Finite Group Databasebeta

← #10847391

Subgroups — #10847391

Order 768.

1194 conjugacy classes of subgroups.

The subgroup lattice has 758 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#5622C211yesmaximal, characteristic, complemented
2C2×C3×#465C211yesmaximal, characteristic
3#82699C211yesmaximal, characteristic
4C2×#5041C211yesmaximal, characteristic
5#72057C211yesmaximal, characteristic, complemented
6#72048C211yesmaximal, characteristic, complemented
7#71972C211yesmaximal, characteristic, complemented
8C2×#4550C211yesmaximal, characteristic, complemented
9#71696C211yesmaximal, characteristic, complemented
10#70588C211yesmaximal, characteristic, complemented
11#70565C211yesmaximal, characteristic, complemented
12#70284C211yesmaximal, characteristic, complemented
13#70237C211yesmaximal, characteristic, complemented
14#70213C211yesmaximal, characteristic, complemented
15#70163C211yesmaximal, characteristic, complemented
16#25497—31nomaximal, Sylow
17C22×C3×SD16C2211yescharacteristic
18C23×C3×C8C2211yescharacteristic
19C2×C3×C22⋊Q8C2211yescharacteristic
20C2×C3×#121C2211yescharacteristic
21C2×Q8×Dic3C2211yescharacteristic
22C2×#944C2211yescharacteristic
23C2×#935—21no—
24C22×#214C2211yescharacteristic
25C2×#924C2211yescharacteristic
26C22×C4×Dic3C2211yescharacteristic
27C23×C3⋊C8C2211yescharacteristic
28#5622—24no—
29#5622—24no—
30C2×#889—21no—
31C2×#888C2211yescharacteristic
32C2×#887—21no—
33C2×#887C2211yescharacteristic
34C2×#878—21no—
35C2×#877—21no—
36C3×#465—24no—
37C2×C3×#106C2211yescharacteristic
38C2×C3×#103C2211yescharacteristic
39C2×C3×#102C2211yescharacteristic
40C2×#835C2211yescharacteristic
41C2×#835C2211yescharacteristic
42#5221C2211yescharacteristic
43#5221C2211yescharacteristic
44#5220—21no—
45C2×#832C2211yescharacteristic
46#5212C2211yescharacteristic
47C2×#816C2211yescharacteristic
48C2×#816C2211yescharacteristic
49#5041—24no—
50#4972C2211yescharacteristic
51#4972C2211yescharacteristic
52C2×#810C2211yescharacteristic
53C2×#808C2211yescharacteristic
54#4944—21no—
55#4944—21no—
56#4551C2211yescharacteristic
57#4551C2211yescharacteristic
58#4550C2211yescharacteristic
59#4550C2211yescharacteristic
60#4550C2211yescharacteristic
61#4550C2211yescharacteristic
62#4529C2211yescharacteristic
63#4529C2211yescharacteristic
64C2×#533—31no—
65C2×#465—31no—
66C2×#465D311yescharacteristic
67#2854—31no—
68#2058—31no—
69#2043—31no—
70#2023—31no—
71#2013—31no—
72#1892—31no—
73#1892—31no—
74#1880—31no—
75#1880—31no—
76#1865—31no—
77#1865—31no—
78C2×#336—31no—
79C22×C3×Q8C2311yescharacteristic
80C22×C3×D4—21no—
81C22×C3×D4C2311yescharacteristic
82C23×C3×C4C2311yescharacteristic
83C23×Dic3D411yescharacteristic
84C23×Dic3D411yescharacteristic
85C22×Dic6—21no—
86C22×Dic6C2311yescharacteristic
87C2×C3×SD16—22no—
88C2×C3×SD16—22no—
89C2×C3×SD16—41no—
90C22×C3×C8—22no—
91C22×C3×C8—22no—
92C22×C3×C8—41no—
93C22×C3×C8C2311yescharacteristic
94C22×C3×C8C2311yescharacteristic
95C3×C22⋊Q8—22no—
96C3×C22⋊Q8D414yes—
97C3×#121—22no—
98C3×#121—22no—
99C2×C3×C4⋊C4—21no—
100C2×C3×C4⋊C4C2311yescharacteristic
101C2×C3×C4⋊C4C2311yescharacteristic
102C2×C3×C22⋊C4—21no—
103C2×C3×C22⋊C4—21no—
104C2×#217—21no—
105C2×#217—21no—
106C2×#217—21no—
107C2×#217—21no—
108C2×#217—21no—
109C2×#217—21no—
110Q8×Dic3—22no—
111Q8×Dic3—22no—
112#944—22no—
113#944—22no—
114#935—44no—
115C2×#214—22no—
116C2×#214—22no—
117C2×#214—41no—
118C2×C4⋊Dic3—21no—
119C2×C4⋊Dic3C2311yescharacteristic
120C2×C4⋊Dic3C2311yescharacteristic
121C2×C4⋊Dic3C2311yescharacteristic
122#924—22no—
123#924D414yes—
124C2×Dic3⋊C4—21no—
125C2×Dic3⋊C4—21no—
126C2×Dic3⋊C4—21no—
127C2×Dic3⋊C4—21no—
128C2×Dic3⋊C4—21no—
129C2×Dic3⋊C4—21no—
130C2×Dic3⋊C4—21no—
131C2×C4×Dic3—22no—
132C2×C4×Dic3—22no—
133C2×C4×Dic3—21no—
134C2×C4×Dic3—21no—
135C2×C4×Dic3D411yescharacteristic
136C2×C4×Dic3D411yescharacteristic
137C2×C4×Dic3C2311yescharacteristic
138C2×C4×Dic3C2311yescharacteristic
139C22×C3⋊C8—22no—
140C22×C3⋊C8—22no—
141C22×C3⋊C8—41no—
142C22×C3⋊C8C2311yescharacteristic
143C22×C3⋊C8C2311yescharacteristic
144#889—28no—
145#888—22no—
146#888—22no—
147#887—28no—
148#887—22no—
149#887—22no—
150#878—28no—
151#877—28no—
152C3×#106—22no—
153C3×#103—22no—
154C3×#102—22no—
155#835—22no—
156#835—41no—
157#832—22no—
158C3⋊#95—21no—
159C3⋊#95—21no—
160C3⋊#95—21no—
161#816—22no—
162#816—41no—
163#810—22no—
164#808—22no—
165C22×SD16—31no—
166C22×SD16C2×D311yescharacteristic
167C23×C8—31no—
168C23×C8C2×D311yescharacteristic
169#533—64no—
170#533—64no—
171C2×C4⋊Q8—31no—
172C2×C4⋊Q8—31no—
173C2×#125—61no—
174C2×#123—61no—
175C2×C22⋊Q8—31no—
176C2×C22⋊Q8—61no—
177C2×C22⋊Q8C2×D311yescharacteristic
178C2×#121C2×D311yescharacteristic
179C2×C4×Q8—31no—
180C2×C4×Q8—31no—
181C2×C4×Q8—61no—
182C2×#117—61no—
183C22×C42—31no—
184#465—24no—
185#465—64no—
186C2×#106—31no—
187C2×#106C2×D311yescharacteristic
188C2×#103—31no—
189C2×#103—31no—
190C2×#103—31no—
191C2×#103—31no—
192C2×#103—31no—
193C2×#103C2×D311yescharacteristic
194C2×#102—31no—
195C2×#102C2×D311yescharacteristic
196#390—31no—
197#390—31no—
198#389—31no—
199#389—31no—
200#388—61no—
201#388—61no—
202#386—61no—
203#380—31no—
204#340—31no—
205#340—31no—
206#340—31no—
207#340—31no—
208#336—31no—
209#336—31no—
210#336—31no—
211#336—31no—
212C24×C3—21no—
213C24×C3C2×D411yescharacteristic
214C2×C3×Q8—21no—
215C2×C3×Q8—21no—
216C2×C3×Q8—21no—
217C2×C3×Q8—21no—
218C2×C3×Q8—21no—
219C2×C3×Q8C2×D412yes—
220C2×C3×D4—21no—
221C2×C3×D4—21no—
222C2×C3×D4—21no—
223C2×C3×D4—21no—
224C2×C3×D4—21no—
225C2×C3×D4—21no—
226C2×C3×D4—42no—
227C2×C3×D4—42no—
228C2×C3×D4—42no—
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×C4C2×D411yescharacteristic
237C22×C3×C4C2×D412yes—
238C22×C3×C4C2×D412yes—
239C22×C3×C4C2411yescharacteristic
240C22×Dic3—22no—
241C22×Dic3—22no—
242C22×Dic3—22no—
243C22×Dic3—21no—
244C22×Dic3—21no—
245C22×Dic3—22no—
246C22×Dic3—21no—
247C22×Dic3—21no—
248C22×Dic3—41no—
249C22×Dic3SD1614yescomplemented
250C22×Dic3C2×D411yescharacteristic
251C22×Dic3C2×D411yescharacteristic
252C22×Dic3C2×D411yescharacteristic
253C22×Dic3C2×D411yescharacteristic
254C2×Dic6—21no—
255C2×Dic6—21no—
256C2×Dic6—21no—
257C2×Dic6—21no—
258C2×Dic6—24no—
259C2×Dic6—21no—
260C2×Dic6—42no—
261C2×Dic6—42no—
262C2×Dic6C2×D412yes—
263C3×SD16—44no—
264C2×C3×C8—21no—
265C2×C3×C8—21no—
266C2×C3×C8—21no—
267C2×C3×C8—21no—
268C2×C3×C8—21no—
269C2×C3×C8—44no—
270C2×C3×C8#4112yes—
271C3×C4⋊C4—24no—
272C3×C4⋊C4—21no—
273C3×C4⋊C4—21no—
274C3×C4⋊C4—21no—
275C3×C4⋊C4C2×D412yes—
276C3×C22⋊C4—24no—
277C3×C22⋊C4—42no—
278#217—24no—
279#217—42no—
280#217—42no—
281#217—42no—
282#217—42no—
283#217—42no—
284#214—44no—
285C4⋊Dic3—24no—
286C4⋊Dic3—21no—
287C4⋊Dic3—21no—
288C4⋊Dic3—21no—
289C4⋊Dic3—21no—
290C4⋊Dic3—21no—
291C4⋊Dic3C2×D412yes—
292Dic3⋊C4—24no—
293Dic3⋊C4—24no—
294Dic3⋊C4—24no—
295Dic3⋊C4—24no—
296Dic3⋊C4—24no—
297Dic3⋊C4—42no—
298Dic3⋊C4—42no—
299C4×Dic3—24no—
300C4×Dic3—24no—
301C4×Dic3—22no—
302C4×Dic3—22no—
303C4×Dic3—21no—
304C4×Dic3—21no—
305C4×Dic3—21no—
306C4×Dic3—21no—
307C2×C3⋊C8—21no—
308C2×C3⋊C8—21no—
309C2×C3⋊C8—21no—
310C2×C3⋊C8—21no—
311C2×C3⋊C8—21no—
312C2×C3⋊C8—44no—
313C2×C3⋊C8#4112yes—
314C22×Q8—31no—
315C22×Q8—61no—
316C22×Q8C22×D311yescharacteristic
317C22×D4—21no—
318C22×D4C22×D311yescharacteristic
319C23×C4—31no—
320C23×C4—31no—
321C23×C4C22×D311yescharacteristic
322C2×SD16—22no—
323C2×SD16—22no—
324C2×SD16—41no—
325C2×SD16—62no—
326C2×SD16—62no—
327C2×SD16—121no—
328C22×C8—22no—
329C22×C8—22no—
330C22×C8—31no—
331C22×C8—31no—
332C22×C8—41no—
333C22×C8—62no—
334C22×C8—62no—
335C22×C8—121no—
336C22×C8C22×D311yescharacteristic
337C22×C8C22×D311yescharacteristic
338C4⋊Q8—62no—
339C4⋊Q8—62no—
340C4⋊Q8—62no—
341C4⋊Q8—62no—
342#125—68no—
343#123—124no—
344C22⋊Q8—22no—
345C22⋊Q8—34no—
346C22⋊Q8—68no—
347C22⋊Q8—62no—
348C22⋊Q8#6714yes—
349#121—22no—
350#121—22no—
351C4×Q8—62no—
352C4×Q8—68no—
353C4×Q8—62no—
354C4×Q8—62no—
355C4×Q8—62no—
356#117—68no—
357C2×C4⋊C4—21no—
358C2×C4⋊C4—31no—
359C2×C4⋊C4—31no—
360C2×C4⋊C4—31no—
361C2×C4⋊C4—61no—
362C2×C4⋊C4—61no—
363C2×C4⋊C4—61no—
364C2×C4⋊C4—61no—
365C2×C4⋊C4—61no—
366C2×C4⋊C4—61no—
367C2×C4⋊C4—61no—
368C2×C4⋊C4—61no—
369C2×C4⋊C4C22×D311yescharacteristic
370C2×C4⋊C4C22×D311yescharacteristic
371C2×C22⋊C4—21no—
372C2×C22⋊C4—21no—
373C2×C22⋊C4—61no—
374C2×C22⋊C4—61no—
375C2×C22⋊C4—61no—
376C2×C22⋊C4—61no—
377C2×C22⋊C4—61no—
378C2×C22⋊C4—61no—
379C2×C42—31no—
380C2×C42—31no—
381C2×C42—31no—
382C2×C42—31no—
383C2×C42—61no—
384C2×C42—61no—
385C2×C42—62no—
386C2×C42—62no—
387#106—22no—
388#106—62no—
389#103—22no—
390#103—62no—
391#103—62no—
392#103—62no—
393#103—121no—
394#103—121no—
395#102—22no—
396#102—62no—
397#95—61no—
398#95—61no—
399#95—61no—
400C23×C3—21no—
401C23×C3—21no—
402C23×C3—21no—
403C23×C3—21no—
404C23×C3—41no—
405C23×C3—41no—
406C23×C3—41no—
407C23×C3—41no—
408C23×C3—41no—
409C23×C3—41no—
410C23×C3—41no—
411C23×C3#12012yes—
412C23×C3C2×SD1612yes—
413C23×C3#13712yes—
414C23×C3C22×D411yescharacteristic
415C3×Q8—22no—
416C3×Q8—22no—
417C3×Q8—41no—
418C3×Q8—41no—
419C3×D4—41no—
420C3×D4—41no—
421C3×D4—41no—
422C3×D4—41no—
423C3×D4—84no—
424C2×C3×C4—21no—
425C2×C3×C4—21no—
426C2×C3×C4—22no—
427C2×C3×C4—22no—
428C2×C3×C4—22no—
429C2×C3×C4—22no—
430C2×C3×C4—22no—
431C2×C3×C4—22no—
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#12012yes—
440C2×C3×C4C22×D411yescharacteristic
441C2×C3×C4C22×D411yescharacteristic
442C2×C3×C4C2×#4111yescharacteristic
443C2×C3×C4C2×#4111yescharacteristic
444C2×C3×C4H(5,𝔽2)11yescharacteristic
445C2×C3×C42−1+411yescharacteristic
446C2×Dic3—21no—
447C2×Dic3—21no—
448C2×Dic3—21no—
449C2×Dic3—21no—
450C2×Dic3—21no—
451C2×Dic3—21no—
452C2×Dic3—28no—
453C2×Dic3—21no—
454C2×Dic3—22no—
455C2×Dic3—22no—
456C2×Dic3—21no—
457C2×Dic3—21no—
458C2×Dic3—44no—
459C2×Dic3—41no—
460C2×Dic3—41no—
461C2×Dic3—41no—
462C2×Dic3—41no—
463C2×Dic3—41no—
464C2×Dic3—41no—
465C2×Dic3—41no—
466C2×Dic3—41no—
467C2×Dic3—41no—
468C2×Dic3—41no—
469C2×Dic3C2×SD1612yes—
470C2×Dic3C2×SD1612yes—
471C2×Dic3#13512yes—
472Dic6—22no—
473Dic6—22no—
474Dic6—48no—
475Dic6—41no—
476Dic6—41no—
477C3×C8—22no—
478C3×C8—41no—
479C3⋊C8—22no—
480C3⋊C8—41no—
481C24—21no—
482C24D3×D411yescharacteristic
483C2×Q8—21no—
484C2×Q8—21no—
485C2×Q8—21no—
486C2×Q8—21no—
487C2×Q8—21no—
488C2×Q8—32no—
489C2×Q8—64no—
490C2×Q8—61no—
491C2×Q8—61no—
492C2×Q8—61no—
493C2×Q8—61no—
494C2×Q8—61no—
495C2×Q8—122no—
496C2×Q8—122no—
497C2×Q8C2×#6712yes—
498C2×D4—21no—
499C2×D4—21no—
500C2×D4—21no—
501C2×D4—21no—
502C2×D4—21no—
503C2×D4—21no—
504C2×D4—42no—
505C2×D4—42no—
506C2×D4—42no—
507C22×C4—21no—
508C22×C4—21no—
509C22×C4—21no—
510C22×C4—21no—
511C22×C4—21no—
512C22×C4—21no—
513C22×C4—21no—
514C22×C4—34no—
515C22×C4—31no—
516C22×C4—31no—
517C22×C4—31no—
518C22×C4—31no—
519C22×C4—62no—
520C22×C4—62no—
521C22×C4—62no—
522C22×C4—62no—
523C22×C4—61no—
524C22×C4—61no—
525C22×C4—61no—
526C22×C4—61no—
527C22×C4—121no—
528C22×C4D3×D411yescharacteristic
529C22×C4D3×D412yes—
530C22×C4C2×#6712yes—
531C22×C4C23×D311yescharacteristic
532SD16—44no—
533SD16—124no—
534C2×C8—21no—
535C2×C8—21no—
536C2×C8—21no—
537C2×C8—21no—
538C2×C8—21no—
539C2×C8—32no—
540C2×C8—44no—
541C2×C8—61no—
542C2×C8—61no—
543C2×C8—61no—
544C2×C8—61no—
545C2×C8—61no—
546C2×C8—124no—
547C2×C8#23712yes—
548C4⋊C4—24no—
549C4⋊C4—21no—
550C4⋊C4—21no—
551C4⋊C4—21no—
552C4⋊C4—32no—
553C4⋊C4—64no—
554C4⋊C4—64no—
555C4⋊C4—64no—
556C4⋊C4—64no—
557C4⋊C4—64no—
558C4⋊C4—64no—
559C4⋊C4—61no—
560C4⋊C4—61no—
561C4⋊C4—61no—
562C4⋊C4—61no—
563C4⋊C4—61no—
564C4⋊C4—122no—
565C4⋊C4—122no—
566C4⋊C4C2×#6712yes—
567C22⋊C4—24no—
568C22⋊C4—42no—
569C22⋊C4—64no—
570C22⋊C4—122no—
571C22⋊C4—122no—
572C22⋊C4—122no—
573C22⋊C4—122no—
574C22⋊C4—122no—
575C42—64no—
576C42—64no—
577C42—62no—
578C42—62no—
579C42—61no—
580C42—61no—
581C42—61no—
582C42—61no—
583C22×C3—22no—
584C22×C3—22no—
585C22×C3—22no—
586C22×C3—22no—
587C22×C3—22no—
588C22×C3—22no—
589C22×C3—81no—
590C22×C3—81no—
591C22×C3—81no—
592C22×C3—81no—
593C22×C3—81no—
594C22×C3—81no—
595C22×C3—81no—
596C22×C3#44814yes—
597C22×C3C2×#12011yescharacteristic
598C22×C3#53211yescharacteristic
599C22×C3#53711yescharacteristic
600C22×C3C22×SD1611yescharacteristic
601C22×C3C2×#13511yescharacteristic
602C22×C3C2×#13711yescharacteristic
603C22×C3#57511yescharacteristic
604C3×C4—22no—
605C3×C4—42no—
606C3×C4—42no—
607C3×C4—81no—
608C3×C4#54611yescharacteristic
609C3×C4#54611yescharacteristic
610C3×C4#54711yescharacteristic
611C3×C4#54711yescharacteristic
612Dic3—22no—
613Dic3—22no—
614Dic3—22no—
615Dic3—42no—
616Dic3—42no—
617Dic3—41no—
618Dic3—81no—
619Dic3—81no—
620C23—21no—
621C23—21no—
622C23—21no—
623C23—21no—
624C23—41no—
625C23—41no—
626C23—41no—
627C23—41no—
628C23—41no—
629C23—41no—
630C23—41no—
631C23D3×SD1612yes—
632C23#91512yes—
633C23#93712yes—
634C23C2×D3×D411yescharacteristic
635Q8—22no—
636Q8—22no—
637Q8—41no—
638Q8—41no—
639Q8—62no—
640Q8—62no—
641Q8—128no—
642Q8—121no—
643Q8—121no—
644D4—41no—
645D4—41no—
646D4—41no—
647D4—41no—
648D4—84no—
649C2×C4—21no—
650C2×C4—21no—
651C2×C4—22no—
652C2×C4—22no—
653C2×C4—22no—
654C2×C4—22no—
655C2×C4—22no—
656C2×C4—22no—
657C2×C4—32no—
658C2×C4—32no—
659C2×C4—32no—
660C2×C4—41no—
661C2×C4—41no—
662C2×C4—41no—
663C2×C4—41no—
664C2×C4—41no—
665C2×C4—41no—
666C2×C4—41no—
667C2×C4—68no—
668C2×C4—61no—
669C2×C4—61no—
670C2×C4—61no—
671C2×C4—61no—
672C2×C4—61no—
673C2×C4—61no—
674C2×C4—61no—
675C2×C4—61no—
676C2×C4—61no—
677C2×C4—62no—
678C2×C4—62no—
679C2×C4—124no—
680C2×C4—121no—
681C2×C4—121no—
682C2×C4—121no—
683C2×C4—121no—
684C2×C4—121no—
685C2×C4—121no—
686C2×C4—121no—
687C2×C4—121no—
688C2×C4—121no—
689C2×C4—121no—
690C2×C4#93712yes—
691C2×C4C2×D3×D411yescharacteristic
692C2×C4C2×#23711yescharacteristic
693C2×C4#100411yescharacteristic
694C2×C4D3×#4111yescharacteristic
695C2×C4#101011yescharacteristic
696C2×C4C22×#6711yescharacteristic
697C8—22no—
698C8—41no—
699C8—62no—
700C8—121no—
701C2×C3—24no—
702C2×C3—161no—
703C2×C3#243011yescharacteristic
704C2×C3C2×#44811yescharacteristic
705C2×C3#300211yescharacteristic
706C2×C3#316711yescharacteristic
707C2×C3#318111yescharacteristic
708C2×C3#324611yescharacteristic
709C2×C3#324811yescharacteristic
710C22—22no—
711C22—22no—
712C22—22no—
713C22—22no—
714C22—22no—
715C22—22no—
716C22—81no—
717C22—81no—
718C22—81no—
719C22—81no—
720C22—81no—
721C22—81no—
722C22—81no—
723C22#517014yes—
724C22#559611yescharacteristic
725C22#559711yescharacteristic
726C22C2×D3×SD1611yescharacteristic
727C22C2×#91511yescharacteristic
728C22D3×#13511yescharacteristic
729C22#576811yescharacteristic
730C22C2×#93711yescharacteristic
731C4—22no—
732C4—42no—
733C4—42no—
734C4—62no—
735C4—62no—
736C4—62no—
737C4—81no—
738C4—121no—
739C4—122no—
740C4—122no—
741C4—241no—
742C4—241no—
743C4#561011yescharacteristic
744C4#561111yescharacteristic
745C4#580611yescharacteristic
746C4#582411yescharacteristic
747C3#2549711yescharacteristic, complemented, Sylow
748C2—24no—
749C2—161no—
750C2#8063211yescharacteristic
751C2#8063911yescharacteristic
752C2#8064011yescharacteristic
753C2#8064211yescharacteristic
754C2#8265111yescharacteristic
755C2C2×#517011yescharacteristic
756C2#8391111yescharacteristic
subgroupG/H
centerC23C2×D3×D4
commutator, cosocleC22×C3×C4C24
FrattiniC22×C4C23×D3
FittingC2×C3×#465C2
socleC23×C3C22×D4
prime radicalC2×C3×#121C22
hypercenterC2×#465D3
hypocenterC3#25497
LCSG ▷ C22×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#465

Complements

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

NH ≅ G/Ntype
1. C2×#5622C2semidirect
5. #72057C2semidirect
6. #72048C2semidirect
7. #71972C2semidirect
8. C2×#4550C2semidirect
9. #71696C2semidirect
10. #70588C2semidirect
11. #70565C2semidirect
12. #70284C2semidirect
13. #70237C2semidirect
14. #70213C2semidirect
15. #70163C2semidirect
249. C22×Dic3SD16semidirect
747. C3#25497semidirect

Maximal subgroups

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

subgroupindex
C2×#56222
C2×C3×#4652
#826992
C2×#50412
#720572
#720482
#719722
C2×#45502
#716962
#705882
#705652
#702842
#702372
#702132
#701632
#254973