Finite Group Databasebeta

← C2×#19146172 #25971649

Subgroups — C2×#19146172 #25971649

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×#13063358C211yesmaximal, characteristic, complemented
2C22×Q16×D43C211yesmaximal, characteristic, complemented
3C2×#14583562C211yesmaximal, characteristic, complemented
4C2×#14583559C211yesmaximal, characteristic
5#19146172C2116yesmaximal, direct product factor
6C2×#14583292C211yesmaximal, characteristic, complemented
7C2×#14583129C211yesmaximal, characteristic, complemented
8C2×#14583124C211yesmaximal, characteristic, complemented
9C2×#14583108C211yesmaximal, characteristic, complemented
10C2×#14583059C211yesmaximal, characteristic, complemented
11C2×#14583056C211yesmaximal, characteristic, complemented
12C2×#14583054C211yesmaximal, characteristic, complemented
13C2×#14583039C211yesmaximal, characteristic, complemented
14C2×#14583005C211yesmaximal, characteristic, complemented
15C2×#14582968C211yesmaximal, characteristic, complemented
16C2×C43×#470C211yesmaximal, characteristic, complemented
17C22×#10621898C2211yescharacteristic
18C23×Dic86C2211yescharacteristic
19C22×Q8×D43C2211yescharacteristic
20C22×Q8×D43C2211yescharacteristic
21C2×#13063358—28no—
22C2×#13063358C2218yescomplemented
23C22×Dic172C2211yescharacteristic
24C22×Dic172C2211yescharacteristic
25C22×#10621885C2211yescharacteristic
26C22×#10621885C2211yescharacteristic
27C22×#10621885C2211yescharacteristic
28C2×Q16×D43—28no—
29C2×Q16×D43C2218yescomplemented
30C22×#10621873C2211yescharacteristic
31C22×#10621873C2211yescharacteristic
32C22×#10621884C2211yescharacteristic
33C22×C8×D43C2211yescharacteristic
34#14583562—24no—
35#14583562C2218yescomplemented
36#14583559—24no—
37#14583559C2218yes—
38C2×#13063324—21no—
39C2×#13063323C2211yescharacteristic
40C2×#13063314C2211yescharacteristic
41C2×#13063311—21no—
42C2×#13063305C2211yescharacteristic
43C2×#13063303—21no—
44C2×#13063303—21no—
45C2×#13063302—21no—
46C2×#13063300C2211yescharacteristic
47C2×#13063298—21no—
48C2×#13063290C2211yescharacteristic
49C2×#13063290C2211yescharacteristic
50C2×#13063287—21no—
51C2×C4×C22⋊D43C2211yescharacteristic
52C2×(C22⋊D43)⋊C4—21no—
53#14583292C2218yescomplemented
54#14583129C2218yescomplemented
55#14583124C2218yescomplemented
56#14583108C2218yescomplemented
57#14583059C2218yescomplemented
58#14583056C2218yescomplemented
59#14583054C2218yescomplemented
60#14583039C2218yescomplemented
61#14583005C2218yescomplemented
62#14582968C2218yescomplemented
63C2×Dic43⋊C8C2211yescharacteristic
64C2×#13063248C2211yescharacteristic
65C2×#13063248C2211yescharacteristic
66C2×#13063248C2211yescharacteristic
67C2×#13063245C2211yescharacteristic
68C2×C22⋊(C43⋊C8)C2211yescharacteristic
69C2×(C2×D43)⋊C8C2211yescharacteristic
70C2×#13063235C2211yescharacteristic
71C22×Q16×C43C2211yescharacteristic
72C22×M16×C43C2211yescharacteristic
73C2×C22⋊Q8×C43C2211yescharacteristic
74C2×C22⋊Q8×C43C2211yescharacteristic
75C43×#470C2218yescomplemented
76C2×#106×C43C2211yescharacteristic
77C2×#103×C43C2211yescharacteristic
78C2×#103×C43C2211yescharacteristic
79C2×#10621898—22no—
80C2×#10621898—24no—
81C2×#10621898—42no—
82C2×#10621898C2314yes—
83C22×Dic86—24no—
84C22×Dic86—22no—
85C22×Dic86—21no—
86C22×Dic86—21no—
87C22×Dic86—21no—
88C22×Dic86—42no—
89C22×Dic86C2311yescharacteristic
90C22×Dic86C2314yes—
91C22×Dic86C2311yescharacteristic
92C22×Dic86C2311yescharacteristic
93C2×Q8×D43—22no—
94C2×Q8×D43—22no—
95C2×Q8×D43—24no—
96C2×Q8×D43—24no—
97C2×Q8×D43—42no—
98C2×Q8×D43—42no—
99C2×Q8×D43C2314yes—
100C2×Q8×D43C2314yes—
101C22×D172—21no—
102C22×D172C2311yescharacteristic
103C22×C22⋊D43—21no—
104C22×C22⋊D43D411yescharacteristic
105C23×Dic43—21no—
106C22×C4×D43—21no—
107C22×C4×D43—21no—
108C22×C4×D43—21no—
109C22×C4×D43C2311yescharacteristic
110#13063358—232no—
111C2×Dic172—24no—
112C2×Dic172D418yescomplemented
113C2×Dic172C2314yes—
114C2×Dic172C2314yes—
115C2×#10621885—24no—
116C2×#10621885—24no—
117C2×#10621885—42no—
118C2×#10621885C2314yes—
119C2×#10621885C2314yes—
120C2×#10621885C2314yes—
121Q16×D43—232no—
122C2×#10621873—24no—
123C2×#10621873—24no—
124C2×#10621873C2314yes—
125C2×#10621873C2314yes—
126C2×#10621884—42no—
127C2×#10621884C2314yes—
128C22×C43⋊C8C2311yescharacteristic
129C22×C43⋊C8C2311yescharacteristic
130C2×C8×D43—24no—
131C2×C8×D43C2314yes—
132#13063324—28no—
133#13063323—22no—
134#13063323C2314yes—
135#13063314—22no—
136#13063314C2314yes—
137#13063311—28no—
138#13063305—22no—
139#13063305C2314yes—
140#13063303—28no—
141#13063303—28no—
142#13063302—28no—
143#13063300—22no—
144#13063300C2314yes—
145#13063298—28no—
146#13063290—22no—
147#13063290—22no—
148#13063290C2314yes—
149#13063290C2314yes—
150#13063287—28no—
151C4×C22⋊D43D414yes—
152C4×C22⋊D43C2314yes—
153(C22⋊D43)⋊C4—28no—
154C2×C4⋊Dic43—21no—
155C2×Dic43⋊C4—21no—
156C2×Dic43⋊C4—21no—
157C2×Dic43⋊C4—21no—
158C2×Dic43⋊C4—21no—
159C2×Dic43⋊C4D411yescharacteristic
160C2×C22⋊Dic43D411yescharacteristic
161C2×(C2×D43)⋊C4—21no—
162C2×(C2×D43)⋊C4—21no—
163C2×(C2×D43)⋊C4—21no—
164C2×(C2×D43)⋊C4—21no—
165C2×(C2×D43)⋊C4D411yescharacteristic
166C2×C4×Dic43—21no—
167C2×C4×Dic43—21no—
168C2×C4×Dic43C2311yescharacteristic
169Dic43⋊C8C2314yes—
170#13063248C2314yes—
171#13063248C2314yes—
172#13063248C2314yes—
173#13063245C2314yes—
174C22⋊(C43⋊C8)C2314yes—
175(C2×D43)⋊C8C2314yes—
176#13063235C2314yes—
177C22×Q8×C43C2311yescharacteristic
178C22×Q8×C43C2311yescharacteristic
179C23×C4×C43C2311yescharacteristic
180C2×Q16×C43—24no—
181C2×Q16×C43C2314yes—
182C2×M16×C43—24no—
183C2×M16×C43C2314yes—
184C22×C8×C43C2311yescharacteristic
185C22×C8×C43C2311yescharacteristic
186C22⋊Q8×C43—22no—
187C22⋊Q8×C43—22no—
188C22⋊Q8×C43C2314yes—
189C22⋊Q8×C43C2314yes—
190C2×C4⋊C4×C43—21no—
191C2×C4⋊C4×C43—21no—
192C2×C4⋊C4×C43C2311yescharacteristic
193C2×C4⋊C4×C43C2311yescharacteristic
194C2×C22⋊C4×C43—21no—
195C2×C22⋊C4×C43—21no—
196#106×C43C2314yes—
197#103×C43C2314yes—
198#103×C43C2314yes—
199C24×C43C2×D411yescharacteristic
200C23×D43—21no—
201C23×D43C2×D411yescharacteristic
202C2×Q8×C43—21no—
203C2×Q8×C43—21no—
204C2×Q8×C43—22no—
205C2×Q8×C43—22no—
206C2×Q8×C43—22no—
207C2×Q8×C43—22no—
208C2×Q8×C43C2412yes—
209C2×Q8×C43C2412yes—
210C22×C4×C43—22no—
211C22×C4×C43—22no—
212C22×C4×C43—21no—
213C22×C4×C43—21no—
214C22×C4×C43—21no—
215C22×C4×C43—21no—
216C22×C4×C43C2×D411yescharacteristic
217C22×C4×C43C2×D412yes—
218C22×C4×C43C2412yes—
219C22×C4×C43C2411yescharacteristic
220C2×C22⋊D43—24no—
221C2×C22⋊D43—24no—
222C2×C22⋊D43—44no—
223C2×C22⋊D43C2×D414yes—
224C22×Dic43—21no—
225C22×Dic43—21no—
226C22×Dic43—21no—
227C22×Dic43—24no—
228C22×Dic43—44no—
229C22×Dic43C2×D411yescharacteristic
230C22×Dic43C2×D411yescharacteristic
231C22×Dic43C2×D411yescharacteristic
232Q8×D43—28no—
233Q8×D43—28no—
234Q8×D43—44no—
235Q8×D43—44no—
236Q8×D43—48no—
237Q8×D43—48no—
238#10621898—28no—
239#10621898—44no—
240#10621898—48no—
241C2×D172—21no—
242C2×D172—24no—
243C2×D172—22no—
244C2×D172—22no—
245C2×D172—44no—
246C2×D172C2412yes—
247C2×C4×D43—22no—
248C2×C4×D43—22no—
249C2×C4×D43—24no—
250C2×C4×D43—24no—
251C2×C4×D43—24no—
252C2×C4×D43—44no—
253C2×C4×D43—44no—
254C2×C4×D43—44no—
255C2×C4×D43C2×D412yes—
256C2×C4×D43C2412yes—
257C2×Dic86—21no—
258C2×Dic86—21no—
259C2×Dic86—22no—
260C2×Dic86—22no—
261C2×Dic86—22no—
262C2×Dic86—22no—
263C2×Dic86—28no—
264C2×Dic86—24no—
265C2×Dic86—21no—
266C2×Dic86—24no—
267C2×Dic86—24no—
268C2×Dic86—44no—
269C2×Dic86—48no—
270C2×Dic86—44no—
271C2×Dic86—44no—
272C2×Dic86—44no—
273C2×Dic86C2×D414yes—
274C2×Dic86C2×D414yes—
275C2×Dic86C2412yes—
276C2×Dic86C2412yes—
277C2×Dic86C2412yes—
278Q16×C43—28no—
279M16×C43—28no—
280C2×C8×C43—22no—
281C2×C8×C43C2×D414yes—
282C2×C8×C43C2412yes—
283C2×C8×C43C2412yes—
284C4⋊C4×C43—24no—
285C4⋊C4×C43—24no—
286C4⋊C4×C43—21no—
287C4⋊C4×C43—21no—
288C4⋊C4×C43C2412yes—
289C4⋊C4×C43C2412yes—
290C22⋊C4×C43—24no—
291C22⋊C4×C43—24no—
292C22⋊Dic43C2×D414yes—
293#10621885—28no—
294#10621885—28no—
295#10621885—44no—
296#10621884—44no—
297(C2×D43)⋊C4—24no—
298(C2×D43)⋊C4—24no—
299(C2×D43)⋊C4—24no—
300(C2×D43)⋊C4—24no—
301(C2×D43)⋊C4C2×D414yes—
302C4⋊Dic43—24no—
303Dic43⋊C4—24no—
304Dic43⋊C4—24no—
305Dic43⋊C4—24no—
306Dic43⋊C4—24no—
307Dic43⋊C4C2×D414yes—
308C4×Dic43—24no—
309C4×Dic43—24no—
310C4×Dic43C2×D412yes—
311C4×Dic43C2412yes—
312C2×C43⋊C8—22no—
313C2×C43⋊C8—22no—
314C2×C43⋊C8C2412yes—
315C2×C43⋊C8C2412yes—
316Dic172—28no—
317Dic172C2×D4116yescomplemented
318#10621873—28no—
319#10621873—28no—
320C8×D43—28no—
321C23×C43—22no—
322C23×C43—22no—
323C23×C43—22no—
324C23×C43C22×D412yes—
325C23×C43C22×D411yescharacteristic
326C22×D43—22no—
327C22×D43—22no—
328C22×D43—22no—
329C22×D43—42no—
330C22×D43—42no—
331C22×D43—42no—
332C22×D43#13714yescomplemented
333C22×D43C22×D412yes—
334Q8×C43—22no—
335Q8×C43—22no—
336Q8×C43—22no—
337Q8×C43—22no—
338Q8×C43—42no—
339Q8×C43—42no—
340C2×C4×C43—22no—
341C2×C4×C43—24no—
342C2×C4×C43—22no—
343C2×C4×C43—22no—
344C2×C4×C43—22no—
345C2×C4×C43—22no—
346C2×C4×C43—22no—
347C2×C4×C43—22no—
348C2×C4×C43—42no—
349C2×C4×C43—42no—
350C2×C4×C43—42no—
351C2×C4×C43—42no—
352C2×C4×C43C22×D412yes—
353C2×C4×C43C22×D411yescharacteristic
354C2×C4×C43C22×D412yes—
355C2×C4×C43H(5,𝔽2)12yes—
356C2×C4×C43C2511yescharacteristic
357C22⋊D43—28no—
358C22⋊D43—48no—
359C2×Dic43—24no—
360C2×Dic43—24no—
361C2×Dic43—22no—
362C2×Dic43—22no—
363C2×Dic43—22no—
364C2×Dic43—22no—
365C2×Dic43—22no—
366C2×Dic43—22no—
367C2×Dic43—48no—
368C2×Dic43—42no—
369C2×Dic43C22×D412yes—
370C2×Dic43C22×D412yes—
371C2×Dic43C22×D412yes—
372D172—22no—
373D172—22no—
374D172—48no—
375D172—42no—
376C4×D43—24no—
377C4×D43—22no—
378C4×D43—22no—
379C4×D43—48no—
380C4×D43—48no—
381C4×D43—48no—
382Dic86—24no—
383Dic86—24no—
384Dic86—22no—
385Dic86—22no—
386Dic86—22no—
387Dic86—22no—
388Dic86—48no—
389Dic86—48no—
390Dic86—48no—
391Dic86—42no—
392Dic86C22×D414yes—
393Dic86C22×D414yes—
394C8×C43—22no—
395C8×C43C22×D414yes—
396C43⋊C8—22no—
397C43⋊C8—22no—
398C2×#3270—431nomaximal, Sylow
399C22×C43—22no—
400C22×C43—22no—
401C22×C43—22no—
402C22×C43—44no—
403C22×C43D4212yes—
404C22×C43C2×#13712yes—
405C22×C43#57812yes—
406C22×C43C23×D411yescharacteristic
407C2×D43—22no—
408C2×D43—28no—
409C2×D43—22no—
410C2×D43—42no—
411C2×D43—42no—
412C2×D43—42no—
413C2×D43—84no—
414C2×D43C2×#13714yescomplemented
415C4×C43—22no—
416C4×C43—42no—
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—22no—
428Dic43—42no—
429C22×#137—431no—
430C23×Q16—431no—
431C2×D4×Q8—431no—
432C2×#548—431no—
433#3270—4316no—
434C2×#497—431no—
435C2×#470D4311yescharacteristic, complemented
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—42no—
446C2×C43#327014yescomplemented
447C2×C43C2×D4211yescharacteristic
448C2×C43C22×#13711yescharacteristic
449C2×C43C2×#57811yescharacteristic
450D43—24no—
451D43—82no—
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—431no—
464C22×Q16—868no—
465C22×Q16C2×D4311yescharacteristic
466C22×SD16—431no—
467C22×SD16—431no—
468C22×SD16—431no—
469C22×M16C2×D4311yescharacteristic
470C23×C8—431no—
471D4×Q8—438no—
472D4×Q8—864no—
473#548—438no—
474#548—864no—
475C2×C4⋊Q8—431no—
476C2×C4⋊Q8—861no—
477C2×#124—431no—
478C2×#124—861no—
479C2×C22⋊Q8—431no—
480C2×C22⋊Q8—861no—
481C2×C22⋊Q8—861no—
482C2×C22⋊Q8—861no—
483C2×C22⋊Q8C2×D4311yescharacteristic
484C2×C22⋊Q8C2×D4311yescharacteristic
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#497—438no—
493#470C2×D4318yescomplemented
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×#106C2×D4311yescharacteristic
504C2×C4⋊C8—431no—
505C2×#103—431no—
506C2×#103—431no—
507C2×#103—431no—
508C2×#103C2×D4311yescharacteristic
509C2×#103C2×D4311yescharacteristic
510C2×#102—431no—
511C2×C22⋊C8—431no—
512C2×C22⋊C8—431no—
513C2×#97—431no—
514C43C2×#327011yescharacteristic, complemented, Sylow
515C2×#41—434no—
516C2×#41—864no—
517C2×#41—862no—
518C2×#41—1722no—
519C22×Q8—434no—
520C22×Q8—434no—
521C22×Q8—431no—
522C22×Q8—431no—
523C22×Q8—431no—
524C22×Q8—434no—
525C22×Q8—861no—
526C22×Q8—861no—
527C22×Q8—864no—
528C22×Q8—862no—
529C22×Q8—862no—
530C22×Q8—861no—
531C22×Q8—862no—
532C22×Q8—864no—
533C22×Q8—864no—
534C22×Q8—1722no—
535C22×Q8—1722no—
536C22×Q8—1722no—
537C22×Q8C22×D4311yescharacteristic
538C22×Q8C22×D4311yescharacteristic
539C22×D4—431no—
540C22×D4—431no—
541C22×D4—861no—
542C22×D4—861no—
543C23×C4—431no—
544C23×C4—861no—
545C23×C4—861no—
546C23×C4—861no—
547C23×C4—861no—
548C23×C4C22×D4311yescharacteristic
549#137—8632no—
550C2×Q16—24no—
551C2×Q16—434no—
552C2×Q16—434no—
553C2×Q16—434no—
554C2×Q16—438no—
555C2×Q16—434no—
556C2×Q16—434no—
557C2×Q16—864no—
558C2×Q16—8632no—
559C2×Q16—864no—
560C2×Q16—864no—
561C2×Q16—1722no—
562C2×Q16C22×D4314yes—
563C2×SD16—434no—
564C2×SD16—434no—
565C2×SD16—434no—
566C2×SD16—864no—
567C2×SD16—864no—
568C2×SD16—1722no—
569C2×M16—24no—
570C2×M16C22×D4314yes—
571C22×C8—431no—
572C22×C8—431no—
573C22×C8—434no—
574C22×C8—864no—
575C22×C8C22×D4311yescharacteristic
576C22×C8C22×D4311yescharacteristic
577C4⋊Q8—434no—
578C4⋊Q8—862no—
579C4⋊Q8—868no—
580#124—434no—
581#124—862no—
582#124—868no—
583C22⋊Q8—22no—
584C22⋊Q8—22no—
585C22⋊Q8—434no—
586C22⋊Q8—868no—
587C22⋊Q8—868no—
588C22⋊Q8—868no—
589C22⋊Q8—862no—
590C22⋊Q8C22×D4314yes—
591C22⋊Q8C22×D4314yes—
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—861no—
607C2×C4⋊C4—861no—
608C2×C4⋊C4—861no—
609C2×C4⋊C4—861no—
610C2×C4⋊C4—861no—
611C2×C4⋊C4C22×D4311yescharacteristic
612C2×C4⋊C4C22×D4311yescharacteristic
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—431no—
622C2×C42—861no—
623C2×C42—861no—
624#106C22×D4314yes—
625C4⋊C8—434no—
626#103—434no—
627#103—434no—
628#103—434no—
629#103C22×D4314yes—
630#103C22×D4314yes—
631#102—434no—
632C22⋊C8—434no—
633C22⋊C8—434no—
634#97—434no—
635C24—431no—
636C24—861no—
637C24D4×D4311yescharacteristic
638#41—868no—
639#41—1724no—
640#41—1728no—
641C2×Q8—21no—
642C2×Q8—21no—
643C2×Q8—22no—
644C2×Q8—22no—
645C2×Q8—22no—
646C2×Q8—22no—
647C2×Q8—434no—
648C2×Q8—434no—
649C2×Q8—432no—
650C2×Q8—432no—
651C2×Q8—432no—
652C2×Q8—864no—
653C2×Q8—864no—
654C2×Q8—868no—
655C2×Q8—861no—
656C2×Q8—861no—
657C2×Q8—864no—
658C2×Q8—861no—
659C2×Q8—862no—
660C2×Q8—862no—
661C2×Q8—868no—
662C2×Q8—868no—
663C2×Q8—862no—
664C2×Q8—862no—
665C2×Q8—1724no—
666C2×Q8—1724no—
667C2×Q8—1728no—
668C2×Q8—1724no—
669C2×Q8—1724no—
670C2×Q8—1724no—
671C2×Q8—1724no—
672C2×Q8—1728no—
673C2×Q8—1728no—
674C2×Q8C23×D4312yes—
675C2×Q8C23×D4312yes—
676C2×D4—434no—
677C2×D4—432no—
678C2×D4—864no—
679C2×D4—864no—
680C2×D4—864no—
681C2×D4—862no—
682C2×D4—861no—
683C2×D4—862no—
684C2×D4—1724no—
685C2×D4—1724no—
686C22×C4—22no—
687C22×C4—22no—
688C22×C4—21no—
689C22×C4—21no—
690C22×C4—21no—
691C22×C4—21no—
692C22×C4—431no—
693C22×C4—431no—
694C22×C4—431no—
695C22×C4—432no—
696C22×C4—432no—
697C22×C4—864no—
698C22×C4—864no—
699C22×C4—861no—
700C22×C4—861no—
701C22×C4—862no—
702C22×C4—862no—
703C22×C4—864no—
704C22×C4—861no—
705C22×C4—864no—
706C22×C4—1724no—
707C22×C4—1724no—
708C22×C4—1724no—
709C22×C4—1724no—
710C22×C4D4×D4312yes—
711C22×C4D4×D4311yescharacteristic
712C22×C4C23×D4312yes—
713C22×C4C23×D4311yescharacteristic
714Q16—28no—
715Q16—4316no—
716Q16—868no—
717Q16—868no—
718Q16—868no—
719Q16—1724no—
720SD16—868no—
721SD16—868no—
722SD16—1724no—
723M16—28no—
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—21no—
736C4⋊C4—21no—
737C4⋊C4—434no—
738C4⋊C4—864no—
739C4⋊C4—864no—
740C4⋊C4—864no—
741C4⋊C4—864no—
742C4⋊C4—864no—
743C4⋊C4C23×D4312yes—
744C4⋊C4C23×D4312yes—
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—432no—
754C42—432no—
755C42—864no—
756C42—864no—
757C23—22no—
758C23—22no—
759C23—22no—
760C23—434no—
761C23—432no—
762C23—862no—
763C23—862no—
764C23—862no—
765C23—1722no—
766C23—1722no—
767C23—1722no—
768C23C2×D4×D4312yes—
769C23C2×D4×D4311yescharacteristic
770Q8—22no—
771Q8—22no—
772Q8—22no—
773Q8—22no—
774Q8—42no—
775Q8—42no—
776Q8—434no—
777Q8—434no—
778Q8—862no—
779Q8—862no—
780Q8—864no—
781Q8—864no—
782Q8—862no—
783Q8—862no—
784Q8—1728no—
785Q8—1728no—
786Q8—1728no—
787Q8—1722no—
788D4—868no—
789D4—862no—
790D4—862no—
791D4—1728no—
792D4—1728no—
793D4—1722no—
794C2×C4—22no—
795C2×C4—22no—
796C2×C4—22no—
797C2×C4—24no—
798C2×C4—22no—
799C2×C4—22no—
800C2×C4—22no—
801C2×C4—22no—
802C2×C4—42no—
803C2×C4—42no—
804C2×C4—42no—
805C2×C4—42no—
806C2×C4—432no—
807C2×C4—432no—
808C2×C4—432no—
809C2×C4—862no—
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—864no—
819C2×C4—862no—
820C2×C4—1728no—
821C2×C4—1728no—
822C2×C4—1728no—
823C2×C4—1728no—
824C2×C4—1722no—
825C2×C4C2×D4×D4312yes—
826C2×C4C2×D4×D4312yes—
827C2×C4C2×D4×D4311yescharacteristic
828C2×C4#1306337112yes—
829C2×C4C24×D4311yescharacteristic
830C8—22no—
831C8—862no—
832C8—862no—
833C8C2×D4×D4314yes—
834C22—22no—
835C22—22no—
836C22—22no—
837C22—44no—
838C22—434no—
839C22—862no—
840C22—862no—
841C22—868no—
842C22—3444no—
843C22—1722no—
844C22—1722no—
845C22—1722no—
846C22#1458353312yes—
847C22#137×D4312yes—
848C22#1458371512yes—
849C22C22×D4×D4311yescharacteristic
850C4—22no—
851C4—42no—
852C4—42no—
853C4—42no—
854C4—42no—
855C4—862no—
856C4—864no—
857C4—864no—
858C4—862no—
859C4—862no—
860C4—1722no—
861C4#1458353312yes—
862C4C22×D4×D4311yescharacteristic
863C4C2×#1306337111yescharacteristic
864C2—42no—
865C2—864no—
866C2—3442no—
867C2#1914617214yesdirect product factor
868C2C2×#1458353311yescharacteristic
869C2C2×#137×D4311yescharacteristic
870C2C2×#1458371511yescharacteristic
subgroupG/H
centerC23C2×D4×D43
commutator, cosocleC2×C4×C43C25
FrattiniC2×C4C24×D43
FittingC2×C43×#470C2
socleC23×C43C22×D4
prime radicalC2×#14583559C2
hypercenterC2×#470D43
hypocenterC43C2×#3270
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#470

Complements

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

NH ≅ G/Ntype
1. C22×#13063358C2semidirect
2. C22×Q16×D43C2semidirect
3. C2×#14583562C2semidirect
5. #19146172C2direct (N × H)
6. C2×#14583292C2semidirect
7. C2×#14583129C2semidirect
8. C2×#14583124C2semidirect
9. C2×#14583108C2semidirect
10. C2×#14583059C2semidirect
11. C2×#14583056C2semidirect
12. C2×#14583054C2semidirect
13. C2×#14583039C2semidirect
14. C2×#14583005C2semidirect
15. C2×#14582968C2semidirect
16. C2×C43×#470C2semidirect
22. C2×#13063358C22semidirect
29. C2×Q16×D43C22semidirect
35. #14583562C22semidirect
53. #14583292C22semidirect
54. #14583129C22semidirect
55. #14583124C22semidirect
56. #14583108C22semidirect
57. #14583059C22semidirect
58. #14583056C22semidirect
59. #14583054C22semidirect
60. #14583039C22semidirect
61. #14583005C22semidirect
62. #14582968C22semidirect
75. C43×#470C22semidirect
112. C2×Dic172D4semidirect
317. Dic172C2×D4semidirect
332. C22×D43#137semidirect
414. C2×D43C2×#137semidirect
435. C2×#470D43semidirect
446. C2×C43#3270semidirect
493. #470C2×D43semidirect
514. C43C2×#3270semidirect
867. C2#19146172direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#130633582
C22×Q16×D432
C2×#145835622
C2×#145835592
#191461722
C2×#145832922
C2×#145831292
C2×#145831242
C2×#145831082
C2×#145830592
C2×#145830562
C2×#145830542
C2×#145830392
C2×#145830052
C2×#145829682
C2×C43×#4702
C2×#327043