Finite Group Databasebeta

← C2×#19144632 #25964633

Subgroups — C2×#19144632 #25964633

Order 11008.

2138 conjugacy classes of subgroups.

The subgroup lattice has 736 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583453C211yesmaximal, characteristic
2C2×C4×Q8×D43C211yesmaximal, characteristic
3#19144632C2116yesmaximal, direct product factor
4C2×#14583236C211yesmaximal, characteristic
5C2×#14583233C211yesmaximal, characteristic
6C2×#14583193C211yesmaximal, characteristic, complemented
7C2×#14583192C211yesmaximal, characteristic, complemented
8C2×#14583108C211yesmaximal, characteristic, complemented
9C2×#14583107C211yesmaximal, characteristic, complemented
10C2×#14583056C211yesmaximal, characteristic
11C2×#14583053C211yesmaximal, characteristic
12C2×C4×Dic172C211yesmaximal, characteristic, complemented
13C2×C4×#10621885C211yesmaximal, characteristic, complemented
14C2×C4×#10621885C211yesmaximal, characteristic, complemented
15C2×#14582950C211yesmaximal, characteristic
16C2×C4×Q16×C43C211yesmaximal, characteristic, complemented
17C22×Q8×D43C2211yescharacteristic
18C22×Dic172C2211yescharacteristic
19C22×#10621885C2211yescharacteristic
20C22×#10621885C2211yescharacteristic
21#14583453—24no—
22#14583453C2218yes—
23C2×#13063324C2211yescharacteristic
24C2×#13063323C2211yescharacteristic
25C2×#13063315—21no—
26C2×#13063305C2211yescharacteristic
27C2×#13063303—21no—
28C2×#13063301C2211yescharacteristic
29C2×Q8×Dic43C2211yescharacteristic
30C2×C4×Dic86—21no—
31C2×C4×Dic86—21no—
32C2×C4×Dic86C2211yescharacteristic
33C2×C4×Dic86C2211yescharacteristic
34C2×#13063290—21no—
35C2×#13063290C2211yescharacteristic
36C4×Q8×D43—24no—
37C4×Q8×D43C2218yes—
38C2×#13063282—21no—
39C2×C4⋊C4×D43—21no—
40C2×C4⋊C4×D43C2211yescharacteristic
41C2×C42×D43—21no—
42C2×C42×D43C2211yescharacteristic
43#14583236C2218yes—
44#14583233C2218yes—
45#14583193C2218yescomplemented
46#14583192C2218yescomplemented
47#14583108C2218yescomplemented
48#14583107C2218yescomplemented
49#14583056C2218yes—
50#14583053C2218yes—
51C4×Dic172C2218yescomplemented
52C4×#10621885C2218yescomplemented
53C4×#10621885C2218yescomplemented
54#14582950C2218yes—
55C2×#13063259C2211yescharacteristic
56C2×#13063258C2211yescharacteristic
57C2×#13063258C2211yescharacteristic
58C2×Dic43⋊C8C2211yescharacteristic
59C2×Dic43⋊C8C2211yescharacteristic
60C2×#13063250C2211yescharacteristic
61C2×#13063250C2211yescharacteristic
62C2×#13063249C2211yescharacteristic
63C2×#13063249C2211yescharacteristic
64C2×#13063248C2211yescharacteristic
65C2×#13063248C2211yescharacteristic
66C2×(C2×D43)⋊C8C2211yescharacteristic
67C2×(C2×D43)⋊C8C2211yescharacteristic
68C2×C4×C43⋊C8C2211yescharacteristic
69C22×Q16×C43C2211yescharacteristic
70C2×C4×Q8×C43C2211yescharacteristic
71C2×C4×Q8×C43C2211yescharacteristic
72C4×Q16×C43C2218yescomplemented
73C2×#107×C43C2211yescharacteristic
74C2×#103×C43C2211yescharacteristic
75C2×#103×C43C2211yescharacteristic
76C2×C4×C8×C43C2211yescharacteristic
77C22×Dic86—21no—
78C22×Dic86—21no—
79C22×Dic86C2311yescharacteristic
80C22×Dic86C2311yescharacteristic
81C2×Q8×D43—24no—
82C2×Q8×D43—22no—
83C2×Q8×D43—24no—
84C2×Q8×D43C2314yes—
85C22×C4×D43—21no—
86C22×C4×D43—21no—
87C22×C4×D43D411yescharacteristic
88C22×C4×D43D411yescharacteristic
89C22×C4×D43C2311yescharacteristic
90C2×Dic172—24no—
91C2×Dic172C2314yes—
92C2×#10621885—24no—
93C2×#10621885—24no—
94C2×#10621885C2314yes—
95C2×#10621885C2314yes—
96C22×C43⋊C8C2311yescharacteristic
97C22×C43⋊C8C2311yescharacteristic
98#13063324—22no—
99#13063324C2314yes—
100#13063323—22no—
101#13063323C2314yes—
102#13063315—28no—
103#13063305—22no—
104#13063305C2314yes—
105#13063303—28no—
106#13063301—22no—
107#13063301C2314yes—
108Q8×Dic43—22no—
109Q8×Dic43C2314yes—
110C4×Dic86—22no—
111C4×Dic86—22no—
112C4×Dic86—28no—
113C4×Dic86—28no—
114C4×Dic86C2314yes—
115C4×Dic86C2314yes—
116#13063290—22no—
117#13063290—28no—
118#13063290C2314yes—
119#13063282—28no—
120C2×C4⋊Dic43—21no—
121C2×C4⋊Dic43—21no—
122C2×C4⋊Dic43C2311yescharacteristic
123C2×C4⋊Dic43C2311yescharacteristic
124C2×Dic43⋊C4—21no—
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—
132C4⋊C4×D43—28no—
133C4⋊C4×D43—22no—
134C4⋊C4×D43C2314yes—
135C2×(C2×D43)⋊C4—21no—
136C2×(C2×D43)⋊C4—21no—
137C2×C4×Dic43—21no—
138C2×C4×Dic43—21no—
139C2×C4×Dic43—21no—
140C2×C4×Dic43—21no—
141C2×C4×Dic43D411yescharacteristic
142C2×C4×Dic43D411yescharacteristic
143C2×C4×Dic43C2311yescharacteristic
144C42×D43—28no—
145C42×D43D414yes—
146C42×D43C2314yes—
147#13063259C2314yes—
148#13063258C2314yes—
149#13063258C2314yes—
150Dic43⋊C8C2314yes—
151Dic43⋊C8C2314yes—
152#13063250C2314yes—
153#13063250C2314yes—
154#13063249C2314yes—
155#13063249C2314yes—
156#13063248C2314yes—
157#13063248C2314yes—
158(C2×D43)⋊C8C2314yes—
159(C2×D43)⋊C8C2314yes—
160C4×C43⋊C8C2314yes—
161C22×Q8×C43C2311yescharacteristic
162C22×Q8×C43C2311yescharacteristic
163C2×Q16×C43—24no—
164C2×Q16×C43C2314yes—
165C22×C8×C43C2311yescharacteristic
166C22×C8×C43C2311yescharacteristic
167C4×Q8×C43—22no—
168C4×Q8×C43—22no—
169C4×Q8×C43C2314yes—
170C4×Q8×C43C2314yes—
171C2×C4⋊C4×C43—21no—
172C2×C4⋊C4×C43—21no—
173C2×C4⋊C4×C43C2311yescharacteristic
174C2×C4⋊C4×C43C2311yescharacteristic
175C2×C42×C43—21no—
176C2×C42×C43—21no—
177C2×C42×C43C2311yescharacteristic
178#107×C43C2314yes—
179#103×C43C2314yes—
180#103×C43C2314yes—
181C4×C8×C43C2314yes—
182C23×D43C2×D411yescharacteristic
183C2×Q8×C43—21no—
184C2×Q8×C43—21no—
185C2×Q8×C43—22no—
186C2×Q8×C43—22no—
187C2×Q8×C43—22no—
188C2×Q8×C43#4114yes—
189C2×Q8×C43C2412yes—
190C2×Q8×C43C2412yes—
191C22×C4×C43—21no—
192C22×C4×C43—21no—
193C22×C4×C43—21no—
194C22×C4×C43—21no—
195C22×C4×C43C2×D411yescharacteristic
196C22×C4×C43C2×D411yescharacteristic
197C22×C4×C43C2411yescharacteristic
198C22×Dic43—21no—
199C22×Dic43—21no—
200C22×Dic43—21no—
201C22×Dic43—21no—
202C22×Dic43C2×D411yescharacteristic
203C22×Dic43C2×D411yescharacteristic
204C22×Dic43C2×D411yescharacteristic
205Q8×D43—216no—
206Q8×D43—28no—
207Q8×D43—28no—
208C2×C4×D43—28no—
209C2×C4×D43—22no—
210C2×C4×D43—22no—
211C2×C4×D43—24no—
212C2×C4×D43—24no—
213C2×C4×D43—42no—
214C2×C4×D43—44no—
215C2×C4×D43Q1618yescomplemented
216C2×C4×D43C2×D412yes—
217C2×C4×D43C2×D414yes—
218C2×C4×D43C2×D414yes—
219C2×C4×D43C2412yes—
220C2×Dic86—28no—
221C2×Dic86—21no—
222C2×Dic86—22no—
223C2×Dic86—24no—
224C2×Dic86—22no—
225C2×Dic86—22no—
226C2×Dic86—21no—
227C2×Dic86—24no—
228C2×Dic86—44no—
229C2×Dic86#4114yes—
230C2×Dic86C2412yes—
231C2×Dic86C2412yes—
232Q16×C43—28no—
233C2×C8×C43—22no—
234C2×C8×C43—22no—
235C2×C8×C43C2412yes—
236C2×C8×C43C2412yes—
237C4⋊C4×C43—24no—
238C4⋊C4×C43—24no—
239C4⋊C4×C43—21no—
240C4⋊C4×C43—21no—
241C4⋊C4×C43C2412yes—
242C4⋊C4×C43C2412yes—
243C42×C43—24no—
244C42×C43—24no—
245C42×C43C2×D412yes—
246C42×C43C2412yes—
247#10621885—28no—
248#10621885—28no—
249(C2×D43)⋊C4—24no—
250(C2×D43)⋊C4—24no—
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—
265C4×Dic43—24no—
266C4×Dic43—24no—
267C4×Dic43—24no—
268C4×Dic43—24no—
269C4×Dic43C2×D412yes—
270C4×Dic43C2×D414yes—
271C4×Dic43C2×D414yes—
272C4×Dic43C2412yes—
273C2×C43⋊C8—22no—
274C2×C43⋊C8—22no—
275C2×C43⋊C8C2412yes—
276C2×C43⋊C8C2412yes—
277Dic172—28no—
278C23×C43C22×D411yescharacteristic
279C22×D43—22no—
280C22×D43—22no—
281C22×D43C2×Q1614yes—
282C22×D43C22×D412yes—
283Q8×C43—24no—
284Q8×C43—22no—
285Q8×C43—22no—
286Q8×C43—22no—
287Q8×C43—42no—
288Q8×C43C2×#4114yes—
289C2×C4×C43—24no—
290C2×C4×C43—22no—
291C2×C4×C43—22no—
292C2×C4×C43—22no—
293C2×C4×C43—22no—
294C2×C4×C43—22no—
295C2×C4×C43—42no—
296C2×C4×C43—42no—
297C2×C4×C43—42no—
298C2×C4×C43C2×Q1614yes—
299C2×C4×C43C22×D412yes—
300C2×C4×C43C22×D411yescharacteristic
301C2×C4×C43C22×D412yes—
302C2×C4×C43C2×#4112yes—
303C2×C4×C43C2×#4112yes—
304C2×C4×C43C2511yescharacteristic
305C2×Dic43—22no—
306C2×Dic43—24no—
307C2×Dic43—22no—
308C2×Dic43—22no—
309C2×Dic43—22no—
310C2×Dic43—22no—
311C2×Dic43—22no—
312C2×Dic43—42no—
313C2×Dic43—42no—
314C2×Dic43—42no—
315C2×Dic43C2×Q1614yes—
316C2×Dic43C22×D412yes—
317C2×Dic43C22×D412yes—
318C2×Dic43C22×D412yes—
319C4×D43—216no—
320C4×D43—24no—
321C4×D43—22no—
322C4×D43—22no—
323C4×D43—44no—
324C4×D43—48no—
325C4×D43C2×Q16116yescomplemented
326Dic86—216no—
327Dic86—24no—
328Dic86—22no—
329Dic86—22no—
330Dic86—22no—
331Dic86—48no—
332Dic86—42no—
333Dic86C2×#4114yes—
334C8×C43—22no—
335C8×C43—22no—
336C43⋊C8—22no—
337C43⋊C8—22no—
338C2×#3104—431nomaximal, Sylow
339C22×C43#52512yes—
340C22×C43C22×Q1612yes—
341C22×C43#57512yes—
342C22×C43C23×D411yescharacteristic
343C2×D43—28no—
344C2×D43—22no—
345C2×D43—22no—
346C2×D43C22×Q1614yes—
347C4×C43—24no—
348C4×C43—22no—
349C4×C43—42no—
350C4×C43—42no—
351C4×C43—42no—
352C4×C43#52512yes—
353C4×C43C22×Q1614yes—
354C4×C43C22×#4111yescharacteristic
355C4×C43C22×#4111yescharacteristic
356Dic43—22no—
357Dic43—24no—
358Dic43—22no—
359Dic43—42no—
360Dic43—42no—
361Dic43—42no—
362Dic43C22×Q1614yes—
363C2×#533—431no—
364C22×C4×Q8—431no—
365#3104—4316no—
366C2×#484—431no—
367C2×#484—431no—
368C2×#477—431no—
369C2×#477—431no—
370C2×#462—431no—
371C2×#462—431no—
372C2×#451—431no—
373C2×#451—431no—
374C2×C4×Q16—431no—
375C2×C4×Q16—431no—
376C2×C4×Q16—431no—
377C2×C4×Q16D4311yescharacteristic, complemented
378C2×#431—431no—
379C2×C43#310414yescomplemented
380C2×C43C2×#52511yescharacteristic
381C2×C43C23×Q1611yescharacteristic
382C2×C43C2×#57511yescharacteristic
383D43—24no—
384C23×Q8—431no—
385C22×Q16—431no—
386C22×Q16—431no—
387C22×Q16—431no—
388C22×Q16C2×D4311yescharacteristic
389#533—438no—
390#533—864no—
391C2×C4⋊Q8—431no—
392C2×C4⋊Q8—431no—
393C2×#125—861no—
394C2×C22⋊Q8—431no—
395C2×C22⋊Q8—431no—
396C2×C22⋊Q8—861no—
397C2×C4×Q8—431no—
398C2×C4×Q8—438no—
399C2×C4×Q8—431no—
400C2×C4×Q8—431no—
401C2×C4×Q8—431no—
402C2×C4×Q8—861no—
403C2×C4×Q8—861no—
404C2×C4×Q8—861no—
405C2×C4×Q8—864no—
406C2×C4×Q8C2×D4311yescharacteristic
407C2×C4×Q8C2×D4311yescharacteristic
408C2×#117—861no—
409C22×C4⋊C4—431no—
410C22×C4⋊C4—861no—
411C22×C42—431no—
412C22×C42—861no—
413#484—438no—
414#484—438no—
415#477—438no—
416#477—438no—
417#462—438no—
418#462—438no—
419#451—438no—
420#451—438no—
421C4×Q16—438no—
422C4×Q16—438no—
423C4×Q16—438no—
424C4×Q16C2×D4318yescomplemented
425#431—438no—
426C2×#107—431no—
427C2×#107—431no—
428C2×#107—431no—
429C2×#107C2×D4311yescharacteristic
430C2×C4⋊C8—431no—
431C2×C4⋊C8—431no—
432C2×#103—431no—
433C2×#103—431no—
434C2×#103—431no—
435C2×#103—431no—
436C2×#103—431no—
437C2×#103—431no—
438C2×#103C2×D4311yescharacteristic
439C2×#103C2×D4311yescharacteristic
440C2×C22⋊C8—431no—
441C2×C22⋊C8—431no—
442C2×C4×C8—431no—
443C2×C4×C8C2×D4311yescharacteristic
444C43C2×#310411yescharacteristic, complemented, Sylow
445C22×Q8—434no—
446C22×Q8—431no—
447C22×Q8—431no—
448C22×Q8—861no—
449C22×Q8—861no—
450C22×Q8—862no—
451C22×Q8—864no—
452C22×Q8—864no—
453C22×Q8C22×D4311yescharacteristic
454C22×Q8C22×D4311yescharacteristic
455C23×C4—431no—
456C23×C4—431no—
457C23×C4—431no—
458C23×C4—861no—
459C23×C4—861no—
460C2×Q16—24no—
461C2×Q16—434no—
462C2×Q16—434no—
463C2×Q16—434no—
464C2×Q16—864no—
465C2×Q16—864no—
466C2×Q16—864no—
467C2×Q16C22×D4314yes—
468C22×C8—431no—
469C22×C8—431no—
470C22×C8C22×D4311yescharacteristic
471C22×C8C22×D4311yescharacteristic
472C4⋊Q8—434no—
473C4⋊Q8—434no—
474C4⋊Q8—862no—
475C4⋊Q8—862no—
476#125—868no—
477C22⋊Q8—434no—
478C22⋊Q8—434no—
479C22⋊Q8—862no—
480C22⋊Q8—868no—
481C22⋊Q8—862no—
482C4×Q8—22no—
483C4×Q8—22no—
484C4×Q8—434no—
485C4×Q8—434no—
486C4×Q8—434no—
487C4×Q8—434no—
488C4×Q8—868no—
489C4×Q8—868no—
490C4×Q8—868no—
491C4×Q8—862no—
492C4×Q8—862no—
493C4×Q8—862no—
494C4×Q8—862no—
495C4×Q8C22×D4314yes—
496C4×Q8C22×D4314yes—
497#117—868no—
498C2×C4⋊C4—21no—
499C2×C4⋊C4—21no—
500C2×C4⋊C4—431no—
501C2×C4⋊C4—431no—
502C2×C4⋊C4—434no—
503C2×C4⋊C4—862no—
504C2×C4⋊C4—868no—
505C2×C4⋊C4—861no—
506C2×C4⋊C4—861no—
507C2×C4⋊C4—861no—
508C2×C4⋊C4—861no—
509C2×C4⋊C4—861no—
510C2×C4⋊C4—861no—
511C2×C4⋊C4—861no—
512C2×C4⋊C4—861no—
513C2×C4⋊C4—861no—
514C2×C4⋊C4—861no—
515C2×C4⋊C4C22×D4311yescharacteristic
516C2×C4⋊C4C22×D4311yescharacteristic
517C2×C22⋊C4—861no—
518C2×C22⋊C4—861no—
519C2×C42—21no—
520C2×C42—21no—
521C2×C42—431no—
522C2×C42—431no—
523C2×C42—431no—
524C2×C42—434no—
525C2×C42—434no—
526C2×C42—868no—
527C2×C42—861no—
528C2×C42—861no—
529C2×C42—861no—
530C2×C42—861no—
531C2×C42C22×D4311yescharacteristic
532#107—434no—
533#107—434no—
534#107—434no—
535#107C22×D4314yes—
536C4⋊C8—434no—
537C4⋊C8—434no—
538#103—434no—
539#103—434no—
540#103—434no—
541#103—434no—
542#103—434no—
543#103—434no—
544#103C22×D4314yes—
545#103C22×D4314yes—
546C22⋊C8—434no—
547C22⋊C8—434no—
548C4×C8—434no—
549C4×C8C22×D4314yes—
550C24—431no—
551C2×Q8—21no—
552C2×Q8—21no—
553C2×Q8—22no—
554C2×Q8—22no—
555C2×Q8—22no—
556C2×Q8—434no—
557C2×Q8—432no—
558C2×Q8—432no—
559C2×Q8—864no—
560C2×Q8—864no—
561C2×Q8—868no—
562C2×Q8—868no—
563C2×Q8—8616no—
564C2×Q8—868no—
565C2×Q8—861no—
566C2×Q8—861no—
567C2×Q8—862no—
568C2×Q8—862no—
569C2×Q8—862no—
570C2×Q8—1724no—
571C2×Q8#1062189814yes—
572C2×Q8C23×D4312yes—
573C2×Q8C23×D4312yes—
574C22×C4—21no—
575C22×C4—21no—
576C22×C4—21no—
577C22×C4—21no—
578C22×C4—431no—
579C22×C4—438no—
580C22×C4—434no—
581C22×C4—431no—
582C22×C4—431no—
583C22×C4—432no—
584C22×C4—432no—
585C22×C4—434no—
586C22×C4—864no—
587C22×C4—868no—
588C22×C4—864no—
589C22×C4—861no—
590C22×C4—862no—
591C22×C4—862no—
592C22×C4—861no—
593C22×C4—861no—
594C22×C4—861no—
595C22×C4—1722no—
596C22×C4—1724no—
597C22×C4D4×D4311yescharacteristic
598C22×C4D4×D4311yescharacteristic
599C22×C4C23×D4311yescharacteristic
600Q16—28no—
601Q16—868no—
602Q16—868no—
603Q16—868no—
604C2×C8—22no—
605C2×C8—22no—
606C2×C8—432no—
607C2×C8—432no—
608C2×C8—862no—
609C2×C8—862no—
610C2×C8C23×D4312yes—
611C2×C8C23×D4312yes—
612C4⋊C4—24no—
613C4⋊C4—24no—
614C4⋊C4—21no—
615C4⋊C4—21no—
616C4⋊C4—432no—
617C4⋊C4—432no—
618C4⋊C4—864no—
619C4⋊C4—864no—
620C4⋊C4—864no—
621C4⋊C4—864no—
622C4⋊C4—864no—
623C4⋊C4—864no—
624C4⋊C4—864no—
625C4⋊C4—864no—
626C4⋊C4—861no—
627C4⋊C4—861no—
628C4⋊C4—864no—
629C4⋊C4—864no—
630C4⋊C4C23×D4312yes—
631C4⋊C4C23×D4312yes—
632C22⋊C4—864no—
633C22⋊C4—864no—
634C42—24no—
635C42—24no—
636C42—434no—
637C42—434no—
638C42—432no—
639C42—432no—
640C42—864no—
641C42—864no—
642C42—864no—
643C42—864no—
644C42D4×D4312yes—
645C42C23×D4312yes—
646C23—434no—
647C23—432no—
648C23—862no—
649C23—862no—
650C23C2×D4×D4311yescharacteristic
651Q8—24no—
652Q8—22no—
653Q8—22no—
654Q8—22no—
655Q8—42no—
656Q8—434no—
657Q8—8616no—
658Q8—864no—
659Q8—862no—
660Q8—862no—
661Q8—862no—
662Q8—1728no—
663Q8—1722no—
664Q8C2×#1062189814yes—
665C2×C4—24no—
666C2×C4—22no—
667C2×C4—22no—
668C2×C4—22no—
669C2×C4—22no—
670C2×C4—22no—
671C2×C4—42no—
672C2×C4—42no—
673C2×C4—42no—
674C2×C4—434no—
675C2×C4—432no—
676C2×C4—4316no—
677C2×C4—432no—
678C2×C4—432no—
679C2×C4—8616no—
680C2×C4—862no—
681C2×C4—864no—
682C2×C4—862no—
683C2×C4—862no—
684C2×C4—864no—
685C2×C4—862no—
686C2×C4—862no—
687C2×C4—862no—
688C2×C4—862no—
689C2×C4—862no—
690C2×C4—1724no—
691C2×C4—1728no—
692C2×C4—1722no—
693C2×C4—1722no—
694C2×C4—1722no—
695C2×C4Q16×D4314yes—
696C2×C4C2×D4×D4312yes—
697C2×C4C2×D4×D4311yescharacteristic
698C2×C4C2×D4×D4312yes—
699C2×C4#41×D4312yes—
700C2×C4C2×#1062189812yes—
701C2×C4C24×D4311yescharacteristic
702C8—22no—
703C8—22no—
704C8—862no—
705C8—862no—
706C22—434no—
707C22—862no—
708C22—862no—
709C22—868no—
710C22#1458340812yes—
711C22C2×Q16×D4312yes—
712C22#1458369612yes—
713C22C22×D4×D4311yescharacteristic
714C4—22no—
715C4—24no—
716C4—42no—
717C4—42no—
718C4—42no—
719C4—434no—
720C4—862no—
721C4—862no—
722C4—864no—
723C4—1722no—
724C4—1722no—
725C4—1722no—
726C4#1458340812yes—
727C4C2×Q16×D4314yes—
728C4C2×#41×D4311yescharacteristic
729C4C22×#1062189811yescharacteristic
730C2—864no—
731C2#1914463214yesdirect product factor
732C2C2×#1458340811yescharacteristic
733C2C22×Q16×D4311yescharacteristic
734C2C2×#1458369611yescharacteristic
subgroupG/H
centerC22×C4D4×D43
commutator, cosocleC2×C4×C43C25
FrattiniC2×C4C24×D43
FittingC2×C4×Q16×C43C2
socleC23×C43C22×D4
prime radicalC23×D43C2×D4
hypercenterC2×C4×Q16D43
hypocenterC43C2×#3104
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22×C4 ◁ C2×C42 ◁ C2×C4×Q16

Complements

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

NH ≅ G/Ntype
3. #19144632C2direct (N × H)
6. C2×#14583193C2semidirect
7. C2×#14583192C2semidirect
8. C2×#14583108C2semidirect
9. C2×#14583107C2semidirect
12. C2×C4×Dic172C2semidirect
13. C2×C4×#10621885C2semidirect
14. C2×C4×#10621885C2semidirect
16. C2×C4×Q16×C43C2semidirect
45. #14583193C22semidirect
46. #14583192C22semidirect
47. #14583108C22semidirect
48. #14583107C22semidirect
51. C4×Dic172C22semidirect
52. C4×#10621885C22semidirect
53. C4×#10621885C22semidirect
72. C4×Q16×C43C22semidirect
215. C2×C4×D43Q16semidirect
325. C4×D43C2×Q16semidirect
377. C2×C4×Q16D43semidirect
379. C2×C43#3104semidirect
424. C4×Q16C2×D43semidirect
444. C43C2×#3104semidirect
731. C2#19144632direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#145834532
C2×C4×Q8×D432
#191446322
C2×#145832362
C2×#145832332
C2×#145831932
C2×#145831922
C2×#145831082
C2×#145831072
C2×#145830562
C2×#145830532
C2×C4×Dic1722
C2×C4×#106218852
C2×#145829502
C2×C4×Q16×C432
C2×#310443