C2×#124C2×D313yescomplemented
250C2×C22⋊Q8—33no—
251C2×C22⋊Q8—33no—
252C2×C22⋊Q8—348no—
253C2×C22⋊Q8—36no—
254C2×C22⋊Q8—33no—
255C2×C22⋊Q8—36no—
256C2×C22⋊Q8C2×D313yescomplemented
257C2×#121—33no—
258C2×#121—36no—
259C2×#121—33no—
260C2×#121—348no—
261C2×#121—33no—
262C2×#121—36no—
263C2×#121C2×D313yescomplemented
264C2×C4×Q8—31no—
265C2×C4×Q8—316no—
266C2×C4×Q8—33no—
267C2×C4×Q8—33no—
268C2×C4×Q8C2×D311yescharacteristic, complemented
269C2×C4×D4—33no—
270C2×C4×D4—33no—
271C2×C4×D4—33no—
272C2×C4×D4—348no—
273C2×C4×D4—33no—
274C2×C4×D4—33no—
275C2×C4×D4—33no—
276C2×C4×D4—33no—
277C2×C4×D4C2×D313yescomplemented
278C22×C4⋊C4—33no—
279C22×C4⋊C4—33no—
280C22×C22⋊C4—31no—
281C22×C22⋊C4—33no—
282C22×C22⋊C4—36no—
283C22×C42—33no—
284C24×C3C2413yes—
285C24×C3C2411yescharacteristic
286C23×D3—24no—
287C23×D3—24no—
288C23×D3—212no—
289C23×D3—212no—
290C23×D3—212no—
291C23×D3#4118yescomplemented
292C23×D3C24112yes—
293C23×D3C2413yes—
294C23×D3C2414yes—
295C23×D3C2411yescharacteristic
296C23×D3C2411yescharacteristic
297C3×#41—232no—
298C2×C3×Q8—232no—
299C2×C3×Q8—212no—
300C2×C3×Q8C2×D418yescomplemented
301C2×C3×Q8C24112yes—
302C2×C3×Q8C2414yes—
303C2×C3×D4—212no—
304C2×C3×D4—212no—
305C2×C3×D4C24112yes—
306C2×C3×D4C24112yes—
307C22×C3×C4—212no—
308C22×C3×C4—212no—
309C22×C3×C4C2411yescharacteristic
310C22×C3×C4C2413yes—
311C22×C3×C4C2411yescharacteristic
312C22×C3×C4C2413yes—
313C22×C3×C4C24112yes—
314C22×C3×C4C24112yes—
315C22×C3×C4C2413yes—
316C2×#67—212no—
317C2×#67—212no—
318C2×#67—224no—
319C2×#67C24112yes—
320C2×#67C24112yes—
321C2×#67C24124yes—
322C22×Dic3—212no—
323C22×Dic3—212no—
324C22×Dic3C24112yes—
325C22×Dic3C24112yes—
326C22×Dic3C2411yescharacteristic
327C22×Dic3C2413yes—
328C22×Dic3C2411yescharacteristic
329C22×Dic3C2413yes—
330C22×Dic3C2413yes—
331#239—232no—
332D3×Q8—232no—
333D3×Q8—296no—
334D3×Q8—296no—
335D3×Q8C2×D4164yescomplemented
336#237—296no—
337D3×D4—296no—
338D3×D4—296no—
339#235—296no—
340C2×D12—212no—
341C2×D12—212no—
342C2×D12C24112yes—
343C2×D12C24112yes—
344C2×C4×D3—24no—
345C2×C4×D3—212no—
346C2×C4×D3—212no—
347C2×C4×D3—24no—
348C2×C4×D3—212no—
349C2×C4×D3—212no—
350C2×C4×D3—212no—
351C2×C4×D3—212no—
352C2×C4×D3—296no—
353C2×C4×D3—296no—
354C2×C4×D3C2×D4124yes—
355C2×C4×D3C2414yes—
356C2×C4×D3C24112yes—
357C2×C4×D3C24112yes—
358C2×C4×D3C24112yes—
359C2×C4×D3C24112yes—
360C2×C4×D3C2414yes—
361C2×C4×D3C24112yes—
362C2×C4×D3C24112yes—
363C2×C4×D3C24112yes—
364C2×Dic6—212no—
365C2×Dic6—224no—
366C2×Dic6—296no—
367C2×Dic6C2×D4124yescomplemented
368C2×Dic6C24112yes—
369C2×Dic6C24124yes—
370C2×Dic6C24112yes—
371C3×C4⋊C4C24112yes—
372C3×C4⋊C4C24112yes—
373C3×C22⋊C4C24124yes—
374C3×C22⋊C4C2414yes—
375C3×C22⋊C4C24112yes—
376C3×C42C24112yes—
377#217C24124yes—
378#217C24112yes—
379#217C2414yes—
380(C2×D3)⋊C4C2414yes—
381(C2×D3)⋊C4C24112yes—
382(C2×D3)⋊C4C24124yes—
383(C2×D3)⋊C4C24124yes—
384(C2×D3)⋊C4C24112yes—
385(C2×D3)⋊C4C2414yes—
386C4⋊Dic3C24112yes—
387C4⋊Dic3C24112yes—
388Dic3⋊C4C24124yes—
389Dic3⋊C4C24112yes—
390Dic3⋊C4C24112yes—
391C4×Dic3C24112yes—
392C4×Dic3C24112yes—
393C4×Dic3C24112yes—
394C25—31no—
395C25—33no—
396C2×#41—28no—
397C2×#41—38no—
398C2×#41—324no—
399C2×#41—324no—
400C2×#41—624no—
401C2×#41—624no—
402C2×#41—6128no—
403C2×#41—68no—
404C2×#41C22×D318yescomplemented
405C22×Q8—28no—
406C22×Q8—316no—
407C22×Q8—38no—
408C22×Q8—324no—
409C22×Q8—324no—
410C22×Q8—38no—
411C22×Q8—33no—
412C22×Q8—36no—
413C22×Q8—33no—
414C22×Q8—324no—
415C22×Q8—624no—
416C22×Q8—624no—
417C22×Q8—6128no—
418C22×Q8—624no—
419C22×Q8—68no—
420C22×Q8C22×D313yes—
421C22×Q8C22×D311yescharacteristic
422C22×Q8C22×D318yescomplemented
423C22×D4—33no—
424C22×D4—33no—
425C22×D4—36no—
426C22×D4—324no—
427C22×D4—324no—
428C22×D4—33no—
429C22×D4—33no—
430C22×D4—624no—
431C22×D4—624no—
432C22×D4C22×D313yes—
433C22×D4C22×D313yes—
434C23×C4—33no—
435C23×C4—33no—
436C23×C4—33no—
437C23×C4—31no—
438C23×C4—33no—
439C23×C4—33no—
440C23×C4—31no—
441C23×C4—33no—
442C23×C4—324no—
443C23×C4—33no—
444C23×C4—33no—
445C23×C4—324no—
446C23×C4—33no—
447C23×C4—624no—
448C23×C4—624no—
449C23×C4C22×D313yes—
450C23×C4C22×D313yes—
451#124—324no—
452#124—324no—
453#124—348no—
454#124—348no—
455#124—324no—
456#124C22×D3124yescomplemented
457C22⋊Q8—324no—
458C22⋊Q8—324no—
459C22⋊Q8—348no—
460C22⋊Q8—324no—
461C22⋊Q8—348no—
462C22⋊Q8C22×D3124yescomplemented
463#121—324no—
464#121—348no—
465#121—324no—
466#121—324no—
467#121—348no—
468#121C22×D3124yescomplemented
469C4×Q8—38no—
470C4×Q8—324no—
471C4×Q8—324no—
472C4×Q8C22×D318yescomplemented
473C4×D4—324no—
474C4×D4—324no—
475C4×D4—324no—
476C4×D4—324no—
477C4×D4—324no—
478C4×D4—324no—
479C4×D4—324no—
480C4×D4C22×D3124yescomplemented
481C2×C4⋊C4—33no—
482C2×C4⋊C4—33no—
483C2×C4⋊C4—33no—
484C2×C4⋊C4—36no—
485C2×C4⋊C4—33no—
486C2×C4⋊C4—324no—
487C2×C4⋊C4—324no—
488C2×C4⋊C4C22×D313yes—
489C2×C4⋊C4C22×D313yes—
490C2×C22⋊C4—31no—
491C2×C22⋊C4—33no—
492C2×C22⋊C4—36no—
493C2×C22⋊C4—31no—
494C2×C22⋊C4—31no—
495C2×C22⋊C4—33no—
496C2×C22⋊C4—33no—
497C2×C22⋊C4—36no—
498C2×C22⋊C4—36no—
499C2×C22⋊C4—38no—
500C2×C22⋊C4—324no—
501C2×C22⋊C4—348no—
502C2×C22⋊C4C22×D311yescharacteristic
503C2×C22⋊C4C22×D313yes—
504C2×C22⋊C4C22×D316yes—
505C2×C42—33no—
506C2×C42—33no—
507C2×C42—33no—
508C2×C42—324no—
509C2×C42C22×D313yes—
510C23×C3—22no—
511C23×C3—22no—
512C23×C3—26no—
513C23×C3—26no—
514C23×C3—26no—
515C23×C3C2×#4114yescomplemented
516C23×C3C2516yes—
517C23×C3C2512yes—
518C23×C3C2511yescharacteristic
519C22×D3—22no—
520C22×D3—22no—
521C22×D3—232no—
522C22×D3—28no—
523C22×D3—28no—
524C22×D3—26no—
525C22×D3—26no—
526C22×D3—26no—
527C22×D3—224no—
528C22×D3—224no—
529C22×D3—224no—
530C22×D3—448no—
531C22×D3C22×D414yes—
532C22×D3C2×#4114yes—
533C22×D3C2×#41116yescomplemented
534C22×D3C2×#4114yescomplemented
535C22×D32−1+414yes—
536C22×D3C2516yes—
537C22×D3C2512yes—
538C22×D3C2512yes—
539C3×Q8—224no—
540C3×Q8C22×D4116yescomplemented
541C3×D4—224no—
542C3×D4—224no—
543C2×C3×C4—26no—
544C2×C3×C4—22no—
545C2×C3×C4—26no—
546C2×C3×C4—22no—
547C2×C3×C4—224no—
548C2×C3×C4—224no—
549C2×C3×C4C22×D4112yes—
550C2×C3×C4C2512yes—
551C2×C3×C4C2516yes—
552C2×C3×C4C2512yes—
553C2×C3×C4C2516yes—
554C2×C3×C4C2516yes—
555#67—224no—
556#67—224no—
557#67—248no—
558C2×Dic3—26no—
559C2×Dic3—22no—
560C2×Dic3—26no—
561C2×Dic3—22no—
562C2×Dic3—224no—
563C2×Dic3—224no—
564C2×Dic3C22×D4112yes—
565C2×Dic3C2512yes—
566C2×Dic3C2516yes—
567C2×Dic3C2512yes—
568C2×Dic3C2516yes—
569C2×Dic3C2516yes—
570D12—224no—
571D12—224no—
572C4×D3—28no—
573C4×D3—224no—
574C4×D3—224no—
575C4×D3—28no—
576C4×D3—224no—
577C4×D3—224no—
578C4×D3—224no—
579C4×D3—224no—
580C4×D3C22×D4148yes—
581Dic6—224no—
582Dic6—248no—
583Dic6C22×D4148yescomplemented
584C24—31no—
585C24—38no—
586C24—34no—
587C24—31no—
588C24—312no—
589C24—33no—
590C24—64no—
591C24—64no—
592C24—612no—
593C24—612no—
594C24—612no—
595C24C23×D313yes—
596C24C23×D311yescharacteristic
597#41—232no—
598#41—696no—
599#41—696no—
600#41—632no—
601C2×Q8—232no—
602C2×Q8—212no—
603C2×Q8—364no—
604C2×Q8—324no—
605C2×Q8—312no—
606C2×Q8—324no—
607C2×Q8—312no—
608C2×Q8—624no—
609C2×Q8—696no—
610C2×Q8—696no—
611C2×Q8—696no—
612C2×Q8—632no—
613C2×Q8—612no—
614C2×Q8D3×D418yescomplemented
615C2×Q8C23×D3112yes—
616C2×Q8C23×D314yes—
617C2×D4—212no—
618C2×D4—212no—
619C2×D4—312no—
620C2×D4—312no—
621C2×D4—324no—
622C2×D4—312no—
623C2×D4—312no—
624C2×D4—612no—
625C2×D4—696no—
626C2×D4—624no—
627C2×D4—696no—
628C2×D4—612no—
629C2×D4—612no—
630C2×D4—612no—
631C2×D4C23×D3112yes—
632C2×D4C23×D3112yes—
633C22×C4—212no—
634C22×C4—212no—
635C22×C4—33no—
636C22×C4—324no—
637C22×C4—312no—
638C22×C4—312no—
639C22×C4—312no—
640C22×C4—31no—
641C22×C4—33no—
642C22×C4—33no—
643C22×C4—31no—
644C22×C4—34no—
645C22×C4—312no—
646C22×C4—312no—
647C22×C4—34no—
648C22×C4—312no—
649C22×C4—312no—
650C22×C4—312no—
651C22×C4—312no—
652C22×C4—612no—
653C22×C4—696no—
654C22×C4—612no—
655C22×C4—696no—
656C22×C4—64no—
657C22×C4—612no—
658C22×C4—612no—
659C22×C4—64no—
660C22×C4—612no—
661C22×C4—612no—
662C22×C4—612no—
663C22×C4—612no—
664C22×C4C23×D3112yes—
665C22×C4C23×D3112yes—
666C22×C4C23×D311yescharacteristic
667C22×C4C23×D313yes—
668C22×C4C23×D313yes—
669C22×C4C23×D311yescharacteristic
670C22×C4C23×D313yes—
671C4⋊C4—312no—
672C4⋊C4—312no—
673C4⋊C4—312no—
674C4⋊C4—324no—
675C4⋊C4—312no—
676C4⋊C4C23×D3112yes—
677C4⋊C4C23×D3112yes—
678C22⋊C4—34no—
679C22⋊C4—312no—
680C22⋊C4—324no—
681C22⋊C4—34no—
682C22⋊C4—34no—
683C22⋊C4—312no—
684C22⋊C4—312no—
685C22⋊C4—324no—
686C22⋊C4—324no—
687C22⋊C4C23×D314yes—
688C22⋊C4C23×D3112yes—
689C22⋊C4C23×D3124yes—
690C42—312no—
691C42—312no—
692C42—312no—
693C42C23×D3112yes—
694C22×C3—22no—
695C22×C3—22no—
696C22×C3—28no—
697C22×C3—26no—
698C22×C3—26no—
699C22×C3—26no—
700C22×C3—412no—
701C22×C3C23×D412yes—
702C22×C3C22×#4112yes—
703C22×C3C22×#4114yescomplemented
704C22×C3C2×2−1+412yes—
705C22×C3C2611yescharacteristic
706C2×D3—22no—
707C2×D3—22no—
708C2×D3—28no—
709C2×D3—232no—
710C2×D3—26no—
711C2×D3—26no—
712C2×D3—26no—
713C2×D3—412no—
714C2×D3—448no—
715C2×D3#548116yesdirect product factor
716C2×D3C23×D414yes—
717C2×D3C22×#4114yes—
718C2×D3C22×#4114yescomplemented
719C2×D3C2×2−1+414yes—
720C3×C4—26no—
721C3×C4—22no—
722C3×C4—26no—
723C3×C4—22no—
724C3×C4C23×D4112yes—
725Dic3—26no—
726Dic3—22no—
727Dic3—26no—
728Dic3—22no—
729Dic3C23×D4112yes—
730C23—22no—
731C23—22no—
732C23—26no—
733C23—26no—
734C23—26no—
735C23—34no—
736C23—34no—
737C23—34no—
738C23—32no—
739C23—34no—
740C23—316no—
741C23—32no—
742C23—36no—
743C23—68no—
744C23—68no—
745C23—632no—
746C23—624no—
747C23—624no—
748C23—624no—
749C23—62no—
750C23—62no—
751C23—66no—
752C23—66no—
753C23—66no—
754C23—1248no—
755C23D3×#4114yescomplemented
756C23C24×D316yes—
757C23C24×D312yes—
758C23C24×D311yescharacteristic
759Q8—224no—
760Q8—348no—
761Q8—648no—
762Q8—624no—
763Q8C2×D3×D4116yescomplemented
764D4—224no—
765D4—224no—
766D4—624no—
767D4—648no—
768D4—624no—
769D4—624no—
770D4—624no—
771C2×C4—22no—
772C2×C4—26no—
773C2×C4—26no—
774C2×C4—22no—
775C2×C4—224no—
776C2×C4—224no—
777C2×C4—312no—
778C2×C4—36no—
779C2×C4—348no—
780C2×C4—32no—
781C2×C4—36no—
782C2×C4—36no—
783C2×C4—32no—
784C2×C4—624no—
785C2×C4—624no—
786C2×C4—68no—
787C2×C4—624no—
788C2×C4—624no—
789C2×C4—68no—
790C2×C4—624no—
791C2×C4—624no—
792C2×C4—62no—
793C2×C4—66no—
794C2×C4—66no—
795C2×C4—62no—
796C2×C4—624no—
797C2×C4—624no—
798C2×C4C2×D3×D4112yes—
799C2×C4C24×D312yes—
800C2×C4C24×D316yes—
801C2×C4C24×D316yes—
802C2×C4C24×D312yes—
803C2×C4C24×D316yes—
804C2×C3—24no—
805C2×C3—46no—
806C2×C3C2×#54814yescomplemented
807C2×C3C24×D411yescharacteristic
808C2×C3C23×#4111yescharacteristic
809C2×C3C22×2−1+411yescharacteristic
810D3—24no—
811D3—46no—
812D3C2×#54818yesdirect product factor
813C22—22no—
814C22—22no—
815C22—28no—
816C22—26no—
817C22—26no—
818C22—26no—
819C22—34no—
820C22—34no—
821C22—34no—
822C22—316no—
823C22—34no—
824C22—412no—
825C22—632no—
826C22—62no—
827C22—62no—
828C22—68no—
829C22—66no—
830C22—66no—
831C22—66no—
832C22—1248no—
833C22—1212no—
834C22C22×D3×D412yes—
835C22C2×D3×#4112yes—
836C22C2×D3×#4114yescomplemented
837C22D3×2−1+412yes—
838C22C25×D311yescharacteristic
839C4—22no—
840C4—26no—
841C4—26no—
842C4—22no—
843C4—312no—
844C4—62no—
845C4—66no—
846C4—66no—
847C4—62no—
848C4C22×D3×D4112yes—
849C3C22×#54811yescharacteristic, complemented, Sylow
850C2—24no—
851C2—38no—
852C2—46no—
853C2—64no—
854C2—126no—
855C2D3×#54814yesdirect product factor
856C2C23×D3×D411yescharacteristic
857C2C22×D3×#4111yescharacteristic
858C2C2×D3×2−1+411yescharacteristic
subgroupG/H
centerC23C24×D3
commutator, cosocleC22×C3C26
FrattiniC22C25×D3
FittingC2×C3×#548C2
socleC23×C3C25
hypercenterC2×#548D3
hypocenterC3C22×#548
LCSG ▷ C22×C3 ▷ C3
UCSC1 ◁ C23 ◁ C2×#548

Complements

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

NH ≅ G/Ntype
1. C22×D3×#41C2semidirect
2. C23×D3×Q8C2semidirect
3. C2×C3×#548C2semidirect
4. C2×#5831C2semidirect
5. C2×#5817C2semidirect
6. D3×#548C2direct (N × H)
7. C2×#5677C2semidirect
8. C2×D3×#124C2semidirect
9. C2×#5633C2semidirect
10. C2×D3×C22⋊Q8C2semidirect
11. C2×D3×#121C2semidirect
12. C2×#5598C2semidirect
13. C2×#5576C2semidirect
14. C2×C4×D3×Q8C2semidirect
15. C2×C4×D3×D4C2semidirect
16. C2×#5552C2semidirect
18. C22×C3×#41C22semidirect
19. C23×C3×Q8C22semidirect
21. C2×D3×#41C22semidirect
22. C22×#239C22semidirect
26. C22×D3×Q8C22semidirect
27. C22×D3×Q8C22semidirect
28. C22×D3×Q8C22semidirect
29. C22×#237C22semidirect
32. C22×#235C22semidirect
35. C23×Dic6C22semidirect
36. C3×#548C22semidirect
37. C2×C3×#124C22semidirect
38. C2×C3×C22⋊Q8C22semidirect
39. C2×C3×#121C22semidirect
40. C2×C3×C4×Q8C22semidirect
41. C2×C3×C4×D4C22semidirect
42. #5831C22semidirect
43. #5817C22semidirect
44. C2×#947C22semidirect
45. C2×#946C22semidirect
46. C2×Q8×Dic3C22semidirect
47. C2×#939C22semidirect
48. C2×#938C22semidirect
49. C2×#936C22semidirect
50. C2×D4×Dic3C22semidirect
51. C2×#930C22semidirect
52. C2×C4×#67C22semidirect
53. C2×C4×#67C22semidirect
54. C2×#924C22semidirect
55. #5677C22semidirect
56. D3×#124C22semidirect
57. #5633C22semidirect
58. D3×C22⋊Q8C22semidirect
59. D3×#121C22semidirect
60. #5598C22semidirect
61. #5576C22semidirect
62. C4×D3×Q8C22semidirect
63. #5552C22semidirect
64. C4×D3×D4C22semidirect
65. C2×#897C22semidirect
66. C2×#896C22semidirect
67. C2×#895C22semidirect
68. C2×#893C22semidirect
71. C2×#887C22semidirect
72. C2×#885C22semidirect
73. C2×#885C22semidirect
74. C2×#884C22semidirect
75. C2×#67⋊C4C22semidirect
76. C2×#67⋊C4C22semidirect
80. C2×#878C22semidirect
81. C2×#875C22semidirect
82. C2×C4×D12C22semidirect
84. C2×C4×Dic6C22semidirect
95. C2×#548D3direct (N × H)
104. C2×C3×#41C23semidirect
108. C22×C3×Q8C23semidirect
120. C2×#239C23semidirect
125. C2×D3×Q8D4semidirect
128. C2×D3×Q8C23semidirect
129. C2×D3×Q8C23semidirect
131. C2×#237C23semidirect
137. C2×#235C23semidirect
157. C22×Dic6C23semidirect
158. C3×#124C23semidirect
159. C3×C22⋊Q8C23semidirect
160. C3×#121C23semidirect
161. C3×C4×Q8C23semidirect
162. C3×C4×D4C23semidirect
172. #947C23semidirect
173. #946C23semidirect
174. Q8×Dic3C23semidirect
175. #939C23semidirect
176. #938C23semidirect
177. #936C23semidirect
178. D4×Dic3C23semidirect
179. #930C23semidirect
180. C4×#67C23semidirect
181. C4×#67C23semidirect
190. #924C23semidirect
197. #897C23semidirect
198. #896C23semidirect
199. #895C23semidirect
200. #893C23semidirect
203. #887C23semidirect
204. #885C23semidirect
205. #885C23semidirect
206. #884C23semidirect
207. #67⋊C4C23semidirect
208. #67⋊C4C23semidirect
212. #878C23semidirect
213. #875C23semidirect
214. C4×D12C23semidirect
216. C4×Dic6C23semidirect
222. C22×#41C2×D3semidirect
230. C23×Q8C2×D3semidirect
242. #548C2×D3direct (N × H)
249. C2×#124C2×D3semidirect
256. C2×C22⋊Q8C2×D3semidirect
263. C2×#121C2×D3semidirect
268. C2×C4×Q8C2×D3semidirect
277. C2×C4×D4C2×D3semidirect
291. C23×D3#41semidirect
300. C2×C3×Q8C2×D4semidirect
335. D3×Q8C2×D4semidirect
367. C2×Dic6C2×D4semidirect
404. C2×#41C22×D3semidirect
422. C22×Q8C22×D3semidirect
456. #124C22×D3semidirect
462. C22⋊Q8C22×D3semidirect
468. #121C22×D3semidirect
472. C4×Q8C22×D3semidirect
480. C4×D4C22×D3semidirect
515. C23×C3C2×#41semidirect
533. C22×D3C2×#41semidirect
534. C22×D3C2×#41semidirect
540. C3×Q8C22×D4semidirect
583. Dic6C22×D4semidirect
614. C2×Q8D3×D4semidirect
703. C22×C3C22×#41semidirect
715. C2×D3#548direct (N × H)
718. C2×D3C22×#41semidirect
755. C23D3×#41semidirect
763. Q8C2×D3×D4semidirect
806. C2×C3C2×#548semidirect
812. D3C2×#548direct (N × H)
836. C22C2×D3×#41semidirect
849. C3C22×#548semidirect
855. C2D3×#548direct (N × H)

Maximal subgroups

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

subgroupindex
C22×D3×#412
C23×D3×Q82
C2×C3×#5482
C2×#58312
C2×#58172
D3×#5482
C2×#56772
C2×D3×#1242
C2×#56332
C2×D3×C22⋊Q82
C2×D3×#1212
C2×#55982
C2×#55762
C2×C4×D3×Q82
C2×C4×D3×D42
C2×#55522
C22×#5483