Finite Group Databasebeta

← C2×#19146722 #25973316

Subgroups — C2×#19146722 #25973316

Order 11008.

2178 conjugacy classes of subgroups.

The subgroup lattice has 812 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583584C211yesmaximal, characteristic, complemented
2C2×#14583568C211yesmaximal, characteristic
3#19146722C2116yesmaximal, direct product factor
4C2×#14583262C211yesmaximal, characteristic, complemented
5C2×#14583217C211yesmaximal, characteristic, complemented
6C2×#14583221C211yesmaximal, characteristic, complemented
7C2×#14583208C211yesmaximal, characteristic, complemented
8C2×#14583145C211yesmaximal, characteristic, complemented
9C2×#14583127C211yesmaximal, characteristic, complemented
10C2×#14583098C211yesmaximal, characteristic, complemented
11C2×#14583064C211yesmaximal, characteristic, complemented
12C2×#14583061C211yesmaximal, characteristic, complemented
13C2×#14583003C211yesmaximal, characteristic, complemented
14C2×#14582968C211yesmaximal, characteristic, complemented
15C2×#14582894C211yesmaximal, characteristic, complemented
16C2×C43×#417C211yesmaximal, characteristic, complemented
17C22×#10621902C2211yescharacteristic
18C22×#10621885C2211yescharacteristic
19C22×#10621873C2211yescharacteristic
20C22×#10621883C2211yescharacteristic
21C22×C8×D43C2211yescharacteristic
22#14583584—24no—
23#14583584C2218yescomplemented
24#14583568—24no—
25#14583568C2218yes—
26C2×#13063321—21no—
27C2×#13063321C2211yescharacteristic
28C2×#13063320—21no—
29C2×#13063316C2211yescharacteristic
30C2×#13063315—21no—
31C2×#13063308—21no—
32C2×#13063305C2211yescharacteristic
33C2×#13063304C2211yescharacteristic
34C2×#13063299—21no—
35C2×#13063299C2211yescharacteristic
36C2×#13063296—21no—
37C2×#13063296C2211yescharacteristic
38C2×Q8×Dic43C2211yescharacteristic
39C2×#13063290C2211yescharacteristic
40C2×C4×C22⋊D43—21no—
41C2×C4×C22⋊D43C2211yescharacteristic
42C2×#13063284—21no—
43C2×#13063283C2211yescharacteristic
44#14583262C2218yescomplemented
45#14583221C2218yescomplemented
46#14583217C2218yescomplemented
47#14583208C2218yescomplemented
48#14583145C2218yescomplemented
49#14583127C2218yescomplemented
50#14583098C2218yescomplemented
51#14583064C2218yescomplemented
52#14583061C2218yescomplemented
53#14583003C2218yescomplemented
54#14582968C2218yescomplemented
55C2×#13063259C2211yescharacteristic
56C2×#13063256C2211yescharacteristic
57C2×#13063256C2211yescharacteristic
58C2×Dic43⋊C8C2211yescharacteristic
59#14582894C2218yescomplemented
60C2×#13063250C2211yescharacteristic
61C2×#13063249C2211yescharacteristic
62C2×#13063247C2211yescharacteristic
63C2×#13063246C2211yescharacteristic
64C2×#13063245C2211yescharacteristic
65C2×#13063245C2211yescharacteristic
66C2×C22⋊(C43⋊C8)C2211yescharacteristic
67C2×(C2×D43)⋊C8C2211yescharacteristic
68C2×#13063235C2211yescharacteristic
69C22×#41×C43C2211yescharacteristic
70C22×M16×C43C2211yescharacteristic
71C22×C4⋊C4×C43C2211yescharacteristic
72C43×#417C2218yescomplemented
73C2×#103×C43C2211yescharacteristic
74C2×#103×C43C2211yescharacteristic
75C2×#102×C43C2211yescharacteristic
76C2×#102×C43C2211yescharacteristic
77C2×#10621902—22no—
78C2×#10621902—24no—
79C2×#10621902—42no—
80C2×#10621902C2314yes—
81C22×Dic86C2311yescharacteristic
82C22×D172—21no—
83C22×D172C2311yescharacteristic
84C22×C22⋊D43—21no—
85C22×C22⋊D43—21no—
86C22×C22⋊D43—21no—
87C22×C22⋊D43—21no—
88C22×C22⋊D43D411yescharacteristic
89C22×C4×D43—21no—
90C22×C4×D43C2311yescharacteristic
91C2×#10621885—24no—
92C2×#10621885C2314yes—
93C2×#10621873—42no—
94C2×#10621873C2314yes—
95C2×#10621883—42no—
96C2×#10621883C2314yes—
97C22×C43⋊C8C2311yescharacteristic
98C22×C43⋊C8C2311yescharacteristic
99C2×C8×D43—42no—
100C2×C8×D43C2314yes—
101#13063321—28no—
102#13063321—22no—
103#13063321C2314yes—
104#13063320—28no—
105#13063316—22no—
106#13063316C2314yes—
107#13063315—28no—
108#13063308—28no—
109#13063305—22no—
110#13063305C2314yes—
111#13063304—22no—
112#13063304C2314yes—
113#13063299—22no—
114#13063299—28no—
115#13063299C2314yes—
116#13063296—22no—
117#13063296—28no—
118#13063296C2314yes—
119Q8×Dic43—22no—
120Q8×Dic43C2314yes—
121#13063290—22no—
122#13063290C2314yes—
123C4×C22⋊D43—28no—
124C4×C22⋊D43D414yes—
125C4×C22⋊D43C2314yes—
126#13063284—28no—
127#13063283—22no—
128#13063283C2314yes—
129C2×C4⋊Dic43—21no—
130C2×C4⋊Dic43—21no—
131C2×C4⋊Dic43—21no—
132C2×C4⋊Dic43C2311yescharacteristic
133C2×C4⋊Dic43C2311yescharacteristic
134C2×Dic43⋊C4—21no—
135C2×Dic43⋊C4—21no—
136C2×Dic43⋊C4—21no—
137C2×Dic43⋊C4D411yescharacteristic
138C2×C22⋊Dic43—21no—
139C2×C22⋊Dic43—21no—
140C2×C22⋊Dic43D411yescharacteristic
141C2×(C2×D43)⋊C4—21no—
142C2×(C2×D43)⋊C4—21no—
143C2×(C2×D43)⋊C4—21no—
144C2×(C2×D43)⋊C4D411yescharacteristic
145C2×C4×Dic43—21no—
146C2×C4×Dic43—21no—
147C2×C4×Dic43—21no—
148C2×C4×Dic43C2311yescharacteristic
149#13063259C2314yes—
150#13063256C2314yes—
151#13063256C2314yes—
152Dic43⋊C8C2314yes—
153#13063250C2314yes—
154#13063249C2314yes—
155#13063247C2314yes—
156#13063246C2314yes—
157#13063245C2314yes—
158#13063245C2314yes—
159C22⋊(C43⋊C8)C2314yes—
160(C2×D43)⋊C8C2314yes—
161#13063235C2314yes—
162C2×#41×C43—22no—
163C2×#41×C43—24no—
164C2×#41×C43—42no—
165C2×#41×C43C2314yes—
166C22×Q8×C43C2311yescharacteristic
167C22×D4×C43—21no—
168C22×D4×C43C2311yescharacteristic
169C23×C4×C43—21no—
170C23×C4×C43—21no—
171C23×C4×C43C2311yescharacteristic
172C2×M16×C43—42no—
173C2×M16×C43C2314yes—
174C22×C8×C43C2311yescharacteristic
175C22×C8×C43C2311yescharacteristic
176C2×C4⋊C4×C43—22no—
177C2×C4⋊C4×C43—21no—
178C2×C4⋊C4×C43C2314yes—
179C2×C4⋊C4×C43C2311yescharacteristic
180C2×C4⋊C4×C43C2311yescharacteristic
181#103×C43C2314yes—
182#103×C43C2314yes—
183#102×C43C2314yes—
184#102×C43C2314yes—
185C24×C43—21no—
186C24×C43C2×D411yescharacteristic
187C23×D43—21no—
188C23×D43C2×D411yescharacteristic
189#41×C43—28no—
190#41×C43—44no—
191#41×C43—48no—
192C2×Q8×C43—21no—
193C2×Q8×C43—22no—
194C2×Q8×C43#4114yes—
195C2×Q8×C43C2412yes—
196C2×D4×C43—21no—
197C2×D4×C43—24no—
198C2×D4×C43—22no—
199C2×D4×C43—22no—
200C2×D4×C43—44no—
201C2×D4×C43C2412yes—
202C22×C4×C43—22no—
203C22×C4×C43—22no—
204C22×C4×C43—24no—
205C22×C4×C43—21no—
206C22×C4×C43—21no—
207C22×C4×C43—21no—
208C22×C4×C43—24no—
209C22×C4×C43—44no—
210C22×C4×C43—44no—
211C22×C4×C43C2×D411yescharacteristic
212C22×C4×C43C2×D412yes—
213C22×C4×C43C2412yes—
214C22×C4×C43C2411yescharacteristic
215C2×C22⋊D43—24no—
216C2×C22⋊D43—24no—
217C2×C22⋊D43—24no—
218C2×C22⋊D43—24no—
219C2×C22⋊D43—42no—
220C2×C22⋊D43—44no—
221C2×C22⋊D43—82no—
222C2×C22⋊D43—82no—
223C2×C22⋊D43—82no—
224C2×C22⋊D43C2×D414yes—
225C22×Dic43—21no—
226C22×Dic43—21no—
227C22×Dic43—21no—
228C22×Dic43C2×D411yescharacteristic
229C22×Dic43C2×D411yescharacteristic
230C22×Dic43C2×D411yescharacteristic
231#10621902—28no—
232#10621902—44no—
233#10621902—48no—
234C2×D172—21no—
235C2×D172—24no—
236C2×D172—22no—
237C2×D172—22no—
238C2×D172—44no—
239C2×D172C2412yes—
240C2×C4×D43—22no—
241C2×C4×D43—22no—
242C2×C4×D43—24no—
243C2×C4×D43—44no—
244C2×C4×D43C2×D412yes—
245C2×C4×D43C2412yes—
246C2×Dic86—22no—
247C2×Dic86—22no—
248C2×Dic86—21no—
249C2×Dic86C2412yes—
250M16×C43—44no—
251C2×C8×C43—22no—
252C2×C8×C43—22no—
253C2×C8×C43C2412yes—
254C2×C8×C43C2412yes—
255C4⋊C4×C43—21no—
256C4⋊C4×C43—21no—
257C4⋊C4×C43—24no—
258C4⋊C4×C43C2412yes—
259C4⋊C4×C43C2412yes—
260C22⋊Dic43—24no—
261C22⋊Dic43—24no—
262C22⋊Dic43C2×D414yes—
263#10621885—28no—
264#10621883—44no—
265(C2×D43)⋊C4—24no—
266(C2×D43)⋊C4—24no—
267(C2×D43)⋊C4—24no—
268(C2×D43)⋊C4C2×D414yes—
269C4⋊Dic43—21no—
270C4⋊Dic43—21no—
271C4⋊Dic43—24no—
272C4⋊Dic43—24no—
273C4⋊Dic43—24no—
274C4⋊Dic43C2412yes—
275C4⋊Dic43C2412yes—
276Dic43⋊C4—24no—
277Dic43⋊C4—24no—
278Dic43⋊C4—24no—
279Dic43⋊C4C2×D414yes—
280C4×Dic43—24no—
281C4×Dic43—24no—
282C4×Dic43—24no—
283C4×Dic43C2×D412yes—
284C4×Dic43C2412yes—
285C2×C43⋊C8—22no—
286C2×C43⋊C8—22no—
287C2×C43⋊C8C2412yes—
288C2×C43⋊C8C2412yes—
289#10621873—44no—
290C8×D43—44no—
291C23×C43—22no—
292C23×C43—22no—
293C23×C43—22no—
294C23×C43—22no—
295C23×C43—42no—
296C23×C43—42no—
297C23×C43—42no—
298C23×C43C22×D412yes—
299C23×C43C22×D411yescharacteristic
300C22×D43—22no—
301C22×D43—22no—
302C22×D43—22no—
303C22×D43—22no—
304C22×D43—42no—
305C22×D43—42no—
306C22×D43—42no—
307C22×D43C22×D412yes—
308Q8×C43—24no—
309Q8×C43—22no—
310Q8×C43C2×#4114yes—
311D4×C43—22no—
312D4×C43—22no—
313D4×C43—48no—
314D4×C43—42no—
315C2×C4×C43—24no—
316C2×C4×C43—22no—
317C2×C4×C43—22no—
318C2×C4×C43—24no—
319C2×C4×C43—22no—
320C2×C4×C43—22no—
321C2×C4×C43—22no—
322C2×C4×C43—22no—
323C2×C4×C43—48no—
324C2×C4×C43—48no—
325C2×C4×C43—42no—
326C2×C4×C43—42no—
327C2×C4×C43C22×D412yes—
328C2×C4×C43C22×D411yescharacteristic
329C2×C4×C43C2×#4112yes—
330C2×C4×C43H(5,𝔽2)12yes—
331C2×C4×C43C2511yescharacteristic
332C22⋊D43—44no—
333C22⋊D43—48no—
334C22⋊D43—84no—
335C22⋊D43—84no—
336C22⋊D43—84no—
337C2×Dic43—22no—
338C2×Dic43—22no—
339C2×Dic43—22no—
340C2×Dic43—22no—
341C2×Dic43—22no—
342C2×Dic43—22no—
343C2×Dic43—42no—
344C2×Dic43—42no—
345C2×Dic43—42no—
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—
357Dic86—22no—
358Dic86—22no—
359Dic86—42no—
360C8×C43—22no—
361C8×C43—22no—
362C43⋊C8—22no—
363C43⋊C8—22no—
364C2×#3317—431nomaximal, Sylow
365C22×C43—22no—
366C22×C43—22no—
367C22×C43—22no—
368C22×C43—44no—
369C22×C43—42no—
370C22×C43—42no—
371C22×C43—42no—
372C22×C43—84no—
373C22×C43#54612yes—
374C22×C43#57512yes—
375C22×C43#57712yes—
376C22×C43C23×D411yescharacteristic
377C2×D43—22no—
378C2×D43—22no—
379C2×D43—22no—
380C2×D43—44no—
381C2×D43—42no—
382C2×D43—42no—
383C2×D43—42no—
384C2×D43—84no—
385C4×C43—24no—
386C4×C43—22no—
387C4×C43—42no—
388C4×C43—42no—
389C4×C43#54612yes—
390C4×C43C22×#4111yescharacteristic
391C4×C43C2×H(5,𝔽2)11yescharacteristic
392Dic43—22no—
393Dic43—22no—
394Dic43—22no—
395Dic43—42no—
396Dic43—42no—
397Dic43—42no—
398C2×#552—431no—
399C2×#550—431no—
400#3317—4316no—
401C2×#490—431no—
402C2×#481—431no—
403C2×#482—431no—
404C2×#479—431no—
405C2×#468—431no—
406C2×#465—431no—
407C2×#460—431no—
408C2×#452—431no—
409C2×#452—431no—
410C2×#441—431no—
411C2×#435—431no—
412C2×#417D4311yescharacteristic, complemented
413C2×#416—431no—
414C2×C43—42no—
415C2×C43—82no—
416C2×C43#331714yescomplemented
417C2×C43C2×#54611yescharacteristic
418C2×C43C2×#57511yescharacteristic
419C2×C43C2×#57711yescharacteristic
420D43—42no—
421D43—82no—
422C22×#41—431no—
423C22×#41C2×D4311yescharacteristic
424C22×Q16—431no—
425C22×SD16—431no—
426C22×SD16—431no—
427C22×M16C2×D4311yescharacteristic
428C23×C8—431no—
429#552—438no—
430#552—864no—
431#550—438no—
432#550—864no—
433C2×#127—431no—
434C2×#127—861no—
435C2×#126—861no—
436C2×#125—431no—
437C2×#125—861no—
438C2×#123—861no—
439C2×C22⋊Q8—431no—
440C2×C22⋊Q8—431no—
441C2×#121—431no—
442C2×#121—431no—
443C2×#121—861no—
444C2×#121—861no—
445C2×C4×Q8—431no—
446C2×C4×Q8—431no—
447C2×C4×D4—431no—
448C2×C4×D4—861no—
449C2×#117—431no—
450C2×#117—861no—
451C22×C4⋊C4C2×D4311yescharacteristic
452#490—438no—
453#482—438no—
454#481—438no—
455#479—438no—
456#468—438no—
457#465—438no—
458#460—438no—
459#452—438no—
460#452—438no—
461#441—438no—
462#435—438no—
463C2×#107—431no—
464C2×#106—431no—
465C2×#106—431no—
466C2×C4⋊C8—431no—
467#417C2×D4318yescomplemented
468#416—438no—
469C2×#103—431no—
470C2×#103—431no—
471C2×#103C2×D4311yescharacteristic
472C2×#103C2×D4311yescharacteristic
473C2×#102—431no—
474C2×#102—431no—
475C2×#102—431no—
476C2×#102—431no—
477C2×#102C2×D4311yescharacteristic
478C2×#102C2×D4311yescharacteristic
479C2×C22⋊C8—431no—
480C2×C22⋊C8—431no—
481C2×#97—431no—
482C43C2×#331711yescharacteristic, complemented, Sylow
483C2×#41—22no—
484C2×#41—24no—
485C2×#41—42no—
486C2×#41—434no—
487C2×#41—862no—
488C2×#41—864no—
489C2×#41—1722no—
490C2×#41C22×D4314yes—
491C22×Q8—431no—
492C22×Q8C22×D4311yescharacteristic
493C22×D4—21no—
494C22×D4—431no—
495C22×D4—431no—
496C22×D4—861no—
497C22×D4—861no—
498C22×D4—861no—
499C22×D4—861no—
500C22×D4—861no—
501C22×D4C22×D4311yescharacteristic
502C23×C4—21no—
503C23×C4—21no—
504C23×C4—431no—
505C23×C4—861no—
506C23×C4C22×D4311yescharacteristic
507C2×Q16—434no—
508C2×Q16—864no—
509C2×SD16—434no—
510C2×SD16—434no—
511C2×SD16—1722no—
512C2×SD16—1722no—
513C2×M16—42no—
514C2×M16C22×D4314yes—
515C22×C8—431no—
516C22×C8—431no—
517C22×C8—434no—
518C22×C8—1722no—
519C22×C8C22×D4311yescharacteristic
520C22×C8C22×D4311yescharacteristic
521#127—434no—
522#127—862no—
523#127—868no—
524#126—868no—
525#125—434no—
526#125—862no—
527#125—868no—
528#123—868no—
529C22⋊Q8—434no—
530C22⋊Q8—434no—
531C22⋊Q8—862no—
532C22⋊Q8—862no—
533#121—434no—
534#121—434no—
535#121—868no—
536#121—868no—
537#121—862no—
538#121—862no—
539C4×Q8—434no—
540C4×Q8—434no—
541C4×Q8—862no—
542C4×Q8—862no—
543C4×D4—434no—
544C4×D4—434no—
545C4×D4—868no—
546#117—434no—
547#117—868no—
548#117—862no—
549C2×C4⋊C4—21no—
550C2×C4⋊C4—22no—
551C2×C4⋊C4—431no—
552C2×C4⋊C4—431no—
553C2×C4⋊C4—431no—
554C2×C4⋊C4—861no—
555C2×C4⋊C4—861no—
556C2×C4⋊C4—861no—
557C2×C4⋊C4—861no—
558C2×C4⋊C4—861no—
559C2×C4⋊C4—861no—
560C2×C4⋊C4C22×D4311yescharacteristic
561C2×C4⋊C4C22×D4311yescharacteristic
562C2×C4⋊C4C22×D4314yes—
563C2×C22⋊C4—431no—
564C2×C22⋊C4—431no—
565C2×C22⋊C4—861no—
566C2×C22⋊C4—861no—
567C2×C22⋊C4—861no—
568C2×C22⋊C4—861no—
569C2×C22⋊C4—861no—
570C2×C42—431no—
571C2×C42—861no—
572C2×C42—861no—
573C2×C42—861no—
574#107—434no—
575#106—434no—
576#106—434no—
577C4⋊C8—434no—
578#103—434no—
579#103—434no—
580#103C22×D4314yes—
581#103C22×D4314yes—
582#102—434no—
583#102—434no—
584#102—434no—
585#102—434no—
586#102C22×D4314yes—
587#102C22×D4314yes—
588C22⋊C8—434no—
589C22⋊C8—434no—
590#97—434no—
591C24—21no—
592C24—431no—
593C24—861no—
594C24D4×D4311yescharacteristic
595#41—28no—
596#41—44no—
597#41—48no—
598#41—868no—
599#41—1724no—
600#41—1728no—
601C2×Q8—21no—
602C2×Q8—22no—
603C2×Q8—432no—
604C2×Q8—861no—
605C2×Q8—862no—
606C2×Q8—862no—
607C2×Q8#1062189814yes—
608C2×Q8C23×D4312yes—
609C2×D4—24no—
610C2×D4—21no—
611C2×D4—22no—
612C2×D4—22no—
613C2×D4—44no—
614C2×D4—434no—
615C2×D4—432no—
616C2×D4—864no—
617C2×D4—864no—
618C2×D4—864no—
619C2×D4—864no—
620C2×D4—864no—
621C2×D4—861no—
622C2×D4—862no—
623C2×D4—862no—
624C2×D4—3442no—
625C2×D4—3442no—
626C2×D4—3442no—
627C2×D4—1724no—
628C2×D4—1722no—
629C2×D4—1724no—
630C2×D4C23×D4312yes—
631C22×C4—21no—
632C22×C4—22no—
633C22×C4—22no—
634C22×C4—24no—
635C22×C4—21no—
636C22×C4—21no—
637C22×C4—24no—
638C22×C4—44no—
639C22×C4—44no—
640C22×C4—431no—
641C22×C4—431no—
642C22×C4—431no—
643C22×C4—432no—
644C22×C4—432no—
645C22×C4—864no—
646C22×C4—862no—
647C22×C4—862no—
648C22×C4—861no—
649C22×C4—861no—
650C22×C4—861no—
651C22×C4—1724no—
652C22×C4D4×D4312yes—
653C22×C4D4×D4311yescharacteristic
654C22×C4C23×D4312yes—
655C22×C4C23×D4311yescharacteristic
656Q16—868no—
657SD16—1724no—
658SD16—1724no—
659M16—44no—
660C2×C8—22no—
661C2×C8—22no—
662C2×C8—432no—
663C2×C8—432no—
664C2×C8—862no—
665C2×C8—862no—
666C2×C8—1724no—
667C2×C8C23×D4312yes—
668C2×C8C23×D4312yes—
669C4⋊C4—21no—
670C4⋊C4—21no—
671C4⋊C4—24no—
672C4⋊C4—434no—
673C4⋊C4—432no—
674C4⋊C4—432no—
675C4⋊C4—864no—
676C4⋊C4—864no—
677C4⋊C4—864no—
678C4⋊C4—864no—
679C4⋊C4—864no—
680C4⋊C4—861no—
681C4⋊C4—861no—
682C4⋊C4—864no—
683C4⋊C4C23×D4312yes—
684C4⋊C4C23×D4312yes—
685C22⋊C4—434no—
686C22⋊C4—434no—
687C22⋊C4—864no—
688C22⋊C4—864no—
689C22⋊C4—864no—
690C22⋊C4—864no—
691C22⋊C4—864no—
692C42—432no—
693C42—432no—
694C42—864no—
695C42—864no—
696C42—864no—
697C23—22no—
698C23—22no—
699C23—22no—
700C23—22no—
701C23—42no—
702C23—42no—
703C23—42no—
704C23—432no—
705C23—862no—
706C23—862no—
707C23—862no—
708C23—862no—
709C23—1722no—
710C23—1722no—
711C23—1722no—
712C23C2×D4×D4312yes—
713C23C2×D4×D4311yescharacteristic
714Q8—22no—
715Q8—24no—
716Q8—862no—
717Q8—862no—
718Q8—1722no—
719Q8C2×#1062189814yes—
720D4—22no—
721D4—22no—
722D4—48no—
723D4—42no—
724D4—862no—
725D4—862no—
726D4—3444no—
727D4—3444no—
728D4—3444no—
729D4—1728no—
730D4—1724no—
731D4—1728no—
732D4—1722no—
733C2×C4—22no—
734C2×C4—22no—
735C2×C4—24no—
736C2×C4—22no—
737C2×C4—22no—
738C2×C4—24no—
739C2×C4—22no—
740C2×C4—22no—
741C2×C4—48no—
742C2×C4—48no—
743C2×C4—42no—
744C2×C4—42no—
745C2×C4—432no—
746C2×C4—432no—
747C2×C4—432no—
748C2×C4—862no—
749C2×C4—862no—
750C2×C4—862no—
751C2×C4—862no—
752C2×C4—862no—
753C2×C4—864no—
754C2×C4—862no—
755C2×C4—862no—
756C2×C4—862no—
757C2×C4—1728no—
758C2×C4—1722no—
759C2×C4—1722no—
760C2×C4—1722no—
761C2×C4C2×D4×D4312yes—
762C2×C4C2×D4×D4311yescharacteristic
763C2×C4C2×#1062189812yes—
764C2×C4#1306337012yes—
765C2×C4C24×D4311yescharacteristic
766C8—22no—
767C8—22no—
768C8—862no—
769C8—862no—
770C22—22no—
771C22—22no—
772C22—22no—
773C22—44no—
774C22—42no—
775C22—42no—
776C22—42no—
777C22—84no—
778C22—862no—
779C22—862no—
780C22—862no—
781C22—3444no—
782C22—1722no—
783C22—1722no—
784C22—1722no—
785C22—1724no—
786C22#1458353912yes—
787C22#1458369512yes—
788C22#1458370812yes—
789C22C22×D4×D4311yescharacteristic
790C4—22no—
791C4—24no—
792C4—42no—
793C4—42no—
794C4—862no—
795C4—862no—
796C4—862no—
797C4—1722no—
798C4—1722no—
799C4—1722no—
800C4#1458353912yes—
801C4C22×#1062189811yescharacteristic
802C4C2×#1306337011yescharacteristic
803C2—42no—
804C2—82no—
805C2—3442no—
806C2—1722no—
807C2#1914672214yesdirect product factor
808C2C2×#1458353911yescharacteristic
809C2C2×#1458369511yescharacteristic
810C2C2×#1458370811yescharacteristic
subgroupG/H
centerC23C2×D4×D43
commutator, cosocleC2×C4×C43C25
FrattiniC2×C4C24×D43
FittingC2×C43×#417C2
socleC23×C43C22×D4
prime radicalC2×#14583568C2
hypercenterC2×#417D43
hypocenterC43C2×#3317
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#417

Complements

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

NH ≅ G/Ntype
1. C2×#14583584C2semidirect
3. #19146722C2direct (N × H)
4. C2×#14583262C2semidirect
5. C2×#14583217C2semidirect
6. C2×#14583221C2semidirect
7. C2×#14583208C2semidirect
8. C2×#14583145C2semidirect
9. C2×#14583127C2semidirect
10. C2×#14583098C2semidirect
11. C2×#14583064C2semidirect
12. C2×#14583061C2semidirect
13. C2×#14583003C2semidirect
14. C2×#14582968C2semidirect
15. C2×#14582894C2semidirect
16. C2×C43×#417C2semidirect
23. #14583584C22semidirect
44. #14583262C22semidirect
45. #14583221C22semidirect
46. #14583217C22semidirect
47. #14583208C22semidirect
48. #14583145C22semidirect
49. #14583127C22semidirect
50. #14583098C22semidirect
51. #14583064C22semidirect
52. #14583061C22semidirect
53. #14583003C22semidirect
54. #14582968C22semidirect
59. #14582894C22semidirect
72. C43×#417C22semidirect
412. C2×#417D43semidirect
416. C2×C43#3317semidirect
467. #417C2×D43semidirect
482. C43C2×#3317semidirect
807. C2#19146722direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#145835842
C2×#145835682
#191467222
C2×#145832622
C2×#145832172
C2×#145832212
C2×#145832082
C2×#145831452
C2×#145831272
C2×#145830982
C2×#145830642
C2×#145830612
C2×#145830032
C2×#145829682
C2×#145828942
C2×C43×#4172
C2×#331743