Finite Group Databasebeta

← #10829207

Subgroups — #10829207

Order 768.

1088 conjugacy classes of subgroups.

The subgroup lattice has 736 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#552C211yesmaximal, characteristic
2C2×#5063C211yesmaximal, characteristic, complemented
3C2×C4×#216C211yesmaximal, characteristic, complemented
4#82375C211yesmaximal, characteristic
5#71740C211yesmaximal, characteristic, complemented
6#71700C211yesmaximal, characteristic, complemented
7#71700C211yesmaximal, characteristic, complemented
8#71695C211yesmaximal, characteristic, complemented
9#71694C211yesmaximal, characteristic, complemented
10#71627C211yesmaximal, characteristic, complemented
11#71614C211yesmaximal, characteristic
12#71585C211yesmaximal, characteristic, complemented
13#71576C211yesmaximal, characteristic, complemented
14#71559C211yesmaximal, characteristic, complemented
15#71555C211yesmaximal, characteristic, complemented
16#24127—31nomaximal, Sylow
17C3×#552—24no—
18C3×#552—24no—
19C2×C3×#126—21no—
20C2×C3×#125—21no—
21C2×C3×#125C2211yescharacteristic
22C2×C3×#123—21no—
23C2×C3×C22⋊Q8C2211yescharacteristic
24C2×C3×C22⋊Q8C2211yescharacteristic
25C2×C3×C4×Q8C2211yescharacteristic
26C2×C3×C4×D4C2211yescharacteristic
27C2×C3×#117—21no—
28C2×C3×#117C2211yescharacteristic
29C22×C3×C4⋊C4C2211yescharacteristic
30C22×#216C2211yescharacteristic
31C2×#924C2211yescharacteristic
32C2×#924C2211yescharacteristic
33C2×C4×Dic6C2211yescharacteristic
34C2×#835C2211yescharacteristic
35C2×#835C2211yescharacteristic
36C2×#835C2211yescharacteristic
37#5222—21no—
38#5212C2211yescharacteristic
39#5212C2211yescharacteristic
40C2×#830C2211yescharacteristic
41C2×#830C2211yescharacteristic
42C2×#830C2211yescharacteristic
43C2×#830C2211yescharacteristic
44#5063—24no—
45C4×#216—24no—
46#4983—21no—
47C2×#810C2211yescharacteristic
48C2×#810C2211yescharacteristic
49C2×#810C2211yescharacteristic
50C2×#808C2211yescharacteristic
51C2×#807C2211yescharacteristic
52C2×#807C2211yescharacteristic
53#4944—21no—
54#4944—21no—
55#4936C2211yescharacteristic
56C2×C4⋊(C3⋊C8)C2211yescharacteristic
57C2×C4×C3⋊C8C2211yescharacteristic
58#4529C2211yescharacteristic
59#4529C2211yescharacteristic
60#4529C2211yescharacteristic
61#4529C2211yescharacteristic
62#4529C2211yescharacteristic
63#4529C2211yescharacteristic
64C2×#552D311yescharacteristic
65C2×#479—31no—
66C2×C4×Q16—31no—
67#2536—31no—
68#2036—31no—
69#2035—31no—
70#2001—31no—
71#2001—31no—
72#1991—31no—
73#1954—31no—
74#1873—31no—
75#1872—31no—
76#1854—31no—
77#1852—31no—
78#1805—31no—
79C22×C3×Q8C2311yescharacteristic
80C22×C3×D4D411yescharacteristic
81C23×C3×C4—21no—
82C23×C3×C4C2311yescharacteristic
83C23×C3×C4C2311yescharacteristic
84C22×Dic6C2311yescharacteristic
85C3×#126—28no—
86C3×#125—28no—
87C3×#125—22no—
88C3×#125D414yes—
89C3×#123—28no—
90C3×C22⋊Q8—22no—
91C3×C22⋊Q8—22no—
92C3×C22⋊Q8—22no—
93C3×C22⋊Q8—22no—
94C3×C4×Q8—22no—
95C3×C4×Q8D414yes—
96C3×C4×D4—22no—
97C3×C4×D4—22no—
98C3×#117—28no—
99C3×#117—22no—
100C3×#117—22no—
101C2×C3×C4⋊C4—21no—
102C2×C3×C4⋊C4—21no—
103C2×C3×C4⋊C4—21no—
104C2×C3×C4⋊C4—21no—
105C2×C3×C4⋊C4—21no—
106C2×C3×C4⋊C4—21no—
107C2×C3×C4⋊C4—22no—
108C2×C3×C4⋊C4—22no—
109C2×C3×C4⋊C4D411yescharacteristic
110C2×C3×C4⋊C4C2311yescharacteristic
111C2×C3×C4⋊C4C2311yescharacteristic
112C2×C3×C4⋊C4C2311yescharacteristic
113C2×C3×C22⋊C4—21no—
114C2×C3×C22⋊C4—21no—
115C2×C3×C22⋊C4—21no—
116C2×C3×C22⋊C4D411yescharacteristic
117C2×C3×C22⋊C4D411yescharacteristic
118C2×C3×C42—21no—
119C2×C3×C42—21no—
120C2×C3×C42C2311yescharacteristic
121C2×#217—21no—
122C2×#217—21no—
123C2×#217—21no—
124C2×#217—21no—
125C2×#216—22no—
126C2×#216—22no—
127C2×#216—22no—
128C2×C4⋊Dic3C2311yescharacteristic
129C2×C4⋊Dic3C2311yescharacteristic
130C2×C4⋊Dic3C2311yescharacteristic
131#924—22no—
132#924—22no—
133#924—41no—
134#924—41no—
135C2×Dic3⋊C4—21no—
136C2×Dic3⋊C4—21no—
137C2×Dic3⋊C4—21no—
138C2×C4×Dic3—21no—
139C22×C3⋊C8C2311yescharacteristic
140C22×C3⋊C8C2311yescharacteristic
141C22×C3⋊C8C2311yescharacteristic
142C22×C3⋊C8C2311yescharacteristic
143C4×Dic6—22no—
144C4×Dic6—22no—
145#835—22no—
146#835—41no—
147#835—41no—
148C3⋊#95—21no—
149C3⋊#95—21no—
150C3⋊#95—21no—
151C3⋊#95—21no—
152#830—22no—
153#830—22no—
154#830—41no—
155#830—41no—
156#810—22no—
157#810—22no—
158#810—22no—
159#808—22no—
160#807—22no—
161#807—22no—
162C4⋊(C3⋊C8)—22no—
163C4×C3⋊C8—22no—
164C22×Q16—31no—
165#552—24no—
166#552—24no—
167C2×#126—21no—
168C2×#125—21no—
169C2×#125C2×D311yescharacteristic
170C2×#123—21no—
171C2×C22⋊Q8—31no—
172C2×C22⋊Q8—31no—
173C2×C22⋊Q8C2×D311yescharacteristic
174C2×C22⋊Q8C2×D311yescharacteristic
175C2×C4×Q8—31no—
176C2×C4×Q8C2×D311yescharacteristic
177C2×C4×D4C2×D311yescharacteristic
178C2×#117—21no—
179C2×#117C2×D311yescharacteristic
180C22×C4⋊C4C2×D311yescharacteristic
181#479—64no—
182C4×Q16—64no—
183C2×#107—31no—
184C2×#107—31no—
185C2×#106—31no—
186C2×C4⋊C8—31no—
187C2×#103—31no—
188C2×#103—31no—
189C2×#103—31no—
190C2×#103—31no—
191C2×#103—31no—
192C2×#103—31no—
193C2×C22⋊C8—31no—
194C2×C22⋊C8—31no—
195C2×C22⋊C8—31no—
196C2×C22⋊C8—31no—
197C2×C4×C8—31no—
198#398—61no—
199#394—61no—
200#388—61no—
201#388—61no—
202#382—31no—
203#380—31no—
204#380—31no—
205#340—31no—
206#340—31no—
207#340—31no—
208#340—31no—
209#340—31no—
210#340—31no—
211C24×C3C2×D411yescharacteristic
212C24×C3C2×D411yescharacteristic
213C2×C3×Q8—21no—
214C2×C3×Q8—21no—
215C2×C3×Q8—21no—
216C2×C3×Q8—21no—
217C2×C3×Q8—21no—
218C2×C3×Q8C2×D412yes—
219C2×C3×D4—22no—
220C2×C3×D4—22no—
221C2×C3×D4—41no—
222C22×C3×C4—24no—
223C22×C3×C4—21no—
224C22×C3×C4—21no—
225C22×C3×C4—21no—
226C22×C3×C4—21no—
227C22×C3×C4—21no—
228C22×C3×C4—21no—
229C22×C3×C4—21no—
230C22×C3×C4—21no—
231C22×C3×C4—21no—
232C22×C3×C4—21no—
233C22×C3×C4—21no—
234C22×C3×C4—21no—
235C22×C3×C4—21no—
236C22×C3×C4—21no—
237C22×C3×C4—21no—
238C22×C3×C4—21no—
239C22×C3×C4—42no—
240C22×C3×C4—42no—
241C22×C3×C4C2×D411yescharacteristic
242C22×C3×C4C2×D411yescharacteristic
243C22×C3×C4C2×D411yescharacteristic
244C22×C3×C4C2×D411yescharacteristic
245C22×C3×C4C2411yescharacteristic
246C22×Dic3—21no—
247C22×Dic3—21no—
248C22×Dic3—21no—
249C22×Dic3—21no—
250C2×Dic6—21no—
251C2×Dic6—21no—
252C2×Dic6—21no—
253C2×Dic6—21no—
254C2×Dic6—21no—
255C2×Dic6#4112yes—
256C3×C4⋊C4—24no—
257C3×C4⋊C4—24no—
258C3×C4⋊C4—24no—
259C3×C4⋊C4—24no—
260C3×C4⋊C4—24no—
261C3×C4⋊C4—24no—
262C3×C4⋊C4—22no—
263C3×C4⋊C4—21no—
264C3×C4⋊C4—21no—
265C3×C4⋊C4—21no—
266C3×C4⋊C4C2×D412yes—
267C3×C4⋊C4C2×D412yes—
268C3×C4⋊C4C2×D412yes—
269C3×C22⋊C4—24no—
270C3×C22⋊C4—24no—
271C3×C22⋊C4—24no—
272C3×C22⋊C4—22no—
273C3×C22⋊C4—22no—
274C3×C42—24no—
275C3×C42—24no—
276C3×C42C2×D412yes—
277C3×C42C2×D412yes—
278#217—42no—
279#217—42no—
280#217—42no—
281#217—42no—
282#216—28no—
283C4⋊Dic3—21no—
284C4⋊Dic3—21no—
285C4⋊Dic3—21no—
286C4⋊Dic3—21no—
287C4⋊Dic3—21no—
288C4⋊Dic3—21no—
289Dic3⋊C4—42no—
290Dic3⋊C4—42no—
291Dic3⋊C4—42no—
292C4×Dic3—42no—
293C2×C3⋊C8—21no—
294C2×C3⋊C8—21no—
295C2×C3⋊C8—21no—
296C2×C3⋊C8—21no—
297C2×C3⋊C8—21no—
298C2×C3⋊C8—21no—
299C2×C3⋊C8—21no—
300C2×C3⋊C8—21no—
301C2×C3⋊C8—21no—
302C2×C3⋊C8—21no—
303C2×C3⋊C8—21no—
304C2×C3⋊C8#4112yes—
305C22×Q8—31no—
306C22×Q8C22×D311yescharacteristic
307C22×D4#6711yescharacteristic
308C23×C4—21no—
309C23×C4C22×D311yescharacteristic
310C23×C4C22×D311yescharacteristic
311C2×Q16—62no—
312C2×Q16—62no—
313C2×Q16—62no—
314C22×C8—31no—
315C22×C8—31no—
316C22×C8—31no—
317C22×C8—31no—
318#126—28no—
319#125—28no—
320#125—22no—
321#125#6714yes—
322#123—28no—
323C22⋊Q8—22no—
324C22⋊Q8—22no—
325C22⋊Q8—22no—
326C22⋊Q8—22no—
327C22⋊Q8—62no—
328C22⋊Q8—62no—
329C22⋊Q8—121no—
330C22⋊Q8—121no—
331C4×Q8—22no—
332C4×Q8—62no—
333C4×Q8—62no—
334C4×Q8#6714yes—
335C4×D4—22no—
336C4×D4—22no—
337#117—28no—
338#117—22no—
339#117—22no—
340C2×C4⋊C4—21no—
341C2×C4⋊C4—21no—
342C2×C4⋊C4—21no—
343C2×C4⋊C4—21no—
344C2×C4⋊C4—21no—
345C2×C4⋊C4—21no—
346C2×C4⋊C4—22no—
347C2×C4⋊C4—22no—
348C2×C4⋊C4—31no—
349C2×C4⋊C4—31no—
350C2×C4⋊C4—31no—
351C2×C4⋊C4—61no—
352C2×C4⋊C4—61no—
353C2×C4⋊C4—61no—
354C2×C4⋊C4#6711yescharacteristic
355C2×C4⋊C4C22×D311yescharacteristic
356C2×C4⋊C4C22×D311yescharacteristic
357C2×C4⋊C4C22×D311yescharacteristic
358C2×C22⋊C4—21no—
359C2×C22⋊C4—21no—
360C2×C22⋊C4—21no—
361C2×C22⋊C4—61no—
362C2×C22⋊C4—61no—
363C2×C22⋊C4—61no—
364C2×C22⋊C4—61no—
365C2×C22⋊C4#6711yescharacteristic
366C2×C22⋊C4#6711yescharacteristic
367C2×C42—21no—
368C2×C42—21no—
369C2×C42—61no—
370C2×C42C22×D311yescharacteristic
371#107—62no—
372#107—62no—
373#106—62no—
374C4⋊C8—62no—
375#103—62no—
376#103—62no—
377#103—62no—
378#103—62no—
379#103—121no—
380#103—121no—
381C22⋊C8—62no—
382C22⋊C8—62no—
383C22⋊C8—121no—
384C22⋊C8—121no—
385C4×C8—62no—
386#95—61no—
387#95—61no—
388#95—61no—
389#95—61no—
390C23×C3—21no—
391C23×C3—21no—
392C23×C3—21no—
393C23×C3—21no—
394C23×C3—21no—
395C23×C3—21no—
396C23×C3—21no—
397C23×C3—21no—
398C23×C3—21no—
399C23×C3—21no—
400C23×C3—21no—
401C23×C3—21no—
402C23×C3—21no—
403C23×C3#13512yes—
404C23×C3C22×D411yescharacteristic
405C3×Q8—22no—
406C3×Q8—22no—
407C3×Q8—41no—
408C3×Q8—41no—
409C3×D4—44no—
410C2×C3×C4—21no—
411C2×C3×C4—21no—
412C2×C3×C4—21no—
413C2×C3×C4—21no—
414C2×C3×C4—21no—
415C2×C3×C4—22no—
416C2×C3×C4—22no—
417C2×C3×C4—22no—
418C2×C3×C4—21no—
419C2×C3×C4—22no—
420C2×C3×C4—21no—
421C2×C3×C4—21no—
422C2×C3×C4—21no—
423C2×C3×C4—21no—
424C2×C3×C4—48no—
425C2×C3×C4—41no—
426C2×C3×C4—41no—
427C2×C3×C4—41no—
428C2×C3×C4—41no—
429C2×C3×C4—41no—
430C2×C3×C4—41no—
431C2×C3×C4—41no—
432C2×C3×C4—41no—
433C2×C3×C4—41no—
434C2×C3×C4—41no—
435C2×C3×C4—41no—
436C2×C3×C4—41no—
437C2×C3×C4—41no—
438C2×C3×C4—41no—
439C2×C3×C4—41no—
440C2×C3×C4—41no—
441C2×C3×C4#12012yes—
442C2×C3×C4#12012yes—
443C2×C3×C4C22×D411yescharacteristic
444C2×C3×C4C22×D411yescharacteristic
445C2×C3×C4C2×#4111yescharacteristic
446C2×C3×C4C2×#4111yescharacteristic
447C2×C3×C4H(5,𝔽2)11yescharacteristic
448C2×C3×C42−1+411yescharacteristic
449C2×Dic3—22no—
450C2×Dic3—41no—
451C2×Dic3—41no—
452C2×Dic3—41no—
453C2×Dic3—41no—
454C2×Dic3—41no—
455C2×Dic3—41no—
456C2×Dic3—41no—
457C2×Dic3—41no—
458C2×Dic3—41no—
459C2×Dic3—41no—
460C2×Dic3—41no—
461Dic6—22no—
462Dic6—22no—
463Dic6—41no—
464Dic6—41no—
465C3⋊C8—22no—
466C3⋊C8—41no—
467C3⋊C8—41no—
468C3⋊C8—41no—
469C24C2×#6711yescharacteristic
470C24C2×#6711yescharacteristic
471C2×Q8—21no—
472C2×Q8—21no—
473C2×Q8—21no—
474C2×Q8—21no—
475C2×Q8—21no—
476C2×Q8—32no—
477C2×Q8—61no—
478C2×Q8—61no—
479C2×Q8—61no—
480C2×Q8—61no—
481C2×Q8—61no—
482C2×Q8C2×#6712yes—
483C2×D4—22no—
484C2×D4—22no—
485C2×D4—41no—
486C22×C4—24no—
487C22×C4—21no—
488C22×C4—21no—
489C22×C4—21no—
490C22×C4—21no—
491C22×C4—21no—
492C22×C4—21no—
493C22×C4—21no—
494C22×C4—21no—
495C22×C4—21no—
496C22×C4—21no—
497C22×C4—21no—
498C22×C4—21no—
499C22×C4—21no—
500C22×C4—21no—
501C22×C4—21no—
502C22×C4—21no—
503C22×C4—42no—
504C22×C4—42no—
505C22×C4—61no—
506C22×C4—61no—
507C22×C4—61no—
508C22×C4—61no—
509C22×C4C2×#6711yescharacteristic
510C22×C4C2×#6711yescharacteristic
511C22×C4C2×#6711yescharacteristic
512C22×C4C2×#6711yescharacteristic
513C22×C4C23×D311yescharacteristic
514Q16—68no—
515C2×C8—32no—
516C2×C8—61no—
517C2×C8—61no—
518C2×C8—61no—
519C2×C8—61no—
520C2×C8—61no—
521C2×C8—61no—
522C2×C8—61no—
523C2×C8—61no—
524C2×C8—61no—
525C2×C8—61no—
526C2×C8—61no—
527C4⋊C4—24no—
528C4⋊C4—24no—
529C4⋊C4—24no—
530C4⋊C4—24no—
531C4⋊C4—24no—
532C4⋊C4—24no—
533C4⋊C4—22no—
534C4⋊C4—21no—
535C4⋊C4—21no—
536C4⋊C4—21no—
537C4⋊C4—61no—
538C4⋊C4—61no—
539C4⋊C4—61no—
540C4⋊C4—61no—
541C4⋊C4—61no—
542C4⋊C4—61no—
543C4⋊C4—122no—
544C4⋊C4—122no—
545C4⋊C4—122no—
546C4⋊C4C2×#6712yes—
547C4⋊C4C2×#6712yes—
548C4⋊C4C2×#6712yes—
549C22⋊C4—24no—
550C22⋊C4—24no—
551C22⋊C4—24no—
552C22⋊C4—22no—
553C22⋊C4—22no—
554C22⋊C4—122no—
555C22⋊C4—122no—
556C22⋊C4—122no—
557C22⋊C4—122no—
558C42—24no—
559C42—24no—
560C42—122no—
561C42C2×#6712yes—
562C42C2×#6712yes—
563C22×C3—22no—
564C22×C3—22no—
565C22×C3—22no—
566C22×C3—41no—
567C22×C3—41no—
568C22×C3—41no—
569C22×C3—41no—
570C22×C3—41no—
571C22×C3—41no—
572C22×C3—41no—
573C22×C3—41no—
574C22×C3—41no—
575C22×C3—41no—
576C22×C3—41no—
577C22×C3C2×#12011yescharacteristic
578C22×C3#54611yescharacteristic
579C22×C3#54711yescharacteristic
580C22×C3C2×#13511yescharacteristic
581C22×C3#57511yescharacteristic
582C22×C3#57811yescharacteristic
583C22×C3#57811yescharacteristic
584C3×C4—22no—
585C3×C4—22no—
586C3×C4—41no—
587C3×C4—41no—
588C3×C4—42no—
589C3×C4—42no—
590C3×C4—42no—
591C3×C4—42no—
592C3×C4#52511yescharacteristic
593C3×C4#53711yescharacteristic
594C3×C4#54811yescharacteristic
595C3×C4#55011yescharacteristic
596Dic3—42no—
597Dic3—81no—
598Dic3—81no—
599Dic3—81no—
600C23—21no—
601C23—21no—
602C23—21no—
603C23—21no—
604C23—21no—
605C23—21no—
606C23—21no—
607C23—21no—
608C23—21no—
609C23—21no—
610C23—21no—
611C23—21no—
612C23—21no—
613C23#95012yes—
614C23C22×#6711yescharacteristic
615Q8—22no—
616Q8—22no—
617Q8—41no—
618Q8—41no—
619Q8—62no—
620Q8—62no—
621Q8—121no—
622Q8—121no—
623D4—44no—
624C2×C4—21no—
625C2×C4—21no—
626C2×C4—21no—
627C2×C4—21no—
628C2×C4—21no—
629C2×C4—21no—
630C2×C4—21no—
631C2×C4—21no—
632C2×C4—21no—
633C2×C4—22no—
634C2×C4—22no—
635C2×C4—22no—
636C2×C4—21no—
637C2×C4—22no—
638C2×C4—48no—
639C2×C4—41no—
640C2×C4—41no—
641C2×C4—41no—
642C2×C4—41no—
643C2×C4—41no—
644C2×C4—41no—
645C2×C4—41no—
646C2×C4—41no—
647C2×C4—41no—
648C2×C4—41no—
649C2×C4—41no—
650C2×C4—41no—
651C2×C4—41no—
652C2×C4—41no—
653C2×C4—41no—
654C2×C4—41no—
655C2×C4—62no—
656C2×C4—121no—
657C2×C4—121no—
658C2×C4—121no—
659C2×C4—121no—
660C2×C4—121no—
661C2×C4—121no—
662C2×C4—121no—
663C2×C4—121no—
664C2×C4—121no—
665C2×C4—121no—
666C2×C4—121no—
667C2×C4#95312yes—
668C2×C4#95312yes—
669C2×C4D3×#4111yescharacteristic
670C2×C4D3×#4111yescharacteristic
671C2×C4#100911yescharacteristic
672C2×C4#101011yescharacteristic
673C2×C4C22×#6711yescharacteristic
674C2×C4C22×#6711yescharacteristic
675C8—62no—
676C8—121no—
677C8—121no—
678C8—121no—
679C2×C3—42no—
680C2×C3—81no—
681C2×C3#240711yescharacteristic
682C2×C3#300211yescharacteristic
683C2×C3#301111yescharacteristic
684C2×C3#330011yescharacteristic
685C2×C3#332711yescharacteristic
686C2×C3#333611yescharacteristic
687C2×C3#335211yescharacteristic
688C22—22no—
689C22—22no—
690C22—22no—
691C22—41no—
692C22—41no—
693C22—41no—
694C22—41no—
695C22—41no—
696C22—41no—
697C22—41no—
698C22—41no—
699C22—41no—
700C22—41no—
701C22—41no—
702C22C2×#95011yescharacteristic
703C22#582211yescharacteristic
704C22#582411yescharacteristic
705C22#582911yescharacteristic
706C22#583811yescharacteristic
707C22#583811yescharacteristic
708C22C2×#95311yescharacteristic
709C4—22no—
710C4—22no—
711C4—42no—
712C4—42no—
713C4—41no—
714C4—41no—
715C4—42no—
716C4—42no—
717C4—122no—
718C4—241no—
719C4—241no—
720C4—241no—
721C4#582811yescharacteristic
722C4#583111yescharacteristic
723C4#583311yescharacteristic
724C4#583411yescharacteristic
725C3#2412711yescharacteristic, complemented, Sylow
726C2—42no—
727C2—81no—
728C2#8359011yescharacteristic
729C2#8359711yescharacteristic
730C2#8360211yescharacteristic
731C2#8360511yescharacteristic
732C2#8408011yescharacteristic
733C2#8409711yescharacteristic
734C2#8411711yescharacteristic
subgroupG/H
centerC23C22×#67
commutator, cosocleC22×C3×C4C24
FrattiniC22×C4C23×D3
FittingC2×C3×#552C2
socleC23×C3C22×D4
prime radicalC22×C3×D4D4
hypercenterC2×#552D3
hypocenterC3#24127
LCSG ▷ C22×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C23 ◁ C2×C4×D4 ◁ C2×#552

Complements

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

NH ≅ G/Ntype
2. C2×#5063C2semidirect
3. C2×C4×#216C2semidirect
5. #71740C2semidirect
6. #71700C2semidirect
7. #71700C2semidirect
8. #71695C2semidirect
9. #71694C2semidirect
10. #71627C2semidirect
12. #71585C2semidirect
13. #71576C2semidirect
14. #71559C2semidirect
15. #71555C2semidirect
725. C3#24127semidirect

Maximal subgroups

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

subgroupindex
C2×C3×#5522
C2×#50632
C2×C4×#2162
#823752
#717402
#717002
#716952
#716942
#716272
#716142
#715852
#715762
#715592
#715552
#241273