Finite Group Databasebeta

← C2×#19145699 #25967987

Subgroups — C2×#19145699 #25967987

Order 11008.

2086 conjugacy classes of subgroups.

The subgroup lattice has 810 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583518C211yesmaximal, characteristic, complemented
2C2×#14583474C211yesmaximal, characteristic, complemented
3#19145699C2116yesmaximal, direct product factor
4C2×#14583281C211yesmaximal, characteristic, complemented
5C2×#14583259C211yesmaximal, characteristic, complemented
6C2×#14583249C211yesmaximal, characteristic, complemented
7C2×#14583123C211yesmaximal, characteristic, complemented
8C2×#14583107C211yesmaximal, characteristic, complemented
9C2×#14583116C211yesmaximal, characteristic, complemented
10C2×#14583102C211yesmaximal, characteristic, complemented
11C2×#14583060C211yesmaximal, characteristic, complemented
12C2×#14583043C211yesmaximal, characteristic
13C2×#14583053C211yesmaximal, characteristic, complemented
14C2×#14583036C211yesmaximal, characteristic, complemented
15C2×#14582961C211yesmaximal, characteristic, complemented
16C2×C43×#497C211yesmaximal, characteristic, complemented
17C22×#10621902C2211yescharacteristic
18C22×Q8×D43C2211yescharacteristic
19C22×#10621885C2211yescharacteristic
20C22×#10621883C2211yescharacteristic
21C22×#10621884C2211yescharacteristic
22C22×#10621882C2211yescharacteristic
23#14583518—24no—
24#14583518C2218yescomplemented
25#14583474—24no—
26#14583474C2218yescomplemented
27C2×#13063325C2211yescharacteristic
28C2×#13063323C2211yescharacteristic
29C2×#13063318—21no—
30C2×#13063314C2211yescharacteristic
31C2×#13063313C2211yescharacteristic
32C2×#13063311—21no—
33C2×#13063310—21no—
34C2×#13063310—21no—
35C2×#13063309—21no—
36C2×#13063303—21no—
37C2×#13063303—21no—
38C2×#13063302—21no—
39C2×#13063301C2211yescharacteristic
40C2×#13063296C2211yescharacteristic
41C2×Q8×Dic43C2211yescharacteristic
42C2×D4×Dic43C2211yescharacteristic
43C2×#13063282C2211yescharacteristic
44#14583281C2218yescomplemented
45#14583259C2218yescomplemented
46#14583249C2218yescomplemented
47#14583123C2218yescomplemented
48#14583116C2218yescomplemented
49#14583107C2218yescomplemented
50#14583102C2218yescomplemented
51#14583060C2218yescomplemented
52#14583053C2218yescomplemented
53#14583043C2218yes—
54#14583036C2218yescomplemented
55#14582961C2218yescomplemented
56C2×Dic43⋊C8C2211yescharacteristic
57C2×Dic43⋊C8C2211yescharacteristic
58C2×#13063250C2211yescharacteristic
59C2×#13063250C2211yescharacteristic
60C2×#13063249C2211yescharacteristic
61C2×#13063249C2211yescharacteristic
62C2×#13063249C2211yescharacteristic
63C2×#13063249C2211yescharacteristic
64C2×#13063247C2211yescharacteristic
65C2×#13063247C2211yescharacteristic
66C2×(C2×D43)⋊C8C2211yescharacteristic
67C2×(C2×D43)⋊C8C2211yescharacteristic
68C2×C4×C43⋊C8C2211yescharacteristic
69C22×Q16×C43C2211yescharacteristic
70C22×Q16×C43C2211yescharacteristic
71C22×SD16×C43C2211yescharacteristic
72C22×SD16×C43C2211yescharacteristic
73C2×C4⋊Q8×C43C2211yescharacteristic
74C2×#124×C43C2211yescharacteristic
75C43×#497C2218yescomplemented
76C2×#97×C43C2211yescharacteristic
77C2×#10621902—22no—
78C2×#10621902—42no—
79C2×#10621902—42no—
80C2×#10621902C2314yes—
81C22×Dic86—21no—
82C22×Dic86—21no—
83C22×Dic86C2311yescharacteristic
84C2×Q8×D43—22no—
85C2×Q8×D43—42no—
86C2×Q8×D43—42no—
87C2×Q8×D43C2314yes—
88C22×D172—21no—
89C22×D172C2311yescharacteristic
90C22×C22⋊D43—21no—
91C23×Dic43—21no—
92C22×C4×D43—21no—
93C22×C4×D43—21no—
94C22×C4×D43C2311yescharacteristic
95C2×#10621885—42no—
96C2×#10621885C2314yes—
97C2×#10621883—42no—
98C2×#10621883C2314yes—
99C2×#10621884—42no—
100C2×#10621884C2314yes—
101C2×#10621882—42no—
102C2×#10621882C2314yes—
103C22×C43⋊C8C2311yescharacteristic
104C22×C43⋊C8C2311yescharacteristic
105#13063325—22no—
106#13063325C2314yes—
107#13063323—22no—
108#13063323C2314yes—
109#13063318—28no—
110#13063314—22no—
111#13063314C2314yes—
112#13063313—22no—
113#13063313C2314yes—
114#13063311—28no—
115#13063310—28no—
116#13063310—28no—
117#13063309—28no—
118#13063303—28no—
119#13063303—28no—
120#13063302—28no—
121#13063301—22no—
122#13063301C2314yes—
123#13063296—22no—
124#13063296C2314yes—
125Q8×Dic43—22no—
126Q8×Dic43C2314yes—
127D4×Dic43—22no—
128D4×Dic43C2314yes—
129#13063282D414yes—
130#13063282C2314yes—
131C2×C4⋊Dic43—21no—
132C2×C4⋊Dic43—21no—
133C2×C4⋊Dic43C2311yescharacteristic
134C2×C4⋊Dic43C2311yescharacteristic
135C2×Dic43⋊C4—21no—
136C2×Dic43⋊C4—21no—
137C2×Dic43⋊C4—21no—
138C2×Dic43⋊C4D411yescharacteristic
139C2×Dic43⋊C4D411yescharacteristic
140C2×C22⋊Dic43—21no—
141C2×C22⋊Dic43—21no—
142C2×(C2×D43)⋊C4—21no—
143C2×(C2×D43)⋊C4—21no—
144C2×(C2×D43)⋊C4—21no—
145C2×(C2×D43)⋊C4—21no—
146C2×(C2×D43)⋊C4—21no—
147C2×(C2×D43)⋊C4D411yescharacteristic
148C2×(C2×D43)⋊C4D411yescharacteristic
149C2×C4×Dic43—21no—
150C2×C4×Dic43C2311yescharacteristic
151Dic43⋊C8C2314yes—
152Dic43⋊C8C2314yes—
153#13063250C2314yes—
154#13063250C2314yes—
155#13063249C2314yes—
156#13063249C2314yes—
157#13063249C2314yes—
158#13063249C2314yes—
159#13063247C2314yes—
160#13063247C2314yes—
161(C2×D43)⋊C8C2314yes—
162(C2×D43)⋊C8C2314yes—
163C4×C43⋊C8C2314yes—
164C22×Q8×C43C2311yescharacteristic
165C22×Q8×C43C2311yescharacteristic
166C22×Q8×C43C2311yescharacteristic
167C22×D4×C43C2311yescharacteristic
168C2×Q16×C43—42no—
169C2×Q16×C43—42no—
170C2×Q16×C43C2314yes—
171C2×Q16×C43C2314yes—
172C2×SD16×C43—42no—
173C2×SD16×C43—42no—
174C2×SD16×C43C2314yes—
175C2×SD16×C43C2314yes—
176C22×C8×C43C2311yescharacteristic
177C22×C8×C43C2311yescharacteristic
178C4⋊Q8×C43—22no—
179C4⋊Q8×C43C2314yes—
180#124×C43—22no—
181#124×C43C2314yes—
182C2×C4⋊C4×C43—21no—
183C2×C4⋊C4×C43—21no—
184C2×C22⋊C4×C43—21no—
185C2×C22⋊C4×C43—21no—
186C2×C42×C43C2311yescharacteristic
187#97×C43C2314yes—
188C24×C43—21no—
189C23×D43—21no—
190C23×D43C2×D411yescharacteristic
191C2×Q8×C43—21no—
192C2×Q8×C43—21no—
193C2×Q8×C43—21no—
194C2×Q8×C43—22no—
195C2×Q8×C43—22no—
196C2×Q8×C43—22no—
197C2×Q8×C43—22no—
198C2×Q8×C43—22no—
199C2×Q8×C43—22no—
200C2×Q8×C43C2412yes—
201C2×Q8×C43C2412yes—
202C2×Q8×C43C2412yes—
203C2×D4×C43—21no—
204C2×D4×C43—22no—
205C2×D4×C43—22no—
206C2×D4×C43C2412yes—
207C22×C4×C43—21no—
208C22×C4×C43—21no—
209C22×C4×C43—21no—
210C22×C4×C43C2×D411yescharacteristic
211C22×C4×C43C2×D411yescharacteristic
212C22×C4×C43C2411yescharacteristic
213C2×C22⋊D43—24no—
214C2×C22⋊D43—82no—
215C22×Dic43—24no—
216C22×Dic43—21no—
217C22×Dic43—21no—
218C22×Dic43—21no—
219C22×Dic43—82no—
220C22×Dic43C2×D411yescharacteristic
221C22×Dic43C2×D411yescharacteristic
222C22×Dic43C2×D411yescharacteristic
223#10621902—44no—
224#10621902—44no—
225#10621902—48no—
226Q8×D43—44no—
227Q8×D43—44no—
228Q8×D43—48no—
229C2×D172—21no—
230C2×D172—24no—
231C2×D172—22no—
232C2×D172—22no—
233C2×D172—44no—
234C2×D172C2412yes—
235C2×C4×D43—22no—
236C2×C4×D43—22no—
237C2×C4×D43—24no—
238C2×C4×D43—24no—
239C2×C4×D43—44no—
240C2×C4×D43—44no—
241C2×C4×D43C2×D412yes—
242C2×C4×D43C2412yes—
243C2×Dic86—22no—
244C2×Dic86—22no—
245C2×Dic86—21no—
246C2×Dic86—24no—
247C2×Dic86—24no—
248C2×Dic86—44no—
249C2×Dic86—82no—
250C2×Dic86C2412yes—
251Q16×C43—44no—
252Q16×C43—44no—
253SD16×C43—44no—
254SD16×C43—44no—
255C2×C8×C43—22no—
256C2×C8×C43—22no—
257C2×C8×C43C2412yes—
258C2×C8×C43C2412yes—
259C4⋊C4×C43—24no—
260C4⋊C4×C43—24no—
261C22⋊C4×C43—24no—
262C22⋊C4×C43—24no—
263C42×C43C2×D412yes—
264C42×C43C2412yes—
265C22⋊Dic43—24no—
266C22⋊Dic43—24no—
267#10621885—44no—
268#10621884—44no—
269#10621883—44no—
270#10621882—44no—
271(C2×D43)⋊C4—24no—
272(C2×D43)⋊C4—24no—
273(C2×D43)⋊C4—24no—
274(C2×D43)⋊C4—24no—
275(C2×D43)⋊C4—24no—
276(C2×D43)⋊C4C2×D414yes—
277(C2×D43)⋊C4C2×D414yes—
278C4⋊Dic43—24no—
279C4⋊Dic43—21no—
280C4⋊Dic43—21no—
281C4⋊Dic43—24no—
282C4⋊Dic43C2412yes—
283C4⋊Dic43C2412yes—
284Dic43⋊C4—24no—
285Dic43⋊C4—24no—
286Dic43⋊C4—24no—
287Dic43⋊C4C2×D414yes—
288Dic43⋊C4C2×D414yes—
289C4×Dic43—24no—
290C4×Dic43C2×D412yes—
291C4×Dic43C2412yes—
292C2×C43⋊C8—22no—
293C2×C43⋊C8—22no—
294C2×C43⋊C8C2412yes—
295C2×C43⋊C8C2412yes—
296C23×C43—22no—
297C23×C43—42no—
298C23×C43—42no—
299C23×C43—42no—
300C23×C43C22×D411yescharacteristic
301C22×D43—22no—
302C22×D43—22no—
303C22×D43—22no—
304C22×D43—22no—
305C22×D43—42no—
306C22×D43—42no—
307C22×D43—42no—
308C22×D43C22×D412yes—
309Q8×C43—22no—
310Q8×C43—22no—
311Q8×C43—22no—
312Q8×C43—22no—
313Q8×C43—22no—
314Q8×C43—22no—
315Q8×C43—42no—
316Q8×C43—42no—
317Q8×C43—42no—
318D4×C43—22no—
319D4×C43—22no—
320D4×C43—42no—
321C2×C4×C43—22no—
322C2×C4×C43—22no—
323C2×C4×C43—22no—
324C2×C4×C43—22no—
325C2×C4×C43—22no—
326C2×C4×C43—42no—
327C2×C4×C43—42no—
328C2×C4×C43—42no—
329C2×C4×C43C22×D412yes—
330C2×C4×C43C22×D412yes—
331C2×C4×C43C22×D411yescharacteristic
332C2×C4×C43H(5,𝔽2)12yes—
333C2×C4×C43H(5,𝔽2)12yes—
334C2×C4×C43C2511yescharacteristic
335C22⋊D43—84no—
336C2×Dic43—22no—
337C2×Dic43—22no—
338C2×Dic43—22no—
339C2×Dic43—22no—
340C2×Dic43—22no—
341C2×Dic43—22no—
342C2×Dic43—42no—
343C2×Dic43—42no—
344C2×Dic43—42no—
345C2×Dic43—84no—
346C2×Dic43C22×D412yes—
347C2×Dic43C22×D412yes—
348C2×Dic43C22×D412yes—
349D172—22no—
350D172—22no—
351D172—48no—
352D172—42no—
353C4×D43—24no—
354C4×D43—22no—
355C4×D43—22no—
356C4×D43—48no—
357C4×D43—48no—
358Dic86—22no—
359Dic86—22no—
360Dic86—48no—
361Dic86—42no—
362Dic86—84no—
363C8×C43—22no—
364C8×C43—22no—
365C43⋊C8—22no—
366C43⋊C8—22no—
367C2×#3225—431nomaximal, Sylow
368C22×C43—42no—
369C22×C43—42no—
370C22×C43—42no—
371C22×C43—84no—
372C22×C43#53512yes—
373C22×C43#57712yes—
374C22×C43#57812yes—
375C22×C43C23×D411yescharacteristic
376C2×D43—22no—
377C2×D43—22no—
378C2×D43—22no—
379C2×D43—44no—
380C2×D43—42no—
381C2×D43—42no—
382C2×D43—42no—
383C2×D43—84no—
384C4×C43—22no—
385C4×C43—22no—
386C4×C43—42no—
387C4×C43—42no—
388C4×C43—42no—
389C4×C43#53512yes—
390C4×C43C2×H(5,𝔽2)11yescharacteristic
391C4×C43C2×H(5,𝔽2)11yescharacteristic
392Dic43—22no—
393Dic43—22no—
394Dic43—22no—
395Dic43—42no—
396Dic43—42no—
397Dic43—42no—
398C2×#542—431no—
399C2×#536—431no—
400#3225—4316no—
401C2×#497D4311yescharacteristic, complemented
402C2×#495—431no—
403C2×#489—431no—
404C2×#487—431no—
405C2×#464—431no—
406C2×#462—431no—
407C2×#463—431no—
408C2×#461—431no—
409C2×#452—431no—
410C2×#449—431no—
411C2×#451—431no—
412C2×#448—431no—
413C2×#433—431no—
414C2×C43—82no—
415C2×C43#322514yescomplemented
416C2×C43C2×#53511yescharacteristic
417C2×C43C2×#57711yescharacteristic
418C2×C43C2×#57811yescharacteristic
419D43—42no—
420D43—82no—
421C22×#41—431no—
422C23×Q8—431no—
423C22×Q16—431no—
424C22×Q16C2×D4311yescharacteristic
425C22×Q16C2×D4311yescharacteristic
426C22×SD16—431no—
427C22×SD16—431no—
428C22×SD16C2×D4311yescharacteristic
429C22×SD16C2×D4311yescharacteristic
430C22×D8—431no—
431#542—438no—
432#542—864no—
433#536—438no—
434#536—864no—
435C2×C4⋊Q8—431no—
436C2×C4⋊Q8—431no—
437C2×C4⋊Q8C2×D4311yescharacteristic
438C2×#126—861no—
439C2×#124—431no—
440C2×#124—431no—
441C2×#124—861no—
442C2×#124C2×D4311yescharacteristic
443C2×#123—861no—
444C2×#123—861no—
445C2×#123—861no—
446C2×C22⋊Q8—431no—
447C2×C22⋊Q8—861no—
448C2×C22⋊Q8—861no—
449C2×C22⋊Q8—861no—
450C2×#121—431no—
451C2×C4×Q8—431no—
452C2×C4×D4—431no—
453C2×#117—431no—
454#497C2×D4318yescomplemented
455#495—438no—
456#489—438no—
457#487—438no—
458#464—438no—
459#463—438no—
460#462—438no—
461#461—438no—
462#452—438no—
463#451—438no—
464#449—438no—
465#448—438no—
466#433—438no—
467C2×C4⋊C8—431no—
468C2×C4⋊C8—431no—
469C2×#103—431no—
470C2×#103—431no—
471C2×#103—431no—
472C2×#103—431no—
473C2×#103—431no—
474C2×#103—431no—
475C2×#102—431no—
476C2×#102—431no—
477C2×C22⋊C8—431no—
478C2×C22⋊C8—431no—
479C2×#97C2×D4311yescharacteristic
480C2×C4×C8—431no—
481C43C2×#322511yescharacteristic, complemented, Sylow
482C2×#41—434no—
483C2×#41—862no—
484C2×#41—1722no—
485C2×#41—1722no—
486C22×Q8—434no—
487C22×Q8—431no—
488C22×Q8—861no—
489C22×Q8—862no—
490C22×Q8—861no—
491C22×Q8—1722no—
492C22×Q8—1722no—
493C22×Q8C22×D4311yescharacteristic
494C22×Q8C22×D4311yescharacteristic
495C22×Q8C22×D4311yescharacteristic
496C22×D4—431no—
497C22×D4—861no—
498C22×D4—861no—
499C22×D4C22×D4311yescharacteristic
500C23×C4—431no—
501C23×C4—861no—
502C23×C4—861no—
503C23×C4—861no—
504C2×Q16—42no—
505C2×Q16—42no—
506C2×Q16—434no—
507C2×Q16—1722no—
508C2×Q16C22×D4314yes—
509C2×Q16C22×D4314yes—
510C2×SD16—42no—
511C2×SD16—42no—
512C2×SD16—434no—
513C2×SD16—434no—
514C2×SD16—1722no—
515C2×SD16—1722no—
516C2×SD16C22×D4314yes—
517C2×SD16C22×D4314yes—
518C2×D8—434no—
519C2×D8—1722no—
520C22×C8—431no—
521C22×C8—431no—
522C22×C8C22×D4311yescharacteristic
523C22×C8C22×D4311yescharacteristic
524C4⋊Q8—22no—
525C4⋊Q8—434no—
526C4⋊Q8—434no—
527C4⋊Q8—862no—
528C4⋊Q8—862no—
529C4⋊Q8C22×D4314yes—
530#126—868no—
531#124—22no—
532#124—434no—
533#124—434no—
534#124—862no—
535#124—868no—
536#124—862no—
537#124C22×D4314yes—
538#123—868no—
539#123—868no—
540#123—868no—
541C22⋊Q8—434no—
542C22⋊Q8—868no—
543C22⋊Q8—868no—
544C22⋊Q8—868no—
545C22⋊Q8—862no—
546#121—434no—
547#121—862no—
548C4×Q8—434no—
549C4×Q8—862no—
550C4×D4—434no—
551C4×D4—862no—
552#117—434no—
553#117—434no—
554C2×C4⋊C4—21no—
555C2×C4⋊C4—21no—
556C2×C4⋊C4—431no—
557C2×C4⋊C4—431no—
558C2×C4⋊C4—431no—
559C2×C4⋊C4—431no—
560C2×C4⋊C4—861no—
561C2×C4⋊C4—861no—
562C2×C4⋊C4—861no—
563C2×C4⋊C4—861no—
564C2×C4⋊C4—861no—
565C2×C22⋊C4—21no—
566C2×C22⋊C4—21no—
567C2×C22⋊C4—431no—
568C2×C22⋊C4—431no—
569C2×C22⋊C4—861no—
570C2×C22⋊C4—861no—
571C2×C22⋊C4—861no—
572C2×C22⋊C4—861no—
573C2×C22⋊C4—861no—
574C2×C22⋊C4—861no—
575C2×C22⋊C4—861no—
576C2×C42—431no—
577C2×C42—861no—
578C2×C42C22×D4311yescharacteristic
579C4⋊C8—434no—
580C4⋊C8—434no—
581#103—434no—
582#103—434no—
583#103—434no—
584#103—434no—
585#103—434no—
586#103—434no—
587#102—434no—
588#102—434no—
589C22⋊C8—434no—
590C22⋊C8—434no—
591#97C22×D4314yes—
592C4×C8—434no—
593C24—21no—
594C24—431no—
595C24—861no—
596#41—1724no—
597#41—1724no—
598#41—1728no—
599C2×Q8—21no—
600C2×Q8—21no—
601C2×Q8—21no—
602C2×Q8—22no—
603C2×Q8—22no—
604C2×Q8—22no—
605C2×Q8—22no—
606C2×Q8—22no—
607C2×Q8—22no—
608C2×Q8—432no—
609C2×Q8—864no—
610C2×Q8—864no—
611C2×Q8—861no—
612C2×Q8—862no—
613C2×Q8—862no—
614C2×Q8—3442no—
615C2×Q8—1724no—
616C2×Q8—1724no—
617C2×Q8—1724no—
618C2×Q8—1728no—
619C2×Q8C23×D4312yes—
620C2×Q8C23×D4312yes—
621C2×Q8C23×D4312yes—
622C2×D4—21no—
623C2×D4—22no—
624C2×D4—22no—
625C2×D4—432no—
626C2×D4—864no—
627C2×D4—864no—
628C2×D4—861no—
629C2×D4—862no—
630C2×D4—862no—
631C2×D4—3442no—
632C2×D4—1724no—
633C2×D4C23×D4312yes—
634C22×C4—21no—
635C22×C4—21no—
636C22×C4—21no—
637C22×C4—431no—
638C22×C4—431no—
639C22×C4—431no—
640C22×C4—432no—
641C22×C4—432no—
642C22×C4—864no—
643C22×C4—864no—
644C22×C4—864no—
645C22×C4—862no—
646C22×C4—862no—
647C22×C4—861no—
648C22×C4—861no—
649C22×C4—861no—
650C22×C4—3442no—
651C22×C4—1724no—
652C22×C4—1724no—
653C22×C4D4×D4311yescharacteristic
654C22×C4D4×D4311yescharacteristic
655C22×C4C23×D4311yescharacteristic
656Q16—44no—
657Q16—44no—
658Q16—1724no—
659SD16—44no—
660SD16—44no—
661SD16—1724no—
662SD16—1724no—
663D8—1724no—
664C2×C8—22no—
665C2×C8—22no—
666C2×C8—432no—
667C2×C8—432no—
668C2×C8—862no—
669C2×C8—862no—
670C2×C8C23×D4312yes—
671C2×C8C23×D4312yes—
672C4⋊C4—24no—
673C4⋊C4—24no—
674C4⋊C4—434no—
675C4⋊C4—434no—
676C4⋊C4—432no—
677C4⋊C4—432no—
678C4⋊C4—864no—
679C4⋊C4—864no—
680C4⋊C4—864no—
681C4⋊C4—864no—
682C4⋊C4—861no—
683C4⋊C4—861no—
684C4⋊C4—864no—
685C22⋊C4—24no—
686C22⋊C4—24no—
687C22⋊C4—434no—
688C22⋊C4—434no—
689C22⋊C4—864no—
690C22⋊C4—864no—
691C22⋊C4—864no—
692C22⋊C4—864no—
693C22⋊C4—864no—
694C22⋊C4—864no—
695C22⋊C4—864no—
696C42—432no—
697C42—432no—
698C42—864no—
699C42D4×D4312yes—
700C42C23×D4312yes—
701C23—22no—
702C23—42no—
703C23—42no—
704C23—42no—
705C23—432no—
706C23—862no—
707C23—862no—
708C23—862no—
709C23—862no—
710C23—1722no—
711C23—1722no—
712C23—1722no—
713C23C2×D4×D4311yescharacteristic
714Q8—22no—
715Q8—22no—
716Q8—22no—
717Q8—22no—
718Q8—22no—
719Q8—22no—
720Q8—42no—
721Q8—42no—
722Q8—42no—
723Q8—862no—
724Q8—862no—
725Q8—3444no—
726Q8—1728no—
727Q8—1722no—
728D4—22no—
729D4—22no—
730D4—42no—
731D4—862no—
732D4—862no—
733D4—3444no—
734D4—1728no—
735D4—1722no—
736C2×C4—22no—
737C2×C4—22no—
738C2×C4—22no—
739C2×C4—22no—
740C2×C4—22no—
741C2×C4—42no—
742C2×C4—42no—
743C2×C4—42no—
744C2×C4—432no—
745C2×C4—432no—
746C2×C4—432no—
747C2×C4—862no—
748C2×C4—862no—
749C2×C4—862no—
750C2×C4—864no—
751C2×C4—862no—
752C2×C4—862no—
753C2×C4—862no—
754C2×C4—862no—
755C2×C4—862no—
756C2×C4—3444no—
757C2×C4—1728no—
758C2×C4—1728no—
759C2×C4—1722no—
760C2×C4—1722no—
761C2×C4—1722no—
762C2×C4C2×D4×D4312yes—
763C2×C4C2×D4×D4312yes—
764C2×C4C2×D4×D4311yescharacteristic
765C2×C4#1306337012yes—
766C2×C4#1306337012yes—
767C2×C4C24×D4311yescharacteristic
768C8—22no—
769C8—22no—
770C8—862no—
771C8—862no—
772C22—42no—
773C22—42no—
774C22—42no—
775C22—84no—
776C22—862no—
777C22—862no—
778C22—862no—
779C22—3444no—
780C22—1722no—
781C22—1722no—
782C22—1722no—
783C22—1724no—
784C22#1458346212yes—
785C22#1458370812yes—
786C22#1458371512yes—
787C22C22×D4×D4311yescharacteristic
788C4—22no—
789C4—22no—
790C4—42no—
791C4—42no—
792C4—42no—
793C4—862no—
794C4—862no—
795C4—862no—
796C4—1722no—
797C4—1722no—
798C4—1722no—
799C4#1458346212yes—
800C4C2×#1306337011yescharacteristic
801C4C2×#1306337011yescharacteristic
802C2—82no—
803C2—3442no—
804C2—1722no—
805C2#1914569914yesdirect product factor
806C2C2×#1458346211yescharacteristic
807C2C2×#1458370811yescharacteristic
808C2C2×#1458371511yescharacteristic
subgroupG/H
centerC23C2×D4×D43
commutator, cosocleC2×C4×C43C25
FrattiniC2×C4C24×D43
FittingC2×C43×#497C2
socleC23×C43C22×D4
prime radicalC2×#14583043C2
hypercenterC2×#497D43
hypocenterC43C2×#3225
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#497

Complements

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

NH ≅ G/Ntype
1. C2×#14583518C2semidirect
2. C2×#14583474C2semidirect
3. #19145699C2direct (N × H)
4. C2×#14583281C2semidirect
5. C2×#14583259C2semidirect
6. C2×#14583249C2semidirect
7. C2×#14583123C2semidirect
8. C2×#14583107C2semidirect
9. C2×#14583116C2semidirect
10. C2×#14583102C2semidirect
11. C2×#14583060C2semidirect
13. C2×#14583053C2semidirect
14. C2×#14583036C2semidirect
15. C2×#14582961C2semidirect
16. C2×C43×#497C2semidirect
24. #14583518C22semidirect
26. #14583474C22semidirect
44. #14583281C22semidirect
45. #14583259C22semidirect
46. #14583249C22semidirect
47. #14583123C22semidirect
48. #14583116C22semidirect
49. #14583107C22semidirect
50. #14583102C22semidirect
51. #14583060C22semidirect
52. #14583053C22semidirect
54. #14583036C22semidirect
55. #14582961C22semidirect
75. C43×#497C22semidirect
401. C2×#497D43semidirect
415. C2×C43#3225semidirect
454. #497C2×D43semidirect
481. C43C2×#3225semidirect
805. C2#19145699direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#145835182
C2×#145834742
#191456992
C2×#145832812
C2×#145832592
C2×#145832492
C2×#145831232
C2×#145831072
C2×#145831162
C2×#145831022
C2×#145830602
C2×#145830432
C2×#145830532
C2×#145830362
C2×#145829612
C2×C43×#4972
C2×#322543