Finite Group Databasebeta

← #14224539

Subgroups — #14224539

Order 1792.

2686 conjugacy classes of subgroups.

The subgroup lattice has 1060 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C7×#121C211yesmaximal, characteristic, complemented
2C2×#90482C211yesmaximal, characteristic, complemented
3#11741483C212yesmaximal, complemented
4C2×#89979C211yesmaximal, characteristic, complemented
5#11740076C212yesmaximal, complemented
6#11740075C212yesmaximal, complemented
7#11740073C214yesmaximal, complemented
8#11740072C212yesmaximal, complemented
9#11740071C214yesmaximal, complemented
10#11740070C212yesmaximal, complemented
11#11740069C212yesmaximal, complemented
12#11740066C214yesmaximal, complemented
13#11740061C212yesmaximal, complemented
14#11739584C212yesmaximal, complemented
15C23×C7×D4—21no—
16C23×C7×D4C2211yescharacteristic, complemented
17C24×C4×C7C2211yescharacteristic
18C22×#1157C2211yescharacteristic, complemented
19C2×C7×#121—21no—
20C2×C7×#121—21no—
21C2×C7×#121—21no—
22C2×C7×#121—21no—
23C2×C7×#121—21no—
24C2×C7×#121—21no—
25C2×C7×#121C2212yes—
26C2×C7×#121C2212yes—
27C2×C7×#121C2212yes—
28C2×C7×#121C2212yescomplemented
29C2×C7×#121C2212yescomplemented
30C2×C7×#121C2212yescomplemented
31C22×C7×C4⋊C4C2211yescharacteristic, complemented
32C22×C7×C22⋊C4—21no—
33C2×#6516—21no—
34C2×#6495C2214yescomplemented
35#90482—21no—
36#90482—21no—
37#90482—21no—
38#90482—21no—
39#90482C2212yes—
40#90482C2212yescomplemented
41#90482C2212yescomplemented
42#90482C2212yescomplemented
43C2×#6493C2211yescharacteristic, complemented
44C2×#6493C2211yescharacteristic, complemented
45C2×#6492—21no—
46C2×C4×C22⋊D7—21no—
47C2×C4×C22⋊D7—21no—
48C2×#6489C2211yescharacteristic, complemented
49C2×#6487C2211yescharacteristic, complemented
50C2×#6487C2211yescharacteristic, complemented
51C22×#1136C2212yescomplemented
52#89990C2214yescomplemented
53#89990C2214yescomplemented
54#89989C2214yescomplemented
55#89989C2214yescomplemented
56#89987C2214yescomplemented
57#89979C2212yescomplemented
58#89979C2212yescomplemented
59#89979C2212yescomplemented
60#89979C2212yescomplemented
61C2×C22⋊(C7⋊C8)C2212yescomplemented
62C2×C22⋊(C7⋊C8)C2212yescomplemented
63#89814C2218yescomplemented
64#89813C2218yescomplemented
65#89812C2214yescomplemented
66#89811C2218yescomplemented
67#89810C2218yescomplemented
68#89809C2218yescomplemented
69#89808C2214yescomplemented
70#89807C2218yescomplemented
71#89806C2214yescomplemented
72#89805C2214yescomplemented
73#89743C2214yescomplemented
74#89742C2214yescomplemented
75#89740C2214yescomplemented
76#89739C2214yescomplemented
77#89738C2214yescomplemented
78#89736C2214yescomplemented
79#60750—71nomaximal, Sylow
80C25×C7—21no—
81C25×C7D411yescharacteristic
82C22×C7×D4—22no—
83C22×C7×D4—22no—
84C22×C7×D4—22no—
85C22×C7×D4—22no—
86C22×C7×D4—22no—
87C22×C7×D4—22no—
88C22×C7×D4—21no—
89C22×C7×D4—21no—
90C22×C7×D4—21no—
91C22×C7×D4—44no—
92C22×C7×D4—48no—
93C22×C7×D4C2312yes—
94C22×C7×D4C2312yes—
95C22×C7×D4C2312yes—
96C23×C4×C7—21no—
97C23×C4×C7—44no—
98C23×C4×C7D411yescharacteristic
99C23×C4×C7D411yescharacteristic
100C23×C4×C7D411yescharacteristic
101C23×C4×C7D411yescharacteristic
102C23×C4×C7D411yescharacteristic
103C23×C4×C7D411yescharacteristic
104C23×C4×C7D411yescharacteristic
105C23×C4×C7C2311yescharacteristic
106C23×C4×C7C2311yescharacteristic
107C23×C4×C7C2311yescharacteristic
108C23×C4×C7C2311yescharacteristic
109C23×C4×C7C2311yescharacteristic
110C23×C4×C7C2311yescharacteristic
111C23×C4×C7C2311yescharacteristic
112C22×C22⋊D7—21no—
113C22×C22⋊D7—21no—
114C22×C22⋊D7—21no—
115C2×#1157—21no—
116C2×#1157—21no—
117C2×#1157—44no—
118C2×#1157C2312yes—
119C2×#1157C2312yescomplemented
120C22×D28C2311yescharacteristic, complemented
121C22×C4×D7—21no—
122C22×Dic14C2311yescharacteristic, complemented
123C7×#121—22no—
124C7×#121—22no—
125C7×#121—22no—
126C7×#121—22no—
127C7×#121—22no—
128C7×#121—22no—
129C7×#121—22no—
130C7×#121—22no—
131C7×#121—22no—
132C7×#121—22no—
133C7×#121—22no—
134C7×#121—22no—
135C7×#121C2314yes—
136C7×#121C2314yes—
137C7×#121C2314yes—
138C7×#121C2314yes—
139C2×C7×C4⋊C4—21no—
140C2×C7×C4⋊C4—21no—
141C2×C7×C4⋊C4—21no—
142C2×C7×C4⋊C4C2312yes—
143C2×C7×C4⋊C4C2312yes—
144C2×C7×C4⋊C4C2312yes—
145C2×C7×C22⋊C4—22no—
146C2×C7×C22⋊C4—22no—
147C2×C7×C22⋊C4—22no—
148C2×C7×C22⋊C4—22no—
149C2×C7×C22⋊C4—22no—
150C2×C7×C22⋊C4—22no—
151#6516—22no—
152#6516—22no—
153#6516—22no—
154#6516—22no—
155C2×C22⋊Dic7—21no—
156C2×C22⋊Dic7—21no—
157C2×C22⋊Dic7—21no—
158C2×#1142C2318yescomplemented
159#6495—48no—
160C2×#1141C2318yescomplemented
161#6493—21no—
162#6493—21no—
163#6493—21no—
164#6493—21no—
165#6493C2312yes—
166#6493C2312yes—
167#6493C2312yescomplemented
168#6493C2312yescomplemented
169#6492—22no—
170#6492—22no—
171#6492—22no—
172#6492—22no—
173C4×C22⋊D7—22no—
174C4×C22⋊D7—22no—
175C4×C22⋊D7—22no—
176C4×C22⋊D7—22no—
177C4×C22⋊D7—22no—
178C4×C22⋊D7—22no—
179C4×C22⋊D7—22no—
180C4×C22⋊D7—22no—
181C2×(C2×D7)⋊C4—21no—
182C2×(C2×D7)⋊C4—21no—
183#6489—21no—
184#6489—21no—
185#6489C2312yes—
186#6489C2312yescomplemented
187C2×C4⋊Dic7C2311yescharacteristic, complemented
188C2×C4⋊Dic7C2311yescharacteristic, complemented
189#6487—21no—
190#6487—21no—
191#6487—21no—
192#6487—21no—
193#6487C2312yes—
194#6487C2312yes—
195#6487C2312yescomplemented
196#6487C2312yescomplemented
197C2×Dic7⋊C4—21no—
198C2×Dic7⋊C4—21no—
199C2×C4×Dic7—21no—
200C2×#1136—44no—
201C2×#1136C2314yes—
202C2×#1136C2314yescomplemented
203C22×C7⋊C8C2314yescomplemented
204#6406C2318yescomplemented
205#6406C2318yescomplemented
206C22⋊(C7⋊C8)C2314yes—
207C22⋊(C7⋊C8)C2314yes—
208C22⋊(C7⋊C8)C2314yescomplemented
209C22⋊(C7⋊C8)C2314yescomplemented
210#6384C2318yescomplemented
211#6383C2318yescomplemented
212#6382C2318yescomplemented
213#6381C2318yescomplemented
214C2×#525—71no—
215C22×#121D711yescharacteristic, complemented
216#3194—74no—
217#3193—72no—
218#3192—72no—
219#3188—74no—
220#3187—72no—
221#3186—72no—
222#3094—72no—
223#3092—72no—
224#3055—74no—
225#3006—72no—
226#3003—72no—
227C2×#407—71no—
228C24×C7—24no—
229C24×C7—22no—
230C24×C7—22no—
231C24×C7—22no—
232C24×C7—42no—
233C24×C7—42no—
234C24×C7—44no—
235C24×C7—44no—
236C24×C7—44no—
237C24×C7C2×D411yescharacteristic
238C24×C7C2×D411yescharacteristic
239C24×C7C2×D411yescharacteristic
240C24×C7C2×D411yescharacteristic
241C24×C7C2×D411yescharacteristic
242C24×C7C2×D411yescharacteristic
243C24×C7C2×D411yescharacteristic
244C23×D7—21no—
245C2×C7×D4—24no—
246C2×C7×D4—24no—
247C2×C7×D4—24no—
248C2×C7×D4—24no—
249C2×C7×D4—22no—
250C2×C7×D4—22no—
251C2×C7×D4—22no—
252C2×C7×D4—28no—
253C2×C7×D4—44no—
254C2×C7×D4—44no—
255C2×C7×D4—44no—
256C2×C7×D4—44no—
257C2×C7×D4—44no—
258C2×C7×D4—48no—
259C2×C7×D4—48no—
260C2×C7×D4—48no—
261C2×C7×D4—48no—
262C2×C7×D4—48no—
263C2×C7×D4—48no—
264C2×C7×D4C2414yes—
265C22×C4×C7—24no—
266C22×C4×C7—24no—
267C22×C4×C7—24no—
268C22×C4×C7—22no—
269C22×C4×C7—22no—
270C22×C4×C7—22no—
271C22×C4×C7—42no—
272C22×C4×C7—42no—
273C22×C4×C7—42no—
274C22×C4×C7—42no—
275C22×C4×C7—42no—
276C22×C4×C7—42no—
277C22×C4×C7—42no—
278C22×C4×C7—42no—
279C22×C4×C7—42no—
280C22×C4×C7—42no—
281C22×C4×C7—42no—
282C22×C4×C7—44no—
283C22×C4×C7C2×D411yescharacteristic
284C22×C4×C7C2×D411yescharacteristic
285C22×C4×C7C2×D411yescharacteristic
286C22×C4×C7C2×D411yescharacteristic
287C22×C4×C7C2×D411yescharacteristic
288C22×C4×C7C2×D411yescharacteristic
289C22×C4×C7C2×D411yescharacteristic
290C22×C4×C7C2×D411yescharacteristic
291C22×C4×C7C2×D411yescharacteristic
292C22×C4×C7C2×D411yescharacteristic
293C22×C4×C7C2×D411yescharacteristic
294C22×C4×C7C2×D411yescharacteristic
295C22×C4×C7C2×D411yescharacteristic
296C22×C4×C7C2×D411yescharacteristic
297C22×C4×C7C2×D411yescharacteristic
298C22×C4×C7C2×D411yescharacteristic
299C22×C4×C7C2×D411yescharacteristic
300C22×C4×C7C2×D411yescharacteristic
301C22×C4×C7C2×D411yescharacteristic
302C22×C4×C7C2×D411yescharacteristic
303C22×C4×C7C2×D411yescharacteristic
304C22×C4×C7C2411yescharacteristic
305C22×C4×C7C2411yescharacteristic
306C22×C4×C7C2411yescharacteristic
307C22×C4×C7C2411yescharacteristic
308C22×C4×C7C2411yescharacteristic
309C22×C4×C7C2411yescharacteristic
310C22×C4×C7C2411yescharacteristic
311C2×C22⋊D7—22no—
312C2×C22⋊D7—22no—
313C2×C22⋊D7—22no—
314C2×C22⋊D7—22no—
315C2×C22⋊D7—22no—
316C2×C22⋊D7—22no—
317C2×C22⋊D7—44no—
318C2×C22⋊D7—44no—
319C2×C22⋊D7—44no—
320C22×Dic7—21no—
321C22×Dic7—21no—
322C22×Dic7—21no—
323#1157—28no—
324#1157—44no—
325#1157—44no—
326#1157—44no—
327C2×D28—21no—
328C2×D28—42no—
329C2×D28C2412yes—
330C2×C4×D7—22no—
331C2×C4×D7—22no—
332C2×C4×D7—44no—
333C2×Dic14—21no—
334C2×Dic14—42no—
335C2×Dic14C2412yes—
336C7×C4⋊C4—22no—
337C7×C4⋊C4—22no—
338C7×C4⋊C4—22no—
339C7×C4⋊C4C2414yes—
340C7×C22⋊C4—24no—
341C7×C22⋊C4—24no—
342C7×C22⋊C4—24no—
343C7×C22⋊C4—24no—
344C22⋊Dic7—22no—
345C22⋊Dic7—22no—
346C22⋊Dic7—22no—
347C22⋊Dic7—22no—
348C22⋊Dic7—22no—
349C22⋊Dic7—22no—
350#1142—48no—
351#1141—48no—
352(C2×D7)⋊C4—22no—
353(C2×D7)⋊C4—22no—
354(C2×D7)⋊C4—22no—
355(C2×D7)⋊C4—22no—
356C4⋊Dic7—21no—
357C4⋊Dic7—21no—
358C4⋊Dic7C2412yes—
359C4⋊Dic7C2412yes—
360Dic7⋊C4—22no—
361Dic7⋊C4—22no—
362Dic7⋊C4—22no—
363Dic7⋊C4—22no—
364C4×Dic7—22no—
365C4×Dic7—22no—
366#1136—28no—
367#1136—44no—
368C2×C7⋊C8—44no—
369C2×C7⋊C8C2418yes—
370C22×#41—71no—
371C23×D4—21no—
372C23×D4C2×D711yescharacteristic, complemented
373C24×C4C2×D711yescharacteristic
374C2×AGL(1,ℤ/8)—74no—
375C22×M16—72no—
376#525—72no—
377#525—72no—
378#525—72no—
379#525—72no—
380#525—141no—
381#525—141no—
382#525—141no—
383#525—141no—
384C2×#123—141no—
385C2×C22⋊Q8—71no—
386C2×C22⋊Q8—71no—
387C2×#121—21no—
388C2×#121—21no—
389C2×#121—21no—
390C2×#121—21no—
391C2×#121—21no—
392C2×#121—21no—
393C2×#121—71no—
394C2×#121—71no—
395C2×#121C2×D712yes—
396C2×#121C2×D712yes—
397C2×#121C2×D712yes—
398C2×#121C2×D712yescomplemented
399C2×#121C2×D712yescomplemented
400C2×#121C2×D712yescomplemented
401C2×#120—141no—
402C2×C4×D4—141no—
403C2×C4×D4—141no—
404C2×#117—71no—
405C22×C4⋊C4C2×D711yescharacteristic, complemented
406C22×C22⋊C4—21no—
407#484—74no—
408#483—74no—
409#482—78no—
410#481—74no—
411#481—74no—
412#480—74no—
413#480—74no—
414#469—78no—
415#468—78no—
416#466—78no—
417#465—78no—
418#450—74no—
419#450—74no—
420#449—78no—
421#448—74no—
422#447—74no—
423#447—74no—
424#447—74no—
425#428—74no—
426#418—74no—
427#417—74no—
428#407—72no—
429#407—72no—
430#407—72no—
431#407—72no—
432C2×C22⋊C8—72no—
433C2×C22⋊C8—72no—
434C23×C7—22no—
435C23×C7—22no—
436C23×C7—22no—
437C23×C7—22no—
438C23×C7—22no—
439C23×C7—22no—
440C23×C7—22no—
441C23×C7—22no—
442C23×C7—22no—
443C23×C7—22no—
444C23×C7—22no—
445C23×C7—22no—
446C23×C7—24no—
447C23×C7—41no—
448C23×C7—41no—
449C23×C7—41no—
450C23×C7—41no—
451C23×C7—41no—
452C23×C7—41no—
453C23×C7—41no—
454C23×C7—41no—
455C23×C7—416no—
456C23×C7—44no—
457C23×C7—44no—
458C23×C7—44no—
459C23×C7—44no—
460C23×C7—44no—
461C23×C7—44no—
462C23×C7—44no—
463C23×C7—44no—
464C23×C7—44no—
465C23×C7—816no—
466C23×C7AGL(1,ℤ/8)14yescomplemented
467C23×C7C22×D411yescharacteristic
468C23×C7C22×D411yescharacteristic
469C23×C7C22×D411yescharacteristic
470C23×C7C22×D411yescharacteristic
471C23×C7C22×D411yescharacteristic
472C23×C7C22×D411yescharacteristic
473C23×C7C22×D411yescharacteristic
474C22×D7—22no—
475C22×D7—42no—
476C22×D7—42no—
477C22×D7—42no—
478C7×D4—28no—
479C7×D4—44no—
480C7×D4—44no—
481C7×D4—48no—
482C7×D4—48no—
483C7×D4—48no—
484C7×D4—48no—
485C7×D4—44no—
486C2×C4×C7—22no—
487C2×C4×C7—22no—
488C2×C4×C7—22no—
489C2×C4×C7—22no—
490C2×C4×C7—22no—
491C2×C4×C7—22no—
492C2×C4×C7—22no—
493C2×C4×C7—22no—
494C2×C4×C7—22no—
495C2×C4×C7—22no—
496C2×C4×C7—22no—
497C2×C4×C7—22no—
498C2×C4×C7—22no—
499C2×C4×C7—22no—
500C2×C4×C7—22no—
501C2×C4×C7—24no—
502C2×C4×C7—41no—
503C2×C4×C7—41no—
504C2×C4×C7—41no—
505C2×C4×C7—41no—
506C2×C4×C7—41no—
507C2×C4×C7—41no—
508C2×C4×C7—41no—
509C2×C4×C7—41no—
510C2×C4×C7—41no—
511C2×C4×C7—41no—
512C2×C4×C7—41no—
513C2×C4×C7—41no—
514C2×C4×C7—44no—
515C2×C4×C7—44no—
516C2×C4×C7—44no—
517C2×C4×C7C22×D411yescharacteristic
518C2×C4×C7C22×D411yescharacteristic
519C2×C4×C7C22×D411yescharacteristic
520C2×C4×C7C22×D411yescharacteristic
521C2×C4×C7C22×D411yescharacteristic
522C2×C4×C7C22×D411yescharacteristic
523C2×C4×C7C22×D411yescharacteristic
524C2×C4×C7H(5,𝔽2)14yes—
525C2×C4×C7C2511yescharacteristic
526C22⋊D7—44no—
527C22⋊D7—44no—
528C22⋊D7—44no—
529C22⋊D7—44no—
530C22⋊D7—44no—
531C22⋊D7—44no—
532C2×Dic7—22no—
533C2×Dic7—22no—
534C2×Dic7—22no—
535C2×Dic7—42no—
536C2×Dic7—42no—
537C2×Dic7—42no—
538D28—24no—
539D28—42no—
540C4×D7—44no—
541C4×D7—44no—
542Dic14—24no—
543Dic14—42no—
544C7⋊C8—28no—
545C25—21no—
546C25C22⋊D711yescharacteristic
547C2×#41—72no—
548C2×#41—72no—
549C2×#41—141no—
550C2×#41—141no—
551C2×#41—284no—
552C22×Q8—71no—
553C22×D4—22no—
554C22×D4—22no—
555C22×D4—22no—
556C22×D4—22no—
557C22×D4—22no—
558C22×D4—22no—
559C22×D4—21no—
560C22×D4—21no—
561C22×D4—21no—
562C22×D4—44no—
563C22×D4—48no—
564C22×D4—71no—
565C22×D4—141no—
566C22×D4—141no—
567C22×D4—141no—
568C22×D4C22×D712yes—
569C22×D4C22×D712yes—
570C22×D4C22×D712yes—
571C23×C4—21no—
572C23×C4—44no—
573C23×C4—141no—
574C23×C4C22⋊D711yescharacteristic
575C23×C4C22⋊D711yescharacteristic
576C23×C4C22⋊D711yescharacteristic
577C23×C4C22⋊D711yescharacteristic
578C23×C4C22⋊D711yescharacteristic
579C23×C4C22⋊D711yescharacteristic
580C23×C4C22⋊D711yescharacteristic
581C23×C4C22×D711yescharacteristic
582C23×C4C22×D711yescharacteristic
583C23×C4C22×D711yescharacteristic
584C23×C4C22×D711yescharacteristic
585C23×C4C22×D711yescharacteristic
586C23×C4C22×D711yescharacteristic
587C23×C4C22×D711yescharacteristic
588AGL(1,ℤ/8)—288no—
589C2×SD16—78no—
590C2×D8—78no—
591C2×M16—74no—
592C2×M16—74no—
593C2×M16—284no—
594C22×C8—74no—
595#123—142no—
596#123—142no—
597#123—142no—
598#123—142no—
599C22⋊Q8—72no—
600C22⋊Q8—72no—
601C22⋊Q8—72no—
602C22⋊Q8—72no—
603C22⋊Q8—141no—
604C22⋊Q8—141no—
605C22⋊Q8—141no—
606C22⋊Q8—141no—
607#121—22no—
608#121—22no—
609#121—22no—
610#121—22no—
611#121—22no—
612#121—22no—
613#121—22no—
614#121—22no—
615#121—22no—
616#121—22no—
617#121—22no—
618#121—22no—
619#121—72no—
620#121—72no—
621#121—72no—
622#121—72no—
623#121—141no—
624#121—141no—
625#121—141no—
626#121—141no—
627#121C22×D714yes—
628#121C22×D714yes—
629#121C22×D714yes—
630#121C22×D714yes—
631#120—142no—
632#120—142no—
633#120—142no—
634#120—142no—
635C4×D4—142no—
636C4×D4—142no—
637C4×D4—142no—
638C4×D4—142no—
639C4×D4—142no—
640C4×D4—142no—
641C4×D4—142no—
642C4×D4—142no—
643#117—72no—
644#117—72no—
645#117—141no—
646#117—141no—
647C2×C4⋊C4—21no—
648C2×C4⋊C4—21no—
649C2×C4⋊C4—21no—
650C2×C4⋊C4—71no—
651C2×C4⋊C4—71no—
652C2×C4⋊C4—141no—
653C2×C4⋊C4—141no—
654C2×C4⋊C4C22×D712yes—
655C2×C4⋊C4C22×D712yes—
656C2×C4⋊C4C22×D712yes—
657C2×C22⋊C4—22no—
658C2×C22⋊C4—22no—
659C2×C22⋊C4—22no—
660C2×C22⋊C4—22no—
661C2×C22⋊C4—22no—
662C2×C22⋊C4—22no—
663C2×C22⋊C4—141no—
664C2×C22⋊C4—141no—
665C2×C22⋊C4—141no—
666C2×C22⋊C4—141no—
667C2×C22⋊C4—141no—
668C2×C42—141no—
669#107—78no—
670#106—78no—
671#103—78no—
672#102—78no—
673#102—78no—
674#102—78no—
675C22⋊C8—74no—
676C22⋊C8—74no—
677C22⋊C8—74no—
678C22⋊C8—74no—
679C22×C7—28no—
680C22×C7—21no—
681C22×C7—21no—
682C22×C7—21no—
683C22×C7—21no—
684C22×C7—21no—
685C22×C7—21no—
686C22×C7—21no—
687C22×C7—21no—
688C22×C7—21no—
689C22×C7—21no—
690C22×C7—21no—
691C22×C7—21no—
692C22×C7—21no—
693C22×C7—21no—
694C22×C7—21no—
695C22×C7—21no—
696C22×C7—44no—
697C22×C7—44no—
698C22×C7—44no—
699C22×C7—44no—
700C22×C7—44no—
701C22×C7—44no—
702C22×C7—44no—
703C22×C7—44no—
704C22×C7—44no—
705C22×C7—88no—
706C22×C7—88no—
707C22×C7—88no—
708C22×C7#53412yes—
709C22×C7C2×AGL(1,ℤ/8)12yes—
710C22×C7C2×AGL(1,ℤ/8)12yes—
711C22×C7C2×AGL(1,ℤ/8)12yes—
712C22×C7#57512yes—
713C22×C7C23×D411yescharacteristic
714C2×D7—42no—
715C2×D7—42no—
716C2×D7—42no—
717C2×D7—84no—
718C4×C7—21no—
719C4×C7—21no—
720C4×C7—21no—
721C4×C7—21no—
722C4×C7—21no—
723C4×C7—21no—
724C4×C7—44no—
725C4×C7#53412yes—
726C4×C7C2×H(5,𝔽2)12yes—
727Dic7—42no—
728Dic7—42no—
729Dic7—42no—
730C24—24no—
731C24—22no—
732C24—22no—
733C24—22no—
734C24—42no—
735C24—42no—
736C24—44no—
737C24—44no—
738C24—44no—
739C24—141no—
740C24C2×C22⋊D711yescharacteristic
741C24C2×C22⋊D711yescharacteristic
742C24C2×C22⋊D711yescharacteristic
743C24C2×C22⋊D711yescharacteristic
744C24C2×C22⋊D711yescharacteristic
745C24C2×C22⋊D711yescharacteristic
746C24C2×C22⋊D711yescharacteristic
747#41—148no—
748#41—284no—
749#41—284no—
750#41—284no—
751C2×Q8—72no—
752C2×Q8—141no—
753C2×Q8—282no—
754C2×D4—24no—
755C2×D4—24no—
756C2×D4—24no—
757C2×D4—24no—
758C2×D4—28no—
759C2×D4—22no—
760C2×D4—22no—
761C2×D4—22no—
762C2×D4—44no—
763C2×D4—44no—
764C2×D4—44no—
765C2×D4—44no—
766C2×D4—44no—
767C2×D4—48no—
768C2×D4—48no—
769C2×D4—48no—
770C2×D4—48no—
771C2×D4—48no—
772C2×D4—48no—
773C2×D4—72no—
774C2×D4—142no—
775C2×D4—142no—
776C2×D4—142no—
777C2×D4—142no—
778C2×D4—142no—
779C2×D4—142no—
780C2×D4—141no—
781C2×D4—282no—
782C2×D4—284no—
783C2×D4—284no—
784C2×D4—284no—
785C2×D4C23×D714yes—
786C22×C4—24no—
787C22×C4—24no—
788C22×C4—24no—
789C22×C4—22no—
790C22×C4—22no—
791C22×C4—22no—
792C22×C4—42no—
793C22×C4—42no—
794C22×C4—42no—
795C22×C4—42no—
796C22×C4—42no—
797C22×C4—42no—
798C22×C4—42no—
799C22×C4—42no—
800C22×C4—42no—
801C22×C4—42no—
802C22×C4—42no—
803C22×C4—44no—
804C22×C4—141no—
805C22×C4—141no—
806C22×C4—141no—
807C22×C4—142no—
808C22×C4—142no—
809C22×C4—284no—
810C22×C4C2×C22⋊D711yescharacteristic
811C22×C4C2×C22⋊D711yescharacteristic
812C22×C4C2×C22⋊D711yescharacteristic
813C22×C4C2×C22⋊D711yescharacteristic
814C22×C4C2×C22⋊D711yescharacteristic
815C22×C4C2×C22⋊D711yescharacteristic
816C22×C4C2×C22⋊D711yescharacteristic
817C22×C4C2×C22⋊D711yescharacteristic
818C22×C4C2×C22⋊D711yescharacteristic
819C22×C4C2×C22⋊D711yescharacteristic
820C22×C4C2×C22⋊D711yescharacteristic
821C22×C4C2×C22⋊D711yescharacteristic
822C22×C4C2×C22⋊D711yescharacteristic
823C22×C4C2×C22⋊D711yescharacteristic
824C22×C4C2×C22⋊D711yescharacteristic
825C22×C4C2×C22⋊D711yescharacteristic
826C22×C4C2×C22⋊D711yescharacteristic
827C22×C4C2×C22⋊D711yescharacteristic
828C22×C4C2×C22⋊D711yescharacteristic
829C22×C4C2×C22⋊D711yescharacteristic
830C22×C4C2×C22⋊D711yescharacteristic
831C22×C4C23×D711yescharacteristic
832C22×C4C23×D711yescharacteristic
833C22×C4C23×D711yescharacteristic
834C22×C4C23×D711yescharacteristic
835C22×C4C23×D711yescharacteristic
836C22×C4C23×D711yescharacteristic
837C22×C4C23×D711yescharacteristic
838SD16—288no—
839D8—288no—
840M16—148no—
841M16—284no—
842C2×C8—78no—
843C2×C8—284no—
844C4⋊C4—22no—
845C4⋊C4—22no—
846C4⋊C4—22no—
847C4⋊C4—72no—
848C4⋊C4—72no—
849C4⋊C4—142no—
850C4⋊C4—142no—
851C4⋊C4—142no—
852C4⋊C4—142no—
853C4⋊C4—141no—
854C4⋊C4—141no—
855C4⋊C4C23×D714yes—
856C22⋊C4—24no—
857C22⋊C4—24no—
858C22⋊C4—24no—
859C22⋊C4—24no—
860C22⋊C4—142no—
861C22⋊C4—142no—
862C22⋊C4—142no—
863C22⋊C4—142no—
864C22⋊C4—142no—
865C22⋊C4—142no—
866C22⋊C4—142no—
867C22⋊C4—142no—
868C22⋊C4—142no—
869C22⋊C4—142no—
870C42—142no—
871C42—142no—
872C2×C7—22no—
873C2×C7—22no—
874C2×C7—22no—
875C2×C7—22no—
876C2×C7—22no—
877C2×C7—41no—
878C2×C7—41no—
879C2×C7—84no—
880C2×C7C2×#53411yescharacteristic
881C2×C7C22×AGL(1,ℤ/8)11yescharacteristic
882C2×C7C2×#57511yescharacteristic
883D7—82no—
884C23—22no—
885C23—22no—
886C23—22no—
887C23—22no—
888C23—22no—
889C23—22no—
890C23—22no—
891C23—22no—
892C23—22no—
893C23—22no—
894C23—22no—
895C23—22no—
896C23—24no—
897C23—41no—
898C23—41no—
899C23—41no—
900C23—41no—
901C23—41no—
902C23—41no—
903C23—41no—
904C23—41no—
905C23—416no—
906C23—44no—
907C23—44no—
908C23—44no—
909C23—44no—
910C23—44no—
911C23—44no—
912C23—44no—
913C23—44no—
914C23—44no—
915C23—816no—
916C23—142no—
917C23—282no—
918C23—282no—
919C23—282no—
920C23#649514yescomplemented
921C23C22×C22⋊D711yescharacteristic
922C23C22×C22⋊D711yescharacteristic
923C23C22×C22⋊D711yescharacteristic
924C23C22×C22⋊D711yescharacteristic
925C23C22×C22⋊D711yescharacteristic
926C23C22×C22⋊D711yescharacteristic
927C23C22×C22⋊D711yescharacteristic
928Q8—144no—
929Q8—282no—
930D4—28no—
931D4—44no—
932D4—44no—
933D4—48no—
934D4—48no—
935D4—48no—
936D4—48no—
937D4—44no—
938D4—144no—
939D4—282no—
940D4—284no—
941D4—284no—
942D4—284no—
943D4—284no—
944D4—284no—
945D4—284no—
946C2×C4—22no—
947C2×C4—22no—
948C2×C4—22no—
949C2×C4—22no—
950C2×C4—22no—
951C2×C4—22no—
952C2×C4—22no—
953C2×C4—22no—
954C2×C4—22no—
955C2×C4—22no—
956C2×C4—22no—
957C2×C4—22no—
958C2×C4—22no—
959C2×C4—22no—
960C2×C4—22no—
961C2×C4—24no—
962C2×C4—41no—
963C2×C4—41no—
964C2×C4—41no—
965C2×C4—41no—
966C2×C4—41no—
967C2×C4—41no—
968C2×C4—41no—
969C2×C4—41no—
970C2×C4—41no—
971C2×C4—41no—
972C2×C4—41no—
973C2×C4—41no—
974C2×C4—44no—
975C2×C4—44no—
976C2×C4—44no—
977C2×C4—142no—
978C2×C4—142no—
979C2×C4—142no—
980C2×C4—284no—
981C2×C4—282no—
982C2×C4—282no—
983C2×C4—282no—
984C2×C4—284no—
985C2×C4#654814yes—
986C2×C4C22×C22⋊D711yescharacteristic
987C2×C4C22×C22⋊D711yescharacteristic
988C2×C4C22×C22⋊D711yescharacteristic
989C2×C4C22×C22⋊D711yescharacteristic
990C2×C4C22×C22⋊D711yescharacteristic
991C2×C4C22×C22⋊D711yescharacteristic
992C2×C4C22×C22⋊D711yescharacteristic
993C2×C4C24×D711yescharacteristic
994C8—148no—
995C7#6075011yescharacteristic, complemented, Sylow
996C22—28no—
997C22—21no—
998C22—21no—
999C22—21no—
1000C22—21no—
1001C22—21no—
1002C22—21no—
1003C22—21no—
1004C22—21no—
1005C22—21no—
1006C22—21no—
1007C22—21no—
1008C22—21no—
1009C22—21no—
1010C22—21no—
1011C22—21no—
1012C22—21no—
1013C22—44no—
1014C22—44no—
1015C22—44no—
1016C22—44no—
1017C22—44no—
1018C22—44no—
1019C22—44no—
1020C22—44no—
1021C22—44no—
1022C22—88no—
1023C22—88no—
1024C22—88no—
1025C22—282no—
1026C22—282no—
1027C22—282no—
1028C22—564no—
1029C22C2×#649512yes—
1030C22C2×#649512yes—
1031C22C2×#649512yes—
1032C22#9049512yes—
1033C22#9051312yes—
1034C22C23×C22⋊D711yescharacteristic
1035C4—21no—
1036C4—21no—
1037C4—21no—
1038C4—21no—
1039C4—21no—
1040C4—21no—
1041C4—44no—
1042C4—282no—
1043C4—282no—
1044C4—282no—
1045C4#9049512yes—
1046C4C2×#654812yes—
1047C2—22no—
1048C2—22no—
1049C2—22no—
1050C2—22no—
1051C2—22no—
1052C2—41no—
1053C2—41no—
1054C2—84no—
1055C2—562no—
1056C2C22×#649511yescharacteristic
1057C2C2×#9049511yescharacteristic
1058C2C2×#9051311yescharacteristic
subgroupG/H
centerC22C23×C22⋊D7
commutator, cosocleC2×C4×C7C25
FrattiniC2×C4C24×D7
FittingC22×C7×#121C2
socleC22×C7C23×D4
hypercenterC22×#121D7
hypocenterC7#60750
LCSG ▷ C2×C4×C7 ▷ C2×C7 ▷ C7
UCSC1 ◁ C22 ◁ C24×C4 ◁ C22×#121

Complements

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

NH ≅ G/Ntype
1. C22×C7×#121C2semidirect
2. C2×#90482C2semidirect
3. #11741483C2semidirect
4. C2×#89979C2semidirect
5. #11740076C2semidirect
6. #11740075C2semidirect
7. #11740073C2semidirect
8. #11740072C2semidirect
9. #11740071C2semidirect
10. #11740070C2semidirect
11. #11740069C2semidirect
12. #11740066C2semidirect
13. #11740061C2semidirect
14. #11739584C2semidirect
16. C23×C7×D4C22semidirect
18. C22×#1157C22semidirect
28. C2×C7×#121C22semidirect
29. C2×C7×#121C22semidirect
30. C2×C7×#121C22semidirect
31. C22×C7×C4⋊C4C22semidirect
34. C2×#6495C22semidirect
40. #90482C22semidirect
41. #90482C22semidirect
42. #90482C22semidirect
43. C2×#6493C22semidirect
44. C2×#6493C22semidirect
48. C2×#6489C22semidirect
49. C2×#6487C22semidirect
50. C2×#6487C22semidirect
51. C22×#1136C22semidirect
52. #89990C22semidirect
53. #89990C22semidirect
54. #89989C22semidirect
55. #89989C22semidirect
56. #89987C22semidirect
57. #89979C22semidirect
58. #89979C22semidirect
59. #89979C22semidirect
60. #89979C22semidirect
61. C2×C22⋊(C7⋊C8)C22semidirect
62. C2×C22⋊(C7⋊C8)C22semidirect
63. #89814C22semidirect
64. #89813C22semidirect
65. #89812C22semidirect
66. #89811C22semidirect
67. #89810C22semidirect
68. #89809C22semidirect
69. #89808C22semidirect
70. #89807C22semidirect
71. #89806C22semidirect
72. #89805C22semidirect
73. #89743C22semidirect
74. #89742C22semidirect
75. #89740C22semidirect
76. #89739C22semidirect
77. #89738C22semidirect
78. #89736C22semidirect
119. C2×#1157C23semidirect
120. C22×D28C23semidirect
122. C22×Dic14C23semidirect
158. C2×#1142C23semidirect
160. C2×#1141C23semidirect
167. #6493C23semidirect
168. #6493C23semidirect
186. #6489C23semidirect
187. C2×C4⋊Dic7C23semidirect
188. C2×C4⋊Dic7C23semidirect
195. #6487C23semidirect
196. #6487C23semidirect
202. C2×#1136C23semidirect
203. C22×C7⋊C8C23semidirect
204. #6406C23semidirect
205. #6406C23semidirect
208. C22⋊(C7⋊C8)C23semidirect
209. C22⋊(C7⋊C8)C23semidirect
210. #6384C23semidirect
211. #6383C23semidirect
212. #6382C23semidirect
213. #6381C23semidirect
215. C22×#121D7semidirect
372. C23×D4C2×D7semidirect
398. C2×#121C2×D7semidirect
399. C2×#121C2×D7semidirect
400. C2×#121C2×D7semidirect
405. C22×C4⋊C4C2×D7semidirect
466. C23×C7AGL(1,ℤ/8)semidirect
920. C23#6495semidirect
995. C7#60750semidirect

Maximal subgroups

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

subgroupindex
C22×C7×#1212
C2×#904822
#117414832
C2×#899792
#117400762
#117400752
#117400732
#117400722
#117400712
#117400702
#117400692
#117400662
#117400612
#117395842
#607507