Finite Group Databasebeta

← C2×#24919332 #36280792

Subgroups — C2×#24919332 #36280792

Order 21248.

2158 conjugacy classes of subgroups.

The subgroup lattice has 780 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#19128409C211yesmaximal, characteristic
2C2×Q8×C22⋊D83C211yesmaximal, characteristic
3#24919332C2116yesmaximal, direct product factor
4C2×#19128050C211yesmaximal, characteristic, complemented
5C2×#19128037C211yesmaximal, characteristic, complemented
6C2×#19128035C211yesmaximal, characteristic, complemented
7C2×#19127994C211yesmaximal, characteristic, complemented
8C2×#19127940C211yesmaximal, characteristic, complemented
9C2×#19127939C211yesmaximal, characteristic, complemented
10C2×#19127909C211yesmaximal, characteristic, complemented
11C2×#19127855C211yesmaximal, characteristic, complemented
12C2×Q16×Dic83C211yesmaximal, characteristic, complemented
13C2×(C22⋊D83)⋊C8C211yesmaximal, characteristic
14C22×#14581716C211yesmaximal, characteristic, complemented
15C2×#103×D83C211yesmaximal, characteristic, complemented
16C2×#451×C83C211yesmaximal, characteristic, complemented
17C22×Q8×D83C2211yescharacteristic
18C22×#13050580C2211yescharacteristic
19C23×C83⋊C8C2211yescharacteristic
20C22×C8×D83C2211yescharacteristic
21#19128409—24no—
22#19128409C2218yes—
23Q8×C22⋊D83—24no—
24Q8×C22⋊D83C2218yes—
25C2×#14581791C2211yescharacteristic
26C2×#14581790—21no—
27C2×#14581790C2211yescharacteristic
28C2×#14581782—21no—
29C2×#14581772—21no—
30C2×#14581771—21no—
31C2×#14581771C2211yescharacteristic
32C2×#14581769—21no—
33C2×#14581768—21no—
34C2×#14581768C2211yescharacteristic
35C2×#14581768C2211yescharacteristic
36C2×Q8×Dic83C2211yescharacteristic
37C2×Q8×Dic83C2211yescharacteristic
38C2×C4×C22⋊D83—21no—
39C2×C4×C22⋊D83C2211yescharacteristic
40C2×(C22⋊D83)⋊C4—21no—
41C22×C4⋊Dic83C2211yescharacteristic
42C2×C4⋊C4×D83C2211yescharacteristic
43#19128050C2218yescomplemented
44#19128037C2218yescomplemented
45#19128035C2218yescomplemented
46#19127994C2218yescomplemented
47#19127940C2218yescomplemented
48#19127939C2218yescomplemented
49#19127909C2218yescomplemented
50#19127855C2218yescomplemented
51Q16×Dic83C2218yescomplemented
52(C22⋊D83)⋊C8C2218yes—
53C2×#14581726C2211yescharacteristic
54C2×#14581726C2211yescharacteristic
55C2×#14581725C2211yescharacteristic
56C2×Dic83⋊C8C2211yescharacteristic
57C2×#14581717C2211yescharacteristic
58C2×#14581717C2211yescharacteristic
59C2×#14581716C2211yescharacteristic
60C2×#14581716C2211yescharacteristic
61C2×#14581716C2211yescharacteristic
62C2×#14581716C2211yescharacteristic
63C2×#14581716C2211yescharacteristic
64C2×#14581716C2218yescomplemented
65C2×#14581715C2211yescharacteristic
66#103×D83C2218yescomplemented
67C2×(C2×D83)⋊C8C2211yescharacteristic
68C2×C8×Dic83C2211yescharacteristic
69C23×Q8×C83C2211yescharacteristic
70C22×Q16×C83C2211yescharacteristic
71C22×Q16×C83C2211yescharacteristic
72C2×C22⋊Q8×C83C2211yescharacteristic
73#451×C83C2218yescomplemented
74C2×#103×C83C2211yescharacteristic
75C2×#103×C83C2211yescharacteristic
76C2×C22⋊C8×C83C2211yescharacteristic
77C22×Dic166—21no—
78C22×Dic166—21no—
79C22×Dic166C2311yescharacteristic
80C2×Q8×D83—22no—
81C2×Q8×D83—24no—
82C2×Q8×D83—42no—
83C2×Q8×D83C2314yes—
84C22×C22⋊D83D411yescharacteristic
85C23×Dic83—21no—
86C22×C4×D83—21no—
87C22×C4×D83—21no—
88C22×C4×D83C2311yescharacteristic
89C2×#13050580—42no—
90C2×#13050580C2314yes—
91C22×C83⋊C8—42no—
92C22×C83⋊C8C2311yescharacteristic
93C22×C83⋊C8C2311yescharacteristic
94C22×C83⋊C8C2314yes—
95C2×C8×D83—42no—
96C2×C8×D83C2314yes—
97#14581791—22no—
98#14581791C2314yes—
99#14581790—28no—
100#14581790—22no—
101#14581790C2314yes—
102#14581782—28no—
103#14581772—28no—
104#14581771—28no—
105#14581771—22no—
106#14581771C2314yes—
107#14581769—28no—
108#14581768—22no—
109#14581768—22no—
110#14581768—28no—
111#14581768C2314yes—
112#14581768C2314yes—
113Q8×Dic83—22no—
114Q8×Dic83—22no—
115Q8×Dic83C2314yes—
116Q8×Dic83C2314yes—
117C4×C22⋊D83—28no—
118C4×C22⋊D83D414yes—
119C4×C22⋊D83C2314yes—
120(C22⋊D83)⋊C4—28no—
121C2×C4⋊Dic83—21no—
122C2×C4⋊Dic83—21no—
123C2×C4⋊Dic83—22no—
124C2×C4⋊Dic83—21no—
125C2×C4⋊Dic83C2311yescharacteristic
126C2×C4⋊Dic83C2314yes—
127C2×C4⋊Dic83C2311yescharacteristic
128C2×C4⋊Dic83C2311yescharacteristic
129C2×Dic83⋊C4—21no—
130C2×Dic83⋊C4—21no—
131C2×Dic83⋊C4—21no—
132C2×Dic83⋊C4—21no—
133C2×Dic83⋊C4—21no—
134C2×Dic83⋊C4—21no—
135C2×Dic83⋊C4—21no—
136C2×Dic83⋊C4D411yescharacteristic
137C4⋊C4×D83—22no—
138C4⋊C4×D83C2314yes—
139C2×C22⋊Dic83—21no—
140C2×C22⋊Dic83D411yescharacteristic
141C2×(C2×D83)⋊C4—21no—
142C2×(C2×D83)⋊C4—21no—
143C2×(C2×D83)⋊C4D411yescharacteristic
144C2×C4×Dic83—21no—
145C2×C4×Dic83—21no—
146C2×C4×Dic83C2311yescharacteristic
147#14581726C2314yes—
148#14581726C2314yes—
149#14581725C2314yes—
150Dic83⋊C8C2314yes—
151#14581717C2314yes—
152#14581717C2314yes—
153#14581716C2314yes—
154#14581716C2314yes—
155#14581716C2314yes—
156#14581716C2314yes—
157#14581716C2314yes—
158#14581715C2314yes—
159(C2×D83)⋊C8C2314yes—
160C8×Dic83C2314yes—
161C22×Q8×C83—22no—
162C22×Q8×C83—21no—
163C22×Q8×C83—24no—
164C22×Q8×C83—42no—
165C22×Q8×C83C2311yescharacteristic
166C22×Q8×C83C2311yescharacteristic
167C22×Q8×C83C2314yes—
168C22×Q8×C83C2311yescharacteristic
169C23×C4×C83—21no—
170C23×C4×C83C2311yescharacteristic
171C2×Q16×C83—24no—
172C2×Q16×C83—42no—
173C2×Q16×C83C2314yes—
174C2×Q16×C83C2314yes—
175C22×C8×C83C2311yescharacteristic
176C22×C8×C83C2311yescharacteristic
177C22⋊Q8×C83—22no—
178C22⋊Q8×C83C2314yes—
179C2×C4⋊C4×C83—21no—
180C2×C4⋊C4×C83C2311yescharacteristic
181C2×C22⋊C4×C83—21no—
182#103×C83C2314yes—
183#103×C83C2314yes—
184C22⋊C8×C83C2314yes—
185C23×D83C2×D411yescharacteristic
186C2×Dic166—22no—
187C2×Dic166—22no—
188C2×Dic166—21no—
189C2×Dic166—24no—
190C2×Dic166—24no—
191C2×Dic166—44no—
192C2×Dic166—82no—
193C2×Dic166C2412yes—
194Q8×D83—28no—
195Q8×D83—44no—
196Q8×D83—48no—
197C2×C22⋊D83Q1618yescomplemented
198C2×C22⋊D83C2×D414yes—
199C22×Dic83—21no—
200C22×Dic83—21no—
201C22×Dic83—21no—
202C22×Dic83—21no—
203C22×Dic83—24no—
204C22×Dic83—82no—
205C22×Dic83C2×D411yescharacteristic
206C22×Dic83C2×D411yescharacteristic
207C22×Dic83C2×D411yescharacteristic
208C2×C4×D83—22no—
209C2×C4×D83—22no—
210C2×C4×D83—24no—
211C2×C4×D83—24no—
212C2×C4×D83—44no—
213C2×C4×D83—82no—
214C2×C4×D83C2×D412yes—
215C2×C4×D83C2412yes—
216#13050580—44no—
217C2×C83⋊C8—22no—
218C2×C83⋊C8—22no—
219C2×C83⋊C8—44no—
220C2×C83⋊C8C2412yes—
221C2×C83⋊C8C2412yes—
222C8×D83—44no—
223C4⋊Dic83—21no—
224C4⋊Dic83—21no—
225C4⋊Dic83—24no—
226C4⋊Dic83—21no—
227C4⋊Dic83—24no—
228C4⋊Dic83—24no—
229C4⋊Dic83C2412yes—
230C4⋊Dic83C2412yes—
231C4⋊Dic83C2412yes—
232Dic83⋊C4—24no—
233Dic83⋊C4—24no—
234Dic83⋊C4—24no—
235Dic83⋊C4—24no—
236Dic83⋊C4—24no—
237Dic83⋊C4—24no—
238Dic83⋊C4—24no—
239Dic83⋊C4C2×D414yes—
240C22⋊Dic83—24no—
241C22⋊Dic83C2×D414yes—
242(C2×D83)⋊C4—24no—
243(C2×D83)⋊C4—24no—
244(C2×D83)⋊C4C2×D414yes—
245C4×Dic83—24no—
246C4×Dic83—24no—
247C4×Dic83C2×D412yes—
248C4×Dic83C2412yes—
249C24×C83C2×D411yescharacteristic
250C2×Q8×C83—21no—
251C2×Q8×C83—24no—
252C2×Q8×C83—21no—
253C2×Q8×C83—21no—
254C2×Q8×C83—22no—
255C2×Q8×C83—28no—
256C2×Q8×C83—22no—
257C2×Q8×C83—22no—
258C2×Q8×C83—22no—
259C2×Q8×C83—22no—
260C2×Q8×C83—44no—
261C2×Q8×C83—44no—
262C2×Q8×C83—48no—
263C2×Q8×C83#4114yes—
264C2×Q8×C83C2412yes—
265C2×Q8×C83C2412yes—
266C2×Q8×C83C2412yes—
267C22×C4×C83—21no—
268C22×C4×C83—22no—
269C22×C4×C83—22no—
270C22×C4×C83—24no—
271C22×C4×C83—21no—
272C22×C4×C83—21no—
273C22×C4×C83—21no—
274C22×C4×C83—44no—
275C22×C4×C83C2×D412yes—
276C22×C4×C83C2×D411yescharacteristic
277C22×C4×C83C2412yes—
278C22×C4×C83C2411yescharacteristic
279Q16×C83—28no—
280Q16×C83—44no—
281C2×C8×C83—22no—
282C2×C8×C83—22no—
283C2×C8×C83C2412yes—
284C2×C8×C83C2412yes—
285C4⋊C4×C83—24no—
286C4⋊C4×C83—21no—
287C4⋊C4×C83C2412yes—
288C22⋊C4×C83—24no—
289C23×C83—22no—
290C23×C83—22no—
291C23×C83C2×Q1614yes—
292C23×C83C22×D412yes—
293C23×C83C22×D411yescharacteristic
294C22×D83—22no—
295C22×D83—22no—
296C22×D83C2×Q1614yes—
297C22×D83C22×D412yes—
298Q8×C83—24no—
299Q8×C83—22no—
300Q8×C83—22no—
301Q8×C83—22no—
302Q8×C83—22no—
303Q8×C83—22no—
304Q8×C83—48no—
305Q8×C83—42no—
306Q8×C83—42no—
307Q8×C83C2×#4114yes—
308C2×C4×C83—22no—
309C2×C4×C83—24no—
310C2×C4×C83—22no—
311C2×C4×C83—24no—
312C2×C4×C83—22no—
313C2×C4×C83—22no—
314C2×C4×C83—22no—
315C2×C4×C83—22no—
316C2×C4×C83—22no—
317C2×C4×C83—48no—
318C2×C4×C83—42no—
319C2×C4×C83—42no—
320C2×C4×C83—42no—
321C2×C4×C83C22×D412yes—
322C2×C4×C83C22×D411yescharacteristic
323C2×C4×C83C2×#4112yes—
324C2×C4×C83H(5,𝔽2)12yes—
325C2×C4×C83C2511yescharacteristic
326C22⋊D83C2×Q16116yescomplemented
327C2×Dic83—22no—
328C2×Dic83—22no—
329C2×Dic83—22no—
330C2×Dic83—22no—
331C2×Dic83—22no—
332C2×Dic83—22no—
333C2×Dic83—42no—
334C2×Dic83—42no—
335C2×Dic83—42no—
336C2×Dic83—42no—
337C2×Dic83—84no—
338C2×Dic83C2×Q1614yes—
339C2×Dic83C22×D412yes—
340C2×Dic83C22×D412yes—
341C2×Dic83C22×D412yes—
342C4×D83—24no—
343C4×D83—22no—
344C4×D83—22no—
345C4×D83—48no—
346C4×D83—84no—
347Dic166—22no—
348Dic166—22no—
349Dic166—48no—
350Dic166—42no—
351Dic166—84no—
352C8×C83—22no—
353C8×C83—22no—
354C83⋊C8—22no—
355C83⋊C8—22no—
356C22×C83—22no—
357C22×C83—28no—
358C22×C83—22no—
359C22×C83#54612yes—
360C22×C83C22×Q1614yes—
361C22×C83C22×Q1612yes—
362C22×C83#57712yes—
363C22×C83C23×D411yescharacteristic
364C2×D83—22no—
365C2×D83—28no—
366C2×D83—22no—
367C2×D83C22×Q1614yes—
368C4×C83—24no—
369C4×C83—22no—
370C4×C83—42no—
371C4×C83—42no—
372C4×C83—42no—
373C4×C83#54612yes—
374C4×C83C22×#4111yescharacteristic
375C4×C83C2×H(5,𝔽2)11yescharacteristic
376Dic83—22no—
377Dic83—22no—
378Dic83—42no—
379Dic83—42no—
380Dic83—42no—
381Dic83—42no—
382Dic83C22×Q1614yes—
383C2×#3299—831nomaximal, Sylow
384C2×C83—24no—
385C2×C83#329914yescomplemented
386C2×C83C2×#54611yescharacteristic
387C2×C83C23×Q1611yescharacteristic
388C2×C83C2×#57711yescharacteristic
389D83—24no—
390C2×#554—831no—
391C2×D4×Q8—831no—
392#3299—8316no—
393C2×#487—831no—
394C2×#484—831no—
395C2×#484—831no—
396C2×#477—831no—
397C2×#467—831no—
398C2×#467—831no—
399C2×#462—831no—
400C2×#451—831no—
401C2×#451D8311yescharacteristic, complemented
402C2×C4×Q16—831no—
403C2×C8×D4—831no—
404C22×#103—831no—
405C22×#103—831no—
406C83C2×#329911yescharacteristic, complemented, Sylow
407C23×Q8—831no—
408C23×Q8C2×D8311yescharacteristic
409C22×Q16—831no—
410C22×Q16C2×D8311yescharacteristic
411C22×Q16C2×D8311yescharacteristic
412C23×C8—831no—
413C23×C8—831no—
414#554—838no—
415#554—1664no—
416D4×Q8—838no—
417D4×Q8—1664no—
418C2×C4⋊Q8—831no—
419C2×C4⋊Q8—831no—
420C2×C4⋊Q8—1661no—
421C2×#125—1661no—
422C2×C22⋊Q8—831no—
423C2×C22⋊Q8—831no—
424C2×C22⋊Q8—831no—
425C2×C22⋊Q8—1661no—
426C2×C22⋊Q8—1661no—
427C2×C22⋊Q8—1661no—
428C2×C22⋊Q8—1661no—
429C2×C22⋊Q8C2×D8311yescharacteristic
430C2×C4×Q8—831no—
431C2×C4×Q8—831no—
432C2×C4×D4—831no—
433C2×C4×D4—1661no—
434C2×C4×D4—1661no—
435C22×C4⋊C4—831no—
436C22×C4⋊C4—831no—
437#487—838no—
438#484—838no—
439#484—838no—
440#477—838no—
441#467—838no—
442#467—838no—
443#462—838no—
444#451—838no—
445#451C2×D8318yescomplemented
446C4×Q16—838no—
447C8×D4—838no—
448C2×#107—831no—
449C2×#107—831no—
450C2×#107—831no—
451C2×C4⋊C8—831no—
452C2×#103—831no—
453C2×#103—831no—
454C2×#103—831no—
455C2×#103—831no—
456C2×#103—838no—
457C2×#103—831no—
458C2×#103—831no—
459C2×#103—831no—
460C2×#103—831no—
461C2×#103—838no—
462C2×#103C2×D8311yescharacteristic
463C2×#103C2×D8311yescharacteristic
464C2×C22⋊C8—831no—
465C2×C22⋊C8C2×D8311yescharacteristic
466C2×C4×C8—831no—
467C22×Q8—21no—
468C22×Q8—22no—
469C22×Q8—24no—
470C22×Q8—42no—
471C22×Q8—3322no—
472C22×Q8—834no—
473C22×Q8—831no—
474C22×Q8—1661no—
475C22×Q8—1661no—
476C22×Q8—1664no—
477C22×Q8—1662no—
478C22×Q8C22×D8311yescharacteristic
479C22×Q8C22×D8311yescharacteristic
480C22×Q8C22×D8314yes—
481C22×Q8C22×D8311yescharacteristic
482C22×D4—831no—
483C23×C4—21no—
484C23×C4—831no—
485C23×C4—1661no—
486C23×C4—1661no—
487C23×C4—1661no—
488C23×C4C22×D8311yescharacteristic
489C2×Q16—24no—
490C2×Q16—42no—
491C2×Q16—3322no—
492C2×Q16—834no—
493C2×Q16C22×D8314yes—
494C2×Q16C22×D8314yes—
495C22×C8—3322no—
496C22×C8—3322no—
497C22×C8—834no—
498C22×C8—834no—
499C22×C8—831no—
500C22×C8—831no—
501C22×C8C22×D8311yescharacteristic
502C22×C8C22×D8311yescharacteristic
503C4⋊Q8—834no—
504C4⋊Q8—834no—
505C4⋊Q8—1662no—
506C4⋊Q8—1662no—
507C4⋊Q8—1668no—
508#125—1668no—
509C22⋊Q8—22no—
510C22⋊Q8—834no—
511C22⋊Q8—834no—
512C22⋊Q8—834no—
513C22⋊Q8—1668no—
514C22⋊Q8—1668no—
515C22⋊Q8—1668no—
516C22⋊Q8—1668no—
517C22⋊Q8—1662no—
518C22⋊Q8—1662no—
519C22⋊Q8—1662no—
520C22⋊Q8C22×D8314yes—
521C4×Q8—834no—
522C4×Q8—834no—
523C4×Q8—1662no—
524C4×Q8—1662no—
525C4×D4—834no—
526C4×D4—834no—
527C4×D4—1668no—
528C4×D4—1668no—
529C2×C4⋊C4—21no—
530C2×C4⋊C4—831no—
531C2×C4⋊C4—831no—
532C2×C4⋊C4—831no—
533C2×C4⋊C4—834no—
534C2×C4⋊C4—831no—
535C2×C4⋊C4—834no—
536C2×C4⋊C4—1662no—
537C2×C4⋊C4—1661no—
538C2×C4⋊C4—1661no—
539C2×C4⋊C4—1661no—
540C2×C4⋊C4—1661no—
541C2×C4⋊C4—1661no—
542C2×C4⋊C4—1661no—
543C2×C4⋊C4—1661no—
544C2×C4⋊C4—1661no—
545C2×C4⋊C4—1661no—
546C2×C4⋊C4—1662no—
547C2×C4⋊C4—1661no—
548C2×C4⋊C4C22×D8311yescharacteristic
549C2×C22⋊C4—21no—
550C2×C22⋊C4—831no—
551C2×C22⋊C4—831no—
552C2×C22⋊C4—1661no—
553C2×C22⋊C4—1661no—
554C2×C22⋊C4—1661no—
555C2×C42—831no—
556C2×C42—1661no—
557C2×C42—1661no—
558#107—834no—
559#107—834no—
560#107—834no—
561C4⋊C8—834no—
562#103—834no—
563#103—834no—
564#103—834no—
565#103—834no—
566#103—834no—
567#103—834no—
568#103—834no—
569#103—834no—
570#103C22×D8314yes—
571#103C22×D8314yes—
572C22⋊C8—834no—
573C22⋊C8C22×D8314yes—
574C4×C8—834no—
575C24—831no—
576C24D4×D8311yescharacteristic
577C2×Q8—21no—
578C2×Q8—21no—
579C2×Q8—24no—
580C2×Q8—21no—
581C2×Q8—22no—
582C2×Q8—28no—
583C2×Q8—22no—
584C2×Q8—22no—
585C2×Q8—22no—
586C2×Q8—22no—
587C2×Q8—44no—
588C2×Q8—44no—
589C2×Q8—48no—
590C2×Q8—3324no—
591C2×Q8—3328no—
592C2×Q8—3324no—
593C2×Q8—832no—
594C2×Q8—6642no—
595C2×Q8—1664no—
596C2×Q8—1664no—
597C2×Q8—1668no—
598C2×Q8—1662no—
599C2×Q8—1662no—
600C2×Q8—1661no—
601C2×Q8#1305058914yes—
602C2×Q8C23×D8312yes—
603C2×Q8C23×D8312yes—
604C2×Q8C23×D8312yes—
605C2×D4—838no—
606C2×D4—834no—
607C22×C4—21no—
608C22×C4—22no—
609C22×C4—22no—
610C22×C4—24no—
611C22×C4—21no—
612C22×C4—21no—
613C22×C4—21no—
614C22×C4—44no—
615C22×C4—3324no—
616C22×C4—831no—
617C22×C4—831no—
618C22×C4—831no—
619C22×C4—832no—
620C22×C4—832no—
621C22×C4—6642no—
622C22×C4—6642no—
623C22×C4—1664no—
624C22×C4—1664no—
625C22×C4—1661no—
626C22×C4—1661no—
627C22×C4—1661no—
628C22×C4—1661no—
629C22×C4—1664no—
630C22×C4—1662no—
631C22×C4—1662no—
632C22×C4D4×D8312yes—
633C22×C4D4×D8311yescharacteristic
634C22×C4C23×D8312yes—
635C22×C4C23×D8311yescharacteristic
636Q16—28no—
637Q16—44no—
638Q16—3324no—
639C2×C8—22no—
640C2×C8—22no—
641C2×C8—3324no—
642C2×C8—3324no—
643C2×C8—832no—
644C2×C8—832no—
645C2×C8—1662no—
646C2×C8—1662no—
647C2×C8C23×D8312yes—
648C2×C8C23×D8312yes—
649C4⋊C4—24no—
650C4⋊C4—21no—
651C4⋊C4—834no—
652C4⋊C4—832no—
653C4⋊C4—832no—
654C4⋊C4—832no—
655C4⋊C4—1664no—
656C4⋊C4—1664no—
657C4⋊C4—1664no—
658C4⋊C4—1664no—
659C4⋊C4—1664no—
660C4⋊C4—1664no—
661C4⋊C4—1664no—
662C4⋊C4—1664no—
663C4⋊C4—1661no—
664C4⋊C4—1664no—
665C4⋊C4—1661no—
666C4⋊C4—1661no—
667C4⋊C4—1664no—
668C4⋊C4C23×D8312yes—
669C22⋊C4—24no—
670C22⋊C4—834no—
671C22⋊C4—834no—
672C22⋊C4—1664no—
673C22⋊C4—1664no—
674C22⋊C4—1664no—
675C42—832no—
676C42—832no—
677C42—1664no—
678C42—1664no—
679C23—22no—
680C23—22no—
681C23—834no—
682C23—832no—
683C23—1662no—
684C23—1662no—
685C23Q16×D8314yes—
686C23C2×D4×D8312yes—
687C23C2×D4×D8311yescharacteristic
688Q8—24no—
689Q8—22no—
690Q8—22no—
691Q8—22no—
692Q8—22no—
693Q8—22no—
694Q8—48no—
695Q8—42no—
696Q8—42no—
697Q8—3328no—
698Q8—3322no—
699Q8—6644no—
700Q8—1662no—
701Q8—1662no—
702Q8C2×#1305058914yes—
703D4—8316no—
704C2×C4—22no—
705C2×C4—24no—
706C2×C4—22no—
707C2×C4—24no—
708C2×C4—22no—
709C2×C4—22no—
710C2×C4—22no—
711C2×C4—22no—
712C2×C4—22no—
713C2×C4—48no—
714C2×C4—42no—
715C2×C4—42no—
716C2×C4—42no—
717C2×C4—3328no—
718C2×C4—3322no—
719C2×C4—3322no—
720C2×C4—3322no—
721C2×C4—3322no—
722C2×C4—834no—
723C2×C4—832no—
724C2×C4—832no—
725C2×C4—832no—
726C2×C4—6644no—
727C2×C4—6644no—
728C2×C4—1662no—
729C2×C4—1662no—
730C2×C4—1662no—
731C2×C4—1662no—
732C2×C4—1662no—
733C2×C4—1662no—
734C2×C4—1664no—
735C2×C4—1662no—
736C2×C4—1662no—
737C2×C4C2×D4×D8312yes—
738C2×C4C2×D4×D8311yescharacteristic
739C2×C4C2×#1305058912yes—
740C2×C4#1458183712yes—
741C2×C4C24×D8311yescharacteristic
742C8—22no—
743C8—22no—
744C8—1662no—
745C8—1662no—
746C22—28no—
747C22—22no—
748C22—22no—
749C22—834no—
750C22—1668no—
751C22—1662no—
752C22—1662no—
753C22#1912833812yes—
754C22C2×Q16×D8314yes—
755C22C2×Q16×D8312yes—
756C22#1912851012yes—
757C22C22×D4×D8311yescharacteristic
758C4—22no—
759C4—24no—
760C4—42no—
761C4—42no—
762C4—42no—
763C4—3322no—
764C4—3322no—
765C4—3322no—
766C4—3322no—
767C4—834no—
768C4—1662no—
769C4—1662no—
770C4#1912833812yes—
771C4C22×#1305058911yescharacteristic
772C4C2×#1458183711yescharacteristic
773C2—24no—
774C2—1664no—
775C2#2491933214yesdirect product factor
776C2C2×#1912833811yescharacteristic
777C2C22×Q16×D8311yescharacteristic
778C2C2×#1912851011yescharacteristic
subgroupG/H
centerC23C2×D4×D83
commutator, cosocleC2×C4×C83C25
FrattiniC2×C4C24×D83
FittingC2×#451×C83C2
socleC23×C83C22×D4
prime radicalC22×C22⋊D83D4
hypercenterC2×#451D83
hypocenterC83C2×#3299
LCSG ▷ C2×C4×C83 ▷ C2×C83 ▷ C83
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#451

Complements

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

NH ≅ G/Ntype
3. #24919332C2direct (N × H)
4. C2×#19128050C2semidirect
5. C2×#19128037C2semidirect
6. C2×#19128035C2semidirect
7. C2×#19127994C2semidirect
8. C2×#19127940C2semidirect
9. C2×#19127939C2semidirect
10. C2×#19127909C2semidirect
11. C2×#19127855C2semidirect
12. C2×Q16×Dic83C2semidirect
14. C22×#14581716C2semidirect
15. C2×#103×D83C2semidirect
16. C2×#451×C83C2semidirect
43. #19128050C22semidirect
44. #19128037C22semidirect
45. #19128035C22semidirect
46. #19127994C22semidirect
47. #19127940C22semidirect
48. #19127939C22semidirect
49. #19127909C22semidirect
50. #19127855C22semidirect
51. Q16×Dic83C22semidirect
64. C2×#14581716C22semidirect
66. #103×D83C22semidirect
73. #451×C83C22semidirect
197. C2×C22⋊D83Q16semidirect
326. C22⋊D83C2×Q16semidirect
385. C2×C83#3299semidirect
401. C2×#451D83semidirect
406. C83C2×#3299semidirect
445. #451C2×D83semidirect
775. C2#24919332direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#191284092
C2×Q8×C22⋊D832
#249193322
C2×#191280502
C2×#191280372
C2×#191280352
C2×#191279942
C2×#191279402
C2×#191279392
C2×#191279092
C2×#191278552
C2×Q16×Dic832
C2×(C22⋊D83)⋊C82
C22×#145817162
C2×#103×D832
C2×#451×C832
C2×#329983