Finite Group Databasebeta

← C2×#19146166 #25971643

Subgroups — C2×#19146166 #25971643

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×#13063356C211yesmaximal, characteristic, complemented
2C23×#10621885C211yesmaximal, characteristic, complemented
3C2×#14583558C211yesmaximal, characteristic
4#19146166C2116yesmaximal, direct product factor
5C2×#14583291C211yesmaximal, characteristic, complemented
6C2×#14583155C211yesmaximal, characteristic, complemented
7C2×#14583130C211yesmaximal, characteristic, complemented
8C2×#14583121C211yesmaximal, characteristic, complemented
9C2×#14583106C211yesmaximal, characteristic, complemented
10C2×#14583059C211yesmaximal, characteristic, complemented
11C2×#14583055C211yesmaximal, characteristic, complemented
12C2×#14583054C211yesmaximal, characteristic, complemented
13C2×#14583038C211yesmaximal, characteristic, complemented
14C2×#14583004C211yesmaximal, characteristic, complemented
15C2×#14582971C211yesmaximal, characteristic, complemented
16C2×D4×Q8×C43C211yesmaximal, characteristic, complemented
17C22×#10621898C2211yescharacteristic
18C23×Dic86C2211yescharacteristic
19C2×#13063356—28no—
20C2×#13063356C2218yescomplemented
21C22×#10621885—28no—
22C22×#10621885C2211yescharacteristic
23C22×#10621885C2211yescharacteristic
24C22×#10621885C2211yescharacteristic
25C22×#10621885C2211yescharacteristic
26C22×#10621885C2211yescharacteristic
27C22×#10621885C2211yescharacteristic
28C22×#10621885C2218yescomplemented
29C22×#10621884C2211yescharacteristic
30C22×#10621884C2211yescharacteristic
31C22×#10621884C2211yescharacteristic
32C22×#10621877C2211yescharacteristic
33C23×C43⋊C8C2211yescharacteristic
34#14583558—24no—
35#14583558C2218yes—
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#14583155C2218yescomplemented
46#14583130C2218yescomplemented
47#14583121C2218yescomplemented
48#14583106C2218yescomplemented
49#14583059C2218yescomplemented
50#14583055C2218yescomplemented
51#14583054C2218yescomplemented
52#14583038C2218yescomplemented
53#14583004C2218yescomplemented
54#14582971C2218yescomplemented
55C2×#13063256C2211yescharacteristic
56C2×C4⋊(C43⋊C8)C2211yescharacteristic
57C2×#13063249C2211yescharacteristic
58C2×#13063249C2211yescharacteristic
59C2×#13063249C2211yescharacteristic
60C2×#13063248C2211yescharacteristic
61C2×#13063248C2211yescharacteristic
62C2×#13063245C2211yescharacteristic
63C2×C22⋊(C43⋊C8)C2211yescharacteristic
64C2×C22⋊(C43⋊C8)C2211yescharacteristic
65C2×#13063236C2211yescharacteristic
66C23×Q8×C43C2211yescharacteristic
67C23×Q8×C43C2211yescharacteristic
68D4×Q8×C43—24no—
69D4×Q8×C43C2218yescomplemented
70C2×C4⋊Q8×C43—21no—
71C2×C4⋊Q8×C43C2211yescharacteristic
72C2×C22⋊Q8×C43—21no—
73C2×C22⋊Q8×C43—21no—
74C2×C22⋊Q8×C43C2211yescharacteristic
75C2×C22⋊Q8×C43C2211yescharacteristic
76C2×C4×Q8×C43C2211yescharacteristic
77C2×C4×D4×C43—21no—
78C2×C4×D4×C43C2211yescharacteristic
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#13063356—232no—
96C2×#10621885—24no—
97C2×#10621885—24no—
98C2×#10621885—24no—
99C2×#10621885—232no—
100C2×#10621885—24no—
101C2×#10621885—42no—
102C2×#10621885D418yescomplemented
103C2×#10621885C2314yes—
104C2×#10621885C2314yes—
105C2×#10621885C2314yes—
106C2×#10621885C2314yes—
107C2×#10621885C2314yes—
108C2×#10621885C2314yes—
109C2×#10621884—24no—
110C2×#10621884—24no—
111C2×#10621884—42no—
112C2×#10621884C2314yes—
113C2×#10621884C2314yes—
114C2×#10621884C2314yes—
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#13063256C2314yes—
144C4⋊(C43⋊C8)C2314yes—
145#13063249C2314yes—
146#13063249C2314yes—
147#13063249C2314yes—
148#13063248C2314yes—
149#13063248C2314yes—
150#13063245C2314yes—
151C22⋊(C43⋊C8)C2314yes—
152C22⋊(C43⋊C8)C2314yes—
153#13063236C2314yes—
154C22×Q8×C43—21no—
155C22×Q8×C43—21no—
156C22×Q8×C43—22no—
157C22×Q8×C43—22no—
158C22×Q8×C43—24no—
159C22×Q8×C43—24no—
160C22×Q8×C43—42no—
161C22×Q8×C43—42no—
162C22×Q8×C43C2311yescharacteristic
163C22×Q8×C43C2311yescharacteristic
164C22×Q8×C43C2314yes—
165C22×Q8×C43C2314yes—
166C22×Q8×C43C2311yescharacteristic
167C22×D4×C43D411yescharacteristic
168C23×C4×C43—21no—
169C23×C4×C43—21no—
170C23×C4×C43C2311yescharacteristic
171C23×C4×C43C2311yescharacteristic
172C4⋊Q8×C43—28no—
173C4⋊Q8×C43—22no—
174C4⋊Q8×C43C2314yes—
175C22⋊Q8×C43—22no—
176C22⋊Q8×C43—22no—
177C22⋊Q8×C43—28no—
178C22⋊Q8×C43—28no—
179C22⋊Q8×C43C2314yes—
180C22⋊Q8×C43C2314yes—
181C4×Q8×C43—22no—
182C4×Q8×C43C2314yes—
183C4×D4×C43—28no—
184C4×D4×C43D414yes—
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—21no—
191C2×C4⋊C4×C43D411yescharacteristic
192C2×C4⋊C4×C43C2311yescharacteristic
193C2×C22⋊C4×C43—21no—
194C2×C22⋊C4×C43—21no—
195C2×C22⋊C4×C43D411yescharacteristic
196C2×C22⋊C4×C43D411yescharacteristic
197C2×C42×C43—21no—
198C2×C42×C43C2311yescharacteristic
199C24×C43C2×D411yescharacteristic
200C24×C43C2×D411yescharacteristic
201C23×D43—21no—
202C2×Q8×C43—21no—
203C2×Q8×C43—24no—
204C2×Q8×C43—24no—
205C2×Q8×C43—21no—
206C2×Q8×C43—21no—
207C2×Q8×C43—22no—
208C2×Q8×C43—28no—
209C2×Q8×C43—28no—
210C2×Q8×C43—22no—
211C2×Q8×C43—22no—
212C2×Q8×C43—22no—
213C2×Q8×C43—22no—
214C2×Q8×C43—44no—
215C2×Q8×C43—44no—
216C2×Q8×C43—44no—
217C2×Q8×C43—44no—
218C2×Q8×C43—48no—
219C2×Q8×C43—48no—
220C2×Q8×C43C2×D414yes—
221C2×Q8×C43C2412yes—
222C2×Q8×C43C2412yes—
223C2×Q8×C43C2412yes—
224C2×D4×C43—24no—
225C2×D4×C43C2×D414yes—
226C22×C4×C43—22no—
227C22×C4×C43—22no—
228C22×C4×C43—22no—
229C22×C4×C43—22no—
230C22×C4×C43—21no—
231C22×C4×C43—21no—
232C22×C4×C43—21no—
233C22×C4×C43—21no—
234C22×C4×C43—24no—
235C22×C4×C43—24no—
236C22×C4×C43—44no—
237C22×C4×C43—44no—
238C22×C4×C43C2×D411yescharacteristic
239C22×C4×C43C2×D411yescharacteristic
240C22×C4×C43C2×D411yescharacteristic
241C22×C4×C43C2×D411yescharacteristic
242C22×C4×C43C2×D412yes—
243C22×C4×C43C2×D412yes—
244C22×C4×C43C2412yes—
245C22×C4×C43C2412yes—
246C22×C4×C43C2411yescharacteristic
247C2×C22⋊D43—24no—
248C2×C22⋊D43—24no—
249C2×C22⋊D43—44no—
250C2×C22⋊D43—44no—
251C22×Dic43—21no—
252C22×Dic43—21no—
253C22×Dic43—21no—
254C22×Dic43—24no—
255C22×Dic43—44no—
256#10621898—28no—
257#10621898—44no—
258#10621898—48no—
259C2×D172—21no—
260C2×D172—22no—
261C2×D172—22no—
262C2×D172C2412yes—
263C2×C4×D43—24no—
264C2×C4×D43—44no—
265C2×Dic86—21no—
266C2×Dic86—22no—
267C2×Dic86—22no—
268C2×Dic86—22no—
269C2×Dic86—28no—
270C2×Dic86—24no—
271C2×Dic86—21no—
272C2×Dic86—44no—
273C2×Dic86—48no—
274C2×Dic86—44no—
275C2×Dic86C2×D414yes—
276C2×Dic86C2412yes—
277C2×Dic86C2412yes—
278C4⋊C4×C43—24no—
279C4⋊C4×C43—24no—
280C4⋊C4×C43—24no—
281C4⋊C4×C43—24no—
282C4⋊C4×C43—24no—
283C4⋊C4×C43—21no—
284C4⋊C4×C43C2×D414yes—
285C4⋊C4×C43C2412yes—
286C22⋊C4×C43—24no—
287C22⋊C4×C43—24no—
288C22⋊C4×C43C2×D414yes—
289C22⋊C4×C43C2×D414yes—
290C42×C43—24no—
291C42×C43C2×D412yes—
292C42×C43C2412yes—
293C22⋊Dic43—24no—
294#10621885—28no—
295#10621885—28no—
296#10621885—28no—
297#10621885—28no—
298#10621885—44no—
299#10621885C2×D4116yescomplemented
300#10621884—28no—
301#10621884—28no—
302#10621884—44no—
303(C2×D43)⋊C4—24no—
304(C2×D43)⋊C4—24no—
305(C2×D43)⋊C4—24no—
306C4⋊Dic43—21no—
307C4⋊Dic43C2412yes—
308Dic43⋊C4—24no—
309Dic43⋊C4—24no—
310C4×Dic43—24no—
311#10621877—28no—
312C2×C43⋊C8—22no—
313C2×C43⋊C8—22no—
314C2×C43⋊C8—22no—
315C2×C43⋊C8—28no—
316C2×C43⋊C8C2×D414yes—
317C2×C43⋊C8C2412yes—
318C2×C43⋊C8C2412yes—
319C2×C43⋊C8C2412yes—
320C2×C43⋊C8C2412yes—
321C23×C43—22no—
322C23×C43—22no—
323C23×C43—22no—
324C23×C43—22no—
325C23×C43—22no—
326C23×C43#13714yescomplemented
327C23×C43C22×D412yes—
328C23×C43C22×D412yes—
329C23×C43C22×D411yescharacteristic
330C22×D43—22no—
331C22×D43—42no—
332C22×D43—42no—
333C22×D43—42no—
334Q8×C43—24no—
335Q8×C43—22no—
336Q8×C43—22no—
337Q8×C43—22no—
338Q8×C43—22no—
339Q8×C43—22no—
340Q8×C43—48no—
341Q8×C43—48no—
342Q8×C43—42no—
343Q8×C43—42no—
344Q8×C43C22×D414yes—
345D4×C43—28no—
346C2×C4×C43—22no—
347C2×C4×C43—22no—
348C2×C4×C43—24no—
349C2×C4×C43—22no—
350C2×C4×C43—22no—
351C2×C4×C43—22no—
352C2×C4×C43—24no—
353C2×C4×C43—24no—
354C2×C4×C43—22no—
355C2×C4×C43—22no—
356C2×C4×C43—22no—
357C2×C4×C43—22no—
358C2×C4×C43—22no—
359C2×C4×C43—22no—
360C2×C4×C43—22no—
361C2×C4×C43—48no—
362C2×C4×C43—48no—
363C2×C4×C43—42no—
364C2×C4×C43—42no—
365C2×C4×C43—42no—
366C2×C4×C43C22×D412yes—
367C2×C4×C43C22×D412yes—
368C2×C4×C43C22×D412yes—
369C2×C4×C43C22×D412yes—
370C2×C4×C43C22×D412yes—
371C2×C4×C43C22×D411yescharacteristic
372C2×C4×C43H(5,𝔽2)12yes—
373C2×C4×C43C2511yescharacteristic
374C22⋊D43—48no—
375C22⋊D43—48no—
376C2×Dic43—24no—
377C2×Dic43—22no—
378C2×Dic43—22no—
379C2×Dic43—22no—
380C2×Dic43—48no—
381C2×Dic43—42no—
382C2×Dic43—42no—
383D172—22no—
384D172—22no—
385D172—42no—
386C4×D43—48no—
387Dic86—24no—
388Dic86—22no—
389Dic86—22no—
390Dic86—22no—
391Dic86—48no—
392Dic86—42no—
393Dic86C22×D414yes—
394C43⋊C8—22no—
395C43⋊C8—22no—
396C43⋊C8—22no—
397C43⋊C8C22×D414yes—
398C2×#3270—431nomaximal, Sylow
399C22×C43—22no—
400C22×C43—28no—
401C22×C43—22no—
402C22×C43—22no—
403C22×C43—22no—
404C22×C43—22no—
405C22×C43—44no—
406C22×C43D4212yes—
407C22×C43C2×#13712yes—
408C22×C43C2×#13714yescomplemented
409C22×C43#57812yes—
410C22×C43C23×D411yescharacteristic
411C2×D43—42no—
412C2×D43—42no—
413C2×D43—42no—
414C2×D43—84no—
415C4×C43—22no—
416C4×C43—22no—
417C4×C43—24no—
418C4×C43—22no—
419C4×C43—22no—
420C4×C43—42no—
421C4×C43—42no—
422C4×C43—42no—
423C4×C43D4212yes—
424C4×C43C23×D411yescharacteristic
425C4×C43C2×H(5,𝔽2)11yescharacteristic
426Dic43—24no—
427Dic43—42no—
428Dic43—42no—
429C22×#137—431no—
430C23×Q16—431no—
431C2×D4×Q8D4311yescharacteristic, complemented
432C2×#548—431no—
433#3270—4316no—
434C2×#497—431no—
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—24no—
446C2×C43—42no—
447C2×C43#327014yescomplemented
448C2×C43C2×D4211yescharacteristic
449C2×C43C22×#13711yescharacteristic
450C2×C43C2×#57811yescharacteristic
451D43—82no—
452C22×#41—431no—
453C23×Q8—431no—
454C23×Q8C2×D4311yescharacteristic
455C23×Q8C2×D4311yescharacteristic
456C2×#137—438no—
457C2×#137—868no—
458C22×Q16—431no—
459C22×Q16—431no—
460C22×Q16—431no—
461C22×Q16—431no—
462C22×Q16—431no—
463C22×Q16—438no—
464C22×Q16—431no—
465C22×Q16—868no—
466C22×SD16—431no—
467C22×SD16—431no—
468C22×SD16—431no—
469C22×M16—431no—
470C23×C8—431no—
471D4×Q8—24no—
472D4×Q8C2×D4318yescomplemented
473#548—438no—
474#548—864no—
475C2×C4⋊Q8—21no—
476C2×C4⋊Q8C2×D4311yescharacteristic
477C2×#124—431no—
478C2×#124—861no—
479C2×C22⋊Q8—21no—
480C2×C22⋊Q8—21no—
481C2×C22⋊Q8—431no—
482C2×C22⋊Q8—861no—
483C2×C22⋊Q8C2×D4311yescharacteristic
484C2×C22⋊Q8C2×D4311yescharacteristic
485C2×#121—431no—
486C2×#121—861no—
487C2×C4×Q8—431no—
488C2×C4×Q8C2×D4311yescharacteristic
489C2×C4×D4—21no—
490C2×C4×D4—861no—
491C2×C4×D4C2×D4311yescharacteristic
492#497—438no—
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×#97—431no—
514C43C2×#327011yescharacteristic, complemented, Sylow
515C2×#41—434no—
516C2×#41—864no—
517C2×#41—862no—
518C2×#41—1722no—
519C22×Q8—21no—
520C22×Q8—21no—
521C22×Q8—22no—
522C22×Q8—22no—
523C22×Q8—24no—
524C22×Q8—24no—
525C22×Q8—42no—
526C22×Q8—42no—
527C22×Q8—431no—
528C22×Q8—431no—
529C22×Q8—434no—
530C22×Q8—864no—
531C22×Q8—861no—
532C22×Q8—862no—
533C22×Q8—1722no—
534C22×Q8C22×D4311yescharacteristic
535C22×Q8C22×D4311yescharacteristic
536C22×Q8C22×D4314yes—
537C22×Q8C22×D4314yes—
538C22×Q8C22×D4311yescharacteristic
539C22×D4—431no—
540C22×D4—861no—
541C22×D4—861no—
542C22×D4C22⋊D4311yescharacteristic
543C23×C4—21no—
544C23×C4—21no—
545C23×C4—861no—
546C23×C4—861no—
547C23×C4C22×D4311yescharacteristic
548C23×C4C22×D4311yescharacteristic
549#137—8632no—
550C2×Q16—438no—
551C2×Q16—434no—
552C2×Q16—434no—
553C2×Q16—434no—
554C2×Q16—434no—
555C2×Q16—434no—
556C2×Q16—434no—
557C2×Q16—864no—
558C2×Q16—8632no—
559C2×Q16—864no—
560C2×Q16—864no—
561C2×Q16—864no—
562C2×Q16—1722no—
563C2×SD16—434no—
564C2×SD16—434no—
565C2×SD16—434no—
566C2×SD16—864no—
567C2×SD16—864no—
568C2×SD16—1722no—
569C2×M16—434no—
570C2×M16—864no—
571C22×C8—431no—
572C22×C8—431no—
573C22×C8—434no—
574C22×C8—431no—
575C22×C8—431no—
576C22×C8—864no—
577C4⋊Q8—28no—
578C4⋊Q8—22no—
579C4⋊Q8C22×D4314yes—
580#124—434no—
581#124—868no—
582#124—862no—
583C22⋊Q8—22no—
584C22⋊Q8—22no—
585C22⋊Q8—28no—
586C22⋊Q8—28no—
587C22⋊Q8—434no—
588C22⋊Q8—862no—
589C22⋊Q8—868no—
590C22⋊Q8C22×D4314yes—
591C22⋊Q8C22×D4314yes—
592#121—434no—
593#121—868no—
594#121—862no—
595C4×Q8—22no—
596C4×Q8—434no—
597C4×Q8—862no—
598C4×Q8C22×D4314yes—
599C4×D4—28no—
600C4×D4—868no—
601C4×D4C22⋊D4314yes—
602C4×D4C22×D4314yes—
603C2×C4⋊C4—21no—
604C2×C4⋊C4—21no—
605C2×C4⋊C4—21no—
606C2×C4⋊C4—21no—
607C2×C4⋊C4—21no—
608C2×C4⋊C4—431no—
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—861no—
616C2×C22⋊C4—861no—
617C2×C22⋊C4—861no—
618C2×C22⋊C4—861no—
619C2×C22⋊C4C22⋊D4311yescharacteristic
620C2×C22⋊C4C22⋊D4311yescharacteristic
621C2×C42—21no—
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#97—434no—
635C24—861no—
636C24C2×C22⋊D4311yescharacteristic
637C24C2×C22⋊D4311yescharacteristic
638#41—868no—
639#41—1724no—
640#41—1728no—
641C2×Q8—21no—
642C2×Q8—24no—
643C2×Q8—24no—
644C2×Q8—21no—
645C2×Q8—21no—
646C2×Q8—22no—
647C2×Q8—28no—
648C2×Q8—28no—
649C2×Q8—22no—
650C2×Q8—22no—
651C2×Q8—22no—
652C2×Q8—22no—
653C2×Q8—44no—
654C2×Q8—44no—
655C2×Q8—44no—
656C2×Q8—44no—
657C2×Q8—48no—
658C2×Q8—48no—
659C2×Q8—434no—
660C2×Q8—432no—
661C2×Q8—432no—
662C2×Q8—868no—
663C2×Q8—861no—
664C2×Q8—864no—
665C2×Q8—861no—
666C2×Q8—862no—
667C2×Q8—862no—
668C2×Q8—862no—
669C2×Q8—1724no—
670C2×Q8—1724no—
671C2×Q8—1728no—
672C2×Q8D4×D4314yes—
673C2×Q8C23×D4312yes—
674C2×Q8C23×D4312yes—
675C2×Q8C23×D4312yes—
676C2×D4—24no—
677C2×D4—432no—
678C2×D4—864no—
679C2×D4—864no—
680C2×D4—862no—
681C2×D4—861no—
682C2×D4—862no—
683C2×D4—1724no—
684C2×D4—1724no—
685C2×D4C2×C22⋊D4314yes—
686C22×C4—21no—
687C22×C4—22no—
688C22×C4—22no—
689C22×C4—22no—
690C22×C4—22no—
691C22×C4—24no—
692C22×C4—24no—
693C22×C4—21no—
694C22×C4—21no—
695C22×C4—21no—
696C22×C4—44no—
697C22×C4—44no—
698C22×C4—861no—
699C22×C4—864no—
700C22×C4—861no—
701C22×C4—861no—
702C22×C4—864no—
703C22×C4—1724no—
704C22×C4—1724no—
705C22×C4C2×C22⋊D4312yes—
706C22×C4C2×C22⋊D4312yes—
707C22×C4C2×C22⋊D4311yescharacteristic
708C22×C4C2×C22⋊D4311yescharacteristic
709C22×C4C2×C22⋊D4311yescharacteristic
710C22×C4C2×C22⋊D4311yescharacteristic
711C22×C4C23×D4312yes—
712C22×C4C23×D4312yes—
713C22×C4C23×D4311yescharacteristic
714Q16—4316no—
715Q16—868no—
716Q16—868no—
717Q16—868no—
718Q16—868no—
719Q16—1724no—
720SD16—868no—
721SD16—868no—
722SD16—1724no—
723M16—868no—
724C2×C8—434no—
725C2×C8—432no—
726C2×C8—432no—
727C2×C8—432no—
728C2×C8—432no—
729C2×C8—868no—
730C2×C8—862no—
731C2×C8—862no—
732C2×C8—862no—
733C4⋊C4—24no—
734C4⋊C4—24no—
735C4⋊C4—24no—
736C4⋊C4—24no—
737C4⋊C4—24no—
738C4⋊C4—21no—
739C4⋊C4—432no—
740C4⋊C4—861no—
741C4⋊C4—864no—
742C4⋊C4—864no—
743C4⋊C4C2×C22⋊D4314yes—
744C4⋊C4C23×D4312yes—
745C22⋊C4—24no—
746C22⋊C4—24no—
747C22⋊C4—864no—
748C22⋊C4—864no—
749C22⋊C4—864no—
750C22⋊C4—864no—
751C22⋊C4C2×C22⋊D4314yes—
752C22⋊C4C2×C22⋊D4314yes—
753C42—24no—
754C42—864no—
755C42C2×C22⋊D4312yes—
756C42C23×D4312yes—
757C23—22no—
758C23—22no—
759C23—22no—
760C23—22no—
761C23—22no—
762C23—862no—
763C23—1722no—
764C23—1722no—
765C23—1722no—
766C23#1306335614yescomplemented
767C23C22×C22⋊D4312yes—
768C23C22×C22⋊D4312yes—
769C23C22×C22⋊D4311yescharacteristic
770Q8—22no—
771Q8—24no—
772Q8—22no—
773Q8—22no—
774Q8—22no—
775Q8—22no—
776Q8—48no—
777Q8—48no—
778Q8—42no—
779Q8—42no—
780Q8—434no—
781Q8—862no—
782Q8—864no—
783Q8—862no—
784Q8—862no—
785Q8—1728no—
786Q8—1722no—
787Q8C2×D4×D4314yes—
788D4—28no—
789D4—862no—
790D4—862no—
791D4—1728no—
792D4—1728no—
793D4—1722no—
794C2×C4—22no—
795C2×C4—22no—
796C2×C4—22no—
797C2×C4—22no—
798C2×C4—22no—
799C2×C4—24no—
800C2×C4—22no—
801C2×C4—22no—
802C2×C4—22no—
803C2×C4—22no—
804C2×C4—24no—
805C2×C4—24no—
806C2×C4—22no—
807C2×C4—22no—
808C2×C4—22no—
809C2×C4—48no—
810C2×C4—48no—
811C2×C4—42no—
812C2×C4—42no—
813C2×C4—42no—
814C2×C4—862no—
815C2×C4—864no—
816C2×C4—862no—
817C2×C4—862no—
818C2×C4—1728no—
819C2×C4—1728no—
820C2×C4—1722no—
821C2×C4—1722no—
822C2×C4C2×D4×D4312yes—
823C2×C4C22×C22⋊D4312yes—
824C2×C4C22×C22⋊D4312yes—
825C2×C4C22×C22⋊D4312yes—
826C2×C4C22×C22⋊D4312yes—
827C2×C4C22×C22⋊D4311yescharacteristic
828C2×C4#1306337012yes—
829C2×C4C24×D4311yescharacteristic
830C8—434no—
831C8—862no—
832C8—862no—
833C8—862no—
834C22—22no—
835C22—22no—
836C22—28no—
837C22—22no—
838C22—22no—
839C22—22no—
840C22—44no—
841C22—3444no—
842C22—1722no—
843C22—1722no—
844C22—1722no—
845C22D4×C22⋊D4312yes—
846C22C2×#1306335612yes—
847C22C2×#1306335614yescomplemented
848C22#1458371412yes—
849C22C23×C22⋊D4311yescharacteristic
850C4—22no—
851C4—22no—
852C4—24no—
853C4—22no—
854C4—22no—
855C4—42no—
856C4—42no—
857C4—42no—
858C4—864no—
859C4—1722no—
860C4—1722no—
861C4D4×C22⋊D4312yes—
862C4C22×D4×D4311yescharacteristic
863C4C2×#1306337011yescharacteristic
864C2—24no—
865C2—42no—
866C2—3442no—
867C2#1914616614yesdirect product factor
868C2C2×D4×C22⋊D4311yescharacteristic
869C2C22×#1306335611yescharacteristic
870C2C2×#1458371411yescharacteristic
subgroupG/H
centerC23C22×C22⋊D43
commutator, cosocleC2×C4×C43C25
FrattiniC2×C4C24×D43
FittingC2×D4×Q8×C43C2
socleC23×C43C22×D4
prime radicalC2×#14583558C2
hypercenterC2×D4×Q8D43
hypocenterC43C2×#3270
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×C4×D4 ◁ C2×D4×Q8

Complements

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

NH ≅ G/Ntype
1. C22×#13063356C2semidirect
2. C23×#10621885C2semidirect
4. #19146166C2direct (N × H)
5. C2×#14583291C2semidirect
6. C2×#14583155C2semidirect
7. C2×#14583130C2semidirect
8. C2×#14583121C2semidirect
9. C2×#14583106C2semidirect
10. C2×#14583059C2semidirect
11. C2×#14583055C2semidirect
12. C2×#14583054C2semidirect
13. C2×#14583038C2semidirect
14. C2×#14583004C2semidirect
15. C2×#14582971C2semidirect
16. C2×D4×Q8×C43C2semidirect
20. C2×#13063356C22semidirect
28. C22×#10621885C22semidirect
44. #14583291C22semidirect
45. #14583155C22semidirect
46. #14583130C22semidirect
47. #14583121C22semidirect
48. #14583106C22semidirect
49. #14583059C22semidirect
50. #14583055C22semidirect
51. #14583054C22semidirect
52. #14583038C22semidirect
53. #14583004C22semidirect
54. #14582971C22semidirect
69. D4×Q8×C43C22semidirect
102. C2×#10621885D4semidirect
299. #10621885C2×D4semidirect
326. C23×C43#137semidirect
408. C22×C43C2×#137semidirect
431. C2×D4×Q8D43semidirect
447. C2×C43#3270semidirect
472. D4×Q8C2×D43semidirect
514. C43C2×#3270semidirect
766. C23#13063356semidirect
847. C22C2×#13063356semidirect
867. C2#19146166direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#130633562
C23×#106218852
C2×#145835582
#191461662
C2×#145832912
C2×#145831552
C2×#145831302
C2×#145831212
C2×#145831062
C2×#145830592
C2×#145830552
C2×#145830542
C2×#145830382
C2×#145830042
C2×#145829712
C2×D4×Q8×C432
C2×#327043