Finite Group Databasebeta

← C2×#19146146 #25971622

Subgroups — C2×#19146146 #25971622

Order 11008.

2774 conjugacy classes of subgroups.

The subgroup lattice has 888 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#13063355C211yesmaximal, characteristic, complemented
2C22×#13063345C211yesmaximal, characteristic, complemented
3C2×#14583558C211yesmaximal, characteristic, complemented
4#19146146C2116yesmaximal, direct product factor
5C2×#14583291C211yesmaximal, characteristic, complemented
6C2×#14583147C211yesmaximal, characteristic, complemented
7C2×#14583138C211yesmaximal, characteristic, complemented
8C2×#14583106C211yesmaximal, characteristic, complemented
9C2×#14583114C211yesmaximal, characteristic, complemented
10C2×#14583061C211yesmaximal, characteristic, complemented
11C2×#14583059C211yesmaximal, characteristic, complemented
12C2×#14583044C211yesmaximal, characteristic, complemented
13C2×#14583054C211yesmaximal, characteristic, complemented
14C2×#14582999C211yesmaximal, characteristic, complemented
15C2×#14582971C211yesmaximal, characteristic, complemented
16C2×C43×#547C211yesmaximal, characteristic, complemented
17C22×#10621898C2211yescharacteristic
18C23×Dic86C2211yescharacteristic
19C2×#13063355—28no—
20C2×#13063355C2218yescomplemented
21C2×#13063345—28no—
22C2×#13063345C2218yescomplemented
23C22×#10621885C2211yescharacteristic
24C22×#10621885C2211yescharacteristic
25C22×#10621885C2211yescharacteristic
26C22×#10621885C2211yescharacteristic
27C22×#10621883C2211yescharacteristic
28C22×#10621883C2211yescharacteristic
29C22×#10621884C2211yescharacteristic
30C22×#10621884C2211yescharacteristic
31C22×#10621882C2211yescharacteristic
32C22×#10621877C2211yescharacteristic
33C23×C43⋊C8C2211yescharacteristic
34#14583558—24no—
35#14583558C2218yescomplemented
36C2×#13063313C2211yescharacteristic
37C2×#13063311—21no—
38C2×#13063304C2211yescharacteristic
39C2×#13063303—21no—
40C2×#13063299C2211yescharacteristic
41C2×#13063297—21no—
42C2×C4×Dic86C2211yescharacteristic
43C2×(C22⋊D43)⋊C4—21no—
44#14583291C2218yescomplemented
45#14583147C2218yescomplemented
46#14583138C2218yescomplemented
47#14583114C2218yescomplemented
48#14583106C2218yescomplemented
49#14583061C2218yescomplemented
50#14583059C2218yescomplemented
51#14583054C2218yescomplemented
52#14583044C2218yescomplemented
53#14582999C2218yescomplemented
54#14582971C2218yescomplemented
55C2×#13063258C2211yescharacteristic
56C2×C4⋊(C43⋊C8)C2211yescharacteristic
57C2×#13063249C2211yescharacteristic
58C2×#13063249C2211yescharacteristic
59C2×#13063248C2211yescharacteristic
60C2×#13063248C2211yescharacteristic
61C2×#13063246C2211yescharacteristic
62C2×#13063245C2211yescharacteristic
63C2×C22⋊(C43⋊C8)C2211yescharacteristic
64C2×C22⋊(C43⋊C8)C2211yescharacteristic
65C2×#13063236C2211yescharacteristic
66C22×#41×C43C2211yescharacteristic
67C22×#41×C43C2211yescharacteristic
68C43×#547—24no—
69C43×#547C2218yescomplemented
70C2×C4⋊Q8×C43C2211yescharacteristic
71C2×#123×C43—21no—
72C2×#123×C43—21no—
73C2×C22⋊Q8×C43C2211yescharacteristic
74C2×C22⋊Q8×C43C2211yescharacteristic
75C2×#121×C43—21no—
76C2×C4×D4×C43C2211yescharacteristic
77C2×C4×D4×C43C2211yescharacteristic
78C22×C4⋊C4×C43—21no—
79C2×#10621898—22no—
80C2×#10621898—24no—
81C2×#10621898—42no—
82C2×#10621898C2314yes—
83C22×Dic86—24no—
84C22×Dic86—22no—
85C22×Dic86—21no—
86C22×Dic86—42no—
87C22×Dic86C2311yescharacteristic
88C22×Dic86C2314yes—
89C22×Dic86C2311yescharacteristic
90C22×D172C2311yescharacteristic
91C22×C22⋊D43—21no—
92C22×C22⋊D43—21no—
93C23×Dic43—21no—
94C22×C4×D43—21no—
95#13063355—232no—
96#13063345—232no—
97C2×#10621885—24no—
98C2×#10621885—24no—
99C2×#10621885—24no—
100C2×#10621885—42no—
101C2×#10621885C2314yes—
102C2×#10621885C2314yes—
103C2×#10621885C2314yes—
104C2×#10621885C2314yes—
105C2×#10621883—24no—
106C2×#10621883D418yescomplemented
107C2×#10621883C2314yes—
108C2×#10621883C2314yes—
109C2×#10621884—24no—
110C2×#10621884—42no—
111C2×#10621884C2314yes—
112C2×#10621884C2314yes—
113C2×#10621882—24no—
114C2×#10621882C2314yes—
115C2×#10621877—24no—
116C2×#10621877C2314yes—
117C22×C43⋊C8—24no—
118C22×C43⋊C8C2311yescharacteristic
119C22×C43⋊C8C2311yescharacteristic
120C22×C43⋊C8C2311yescharacteristic
121C22×C43⋊C8C2314yes—
122C22×C43⋊C8C2311yescharacteristic
123#13063313—22no—
124#13063313C2314yes—
125#13063311—28no—
126#13063304—22no—
127#13063304C2314yes—
128#13063303—28no—
129#13063299—22no—
130#13063299C2314yes—
131#13063297—28no—
132C4×Dic86—22no—
133C4×Dic86C2314yes—
134(C22⋊D43)⋊C4—28no—
135C2×C4⋊Dic43C2311yescharacteristic
136C2×Dic43⋊C4—21no—
137C2×Dic43⋊C4—21no—
138C2×C22⋊Dic43—21no—
139C2×(C2×D43)⋊C4—21no—
140C2×(C2×D43)⋊C4—21no—
141C2×(C2×D43)⋊C4—21no—
142C2×C4×Dic43—21no—
143#13063258C2314yes—
144C4⋊(C43⋊C8)C2314yes—
145#13063249C2314yes—
146#13063249C2314yes—
147#13063248C2314yes—
148#13063248C2314yes—
149#13063246C2314yes—
150#13063245C2314yes—
151C22⋊(C43⋊C8)C2314yes—
152C22⋊(C43⋊C8)C2314yes—
153#13063236C2314yes—
154C2×#41×C43—22no—
155C2×#41×C43—22no—
156C2×#41×C43—24no—
157C2×#41×C43—24no—
158C2×#41×C43—42no—
159C2×#41×C43—42no—
160C2×#41×C43C2314yes—
161C2×#41×C43C2314yes—
162C22×Q8×C43C2311yescharacteristic
163C22×Q8×C43C2311yescharacteristic
164C22×D4×C43—21no—
165C22×D4×C43—21no—
166C22×D4×C43D411yescharacteristic
167C22×D4×C43C2311yescharacteristic
168C23×C4×C43—21no—
169C23×C4×C43—21no—
170C23×C4×C43—21no—
171C23×C4×C43C2311yescharacteristic
172C23×C4×C43C2311yescharacteristic
173C4⋊Q8×C43—22no—
174C4⋊Q8×C43C2314yes—
175#123×C43—28no—
176#123×C43—28no—
177C22⋊Q8×C43—22no—
178C22⋊Q8×C43—22no—
179C22⋊Q8×C43C2314yes—
180C22⋊Q8×C43C2314yes—
181#121×C43—28no—
182C4×D4×C43—22no—
183C4×D4×C43D414yes—
184C4×D4×C43C2314yes—
185C4×D4×C43C2314yes—
186C2×C4⋊C4×C43—21no—
187C2×C4⋊C4×C43—21no—
188C2×C4⋊C4×C43—21no—
189C2×C4⋊C4×C43—21no—
190C2×C4⋊C4×C43—28no—
191C2×C4⋊C4×C43D411yescharacteristic
192C2×C4⋊C4×C43C2311yescharacteristic
193C2×C22⋊C4×C43—21no—
194C2×C22⋊C4×C43—21no—
195C2×C22⋊C4×C43—21no—
196C2×C22⋊C4×C43D411yescharacteristic
197C2×C22⋊C4×C43D411yescharacteristic
198C2×C42×C43C2311yescharacteristic
199C24×C43—21no—
200C24×C43C2×D411yescharacteristic
201C24×C43C2×D411yescharacteristic
202C23×D43—21no—
203#41×C43—28no—
204#41×C43—28no—
205#41×C43—44no—
206#41×C43—44no—
207#41×C43—48no—
208#41×C43—48no—
209C2×Q8×C43—21no—
210C2×Q8×C43—21no—
211C2×Q8×C43—22no—
212C2×Q8×C43—22no—
213C2×Q8×C43—22no—
214C2×Q8×C43—22no—
215C2×Q8×C43C2412yes—
216C2×Q8×C43C2412yes—
217C2×D4×C43—21no—
218C2×D4×C43—22no—
219C2×D4×C43—24no—
220C2×D4×C43—24no—
221C2×D4×C43—42no—
222C2×D4×C43—44no—
223C2×D4×C43—44no—
224C2×D4×C43C2×D414yes—
225C2×D4×C43C2×D414yes—
226C2×D4×C43C2412yes—
227C22×C4×C43—22no—
228C22×C4×C43—22no—
229C22×C4×C43—22no—
230C22×C4×C43—22no—
231C22×C4×C43—24no—
232C22×C4×C43—24no—
233C22×C4×C43—24no—
234C22×C4×C43—21no—
235C22×C4×C43—21no—
236C22×C4×C43—21no—
237C22×C4×C43—44no—
238C22×C4×C43—44no—
239C22×C4×C43—44no—
240C22×C4×C43C2×D411yescharacteristic
241C22×C4×C43C2×D411yescharacteristic
242C22×C4×C43C2×D411yescharacteristic
243C22×C4×C43C2×D411yescharacteristic
244C22×C4×C43C2×D412yes—
245C22×C4×C43C2×D412yes—
246C22×C4×C43C2412yes—
247C22×C4×C43C2412yes—
248C22×C4×C43C2411yescharacteristic
249C2×C22⋊D43—24no—
250C2×C22⋊D43—24no—
251C2×C22⋊D43—44no—
252C2×C22⋊D43—44no—
253C22×Dic43—21no—
254C22×Dic43—21no—
255C22×Dic43—21no—
256C22×Dic43—24no—
257C22×Dic43—44no—
258#10621898—28no—
259#10621898—44no—
260#10621898—48no—
261C2×D172—21no—
262C2×D172—22no—
263C2×D172—22no—
264C2×D172C2412yes—
265C2×C4×D43—24no—
266C2×C4×D43—44no—
267C2×Dic86—21no—
268C2×Dic86—22no—
269C2×Dic86—22no—
270C2×Dic86—22no—
271C2×Dic86—28no—
272C2×Dic86—24no—
273C2×Dic86—21no—
274C2×Dic86—44no—
275C2×Dic86—48no—
276C2×Dic86—44no—
277C2×Dic86C2×D414yes—
278C2×Dic86C2412yes—
279C2×Dic86C2412yes—
280C4⋊C4×C43—24no—
281C4⋊C4×C43—24no—
282C4⋊C4×C43—24no—
283C4⋊C4×C43—24no—
284C4⋊C4×C43—21no—
285C4⋊C4×C43C2×D414yes—
286C4⋊C4×C43C2412yes—
287C22⋊C4×C43—24no—
288C22⋊C4×C43—24no—
289C22⋊C4×C43—24no—
290C22⋊C4×C43C2×D414yes—
291C22⋊C4×C43C2×D414yes—
292C42×C43C2×D412yes—
293C42×C43C2412yes—
294C22⋊Dic43—24no—
295#10621885—28no—
296#10621885—28no—
297#10621885—28no—
298#10621885—44no—
299#10621884—28no—
300#10621884—44no—
301#10621883—28no—
302#10621883C2×D4116yescomplemented
303#10621882—28no—
304(C2×D43)⋊C4—24no—
305(C2×D43)⋊C4—24no—
306(C2×D43)⋊C4—24no—
307C4⋊Dic43—21no—
308C4⋊Dic43C2412yes—
309Dic43⋊C4—24no—
310Dic43⋊C4—24no—
311C4×Dic43—24no—
312#10621877—28no—
313C2×C43⋊C8—22no—
314C2×C43⋊C8—22no—
315C2×C43⋊C8—22no—
316C2×C43⋊C8—28no—
317C2×C43⋊C8C2×D414yes—
318C2×C43⋊C8C2412yes—
319C2×C43⋊C8C2412yes—
320C2×C43⋊C8C2412yes—
321C2×C43⋊C8C2412yes—
322C23×C43—22no—
323C23×C43—22no—
324C23×C43—24no—
325C23×C43—22no—
326C23×C43—22no—
327C23×C43—22no—
328C23×C43—22no—
329C23×C43—22no—
330C23×C43—42no—
331C23×C43—42no—
332C23×C43C22×D412yes—
333C23×C43C22×D412yes—
334C23×C43C22×D411yescharacteristic
335C22×D43—22no—
336C22×D43—42no—
337C22×D43—42no—
338C22×D43—42no—
339Q8×C43—22no—
340Q8×C43—22no—
341Q8×C43—22no—
342Q8×C43—22no—
343Q8×C43—42no—
344Q8×C43—42no—
345D4×C43—24no—
346D4×C43—22no—
347D4×C43—44no—
348D4×C43—48no—
349D4×C43—48no—
350D4×C43C22×D414yes—
351C2×C4×C43—22no—
352C2×C4×C43—22no—
353C2×C4×C43—22no—
354C2×C4×C43—22no—
355C2×C4×C43—24no—
356C2×C4×C43—24no—
357C2×C4×C43—22no—
358C2×C4×C43—22no—
359C2×C4×C43—22no—
360C2×C4×C43—22no—
361C2×C4×C43—22no—
362C2×C4×C43—22no—
363C2×C4×C43—22no—
364C2×C4×C43—48no—
365C2×C4×C43—48no—
366C2×C4×C43—48no—
367C2×C4×C43—42no—
368C2×C4×C43—42no—
369C2×C4×C43—42no—
370C2×C4×C43C22×D412yes—
371C2×C4×C43C22×D412yes—
372C2×C4×C43C22×D412yes—
373C2×C4×C43C22×D412yes—
374C2×C4×C43C22×D412yes—
375C2×C4×C43C22×D411yescharacteristic
376C2×C4×C43H(5,𝔽2)12yes—
377C2×C4×C43C2511yescharacteristic
378C22⋊D43—48no—
379C22⋊D43—48no—
380C2×Dic43—24no—
381C2×Dic43—22no—
382C2×Dic43—22no—
383C2×Dic43—22no—
384C2×Dic43—48no—
385C2×Dic43—42no—
386C2×Dic43—42no—
387D172—22no—
388D172—22no—
389D172—42no—
390C4×D43—48no—
391Dic86—24no—
392Dic86—22no—
393Dic86—22no—
394Dic86—22no—
395Dic86—48no—
396Dic86—42no—
397Dic86C22×D414yes—
398C43⋊C8—22no—
399C43⋊C8—22no—
400C43⋊C8—22no—
401C43⋊C8C22×D414yes—
402C2×#3269—431nomaximal, Sylow
403C22×C43—24no—
404C22×C43—22no—
405C22×C43—22no—
406C22×C43—22no—
407C22×C43—22no—
408C22×C43—22no—
409C22×C43—22no—
410C22×C43—44no—
411C22×C43—44no—
412C22×C43—48no—
413C22×C43—42no—
414C22×C43—42no—
415C22×C43D4212yes—
416C22×C43#57512yes—
417C22×C43#57812yes—
418C22×C43C23×D411yescharacteristic
419C2×D43—42no—
420C2×D43—42no—
421C2×D43—42no—
422C2×D43—84no—
423C4×C43—22no—
424C4×C43—22no—
425C4×C43—22no—
426C4×C43—22no—
427C4×C43—42no—
428C4×C43—42no—
429C4×C43—42no—
430C4×C43D4212yes—
431C4×C43C23×D411yescharacteristic
432C4×C43C2×H(5,𝔽2)11yescharacteristic
433Dic43—24no—
434Dic43—42no—
435Dic43—42no—
436C22×#137—431no—
437C22×#135—431no—
438C2×#548—431no—
439C2×#547D4311yescharacteristic, complemented
440#3269—4316no—
441C2×#497—431no—
442C2×#468—431no—
443C2×#467—431no—
444C2×#462—431no—
445C2×#463—431no—
446C2×#452—431no—
447C2×#452—431no—
448C2×#449—431no—
449C2×#451—431no—
450C2×#440—431no—
451C2×#435—431no—
452C2×C43—42no—
453C2×C43—42no—
454C2×C43—44no—
455C2×C43#326914yescomplemented
456C2×C43C2×D4211yescharacteristic
457C2×C43C2×#57511yescharacteristic
458C2×C43C2×#57811yescharacteristic
459D43—82no—
460C22×#41—431no—
461C22×#41C2×D4311yescharacteristic
462C22×#41C2×D4311yescharacteristic
463C23×Q8—431no—
464C2×#137—438no—
465C2×#137—868no—
466C2×#135—438no—
467C2×#135—868no—
468C22×Q16—431no—
469C22×Q16—431no—
470C22×Q16—431no—
471C22×Q16—431no—
472C22×SD16—431no—
473C22×SD16—431no—
474C22×SD16—431no—
475C22×SD16—431no—
476C22×D8—431no—
477C22×M16—431no—
478C23×C8—431no—
479#548—438no—
480#548—864no—
481#547—24no—
482#547C2×D4318yescomplemented
483C2×C4⋊Q8C2×D4311yescharacteristic
484C2×#124—431no—
485C2×#124—861no—
486C2×#123—21no—
487C2×#123—21no—
488C2×C22⋊Q8—431no—
489C2×C22⋊Q8—861no—
490C2×C22⋊Q8C2×D4311yescharacteristic
491C2×C22⋊Q8C2×D4311yescharacteristic
492C2×#121—21no—
493C2×#121—431no—
494C2×#121—861no—
495C2×C4×Q8—431no—
496C2×C4×D4—861no—
497C2×C4×D4C2×D4311yescharacteristic
498C2×C4×D4C2×D4311yescharacteristic
499C22×C4⋊C4—21no—
500#497—438no—
501#468—438no—
502#467—438no—
503#463—438no—
504#462—438no—
505#452—438no—
506#452—438no—
507#451—438no—
508#449—438no—
509#440—438no—
510#435—438no—
511C2×#107—431no—
512C2×C4⋊C8—431no—
513C2×#103—431no—
514C2×#103—431no—
515C2×#103—431no—
516C2×#103—431no—
517C2×#102—431no—
518C2×#102—431no—
519C2×C22⋊C8—431no—
520C2×C22⋊C8—431no—
521C2×#97—431no—
522C43C2×#326911yescharacteristic, complemented, Sylow
523C2×#41—22no—
524C2×#41—22no—
525C2×#41—24no—
526C2×#41—24no—
527C2×#41—42no—
528C2×#41—42no—
529C2×#41—434no—
530C2×#41—864no—
531C2×#41—862no—
532C2×#41—1722no—
533C2×#41C22×D4314yes—
534C2×#41C22×D4314yes—
535C22×Q8—431no—
536C22×Q8—431no—
537C22×Q8—434no—
538C22×Q8—864no—
539C22×Q8—861no—
540C22×Q8—862no—
541C22×Q8—1722no—
542C22×Q8C22×D4311yescharacteristic
543C22×Q8C22×D4311yescharacteristic
544C22×D4—21no—
545C22×D4—21no—
546C22×D4—431no—
547C22×D4—861no—
548C22×D4—861no—
549C22×D4C22⋊D4311yescharacteristic
550C22×D4C22×D4311yescharacteristic
551C23×C4—21no—
552C23×C4—21no—
553C23×C4—21no—
554C23×C4—861no—
555C23×C4—861no—
556C23×C4C22×D4311yescharacteristic
557C23×C4C22×D4311yescharacteristic
558#137—8632no—
559#135—8632no—
560C2×Q16—434no—
561C2×Q16—434no—
562C2×Q16—434no—
563C2×Q16—434no—
564C2×Q16—864no—
565C2×Q16—864no—
566C2×Q16—864no—
567C2×Q16—1722no—
568C2×SD16—438no—
569C2×SD16—434no—
570C2×SD16—434no—
571C2×SD16—434no—
572C2×SD16—434no—
573C2×SD16—864no—
574C2×SD16—864no—
575C2×SD16—1722no—
576C2×D8—434no—
577C2×D8—864no—
578C2×M16—434no—
579C2×M16—864no—
580C22×C8—431no—
581C22×C8—431no—
582C22×C8—434no—
583C22×C8—431no—
584C22×C8—431no—
585C22×C8—864no—
586C4⋊Q8—22no—
587C4⋊Q8C22×D4314yes—
588#124—434no—
589#124—868no—
590#124—862no—
591#123—28no—
592#123—28no—
593C22⋊Q8—22no—
594C22⋊Q8—22no—
595C22⋊Q8—434no—
596C22⋊Q8—862no—
597C22⋊Q8—868no—
598C22⋊Q8C22×D4314yes—
599C22⋊Q8C22×D4314yes—
600#121—28no—
601#121—434no—
602#121—868no—
603#121—862no—
604C4×Q8—434no—
605C4×Q8—862no—
606C4×D4—22no—
607C4×D4—868no—
608C4×D4C22⋊D4314yes—
609C4×D4C22×D4314yes—
610C4×D4C22×D4314yes—
611C2×C4⋊C4—21no—
612C2×C4⋊C4—21no—
613C2×C4⋊C4—21no—
614C2×C4⋊C4—21no—
615C2×C4⋊C4—28no—
616C2×C4⋊C4—431no—
617C2×C4⋊C4—861no—
618C2×C4⋊C4—861no—
619C2×C4⋊C4C22⋊D4311yescharacteristic
620C2×C4⋊C4C22×D4311yescharacteristic
621C2×C22⋊C4—21no—
622C2×C22⋊C4—21no—
623C2×C22⋊C4—21no—
624C2×C22⋊C4—861no—
625C2×C22⋊C4—861no—
626C2×C22⋊C4—861no—
627C2×C22⋊C4—861no—
628C2×C22⋊C4C22⋊D4311yescharacteristic
629C2×C22⋊C4C22⋊D4311yescharacteristic
630C2×C42—861no—
631C2×C42C22×D4311yescharacteristic
632#107—434no—
633C4⋊C8—434no—
634#103—434no—
635#103—434no—
636#103—434no—
637#103—434no—
638#102—434no—
639#102—434no—
640C22⋊C8—434no—
641C22⋊C8—434no—
642#97—434no—
643C24—21no—
644C24—861no—
645C24C2×C22⋊D4311yescharacteristic
646C24C2×C22⋊D4311yescharacteristic
647#41—28no—
648#41—28no—
649#41—44no—
650#41—44no—
651#41—48no—
652#41—48no—
653#41—868no—
654#41—1724no—
655#41—1728no—
656C2×Q8—21no—
657C2×Q8—21no—
658C2×Q8—22no—
659C2×Q8—22no—
660C2×Q8—22no—
661C2×Q8—22no—
662C2×Q8—434no—
663C2×Q8—432no—
664C2×Q8—432no—
665C2×Q8—868no—
666C2×Q8—861no—
667C2×Q8—864no—
668C2×Q8—861no—
669C2×Q8—862no—
670C2×Q8—862no—
671C2×Q8—862no—
672C2×Q8—1724no—
673C2×Q8—1724no—
674C2×Q8—1728no—
675C2×Q8C23×D4312yes—
676C2×Q8C23×D4312yes—
677C2×D4—24no—
678C2×D4—24no—
679C2×D4—21no—
680C2×D4—22no—
681C2×D4—42no—
682C2×D4—44no—
683C2×D4—44no—
684C2×D4—432no—
685C2×D4—864no—
686C2×D4—864no—
687C2×D4—862no—
688C2×D4—861no—
689C2×D4—862no—
690C2×D4—1724no—
691C2×D4—1724no—
692C2×D4D4×D4314yes—
693C2×D4C2×C22⋊D4314yes—
694C2×D4C23×D4312yes—
695C22×C4—22no—
696C22×C4—22no—
697C22×C4—22no—
698C22×C4—22no—
699C22×C4—21no—
700C22×C4—21no—
701C22×C4—21no—
702C22×C4—24no—
703C22×C4—24no—
704C22×C4—24no—
705C22×C4—44no—
706C22×C4—44no—
707C22×C4—44no—
708C22×C4—861no—
709C22×C4—864no—
710C22×C4—861no—
711C22×C4—861no—
712C22×C4—864no—
713C22×C4—1724no—
714C22×C4—1724no—
715C22×C4C2×C22⋊D4312yes—
716C22×C4C2×C22⋊D4312yes—
717C22×C4C2×C22⋊D4311yescharacteristic
718C22×C4C2×C22⋊D4311yescharacteristic
719C22×C4C2×C22⋊D4311yescharacteristic
720C22×C4C2×C22⋊D4311yescharacteristic
721C22×C4C23×D4312yes—
722C22×C4C23×D4312yes—
723C22×C4C23×D4311yescharacteristic
724Q16—868no—
725Q16—868no—
726Q16—868no—
727Q16—1724no—
728SD16—4316no—
729SD16—868no—
730SD16—868no—
731SD16—1724no—
732D8—868no—
733M16—868no—
734C2×C8—434no—
735C2×C8—432no—
736C2×C8—432no—
737C2×C8—432no—
738C2×C8—432no—
739C2×C8—868no—
740C2×C8—862no—
741C2×C8—862no—
742C2×C8—862no—
743C4⋊C4—24no—
744C4⋊C4—24no—
745C4⋊C4—24no—
746C4⋊C4—24no—
747C4⋊C4—21no—
748C4⋊C4—432no—
749C4⋊C4—861no—
750C4⋊C4—864no—
751C4⋊C4—864no—
752C4⋊C4C2×C22⋊D4314yes—
753C4⋊C4C23×D4312yes—
754C22⋊C4—24no—
755C22⋊C4—24no—
756C22⋊C4—24no—
757C22⋊C4—864no—
758C22⋊C4—864no—
759C22⋊C4—864no—
760C22⋊C4—864no—
761C22⋊C4C2×C22⋊D4314yes—
762C22⋊C4C2×C22⋊D4314yes—
763C42—864no—
764C42C2×C22⋊D4312yes—
765C42C23×D4312yes—
766C23—22no—
767C23—22no—
768C23—22no—
769C23—22no—
770C23—22no—
771C23—22no—
772C23—22no—
773C23—24no—
774C23—42no—
775C23—42no—
776C23—862no—
777C23—1722no—
778C23—1722no—
779C23—1722no—
780C23C22×C22⋊D4312yes—
781C23C22×C22⋊D4312yes—
782C23C22×C22⋊D4311yescharacteristic
783Q8—22no—
784Q8—22no—
785Q8—22no—
786Q8—22no—
787Q8—42no—
788Q8—42no—
789Q8—434no—
790Q8—862no—
791Q8—864no—
792Q8—862no—
793Q8—862no—
794Q8—1728no—
795Q8—1722no—
796D4—22no—
797D4—24no—
798D4—44no—
799D4—48no—
800D4—48no—
801D4—862no—
802D4—862no—
803D4—1728no—
804D4—1728no—
805D4—1722no—
806D4C2×D4×D4314yes—
807C2×C4—22no—
808C2×C4—22no—
809C2×C4—22no—
810C2×C4—22no—
811C2×C4—22no—
812C2×C4—22no—
813C2×C4—22no—
814C2×C4—22no—
815C2×C4—24no—
816C2×C4—24no—
817C2×C4—22no—
818C2×C4—22no—
819C2×C4—22no—
820C2×C4—48no—
821C2×C4—48no—
822C2×C4—48no—
823C2×C4—42no—
824C2×C4—42no—
825C2×C4—42no—
826C2×C4—862no—
827C2×C4—864no—
828C2×C4—862no—
829C2×C4—862no—
830C2×C4—1728no—
831C2×C4—1728no—
832C2×C4—1722no—
833C2×C4—1722no—
834C2×C4C2×D4×D4312yes—
835C2×C4C22×C22⋊D4312yes—
836C2×C4C22×C22⋊D4312yes—
837C2×C4C22×C22⋊D4312yes—
838C2×C4C22×C22⋊D4312yes—
839C2×C4C22×C22⋊D4311yescharacteristic
840C2×C4#1306337012yes—
841C2×C4C24×D4311yescharacteristic
842C8—434no—
843C8—862no—
844C8—862no—
845C8—862no—
846C22—22no—
847C22—22no—
848C22—24no—
849C22—22no—
850C22—22no—
851C22—22no—
852C22—22no—
853C22—42no—
854C22—42no—
855C22—44no—
856C22—44no—
857C22—48no—
858C22—3444no—
859C22—1722no—
860C22—1722no—
861C22—1722no—
862C22D4×C22⋊D4312yes—
863C22#1458369712yes—
864C22#1458371412yes—
865C22C23×C22⋊D4311yescharacteristic
866C4—22no—
867C4—22no—
868C4—22no—
869C4—22no—
870C4—42no—
871C4—42no—
872C4—42no—
873C4—864no—
874C4—1722no—
875C4—1722no—
876C4D4×C22⋊D4312yes—
877C4C22×D4×D4311yescharacteristic
878C4C2×#1306337011yescharacteristic
879C2—42no—
880C2—42no—
881C2—44no—
882C2—3442no—
883C2#1914614614yesdirect product factor
884C2C2×D4×C22⋊D4311yescharacteristic
885C2C2×#1458369711yescharacteristic
886C2C2×#1458371411yescharacteristic
subgroupG/H
centerC23C22×C22⋊D43
commutator, cosocleC2×C4×C43C25
FrattiniC2×C4C24×D43
FittingC2×C43×#547C2
socleC23×C43C22×D4
hypercenterC2×#547D43
hypocenterC43C2×#3269
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×C4×D4 ◁ C2×#547

Complements

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

NH ≅ G/Ntype
1. C22×#13063355C2semidirect
2. C22×#13063345C2semidirect
3. C2×#14583558C2semidirect
4. #19146146C2direct (N × H)
5. C2×#14583291C2semidirect
6. C2×#14583147C2semidirect
7. C2×#14583138C2semidirect
8. C2×#14583106C2semidirect
9. C2×#14583114C2semidirect
10. C2×#14583061C2semidirect
11. C2×#14583059C2semidirect
12. C2×#14583044C2semidirect
13. C2×#14583054C2semidirect
14. C2×#14582999C2semidirect
15. C2×#14582971C2semidirect
16. C2×C43×#547C2semidirect
20. C2×#13063355C22semidirect
22. C2×#13063345C22semidirect
35. #14583558C22semidirect
44. #14583291C22semidirect
45. #14583147C22semidirect
46. #14583138C22semidirect
47. #14583114C22semidirect
48. #14583106C22semidirect
49. #14583061C22semidirect
50. #14583059C22semidirect
51. #14583054C22semidirect
52. #14583044C22semidirect
53. #14582999C22semidirect
54. #14582971C22semidirect
69. C43×#547C22semidirect
106. C2×#10621883D4semidirect
302. #10621883C2×D4semidirect
439. C2×#547D43semidirect
455. C2×C43#3269semidirect
482. #547C2×D43semidirect
522. C43C2×#3269semidirect
883. C2#19146146direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#130633552
C22×#130633452
C2×#145835582
#191461462
C2×#145832912
C2×#145831472
C2×#145831382
C2×#145831062
C2×#145831142
C2×#145830612
C2×#145830592
C2×#145830442
C2×#145830542
C2×#145829992
C2×#145829712
C2×C43×#5472
C2×#326943