Finite Group Databasebeta

← #6381817

Subgroups — #6381817

Order 512.

2712 conjugacy classes of subgroups.

The subgroup lattice has 863 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#2935C211yesmaximal, characteristic, complemented
2C2×#2932C211yesmaximal, characteristic, complemented
3C2×#2931C211yesmaximal, characteristic, complemented
4C2×#2906C211yesmaximal, characteristic, complemented
5#34937C211yesmaximal, characteristic
6#22994C214yesmaximal, complemented
7#22991C214yesmaximal, complemented
8#22988C214yesmaximal, complemented
9#22987C214yesmaximal, complemented
10#21188C211yesmaximal, characteristic, complemented
11#21146C211yesmaximal, characteristic, complemented
12#21047C211yesmaximal, characteristic, complemented
13#21046C211yesmaximal, characteristic, complemented
14#20900C211yesmaximal, characteristic, complemented
15#20900C211yesmaximal, characteristic, complemented
16#20839C211yesmaximal, characteristic, complemented
17#20839C211yesmaximal, characteristic, complemented
18C2×#1771C211yesmaximal, characteristic, complemented
19#20375C211yesmaximal, characteristic, complemented
20C22×#131C2211yescharacteristic
21C22×#131C2211yescharacteristic
22C22×#131C2211yescharacteristic
23C22×#131C2211yescharacteristic
24C2×#532C2211yescharacteristic
25C2×#532C2211yescharacteristic
26C2×#532C2211yescharacteristic
27C2×C4×#41C2211yescharacteristic
28#2935—28no—
29#2932—28no—
30#2931—28no—
31C2×#436C2214yes—
32C2×#436C2212yes—
33C2×#435C2212yes—
34C2×#435C2214yes—
35C2×#435C2212yes—
36C2×#435C2214yes—
37C2×C8×D4C2214yes—
38C2×C8×D4C2212yes—
39#2906—28no—
40C2×#424C2211yescharacteristic
41C2×#424C2211yescharacteristic
42C2×#424C2212yes—
43C2×#424C2212yes—
44C2×#423C2211yescharacteristic
45C2×#423C2211yescharacteristic
46C2×#423C2211yescharacteristic
47C2×#423C2212yes—
48C22×C4⋊C8C2212yes—
49C22×C4⋊C8C2211yescharacteristic
50C2×#408C2211yescharacteristic
51C2×#408C2211yescharacteristic
52C2×#408C2211yescharacteristic
53C2×#408C2211yescharacteristic
54C2×#408C2211yescharacteristic
55C2×#408C2211yescharacteristic
56C2×#408C2211yescharacteristic
57C2×#408C2211yescharacteristic
58C2×C4×M16C2211yescharacteristic
59C22×#97C2211yescharacteristic
60C22×#97C2211yescharacteristic
61C22×C4×C8C2211yescharacteristic
62#2548C411yescharacteristic
63#2547C411yescharacteristic
64#2546C411yescharacteristic
65#2545C411yescharacteristic
66#2545C411yescharacteristic
67#2544C411yescharacteristic
68#2544C411yescharacteristic
69#2543C414yes—
70#2541C411yescharacteristic
71#2416C414yes—
72#2392C2214yes—
73C4×#121C2214yes—
74#2297C2211yescharacteristic
75#2297C2211yescharacteristic
76C2×C4×C4⋊C4C2211yescharacteristic
77#1955C2214yes—
78#1955C2214yes—
79#1940C2214yes—
80#1939C2214yes—
81#1924C2214yes—
82#1924C2214yes—
83#1923C2214yes—
84#1923C2214yes—
85#1870C2214yes—
86#1870C2214yes—
87#1869C2214yes—
88#1869C2214yes—
89#1851C2214yes—
90#1851C2214yes—
91#1850C2214yes—
92#1850C2214yes—
93#1771C2212yes—
94#1771C2212yes—
95#1771C2212yes—
96#1771C2212yes—
97#1750C2214yes—
98#1749C2214yes—
99#1729C2211yescharacteristic
100#1729C2211yescharacteristic
101#1728C2211yescharacteristic
102#1728C2211yescharacteristic
103C2×#336C2211yescharacteristic
104C2×#336C2211yescharacteristic
105C22×#41C2311yescharacteristic
106C22×#41C2311yescharacteristic
107C22×#41C2311yescharacteristic
108C2×#131—24no—
109C2×#131—24no—
110C2×#131—24no—
111C2×#131—24no—
112C2×#131—24no—
113C2×#131—24no—
114C2×#131—24no—
115C2×#131—24no—
116C2×#131—42no—
117C2×#131—42no—
118C2×#131—42no—
119C2×#131—42no—
120C22×M16C2311yescharacteristic
121C22×M16C2311yescharacteristic
122C22×M16C2311yescharacteristic
123C22×M16C2312yes—
124C22×M16C2312yes—
125C22×M16C2312yes—
126C22×M16C2312yes—
127C22×M16C2311yescharacteristic
128C23×C8C2311yescharacteristic
129C23×C8C2312yes—
130C23×C8C2312yes—
131C23×C8C2312yes—
132C23×C8C2312yes—
133C23×C8C2311yescharacteristic
134C23×C8C2311yescharacteristic
135C23×C8C2311yescharacteristic
136#532—24no—
137#532—24no—
138#532—24no—
139#532—24no—
140#532—24no—
141#532—24no—
142C2×C4⋊Q8C2×C411yescharacteristic
143C2×C4⋊Q8C2×C411yescharacteristic
144C2×C4⋊Q8C2×C411yescharacteristic
145C2×#127C2×C411yescharacteristic
146C2×#127C2×C411yescharacteristic
147C2×#127C2×C411yescharacteristic
148C2×#124C2×C411yescharacteristic
149C2×#124C2×C411yescharacteristic
150C2×#124C2×C411yescharacteristic
151C2×#124C2×C411yescharacteristic
152C2×#124C2×C411yescharacteristic
153C2×#124C2×C411yescharacteristic
154C2×#121C2×C412yes—
155C2×#121C2×C414yes—
156C2×#121C2×C414yes—
157C2×#121C2×C412yes—
158C2×#121C2×C414yes—
159C4×#41—24no—
160C4×#41—24no—
161C2×C4×Q8C2×C411yescharacteristic
162C2×C4×Q8C2×C411yescharacteristic
163C2×C4×D4C2×C412yes—
164C2×C4×D4C2×C411yescharacteristic
165C2×C4×D4C2×C412yes—
166C2×C4×D4C2×C411yescharacteristic
167C2×C4×D4C2314yes—
168C2×C4×D4C2314yes—
169C2×C4×D4C2312yes—
170C2×C4×D4C2312yes—
171C2×#117C2312yes—
172C2×#117C2311yescharacteristic
173C22×C4⋊C4C2×C412yes—
174C22×C42C2311yescharacteristic
175C22×C42C2311yescharacteristic
176C22×C42C2312yes—
177C22×C42C2311yescharacteristic
178#436—28no—
179#436—216no—
180#435—28no—
181#435—28no—
182#435—216no—
183#435—216no—
184C8×D4—28no—
185C8×D4—216no—
186#424—24no—
187#424—24no—
188#424—28no—
189#424—28no—
190#423—24no—
191#423—24no—
192#423—24no—
193#423—28no—
194C2×C4⋊C8—28no—
195C2×C4⋊C8D418yescomplemented
196C2×C4⋊C8C2312yes—
197C2×C4⋊C8C2312yes—
198C2×C4⋊C8C2314yes—
199C2×C4⋊C8C2314yes—
200C2×C4⋊C8C2312yes—
201C2×C4⋊C8C2312yes—
202C2×C4⋊C8C2312yes—
203C2×C4⋊C8C2312yes—
204C2×C4⋊C8C2311yescharacteristic
205C2×C4⋊C8C2311yescharacteristic
206C2×C4⋊C8C2311yescharacteristic
207C2×C4⋊C8C2311yescharacteristic
208#408—24no—
209#408—24no—
210#408—24no—
211#408—24no—
212#408—24no—
213#408—42no—
214#408—42no—
215#408D418yescomplemented
216C2×C22⋊C8C2314yes—
217C2×C22⋊C8C2312yes—
218C2×C22⋊C8C2312yes—
219C2×C22⋊C8C2312yes—
220C2×C22⋊C8C2312yes—
221C2×C22⋊C8C2314yes—
222C2×C22⋊C8C2314yes—
223C2×C22⋊C8C2314yes—
224C2×C22⋊C8C2314yes—
225C2×C22⋊C8C2314yes—
226C4×M16—24no—
227C2×#97—24no—
228C2×#97—24no—
229C2×#97C2312yes—
230C2×#97C2312yes—
231C2×#97C2312yes—
232C2×#97C2312yes—
233C2×#97C2312yes—
234C2×C4×C8—24no—
235C2×C4×C8C2312yes—
236C2×C4×C8C2312yes—
237C2×C4×C8C2312yes—
238#398C2×C414yes—
239#397C2×C414yes—
240#396C2×C414yes—
241#396C2×C414yes—
242#394C2×C414yes—
243#394C2×C414yes—
244#394C2×C414yes—
245#392C2×C414yes—
246#391C2×C411yescharacteristic
247#391C2×C411yescharacteristic
248#391C2×C411yescharacteristic
249#391C2×C411yescharacteristic
250#390C2×C414yes—
251#390C2×C411yescharacteristic
252#390C2×C411yescharacteristic
253#390C2×C411yescharacteristic
254#390C2×C411yescharacteristic
255#389C2×C414yes—
256#388C2×C414yes—
257#388C2×C414yes—
258#386C2×C414yes—
259#386C2×C414yes—
260#386C2×C414yes—
261#386C2×C414yes—
262#380C2×C414yes—
263C4×C4⋊C4C2×C411yescharacteristic
264C4×C4⋊C4C2×C411yescharacteristic
265C4×C4⋊C4C2×C411yescharacteristic
266C4×C4⋊C4C2×C411yescharacteristic
267C4×C4⋊C4C2312yes—
268C4×C4⋊C4C2312yes—
269C4×C22⋊C4C2314yes—
270C4×C22⋊C4C2314yes—
271C2×#95C2×C412yes—
272#336C2314yes—
273#336C2312yes—
274#336C2312yes—
275#336C2312yes—
276#336C2312yes—
277#336C2314yes—
278#336C2314yes—
279#336C2314yes—
280C2×#41—22no—
281C2×#41—22no—
282C2×#41—22no—
283C2×#41—22no—
284C2×#41—22no—
285C2×#41—22no—
286C2×#41—22no—
287C2×#41—22no—
288C2×#41—22no—
289C2×#41—22no—
290C2×#41—22no—
291C2×#41—22no—
292C2×#41—22no—
293C2×#41—22no—
294C2×#41—22no—
295C2×#41—22no—
296C2×#41C2×D414yes—
297C2×#41#4114yes—
298C22×Q8C22×C411yescharacteristic
299C22×Q8C22×C411yescharacteristic
300C22×Q8C22×C411yescharacteristic
301C22×D4C22×C412yes—
302C22×D4C22×C412yes—
303C22×D4C22×C411yescharacteristic
304C22×D4C22×C411yescharacteristic
305C22×D4C22×C414yes—
306C22×D4C22×C412yes—
307C22×D4C22×C411yescharacteristic
308C22×D4C22×C412yes—
309C22×D4C22×C414yes—
310C22×D4C22×C412yes—
311C23×C4C22×C412yes—
312C23×C4C22×C412yes—
313C23×C4C22×C412yes—
314C23×C4C22×C412yes—
315C23×C4C22×C411yescharacteristic
316C23×C4C22×C411yescharacteristic
317C23×C4C2412yes—
318C23×C4C2412yes—
319C23×C4C2412yes—
320C23×C4C2411yescharacteristic
321#131—416no—
322#131—416no—
323#131—416no—
324#131—416no—
325C2×M16—22no—
326C2×M16—22no—
327C2×M16—22no—
328C2×M16—22no—
329C2×M16—22no—
330C2×M16—22no—
331C2×M16—24no—
332C2×M16—24no—
333C2×M16—22no—
334C2×M16—22no—
335C2×M16—22no—
336C2×M16—22no—
337C2×M16—22no—
338C2×M16—24no—
339C2×M16—24no—
340C2×M16—24no—
341C2×M16—24no—
342C2×M16—24no—
343C2×M16—24no—
344C2×M16—42no—
345C2×M16—42no—
346C2×M16—42no—
347C2×M16—42no—
348C2×M16C2×D414yes—
349C22×C8—22no—
350C22×C8—22no—
351C22×C8—22no—
352C22×C8—22no—
353C22×C8—22no—
354C22×C8—22no—
355C22×C8—24no—
356C22×C8—24no—
357C22×C8—22no—
358C22×C8—22no—
359C22×C8—22no—
360C22×C8—24no—
361C22×C8—24no—
362C22×C8—24no—
363C22×C8—24no—
364C22×C8—24no—
365C22×C8—24no—
366C22×C8—42no—
367C22×C8—42no—
368C22×C8—42no—
369C22×C8—42no—
370C22×C8C2×D414yes—
371C22×C8C2×D414yes—
372C22×C8C2×D414yes—
373C22×C8C2412yes—
374C22×C8C2412yes—
375C22×C8C2412yes—
376C22×C8C2412yes—
377C22×C8C2411yescharacteristic
378C22×C8C2411yescharacteristic
379C22×C8C2411yescharacteristic
380C22×C8C2412yes—
381C22×C8C2411yescharacteristic
382C22×C8C2412yes—
383C4⋊Q8—24no—
384C4⋊Q8—24no—
385C4⋊Q8—24no—
386#127—24no—
387#127—24no—
388#127—24no—
389#124—24no—
390#124—24no—
391#124—24no—
392#124—24no—
393#124—24no—
394#124—24no—
395#121—216no—
396#121—216no—
397#121—28no—
398#121—28no—
399#121—48no—
400C4×Q8—24no—
401C4×Q8—24no—
402C4×D4—28no—
403C4×D4—28no—
404C4×D4—28no—
405C4×D4—28no—
406C4×D4—28no—
407C4×D4—28no—
408C4×D4—24no—
409C4×D4—24no—
410C4×D4—24no—
411C4×D4—24no—
412C4×D4—24no—
413C4×D4—24no—
414#117—22no—
415#117—22no—
416#117—24no—
417#117—24no—
418C2×C4⋊C4—44no—
419C2×C4⋊C4C22×C412yes—
420C2×C4⋊C4C22×C412yes—
421C2×C4⋊C4C22×C411yescharacteristic
422C2×C4⋊C4C22×C411yescharacteristic
423C2×C4⋊C4C22×C412yes—
424C2×C4⋊C4C22×C412yes—
425C2×C4⋊C4C22×C412yes—
426C2×C4⋊C4C22×C414yes—
427C2×C4⋊C4C22×C414yes—
428C2×C4⋊C4C22×C412yes—
429C2×C4⋊C4C22×C412yes—
430C2×C4⋊C4C22×C412yes—
431C2×C22⋊C4C22×C412yes—
432C2×C22⋊C4C22×C412yes—
433C2×C22⋊C4C22×C412yes—
434C2×C22⋊C4C22×C414yes—
435C2×C22⋊C4C22×C414yes—
436C2×C22⋊C4C22×C412yes—
437C2×C22⋊C4C22×C412yes—
438C2×C22⋊C4C22×C414yes—
439C2×C22⋊C4C22×C414yes—
440C2×C22⋊C4C22×C412yes—
441C2×C22⋊C4C22×C412yes—
442C2×C22⋊C4C22×C414yes—
443C2×C22⋊C4C22×C414yes—
444C2×C22⋊C4C22×C414yes—
445C2×C22⋊C4C22×C414yes—
446C2×C42—22no—
447C2×C42—22no—
448C2×C42—22no—
449C2×C42—22no—
450C2×C42—24no—
451C2×C42—24no—
452C2×C42C22×C412yes—
453C2×C42C22×C412yes—
454C2×C42C22×C411yescharacteristic
455C2×C42C22×C411yescharacteristic
456C2×C42C22×C411yescharacteristic
457C2×C42C22×C411yescharacteristic
458C2×C42C22×C411yescharacteristic
459C2×C42C22×C411yescharacteristic
460C2×C42C2×D414yes—
461C2×C42#4114yes—
462C2×C42C2412yes—
463C2×C42C2412yes—
464C2×C42C2412yes—
465C2×C42C2411yescharacteristic
466C2×C42C2411yescharacteristic
467C4⋊C8—24no—
468C4⋊C8—24no—
469C4⋊C8—24no—
470C4⋊C8—24no—
471C4⋊C8—28no—
472C4⋊C8—28no—
473C4⋊C8—24no—
474C4⋊C8—24no—
475C4⋊C8C2×D414yes—
476C4⋊C8C2×D414yes—
477C4⋊C8C2×D414yes—
478C4⋊C8C2×D414yes—
479C22⋊C8—28no—
480C22⋊C8—24no—
481C22⋊C8—24no—
482C22⋊C8—28no—
483C22⋊C8—28no—
484C22⋊C8—24no—
485C22⋊C8—24no—
486C22⋊C8—44no—
487C22⋊C8—44no—
488C22⋊C8C2×D4116yes—
489#97—24no—
490#97—24no—
491#97—24no—
492#97—24no—
493#97—24no—
494C4×C8—24no—
495C4×C8—24no—
496C4×C8—24no—
497#95C22×C412yes—
498#95C22×C412yes—
499#95C22×C412yes—
500#95C22×C412yes—
501#95C22×C414yes—
502#95C22×C414yes—
503#95C22×C414yes—
504#95C22×C414yes—
505C24C23×C412yes—
506C24C23×C412yes—
507C24C23×C412yes—
508C24C23×C411yescharacteristic
509#41—28no—
510#41—28no—
511#41—28no—
512#41—28no—
513#41—44no—
514#41—44no—
515#41—44no—
516#41—44no—
517#41—44no—
518#41—44no—
519#41—44no—
520#41—44no—
521C2×Q8—22no—
522C2×Q8—22no—
523C2×Q8—22no—
524C2×Q8—22no—
525C2×Q8—22no—
526C2×Q8—22no—
527C2×Q8—22no—
528C2×Q8—22no—
529C2×Q8C4×D414yes—
530C2×D4—24no—
531C2×D4—24no—
532C2×D4—28no—
533C2×D4—24no—
534C2×D4—24no—
535C2×D4—24no—
536C2×D4—24no—
537C2×D4—24no—
538C2×D4—24no—
539C2×D4—28no—
540C2×D4—22no—
541C2×D4—24no—
542C2×D4—22no—
543C2×D4—22no—
544C2×D4—22no—
545C2×D4—22no—
546C2×D4—24no—
547C2×D4—22no—
548C2×D4—22no—
549C2×D4—22no—
550C2×D4—28no—
551C2×D4—44no—
552C2×D4—44no—
553C2×D4—44no—
554C2×D4—44no—
555C2×D4—44no—
556C2×D4C4×D418yes—
557C2×D4C4×D414yes—
558C22×C4—22no—
559C22×C4—22no—
560C22×C4—22no—
561C22×C4—22no—
562C22×C4—24no—
563C22×C4—24no—
564C22×C4—24no—
565C22×C4—24no—
566C22×C4—22no—
567C22×C4—22no—
568C22×C4—22no—
569C22×C4—22no—
570C22×C4—22no—
571C22×C4—22no—
572C22×C4—22no—
573C22×C4—22no—
574C22×C4—22no—
575C22×C4—22no—
576C22×C4—22no—
577C22×C4—22no—
578C22×C4—24no—
579C22×C4—42no—
580C22×C4—42no—
581C22×C4—44no—
582C22×C4—42no—
583C22×C4—42no—
584C22×C4—44no—
585C22×C4—42no—
586C22×C4C4×D414yes—
587C22×C4C4×D414yes—
588C22×C4C23×C412yes—
589C22×C4C23×C412yes—
590C22×C4C23×C412yes—
591C22×C4C23×C412yes—
592C22×C4C23×C412yes—
593C22×C4C23×C412yes—
594C22×C4C23×C412yes—
595C22×C4C23×C411yescharacteristic
596C22×C4C23×C411yescharacteristic
597C22×C4C23×C411yescharacteristic
598C22×C4C23×C412yes—
599C22×C4C23×C411yescharacteristic
600C22×C4C23×C412yes—
601C22×C4C23×C411yescharacteristic
602C22×C4C22×D414yes—
603C22×C4C22×D412yes—
604C22×C4C22×D412yes—
605C22×C4C2×#4114yes—
606C22×C4C2×#4112yes—
607C22×C4C2×#4112yes—
608C22×C4H(5,𝔽2)12yes—
609C22×C42−1+412yes—
610C22×C4C2511yescharacteristic
611M16—28no—
612M16—48no—
613M16—48no—
614M16—48no—
615M16—48no—
616M16—44no—
617M16—44no—
618M16—44no—
619C2×C8—28no—
620C2×C8—28no—
621C2×C8—28no—
622C2×C8—21no—
623C2×C8—21no—
624C2×C8—22no—
625C2×C8—21no—
626C2×C8—21no—
627C2×C8—22no—
628C2×C8—21no—
629C2×C8—21no—
630C2×C8—21no—
631C2×C8—21no—
632C2×C8—22no—
633C2×C8—22no—
634C2×C8—22no—
635C2×C8—22no—
636C2×C8—22no—
637C2×C8—22no—
638C2×C8—22no—
639C2×C8—22no—
640C2×C8—22no—
641C2×C8—22no—
642C2×C8—22no—
643C2×C8—22no—
644C2×C8—22no—
645C2×C8—22no—
646C2×C8—48no—
647C2×C8—48no—
648C2×C8—48no—
649C2×C8—48no—
650C2×C8—44no—
651C2×C8C22×D414yes—
652C2×C8C22×D412yes—
653C2×C8C22×D412yes—
654C2×C8C22×D412yes—
655C2×C8C22×D412yes—
656C2×C8C22×D414yes—
657C4⋊C4—24no—
658C4⋊C4—24no—
659C4⋊C4—22no—
660C4⋊C4—22no—
661C4⋊C4—28no—
662C4⋊C4—28no—
663C4⋊C4—24no—
664C4⋊C4—24no—
665C4⋊C4—24no—
666C4⋊C4—24no—
667C4⋊C4—42no—
668C4⋊C4—42no—
669C22⋊C4—24no—
670C22⋊C4—28no—
671C22⋊C4—28no—
672C22⋊C4—24no—
673C22⋊C4—24no—
674C22⋊C4—28no—
675C22⋊C4—28no—
676C22⋊C4—24no—
677C22⋊C4—24no—
678C22⋊C4—24no—
679C22⋊C4—24no—
680C22⋊C4—28no—
681C22⋊C4—44no—
682C22⋊C4—44no—
683C22⋊C4—44no—
684C42—24no—
685C42—24no—
686C42—22no—
687C42—22no—
688C42—22no—
689C42—22no—
690C42—22no—
691C42—22no—
692C42—22no—
693C42—22no—
694C42—22no—
695C42—22no—
696C42C4×D414yes—
697C42C4×D414yes—
698C42C22×D412yes—
699C42C22×D412yes—
700C42C2×#4112yes—
701C42C2×#4112yes—
702C23—22no—
703C23—22no—
704C23—22no—
705C23—22no—
706C23—24no—
707C23—24no—
708C23—22no—
709C23—22no—
710C23—22no—
711C23—22no—
712C23—22no—
713C23—22no—
714C23—24no—
715C23—24no—
716C23—24no—
717C23—24no—
718C23C2×C4×D414yes—
719C23C2×C4×D412yes—
720C23C2×C4×D412yes—
721C23#52012yes—
722C23C24×C411yescharacteristic
723Q8—28no—
724Q8—44no—
725Q8—44no—
726D4—216no—
727D4—28no—
728D4—416no—
729D4—48no—
730D4—48no—
731D4—48no—
732D4—44no—
733D4—44no—
734D4—84no—
735D4—88no—
736C2×C4—22no—
737C2×C4—22no—
738C2×C4—22no—
739C2×C4—22no—
740C2×C4—22no—
741C2×C4—22no—
742C2×C4—22no—
743C2×C4—22no—
744C2×C4—24no—
745C2×C4—24no—
746C2×C4—24no—
747C2×C4—24no—
748C2×C4—22no—
749C2×C4—22no—
750C2×C4—22no—
751C2×C4—22no—
752C2×C4—22no—
753C2×C4—22no—
754C2×C4—22no—
755C2×C4—22no—
756C2×C4—22no—
757C2×C4—22no—
758C2×C4—22no—
759C2×C4—24no—
760C2×C4—22no—
761C2×C4—22no—
762C2×C4—22no—
763C2×C4—24no—
764C2×C4—22no—
765C2×C4—22no—
766C2×C4—22no—
767C2×C4—44no—
768C2×C4—44no—
769C2×C4—48no—
770C2×C4—48no—
771C2×C4—42no—
772C2×C4—42no—
773C2×C4—42no—
774C2×C4—42no—
775C2×C4—42no—
776C2×C4—42no—
777C2×C4—42no—
778C2×C4—42no—
779C2×C4—84no—
780C2×C4—84no—
781C2×C4C2×C4×D412yes—
782C2×C4C2×C4×D412yes—
783C2×C4C2×C4×D412yes—
784C2×C4C2×C4×D412yes—
785C2×C4C2×C4×D414yes—
786C2×C4C2×C4×D412yes—
787C2×C4C2×C4×D412yes—
788C2×C4#52012yes—
789C2×C4D4214yes—
790C2×C4#54714yes—
791C2×C4#54814yes—
792C2×C4#55314yes—
793C2×C4#56814yes—
794C2×C4C23×D411yescharacteristic
795C2×C4C23×D411yescharacteristic
796C2×C4C22×#4111yescharacteristic
797C2×C4C22×#4111yescharacteristic
798C2×C4C2×H(5,𝔽2)11yescharacteristic
799C2×C4C2×2−1+411yescharacteristic
800C8—22no—
801C8—22no—
802C8—22no—
803C8—22no—
804C8—24no—
805C8—24no—
806C8—42no—
807C8—42no—
808C8—42no—
809C8—42no—
810C22—24no—
811C22—22no—
812C22—22no—
813C22—24no—
814C22—24no—
815C22—28no—
816C22—44no—
817C22—42no—
818C22—42no—
819C22—42no—
820C22—42no—
821C22—44no—
822C22—44no—
823C22—42no—
824C22—42no—
825C22—42no—
826C22—42no—
827C22—44no—
828C22—44no—
829C22#236114yes—
830C22C22×C4×D411yescharacteristic
831C22C22×C4×D411yescharacteristic
832C22C2×#52011yescharacteristic
833C22C2×#56812yes—
834C22#357312yes—
835C4—24no—
836C4—22no—
837C4—22no—
838C4—22no—
839C4—22no—
840C4—24no—
841C4—42no—
842C4—42no—
843C4—42no—
844C4—42no—
845C4—42no—
846C4—42no—
847C4—42no—
848C4#236114yes—
849C4C2×D4211yescharacteristic
850C4C2×#54711yescharacteristic
851C4C2×#54811yescharacteristic
852C4C2×#55311yescharacteristic
853C2—24no—
854C2—44no—
855C2—82no—
856C2—82no—
857C2C2×#236111yescharacteristic
858C2#6014011yescharacteristic
859C2#6014411yescharacteristic
860C2#6014612yes—
861C2#6027512yes—
subgroupG/H
center, Frattini, cosocleC22×C4C25
commutator, socleC23C24×C4
prime radical#34937C2
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C22×C4 ◁ G
LECSG ▷ C22×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
1. C2×#2935C2semidirect
2. C2×#2932C2semidirect
3. C2×#2931C2semidirect
4. C2×#2906C2semidirect
6. #22994C2semidirect
7. #22991C2semidirect
8. #22988C2semidirect
9. #22987C2semidirect
10. #21188C2semidirect
11. #21146C2semidirect
12. #21047C2semidirect
13. #21046C2semidirect
14. #20900C2semidirect
15. #20900C2semidirect
16. #20839C2semidirect
17. #20839C2semidirect
18. C2×#1771C2semidirect
19. #20375C2semidirect
195. C2×C4⋊C8D4semidirect
215. #408D4semidirect

Maximal subgroups

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

subgroupindex
C2×#29352
C2×#29322
C2×#29312
C2×#29062
#349372
#229942
#229912
#229882
#229872
#211882
#211462
#210472
#210462
#209002
#208392
C2×#17712
#203752