Finite Group Databasebeta

← C2×#19146015 #25969517

Subgroups — C2×#19146015 #25969517

Order 11008.

1818 conjugacy classes of subgroups.

The subgroup lattice has 734 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583520C211yesmaximal, characteristic
2#19146015C2116yesmaximal, direct product factor
3C2×#14583203C211yesmaximal, characteristic, complemented
4C2×#14583194C211yesmaximal, characteristic, complemented
5C2×#14583184C211yesmaximal, characteristic, complemented
6C2×#14583196C211yesmaximal, characteristic, complemented
7C2×#14583155C211yesmaximal, characteristic, complemented
8C2×#14583147C211yesmaximal, characteristic
9C2×#14583138C211yesmaximal, characteristic, complemented
10C2×#14583130C211yesmaximal, characteristic
11C2×#14583121C211yesmaximal, characteristic, complemented
12C2×#14583121C211yesmaximal, characteristic, complemented
13C2×#14583106C211yesmaximal, characteristic, complemented
14C2×#14583101C211yesmaximal, characteristic, complemented
15C2×#14582926C211yesmaximal, characteristic, complemented
16C2×C43×#541C211yesmaximal, characteristic, complemented
17C22×#10621885C2211yescharacteristic
18C22×#10621885C2211yescharacteristic
19C22×#10621884C2211yescharacteristic
20C22×#10621884C2211yescharacteristic
21C22×#10621877C2211yescharacteristic
22C23×C43⋊C8C2211yescharacteristic
23#14583520—24no—
24#14583520C2218yes—
25C2×#13063325C2211yescharacteristic
26C2×#13063320—21no—
27C2×#13063313C2211yescharacteristic
28C2×#13063311—21no—
29C2×#13063307—21no—
30C2×#13063304C2211yescharacteristic
31C2×#13063303—21no—
32C2×#13063299C2211yescharacteristic
33C2×C4×Dic86C2211yescharacteristic
34C2×C4×D172C2211yescharacteristic
35#14583203C2218yescomplemented
36#14583196C2218yescomplemented
37#14583194C2218yescomplemented
38#14583184C2218yescomplemented
39#14583155C2218yescomplemented
40#14583147C2218yes—
41#14583138C2218yescomplemented
42#14583130C2218yes—
43#14583121C2218yescomplemented
44#14583121C2218yescomplemented
45#14583106C2218yescomplemented
46#14583101C2218yescomplemented
47C2×#13063258C2211yescharacteristic
48C2×#13063258C2211yescharacteristic
49C2×#13063256C2211yescharacteristic
50C2×#13063256C2211yescharacteristic
51#14582926C2218yescomplemented
52C2×C4⋊(C43⋊C8)C2211yescharacteristic
53C2×C4⋊(C43⋊C8)C2211yescharacteristic
54C2×C4⋊(C43⋊C8)C2211yescharacteristic
55C2×C4⋊(C43⋊C8)C2211yescharacteristic
56C2×#13063249C2211yescharacteristic
57C2×#13063249C2211yescharacteristic
58C2×#13063249C2211yescharacteristic
59C2×#13063249C2211yescharacteristic
60C2×#13063248C2211yescharacteristic
61C2×#13063248C2211yescharacteristic
62C2×#13063245C2211yescharacteristic
63C2×#13063245C2211yescharacteristic
64C43×#541—24no—
65C43×#541C2218yescomplemented
66C2×C4⋊Q8×C43C2211yescharacteristic
67C2×#126×C43—21no—
68C2×#126×C43—21no—
69C2×#125×C43—21no—
70C2×#125×C43—21no—
71C2×#125×C43C2211yescharacteristic
72C2×C22⋊Q8×C43C2211yescharacteristic
73C2×C22⋊Q8×C43C2211yescharacteristic
74C2×C4×Q8×C43C2211yescharacteristic
75C2×C4×Q8×C43C2211yescharacteristic
76C2×#117×C43C2211yescharacteristic
77C22×Dic86—21no—
78C22×Dic86C2311yescharacteristic
79C22×D172C2311yescharacteristic
80C22×C22⋊D43—21no—
81C22×C4×D43—21no—
82C2×#10621885—42no—
83C2×#10621885—42no—
84C2×#10621885C2314yes—
85C2×#10621885C2314yes—
86C2×#10621884—42no—
87C2×#10621884—42no—
88C2×#10621884C2314yes—
89C2×#10621884C2314yes—
90C2×#10621877—42no—
91C2×#10621877C2314yes—
92C22×C43⋊C8—42no—
93C22×C43⋊C8C2311yescharacteristic
94C22×C43⋊C8C2311yescharacteristic
95C22×C43⋊C8C2311yescharacteristic
96C22×C43⋊C8C2311yescharacteristic
97C22×C43⋊C8C2314yes—
98#13063325—22no—
99#13063325C2314yes—
100#13063320—28no—
101#13063313—22no—
102#13063313C2314yes—
103#13063311—28no—
104#13063307—28no—
105#13063304—22no—
106#13063304C2314yes—
107#13063303—28no—
108#13063299—22no—
109#13063299C2314yes—
110C4×Dic86—22no—
111C4×Dic86C2314yes—
112C4×D172—22no—
113C4×D172C2314yes—
114C2×C4⋊Dic43—21no—
115C2×C4⋊Dic43C2311yescharacteristic
116C2×C4⋊Dic43C2311yescharacteristic
117C2×Dic43⋊C4—21no—
118C2×Dic43⋊C4—21no—
119C2×C22⋊Dic43—21no—
120C2×(C2×D43)⋊C4—21no—
121C2×(C2×D43)⋊C4—21no—
122C2×(C2×D43)⋊C4—21no—
123C2×(C2×D43)⋊C4—21no—
124C2×C4×Dic43—21no—
125#13063258C2314yes—
126#13063258C2314yes—
127#13063256C2314yes—
128#13063256C2314yes—
129C4⋊(C43⋊C8)C2314yes—
130C4⋊(C43⋊C8)C2314yes—
131C4⋊(C43⋊C8)C2314yes—
132C4⋊(C43⋊C8)C2314yes—
133#13063249C2314yes—
134#13063249C2314yes—
135#13063249C2314yes—
136#13063249C2314yes—
137#13063248C2314yes—
138#13063248C2314yes—
139#13063245C2314yes—
140#13063245C2314yes—
141C22×Q8×C43C2311yescharacteristic
142C22×Q8×C43C2311yescharacteristic
143C23×C4×C43C2311yescharacteristic
144C4⋊Q8×C43—22no—
145C4⋊Q8×C43C2314yes—
146#126×C43—28no—
147#126×C43—28no—
148#125×C43—28no—
149#125×C43—28no—
150#125×C43—22no—
151#125×C43C2314yes—
152C22⋊Q8×C43—22no—
153C22⋊Q8×C43—22no—
154C22⋊Q8×C43C2314yes—
155C22⋊Q8×C43C2314yes—
156C4×Q8×C43—22no—
157C4×Q8×C43—22no—
158C4×Q8×C43C2314yes—
159C4×Q8×C43C2314yes—
160#117×C43D414yes—
161#117×C43C2314yes—
162C2×C4⋊C4×C43—21no—
163C2×C4⋊C4×C43—21no—
164C2×C4⋊C4×C43—21no—
165C2×C4⋊C4×C43—21no—
166C2×C4⋊C4×C43—21no—
167C2×C4⋊C4×C43—21no—
168C2×C4⋊C4×C43—21no—
169C2×C4⋊C4×C43—21no—
170C2×C4⋊C4×C43D411yescharacteristic
171C2×C4⋊C4×C43D411yescharacteristic
172C2×C4⋊C4×C43C2311yescharacteristic
173C2×C4⋊C4×C43C2311yescharacteristic
174C2×C22⋊C4×C43—21no—
175C2×C22⋊C4×C43—21no—
176C2×C22⋊C4×C43D411yescharacteristic
177C2×C22⋊C4×C43D411yescharacteristic
178C2×C42×C43—21no—
179C2×C42×C43—21no—
180C2×C42×C43C2311yescharacteristic
181C2×C42×C43C2311yescharacteristic
182C24×C43C2×D411yescharacteristic
183C23×D43—21no—
184C2×Q8×C43—21no—
185C2×Q8×C43—21no—
186C2×Q8×C43—22no—
187C2×Q8×C43—22no—
188C2×Q8×C43—22no—
189C2×Q8×C43—22no—
190C2×Q8×C43C2412yes—
191C2×Q8×C43C2412yes—
192C22×C4×C43—22no—
193C22×C4×C43—22no—
194C22×C4×C43—21no—
195C22×C4×C43—21no—
196C22×C4×C43—21no—
197C22×C4×C43—21no—
198C22×C4×C43C2×D411yescharacteristic
199C22×C4×C43C2×D411yescharacteristic
200C22×C4×C43C2×D411yescharacteristic
201C22×C4×C43C2×D411yescharacteristic
202C22×C4×C43C2×D411yescharacteristic
203C22×C4×C43C2×D412yes—
204C22×C4×C43C2412yes—
205C22×C4×C43C2411yescharacteristic
206C2×C22⋊D43—24no—
207C2×C22⋊D43—82no—
208C22×Dic43—21no—
209C22×Dic43—21no—
210C22×Dic43—21no—
211C2×D172—21no—
212C2×D172—22no—
213C2×D172—22no—
214C2×D172C2412yes—
215C2×C4×D43—24no—
216C2×C4×D43—82no—
217C2×Dic86—22no—
218C2×Dic86—22no—
219C2×Dic86—21no—
220C2×Dic86—24no—
221C2×Dic86—82no—
222C2×Dic86C2412yes—
223C4⋊C4×C43—24no—
224C4⋊C4×C43—24no—
225C4⋊C4×C43—24no—
226C4⋊C4×C43—24no—
227C4⋊C4×C43—24no—
228C4⋊C4×C43—24no—
229C4⋊C4×C43—24no—
230C4⋊C4×C43—24no—
231C4⋊C4×C43—21no—
232C4⋊C4×C43—21no—
233C4⋊C4×C43C2×D414yes—
234C4⋊C4×C43C2×D414yes—
235C4⋊C4×C43C2412yes—
236C4⋊C4×C43C2412yes—
237C22⋊C4×C43—24no—
238C22⋊C4×C43—24no—
239C22⋊C4×C43C2×D414yes—
240C22⋊C4×C43C2×D414yes—
241C42×C43—24no—
242C42×C43—24no—
243C42×C43C2×D412yes—
244C42×C43C2×D412yes—
245C42×C43C2412yes—
246C42×C43C2412yes—
247C22⋊Dic43—24no—
248#10621885—44no—
249#10621885—44no—
250#10621884—44no—
251#10621884—44no—
252(C2×D43)⋊C4—24no—
253(C2×D43)⋊C4—24no—
254(C2×D43)⋊C4—24no—
255(C2×D43)⋊C4—24no—
256C4⋊Dic43—24no—
257C4⋊Dic43—21no—
258C4⋊Dic43—21no—
259C4⋊Dic43C2412yes—
260C4⋊Dic43C2412yes—
261Dic43⋊C4—24no—
262Dic43⋊C4—24no—
263C4×Dic43—24no—
264#10621877—44no—
265C2×C43⋊C8—22no—
266C2×C43⋊C8—22no—
267C2×C43⋊C8—22no—
268C2×C43⋊C8—22no—
269C2×C43⋊C8—44no—
270C2×C43⋊C8C2412yes—
271C2×C43⋊C8C2412yes—
272C2×C43⋊C8C2412yes—
273C2×C43⋊C8C2412yes—
274C23×C43—22no—
275C23×C43—22no—
276C23×C43—22no—
277C23×C43C22×D412yes—
278C23×C43C22×D411yescharacteristic
279C22×D43—22no—
280C22×D43—42no—
281C22×D43—42no—
282C22×D43—42no—
283Q8×C43—22no—
284Q8×C43—22no—
285Q8×C43—22no—
286Q8×C43—22no—
287Q8×C43—42no—
288Q8×C43—42no—
289C2×C4×C43—22no—
290C2×C4×C43—22no—
291C2×C4×C43—22no—
292C2×C4×C43—22no—
293C2×C4×C43—22no—
294C2×C4×C43—24no—
295C2×C4×C43—22no—
296C2×C4×C43—22no—
297C2×C4×C43—22no—
298C2×C4×C43—22no—
299C2×C4×C43—22no—
300C2×C4×C43—22no—
301C2×C4×C43—42no—
302C2×C4×C43—42no—
303C2×C4×C43—42no—
304C2×C4×C43—42no—
305C2×C4×C43C22×D412yes—
306C2×C4×C43C22×D412yes—
307C2×C4×C43C22×D412yes—
308C2×C4×C43C22×D412yes—
309C2×C4×C43C22×D412yes—
310C2×C4×C43C22×D411yescharacteristic
311C2×C4×C43H(5,𝔽2)12yes—
312C2×C4×C432−1+412yes—
313C2×C4×C43C2511yescharacteristic
314C22⋊D43—84no—
315C2×Dic43—22no—
316C2×Dic43—22no—
317C2×Dic43—22no—
318C2×Dic43—42no—
319C2×Dic43—42no—
320C2×Dic43—42no—
321D172—22no—
322D172—22no—
323D172—42no—
324C4×D43—84no—
325Dic86—22no—
326Dic86—22no—
327Dic86—42no—
328Dic86—84no—
329C43⋊C8—22no—
330C43⋊C8—22no—
331C43⋊C8—22no—
332C43⋊C8—22no—
333C2×#3258—431nomaximal, Sylow
334C22×C43—22no—
335C22×C43—22no—
336C22×C43—22no—
337C22×C43—44no—
338C22×C43#53712yes—
339C22×C43#57712yes—
340C22×C43#57812yes—
341C22×C43C23×D411yescharacteristic
342C2×D43—42no—
343C2×D43—42no—
344C2×D43—42no—
345C2×D43—84no—
346C4×C43—22no—
347C4×C43—22no—
348C4×C43—22no—
349C4×C43—22no—
350C4×C43—22no—
351C4×C43—42no—
352C4×C43—42no—
353C4×C43—42no—
354C4×C43—42no—
355C4×C43#53712yes—
356C4×C43C2×H(5,𝔽2)11yescharacteristic
357C4×C43C2×2−1+411yescharacteristic
358Dic43—42no—
359Dic43—42no—
360Dic43—42no—
361C2×#542—431no—
362C2×#541D4311yescharacteristic, complemented
363#3258—4316no—
364C2×#479—431no—
365C2×#477—431no—
366C2×#475—431no—
367C2×#478—431no—
368C2×#470—431no—
369C2×#468—431no—
370C2×#467—431no—
371C2×#465—431no—
372C2×#464—431no—
373C2×#464—431no—
374C2×#462—431no—
375C2×#461—431no—
376C2×#424—431no—
377C2×C43—42no—
378C2×C43#325814yescomplemented
379C2×C43C2×#53711yescharacteristic
380C2×C43C2×#57711yescharacteristic
381C2×C43C2×#57811yescharacteristic
382D43—82no—
383C22×Q16—431no—
384C22×Q16—431no—
385C22×SD16—431no—
386C22×SD16—431no—
387C22×M16—431no—
388C23×C8—431no—
389#542—438no—
390#542—864no—
391#541—24no—
392#541C2×D4318yescomplemented
393C2×C4⋊Q8—431no—
394C2×C4⋊Q8C2×D4311yescharacteristic
395C2×#126—21no—
396C2×#126—21no—
397C2×#126—861no—
398C2×#125—21no—
399C2×#125—21no—
400C2×#125C2×D4311yescharacteristic
401C2×#124—431no—
402C2×#124—861no—
403C2×#123—861no—
404C2×C22⋊Q8—431no—
405C2×C22⋊Q8—861no—
406C2×C22⋊Q8C2×D4311yescharacteristic
407C2×C22⋊Q8C2×D4311yescharacteristic
408C2×#121—431no—
409C2×C4×Q8—431no—
410C2×C4×Q8C2×D4311yescharacteristic
411C2×C4×Q8C2×D4311yescharacteristic
412C2×C4×D4—431no—
413C2×#117C2×D4311yescharacteristic
414#479—438no—
415#478—438no—
416#477—438no—
417#475—438no—
418#470—438no—
419#468—438no—
420#467—438no—
421#465—438no—
422#464—438no—
423#464—438no—
424#462—438no—
425#461—438no—
426C2×#107—431no—
427C2×#107—431no—
428C2×#106—431no—
429C2×#106—431no—
430#424—438no—
431C2×C4⋊C8—431no—
432C2×C4⋊C8—431no—
433C2×C4⋊C8—431no—
434C2×C4⋊C8—431no—
435C2×#103—431no—
436C2×#103—431no—
437C2×#103—431no—
438C2×#103—431no—
439C2×#103—431no—
440C2×#103—431no—
441C2×#102—431no—
442C2×#102—431no—
443C43C2×#325811yescharacteristic, complemented, Sylow
444C22×Q8—431no—
445C22×Q8—861no—
446C22×Q8C22×D4311yescharacteristic
447C22×Q8C22×D4311yescharacteristic
448C22×D4—431no—
449C22×D4—861no—
450C23×C4—861no—
451C23×C4C22×D4311yescharacteristic
452C2×Q16—434no—
453C2×Q16—434no—
454C2×Q16—1722no—
455C2×Q16—1722no—
456C2×SD16—434no—
457C2×SD16—434no—
458C2×SD16—1722no—
459C2×SD16—1722no—
460C2×M16—434no—
461C2×M16—1722no—
462C22×C8—431no—
463C22×C8—431no—
464C22×C8—431no—
465C22×C8—431no—
466C22×C8—434no—
467C22×C8—1722no—
468C4⋊Q8—22no—
469C4⋊Q8—434no—
470C4⋊Q8—862no—
471C4⋊Q8C22×D4314yes—
472#126—28no—
473#126—28no—
474#126—868no—
475#125—28no—
476#125—28no—
477#125—22no—
478#125C22×D4314yes—
479#124—434no—
480#124—868no—
481#124—862no—
482#123—868no—
483C22⋊Q8—22no—
484C22⋊Q8—22no—
485C22⋊Q8—434no—
486C22⋊Q8—862no—
487C22⋊Q8—868no—
488C22⋊Q8C22×D4314yes—
489C22⋊Q8C22×D4314yes—
490#121—434no—
491#121—862no—
492C4×Q8—22no—
493C4×Q8—22no—
494C4×Q8—434no—
495C4×Q8—862no—
496C4×Q8C22×D4314yes—
497C4×Q8C22×D4314yes—
498C4×D4—434no—
499C4×D4—862no—
500#117C22⋊D4314yes—
501#117C22×D4314yes—
502C2×C4⋊C4—21no—
503C2×C4⋊C4—21no—
504C2×C4⋊C4—21no—
505C2×C4⋊C4—21no—
506C2×C4⋊C4—21no—
507C2×C4⋊C4—21no—
508C2×C4⋊C4—21no—
509C2×C4⋊C4—21no—
510C2×C4⋊C4—431no—
511C2×C4⋊C4—431no—
512C2×C4⋊C4—861no—
513C2×C4⋊C4—861no—
514C2×C4⋊C4—861no—
515C2×C4⋊C4C22⋊D4311yescharacteristic
516C2×C4⋊C4C22⋊D4311yescharacteristic
517C2×C4⋊C4C22×D4311yescharacteristic
518C2×C4⋊C4C22×D4311yescharacteristic
519C2×C22⋊C4—21no—
520C2×C22⋊C4—21no—
521C2×C22⋊C4—861no—
522C2×C22⋊C4—861no—
523C2×C22⋊C4—861no—
524C2×C22⋊C4—861no—
525C2×C22⋊C4—861no—
526C2×C22⋊C4C22⋊D4311yescharacteristic
527C2×C22⋊C4C22⋊D4311yescharacteristic
528C2×C42—21no—
529C2×C42—21no—
530C2×C42—861no—
531C2×C42C22×D4311yescharacteristic
532C2×C42C22×D4311yescharacteristic
533#107—434no—
534#107—434no—
535#106—434no—
536#106—434no—
537C4⋊C8—434no—
538C4⋊C8—434no—
539C4⋊C8—434no—
540C4⋊C8—434no—
541#103—434no—
542#103—434no—
543#103—434no—
544#103—434no—
545#103—434no—
546#103—434no—
547#102—434no—
548#102—434no—
549C24—861no—
550C24C2×C22⋊D4311yescharacteristic
551C2×Q8—21no—
552C2×Q8—21no—
553C2×Q8—22no—
554C2×Q8—22no—
555C2×Q8—22no—
556C2×Q8—22no—
557C2×Q8—432no—
558C2×Q8—864no—
559C2×Q8—861no—
560C2×Q8—862no—
561C2×Q8—862no—
562C2×Q8—3442no—
563C2×Q8C23×D4312yes—
564C2×Q8C23×D4312yes—
565C2×D4—432no—
566C2×D4—864no—
567C2×D4—861no—
568C2×D4—862no—
569C2×D4—862no—
570C2×D4—3442no—
571C22×C4—22no—
572C22×C4—22no—
573C22×C4—21no—
574C22×C4—21no—
575C22×C4—21no—
576C22×C4—21no—
577C22×C4—861no—
578C22×C4—861no—
579C22×C4—861no—
580C22×C4—864no—
581C22×C4—3442no—
582C22×C4C2×C22⋊D4312yes—
583C22×C4C2×C22⋊D4311yescharacteristic
584C22×C4C2×C22⋊D4311yescharacteristic
585C22×C4C2×C22⋊D4311yescharacteristic
586C22×C4C2×C22⋊D4311yescharacteristic
587C22×C4C2×C22⋊D4311yescharacteristic
588C22×C4C23×D4312yes—
589C22×C4C23×D4311yescharacteristic
590Q16—1724no—
591Q16—1724no—
592SD16—1724no—
593SD16—1724no—
594M16—1724no—
595C2×C8—432no—
596C2×C8—432no—
597C2×C8—432no—
598C2×C8—432no—
599C2×C8—862no—
600C2×C8—862no—
601C2×C8—862no—
602C2×C8—862no—
603C2×C8—1724no—
604C4⋊C4—24no—
605C4⋊C4—24no—
606C4⋊C4—24no—
607C4⋊C4—24no—
608C4⋊C4—24no—
609C4⋊C4—24no—
610C4⋊C4—24no—
611C4⋊C4—24no—
612C4⋊C4—21no—
613C4⋊C4—21no—
614C4⋊C4—432no—
615C4⋊C4—432no—
616C4⋊C4—861no—
617C4⋊C4—861no—
618C4⋊C4—864no—
619C4⋊C4—864no—
620C4⋊C4—864no—
621C4⋊C4C2×C22⋊D4314yes—
622C4⋊C4C2×C22⋊D4314yes—
623C4⋊C4C23×D4312yes—
624C4⋊C4C23×D4312yes—
625C22⋊C4—24no—
626C22⋊C4—24no—
627C22⋊C4—864no—
628C22⋊C4—864no—
629C22⋊C4—864no—
630C22⋊C4—864no—
631C22⋊C4—864no—
632C22⋊C4C2×C22⋊D4314yes—
633C22⋊C4C2×C22⋊D4314yes—
634C42—24no—
635C42—24no—
636C42—864no—
637C42C2×C22⋊D4312yes—
638C42C2×C22⋊D4312yes—
639C42C23×D4312yes—
640C42C23×D4312yes—
641C23—22no—
642C23—22no—
643C23—22no—
644C23—862no—
645C23—1722no—
646C23—1722no—
647C23—1722no—
648C23C22×C22⋊D4312yes—
649C23C22×C22⋊D4311yescharacteristic
650Q8—22no—
651Q8—22no—
652Q8—22no—
653Q8—22no—
654Q8—42no—
655Q8—42no—
656Q8—862no—
657Q8—862no—
658Q8—3444no—
659Q8—1722no—
660D4—862no—
661D4—862no—
662D4—3444no—
663D4—1722no—
664C2×C4—22no—
665C2×C4—22no—
666C2×C4—22no—
667C2×C4—22no—
668C2×C4—22no—
669C2×C4—22no—
670C2×C4—22no—
671C2×C4—24no—
672C2×C4—22no—
673C2×C4—22no—
674C2×C4—22no—
675C2×C4—22no—
676C2×C4—42no—
677C2×C4—42no—
678C2×C4—42no—
679C2×C4—42no—
680C2×C4—862no—
681C2×C4—862no—
682C2×C4—862no—
683C2×C4—3444no—
684C2×C4—1722no—
685C2×C4—1722no—
686C2×C4—1722no—
687C2×C4C22×C22⋊D4312yes—
688C2×C4C22×C22⋊D4312yes—
689C2×C4C22×C22⋊D4312yes—
690C2×C4C22×C22⋊D4312yes—
691C2×C4C22×C22⋊D4312yes—
692C2×C4C22×C22⋊D4311yescharacteristic
693C2×C4#1306337112yes—
694C2×C4#1306337212yes—
695C2×C4C24×D4311yescharacteristic
696C8—862no—
697C8—862no—
698C8—862no—
699C8—862no—
700C22—22no—
701C22—22no—
702C22—22no—
703C22—44no—
704C22—3444no—
705C22—1722no—
706C22—1722no—
707C22—1722no—
708C22#1458347712yes—
709C22#1458370712yes—
710C22#1458371412yes—
711C22C23×C22⋊D4311yescharacteristic
712C4—22no—
713C4—22no—
714C4—22no—
715C4—22no—
716C4—22no—
717C4—42no—
718C4—42no—
719C4—42no—
720C4—42no—
721C4—1722no—
722C4—1722no—
723C4—1722no—
724C4#1458347712yes—
725C4C2×#1306337111yescharacteristic
726C4C2×#1306337211yescharacteristic
727C2—42no—
728C2—3442no—
729C2#1914601514yesdirect product factor
730C2C2×#1458347711yescharacteristic
731C2C2×#1458370711yescharacteristic
732C2C2×#1458371411yescharacteristic
subgroupG/H
centerC23C22×C22⋊D43
commutator, cosocleC2×C4×C43C25
FrattiniC2×C4C24×D43
FittingC2×C43×#541C2
socleC23×C43C22×D4
prime radicalC2×#13063299C22
hypercenterC2×#541D43
hypocenterC43C2×#3258
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×#117 ◁ C2×#541

Complements

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

NH ≅ G/Ntype
2. #19146015C2direct (N × H)
3. C2×#14583203C2semidirect
4. C2×#14583194C2semidirect
5. C2×#14583184C2semidirect
6. C2×#14583196C2semidirect
7. C2×#14583155C2semidirect
9. C2×#14583138C2semidirect
11. C2×#14583121C2semidirect
12. C2×#14583121C2semidirect
13. C2×#14583106C2semidirect
14. C2×#14583101C2semidirect
15. C2×#14582926C2semidirect
16. C2×C43×#541C2semidirect
35. #14583203C22semidirect
36. #14583196C22semidirect
37. #14583194C22semidirect
38. #14583184C22semidirect
39. #14583155C22semidirect
41. #14583138C22semidirect
43. #14583121C22semidirect
44. #14583121C22semidirect
45. #14583106C22semidirect
46. #14583101C22semidirect
51. #14582926C22semidirect
65. C43×#541C22semidirect
362. C2×#541D43semidirect
378. C2×C43#3258semidirect
392. #541C2×D43semidirect
443. C43C2×#3258semidirect
729. C2#19146015direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#145835202
#191460152
C2×#145832032
C2×#145831942
C2×#145831842
C2×#145831962
C2×#145831552
C2×#145831472
C2×#145831382
C2×#145831302
C2×#145831212
C2×#145831062
C2×#145831012
C2×#145829262
C2×C43×#5412
C2×#325843