Finite Group Databasebeta

← C2×#19146164 #25971641

Subgroups — C2×#19146164 #25971641

Order 11008.

2742 conjugacy classes of subgroups.

The subgroup lattice has 872 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#13063354C211yesmaximal, characteristic, complemented
2C22×Q16×D43C211yesmaximal, characteristic, complemented
3C2×#14583564C211yesmaximal, characteristic, complemented
4C2×#14583557C211yesmaximal, characteristic
5#19146164C2116yesmaximal, direct product factor
6C2×#14583154C211yesmaximal, characteristic, complemented
7C2×#14583125C211yesmaximal, characteristic, complemented
8C2×#14583118C211yesmaximal, characteristic, complemented
9C2×#14583106C211yesmaximal, characteristic, complemented
10C2×#14583058C211yesmaximal, characteristic, complemented
11C2×#14583053C211yesmaximal, characteristic, complemented
12C2×#14583053C211yesmaximal, characteristic, complemented
13C2×#14583036C211yesmaximal, characteristic, complemented
14C2×#14583007C211yesmaximal, characteristic, complemented
15C2×#14582972C211yesmaximal, characteristic, complemented
16C2×C43×#497C211yesmaximal, characteristic, complemented
17C22×#10621900C2211yescharacteristic
18C22×Q8×D43C2211yescharacteristic
19C22×Q8×D43C2211yescharacteristic
20C22×Q8×D43C2211yescharacteristic
21C2×#13063354—28no—
22C2×#13063354C2218yescomplemented
23C22×Dic172C2211yescharacteristic
24C22×#10621885C2211yescharacteristic
25C22×#10621885C2211yescharacteristic
26C22×#10621885C2211yescharacteristic
27C2×Q16×D43—28no—
28C2×Q16×D43C2218yescomplemented
29C22×#10621883C2211yescharacteristic
30C22×#10621872C2211yescharacteristic
31C22×C8×D43C2211yescharacteristic
32#14583564—24no—
33#14583564C2218yescomplemented
34#14583557—24no—
35#14583557C2218yes—
36C2×#13063324—21no—
37C2×#13063311—21no—
38C2×#13063303—21no—
39C2×#13063303—21no—
40C2×#13063302—21no—
41C2×#13063301C2211yescharacteristic
42C2×#13063301C2211yescharacteristic
43C2×#13063301C2211yescharacteristic
44C2×#13063298—21no—
45C2×#13063296C2211yescharacteristic
46C2×C4×Dic86C2211yescharacteristic
47C2×C4×Dic86C2211yescharacteristic
48C2×C4×D172C2211yescharacteristic
49C2×#13063287—21no—
50C2×(C22⋊D43)⋊C4—21no—
51#14583154C2218yescomplemented
52#14583125C2218yescomplemented
53#14583118C2218yescomplemented
54#14583106C2218yescomplemented
55#14583058C2218yescomplemented
56#14583053C2218yescomplemented
57#14583053C2218yescomplemented
58#14583036C2218yescomplemented
59#14583007C2218yescomplemented
60#14582972C2218yescomplemented
61C2×#13063257C2211yescharacteristic
62C2×C4⋊(C43⋊C8)C2211yescharacteristic
63C2×#13063250C2211yescharacteristic
64C2×#13063250C2211yescharacteristic
65C2×#13063249C2211yescharacteristic
66C2×#13063249C2211yescharacteristic
67C2×#13063249C2211yescharacteristic
68C2×#13063246C2211yescharacteristic
69C2×(C2×D43)⋊C8C2211yescharacteristic
70C2×(C2×D43)⋊C8C2211yescharacteristic
71C22×Q16×C43C2211yescharacteristic
72C22×Q16×C43C2211yescharacteristic
73C22×SD16×C43C2211yescharacteristic
74C22×SD16×C43C2211yescharacteristic
75C2×C4⋊Q8×C43C2211yescharacteristic
76C2×#124×C43C2211yescharacteristic
77C43×#497C2218yescomplemented
78C2×#97×C43C2211yescharacteristic
79C2×#10621900—22no—
80C2×#10621900—24no—
81C2×#10621900—42no—
82C2×#10621900C2314yes—
83C22×Dic86—21no—
84C22×Dic86—21no—
85C22×Dic86—21no—
86C22×Dic86C2311yescharacteristic
87C22×Dic86C2311yescharacteristic
88C2×Q8×D43—22no—
89C2×Q8×D43—22no—
90C2×Q8×D43—22no—
91C2×Q8×D43—24no—
92C2×Q8×D43—24no—
93C2×Q8×D43—24no—
94C2×Q8×D43—42no—
95C2×Q8×D43—42no—
96C2×Q8×D43—42no—
97C2×Q8×D43C2314yes—
98C2×Q8×D43C2314yes—
99C2×Q8×D43C2314yes—
100C22×D172D411yescharacteristic
101C22×C22⋊D43—21no—
102C22×C22⋊D43—21no—
103C23×Dic43—21no—
104C22×C4×D43—21no—
105C22×C4×D43—21no—
106C22×C4×D43—21no—
107C22×C4×D43C2311yescharacteristic
108C22×C4×D43C2311yescharacteristic
109#13063354—232no—
110C2×Dic172D418yescomplemented
111C2×Dic172C2314yes—
112C2×#10621885—24no—
113C2×#10621885—24no—
114C2×#10621885—24no—
115C2×#10621885C2314yes—
116C2×#10621885C2314yes—
117C2×#10621885C2314yes—
118Q16×D43—232no—
119C2×#10621883—24no—
120C2×#10621883C2314yes—
121C2×#10621872—24no—
122C2×#10621872C2314yes—
123C22×C43⋊C8C2311yescharacteristic
124C22×C43⋊C8C2311yescharacteristic
125C2×C8×D43—24no—
126C2×C8×D43C2314yes—
127#13063324—28no—
128#13063311—28no—
129#13063303—28no—
130#13063303—28no—
131#13063302—28no—
132#13063301—22no—
133#13063301—22no—
134#13063301—22no—
135#13063301C2314yes—
136#13063301C2314yes—
137#13063301C2314yes—
138#13063298—28no—
139#13063296—22no—
140#13063296C2314yes—
141C4×Dic86—22no—
142C4×Dic86—22no—
143C4×Dic86C2314yes—
144C4×Dic86C2314yes—
145C4×D172D414yes—
146C4×D172C2314yes—
147#13063287—28no—
148(C22⋊D43)⋊C4—28no—
149C2×C4⋊Dic43D411yescharacteristic
150C2×C4⋊Dic43C2311yescharacteristic
151C2×C4⋊Dic43C2311yescharacteristic
152C2×Dic43⋊C4—21no—
153C2×Dic43⋊C4—21no—
154C2×Dic43⋊C4—21no—
155C2×Dic43⋊C4—21no—
156C2×Dic43⋊C4—21no—
157C2×C22⋊Dic43—21no—
158C2×(C2×D43)⋊C4—21no—
159C2×(C2×D43)⋊C4—21no—
160C2×(C2×D43)⋊C4—21no—
161C2×(C2×D43)⋊C4D411yescharacteristic
162C2×(C2×D43)⋊C4D411yescharacteristic
163C2×C4×Dic43—21no—
164C2×C4×Dic43—21no—
165#13063257C2314yes—
166C4⋊(C43⋊C8)C2314yes—
167#13063250C2314yes—
168#13063250C2314yes—
169#13063249C2314yes—
170#13063249C2314yes—
171#13063249C2314yes—
172#13063246C2314yes—
173(C2×D43)⋊C8C2314yes—
174(C2×D43)⋊C8C2314yes—
175C22×Q8×C43C2311yescharacteristic
176C22×Q8×C43C2311yescharacteristic
177C22×Q8×C43C2311yescharacteristic
178C22×D4×C43C2311yescharacteristic
179C2×Q16×C43—24no—
180C2×Q16×C43—42no—
181C2×Q16×C43C2314yes—
182C2×Q16×C43C2314yes—
183C2×SD16×C43—24no—
184C2×SD16×C43—42no—
185C2×SD16×C43C2314yes—
186C2×SD16×C43C2314yes—
187C22×C8×C43C2311yescharacteristic
188C22×C8×C43C2311yescharacteristic
189C4⋊Q8×C43—22no—
190C4⋊Q8×C43C2314yes—
191#124×C43—22no—
192#124×C43C2314yes—
193C2×C4⋊C4×C43—21no—
194C2×C4⋊C4×C43—21no—
195C2×C22⋊C4×C43—21no—
196C2×C22⋊C4×C43—21no—
197C2×C42×C43C2311yescharacteristic
198#97×C43C2314yes—
199C24×C43—21no—
200C23×D43C2×D411yescharacteristic
201C23×D43C2×D411yescharacteristic
202C2×Q8×C43—21no—
203C2×Q8×C43—21no—
204C2×Q8×C43—21no—
205C2×Q8×C43—22no—
206C2×Q8×C43—22no—
207C2×Q8×C43—22no—
208C2×Q8×C43—22no—
209C2×Q8×C43—22no—
210C2×Q8×C43—22no—
211C2×Q8×C43C2412yes—
212C2×Q8×C43C2412yes—
213C2×Q8×C43C2412yes—
214C2×D4×C43—21no—
215C2×D4×C43—22no—
216C2×D4×C43—22no—
217C2×D4×C43C2412yes—
218C22×C4×C43—21no—
219C22×C4×C43—21no—
220C22×C4×C43—21no—
221C22×C4×C43C2×D411yescharacteristic
222C22×C4×C43C2×D411yescharacteristic
223C22×C4×C43C2411yescharacteristic
224C2×C22⋊D43—24no—
225C2×C22⋊D43—24no—
226C2×C22⋊D43—44no—
227C2×C22⋊D43—44no—
228C22×Dic43—24no—
229C22×Dic43—21no—
230C22×Dic43—21no—
231C22×Dic43—21no—
232C22×Dic43—21no—
233C22×Dic43—44no—
234C22×Dic43C2×D411yescharacteristic
235C22×Dic43C2×D411yescharacteristic
236Q8×D43—28no—
237Q8×D43—28no—
238Q8×D43—28no—
239Q8×D43—44no—
240Q8×D43—44no—
241Q8×D43—44no—
242Q8×D43—48no—
243Q8×D43—48no—
244Q8×D43—48no—
245#10621900—28no—
246#10621900—44no—
247#10621900—48no—
248C2×D172—24no—
249C2×D172C2×D414yes—
250C2×C4×D43—22no—
251C2×C4×D43—22no—
252C2×C4×D43—22no—
253C2×C4×D43—22no—
254C2×C4×D43—24no—
255C2×C4×D43—24no—
256C2×C4×D43—24no—
257C2×C4×D43—44no—
258C2×C4×D43—44no—
259C2×C4×D43—44no—
260C2×C4×D43C2×D412yes—
261C2×C4×D43C2×D412yes—
262C2×C4×D43C2412yes—
263C2×C4×D43C2412yes—
264C2×Dic86—21no—
265C2×Dic86—21no—
266C2×Dic86—22no—
267C2×Dic86—22no—
268C2×Dic86—24no—
269C2×Dic86—24no—
270C2×Dic86—24no—
271C2×Dic86—44no—
272C2×Dic86—44no—
273C2×Dic86—44no—
274C2×Dic86C2×D414yes—
275C2×Dic86C2×D414yes—
276C2×Dic86C2412yes—
277C2×Dic86C2412yes—
278Q16×C43—28no—
279Q16×C43—44no—
280SD16×C43—28no—
281SD16×C43—44no—
282C2×C8×C43—22no—
283C2×C8×C43C2×D414yes—
284C2×C8×C43C2412yes—
285C2×C8×C43C2412yes—
286C4⋊C4×C43—24no—
287C4⋊C4×C43—24no—
288C22⋊C4×C43—24no—
289C22⋊C4×C43—24no—
290C42×C43C2×D412yes—
291C42×C43C2412yes—
292C22⋊Dic43—24no—
293#10621885—28no—
294#10621885—28no—
295#10621885—28no—
296#10621883—28no—
297(C2×D43)⋊C4—24no—
298(C2×D43)⋊C4—24no—
299(C2×D43)⋊C4—24no—
300(C2×D43)⋊C4C2×D414yes—
301(C2×D43)⋊C4C2×D414yes—
302C4⋊Dic43—21no—
303C4⋊Dic43—21no—
304C4⋊Dic43C2×D414yes—
305C4⋊Dic43C2412yes—
306C4⋊Dic43C2412yes—
307Dic43⋊C4—24no—
308Dic43⋊C4—24no—
309Dic43⋊C4—24no—
310Dic43⋊C4—24no—
311Dic43⋊C4—24no—
312C4×Dic43—24no—
313C4×Dic43—24no—
314C2×C43⋊C8—22no—
315C2×C43⋊C8—22no—
316C2×C43⋊C8C2412yes—
317C2×C43⋊C8C2412yes—
318Dic172C2×D4116yescomplemented
319#10621872—28no—
320C8×D43—28no—
321C23×C43—22no—
322C23×C43—42no—
323C23×C43—42no—
324C23×C43—42no—
325C23×C43C22×D411yescharacteristic
326C22×D43—22no—
327C22×D43—22no—
328C22×D43—22no—
329C22×D43—22no—
330C22×D43—22no—
331C22×D43#13714yescomplemented
332C22×D43C22×D412yes—
333C22×D43C22×D412yes—
334Q8×C43—22no—
335Q8×C43—22no—
336Q8×C43—22no—
337Q8×C43—22no—
338Q8×C43—22no—
339Q8×C43—22no—
340Q8×C43—42no—
341Q8×C43—42no—
342Q8×C43—42no—
343D4×C43—22no—
344D4×C43—22no—
345D4×C43—42no—
346C2×C4×C43—22no—
347C2×C4×C43—22no—
348C2×C4×C43—22no—
349C2×C4×C43—22no—
350C2×C4×C43—22no—
351C2×C4×C43—42no—
352C2×C4×C43—42no—
353C2×C4×C43—42no—
354C2×C4×C43C22×D412yes—
355C2×C4×C43C22×D412yes—
356C2×C4×C43C22×D411yescharacteristic
357C2×C4×C43C22×D412yes—
358C2×C4×C43H(5,𝔽2)12yes—
359C2×C4×C43C2511yescharacteristic
360C22⋊D43—48no—
361C22⋊D43—48no—
362C2×Dic43—24no—
363C2×Dic43—24no—
364C2×Dic43—22no—
365C2×Dic43—22no—
366C2×Dic43—22no—
367C2×Dic43—22no—
368C2×Dic43—22no—
369C2×Dic43—22no—
370C2×Dic43—48no—
371C2×Dic43—42no—
372C2×Dic43—42no—
373C2×Dic43C22×D412yes—
374C2×Dic43C22×D412yes—
375D172—28no—
376C4×D43—24no—
377C4×D43—24no—
378C4×D43—22no—
379C4×D43—22no—
380C4×D43—22no—
381C4×D43—22no—
382C4×D43—48no—
383C4×D43—48no—
384C4×D43—48no—
385Dic86—24no—
386Dic86—24no—
387Dic86—22no—
388Dic86—22no—
389Dic86—48no—
390Dic86—48no—
391Dic86—48no—
392Dic86C22×D414yes—
393Dic86C22×D414yes—
394C8×C43—22no—
395C8×C43C22×D414yes—
396C43⋊C8—22no—
397C43⋊C8—22no—
398C2×#3270—431nomaximal, Sylow
399C22×C43—42no—
400C22×C43—42no—
401C22×C43—42no—
402C22×C43—84no—
403C22×C43D4212yes—
404C22×C43C2×#13712yes—
405C22×C43#57812yes—
406C22×C43C23×D411yescharacteristic
407C2×D43—22no—
408C2×D43—28no—
409C2×D43—22no—
410C2×D43—22no—
411C2×D43—22no—
412C2×D43—22no—
413C2×D43—44no—
414C2×D43C2×#13714yescomplemented
415C4×C43—22no—
416C4×C43—22no—
417C4×C43—42no—
418C4×C43—42no—
419C4×C43—42no—
420C4×C43D4212yes—
421C4×C43C23×D411yescharacteristic
422C4×C43C2×H(5,𝔽2)11yescharacteristic
423Dic43—24no—
424Dic43—24no—
425Dic43—22no—
426Dic43—22no—
427Dic43—42no—
428Dic43—42no—
429C22×#137—431no—
430C23×Q16—431no—
431C2×D4×Q8—431no—
432C2×#548—431no—
433#3270—4316no—
434C2×#497D4311yescharacteristic, complemented
435C2×#470—431no—
436C2×#465—431no—
437C2×#464—431no—
438C2×#462—431no—
439C2×#452—431no—
440C2×#451—431no—
441C2×#451—431no—
442C2×#448—431no—
443C2×#441—431no—
444C2×#435—431no—
445C2×C43—82no—
446C2×C43#327014yescomplemented
447C2×C43C2×D4211yescharacteristic
448C2×C43C22×#13711yescharacteristic
449C2×C43C2×#57811yescharacteristic
450D43—24no—
451D43—42no—
452C22×#41—431no—
453C23×Q8—431no—
454C23×Q8—431no—
455C23×Q8—431no—
456C2×#137—438no—
457C2×#137—868no—
458C22×Q16—431no—
459C22×Q16—431no—
460C22×Q16—431no—
461C22×Q16—438no—
462C22×Q16—431no—
463C22×Q16—868no—
464C22×Q16C2×D4311yescharacteristic
465C22×Q16C2×D4311yescharacteristic
466C22×SD16—431no—
467C22×SD16C2×D4311yescharacteristic
468C22×SD16C2×D4311yescharacteristic
469C22×M16—431no—
470C23×C8—431no—
471D4×Q8—438no—
472D4×Q8—864no—
473#548—438no—
474#548—864no—
475C2×C4⋊Q8—861no—
476C2×C4⋊Q8C2×D4311yescharacteristic
477C2×#124—861no—
478C2×#124C2×D4311yescharacteristic
479C2×C22⋊Q8—431no—
480C2×C22⋊Q8—431no—
481C2×C22⋊Q8—431no—
482C2×C22⋊Q8—861no—
483C2×C22⋊Q8—861no—
484C2×C22⋊Q8—861no—
485C2×#121—431no—
486C2×#121—861no—
487C2×C4×Q8—431no—
488C2×C4×Q8—431no—
489C2×C4×D4—431no—
490C2×C4×D4—861no—
491C2×C4×D4—861no—
492#497C2×D4318yescomplemented
493#470—438no—
494#465—438no—
495#464—438no—
496#462—438no—
497#452—438no—
498#451—438no—
499#451—438no—
500#448—438no—
501#441—438no—
502#435—438no—
503C2×#106—431no—
504C2×C4⋊C8—431no—
505C2×#103—431no—
506C2×#103—431no—
507C2×#103—431no—
508C2×#103—431no—
509C2×#103—431no—
510C2×#102—431no—
511C2×C22⋊C8—431no—
512C2×C22⋊C8—431no—
513C2×#97C2×D4311yescharacteristic
514C43C2×#327011yescharacteristic, complemented, Sylow
515C2×#41—434no—
516C2×#41—862no—
517C2×#41—864no—
518C2×#41—1722no—
519C22×Q8—434no—
520C22×Q8—434no—
521C22×Q8—434no—
522C22×Q8—431no—
523C22×Q8—431no—
524C22×Q8—861no—
525C22×Q8—861no—
526C22×Q8—861no—
527C22×Q8—862no—
528C22×Q8—862no—
529C22×Q8—862no—
530C22×Q8—864no—
531C22×Q8—864no—
532C22×Q8—864no—
533C22×Q8—1722no—
534C22×Q8—1722no—
535C22×Q8—1722no—
536C22×Q8C22×D4311yescharacteristic
537C22×Q8C22×D4311yescharacteristic
538C22×Q8C22×D4311yescharacteristic
539C22×D4—431no—
540C22×D4—861no—
541C22×D4—861no—
542C22×D4C22×D4311yescharacteristic
543C23×C4—431no—
544C23×C4—431no—
545C23×C4—861no—
546C23×C4—861no—
547C23×C4—861no—
548C23×C4—861no—
549#137—8632no—
550C2×Q16—24no—
551C2×Q16—42no—
552C2×Q16—434no—
553C2×Q16—434no—
554C2×Q16—434no—
555C2×Q16—438no—
556C2×Q16—434no—
557C2×Q16—8632no—
558C2×Q16—864no—
559C2×Q16—864no—
560C2×Q16—864no—
561C2×Q16C22×D4314yes—
562C2×Q16C22×D4314yes—
563C2×SD16—24no—
564C2×SD16—42no—
565C2×SD16—434no—
566C2×SD16—864no—
567C2×SD16C22×D4314yes—
568C2×SD16C22×D4314yes—
569C2×M16—434no—
570C2×M16—864no—
571C22×C8—431no—
572C22×C8—431no—
573C22×C8—434no—
574C22×C8—864no—
575C22×C8C22×D4311yescharacteristic
576C22×C8C22×D4311yescharacteristic
577C4⋊Q8—22no—
578C4⋊Q8—868no—
579C4⋊Q8C22×D4314yes—
580#124—22no—
581#124—868no—
582#124C22×D4314yes—
583C22⋊Q8—434no—
584C22⋊Q8—434no—
585C22⋊Q8—434no—
586C22⋊Q8—868no—
587C22⋊Q8—868no—
588C22⋊Q8—868no—
589C22⋊Q8—862no—
590C22⋊Q8—862no—
591C22⋊Q8—862no—
592#121—434no—
593#121—868no—
594#121—862no—
595C4×Q8—434no—
596C4×Q8—434no—
597C4×Q8—862no—
598C4×Q8—862no—
599C4×D4—434no—
600C4×D4—434no—
601C4×D4—868no—
602C4×D4—868no—
603C2×C4⋊C4—21no—
604C2×C4⋊C4—21no—
605C2×C4⋊C4—431no—
606C2×C4⋊C4—431no—
607C2×C4⋊C4—431no—
608C2×C4⋊C4—861no—
609C2×C4⋊C4—861no—
610C2×C4⋊C4—861no—
611C2×C4⋊C4—861no—
612C2×C4⋊C4—861no—
613C2×C22⋊C4—21no—
614C2×C22⋊C4—21no—
615C2×C22⋊C4—431no—
616C2×C22⋊C4—431no—
617C2×C22⋊C4—861no—
618C2×C22⋊C4—861no—
619C2×C22⋊C4—861no—
620C2×C22⋊C4—861no—
621C2×C42—861no—
622C2×C42—861no—
623C2×C42C22×D4311yescharacteristic
624#106—434no—
625C4⋊C8—434no—
626#103—434no—
627#103—434no—
628#103—434no—
629#103—434no—
630#103—434no—
631#102—434no—
632C22⋊C8—434no—
633C22⋊C8—434no—
634#97C22×D4314yes—
635C24—21no—
636C24—431no—
637C24—431no—
638#41—868no—
639#41—1724no—
640#41—1728no—
641C2×Q8—21no—
642C2×Q8—21no—
643C2×Q8—21no—
644C2×Q8—22no—
645C2×Q8—22no—
646C2×Q8—22no—
647C2×Q8—22no—
648C2×Q8—22no—
649C2×Q8—22no—
650C2×Q8—434no—
651C2×Q8—434no—
652C2×Q8—432no—
653C2×Q8—432no—
654C2×Q8—864no—
655C2×Q8—864no—
656C2×Q8—864no—
657C2×Q8—861no—
658C2×Q8—861no—
659C2×Q8—862no—
660C2×Q8—862no—
661C2×Q8—868no—
662C2×Q8—868no—
663C2×Q8—868no—
664C2×Q8—1724no—
665C2×Q8—1724no—
666C2×Q8—1724no—
667C2×Q8—1724no—
668C2×Q8—1724no—
669C2×Q8—1724no—
670C2×Q8—1728no—
671C2×Q8—1728no—
672C2×Q8—1728no—
673C2×Q8C23×D4312yes—
674C2×Q8C23×D4312yes—
675C2×Q8C23×D4312yes—
676C2×D4—22no—
677C2×D4—21no—
678C2×D4—22no—
679C2×D4—434no—
680C2×D4—864no—
681C2×D4—864no—
682C2×D4—864no—
683C2×D4—1724no—
684C2×D4—1724no—
685C2×D4C23×D4312yes—
686C22×C4—21no—
687C22×C4—21no—
688C22×C4—21no—
689C22×C4—431no—
690C22×C4—431no—
691C22×C4—432no—
692C22×C4—432no—
693C22×C4—432no—
694C22×C4—432no—
695C22×C4—864no—
696C22×C4—864no—
697C22×C4—864no—
698C22×C4—864no—
699C22×C4—861no—
700C22×C4—861no—
701C22×C4—862no—
702C22×C4—862no—
703C22×C4—862no—
704C22×C4—862no—
705C22×C4—861no—
706C22×C4—861no—
707C22×C4—1724no—
708C22×C4—1724no—
709C22×C4—1724no—
710C22×C4—1724no—
711C22×C4D4×D4311yescharacteristic
712C22×C4D4×D4311yescharacteristic
713C22×C4C23×D4311yescharacteristic
714Q16—28no—
715Q16—44no—
716Q16—4316no—
717Q16—868no—
718Q16—868no—
719Q16—868no—
720SD16—28no—
721SD16—44no—
722SD16—868no—
723M16—868no—
724C2×C8—22no—
725C2×C8—432no—
726C2×C8—432no—
727C2×C8—862no—
728C2×C8—862no—
729C2×C8—868no—
730C2×C8D4×D4314yes—
731C2×C8C23×D4312yes—
732C2×C8C23×D4312yes—
733C4⋊C4—24no—
734C4⋊C4—24no—
735C4⋊C4—434no—
736C4⋊C4—432no—
737C4⋊C4—432no—
738C4⋊C4—864no—
739C4⋊C4—864no—
740C4⋊C4—864no—
741C4⋊C4—861no—
742C4⋊C4—861no—
743C4⋊C4—864no—
744C4⋊C4—864no—
745C22⋊C4—24no—
746C22⋊C4—24no—
747C22⋊C4—434no—
748C22⋊C4—434no—
749C22⋊C4—864no—
750C22⋊C4—864no—
751C22⋊C4—864no—
752C22⋊C4—864no—
753C42—864no—
754C42—864no—
755C42D4×D4312yes—
756C42C23×D4312yes—
757C23—22no—
758C23—42no—
759C23—42no—
760C23—42no—
761C23—434no—
762C23—432no—
763C23—432no—
764C23—862no—
765C23—862no—
766C23—862no—
767C23—862no—
768C23—862no—
769C23C2×D4×D4311yescharacteristic
770Q8—22no—
771Q8—22no—
772Q8—22no—
773Q8—22no—
774Q8—22no—
775Q8—22no—
776Q8—42no—
777Q8—42no—
778Q8—42no—
779Q8—434no—
780Q8—434no—
781Q8—862no—
782Q8—862no—
783Q8—864no—
784Q8—864no—
785Q8—1728no—
786Q8—1728no—
787Q8—1728no—
788D4—22no—
789D4—22no—
790D4—42no—
791D4—868no—
792D4—1728no—
793D4—1728no—
794C2×C4—22no—
795C2×C4—22no—
796C2×C4—22no—
797C2×C4—22no—
798C2×C4—22no—
799C2×C4—42no—
800C2×C4—42no—
801C2×C4—42no—
802C2×C4—432no—
803C2×C4—432no—
804C2×C4—862no—
805C2×C4—862no—
806C2×C4—862no—
807C2×C4—862no—
808C2×C4—864no—
809C2×C4—864no—
810C2×C4—862no—
811C2×C4—862no—
812C2×C4—862no—
813C2×C4—862no—
814C2×C4—864no—
815C2×C4—864no—
816C2×C4—862no—
817C2×C4—862no—
818C2×C4—1728no—
819C2×C4—1728no—
820C2×C4—1728no—
821C2×C4—1728no—
822C2×C4—1722no—
823C2×C4—1722no—
824C2×C4C2×D4×D4312yes—
825C2×C4C2×D4×D4312yes—
826C2×C4C2×D4×D4312yes—
827C2×C4C2×D4×D4311yescharacteristic
828C2×C4#1306337012yes—
829C2×C4C24×D4311yescharacteristic
830C8—22no—
831C8—862no—
832C8—862no—
833C8C2×D4×D4314yes—
834C22—42no—
835C22—42no—
836C22—42no—
837C22—84no—
838C22—434no—
839C22—862no—
840C22—862no—
841C22—868no—
842C22—862no—
843C22—862no—
844C22—862no—
845C22—1724no—
846C22#1458353412yes—
847C22#137×D4312yes—
848C22#1458371512yes—
849C22C22×D4×D4311yescharacteristic
850C4—22no—
851C4—22no—
852C4—42no—
853C4—42no—
854C4—42no—
855C4—862no—
856C4—862no—
857C4—864no—
858C4—864no—
859C4—1722no—
860C4—1722no—
861C4#1458353412yes—
862C4C22×D4×D4311yescharacteristic
863C4C2×#1306337011yescharacteristic
864C2—82no—
865C2—864no—
866C2—1722no—
867C2#1914616414yesdirect product factor
868C2C2×#1458353411yescharacteristic
869C2C2×#137×D4311yescharacteristic
870C2C2×#1458371511yescharacteristic
subgroupG/H
centerC23C2×D4×D43
commutator, cosocleC2×C4×C43C25
FrattiniC2×C4C24×D43
FittingC2×C43×#497C2
socleC23×C43C22×D4
prime radicalC2×#14583557C2
hypercenterC2×#497D43
hypocenterC43C2×#3270
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. C22×#13063354C2semidirect
2. C22×Q16×D43C2semidirect
3. C2×#14583564C2semidirect
5. #19146164C2direct (N × H)
6. C2×#14583154C2semidirect
7. C2×#14583125C2semidirect
8. C2×#14583118C2semidirect
9. C2×#14583106C2semidirect
10. C2×#14583058C2semidirect
11. C2×#14583053C2semidirect
12. C2×#14583053C2semidirect
13. C2×#14583036C2semidirect
14. C2×#14583007C2semidirect
15. C2×#14582972C2semidirect
16. C2×C43×#497C2semidirect
22. C2×#13063354C22semidirect
28. C2×Q16×D43C22semidirect
33. #14583564C22semidirect
51. #14583154C22semidirect
52. #14583125C22semidirect
53. #14583118C22semidirect
54. #14583106C22semidirect
55. #14583058C22semidirect
56. #14583053C22semidirect
57. #14583053C22semidirect
58. #14583036C22semidirect
59. #14583007C22semidirect
60. #14582972C22semidirect
77. C43×#497C22semidirect
110. C2×Dic172D4semidirect
318. Dic172C2×D4semidirect
331. C22×D43#137semidirect
414. C2×D43C2×#137semidirect
434. C2×#497D43semidirect
446. C2×C43#3270semidirect
492. #497C2×D43semidirect
514. C43C2×#3270semidirect
867. C2#19146164direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#130633542
C22×Q16×D432
C2×#145835642
C2×#145835572
#191461642
C2×#145831542
C2×#145831252
C2×#145831182
C2×#145831062
C2×#145830582
C2×#145830532
C2×#145830362
C2×#145830072
C2×#145829722
C2×C43×#4972
C2×#327043