Finite Group Databasebeta

← #123663

Subgroups — #123663

Order 512.

2170 conjugacy classes of subgroups.

The subgroup lattice has 918 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#340C212yesmaximal
2C22×#340C212yesmaximal
3C22×#336C211yesmaximal, characteristic
4C2×C4⋊#95C211yesmaximal, characteristic
5C2×C4⋊#95C211yesmaximal, characteristic
6C24×C8C2212yes—
7C23×C4⋊C4C2211yescharacteristic
8C23×C4⋊C4C2212yes—
9C23×C4⋊C4C2211yescharacteristic
10C23×C42C2211yescharacteristic
11C22×#95—21no—
12C22×#95—21no—
13C22×#95—21no—
14C22×#95—21no—
15C2×#340—24no—
16C2×#340—24no—
17C2×#340—24no—
18C2×#340—24no—
19C2×#340—24no—
20C2×#340C418yescomplemented
21C2×#336—22no—
22C2×#336—24no—
23C4⋊#95—22no—
24C4⋊#95—24no—
25C4⋊#95C414yescomplemented
26C24×C4—21no—
27C24×C4—21no—
28C24×C4—22no—
29C24×C4D411yescharacteristic
30C24×C4D411yescharacteristic
31C24×C4C2311yescharacteristic
32C23×C8—22no—
33C23×C8—22no—
34C23×C8—22no—
35C23×C8—22no—
36C23×C8—22no—
37C23×C8—22no—
38C23×C8—22no—
39C23×C8—22no—
40C23×C8—22no—
41C23×C8—22no—
42C23×C8—22no—
43C23×C8—22no—
44C23×C8C2×C414yes—
45C23×C8D414yes—
46C23×C8Q814yes—
47C22×C4⋊C4—22no—
48C22×C4⋊C4—22no—
49C22×C4⋊C4—22no—
50C22×C4⋊C4—22no—
51C22×C4⋊C4—22no—
52C22×C4⋊C4—22no—
53C22×C4⋊C4—22no—
54C22×C4⋊C4—22no—
55C22×C4⋊C4—22no—
56C22×C4⋊C4—22no—
57C22×C4⋊C4—22no—
58C22×C4⋊C4—22no—
59C22×C4⋊C4—22no—
60C22×C4⋊C4—22no—
61C22×C4⋊C4—22no—
62C22×C4⋊C4—22no—
63C22×C4⋊C4—21no—
64C22×C4⋊C4—22no—
65C22×C4⋊C4—21no—
66C22×C4⋊C4—22no—
67C22×C4⋊C4—21no—
68C22×C4⋊C4—21no—
69C22×C4⋊C4—22no—
70C22×C4⋊C4—22no—
71C22×C4⋊C4C2×C412yes—
72C22×C4⋊C4C2×C414yes—
73C22×C4⋊C4C2×C414yes—
74C22×C4⋊C4C2×C412yes—
75C22×C4⋊C4D414yes—
76C22×C4⋊C4D414yes—
77C22×C4⋊C4D412yes—
78C22×C4⋊C4Q812yes—
79C22×C42—22no—
80C22×C42—22no—
81C22×C42—22no—
82C22×C42—22no—
83C22×C42—22no—
84C22×C42—22no—
85C22×C42C2×C412yes—
86C22×C42D412yes—
87C2×#95—24no—
88C2×#95—24no—
89C2×#95—24no—
90C2×#95—24no—
91C2×#95—44no—
92C2×#95—42no—
93C2×#95—42no—
94C2×#95—42no—
95C2×#95—42no—
96C2×#95—42no—
97C2×#95—42no—
98#340—216no—
99#340—216no—
100#336—28no—
101C25C2×D411yescharacteristic
102C23×C4—21no—
103C23×C4—21no—
104C23×C4—22no—
105C23×C4—22no—
106C23×C4—22no—
107C23×C4—22no—
108C23×C4—21no—
109C23×C4—21no—
110C23×C4—22no—
111C23×C4—22no—
112C23×C4—21no—
113C23×C4—21no—
114C23×C4—22no—
115C23×C4—21no—
116C23×C4—21no—
117C23×C4—22no—
118C23×C4—22no—
119C23×C4—22no—
120C23×C4—24no—
121C23×C4—24no—
122C23×C4—24no—
123C23×C4—22no—
124C23×C4—24no—
125C23×C4—22no—
126C23×C4—41no—
127C23×C4—42no—
128C23×C4—42no—
129C23×C4—42no—
130C23×C4—42no—
131C23×C4—42no—
132C23×C4—41no—
133C23×C4—42no—
134C23×C4—42no—
135C23×C4—41no—
136C23×C4—41no—
137C23×C4—42no—
138C23×C4—41no—
139C23×C4—41no—
140C23×C4—42no—
141C23×C4—42no—
142C23×C4—42no—
143C23×C4—42no—
144C23×C4—42no—
145C23×C4—41no—
146C23×C4—41no—
147C23×C4—42no—
148C23×C4—42no—
149C23×C4—42no—
150C23×C4—42no—
151C23×C4—42no—
152C23×C4—41no—
153C23×C4—41no—
154C23×C4—42no—
155C23×C4C22⋊C412yes—
156C23×C4C22⋊C412yes—
157C23×C4D812yes—
158C23×C4SD1612yes—
159C23×C4SD1612yes—
160C23×C4Q1612yes—
161C23×C4C22×C412yes—
162C23×C4C22×C411yescharacteristic
163C23×C4C2×D412yes—
164C23×C4C2×D412yes—
165C23×C4C2×D411yescharacteristic
166C23×C4C2×D412yes—
167C23×C4C2×D411yescharacteristic
168C23×C4C2×Q812yes—
169C23×C4C2×Q811yescharacteristic
170C23×C4#4111yescharacteristic
171C23×C4#4112yes—
172C23×C4#4111yescharacteristic
173C23×C4#4112yes—
174C23×C4#4112yes—
175C23×C4#4112yes—
176C23×C4#4112yes—
177C23×C4#4112yes—
178C23×C4#4112yes—
179C22×C8—24no—
180C22×C8—24no—
181C22×C8—24no—
182C22×C8—24no—
183C22×C8—24no—
184C22×C8—24no—
185C22×C8—24no—
186C22×C8—24no—
187C22×C8—24no—
188C22×C8—24no—
189C22×C8—24no—
190C22×C8—24no—
191C22×C8—24no—
192C22×C8—24no—
193C22×C8—24no—
194C22×C8—24no—
195C22×C8—24no—
196C22×C8—24no—
197C22×C8—42no—
198C22×C8—42no—
199C22×C8—42no—
200C22×C8—42no—
201C22×C8—42no—
202C22×C8—42no—
203C22×C8—42no—
204C22×C8—42no—
205C22×C8—42no—
206C22×C8—42no—
207C22×C8—42no—
208C22×C8—42no—
209C22×C8—42no—
210C22×C8—42no—
211C22×C8—42no—
212C22×C8—42no—
213C22×C8C4⋊C418yes—
214C2×C4⋊C4—24no—
215C2×C4⋊C4—24no—
216C2×C4⋊C4—24no—
217C2×C4⋊C4—24no—
218C2×C4⋊C4—24no—
219C2×C4⋊C4—24no—
220C2×C4⋊C4—24no—
221C2×C4⋊C4—24no—
222C2×C4⋊C4—24no—
223C2×C4⋊C4—24no—
224C2×C4⋊C4—24no—
225C2×C4⋊C4—24no—
226C2×C4⋊C4—24no—
227C2×C4⋊C4—24no—
228C2×C4⋊C4—24no—
229C2×C4⋊C4—24no—
230C2×C4⋊C4—24no—
231C2×C4⋊C4—24no—
232C2×C4⋊C4—24no—
233C2×C4⋊C4—24no—
234C2×C4⋊C4—24no—
235C2×C4⋊C4—24no—
236C2×C4⋊C4—24no—
237C2×C4⋊C4—24no—
238C2×C4⋊C4—22no—
239C2×C4⋊C4—22no—
240C2×C4⋊C4—24no—
241C2×C4⋊C4—24no—
242C2×C4⋊C4—22no—
243C2×C4⋊C4—24no—
244C2×C4⋊C4—22no—
245C2×C4⋊C4—24no—
246C2×C4⋊C4—41no—
247C2×C4⋊C4—42no—
248C2×C4⋊C4—42no—
249C2×C4⋊C4—42no—
250C2×C4⋊C4—42no—
251C2×C4⋊C4—42no—
252C2×C4⋊C4—42no—
253C2×C4⋊C4—42no—
254C2×C4⋊C4—42no—
255C2×C4⋊C4—42no—
256C2×C4⋊C4—42no—
257C2×C4⋊C4—41no—
258C2×C4⋊C4—41no—
259C2×C4⋊C4—42no—
260C2×C4⋊C4—42no—
261C2×C4⋊C4—42no—
262C2×C4⋊C4—42no—
263C2×C4⋊C4—41no—
264C2×C4⋊C4—42no—
265C2×C4⋊C4—42no—
266C2×C4⋊C4—42no—
267C2×C4⋊C4—42no—
268C2×C4⋊C4—42no—
269C2×C4⋊C4—42no—
270C2×C4⋊C4—42no—
271C2×C4⋊C4—41no—
272C2×C4⋊C4—41no—
273C2×C4⋊C4C4214yes—
274C2×C4⋊C4C22⋊C418yes—
275C2×C4⋊C4C4⋊C414yes—
276C2×C42—22no—
277C2×C42—22no—
278C2×C42—24no—
279C2×C42—24no—
280C2×C42—22no—
281C2×C42—24no—
282C2×C42—24no—
283C2×C42—22no—
284C2×C42—42no—
285C2×C42—42no—
286C2×C42—42no—
287C2×C42—42no—
288C2×C42—42no—
289C2×C42—42no—
290C2×C42—42no—
291C2×C42—42no—
292#95—48no—
293#95—48no—
294#95—48no—
295#95—48no—
296C24C2×C22⋊C411yescharacteristic
297C24C4×D412yes—
298C24#12011yescharacteristic
299C24#12111yescharacteristic
300C24#12112yes—
301C24#12112yes—
302C24C22⋊Q811yescharacteristic
303C24#12312yes—
304C24#12311yescharacteristic
305C24#12411yescharacteristic
306C24C4⋊Q811yescharacteristic
307C24C2×D811yescharacteristic
308C24C2×SD1611yescharacteristic
309C24C2×SD1611yescharacteristic
310C24C2×Q1611yescharacteristic
311C24#13512yes—
312C24#13512yes—
313C24AGL(1,ℤ/8)11yescharacteristic
314C24AGL(1,ℤ/8)11yescharacteristic
315C24AGL(1,ℤ/8)12yes—
316C24#13711yescharacteristic
317C24#13711yescharacteristic
318C24#13712yes—
319C22×C4—22no—
320C22×C4—22no—
321C22×C4—22no—
322C22×C4—22no—
323C22×C4—22no—
324C22×C4—22no—
325C22×C4—22no—
326C22×C4—22no—
327C22×C4—22no—
328C22×C4—22no—
329C22×C4—22no—
330C22×C4—22no—
331C22×C4—22no—
332C22×C4—22no—
333C22×C4—22no—
334C22×C4—22no—
335C22×C4—24no—
336C22×C4—24no—
337C22×C4—24no—
338C22×C4—24no—
339C22×C4—24no—
340C22×C4—22no—
341C22×C4—24no—
342C22×C4—22no—
343C22×C4—24no—
344C22×C4—22no—
345C22×C4—24no—
346C22×C4—22no—
347C22×C4—24no—
348C22×C4—24no—
349C22×C4—28no—
350C22×C4—42no—
351C22×C4—42no—
352C22×C4—42no—
353C22×C4—42no—
354C22×C4—42no—
355C22×C4—42no—
356C22×C4—42no—
357C22×C4—42no—
358C22×C4—42no—
359C22×C4—42no—
360C22×C4—42no—
361C22×C4—42no—
362C22×C4—42no—
363C22×C4—42no—
364C22×C4—42no—
365C22×C4—42no—
366C22×C4—42no—
367C22×C4—44no—
368C22×C4—42no—
369C22×C4—44no—
370C22×C4—44no—
371C22×C4—44no—
372C22×C4—42no—
373C22×C4—42no—
374C22×C4—44no—
375C22×C4—44no—
376C22×C4—44no—
377C22×C4—44no—
378C22×C4—44no—
379C22×C4—44no—
380C22×C4—42no—
381C22×C4—42no—
382C22×C4—42no—
383C22×C4—42no—
384C22×C4—42no—
385C22×C4—42no—
386C22×C4—42no—
387C22×C4—42no—
388C22×C4—44no—
389C22×C4—44no—
390C22×C4—44no—
391C22×C4—44no—
392C22×C4—44no—
393C22×C4—44no—
394C22×C4—44no—
395C22×C4—44no—
396C22×C4—44no—
397C22×C4—44no—
398C22×C4—44no—
399C22×C4—44no—
400C22×C4—42no—
401C22×C4—44no—
402C22×C4—42no—
403C22×C4—44no—
404C22×C4—44no—
405C22×C4—44no—
406C22×C4—44no—
407C22×C4—42no—
408C22×C4—42no—
409C22×C4—44no—
410C22×C4—81no—
411C22×C4—81no—
412C22×C4—82no—
413C22×C4—82no—
414C22×C4—82no—
415C22×C4—82no—
416C22×C4—82no—
417C22×C4—82no—
418C22×C4—82no—
419C22×C4—82no—
420C22×C4—82no—
421C22×C4—82no—
422C22×C4—82no—
423C22×C4—82no—
424C22×C4—82no—
425C22×C4—82no—
426C22×C4—82no—
427C22×C4—82no—
428C22×C4—82no—
429C22×C4—82no—
430C22×C4—82no—
431C22×C4—82no—
432C22×C4—82no—
433C22×C4—82no—
434C22×C4—81no—
435C22×C4—82no—
436C22×C4—81no—
437C22×C4—82no—
438C22×C4—82no—
439C22×C4—82no—
440C22×C4—82no—
441C22×C4—82no—
442C22×C4—82no—
443C22×C4—82no—
444C22×C4#10214yes—
445C22×C4#10314yes—
446C22×C4C2×C4211yescharacteristic
447C22×C4C2×C22⋊C412yes—
448C22×C4C2×C4⋊C412yes—
449C22×C4C2×C4⋊C411yescharacteristic
450C22×C4#11712yes—
451C22×C4#11712yes—
452C22×C4#11711yescharacteristic
453C22×C4#11711yescharacteristic
454C22×C4#11712yes—
455C22×C4#11712yes—
456C22×C4#11711yescharacteristic
457C22×C4#11711yescharacteristic
458C22×C4C4×D412yes—
459C22×C4C4×D412yes—
460C22×C4C4×D412yes—
461C22×C4C4×D412yes—
462C22×C4C4×D412yes—
463C22×C4C4×D412yes—
464C22×C4C4×D412yes—
465C22×C4C4×D412yes—
466C22×C4C4×Q812yes—
467C22×C4C4×Q812yes—
468C22×C4C4×Q812yes—
469C22×C4#12012yes—
470C22×C4#12011yescharacteristic
471C22×C4#12112yes—
472C22×C4#12112yes—
473C22×C4#12112yes—
474C22×C4#12112yes—
475C22×C4#12111yescharacteristic
476C22×C4#12112yes—
477C22×C4#12112yes—
478C22×C4C22⋊Q812yes—
479C22×C4C22⋊Q812yes—
480C22×C4C22⋊Q812yes—
481C22×C4C22⋊Q812yes—
482C22×C4C22⋊Q812yes—
483C22×C4C22⋊Q812yes—
484C22×C4C22⋊Q812yes—
485C22×C4C22⋊Q812yes—
486C22×C4C22⋊Q811yescharacteristic
487C22×C4#12312yes—
488C22×C4#12312yes—
489C22×C4#12312yes—
490C22×C4#12312yes—
491C22×C4#12312yes—
492C22×C4#12312yes—
493C22×C4#12312yes—
494C22×C4#12312yes—
495C22×C4#12311yescharacteristic
496C22×C4#12312yes—
497C22×C4#12312yes—
498C22×C4#12412yes—
499C22×C4#12412yes—
500C22×C4#12412yes—
501C22×C4#12412yes—
502C22×C4#12411yescharacteristic
503C22×C4#12412yes—
504C22×C4#12512yes—
505C22×C4#12512yes—
506C22×C4#12512yes—
507C22×C4#12512yes—
508C22×C4#12512yes—
509C22×C4#12512yes—
510C22×C4#12612yes—
511C22×C4#12612yes—
512C22×C4#12612yes—
513C22×C4#12612yes—
514C22×C4#12612yes—
515C22×C4#12612yes—
516C22×C4#12612yes—
517C22×C4#12612yes—
518C22×C4#12612yes—
519C22×C4#12612yes—
520C22×C4#12711yescharacteristic
521C22×C4C4⋊Q812yes—
522C2×C8—28no—
523C2×C8—28no—
524C2×C8—28no—
525C2×C8—44no—
526C2×C8—44no—
527C2×C8—44no—
528C2×C8—44no—
529C2×C8—44no—
530C2×C8—44no—
531C2×C8—44no—
532C2×C8—44no—
533C2×C8—44no—
534C2×C8—44no—
535C2×C8—44no—
536C2×C8—44no—
537C4⋊C4—28no—
538C4⋊C4—28no—
539C4⋊C4—28no—
540C4⋊C4—28no—
541C4⋊C4—44no—
542C4⋊C4—44no—
543C4⋊C4—44no—
544C4⋊C4—44no—
545C4⋊C4—44no—
546C4⋊C4—44no—
547C4⋊C4—42no—
548C4⋊C4—42no—
549C4⋊C4—44no—
550C4⋊C4—42no—
551C4⋊C4—44no—
552C4⋊C4—44no—
553C4⋊C4—44no—
554C4⋊C4—42no—
555C42—44no—
556C42—44no—
557C42—44no—
558C42—44no—
559C23C4×C22⋊C411yescharacteristic
560C23#38011yescharacteristic
561C23#38111yescharacteristic
562C23#38611yescharacteristic
563C23#38612yes—
564C23#38611yescharacteristic
565C23#38712yes—
566C23#38812yes—
567C23#38812yes—
568C23#38812yes—
569C23#38912yes—
570C23#39011yescharacteristic
571C23#39111yescharacteristic
572C23#39412yes—
573C23#39412yes—
574C23#39411yescharacteristic
575C23#39511yescharacteristic
576C23#39612yes—
577C23#39712yes—
578C23#39712yes—
579C23#39811yescharacteristic
580C23#39812yes—
581C23#40011yescharacteristic
582C23C2×#10211yescharacteristic
583C23C2×#10311yescharacteristic
584C23#41611yescharacteristic
585C23#41611yescharacteristic
586C23#41711yescharacteristic
587C23#41711yescharacteristic
588C23#41811yescharacteristic
589C23#41911yescharacteristic
590C23C4×D812yes—
591C23C4×SD1612yes—
592C23C4×SD1612yes—
593C23C4×Q1612yes—
594C23#44012yes—
595C23#44012yes—
596C23#44112yes—
597C23#44212yes—
598C23#44711yescharacteristic
599C23#44811yescharacteristic
600C23#44912yes—
601C23#45011yescharacteristic
602C23#45111yescharacteristic
603C23#45212yes—
604C23#45911yescharacteristic
605C23#45912yes—
606C23#46011yescharacteristic
607C23#46012yes—
608C23#46111yescharacteristic
609C23#46112yes—
610C23#46211yescharacteristic
611C23#46212yes—
612C23#46312yes—
613C23#46312yes—
614C23#46312yes—
615C23#46412yes—
616C23#46412yes—
617C23#46412yes—
618C23#46512yes—
619C23#46512yes—
620C23#46612yes—
621C23#46712yes—
622C23#46812yes—
623C23#46812yes—
624C23#46912yes—
625C23#47012yes—
626C23#47411yescharacteristic
627C23#47511yescharacteristic
628C23#47611yescharacteristic
629C23#47711yescharacteristic
630C23#47812yes—
631C23#47912yes—
632C23#48012yes—
633C23#48011yescharacteristic
634C23#48112yes—
635C23#48111yescharacteristic
636C23#48212yes—
637C23#48212yes—
638C23#48212yes—
639C23#48312yes—
640C23#48311yescharacteristic
641C23#48412yes—
642C23#48411yescharacteristic
643C23#48512yes—
644C23#48512yes—
645C23#48512yes—
646C23#48611yescharacteristic
647C23#48711yescharacteristic
648C23#48812yes—
649C23#48912yes—
650C23#49011yescharacteristic
651C23#49111yescharacteristic
652C23#49811yescharacteristic
653C23#49912yes—
654C23#50011yescharacteristic
655C23#50111yescharacteristic
656C23#50111yescharacteristic
657C23#50112yes—
658C2×C4—24no—
659C2×C4—24no—
660C2×C4—24no—
661C2×C4—24no—
662C2×C4—24no—
663C2×C4—24no—
664C2×C4—44no—
665C2×C4—44no—
666C2×C4—44no—
667C2×C4—44no—
668C2×C4—42no—
669C2×C4—42no—
670C2×C4—42no—
671C2×C4—42no—
672C2×C4—42no—
673C2×C4—42no—
674C2×C4—42no—
675C2×C4—42no—
676C2×C4—44no—
677C2×C4—44no—
678C2×C4—44no—
679C2×C4—44no—
680C2×C4—44no—
681C2×C4—44no—
682C2×C4—48no—
683C2×C4—48no—
684C2×C4—44no—
685C2×C4—44no—
686C2×C4—48no—
687C2×C4—44no—
688C2×C4—44no—
689C2×C4—84no—
690C2×C4—84no—
691C2×C4—84no—
692C2×C4—84no—
693C2×C4—84no—
694C2×C4—84no—
695C2×C4—84no—
696C2×C4—84no—
697C2×C4—82no—
698C2×C4—82no—
699C2×C4—84no—
700C2×C4—84no—
701C2×C4—82no—
702C2×C4—82no—
703C2×C4—84no—
704C2×C4—84no—
705C2×C4—84no—
706C2×C4—84no—
707C2×C4—84no—
708C2×C4—84no—
709C2×C4—82no—
710C2×C4—82no—
711C2×C4—82no—
712C2×C4—82no—
713C2×C4—84no—
714C2×C4—84no—
715C2×C4—84no—
716C2×C4—84no—
717C2×C4#37611yescharacteristic
718C2×C4C4×C22⋊C412yes—
719C2×C4C4×C4⋊C412yes—
720C2×C4C4×C4⋊C411yescharacteristic
721C2×C4#38012yes—
722C2×C4#38112yes—
723C2×C4#38212yes—
724C2×C4#38211yescharacteristic
725C2×C4#38312yes—
726C2×C4#38311yescharacteristic
727C2×C4#38512yes—
728C2×C4#38512yes—
729C2×C4#38512yes—
730C2×C4#38612yes—
731C2×C4#38712yes—
732C2×C4#38712yes—
733C2×C4#38712yes—
734C2×C4#38712yes—
735C2×C4#38712yes—
736C2×C4#38712yes—
737C2×C4#38712yes—
738C2×C4#38712yes—
739C2×C4#38712yes—
740C2×C4#38712yes—
741C2×C4#38712yes—
742C2×C4#38812yes—
743C2×C4#38812yes—
744C2×C4#38812yes—
745C2×C4#38812yes—
746C2×C4#38812yes—
747C2×C4#38812yes—
748C2×C4#38812yes—
749C2×C4#38812yes—
750C2×C4#38812yes—
751C2×C4#38912yes—
752C2×C4#38912yes—
753C2×C4#39012yes—
754C2×C4#39112yes—
755C2×C4#39211yescharacteristic
756C2×C4#39312yes—
757C2×C4#39311yescharacteristic
758C2×C4#39412yes—
759C2×C4#39412yes—
760C2×C4#39612yes—
761C2×C4#39612yes—
762C2×C4#39712yes—
763C2×C4#39712yes—
764C2×C4#39712yes—
765C2×C4#39711yescharacteristic
766C2×C4#39712yes—
767C2×C4#39712yes—
768C2×C4#39812yes—
769C2×C4#39812yes—
770C2×C4#39812yes—
771C2×C4#39912yes—
772C2×C4#39911yescharacteristic
773C2×C4#40012yes—
774C2×C4#40012yes—
775C2×C4#40012yes—
776C2×C4#40012yes—
777C2×C4#40012yes—
778C2×C4#40012yes—
779C2×C4#40012yes—
780C2×C4#40112yes—
781C8—48no—
782C22#143411yescharacteristic
783C22#143611yescharacteristic
784C22#143711yescharacteristic
785C22#143911yescharacteristic
786C22#144012yes—
787C22#144011yescharacteristic
788C22#144111yescharacteristic
789C22#144112yes—
790C22#144212yes—
791C22#144312yes—
792C22#144511yescharacteristic
793C22C4×#10211yescharacteristic
794C22C4×#10311yescharacteristic
795C22#176211yescharacteristic
796C22#176311yescharacteristic
797C22#180211yescharacteristic
798C22#180311yescharacteristic
799C22#180411yescharacteristic
800C22#180511yescharacteristic
801C22#182311yescharacteristic
802C22#182411yescharacteristic
803C22#182511yescharacteristic
804C22#182511yescharacteristic
805C22#187211yescharacteristic
806C22#187311yescharacteristic
807C22#187411yescharacteristic
808C22#187511yescharacteristic
809C22#187712yes—
810C22#187812yes—
811C22#187912yes—
812C22#188012yes—
813C22#189211yescharacteristic
814C22#189311yescharacteristic
815C22#189411yescharacteristic
816C22#189511yescharacteristic
817C22#191812yes—
818C22#191912yes—
819C22#192012yes—
820C22#192112yes—
821C22#192512yes—
822C22#192512yes—
823C22#192612yes—
824C22#192612yes—
825C22#192712yes—
826C22#192712yes—
827C22#192812yes—
828C22#192812yes—
829C22#193312yes—
830C22#193412yes—
831C22#193512yes—
832C22#193612yes—
833C22#194112yes—
834C22#194212yes—
835C22#194312yes—
836C22#194412yes—
837C22#198111yescharacteristic
838C22#198211yescharacteristic
839C22#198311yescharacteristic
840C22#198311yescharacteristic
841C22#199011yescharacteristic
842C22#199111yescharacteristic
843C22#199211yescharacteristic
844C22#199311yescharacteristic
845C22#203312yes—
846C22#203412yes—
847C22#203512yes—
848C22#203612yes—
849C22#204111yescharacteristic
850C22#204212yes—
851C22#204311yescharacteristic
852C22#205412yes—
853C22#205512yes—
854C22#205512yes—
855C22#205612yes—
856C22#205711yescharacteristic
857C22#205811yescharacteristic
858C22#205912yes—
859C22#206512yes—
860C22#206612yes—
861C22#206712yes—
862C22#206812yes—
863C22#207112yes—
864C22#207212yes—
865C22#207312yes—
866C22#207412yes—
867C22#207512yes—
868C22#207612yes—
869C22#207712yes—
870C22#207712yes—
871C22#208312yes—
872C22#208311yescharacteristic
873C22#208412yes—
874C22#208411yescharacteristic
875C22#208512yes—
876C22#208512yes—
877C22#208512yes—
878C22#209911yescharacteristic
879C22#210011yescharacteristic
880C22#210112yes—
881C4—44no—
882C4—44no—
883C4—84no—
884C4—84no—
885C4—88no—
886C4#143412yes—
887C4#143612yes—
888C4#143912yes—
889C4#144212yes—
890C4#144212yes—
891C4#144312yes—
892C4#144312yes—
893C4#144512yes—
894C2#755611yescharacteristic
895C2#1080611yescharacteristic
896C2#1080711yescharacteristic
897C2#1088011yescharacteristic
898C2#1088111yescharacteristic
899C2#1093111yescharacteristic
900C2#1093211yescharacteristic
901C2#1107611yescharacteristic
902C2#1107711yescharacteristic
903C2#1118912yes—
904C2#1119012yes—
905C2#1119911yescharacteristic
906C2#1120011yescharacteristic
907C2#1120711yescharacteristic
908C2#1120811yescharacteristic
909C2#1121912yes—
910C2#1122012yes—
911C2#1125612yes—
912C2#1125712yes—
913C2#1131512yes—
914C2#1131612yes—
915C2#1135711yescharacteristic
916C2#1135811yescharacteristic
subgroupG/H
center, socle, prime radicalC25C2×D4
commutatorC22×C4C2×C42
Frattini, cosocleC24×C4C23
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C25 ◁ C23×C42 ◁ G
LECSG ▷ C24×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
20. C2×#340C4semidirect
25. C4⋊#95C4semidirect

Maximal subgroups

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

subgroupindex
C22×#3402
C22×#3362
C2×C4⋊#952