Finite Group Databasebeta

← #25062686

Subgroups — #25062686

Order 11008.

1386 conjugacy classes of subgroups.

The subgroup lattice has 784 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C22⋊Q8×D43C211yesmaximal, characteristic
2C2×#14582861C211yesmaximal, characteristic
3#407×D43C211yesmaximal, characteristic
4#19132960C211yesmaximal, characteristic, complemented
5#19132959C211yesmaximal, characteristic, complemented
6#19132958C211yesmaximal, characteristic, complemented
7#19132957C214yesmaximal, complemented
8#19132923C214yesmaximal, complemented
9C43×#1472C211yesmaximal, characteristic, complemented
10C22×Q8×D43C411yescharacteristic
11C23×C4×D43C2211yescharacteristic
12C22×#10621872—21no—
13C2×M16×D43—21no—
14C2×#13063305C411yescharacteristic
15C2×#13063304C2211yescharacteristic
16C2×#13063303C2212yes—
17C2×#13063302C412yes—
18C2×#13063301C411yescharacteristic
19C22⋊Q8×D43—21no—
20C22⋊Q8×D43—21no—
21C22⋊Q8×D43—21no—
22C22⋊Q8×D43—21no—
23C22⋊Q8×D43—21no—
24C22⋊Q8×D43—21no—
25C22⋊Q8×D43—21no—
26C22⋊Q8×D43—21no—
27C2×C4⋊C4×D43C411yescharacteristic
28C2×C4⋊C4×D43C2212yes—
29C2×C22⋊C4×D43C412yes—
30#14582863C2211yescharacteristic
31#14582862—21no—
32#14582861—21no—
33#14582861—21no—
34#14582861—21no—
35#14582861C2212yes—
36#14582861C2212yes—
37#14582861C2212yes—
38C2×C22⋊(C43⋊C8)C2211yescharacteristic
39C2×(C2×D43)⋊C8—21no—
40C22⋊C8×D43—21no—
41C22⋊C8×D43C2212yes—
42#14582625C2214yescomplemented
43#14582624C2214yescomplemented
44#14582624C2214yescomplemented
45C2×C22⋊Q8×C43C2211yescharacteristic
46C43×#407C2211yescharacteristic
47C2×C22⋊C8×C43C2211yescharacteristic
48C43×#324C2214yescomplemented
49C24×D43C2×C411yescharacteristic
50C22×Dic86C2×C412yes—
51C22×Dic86C2×C411yescharacteristic
52C2×Q8×D43—21no—
53C2×Q8×D43—21no—
54C2×Q8×D43—21no—
55C2×Q8×D43—21no—
56C2×Q8×D43—44no—
57C23×Dic43C2×C411yescharacteristic
58C22×C4×D43—44no—
59C22×C4×D43C2×C411yescharacteristic
60C22×C4×D43C2×C412yes—
61C22×C4×D43C2×C412yes—
62C22×C4×D43C2×C411yescharacteristic
63C22×C4×D43D411yescharacteristic
64C22×C4×D43D411yescharacteristic
65C22×C4×D43D411yescharacteristic
66C22×C4×D43D411yescharacteristic
67C22×C4×D43D411yescharacteristic
68C22×C4×D43D411yescharacteristic
69C22×C4×D43D411yescharacteristic
70C22×C4×D43D411yescharacteristic
71C22×C4×D43C2311yescharacteristic
72C22×C4×D43C2311yescharacteristic
73C2×#10621877—21no—
74C2×#10621872—22no—
75C2×#10621872—22no—
76C2×#10621872—22no—
77C2×#10621872—44no—
78M16×D43—44no—
79C22×C43⋊C8—21no—
80C2×C8×D43—22no—
81#13063305—21no—
82#13063305—21no—
83#13063305—21no—
84#13063305—21no—
85#13063304—21no—
86#13063304—21no—
87#13063304—21no—
88#13063304—21no—
89#13063303—22no—
90#13063303—22no—
91#13063303—22no—
92#13063303—22no—
93#13063302—22no—
94#13063302—22no—
95#13063302—22no—
96#13063302—22no—
97#13063301—21no—
98#13063301—21no—
99#13063301—21no—
100#13063301—21no—
101C2×C4⋊Dic43C2×C411yescharacteristic
102C2×C4⋊Dic43C2×C412yes—
103C2×Dic43⋊C4C2×C412yes—
104C2×Dic43⋊C4C2×C412yes—
105C2×Dic43⋊C4C2312yes—
106C4⋊C4×D43—21no—
107C4⋊C4×D43—21no—
108C4⋊C4×D43—21no—
109C4⋊C4×D43—21no—
110C4⋊C4×D43—22no—
111C4⋊C4×D43—22no—
112C4⋊C4×D43—22no—
113C4⋊C4×D43—22no—
114C2×C22⋊Dic43C2×C412yes—
115C2×(C2×D43)⋊C4C2×C412yes—
116C2×(C2×D43)⋊C4C2×C412yes—
117C22⋊C4×D43—22no—
118C22⋊C4×D43—22no—
119C22⋊C4×D43—22no—
120C22⋊C4×D43—22no—
121C22⋊(C43⋊C8)—21no—
122C22⋊(C43⋊C8)—21no—
123C22⋊(C43⋊C8)C2312yes—
124C22⋊(C43⋊C8)C2312yes—
125(C2×D43)⋊C8—22no—
126(C2×D43)⋊C8—22no—
127(C2×D43)⋊C8—22no—
128(C2×D43)⋊C8—22no—
129C22×Q8×C43C2×C411yescharacteristic
130C23×C4×C43C2311yescharacteristic
131C2×M16×C43—21no—
132C22×C8×C43—21no—
133C22⋊Q8×C43—21no—
134C22⋊Q8×C43—21no—
135C22⋊Q8×C43—21no—
136C22⋊Q8×C43—21no—
137C2×C4⋊C4×C43C2×C411yescharacteristic
138C2×C4⋊C4×C43C2312yes—
139C2×C22⋊C4×C43C2×C412yes—
140C22⋊C8×C43—21no—
141C22⋊C8×C43—21no—
142C22⋊C8×C43C2312yes—
143C22⋊C8×C43C2312yes—
144C24×C43C22×C411yescharacteristic
145C23×D43—24no—
146C23×D43—42no—
147C23×D43—42no—
148C23×D43C22⋊C411yescharacteristic
149C23×D43C22⋊C411yescharacteristic
150C23×D43C22⋊C411yescharacteristic
151C23×D43C22⋊C411yescharacteristic
152C23×D43C22×C411yescharacteristic
153C23×D43C22×C411yescharacteristic
154C2×Q8×C43—21no—
155C2×Q8×C43—21no—
156C2×Q8×C43—42no—
157C22×C4×C43—42no—
158C22×C4×C43C22×C412yes—
159C22×C4×C43C22×C411yescharacteristic
160C22×C4×C43C22×C412yes—
161C22×C4×C43C2×D411yescharacteristic
162C22×C4×C43C2×D411yescharacteristic
163C22×C4×C43C2×D411yescharacteristic
164C22×C4×C43C2×D411yescharacteristic
165C22×C4×C43C2411yescharacteristic
166C22×Dic43—42no—
167C22×Dic43C22⋊C411yescharacteristic
168C22×Dic43C22⋊C411yescharacteristic
169C22×Dic43C22⋊C411yescharacteristic
170C22×Dic43C22⋊C411yescharacteristic
171C22×Dic43C22×C412yes—
172C22×Dic43C22×C411yescharacteristic
173C22×Dic43C22×C412yes—
174C22×Dic43C22×C411yescharacteristic
175Q8×D43—44no—
176Q8×D43—44no—
177Q8×D43—44no—
178Q8×D43—44no—
179C2×C4×D43—24no—
180C2×C4×D43—24no—
181C2×C4×D43—24no—
182C2×C4×D43—22no—
183C2×C4×D43—22no—
184C2×C4×D43—22no—
185C2×C4×D43—22no—
186C2×C4×D43—42no—
187C2×C4×D43—42no—
188C2×C4×D43—42no—
189C2×C4×D43—44no—
190C2×C4×D43—44no—
191C2×C4×D43—42no—
192C2×C4×D43—42no—
193C2×C4×D43—42no—
194C2×C4×D43—42no—
195C2×C4×D43—42no—
196C2×C4×D43—42no—
197C2×C4×D43C22⋊C411yescharacteristic
198C2×C4×D43C22⋊C411yescharacteristic
199C2×C4×D43C22⋊C411yescharacteristic
200C2×C4×D43C22⋊C411yescharacteristic
201C2×C4×D43C22⋊C411yescharacteristic
202C2×C4×D43C22⋊C411yescharacteristic
203C2×C4×D43C22⋊C411yescharacteristic
204C2×C4×D43C22⋊C411yescharacteristic
205C2×C4×D43C2×D411yescharacteristic
206C2×C4×D43C2×D411yescharacteristic
207C2×C4×D43C2×D411yescharacteristic
208C2×C4×D43C2×D411yescharacteristic
209C2×C4×D43C2×D411yescharacteristic
210C2×C4×D43C2×D411yescharacteristic
211C2×C4×D43C2×D411yescharacteristic
212C2×C4×D43C2×D411yescharacteristic
213C2×Dic86—21no—
214C2×Dic86—21no—
215C2×Dic86—22no—
216C2×Dic86—22no—
217C2×Dic86—44no—
218C2×Dic86—42no—
219M16×C43—42no—
220C2×C8×C43—22no—
221C2×C8×C43—22no—
222C2×C8×C43—42no—
223C4⋊C4×C43—21no—
224C4⋊C4×C43—21no—
225C4⋊C4×C43—22no—
226C4⋊C4×C43—22no—
227C22⋊C4×C43—22no—
228C22⋊C4×C43—22no—
229C22⋊Dic43—22no—
230C22⋊Dic43—22no—
231(C2×D43)⋊C4—22no—
232(C2×D43)⋊C4—22no—
233(C2×D43)⋊C4—22no—
234(C2×D43)⋊C4—22no—
235C4⋊Dic43—21no—
236C4⋊Dic43—21no—
237C4⋊Dic43—22no—
238C4⋊Dic43—22no—
239Dic43⋊C4—22no—
240Dic43⋊C4—22no—
241Dic43⋊C4—22no—
242Dic43⋊C4—22no—
243Dic43⋊C4—22no—
244Dic43⋊C4—22no—
245#10621877—42no—
246C2×C43⋊C8—22no—
247C2×C43⋊C8—22no—
248C2×C43⋊C8—42no—
249#10621872—44no—
250#10621872—44no—
251#10621872—44no—
252C8×D43—44no—
253C23×C43—22no—
254C23×C43—22no—
255C23×C43—41no—
256C23×C43C2×C22⋊C411yescharacteristic
257C23×C43C2×C22⋊C411yescharacteristic
258C23×C43C23×C411yescharacteristic
259C22×D43—22no—
260C22×D43—22no—
261C22×D43—22no—
262C22×D43—22no—
263C22×D43—22no—
264C22×D43—22no—
265C22×D43—22no—
266C22×D43—22no—
267C22×D43—22no—
268C22×D43—22no—
269C22×D43—41no—
270C22×D43—41no—
271C22×D43—41no—
272C22×D43—41no—
273C22×D43—41no—
274C22×D43—41no—
275C22×D43—41no—
276C22×D43—416no—
277C22×D43#10114yes—
278C22×D43C2×C22⋊C411yescharacteristic
279C22×D43C2×C22⋊C411yescharacteristic
280C22×D43C2×C22⋊C411yescharacteristic
281C22×D43C2×C22⋊C411yescharacteristic
282Q8×C43—42no—
283Q8×C43—42no—
284C2×C4×C43—22no—
285C2×C4×C43—22no—
286C2×C4×C43—22no—
287C2×C4×C43—22no—
288C2×C4×C43—22no—
289C2×C4×C43—24no—
290C2×C4×C43—41no—
291C2×C4×C43—41no—
292C2×C4×C43—41no—
293C2×C4×C43—42no—
294C2×C4×C43C2×C22⋊C411yescharacteristic
295C2×C4×C43C2×C22⋊C411yescharacteristic
296C2×C4×C43C22×D411yescharacteristic
297C2×C4×C43C22×D411yescharacteristic
298C2×Dic43—22no—
299C2×Dic43—22no—
300C2×Dic43—22no—
301C2×Dic43—22no—
302C2×Dic43—22no—
303C2×Dic43—24no—
304C2×Dic43—41no—
305C2×Dic43—41no—
306C2×Dic43—41no—
307C2×Dic43—42no—
308C2×Dic43C2×C22⋊C411yescharacteristic
309C2×Dic43C2×C22⋊C411yescharacteristic
310C2×Dic43C2×C22⋊C411yescharacteristic
311C2×Dic43C2×C22⋊C411yescharacteristic
312C4×D43—22no—
313C4×D43—22no—
314C4×D43—22no—
315C4×D43—22no—
316C4×D43—22no—
317C4×D43—22no—
318C4×D43—22no—
319C4×D43—22no—
320C4×D43—22no—
321C4×D43—41no—
322C4×D43—41no—
323C4×D43—41no—
324C4×D43—41no—
325C4×D43—41no—
326C4×D43—41no—
327C4×D43—44no—
328C4×D43—44no—
329C4×D43—44no—
330C4×D43—44no—
331C4×D43#9914yes—
332Dic86—44no—
333Dic86—42no—
334Dic86—42no—
335Dic86—44no—
336C8×C43—42no—
337C8×C43—42no—
338C43⋊C8—42no—
339C43⋊C8—42no—
340#17397—431nomaximal, Sylow
341C22×C43—21no—
342C22×C43—21no—
343C22×C43—21no—
344C22×C43—21no—
345C22×C43—21no—
346C22×C43—21no—
347C22×C43—21no—
348C22×C43—44no—
349C22×C43C2×#10112yes—
350C22×C43C22×C22⋊C411yescharacteristic
351C22×C43#56812yes—
352C2×D43—28no—
353C2×D43—21no—
354C2×D43—21no—
355C2×D43—21no—
356C2×D43—21no—
357C2×D43—21no—
358C2×D43—21no—
359C2×D43—21no—
360C2×D43—21no—
361C2×D43—21no—
362C2×D43—44no—
363C2×D43—44no—
364C2×D43—44no—
365C2×D43—44no—
366C2×D43—44no—
367C2×D43C2×#9912yes—
368C2×D43C2×#10112yes—
369C2×D43C2×#10112yes—
370C4×C43—21no—
371C4×C43—21no—
372C4×C43—21no—
373C4×C43—42no—
374C4×C43—42no—
375C4×C43C2×#9912yes—
376Dic43—21no—
377Dic43—21no—
378Dic43—21no—
379Dic43—42no—
380Dic43—42no—
381Dic43C2×#9912yes—
382C22×C22⋊Q8—431no—
383C2×#407—431no—
384C2×#407—431no—
385#1472—431no—
386#1472—431no—
387#1472—434no—
388#1472—431no—
389#1472D4311yescharacteristic, complemented
390#1463—434no—
391C2×C43—22no—
392C2×C43—22no—
393C2×C43—41no—
394C2×C43#287911yescharacteristic
395C2×C43C22×#9911yescharacteristic
396C2×C43C22×#10111yescharacteristic
397D43—22no—
398D43—22no—
399D43—22no—
400D43—41no—
401C23×Q8—431no—
402C24×C4—431no—
403C22×M16—861no—
404C22×M16—861no—
405C2×C22⋊Q8—431no—
406C2×C22⋊Q8—431no—
407C2×C22⋊Q8—432no—
408C2×C22⋊Q8—431no—
409C2×C22⋊Q8—432no—
410C2×C22⋊Q8—861no—
411C2×C22⋊Q8—861no—
412C2×C22⋊Q8—861no—
413C2×C22⋊Q8—861no—
414C2×C22⋊Q8—861no—
415C2×C22⋊Q8—861no—
416C2×C22⋊Q8—861no—
417C2×C22⋊Q8—861no—
418C2×C22⋊Q8C2×D4311yescharacteristic
419C22×C4⋊C4—432no—
420C22×C4⋊C4—431no—
421C22×C22⋊C4—432no—
422#407—431no—
423#407—432no—
424#407—432no—
425#407—432no—
426#407—861no—
427#407—861no—
428#407—861no—
429#407—861no—
430#407C2×D4311yescharacteristic
431C2×C22⋊C8—431no—
432C2×C22⋊C8—432no—
433C2×C22⋊C8—861no—
434C2×C22⋊C8—861no—
435C2×C22⋊C8C2×D4311yescharacteristic
436#324—434no—
437#324—434no—
438#324—434no—
439#324C2×D4314yescomplemented
440C43#1739711yescharacteristic, complemented, Sylow
441C25—431no—
442C22×Q8—432no—
443C22×Q8—431no—
444C22×Q8—861no—
445C22×Q8—861no—
446C22×Q8—861no—
447C22×Q8—861no—
448C22×Q8—1724no—
449C22×Q8C4×D4311yescharacteristic
450C23×C4—431no—
451C23×C4—431no—
452C23×C4—431no—
453C23×C4—431no—
454C23×C4—431no—
455C23×C4—431no—
456C23×C4—431no—
457C23×C4—431no—
458C23×C4—431no—
459C23×C4—431no—
460C23×C4—431no—
461C23×C4—431no—
462C23×C4—431no—
463C23×C4—432no—
464C23×C4—432no—
465C23×C4—1724no—
466C23×C4C22×D4311yescharacteristic
467C2×M16—21no—
468C2×M16—862no—
469C2×M16—862no—
470C2×M16—862no—
471C2×M16—861no—
472C2×M16—1724no—
473C2×M16—1724no—
474C22×C8—21no—
475C22×C8—862no—
476C22×C8—861no—
477C22⋊Q8—21no—
478C22⋊Q8—21no—
479C22⋊Q8—21no—
480C22⋊Q8—21no—
481C22⋊Q8—862no—
482C22⋊Q8—862no—
483C22⋊Q8—862no—
484C22⋊Q8—862no—
485C22⋊Q8—862no—
486C22⋊Q8—862no—
487C22⋊Q8—862no—
488C22⋊Q8—862no—
489C22⋊Q8—861no—
490C22⋊Q8—861no—
491C22⋊Q8—861no—
492C22⋊Q8—861no—
493C22⋊Q8—861no—
494C22⋊Q8—861no—
495C22⋊Q8—861no—
496C22⋊Q8—861no—
497C22⋊Q8—861no—
498C22⋊Q8—861no—
499C22⋊Q8—861no—
500C22⋊Q8—861no—
501C2×C4⋊C4—432no—
502C2×C4⋊C4—432no—
503C2×C4⋊C4—432no—
504C2×C4⋊C4—431no—
505C2×C4⋊C4—432no—
506C2×C4⋊C4—861no—
507C2×C4⋊C4—861no—
508C2×C4⋊C4—861no—
509C2×C4⋊C4—861no—
510C2×C4⋊C4—862no—
511C2×C4⋊C4—862no—
512C2×C4⋊C4—862no—
513C2×C4⋊C4—862no—
514C2×C4⋊C4C4×D4311yescharacteristic
515C2×C4⋊C4C22×D4312yes—
516C2×C22⋊C4—432no—
517C2×C22⋊C4—432no—
518C2×C22⋊C4—432no—
519C2×C22⋊C4—862no—
520C2×C22⋊C4—862no—
521C2×C22⋊C4—862no—
522C2×C22⋊C4—862no—
523C2×C22⋊C4C4×D4312yes—
524C22⋊C8—21no—
525C22⋊C8—21no—
526C22⋊C8—432no—
527C22⋊C8—432no—
528C22⋊C8—862no—
529C22⋊C8—862no—
530C22⋊C8—862no—
531C22⋊C8—862no—
532C22⋊C8—861no—
533C22⋊C8—861no—
534C22⋊C8C22×D4312yes—
535C22⋊C8C22×D4312yes—
536C24—431no—
537C24—431no—
538C24—431no—
539C24—431no—
540C24—431no—
541C24—431no—
542C24—864no—
543C24—1722no—
544C24—1722no—
545C24C2×C4×D4311yescharacteristic
546C2×Q8—21no—
547C2×Q8—21no—
548C2×Q8—42no—
549C2×Q8—862no—
550C2×Q8—862no—
551C2×Q8—861no—
552C2×Q8—861no—
553C2×Q8—1722no—
554C2×Q8—1724no—
555C2×Q8—1724no—
556C2×Q8—1724no—
557C2×Q8—1724no—
558C2×Q8—1724no—
559C22×C4—42no—
560C22×C4—431no—
561C22×C4—431no—
562C22×C4—431no—
563C22×C4—431no—
564C22×C4—431no—
565C22×C4—431no—
566C22×C4—431no—
567C22×C4—431no—
568C22×C4—431no—
569C22×C4—431no—
570C22×C4—431no—
571C22×C4—431no—
572C22×C4—431no—
573C22×C4—431no—
574C22×C4—431no—
575C22×C4—431no—
576C22×C4—431no—
577C22×C4—431no—
578C22×C4—431no—
579C22×C4—431no—
580C22×C4—431no—
581C22×C4—431no—
582C22×C4—432no—
583C22×C4—432no—
584C22×C4—864no—
585C22×C4—864no—
586C22×C4—864no—
587C22×C4—862no—
588C22×C4—862no—
589C22×C4—862no—
590C22×C4—862no—
591C22×C4—1722no—
592C22×C4—1722no—
593C22×C4—1722no—
594C22×C4—1724no—
595C22×C4—1722no—
596C22×C4—1722no—
597C22×C4—1722no—
598C22×C4—1722no—
599C22×C4—1722no—
600C22×C4—1722no—
601C22×C4—1724no—
602C22×C4—1722no—
603C22×C4C2×C4×D4312yes—
604C22×C4C2×C4×D4311yescharacteristic
605C22×C4C2×C4×D4312yes—
606C22×C4D4×D4311yescharacteristic
607C22×C4D4×D4311yescharacteristic
608C22×C4D4×D4311yescharacteristic
609C22×C4D4×D4311yescharacteristic
610C22×C4C23×D4311yescharacteristic
611M16—42no—
612M16—1724no—
613M16—1724no—
614M16—1724no—
615M16—1722no—
616C2×C8—22no—
617C2×C8—22no—
618C2×C8—42no—
619C2×C8—862no—
620C2×C8—862no—
621C2×C8—1724no—
622C2×C8—1722no—
623C4⋊C4—21no—
624C4⋊C4—21no—
625C4⋊C4—22no—
626C4⋊C4—22no—
627C4⋊C4—862no—
628C4⋊C4—862no—
629C4⋊C4—862no—
630C4⋊C4—862no—
631C4⋊C4—862no—
632C4⋊C4—862no—
633C4⋊C4—861no—
634C4⋊C4—861no—
635C4⋊C4—862no—
636C4⋊C4—862no—
637C22⋊C4—22no—
638C22⋊C4—22no—
639C22⋊C4—862no—
640C22⋊C4—862no—
641C22⋊C4—862no—
642C22⋊C4—862no—
643C22⋊C4—862no—
644C22⋊C4—862no—
645C23—22no—
646C23—22no—
647C23—41no—
648C23—431no—
649C23—431no—
650C23—431no—
651C23—434no—
652C23—431no—
653C23—862no—
654C23—862no—
655C23—862no—
656C23—862no—
657C23—862no—
658C23—862no—
659C23—862no—
660C23—862no—
661C23—862no—
662C23—862no—
663C23—1721no—
664C23—1721no—
665C23—1721no—
666C23—1721no—
667C23—1721no—
668C23—1721no—
669C23—1721no—
670C23—17216no—
671C23C22⋊C4×D4311yescharacteristic
672C23C22⋊C4×D4311yescharacteristic
673C23C22×C4×D4311yescharacteristic
674Q8—42no—
675Q8—42no—
676Q8—1722no—
677Q8—1724no—
678Q8—1724no—
679Q8—1722no—
680C2×C4—22no—
681C2×C4—22no—
682C2×C4—22no—
683C2×C4—22no—
684C2×C4—22no—
685C2×C4—24no—
686C2×C4—41no—
687C2×C4—41no—
688C2×C4—41no—
689C2×C4—42no—
690C2×C4—431no—
691C2×C4—434no—
692C2×C4—431no—
693C2×C4—431no—
694C2×C4—431no—
695C2×C4—862no—
696C2×C4—862no—
697C2×C4—862no—
698C2×C4—862no—
699C2×C4—862no—
700C2×C4—862no—
701C2×C4—862no—
702C2×C4—862no—
703C2×C4—862no—
704C2×C4—862no—
705C2×C4—862no—
706C2×C4—862no—
707C2×C4—862no—
708C2×C4—862no—
709C2×C4—864no—
710C2×C4—1721no—
711C2×C4—1721no—
712C2×C4—1721no—
713C2×C4—1721no—
714C2×C4—1721no—
715C2×C4—1721no—
716C2×C4—1724no—
717C2×C4—1724no—
718C2×C4—1724no—
719C2×C4—1724no—
720C2×C4—1721no—
721C2×C4—1721no—
722C2×C4—1721no—
723C2×C4—1722no—
724C2×C4C22⋊C4×D4311yescharacteristic
725C2×C4C22⋊C4×D4311yescharacteristic
726C2×C4C2×D4×D4311yescharacteristic
727C2×C4C2×D4×D4311yescharacteristic
728C8—42no—
729C8—42no—
730C8—1722no—
731C8—1722no—
732C22—21no—
733C22—21no—
734C22—21no—
735C22—21no—
736C22—21no—
737C22—21no—
738C22—21no—
739C22—44no—
740C22—432no—
741C22—432no—
742C22—432no—
743C22—868no—
744C22—861no—
745C22—861no—
746C22—861no—
747C22—861no—
748C22—861no—
749C22—861no—
750C22—861no—
751C22—861no—
752C22—861no—
753C22—1724no—
754C22—1724no—
755C22—1724no—
756C22—1724no—
757C22—1724no—
758C22#101×D4312yes—
759C22C2×C22⋊C4×D4311yescharacteristic
760C22#1458366412yes—
761C4—21no—
762C4—21no—
763C4—21no—
764C4—42no—
765C4—42no—
766C4—432no—
767C4—861no—
768C4—861no—
769C4—861no—
770C4—1722no—
771C4—1722no—
772C4#99×D4312yes—
773C2—22no—
774C2—22no—
775C2—41no—
776C2—862no—
777C2—862no—
778C2—862no—
779C2—1721no—
780C2#1914303711yescharacteristic
781C2C2×#99×D4311yescharacteristic
782C2C2×#101×D4311yescharacteristic
subgroupG/H
centerC22C2×C22⋊C4×D43
commutatorC23×C43C23×C4
FrattiniC22×C4C23×D43
FittingC43×#1472C2
socleC22×C43C22×C22⋊C4
prime radicalC24×D43C2×C4
cosocleC22×C4×C43C24
hypercenter#1472D43
hypocenterC43#17397
LCSG ▷ C23×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C23×C4 ◁ #1472

Complements

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

NH ≅ G/Ntype
4. #19132960C2semidirect
5. #19132959C2semidirect
6. #19132958C2semidirect
7. #19132957C2semidirect
8. #19132923C2semidirect
9. C43×#1472C2semidirect
42. #14582625C22semidirect
43. #14582624C22semidirect
44. #14582624C22semidirect
48. C43×#324C22semidirect
389. #1472D43semidirect
439. #324C2×D43semidirect
440. C43#17397semidirect

Maximal subgroups

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

subgroupindex
C2×C22⋊Q8×D432
C2×#145828612
#407×D432
#191329602
#191329592
#191329582
#191329572
#191329232
C43×#14722
#1739743