Finite Group Databasebeta

← C2×#86735 #11703349

Subgroups — C2×#86735 #11703349

Order 768.

11254 conjugacy classes of subgroups.

The subgroup lattice has 836 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#1010C211yesmaximal, characteristic, complemented
2C23×D3×Q8C211yesmaximal, characteristic, complemented
3C2×C3×#548C211yesmaximal, characteristic, complemented
4C2×#5831C211yesmaximal, characteristic, complemented
5C2×Q8×#67C211yesmaximal, characteristic, complemented
6#86735C2132yesmaximal, direct product factor
7C2×#5677C213yesmaximal, complemented
8C2×#5675C213yesmaximal, complemented
9C2×#5628C213yesmaximal, complemented
10C2×#5632C213yesmaximal, complemented
11C2×#5598C213yesmaximal, complemented
12C2×#5606C213yesmaximal, complemented
13C2×Q8×D12C211yesmaximal, characteristic, complemented
14C2×#5572C211yesmaximal, characteristic, complemented
15C2×#5547C213yesmaximal, complemented
16C2×D4×Dic6C213yesmaximal, complemented
17C2×#3486—31nomaximal, Sylow
18C22×C3×#41C2211yescharacteristic, complemented
19C23×C3×Q8C2211yescharacteristic
20C2×#1010—216no—
21C2×#1010C22116yescomplemented
22C22×D3×Q8—216no—
23C22×D3×Q8C2211yescharacteristic
24C22×D3×Q8C2213yes—
25C22×D3×Q8C2213yes—
26C22×D3×Q8C2211yescharacteristic
27C22×D3×Q8C22116yescomplemented
28C22×D3×Q8C2211yescharacteristic, complemented
29C22×#237C2213yes—
30C22×#237C2213yescomplemented
31C22×#235C2213yes—
32C23×C4×D3C2213yes—
33C23×Dic6C2213yes—
34C23×Dic6C2213yescomplemented
35C3×#548C22116yescomplemented
36C2×C3×#124C2213yescomplemented
37C2×C3×C22⋊Q8C2213yescomplemented
38C2×C3×#121C2213yes—
39C2×C3×C4×Q8C2211yescharacteristic, complemented
40C2×C3×C4×D4C2213yes—
41#5831C22116yescomplemented
42Q8×#67C22116yescomplemented
43C2×#946C2213yescomplemented
44C2×Q8×Dic3C2211yescharacteristic, complemented
45C2×#944C2213yescomplemented
46C2×#939C2213yes—
47C2×#938C2213yes—
48C2×#937C2213yes—
49C2×#936C2213yescomplemented
50C2×D4×Dic3C2216yes—
51C2×C4×#67C2213yes—
52C2×C4×#67C2213yes—
53C2×#924C2213yes—
54C2×#924C2213yescomplemented
55#5677C22148yescomplemented
56#5675C22148yescomplemented
57#5632C22148yescomplemented
58#5628C22148yescomplemented
59#5606C22148yescomplemented
60#5598C22148yescomplemented
61Q8×D12C22116yescomplemented
62#5572C22116yescomplemented
63#5547C22148yescomplemented
64D4×Dic6C22148yescomplemented
65C2×#897C2213yes—
66C2×#897C2213yescomplemented
67C2×#896C2213yes—
68C2×#894C2213yes—
69C2×#892C2213yes—
70C2×#888C2216yescomplemented
71C2×#887C2213yescomplemented
72C2×#885C2216yescomplemented
73C2×#884C2213yes—
74C2×#883C2213yes—
75C2×#883C2216yes—
76C2×#882C2211yescharacteristic
77C2×#67⋊C4C2216yes—
78C2×#878C2213yes—
79C2×#878C2216yescomplemented
80C2×#878C2216yescomplemented
81C2×C4×D12C2213yes—
82C2×#872C2213yes—
83C2×#869C2213yescomplemented
84C2×C4×Dic6C2213yescomplemented
85C22×2−1+4—31no—
86C24×Q8—31no—
87#3486—332no—
88C2×D4×Q8—31no—
89C2×D4×Q8—33no—
90C2×D4×Q8—31no—
91C2×D4×Q8—33no—
92C2×#548—31no—
93C2×#548—33no—
94C2×#548—33no—
95C2×#548D311yescharacteristic, complemented
96C2×#536—33no—
97C2×#536—33no—
98C2×#525—33no—
99C2×#525—33no—
100C2×#519—31no—
101C24×D3C2311yescharacteristic
102C2×C3×#41—28no—
103C2×C3×#41C2318yescomplemented
104C22×C3×Q8—28no—
105C22×C3×Q8C2313yes—
106C22×C3×Q8C2318yes—
107C22×C3×Q8C2311yescharacteristic
108C22×C3×D4C2313yes—
109C22×C3×D4C2313yes—
110C23×C3×C4C2313yes—
111C23×C3×C4C2313yes—
112C22×#67C2313yes—
113C22×#67C2313yes—
114C22×#67C2313yes—
115C22×#67C2311yescharacteristic
116C23×Dic3C2313yes—
117C23×Dic3C2316yes—
118#1010—2128no—
119C2×D3×Q8—28no—
120C2×D3×Q8—28no—
121C2×D3×Q8—2128no—
122C2×D3×Q8—224no—
123C2×D3×Q8—224no—
124C2×D3×Q8D4116yescomplemented
125C2×D3×Q8C23124yes—
126C2×D3×Q8C23124yes—
127C2×D3×Q8C2318yes—
128C2×D3×Q8C2318yes—
129C2×D3×Q8C2318yescomplemented
130C2×#237—224no—
131C2×#237—224no—
132C2×#237C23124yes—
133C2×#237C23124yescomplemented
134C2×#235—224no—
135C2×#235C23124yes—
136C22×D12C2311yescharacteristic
137C22×D12C2311yescharacteristic
138C22×C4×D3—224no—
139C22×C4×D3C2313yes—
140C22×C4×D3C2313yes—
141C22×C4×D3C2313yes—
142C22×C4×D3C23124yes—
143C22×C4×D3C2313yes—
144C22×C4×D3C2313yes—
145C22×Dic6—224no—
146C22×Dic6—224no—
147C22×Dic6C2313yes—
148C22×Dic6C2316yes—
149C22×Dic6C23124yes—
150C22×Dic6C2313yes—
151C22×Dic6C2313yes—
152C22×Dic6C2313yes—
153C22×Dic6C23124yescomplemented
154C3×#124C23124yescomplemented
155C3×C22⋊Q8C23124yescomplemented
156C3×#121C23124yes—
157C3×C4×Q8C2318yescomplemented
158C3×C4×D4C23124yes—
159C2×C3×C4⋊C4C2313yes—
160C2×C3×C4⋊C4C2313yes—
161C2×C3×C22⋊C4C2311yescharacteristic
162C2×C3×C22⋊C4C2313yes—
163C2×C3×C22⋊C4C2316yes—
164C2×C3×C42C2313yes—
165C2×#217C2313yes—
166C2×#217C2313yes—
167C2×#217C2316yes—
168#946C23124yescomplemented
169Q8×Dic3C2318yescomplemented
170#944C23124yescomplemented
171#939C23124yes—
172#938C23124yes—
173#937C23124yes—
174#936C23124yescomplemented
175D4×Dic3C23148yes—
176C4×#67C23124yes—
177C4×#67C23124yes—
178C2×(C2×D3)⋊C4C2311yescharacteristic
179C2×(C2×D3)⋊C4C2313yes—
180C2×(C2×D3)⋊C4C2313yes—
181C2×(C2×D3)⋊C4C2313yes—
182C2×(C2×D3)⋊C4C2311yescharacteristic
183C2×(C2×D3)⋊C4C2313yes—
184C2×C4⋊Dic3C2313yes—
185C2×C4⋊Dic3C2313yes—
186C2×C4⋊Dic3C2316yes—
187#924C23124yes—
188#924C23124yescomplemented
189C2×Dic3⋊C4C2313yes—
190C2×Dic3⋊C4C2313yes—
191C2×Dic3⋊C4C2313yes—
192C2×Dic3⋊C4C2313yes—
193C2×Dic3⋊C4C2316yes—
194C2×C4×Dic3C2316yes—
195C2×C4×Dic3C2313yes—
196#897C23124yes—
197#897C23124yescomplemented
198#896C23124yes—
199#894C23124yes—
200#892C23124yes—
201#888C23148yescomplemented
202#887C23124yescomplemented
203#885C23148yescomplemented
204#884C23124yes—
205#883C23124yes—
206#883C23148yes—
207#882C2318yes—
208#67⋊C4C23148yes—
209#878C23124yes—
210#878C23148yescomplemented
211#878C23148yescomplemented
212C4×D12C23124yes—
213#872C23124yes—
214#869C23124yescomplemented
215C4×Dic6C23124yescomplemented
216C2×2−1+4—316no—
217C2×2−1+4—616no—
218C22×#41—33no—
219C22×#41—33no—
220C22×#41—33no—
221C22×#41C2×D311yescharacteristic, complemented
222C23×Q8—31no—
223C23×Q8—33no—
224C23×Q8—33no—
225C23×Q8—31no—
226C23×Q8—316no—
227C23×Q8—31no—
228C23×Q8—33no—
229C23×Q8—33no—
230C23×Q8—616no—
231C23×Q8C2×D311yescharacteristic
232C24×C4—33no—
233D4×Q8—316no—
234D4×Q8—348no—
235D4×Q8—316no—
236D4×Q8—348no—
237#548—316no—
238#548—348no—
239#548—348no—
240#548C2×D3116yescomplemented
241#536—348no—
242#536—348no—
243C2×C4⋊Q8—33no—
244C2×C4⋊Q8—36no—
245C2×C4⋊Q8—33no—
246C2×#124—33no—
247C2×#124—36no—
248C2×#124C2×D313yescomplemented
249#525—348no—
250#525—348no—
251C2×#123—33no—
252C2×#123—36no—
253C2×#123—33no—
254C2×C22⋊Q8—33no—
255C2×C22⋊Q8—33no—
256C2×C22⋊Q8—33no—
257C2×C22⋊Q8—33no—
258C2×C22⋊Q8—33no—
259C2×C22⋊Q8—33no—
260C2×C22⋊Q8—33no—
261C2×C22⋊Q8—36no—
262C2×C22⋊Q8—36no—
263C2×C22⋊Q8C2×D313yescomplemented
264C2×#121—33no—
265C2×#121—33no—
266C2×#121—33no—
267C2×#121C2×D313yes—
268C2×#120—33no—
269C2×#120—31no—
270#519—316no—
271C2×C4×Q8—31no—
272C2×C4×Q8—33no—
273C2×C4×Q8—33no—
274C2×C4×Q8C2×D311yescharacteristic, complemented
275C2×C4×D4—36no—
276C2×C4×D4—33no—
277C2×C4×D4—33no—
278C2×C4×D4—36no—
279C2×C4×D4—33no—
280C2×C4×D4C2×D313yes—
281C2×#117—33no—
282C2×#117—33no—
283C24×C3C2413yes—
284C24×C3C2411yescharacteristic
285C23×D3—24no—
286C23×D3—24no—
287C23×D3—24no—
288C23×D3C2414yes—
289C23×D3C2411yescharacteristic
290C23×D3C2411yescharacteristic
291C23×D3C2411yescharacteristic
292C3×#41—232no—
293C2×C3×Q8—232no—
294C2×C3×Q8—212no—
295C2×C3×Q8C2×D418yes—
296C2×C3×Q8C24112yes—
297C2×C3×Q8C2414yes—
298C2×C3×D4—212no—
299C2×C3×D4—212no—
300C2×C3×D4C24112yes—
301C2×C3×D4C24112yes—
302C22×C3×C4—212no—
303C22×C3×C4—212no—
304C22×C3×C4C2413yes—
305C22×C3×C4C2411yescharacteristic
306C22×C3×C4C2413yes—
307C22×C3×C4C2411yescharacteristic
308C22×C3×C4C24112yes—
309C22×C3×C4C24112yes—
310C22×C3×C4C2413yes—
311C2×#67—24no—
312C2×#67—212no—
313C2×#67—212no—
314C2×#67—212no—
315C2×#67C24112yes—
316C2×#67C2414yes—
317C2×#67C24112yes—
318C2×#67C24112yes—
319C22×Dic3—212no—
320C22×Dic3—224no—
321C22×Dic3C24112yes—
322C22×Dic3C24124yes—
323C22×Dic3C2411yescharacteristic
324C22×Dic3C2413yes—
325C22×Dic3C2413yes—
326C22×Dic3C2413yes—
327C22×Dic3C2413yes—
328D3×Q8—232no—
329D3×Q8—232no—
330D3×Q8—296no—
331D3×Q8—296no—
332D3×Q8C2×D4164yescomplemented
333#237—296no—
334#237—296no—
335#235—296no—
336C2×D12—24no—
337C2×D12—24no—
338C2×D12C2414yes—
339C2×D12C2414yes—
340C2×C4×D3—212no—
341C2×C4×D3—212no—
342C2×C4×D3—212no—
343C2×C4×D3—212no—
344C2×C4×D3—296no—
345C2×C4×D3C2×D4124yes—
346C2×C4×D3C24112yes—
347C2×C4×D3C24112yes—
348C2×C4×D3C24112yes—
349C2×C4×D3C24112yes—
350C2×C4×D3C24112yes—
351C2×Dic6—212no—
352C2×Dic6—212no—
353C2×Dic6—212no—
354C2×Dic6—224no—
355C2×Dic6—296no—
356C2×Dic6—296no—
357C2×Dic6C2×D4124yes—
358C2×Dic6C24112yes—
359C2×Dic6C24112yes—
360C2×Dic6C24112yes—
361C2×Dic6C24124yes—
362C2×Dic6C24112yes—
363C3×C4⋊C4C24112yes—
364C3×C4⋊C4C24112yes—
365C3×C22⋊C4C2414yes—
366C3×C22⋊C4C24112yes—
367C3×C22⋊C4C24124yes—
368C3×C42C24112yes—
369#217C24112yes—
370#217C24112yes—
371#217C24124yes—
372(C2×D3)⋊C4C2414yes—
373(C2×D3)⋊C4C24112yes—
374(C2×D3)⋊C4C24112yes—
375(C2×D3)⋊C4C24112yes—
376(C2×D3)⋊C4C2414yes—
377(C2×D3)⋊C4C24112yes—
378C4⋊Dic3C24112yes—
379C4⋊Dic3C24112yes—
380C4⋊Dic3C24124yes—
381Dic3⋊C4C24112yes—
382Dic3⋊C4C24112yes—
383Dic3⋊C4C24112yes—
384Dic3⋊C4C24112yes—
385Dic3⋊C4C24124yes—
386C4×Dic3C24124yes—
387C4×Dic3C24112yes—
388C25—31no—
3892−1+4—6128no—
390C2×#41—28no—
391C2×#41—324no—
392C2×#41—324no—
393C2×#41—324no—
394C2×#41—624no—
395C2×#41—624no—
396C2×#41—624no—
397C2×#41C22×D318yescomplemented
398C22×Q8—28no—
399C22×Q8—316no—
400C22×Q8—38no—
401C22×Q8—324no—
402C22×Q8—324no—
403C22×Q8—38no—
404C22×Q8—38no—
405C22×Q8—33no—
406C22×Q8—36no—
407C22×Q8—33no—
408C22×Q8—33no—
409C22×Q8—33no—
410C22×Q8—324no—
411C22×Q8—324no—
412C22×Q8—624no—
413C22×Q8—624no—
414C22×Q8—624no—
415C22×Q8—6128no—
416C22×Q8—624no—
417C22×Q8—68no—
418C22×Q8—68no—
419C22×Q8C22×D313yes—
420C22×Q8C22×D318yes—
421C22×Q8C22×D311yescharacteristic
422C22×D4—33no—
423C22×D4—31no—
424C22×D4—33no—
425C22×D4—33no—
426C22×D4—31no—
427C22×D4—31no—
428C22×D4C22×D313yes—
429C22×D4C22×D313yes—
430C23×C4—33no—
431C23×C4—33no—
432C23×C4—36no—
433C23×C4—33no—
434C23×C4—33no—
435C23×C4—33no—
436C23×C4—33no—
437C23×C4—324no—
438C23×C4—624no—
439C23×C4C22×D313yes—
440C23×C4C22×D313yes—
441C4⋊Q8—324no—
442C4⋊Q8—348no—
443C4⋊Q8—324no—
444#124—324no—
445#124—348no—
446#124C22×D3124yescomplemented
447#123—324no—
448#123—348no—
449#123—324no—
450C22⋊Q8—324no—
451C22⋊Q8—324no—
452C22⋊Q8—324no—
453C22⋊Q8—324no—
454C22⋊Q8—324no—
455C22⋊Q8—324no—
456C22⋊Q8—324no—
457C22⋊Q8—348no—
458C22⋊Q8—348no—
459C22⋊Q8C22×D3124yescomplemented
460#121—324no—
461#121—324no—
462#121—324no—
463#121C22×D3124yes—
464#120—324no—
465#120—38no—
466C4×Q8—38no—
467C4×Q8—324no—
468C4×Q8—324no—
469C4×Q8C22×D318yescomplemented
470C4×D4—348no—
471C4×D4—324no—
472C4×D4—324no—
473C4×D4—348no—
474C4×D4—324no—
475C4×D4C22×D3124yes—
476#117—324no—
477#117—324no—
478C2×C4⋊C4—33no—
479C2×C4⋊C4—33no—
480C2×C4⋊C4—33no—
481C2×C4⋊C4—33no—
482C2×C4⋊C4—33no—
483C2×C4⋊C4—36no—
484C2×C4⋊C4—36no—
485C2×C4⋊C4—33no—
486C2×C4⋊C4C22×D313yes—
487C2×C4⋊C4C22×D313yes—
488C2×C22⋊C4—33no—
489C2×C22⋊C4—36no—
490C2×C22⋊C4—33no—
491C2×C22⋊C4—33no—
492C2×C22⋊C4—31no—
493C2×C22⋊C4—31no—
494C2×C22⋊C4—33no—
495C2×C22⋊C4—33no—
496C2×C22⋊C4—33no—
497C2×C22⋊C4C22×D316yes—
498C2×C22⋊C4C22×D311yescharacteristic
499C2×C22⋊C4C22×D313yes—
500C2×C42—36no—
501C2×C42—33no—
502C2×C42C22×D313yes—
503C23×C3—22no—
504C23×C3—22no—
505C23×C3—26no—
506C23×C3—26no—
507C23×C3—26no—
508C23×C32−1+414yescomplemented
509C23×C3C2516yes—
510C23×C3C2512yes—
511C23×C3C2511yescharacteristic
512C22×D3—232no—
513C22×D3—22no—
514C22×D3—22no—
515C22×D3—22no—
516C22×D3—22no—
517C22×D3—28no—
518C22×D3—28no—
519C22×D3—28no—
520C22×D3—22no—
521C22×D3—22no—
522C22×D3—22no—
523C22×D3C22×D414yes—
524C22×D32−1+414yescomplemented
525C22×D3C2512yes—
526C22×D3C2512yes—
527C22×D3C2512yes—
528C3×Q8—224no—
529C3×Q8C22×D4116yes—
530C3×D4—224no—
531C3×D4—224no—
532C2×C3×C4—22no—
533C2×C3×C4—26no—
534C2×C3×C4—22no—
535C2×C3×C4—26no—
536C2×C3×C4—224no—
537C2×C3×C4—224no—
538C2×C3×C4C22×D4112yes—
539C2×C3×C4C2516yes—
540C2×C3×C4C2512yes—
541C2×C3×C4C2516yes—
542C2×C3×C4C2512yes—
543C2×C3×C4C2516yes—
544#67—28no—
545#67—224no—
546#67—224no—
547#67—224no—
548C2×Dic3—26no—
549C2×Dic3—26no—
550C2×Dic3—22no—
551C2×Dic3—26no—
552C2×Dic3—224no—
553C2×Dic3—248no—
554C2×Dic3C22×D4112yes—
555C2×Dic3C2512yes—
556C2×Dic3C2516yes—
557C2×Dic3C2516yes—
558C2×Dic3C2516yes—
559C2×Dic3C2516yes—
560D12—28no—
561D12—28no—
562C4×D3—224no—
563C4×D3—224no—
564C4×D3—224no—
565C4×D3—224no—
566C4×D3C22×D4148yes—
567Dic6—224no—
568Dic6—224no—
569Dic6—224no—
570Dic6—248no—
571Dic6C22×D4148yes—
572C24—31no—
573C24—31no—
574C24—34no—
575C24—31no—
576C24—64no—
577C24—64no—
578C24—64no—
579C24C23×D313yes—
580C24C23×D311yescharacteristic
581#41—232no—
582#41—696no—
583#41—696no—
584#41—696no—
585C2×Q8—232no—
586C2×Q8—212no—
587C2×Q8—364no—
588C2×Q8—324no—
589C2×Q8—312no—
590C2×Q8—324no—
591C2×Q8—312no—
592C2×Q8—312no—
593C2×Q8—312no—
594C2×Q8—624no—
595C2×Q8—612no—
596C2×Q8—696no—
597C2×Q8—696no—
598C2×Q8—696no—
599C2×Q8—696no—
600C2×Q8—632no—
601C2×Q8—632no—
602C2×Q8—612no—
603C2×Q8—612no—
604C2×Q8D3×D418yes—
605C2×Q8C23×D3112yes—
606C2×Q8C23×D314yes—
607C2×D4—212no—
608C2×D4—212no—
609C2×D4—312no—
610C2×D4—34no—
611C2×D4—312no—
612C2×D4—312no—
613C2×D4—34no—
614C2×D4—34no—
615C2×D4—64no—
616C2×D4—64no—
617C2×D4—612no—
618C2×D4—612no—
619C2×D4—612no—
620C2×D4—64no—
621C2×D4C23×D3112yes—
622C2×D4C23×D3112yes—
623C22×C4—212no—
624C22×C4—212no—
625C22×C4—33no—
626C22×C4—324no—
627C22×C4—312no—
628C22×C4—312no—
629C22×C4—324no—
630C22×C4—31no—
631C22×C4—33no—
632C22×C4—33no—
633C22×C4—33no—
634C22×C4—312no—
635C22×C4—312no—
636C22×C4—312no—
637C22×C4—312no—
638C22×C4—612no—
639C22×C4—696no—
640C22×C4—612no—
641C22×C4—612no—
642C22×C4—624no—
643C22×C4—612no—
644C22×C4—612no—
645C22×C4C23×D3112yes—
646C22×C4C23×D3112yes—
647C22×C4C23×D313yes—
648C22×C4C23×D311yescharacteristic
649C22×C4C23×D313yes—
650C22×C4C23×D311yescharacteristic
651C22×C4C23×D313yes—
652C4⋊C4—312no—
653C4⋊C4—312no—
654C4⋊C4—312no—
655C4⋊C4—312no—
656C4⋊C4—312no—
657C4⋊C4—324no—
658C4⋊C4—324no—
659C4⋊C4—312no—
660C4⋊C4C23×D3112yes—
661C4⋊C4C23×D3112yes—
662C22⋊C4—312no—
663C22⋊C4—324no—
664C22⋊C4—312no—
665C22⋊C4—312no—
666C22⋊C4—34no—
667C22⋊C4—34no—
668C22⋊C4—312no—
669C22⋊C4—312no—
670C22⋊C4—312no—
671C22⋊C4C23×D3124yes—
672C22⋊C4C23×D314yes—
673C22⋊C4C23×D3112yes—
674C42—324no—
675C42—312no—
676C42C23×D3112yes—
677C22×C3—22no—
678C22×C3—22no—
679C22×C3—28no—
680C22×C3—26no—
681C22×C3—26no—
682C22×C3—26no—
683C22×C3—412no—
684C22×C3C23×D412yes—
685C22×C3C2×2−1+412yes—
686C22×C3C2×2−1+412yes—
687C22×C3C2×2−1+414yescomplemented
688C22×C3C2611yescharacteristic
689C2×D3—232no—
690C2×D3—22no—
691C2×D3—22no—
692C2×D3—22no—
693C2×D3—22no—
694C2×D3—28no—
695C2×D3—28no—
696C2×D3—22no—
697C2×D3—22no—
698C2×D3—22no—
699C2×D3—44no—
700C2×D3C23×D414yes—
701C2×D3C2×2−1+414yescomplemented
702C3×C4—22no—
703C3×C4—26no—
704C3×C4—22no—
705C3×C4—26no—
706C3×C4C23×D4112yes—
707Dic3—26no—
708Dic3—26no—
709Dic3—22no—
710Dic3—26no—
711Dic3C23×D4112yes—
712C23—22no—
713C23—22no—
714C23—26no—
715C23—26no—
716C23—26no—
717C23—34no—
718C23—34no—
719C23—32no—
720C23—32no—
721C23—32no—
722C23—68no—
723C23—68no—
724C23—632no—
725C23—62no—
726C23—62no—
727C23—62no—
728C23—68no—
729C23—62no—
730C23—62no—
731C23—62no—
732C23—62no—
733C23#101014yescomplemented
734C23C24×D316yes—
735C23C24×D312yes—
736C23C24×D311yescharacteristic
737Q8—224no—
738Q8—348no—
739Q8—648no—
740Q8—624no—
741Q8—624no—
742Q8—624no—
743Q8C2×D3×D4116yes—
744D4—224no—
745D4—224no—
746D4—68no—
747D4—68no—
748D4—624no—
749D4—624no—
750D4—624no—
751D4—68no—
752C2×C4—22no—
753C2×C4—26no—
754C2×C4—26no—
755C2×C4—22no—
756C2×C4—224no—
757C2×C4—224no—
758C2×C4—312no—
759C2×C4—36no—
760C2×C4—348no—
761C2×C4—32no—
762C2×C4—36no—
763C2×C4—36no—
764C2×C4—36no—
765C2×C4—624no—
766C2×C4—624no—
767C2×C4—624no—
768C2×C4—648no—
769C2×C4—66no—
770C2×C4—66no—
771C2×C4—62no—
772C2×C4—66no—
773C2×C4—624no—
774C2×C4—624no—
775C2×C4C2×D3×D4112yes—
776C2×C4C24×D316yes—
777C2×C4C24×D312yes—
778C2×C4C24×D316yes—
779C2×C4C24×D312yes—
780C2×C4C24×D316yes—
781C2×C3—24no—
782C2×C3—46no—
783C2×C3#348614yescomplemented
784C2×C3C24×D411yescharacteristic
785C2×C3C22×2−1+411yescharacteristic
786C2×C3C22×2−1+411yescharacteristic
787D3—24no—
788D3—24no—
789D3—42no—
790C22—22no—
791C22—22no—
792C22—28no—
793C22—26no—
794C22—26no—
795C22—26no—
796C22—34no—
797C22—34no—
798C22—412no—
799C22—632no—
800C22—62no—
801C22—62no—
802C22—62no—
803C22—62no—
804C22—68no—
805C22—68no—
806C22—62no—
807C22—62no—
808C22—62no—
809C22—124no—
810C22C22×D3×D412yes—
811C22C2×#101012yes—
812C22C2×#101014yescomplemented
813C22D3×2−1+412yes—
814C22C25×D311yescharacteristic
815C4—22no—
816C4—26no—
817C4—26no—
818C4—22no—
819C4—312no—
820C4—66no—
821C4—66no—
822C4—62no—
823C4—66no—
824C4C22×D3×D4112yes—
825C3C2×#348611yescharacteristic, complemented, Sylow
826C2—24no—
827C2—46no—
828C2—64no—
829C2—64no—
830C2—122no—
831C2#8673514yesdirect product factor
832C2C23×D3×D411yescharacteristic
833C2C22×#101011yescharacteristic
834C2C2×D3×2−1+411yescharacteristic
subgroupG/H
centerC23C24×D3
commutator, cosocleC22×C3C26
FrattiniC22C25×D3
FittingC2×C3×#548C2
socleC23×C3C25
hypercenterC2×#548D3
hypocenterC3C2×#3486
LCSG ▷ C22×C3 ▷ C3
UCSC1 ◁ C23 ◁ C2×#548

Complements

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

NH ≅ G/Ntype
1. C22×#1010C2semidirect
2. C23×D3×Q8C2semidirect
3. C2×C3×#548C2semidirect
4. C2×#5831C2semidirect
5. C2×Q8×#67C2semidirect
6. #86735C2direct (N × H)
7. C2×#5677C2semidirect
8. C2×#5675C2semidirect
9. C2×#5628C2semidirect
10. C2×#5632C2semidirect
11. C2×#5598C2semidirect
12. C2×#5606C2semidirect
13. C2×Q8×D12C2semidirect
14. C2×#5572C2semidirect
15. C2×#5547C2semidirect
16. C2×D4×Dic6C2semidirect
18. C22×C3×#41C22semidirect
21. C2×#1010C22semidirect
27. C22×D3×Q8C22semidirect
28. C22×D3×Q8C22semidirect
30. C22×#237C22semidirect
34. C23×Dic6C22semidirect
35. C3×#548C22semidirect
36. C2×C3×#124C22semidirect
37. C2×C3×C22⋊Q8C22semidirect
39. C2×C3×C4×Q8C22semidirect
41. #5831C22semidirect
42. Q8×#67C22semidirect
43. C2×#946C22semidirect
44. C2×Q8×Dic3C22semidirect
45. C2×#944C22semidirect
49. C2×#936C22semidirect
54. C2×#924C22semidirect
55. #5677C22semidirect
56. #5675C22semidirect
57. #5632C22semidirect
58. #5628C22semidirect
59. #5606C22semidirect
60. #5598C22semidirect
61. Q8×D12C22semidirect
62. #5572C22semidirect
63. #5547C22semidirect
64. D4×Dic6C22semidirect
66. C2×#897C22semidirect
70. C2×#888C22semidirect
71. C2×#887C22semidirect
72. C2×#885C22semidirect
79. C2×#878C22semidirect
80. C2×#878C22semidirect
83. C2×#869C22semidirect
84. C2×C4×Dic6C22semidirect
95. C2×#548D3semidirect
103. C2×C3×#41C23semidirect
124. C2×D3×Q8D4semidirect
129. C2×D3×Q8C23semidirect
133. C2×#237C23semidirect
153. C22×Dic6C23semidirect
154. C3×#124C23semidirect
155. C3×C22⋊Q8C23semidirect
157. C3×C4×Q8C23semidirect
168. #946C23semidirect
169. Q8×Dic3C23semidirect
170. #944C23semidirect
174. #936C23semidirect
188. #924C23semidirect
197. #897C23semidirect
201. #888C23semidirect
202. #887C23semidirect
203. #885C23semidirect
210. #878C23semidirect
211. #878C23semidirect
214. #869C23semidirect
215. C4×Dic6C23semidirect
221. C22×#41C2×D3semidirect
240. #548C2×D3semidirect
248. C2×#124C2×D3semidirect
263. C2×C22⋊Q8C2×D3semidirect
274. C2×C4×Q8C2×D3semidirect
332. D3×Q8C2×D4semidirect
397. C2×#41C22×D3semidirect
446. #124C22×D3semidirect
459. C22⋊Q8C22×D3semidirect
469. C4×Q8C22×D3semidirect
508. C23×C32−1+4semidirect
524. C22×D32−1+4semidirect
687. C22×C3C2×2−1+4semidirect
701. C2×D3C2×2−1+4semidirect
733. C23#1010semidirect
783. C2×C3#3486semidirect
812. C22C2×#1010semidirect
825. C3C2×#3486semidirect
831. C2#86735direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#10102
C23×D3×Q82
C2×C3×#5482
C2×#58312
C2×Q8×#672
#867352
C2×#56772
C2×#56752
C2×#56282
C2×#56322
C2×#55982
C2×#56062
C2×Q8×D122
C2×#55722
C2×#55472
C2×D4×Dic62
C2×#34863