Finite Group Databasebeta

← C2×#19144805 #25964856

Subgroups — C2×#19144805 #25964856

Order 11008.

2070 conjugacy classes of subgroups.

The subgroup lattice has 744 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583507C211yesmaximal, characteristic, complemented
2C2×#14583378C211yesmaximal, characteristic
3#19144805C2116yesmaximal, direct product factor
4C2×#14583233C211yesmaximal, characteristic, complemented
5C2×#14583231C211yesmaximal, characteristic, complemented
6C2×#14583209C211yesmaximal, characteristic, complemented
7C2×#14583197C211yesmaximal, characteristic, complemented
8C2×#14583108C211yesmaximal, characteristic, complemented
9C2×#14583102C211yesmaximal, characteristic, complemented
10C2×#14583062C211yesmaximal, characteristic
11C2×#14583058C211yesmaximal, characteristic
12C2×#14583004C211yesmaximal, characteristic, complemented
13C2×#14582999C211yesmaximal, characteristic, complemented
14C2×C4×Dic172C211yesmaximal, characteristic, complemented
15C2×#14582958C211yesmaximal, characteristic, complemented
16C2×C4×SD16×C43C211yesmaximal, characteristic, complemented
17C22×#10621900C2211yescharacteristic
18C22×Dic172C2211yescharacteristic
19C22×#10621885C2211yescharacteristic
20C22×#10621883C2211yescharacteristic
21#14583507—24no—
22#14583507C2218yescomplemented
23C2×#13063323C2211yescharacteristic
24C2×#13063320—21no—
25C2×#13063319—21no—
26C2×#13063317—21no—
27C2×#13063316C2211yescharacteristic
28C2×#13063315—21no—
29C2×#13063305C2211yescharacteristic
30C2×#13063301C2211yescharacteristic
31#14583378—24no—
32#14583378C2218yes—
33C2×C4×Dic86C2211yescharacteristic
34C2×C4×Dic86C2211yescharacteristic
35C2×#13063290C2211yescharacteristic
36C2×D4×Dic43C2211yescharacteristic
37C2×C4×C22⋊D43—21no—
38C2×(C22⋊D43)⋊C4—21no—
39C2×#13063282C2211yescharacteristic
40C2×#13063281—21no—
41C22×Dic43⋊C4—21no—
42C2×C4⋊C4×D43C2211yescharacteristic
43#14583233C2218yescomplemented
44#14583231C2218yescomplemented
45#14583209C2218yescomplemented
46#14583197C2218yescomplemented
47#14583108C2218yescomplemented
48#14583102C2218yescomplemented
49#14583062C2218yes—
50#14583058C2218yes—
51#14583004C2218yescomplemented
52#14582999C2218yescomplemented
53C4×Dic172C2218yescomplemented
54#14582958C2218yescomplemented
55C2×#13063259C2211yescharacteristic
56C2×#13063258C2211yescharacteristic
57C2×#13063256C2211yescharacteristic
58C2×Dic43⋊C8C2211yescharacteristic
59C2×Dic43⋊C8C2211yescharacteristic
60C2×#13063250C2211yescharacteristic
61C2×#13063250C2211yescharacteristic
62C2×#13063249C2211yescharacteristic
63C2×#13063248C2211yescharacteristic
64C2×#13063248C2211yescharacteristic
65C2×#13063246C2211yescharacteristic
66C2×(C2×D43)⋊C8C2211yescharacteristic
67C2×(C2×D43)⋊C8C2211yescharacteristic
68C2×#13063236C2211yescharacteristic
69C22×SD16×C43C2211yescharacteristic
70C2×C4×Q8×C43C2211yescharacteristic
71C2×C4×D4×C43C2211yescharacteristic
72C4×SD16×C43C2218yescomplemented
73C2×#106×C43C2211yescharacteristic
74C2×#103×C43C2211yescharacteristic
75C2×#102×C43C2211yescharacteristic
76C2×C4×C8×C43C2211yescharacteristic
77C2×#10621900—24no—
78C2×#10621900—22no—
79C2×#10621900—24no—
80C2×#10621900C2314yes—
81C22×Dic86C2311yescharacteristic
82C22×Dic86C2311yescharacteristic
83C22×C22⋊D43—21no—
84C23×Dic43—21no—
85C23×Dic43—21no—
86C22×C4×D43—21no—
87C22×C4×D43C2311yescharacteristic
88C2×Dic172—24no—
89C2×Dic172C2314yes—
90C2×#10621885—24no—
91C2×#10621885C2314yes—
92C2×#10621883—24no—
93C2×#10621883C2314yes—
94C22×C43⋊C8C2311yescharacteristic
95C22×C43⋊C8C2311yescharacteristic
96#13063323—22no—
97#13063323C2314yes—
98#13063320—28no—
99#13063319—28no—
100#13063317—28no—
101#13063316—22no—
102#13063316C2314yes—
103#13063315—28no—
104#13063305—22no—
105#13063305C2314yes—
106#13063301—22no—
107#13063301C2314yes—
108C4×Dic86—22no—
109C4×Dic86—22no—
110C4×Dic86C2314yes—
111C4×Dic86C2314yes—
112#13063290—22no—
113#13063290C2314yes—
114D4×Dic43—22no—
115D4×Dic43C2314yes—
116C4×C22⋊D43—28no—
117(C22⋊D43)⋊C4—28no—
118#13063282D414yes—
119#13063282C2314yes—
120#13063281—28no—
121C2×C4⋊Dic43—21no—
122C2×C4⋊Dic43—21no—
123C2×C4⋊Dic43C2311yescharacteristic
124C2×C4⋊Dic43C2311yescharacteristic
125C2×Dic43⋊C4—21no—
126C2×Dic43⋊C4—21no—
127C2×Dic43⋊C4—21no—
128C2×Dic43⋊C4—21no—
129C2×Dic43⋊C4—21no—
130C2×Dic43⋊C4—21no—
131C2×Dic43⋊C4—21no—
132C2×Dic43⋊C4—21no—
133C2×Dic43⋊C4—28no—
134C2×Dic43⋊C4D411yescharacteristic
135C2×Dic43⋊C4D411yescharacteristic
136C4⋊C4×D43—22no—
137C4⋊C4×D43C2314yes—
138C2×C22⋊Dic43—21no—
139C2×(C2×D43)⋊C4—21no—
140C2×(C2×D43)⋊C4—21no—
141C2×(C2×D43)⋊C4D411yescharacteristic
142C2×(C2×D43)⋊C4D411yescharacteristic
143C2×C4×Dic43—21no—
144C2×C4×Dic43—21no—
145C2×C4×Dic43—21no—
146C2×C4×Dic43C2311yescharacteristic
147#13063259C2314yes—
148#13063258C2314yes—
149#13063256C2314yes—
150Dic43⋊C8C2314yes—
151Dic43⋊C8C2314yes—
152#13063250C2314yes—
153#13063250C2314yes—
154#13063249C2314yes—
155#13063248C2314yes—
156#13063248C2314yes—
157#13063246C2314yes—
158(C2×D43)⋊C8C2314yes—
159(C2×D43)⋊C8C2314yes—
160#13063236C2314yes—
161C22×Q8×C43C2311yescharacteristic
162C22×D4×C43C2311yescharacteristic
163C23×C4×C43—21no—
164C2×SD16×C43—24no—
165C2×SD16×C43C2314yes—
166C22×C8×C43C2311yescharacteristic
167C22×C8×C43C2311yescharacteristic
168C4×Q8×C43—22no—
169C4×Q8×C43C2314yes—
170C4×D4×C43—22no—
171C4×D4×C43C2314yes—
172C2×C4⋊C4×C43—21no—
173C2×C4⋊C4×C43C2311yescharacteristic
174C2×C4⋊C4×C43C2311yescharacteristic
175C2×C22⋊C4×C43—21no—
176C2×C42×C43—21no—
177C2×C42×C43C2311yescharacteristic
178#106×C43C2314yes—
179#103×C43C2314yes—
180#102×C43C2314yes—
181C4×C8×C43C2314yes—
182C24×C43—21no—
183C23×D43C2×D411yescharacteristic
184C2×Q8×C43—21no—
185C2×Q8×C43—22no—
186C2×Q8×C43—22no—
187C2×Q8×C43C2412yes—
188C2×D4×C43—21no—
189C2×D4×C43—22no—
190C2×D4×C43#4114yes—
191C2×D4×C43C2412yes—
192C22×C4×C43—24no—
193C22×C4×C43—21no—
194C22×C4×C43—21no—
195C22×C4×C43—21no—
196C22×C4×C43—82no—
197C22×C4×C43C2×D411yescharacteristic
198C22×C4×C43C2×D411yescharacteristic
199C22×C4×C43C2411yescharacteristic
200C2×C22⋊D43—28no—
201C2×C22⋊D43—24no—
202C22×Dic43—28no—
203C22×Dic43—24no—
204C22×Dic43—24no—
205C22×Dic43—21no—
206C22×Dic43—21no—
207C22×Dic43—21no—
208C22×Dic43—21no—
209C22×Dic43—82no—
210C22×Dic43C2×D411yescharacteristic
211C22×Dic43C2×D411yescharacteristic
212C22×Dic43C2×D411yescharacteristic
213#10621900—216no—
214#10621900—28no—
215#10621900—28no—
216C2×C4×D43—22no—
217C2×C4×D43—22no—
218C2×C4×D43—24no—
219C2×C4×D43—82no—
220C2×C4×D43C2×D412yes—
221C2×C4×D43C2412yes—
222C2×Dic86—21no—
223C2×Dic86—22no—
224C2×Dic86—22no—
225C2×Dic86—22no—
226C2×Dic86—21no—
227C2×Dic86#4114yes—
228C2×Dic86C2412yes—
229C2×Dic86C2412yes—
230SD16×C43—28no—
231C2×C8×C43—22no—
232C2×C8×C43—22no—
233C2×C8×C43C2412yes—
234C2×C8×C43C2412yes—
235C4⋊C4×C43—24no—
236C4⋊C4×C43—21no—
237C4⋊C4×C43—21no—
238C4⋊C4×C43C2412yes—
239C4⋊C4×C43C2412yes—
240C22⋊C4×C43—24no—
241C42×C43—24no—
242C42×C43C2×D412yes—
243C42×C43C2412yes—
244C22⋊Dic43—24no—
245#10621885—28no—
246#10621883—28no—
247(C2×D43)⋊C4—24no—
248(C2×D43)⋊C4—24no—
249(C2×D43)⋊C4C2×D414yes—
250(C2×D43)⋊C4C2×D414yes—
251C4⋊Dic43—21no—
252C4⋊Dic43—21no—
253C4⋊Dic43—24no—
254C4⋊Dic43—24no—
255C4⋊Dic43C2412yes—
256C4⋊Dic43C2412yes—
257Dic43⋊C4—24no—
258Dic43⋊C4—24no—
259Dic43⋊C4—24no—
260Dic43⋊C4—24no—
261Dic43⋊C4—24no—
262Dic43⋊C4—24no—
263Dic43⋊C4—24no—
264Dic43⋊C4—24no—
265Dic43⋊C4C2×D414yes—
266Dic43⋊C4C2×D414yes—
267C4×Dic43—24no—
268C4×Dic43—24no—
269C4×Dic43—24no—
270C4×Dic43C2×D412yes—
271C4×Dic43C2412yes—
272C2×C43⋊C8—22no—
273C2×C43⋊C8—22no—
274C2×C43⋊C8C2412yes—
275C2×C43⋊C8C2412yes—
276Dic172—28no—
277C23×C43—24no—
278C23×C43—22no—
279C23×C43—42no—
280C23×C43—42no—
281C23×C43C22×D411yescharacteristic
282C22×D43—22no—
283C22×D43—22no—
284C22×D43—22no—
285C22×D43C22×D412yes—
286Q8×C43—22no—
287Q8×C43—22no—
288Q8×C43—42no—
289D4×C43—24no—
290D4×C43—22no—
291D4×C43C2×#4114yes—
292C2×C4×C43—22no—
293C2×C4×C43—22no—
294C2×C4×C43—22no—
295C2×C4×C43—22no—
296C2×C4×C43—22no—
297C2×C4×C43—42no—
298C2×C4×C43—42no—
299C2×C4×C43—42no—
300C2×C4×C43—84no—
301C2×C4×C43C22×D412yes—
302C2×C4×C43C22×D412yes—
303C2×C4×C43C22×D411yescharacteristic
304C2×C4×C43C2×#4112yes—
305C2×C4×C43C2×#4112yes—
306C2×C4×C43C2511yescharacteristic
307C22⋊D43—216no—
308C2×Dic43—216no—
309C2×Dic43—24no—
310C2×Dic43—22no—
311C2×Dic43—22no—
312C2×Dic43—22no—
313C2×Dic43—22no—
314C2×Dic43—22no—
315C2×Dic43—22no—
316C2×Dic43—22no—
317C2×Dic43—42no—
318C2×Dic43—42no—
319C2×Dic43—42no—
320C2×Dic43—84no—
321C2×Dic43C22×D412yes—
322C2×Dic43C22×D412yes—
323C2×Dic43C22×D412yes—
324C4×D43—24no—
325C4×D43—22no—
326C4×D43—22no—
327C4×D43—84no—
328Dic86—24no—
329Dic86—22no—
330Dic86—22no—
331Dic86—22no—
332Dic86—42no—
333Dic86C2×#4114yes—
334C8×C43—22no—
335C8×C43—22no—
336C43⋊C8—22no—
337C43⋊C8—22no—
338C2×#3120—431nomaximal, Sylow
339C22×C43—24no—
340C22×C43—48no—
341C22×C43—42no—
342C22×C43—42no—
343C22×C43#52512yes—
344C22×C43#57712yes—
345C22×C43#57812yes—
346C22×C43C23×D411yescharacteristic
347C2×D43—22no—
348C2×D43—22no—
349C2×D43—22no—
350C2×D43—44no—
351C4×C43—22no—
352C4×C43—22no—
353C4×C43—42no—
354C4×C43—42no—
355C4×C43—42no—
356C4×C43#52512yes—
357C4×C43C22×#4111yescharacteristic
358C4×C43C22×#4111yescharacteristic
359Dic43—24no—
360Dic43—22no—
361Dic43—22no—
362Dic43—22no—
363Dic43—42no—
364Dic43—42no—
365Dic43—42no—
366C2×#541—431no—
367C2×#520—431no—
368#3120—4316no—
369C2×#484—431no—
370C2×#483—431no—
371C2×#479—431no—
372C2×#478—431no—
373C2×#462—431no—
374C2×#461—431no—
375C2×#452—431no—
376C2×#452—431no—
377C2×#441—431no—
378C2×#440—431no—
379C2×C4×Q16—431no—
380C2×C4×SD16D4311yescharacteristic, complemented
381C2×#433—431no—
382C2×C43—44no—
383C2×C43#312014yescomplemented
384C2×C43C2×#52511yescharacteristic
385C2×C43C2×#57711yescharacteristic
386C2×C43C2×#57811yescharacteristic
387D43—42no—
388C22×#41—431no—
389C22×Q16—431no—
390C22×Q16—431no—
391C22×SD16—431no—
392C22×SD16C2×D4311yescharacteristic
393#541—438no—
394#541—864no—
395C2×C4⋊Q8—431no—
396C2×#126—861no—
397C2×#126—861no—
398C2×#125—431no—
399C2×#125—861no—
400C2×#125—861no—
401C2×C22⋊Q8—431no—
402C2×C22⋊Q8—431no—
403#520—438no—
404#520—864no—
405C2×C4×Q8—431no—
406C2×C4×Q8—431no—
407C2×C4×Q8—431no—
408C2×C4×Q8C2×D4311yescharacteristic
409C2×C4×D4—431no—
410C2×C4×D4—861no—
411C2×C4×D4—861no—
412C2×C4×D4C2×D4311yescharacteristic
413C2×#117—431no—
414C2×#117—861no—
415C22×C4⋊C4—431no—
416C22×C4⋊C4—861no—
417#484—438no—
418#483—438no—
419#479—438no—
420#478—438no—
421#462—438no—
422#461—438no—
423#452—438no—
424#452—438no—
425#441—438no—
426#440—438no—
427C4×Q16—438no—
428C4×SD16C2×D4318yescomplemented
429#433—438no—
430C2×#107—431no—
431C2×#107—431no—
432C2×#106—431no—
433C2×#106C2×D4311yescharacteristic
434C2×C4⋊C8—431no—
435C2×C4⋊C8—431no—
436C2×#103—431no—
437C2×#103—431no—
438C2×#103—431no—
439C2×#103—431no—
440C2×#103—431no—
441C2×#103C2×D4311yescharacteristic
442C2×#102—431no—
443C2×#102C2×D4311yescharacteristic
444C2×C22⋊C8—431no—
445C2×C22⋊C8—431no—
446C2×#97—431no—
447C2×C4×C8C2×D4311yescharacteristic
448C43C2×#312011yescharacteristic, complemented, Sylow
449C2×#41—434no—
450C2×#41—862no—
451C2×#41—864no—
452C2×#41—864no—
453C22×Q8—431no—
454C22×Q8—431no—
455C22×Q8C22×D4311yescharacteristic
456C22×D4—861no—
457C22×D4C22×D4311yescharacteristic
458C23×C4—21no—
459C23×C4—431no—
460C23×C4—861no—
461C23×C4—861no—
462C23×C4—861no—
463C2×Q16—434no—
464C2×Q16—434no—
465C2×Q16—864no—
466C2×Q16—864no—
467C2×SD16—24no—
468C2×SD16—434no—
469C2×SD16—864no—
470C2×SD16C22×D4314yes—
471C22×C8—431no—
472C22×C8—431no—
473C22×C8C22×D4311yescharacteristic
474C22×C8C22×D4311yescharacteristic
475C4⋊Q8—434no—
476C4⋊Q8—862no—
477#126—868no—
478#126—868no—
479#125—434no—
480#125—868no—
481#125—862no—
482#125—868no—
483C22⋊Q8—434no—
484C22⋊Q8—434no—
485C22⋊Q8—862no—
486C22⋊Q8—862no—
487C4×Q8—22no—
488C4×Q8—434no—
489C4×Q8—434no—
490C4×Q8—434no—
491C4×Q8—862no—
492C4×Q8—862no—
493C4×Q8—862no—
494C4×Q8C22×D4314yes—
495C4×D4—22no—
496C4×D4—434no—
497C4×D4—862no—
498C4×D4—868no—
499C4×D4—868no—
500C4×D4C22×D4314yes—
501#117—434no—
502#117—434no—
503#117—868no—
504C2×C4⋊C4—21no—
505C2×C4⋊C4—431no—
506C2×C4⋊C4—431no—
507C2×C4⋊C4—431no—
508C2×C4⋊C4—431no—
509C2×C4⋊C4—434no—
510C2×C4⋊C4—862no—
511C2×C4⋊C4—868no—
512C2×C4⋊C4—861no—
513C2×C4⋊C4—861no—
514C2×C4⋊C4—861no—
515C2×C4⋊C4—861no—
516C2×C4⋊C4—861no—
517C2×C4⋊C4—861no—
518C2×C4⋊C4—861no—
519C2×C4⋊C4—861no—
520C2×C4⋊C4—861no—
521C2×C4⋊C4—861no—
522C2×C4⋊C4C22×D4311yescharacteristic
523C2×C4⋊C4C22×D4311yescharacteristic
524C2×C22⋊C4—21no—
525C2×C22⋊C4—431no—
526C2×C22⋊C4—431no—
527C2×C22⋊C4—861no—
528C2×C22⋊C4—861no—
529C2×C22⋊C4—861no—
530C2×C42—21no—
531C2×C42—431no—
532C2×C42—861no—
533C2×C42—861no—
534C2×C42—861no—
535C2×C42C22×D4311yescharacteristic
536#107—434no—
537#107—434no—
538#106—434no—
539#106C22×D4314yes—
540C4⋊C8—434no—
541C4⋊C8—434no—
542#103—434no—
543#103—434no—
544#103—434no—
545#103—434no—
546#103—434no—
547#103C22×D4314yes—
548#102—434no—
549#102C22×D4314yes—
550C22⋊C8—434no—
551C22⋊C8—434no—
552#97—434no—
553C4×C8C22×D4314yes—
554C24—21no—
555C24—431no—
556#41—868no—
557#41—8616no—
558#41—868no—
559C2×Q8—21no—
560C2×Q8—22no—
561C2×Q8—22no—
562C2×Q8—434no—
563C2×Q8—432no—
564C2×Q8—432no—
565C2×Q8—861no—
566C2×Q8—861no—
567C2×Q8—862no—
568C2×Q8—862no—
569C2×Q8—862no—
570C2×Q8C23×D4312yes—
571C2×D4—21no—
572C2×D4—22no—
573C2×D4—864no—
574C2×D4—868no—
575C2×D4#1062189814yes—
576C2×D4C23×D4312yes—
577C22×C4—21no—
578C22×C4—21no—
579C22×C4—21no—
580C22×C4—24no—
581C22×C4—82no—
582C22×C4—431no—
583C22×C4—431no—
584C22×C4—431no—
585C22×C4—432no—
586C22×C4—432no—
587C22×C4—864no—
588C22×C4—864no—
589C22×C4—864no—
590C22×C4—868no—
591C22×C4—861no—
592C22×C4—862no—
593C22×C4—862no—
594C22×C4—861no—
595C22×C4—861no—
596C22×C4—861no—
597C22×C4—3442no—
598C22×C4—3442no—
599C22×C4D4×D4311yescharacteristic
600C22×C4D4×D4311yescharacteristic
601C22×C4C23×D4311yescharacteristic
602Q16—868no—
603Q16—868no—
604SD16—28no—
605SD16—868no—
606C2×C8—22no—
607C2×C8—22no—
608C2×C8—432no—
609C2×C8—432no—
610C2×C8—862no—
611C2×C8—862no—
612C2×C8C23×D4312yes—
613C2×C8C23×D4312yes—
614C4⋊C4—24no—
615C4⋊C4—21no—
616C4⋊C4—21no—
617C4⋊C4—434no—
618C4⋊C4—434no—
619C4⋊C4—432no—
620C4⋊C4—432no—
621C4⋊C4—864no—
622C4⋊C4—864no—
623C4⋊C4—864no—
624C4⋊C4—864no—
625C4⋊C4—864no—
626C4⋊C4—864no—
627C4⋊C4—864no—
628C4⋊C4—864no—
629C4⋊C4—861no—
630C4⋊C4—861no—
631C4⋊C4—864no—
632C4⋊C4—864no—
633C4⋊C4C23×D4312yes—
634C4⋊C4C23×D4312yes—
635C22⋊C4—24no—
636C22⋊C4—434no—
637C22⋊C4—434no—
638C22⋊C4—864no—
639C22⋊C4—864no—
640C22⋊C4—864no—
641C42—24no—
642C42—432no—
643C42—432no—
644C42—864no—
645C42—864no—
646C42—864no—
647C42D4×D4312yes—
648C42C23×D4312yes—
649C23—24no—
650C23—22no—
651C23—42no—
652C23—42no—
653C23—432no—
654C23—862no—
655C23—862no—
656C23—862no—
657C23C2×D4×D4311yescharacteristic
658Q8—22no—
659Q8—22no—
660Q8—42no—
661Q8—434no—
662Q8—864no—
663Q8—862no—
664Q8—862no—
665Q8—862no—
666Q8—1722no—
667D4—24no—
668D4—22no—
669D4—8616no—
670D4C2×#1062189814yes—
671C2×C4—22no—
672C2×C4—22no—
673C2×C4—22no—
674C2×C4—22no—
675C2×C4—22no—
676C2×C4—42no—
677C2×C4—42no—
678C2×C4—42no—
679C2×C4—84no—
680C2×C4—432no—
681C2×C4—432no—
682C2×C4—432no—
683C2×C4—8616no—
684C2×C4—862no—
685C2×C4—864no—
686C2×C4—862no—
687C2×C4—862no—
688C2×C4—862no—
689C2×C4—864no—
690C2×C4—862no—
691C2×C4—862no—
692C2×C4—862no—
693C2×C4—862no—
694C2×C4—862no—
695C2×C4—3444no—
696C2×C4—3444no—
697C2×C4—1722no—
698C2×C4—1722no—
699C2×C4—1722no—
700C2×C4C2×D4×D4312yes—
701C2×C4C2×D4×D4312yes—
702C2×C4C2×D4×D4311yescharacteristic
703C2×C4#41×D4312yes—
704C2×C4C2×#1062189812yes—
705C2×C4C24×D4311yescharacteristic
706C8—22no—
707C8—22no—
708C8—862no—
709C8—862no—
710C22—24no—
711C22—42no—
712C22—42no—
713C22—48no—
714C22—862no—
715C22—862no—
716C22—862no—
717C22—1724no—
718C22#1458340812yes—
719C22#1458370512yes—
720C22#1458371312yes—
721C22C22×D4×D4311yescharacteristic
722C4—22no—
723C4—22no—
724C4—42no—
725C4—42no—
726C4—42no—
727C4—862no—
728C4—862no—
729C4—862no—
730C4—864no—
731C4—1722no—
732C4—1722no—
733C4—1722no—
734C4#1458340812yes—
735C4C2×#41×D4311yescharacteristic
736C4C22×#1062189811yescharacteristic
737C2—44no—
738C2—1722no—
739C2#1914480514yesdirect product factor
740C2C2×#1458340811yescharacteristic
741C2C2×#1458370511yescharacteristic
742C2C2×#1458371311yescharacteristic
subgroupG/H
centerC23C2×D4×D43
commutator, cosocleC2×C4×C43C25
FrattiniC2×C4C24×D43
FittingC2×C4×SD16×C43C2
socleC23×C43C22×D4
prime radicalC22×#10621900C22
hypercenterC2×C4×SD16D43
hypocenterC43C2×#3120
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×C4×SD16

Complements

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

NH ≅ G/Ntype
1. C2×#14583507C2semidirect
3. #19144805C2direct (N × H)
4. C2×#14583233C2semidirect
5. C2×#14583231C2semidirect
6. C2×#14583209C2semidirect
7. C2×#14583197C2semidirect
8. C2×#14583108C2semidirect
9. C2×#14583102C2semidirect
12. C2×#14583004C2semidirect
13. C2×#14582999C2semidirect
14. C2×C4×Dic172C2semidirect
15. C2×#14582958C2semidirect
16. C2×C4×SD16×C43C2semidirect
22. #14583507C22semidirect
43. #14583233C22semidirect
44. #14583231C22semidirect
45. #14583209C22semidirect
46. #14583197C22semidirect
47. #14583108C22semidirect
48. #14583102C22semidirect
51. #14583004C22semidirect
52. #14582999C22semidirect
53. C4×Dic172C22semidirect
54. #14582958C22semidirect
72. C4×SD16×C43C22semidirect
380. C2×C4×SD16D43semidirect
383. C2×C43#3120semidirect
428. C4×SD16C2×D43semidirect
448. C43C2×#3120semidirect
739. C2#19144805direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#145835072
C2×#145833782
#191448052
C2×#145832332
C2×#145832312
C2×#145832092
C2×#145831972
C2×#145831082
C2×#145831022
C2×#145830622
C2×#145830582
C2×#145830042
C2×#145829992
C2×C4×Dic1722
C2×#145829582
C2×C4×SD16×C432
C2×#312043