Finite Group Databasebeta

← #482843

Subgroups — #482843

Order 512.

910 conjugacy classes of subgroups.

The subgroup lattice has 805 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#36079C211yesmaximal, characteristic
2#22477C211yesmaximal, characteristic
3#17422C211yesmaximal, characteristic
4#11897C211yesmaximal, characteristic, complemented
5#11842C211yesmaximal, characteristic, complemented
6#11841C211yesmaximal, characteristic, complemented
7#11823C211yesmaximal, characteristic, complemented
8#11810C211yesmaximal, characteristic, complemented
9#11808C211yesmaximal, characteristic, complemented
10#11784C211yesmaximal, characteristic, complemented
11#11756C211yesmaximal, characteristic, complemented
12#11755C211yesmaximal, characteristic, complemented
13#11728C211yesmaximal, characteristic, complemented
14#11715C211yesmaximal, characteristic, complemented
15C2×#1351C211yesmaximal, characteristic, complemented
16C2×#551C2211yescharacteristic
17C2×#519C411yescharacteristic, complemented
18#2974—21no—
19#2637C411yescharacteristic, complemented
20#2632C411yescharacteristic, complemented
21#2614C411yescharacteristic, complemented
22#2604C411yescharacteristic, complemented
23#2599C2211yescharacteristic
24#2592C411yescharacteristic, complemented
25#2580C2211yescharacteristic
26#2498C411yescharacteristic, complemented
27#2482C2211yescharacteristic
28#2469—21no—
29#2465—21no—
30#2458—21no—
31#2458—21no—
32#2438—21no—
33#2411—21no—
34#2398C2211yescharacteristic
35#2396C2211yescharacteristic
36C2×#393C2211yescharacteristic
37#2359—21no—
38#2343C411yescharacteristic, complemented
39#2342—21no—
40#2342—21no—
41#1996—21no—
42#1899—21no—
43#1898—21no—
44#1820C2211yescharacteristic
45#1819C2211yescharacteristic
46#1799C2211yescharacteristic
47C4×#99C2211yescharacteristic
48#1740C2211yescharacteristic
49C2×#342C2211yescharacteristic
50#1473—21no—
51#1472—21no—
52#1468—21no—
53#1465C2211yescharacteristic
54#1464C2211yescharacteristic
55#1462C2211yescharacteristic
56#1459C2211yescharacteristic
57#1458C2211yescharacteristic
58C2×#323C2211yescharacteristic
59#1352C2211yescharacteristic
60#1352C2211yescharacteristic
61#1352C2211yescharacteristic
62#1352C2211yescharacteristic
63#1351C2211yescharacteristic
64#1351C2211yescharacteristic
65#1351C2211yescharacteristic
66#1351C2211yescharacteristic
67#1351C2211yescharacteristic
68#1351C2211yescharacteristic
69#1351C2211yescharacteristic
70#1351C2211yescharacteristic
71#1344C2211yescharacteristic
72#1344C2211yescharacteristic
73#1344C2211yescharacteristic
74#1344C2211yescharacteristic
75C23×Q8C2×C411yescharacteristic
76#551—41no—
77#551—41no—
78#551—41no—
79#551—41no—
80C2×#126C2×C411yescharacteristic
81C2×#126D411yescharacteristic
82C2×#124C2×C411yescharacteristic
83C2×#123—21no—
84C2×#123C2×C411yescharacteristic
85C2×#123D411yescharacteristic
86C2×#123D411yescharacteristic
87C2×C22⋊Q8D411yescharacteristic
88C2×C22⋊Q8D411yescharacteristic
89C2×#120D411yescharacteristic
90#519—41no—
91#519—41no—
92#519—41no—
93#519—41no—
94C2×C4×Q8—21no—
95C2×C4×Q8—21no—
96C2×C4×Q8C2×C411yescharacteristic, complemented
97C2×C4×Q8C2×C411yescharacteristic, complemented
98C2×C4×Q8C2×C411yescharacteristic, complemented
99C2×C4×Q8C2×C411yescharacteristic, complemented
100C2×C4×D4D411yescharacteristic
101C2×C4×D4C2311yescharacteristic
102C2×#117—21no—
103C2×#117—21no—
104C2×#117—21no—
105C2×#117C2×C411yescharacteristic
106C2×#117C2×C411yescharacteristic
107C2×#117C2311yescharacteristic
108C22×C22⋊C4—21no—
109C22×C22⋊C4—21no—
110C22×C22⋊C4D411yescharacteristic
111C22×C22⋊C4C2311yescharacteristic
112#436—41no—
113#435—41no—
114#435—41no—
115C8×D4—41no—
116#432—21no—
117#431—21no—
118C2×#99—21no—
119C2×#99—21no—
120#407—21no—
121#407—21no—
122C2×C22⋊C8—21no—
123C2×C22⋊C8—21no—
124#400—21no—
125#400C2×C411yescharacteristic, complemented
126#399C2×C411yescharacteristic
127#399C2×C411yescharacteristic, complemented
128#399C2311yescharacteristic
129#398—21no—
130#398—21no—
131#398C2×C411yescharacteristic, complemented
132#397C2×C411yescharacteristic
133#397C2×C411yescharacteristic, complemented
134#397C2311yescharacteristic
135#396—21no—
136#396—21no—
137#395—21no—
138#395—21no—
139#395C2×C411yescharacteristic, complemented
140#395C2×C411yescharacteristic, complemented
141#394—21no—
142#394—21no—
143#393—21no—
144#393—21no—
145#393—21no—
146#393C2×C411yescharacteristic
147#393C2×C411yescharacteristic
148#393C2×C411yescharacteristic, complemented
149#393C2×C411yescharacteristic, complemented
150#393C2311yescharacteristic
151#393C2311yescharacteristic
152#391—21no—
153#390—21no—
154#390—21no—
155#389—21no—
156#389—21no—
157#388—21no—
158#388—21no—
159#388—21no—
160#388—21no—
161#388—21no—
162#388—21no—
163#388—21no—
164#388—21no—
165#388—21no—
166#388—21no—
167#388—21no—
168#388—41no—
169#388—41no—
170#387—21no—
171#387—21no—
172#387—21no—
173#387—21no—
174#387—21no—
175#387—21no—
176#387—21no—
177#386—21no—
178#385—21no—
179#385—21no—
180#385—21no—
181#385—21no—
182#385—21no—
183#385—41no—
184#383C2×C411yescharacteristic, complemented
185#382C2×C411yescharacteristic, complemented
186#381—21no—
187#381—21no—
188#381C2×C411yescharacteristic
189#380—21no—
190#380—21no—
191#379—21no—
192#379—21no—
193C4×C4⋊C4—21no—
194C4×C4⋊C4C2×C411yescharacteristic, complemented
195C4×C22⋊C4—21no—
196C4×C22⋊C4—21no—
197C4×C22⋊C4—21no—
198C4×C22⋊C4—21no—
199C4×C22⋊C4—21no—
200C4×C22⋊C4—41no—
201#376C2×C411yescharacteristic, complemented
202C2×#95—21no—
203C2×#95C2×C411yescharacteristic
204#342—21no—
205#342—21no—
206#342—21no—
207#342—21no—
208#342C2311yescharacteristic
209#342C2311yescharacteristic
210#342C2311yescharacteristic
211#342C2311yescharacteristic
212#324—21no—
213#324—21no—
214#324—21no—
215#324—21no—
216#323—21no—
217#323—21no—
218#323C2311yescharacteristic
219#323C2311yescharacteristic
220#323C2311yescharacteristic
221#323C2311yescharacteristic
222C25C2×D411yescharacteristic
223C22×Q8—21no—
224C22×Q8—44no—
225C22×Q8—41no—
226C22×Q8—41no—
227C22×Q8C22⋊C411yescharacteristic
228C22×Q8C22×C411yescharacteristic
229C22×Q8C22×C411yescharacteristic
230C22×D4C22⋊C411yescharacteristic
231C22×D4C22⋊C411yescharacteristic
232C22×D4C2×D411yescharacteristic
233C23×C4—21no—
234C23×C4—21no—
235C23×C4—41no—
236C23×C4C22×C411yescharacteristic
237C23×C4C2×D411yescharacteristic
238C23×C4C2×D411yescharacteristic
239C23×C4C2×D411yescharacteristic
240C23×C4C2×D411yescharacteristic
241C2×M16—41no—
242C2×M16—41no—
243C22×C8—41no—
244C22×C8—41no—
245#126—41no—
246#126—41no—
247#126—41no—
248#126—41no—
249#124—41no—
250#124—41no—
251#123—41no—
252#123—41no—
253#123—41no—
254#123—41no—
255#123—41no—
256#123—41no—
257#123—44no—
258C22⋊Q8—41no—
259C22⋊Q8—41no—
260C22⋊Q8—41no—
261C22⋊Q8—41no—
262#120—41no—
263#120—41no—
264C4×Q8—41no—
265C4×Q8—41no—
266C4×Q8—41no—
267C4×Q8—41no—
268C4×Q8—41no—
269C4×Q8—41no—
270C4×Q8—41no—
271C4×Q8—41no—
272C4×Q8—42no—
273C4×Q8—42no—
274C4×Q8—42no—
275C4×Q8—42no—
276C4×D4—21no—
277C4×D4—21no—
278C4×D4—21no—
279C4×D4—21no—
280C4×D4—41no—
281C4×D4—41no—
282#117—21no—
283#117—21no—
284#117—21no—
285#117—21no—
286#117—41no—
287#117—41no—
288#117—42no—
289#117—42no—
290#117—41no—
291#117—41no—
292#117—41no—
293#117—41no—
294#117—41no—
295#117—41no—
296#117—42no—
297#117—81no—
298C2×C4⋊C4—21no—
299C2×C4⋊C4—21no—
300C2×C4⋊C4—21no—
301C2×C4⋊C4—21no—
302C2×C4⋊C4—21no—
303C2×C4⋊C4—21no—
304C2×C4⋊C4—21no—
305C2×C4⋊C4—21no—
306C2×C4⋊C4—21no—
307C2×C4⋊C4—21no—
308C2×C4⋊C4—21no—
309C2×C4⋊C4—21no—
310C2×C4⋊C4—41no—
311C2×C4⋊C4—41no—
312C2×C4⋊C4C22⋊C411yescharacteristic
313C2×C4⋊C4C22⋊C411yescharacteristic
314C2×C4⋊C4C22⋊C411yescharacteristic
315C2×C4⋊C4C22⋊C411yescharacteristic
316C2×C4⋊C4C22⋊C411yescharacteristic
317C2×C4⋊C4C22×C411yescharacteristic
318C2×C4⋊C4C22×C411yescharacteristic
319C2×C4⋊C4C22×C411yescharacteristic
320C2×C4⋊C4C2×D411yescharacteristic
321C2×C4⋊C4C2×D411yescharacteristic
322C2×C22⋊C4—21no—
323C2×C22⋊C4—21no—
324C2×C22⋊C4—21no—
325C2×C22⋊C4—21no—
326C2×C22⋊C4—21no—
327C2×C22⋊C4—21no—
328C2×C22⋊C4—21no—
329C2×C22⋊C4—21no—
330C2×C22⋊C4—21no—
331C2×C22⋊C4—21no—
332C2×C22⋊C4—21no—
333C2×C22⋊C4—21no—
334C2×C22⋊C4—21no—
335C2×C22⋊C4—21no—
336C2×C22⋊C4—21no—
337C2×C22⋊C4—21no—
338C2×C22⋊C4—21no—
339C2×C22⋊C4—21no—
340C2×C22⋊C4—21no—
341C2×C22⋊C4—21no—
342C2×C22⋊C4—21no—
343C2×C22⋊C4—21no—
344C2×C22⋊C4—42no—
345C2×C22⋊C4—41no—
346C2×C22⋊C4—41no—
347C2×C22⋊C4—44no—
348C2×C22⋊C4—41no—
349C2×C22⋊C4—41no—
350C2×C22⋊C4—41no—
351C2×C22⋊C4—81no—
352C2×C22⋊C4C22⋊C411yescharacteristic
353C2×C22⋊C4C22⋊C411yescharacteristic
354C2×C22⋊C4C22⋊C411yescharacteristic
355C2×C22⋊C4C22⋊C411yescharacteristic
356C2×C22⋊C4C22⋊C411yescharacteristic
357C2×C22⋊C4C22⋊C411yescharacteristic
358C2×C22⋊C4C22⋊C411yescharacteristic
359C2×C22⋊C4C22⋊C411yescharacteristic
360C2×C22⋊C4C22×C411yescharacteristic
361C2×C22⋊C4C22×C411yescharacteristic
362C2×C22⋊C4C2×D411yescharacteristic
363C2×C22⋊C4C2×D411yescharacteristic
364C2×C22⋊C4C2×D411yescharacteristic
365C2×C22⋊C4C2411yescharacteristic
366C2×C42—21no—
367C2×C42—21no—
368C2×C42—21no—
369C2×C42—21no—
370C2×C42—21no—
371C2×C42—21no—
372C2×C42—21no—
373C2×C42—41no—
374C2×C42—41no—
375C2×C42C22×C411yescharacteristic
376C2×C42C22×C411yescharacteristic
377C2×C42C2×D411yescharacteristic
378C4⋊C8—41no—
379C4⋊C8—41no—
380#99—42no—
381#99—81no—
382C22⋊C8—21no—
383C22⋊C8—21no—
384C22⋊C8—21no—
385C22⋊C8—21no—
386C22⋊C8—41no—
387C22⋊C8—41no—
388C22⋊C8—41no—
389C22⋊C8—41no—
390#97—41no—
391C4×C8—41no—
392#95—21no—
393#95—21no—
394#95—21no—
395#95—21no—
396#95—21no—
397#95—21no—
398#95—21no—
399#95—21no—
400#95—21no—
401#95—21no—
402#95—21no—
403#95—21no—
404#95—21no—
405#95—21no—
406#95—21no—
407#95—21no—
408#95—21no—
409#95—21no—
410#95—21no—
411#95—21no—
412#95—41no—
413#95—41no—
414#95—41no—
415#95—41no—
416#95C22×C411yescharacteristic
417#95C22×C411yescharacteristic
418#95C22×C411yescharacteristic
419#95C22×C411yescharacteristic
420C24—21no—
421C24—21no—
422C24—21no—
423C24—21no—
424C24—41no—
425C24—42no—
426C24—81no—
427C24C2×C22⋊C411yescharacteristic
428C24C2×C22⋊C411yescharacteristic
429C24C2×C22⋊C411yescharacteristic
430C24C22×D411yescharacteristic
431C2×Q8—41no—
432C2×Q8—42no—
433C2×Q8—42no—
434C2×Q8—42no—
435C2×Q8—42no—
436C2×Q8—42no—
437C2×Q8—41no—
438C2×Q8—41no—
439C2×Q8—44no—
440C2×Q8—44no—
441C2×Q8—44no—
442C2×Q8—44no—
443C2×Q8—81no—
444C2×D4—21no—
445C2×D4—21no—
446C2×D4—21no—
447C2×D4—21no—
448C2×D4—41no—
449C2×D4—41no—
450C2×D4—41no—
451C2×D4—42no—
452C2×D4—81no—
453C22×C4—24no—
454C22×C4—21no—
455C22×C4—21no—
456C22×C4—21no—
457C22×C4—21no—
458C22×C4—21no—
459C22×C4—21no—
460C22×C4—21no—
461C22×C4—21no—
462C22×C4—21no—
463C22×C4—21no—
464C22×C4—21no—
465C22×C4—21no—
466C22×C4—21no—
467C22×C4—21no—
468C22×C4—21no—
469C22×C4—21no—
470C22×C4—21no—
471C22×C4—21no—
472C22×C4—21no—
473C22×C4—21no—
474C22×C4—41no—
475C22×C4—42no—
476C22×C4—41no—
477C22×C4—41no—
478C22×C4—42no—
479C22×C4—41no—
480C22×C4—42no—
481C22×C4—41no—
482C22×C4—41no—
483C22×C4—41no—
484C22×C4—81no—
485C22×C4—81no—
486C22×C4—81no—
487C22×C4—81no—
488C22×C4—81no—
489C22×C4—82no—
490C22×C4—82no—
491C22×C4—161no—
492C22×C4C2×C22⋊C411yescharacteristic
493C22×C4C2×C22⋊C411yescharacteristic
494C22×C4C2×C22⋊C411yescharacteristic
495C22×C4C2×C22⋊C411yescharacteristic
496C22×C4C2×C22⋊C411yescharacteristic
497C22×C4C2×C22⋊C411yescharacteristic
498C22×C4C2×C22⋊C411yescharacteristic
499C22×C4C2×C22⋊C411yescharacteristic
500C22×C4C2×C22⋊C411yescharacteristic
501C22×C4C23×C411yescharacteristic
502C22×C4C22×D411yescharacteristic
503M16—161no—
504M16—161no—
505C2×C8—41no—
506C2×C8—41no—
507C2×C8—41no—
508C2×C8—41no—
509C2×C8—161no—
510C2×C8—161no—
511C4⋊C4—21no—
512C4⋊C4—21no—
513C4⋊C4—21no—
514C4⋊C4—21no—
515C4⋊C4—21no—
516C4⋊C4—21no—
517C4⋊C4—41no—
518C4⋊C4—41no—
519C4⋊C4—41no—
520C4⋊C4—41no—
521C4⋊C4—41no—
522C4⋊C4—41no—
523C4⋊C4—41no—
524C4⋊C4—42no—
525C4⋊C4—42no—
526C4⋊C4—42no—
527C4⋊C4—42no—
528C4⋊C4—41no—
529C4⋊C4—41no—
530C4⋊C4—41no—
531C4⋊C4—41no—
532C4⋊C4—81no—
533C4⋊C4—81no—
534C4⋊C4—81no—
535C4⋊C4—81no—
536C4⋊C4—81no—
537C4⋊C4—81no—
538C4⋊C4—82no—
539C4⋊C4—161no—
540C22⋊C4—21no—
541C22⋊C4—21no—
542C22⋊C4—21no—
543C22⋊C4—21no—
544C22⋊C4—21no—
545C22⋊C4—21no—
546C22⋊C4—21no—
547C22⋊C4—21no—
548C22⋊C4—21no—
549C22⋊C4—21no—
550C22⋊C4—22no—
551C22⋊C4—41no—
552C22⋊C4—41no—
553C22⋊C4—41no—
554C22⋊C4—41no—
555C22⋊C4—41no—
556C22⋊C4—41no—
557C22⋊C4—41no—
558C22⋊C4—41no—
559C22⋊C4—42no—
560C22⋊C4—42no—
561C22⋊C4—42no—
562C22⋊C4—42no—
563C22⋊C4—42no—
564C22⋊C4—42no—
565C22⋊C4—42no—
566C22⋊C4—41no—
567C22⋊C4—41no—
568C22⋊C4—41no—
569C22⋊C4—41no—
570C22⋊C4—41no—
571C22⋊C4—41no—
572C22⋊C4—41no—
573C22⋊C4—41no—
574C22⋊C4—41no—
575C22⋊C4—41no—
576C22⋊C4—41no—
577C22⋊C4—81no—
578C22⋊C4—81no—
579C22⋊C4—81no—
580C22⋊C4—81no—
581C22⋊C4—81no—
582C22⋊C4—82no—
583C22⋊C4—82no—
584C22⋊C4—161no—
585C22⋊C4#9911yescharacteristic
586C22⋊C4#9911yescharacteristic
587C22⋊C4#9911yescharacteristic
588C22⋊C4#9911yescharacteristic
589C42—21no—
590C42—21no—
591C42—21no—
592C42—21no—
593C42—21no—
594C42—21no—
595C42—42no—
596C42—42no—
597C42—42no—
598C42—41no—
599C42—41no—
600C42—41no—
601C42—41no—
602C42—81no—
603C42—81no—
604C42—82no—
605C42—161no—
606C23—21no—
607C23—22no—
608C23—21no—
609C23—21no—
610C23—21no—
611C23—21no—
612C23—21no—
613C23—21no—
614C23—21no—
615C23—21no—
616C23—21no—
617C23—41no—
618C23—41no—
619C23—41no—
620C23—41no—
621C23—41no—
622C23—41no—
623C23—41no—
624C23—41no—
625C23—41no—
626C23—41no—
627C23—41no—
628C23—42no—
629C23—81no—
630C23—81no—
631C23—81no—
632C23—82no—
633C23—82no—
634C23—162no—
635C23C2×#9911yescharacteristic
636C23C2×#9911yescharacteristic
637C23C22×C22⋊C411yescharacteristic
638C23#57711yescharacteristic
639C23#57811yescharacteristic
640Q8—42no—
641Q8—42no—
642Q8—42no—
643Q8—42no—
644Q8—48no—
645Q8—161no—
646D4—42no—
647D4—81no—
648D4—81no—
649D4—81no—
650D4—161no—
651C2×C4—21no—
652C2×C4—21no—
653C2×C4—22no—
654C2×C4—22no—
655C2×C4—21no—
656C2×C4—21no—
657C2×C4—21no—
658C2×C4—21no—
659C2×C4—21no—
660C2×C4—21no—
661C2×C4—21no—
662C2×C4—21no—
663C2×C4—21no—
664C2×C4—21no—
665C2×C4—21no—
666C2×C4—21no—
667C2×C4—21no—
668C2×C4—41no—
669C2×C4—41no—
670C2×C4—41no—
671C2×C4—41no—
672C2×C4—41no—
673C2×C4—41no—
674C2×C4—41no—
675C2×C4—44no—
676C2×C4—42no—
677C2×C4—41no—
678C2×C4—41no—
679C2×C4—44no—
680C2×C4—42no—
681C2×C4—41no—
682C2×C4—41no—
683C2×C4—41no—
684C2×C4—41no—
685C2×C4—41no—
686C2×C4—41no—
687C2×C4—41no—
688C2×C4—42no—
689C2×C4—41no—
690C2×C4—41no—
691C2×C4—41no—
692C2×C4—41no—
693C2×C4—41no—
694C2×C4—41no—
695C2×C4—41no—
696C2×C4—41no—
697C2×C4—41no—
698C2×C4—41no—
699C2×C4—41no—
700C2×C4—41no—
701C2×C4—41no—
702C2×C4—41no—
703C2×C4—41no—
704C2×C4—41no—
705C2×C4—41no—
706C2×C4—41no—
707C2×C4—81no—
708C2×C4—81no—
709C2×C4—81no—
710C2×C4—81no—
711C2×C4—81no—
712C2×C4—81no—
713C2×C4—81no—
714C2×C4—81no—
715C2×C4—81no—
716C2×C4—81no—
717C2×C4—81no—
718C2×C4—81no—
719C2×C4—81no—
720C2×C4—81no—
721C2×C4—81no—
722C2×C4—81no—
723C2×C4—81no—
724C2×C4—162no—
725C2×C4—164no—
726C2×C4C2×#9911yescharacteristic
727C2×C4C2×#9911yescharacteristic
728C2×C4C2×#9911yescharacteristic
729C2×C4C2×#9911yescharacteristic
730C8—81no—
731C8—81no—
732C8—81no—
733C8—81no—
734C22—21no—
735C22—21no—
736C22—21no—
737C22—21no—
738C22—21no—
739C22—21no—
740C22—21no—
741C22—21no—
742C22—21no—
743C22—42no—
744C22—42no—
745C22—41no—
746C22—41no—
747C22—41no—
748C22—41no—
749C22—41no—
750C22—41no—
751C22—41no—
752C22—41no—
753C22—41no—
754C22—41no—
755C22—81no—
756C22—82no—
757C22—82no—
758C22—81no—
759C22—81no—
760C22—81no—
761C22—81no—
762C22—161no—
763C22—161no—
764C22#212012yes—
765C22C22×#9911yescharacteristic
766C22#289811yescharacteristic
767C22#290111yescharacteristic
768C4—21no—
769C4—21no—
770C4—21no—
771C4—21no—
772C4—42no—
773C4—42no—
774C4—41no—
775C4—41no—
776C4—41no—
777C4—41no—
778C4—41no—
779C4—41no—
780C4—41no—
781C4—41no—
782C4—41no—
783C4—81no—
784C4—81no—
785C4—81no—
786C4—81no—
787C4—82no—
788C4—81no—
789C4—81no—
790C4—161no—
791C4—161no—
792C4—161no—
793C2—21no—
794C2—21no—
795C2—22no—
796C2—41no—
797C2—41no—
798C2—41no—
799C2—81no—
800C2—81no—
801C2#1760811yescharacteristic
802C2C2×#212011yescharacteristic
803C2#3336111yescharacteristic
subgroupG/H
center, socleC22C22×#99
commutatorC22×C4C23×C4
Frattini, cosocleC2×C22⋊C4C24
prime radicalC2×#120D4
LCSG ▷ C22×C4 ▷ C23 ▷ C2 ▷ C1
UCSC1 ◁ C22 ◁ C2×C22⋊C4 ◁ C2×#551 ◁ G
LECSG ▷ C2×C22⋊C4 ▷ C23 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
4. #11897C2semidirect
5. #11842C2semidirect
6. #11841C2semidirect
7. #11823C2semidirect
8. #11810C2semidirect
9. #11808C2semidirect
10. #11784C2semidirect
11. #11756C2semidirect
12. #11755C2semidirect
13. #11728C2semidirect
14. #11715C2semidirect
15. C2×#1351C2semidirect
17. C2×#519C4semidirect
19. #2637C4semidirect
20. #2632C4semidirect
21. #2614C4semidirect
22. #2604C4semidirect
24. #2592C4semidirect
26. #2498C4semidirect
38. #2343C4semidirect
96. C2×C4×Q8C2×C4semidirect
97. C2×C4×Q8C2×C4semidirect
98. C2×C4×Q8C2×C4semidirect
99. C2×C4×Q8C2×C4semidirect
125. #400C2×C4semidirect
127. #399C2×C4semidirect
131. #398C2×C4semidirect
133. #397C2×C4semidirect
139. #395C2×C4semidirect
140. #395C2×C4semidirect
148. #393C2×C4semidirect
149. #393C2×C4semidirect
184. #383C2×C4semidirect
185. #382C2×C4semidirect
194. C4×C4⋊C4C2×C4semidirect
201. #376C2×C4semidirect

Maximal subgroups

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

subgroupindex
#360792
#224772
#174222
#118972
#118422
#118412
#118232
#118102
#118082
#117842
#117562
#117552
#117282
#117152
C2×#13512