Finite Group Databasebeta

← C7×#61283 #13238499

Subgroups — C7×#61283 #13238499

Order 1792.

1824 conjugacy classes of subgroups.

The subgroup lattice has 1138 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C7×#3512C211yesmaximal, characteristic, complemented
2C7×#3506C211yesmaximal, characteristic, complemented
3C7×#3355C212yesmaximal, complemented
4C7×#3351C212yesmaximal, complemented
5C7×#3348C212yesmaximal, complemented
6C7×#3347C212yesmaximal, complemented
7C7×#3345C212yesmaximal, complemented
8C7×#3343C212yesmaximal, complemented
9C7×#3339C212yesmaximal, complemented
10C7×#3337C212yesmaximal, complemented
11C7×#3166C211yesmaximal, characteristic, complemented
12C7×#3099C211yesmaximal, characteristic, complemented
13C7×#3098C211yesmaximal, characteristic, complemented
14C7×#3096C211yesmaximal, characteristic, complemented
15C7×#3096C211yesmaximal, characteristic, complemented
16C7×#3076C211yesmaximal, characteristic, complemented
17C2×C7×#478C211yesmaximal, characteristic, complemented
18C7×#3062C211yesmaximal, characteristic, complemented
19C7×#3062C211yesmaximal, characteristic, complemented
20C4×C7×AGL(1,ℤ/8)C211yesmaximal, characteristic, complemented
21C7×#2935C211yesmaximal, characteristic, complemented
22C7×#2913C211yesmaximal, characteristic, complemented
23C7×#2912C211yesmaximal, characteristic, complemented
24C2×C7×AGL(1,ℤ/8)C2211yescharacteristic
25C2×C7×#131C2211yescharacteristic
26C2×C7×#131C2211yescharacteristic
27C7×#559—21no—
28C7×#559—21no—
29C7×#556—21no—
30C7×#555C2212yes—
31C7×#553—22no—
32C7×#553—22no—
33C7×#553C2212yes—
34C7×#553C2212yes—
35C7×#553C2212yescomplemented
36C7×#553C2212yescomplemented
37C7×#552C2212yescomplemented
38C7×#552C2212yescomplemented
39C7×#550—21no—
40C7×#547C2212yes—
41C7×#541—21no—
42C7×#540—21no—
43C7×#538—22no—
44C7×#537C2211yescharacteristic
45C7×#537C2211yescharacteristic
46C7×#535C2211yescharacteristic
47C7×#535C2211yescharacteristic
48C7×#533C2211yescharacteristic
49C7×#532C2211yescharacteristic
50C7×#529—21no—
51C7×#529—21no—
52C2×C7×#125C2211yescharacteristic
53C7×#525—22no—
54C7×#520C2211yescharacteristic
55C7×#520C2211yescharacteristic
56C7×#520C2211yescharacteristic
57C7×#520C2211yescharacteristic
58C4×C7×#41C2211yescharacteristic
59C2×C4×C7×D4C2211yescharacteristic
60C7×#501C2212yescomplemented
61C7×#501C2212yescomplemented
62C7×#499C2212yescomplemented
63C7×#499C2212yescomplemented
64C7×#485C2212yescomplemented
65C7×#485C2212yescomplemented
66C7×#484C2212yescomplemented
67C7×#483C2212yescomplemented
68C7×#482C2212yes—
69C7×#482C2212yes—
70C7×#482C2212yes—
71C7×#482C2212yes—
72C7×#482C2212yescomplemented
73C7×#482C2212yescomplemented
74C7×#481C2212yes—
75C7×#481C2212yes—
76C7×#481C2212yescomplemented
77C7×#480C2212yes—
78C7×#480C2212yes—
79C7×#480C2212yescomplemented
80C7×#479C2211yescharacteristic, complemented
81C7×#479C2211yescharacteristic, complemented
82C7×#478C2212yes—
83C7×#478C2212yes—
84C7×#478C2212yes—
85C7×#478C2212yes—
86C7×#478C2211yescharacteristic, complemented
87C7×#478C2211yescharacteristic, complemented
88C7×#477C2211yescharacteristic, complemented
89C7×#476C2211yescharacteristic, complemented
90C7×#475C2211yescharacteristic, complemented
91C7×#474C2211yescharacteristic, complemented
92C7×#469C2212yes—
93C7×#469C2212yes—
94C7×#468C2212yes—
95C7×#468C2212yes—
96C7×#466C2212yes—
97C7×#466C2212yes—
98C7×#465C2212yes—
99C7×#465C2212yes—
100C7×#442C2212yes—
101C7×#440C2212yes—
102C4×C7×SD16C2212yes—
103C4×C7×D8C2212yes—
104C7×#436C2212yescomplemented
105C7×#435C2212yescomplemented
106C7×#435C2212yescomplemented
107C7×C8×D4C2212yescomplemented
108C7×#428C2211yescharacteristic
109C7×#428C2211yescharacteristic
110C7×#428C2211yescharacteristic
111C7×#428C2211yescharacteristic
112C7×#428C2211yescharacteristic
113C7×#428C2212yescomplemented
114C7×#428C2212yescomplemented
115C7×#428C2212yescomplemented
116C7×#428C2212yescomplemented
117C7×#427C2211yescharacteristic
118C7×#427C2211yescharacteristic
119C7×#427C2212yescomplemented
120C7×#427C2212yescomplemented
121C2×C7×#107C2211yescharacteristic
122C2×C7×#107C2212yescomplemented
123C2×C7×#106C2211yescharacteristic
124C2×C7×#106C2212yescomplemented
125C2×C7×C4⋊C8C2211yescharacteristic
126C7×#418C2211yescharacteristic
127C7×#417C2211yescharacteristic
128C7×#416C2211yescharacteristic
129C7×#416C2211yescharacteristic
130C2×C7×#102C2211yescharacteristic
131C2×C7×#102C2211yescharacteristic
132C7×#408C2211yescharacteristic
133C7×#408C2211yescharacteristic
134C4×C7×M16C2211yescharacteristic
135#61283C711yesmaximal, characteristic, direct product factor, Sylow
136C2×C7×#41—22no—
137C2×C7×#41C2311yescharacteristic
138C2×C7×#41C2311yescharacteristic
139C2×C7×#41C2311yescharacteristic
140C22×C7×D4C2311yescharacteristic
141C23×C4×C7—21no—
142C7×AGL(1,ℤ/8)—24no—
143C2×C7×SD16C2312yes—
144C2×C7×D8C2312yes—
145C7×#131—24no—
146C7×#131—24no—
147C2×C7×M16C2312yes—
148C2×C7×M16C2312yes—
149C2×C7×M16C2311yescharacteristic
150C2×C7×M16C2311yescharacteristic
151C22×C7×C8C2312yes—
152C22×C7×C8C2312yes—
153C22×C7×C8C2311yescharacteristic
154C22×C7×C8C2311yescharacteristic
155C7×C4⋊Q8D411yescharacteristic
156C7×C4⋊Q8C2311yescharacteristic
157C7×C4⋊Q8C2311yescharacteristic
158C7×#127—21no—
159C7×#127—21no—
160C7×#127D411yescharacteristic
161C7×#126—22no—
162C7×#126—22no—
163C7×#126—22no—
164C7×#126—22no—
165C7×#126—22no—
166C7×#126—22no—
167C7×#125—22no—
168C7×#125—22no—
169C7×#125—21no—
170C7×#125—21no—
171C7×#125C2312yes—
172C7×#125C2312yes—
173C7×#125C2311yescharacteristic
174C7×#125C2311yescharacteristic
175C7×#124—21no—
176C7×#124—21no—
177C7×#124—22no—
178C7×#124—22no—
179C7×#124D411yescharacteristic
180C7×#124D411yescharacteristic
181C7×#123—22no—
182C7×#123—22no—
183C7×#123—22no—
184C7×#123—22no—
185C7×#123—22no—
186C7×#123—22no—
187C7×#123—22no—
188C7×#123—22no—
189C7×C22⋊Q8—21no—
190C7×C22⋊Q8—21no—
191C7×C22⋊Q8—21no—
192C7×C22⋊Q8—21no—
193C7×C22⋊Q8—22no—
194C7×C22⋊Q8C2312yes—
195C7×C22⋊Q8C2312yes—
196C7×#121—22no—
197C7×#121—21no—
198C7×#121—21no—
199C7×#121—22no—
200C7×#121—22no—
201C7×#121—22no—
202C7×#121—22no—
203C7×#121—22no—
204C7×#121—22no—
205C7×#121D412yes—
206C7×#121D412yes—
207C7×#121C2312yes—
208C7×#121C2312yes—
209C7×#121C2312yes—
210C7×#121C2312yes—
211C7×#121C2312yes—
212C7×#121C2312yes—
213C7×#120—22no—
214C7×#120—22no—
215C4×C7×Q8—21no—
216C4×C7×Q8—21no—
217C4×C7×Q8—21no—
218C4×C7×Q8—21no—
219C4×C7×Q8—21no—
220C4×C7×Q8—21no—
221C4×C7×Q8C2311yescharacteristic
222C4×C7×Q8C2311yescharacteristic
223C4×C7×D4—22no—
224C4×C7×D4—22no—
225C4×C7×D4—21no—
226C4×C7×D4—21no—
227C4×C7×D4—21no—
228C4×C7×D4—21no—
229C4×C7×D4—22no—
230C4×C7×D4—22no—
231C4×C7×D4—21no—
232C4×C7×D4—21no—
233C4×C7×D4—22no—
234C4×C7×D4—22no—
235C4×C7×D4—22no—
236C4×C7×D4—22no—
237C4×C7×D4—21no—
238C4×C7×D4—21no—
239C4×C7×D4C2311yescharacteristic
240C4×C7×D4C2312yes—
241C4×C7×D4C2312yes—
242C4×C7×D4C2311yescharacteristic
243C4×C7×D4C2312yes—
244C4×C7×D4C2312yes—
245C7×#117—22no—
246C7×#117—22no—
247C7×#117—22no—
248C7×#117—21no—
249C7×#117C2312yes—
250C7×#117C2312yes—
251C7×#117C2312yes—
252C7×#117C2312yes—
253C7×#117C2311yescharacteristic
254C7×#117C2311yescharacteristic
255C7×#117C2311yescharacteristic
256C2×C7×C4⋊C4—21no—
257C2×C7×C4⋊C4—21no—
258C2×C7×C4⋊C4C2312yes—
259C2×C7×C4⋊C4C2312yes—
260C2×C7×C4⋊C4C2312yes—
261C2×C7×C4⋊C4C2312yes—
262C2×C7×C4⋊C4C2311yescharacteristic
263C2×C7×C4⋊C4C2311yescharacteristic
264C2×C7×C4⋊C4C2311yescharacteristic
265C2×C7×C22⋊C4—21no—
266C2×C42×C7—21no—
267C2×C42×C7C2311yescharacteristic
268C7×#107C2312yes—
269C7×#107C2312yes—
270C7×#107C2311yescharacteristic
271C7×#107C2311yescharacteristic
272C7×#107C2311yescharacteristic
273C7×#107C2311yescharacteristic
274C7×#107C2312yes—
275C7×#107C2312yes—
276C7×#107C2312yes—
277C7×#107C2312yes—
278C7×#107C2312yes—
279C7×#106C2312yes—
280C7×#106C2312yes—
281C7×#106C2311yescharacteristic
282C7×#106C2311yescharacteristic
283C7×#106C2311yescharacteristic
284C7×#106C2311yescharacteristic
285C7×#106C2312yes—
286C7×#106C2312yes—
287C7×#106C2312yes—
288C7×#106C2312yes—
289C7×#106C2312yes—
290C7×C4⋊C8C2311yescharacteristic
291C7×C4⋊C8C2311yescharacteristic
292C7×C4⋊C8C2311yescharacteristic
293C7×C4⋊C8C2311yescharacteristic
294C7×#103C2311yescharacteristic
295C7×#103C2311yescharacteristic
296C7×#103C2311yescharacteristic
297C7×#103C2311yescharacteristic
298C7×#103C2312yes—
299C7×#102C2311yescharacteristic
300C7×#102C2311yescharacteristic
301C7×#102C2312yes—
302C7×#102C2312yes—
303C7×#102C2312yes—
304C7×#102C2312yes—
305C7×#102C2311yescharacteristic
306C7×#102C2311yescharacteristic
307C7×#102C2312yes—
308C7×#102C2312yes—
309C7×#102C2312yes—
310C7×C22⋊C8C2312yes—
311C7×C22⋊C8C2312yes—
312C7×C22⋊C8C2312yes—
313C7×C22⋊C8C2312yes—
314C7×#97C2312yes—
315C4×C7×C8C2312yes—
316#3512C2×C711yescharacteristic, complemented
317#3506C2×C711yescharacteristic, complemented
318#3355C2×C712yescomplemented
319#3351C2×C712yescomplemented
320#3348C2×C712yescomplemented
321#3347C2×C712yescomplemented
322#3345C2×C712yescomplemented
323#3343C2×C712yescomplemented
324#3339C2×C712yescomplemented
325#3337C2×C712yescomplemented
326#3166C2×C711yescharacteristic, complemented
327#3099C2×C711yescharacteristic, complemented
328#3098C2×C711yescharacteristic, complemented
329#3096C2×C711yescharacteristic, complemented
330#3096C2×C711yescharacteristic, complemented
331#3076C2×C711yescharacteristic, complemented
332C2×#478C2×C711yescharacteristic, complemented
333#3062C2×C711yescharacteristic, complemented
334#3062C2×C711yescharacteristic, complemented
335C4×AGL(1,ℤ/8)C2×C711yescharacteristic, complemented
336#2935C2×C711yescharacteristic, complemented
337#2913C2×C711yescharacteristic, complemented
338#2912C2×C711yescharacteristic, complemented
339C24×C7—21no—
340C7×#41—22no—
341C7×#41—22no—
342C7×#41—22no—
343C7×#41—22no—
344C7×#41—22no—
345C7×#41—22no—
346C7×#41—84no—
347C2×C7×Q8—21no—
348C2×C7×Q8—21no—
349C2×C7×Q8C2×D411yescharacteristic
350C2×C7×Q8C2×D411yescharacteristic
351C2×C7×Q8C2411yescharacteristic
352C2×C7×D4—21no—
353C2×C7×D4—22no—
354C2×C7×D4—22no—
355C2×C7×D4—22no—
356C2×C7×D4—22no—
357C2×C7×D4—22no—
358C2×C7×D4—22no—
359C2×C7×D4—21no—
360C2×C7×D4—22no—
361C2×C7×D4—22no—
362C2×C7×D4C2×D412yes—
363C2×C7×D4C2×D412yes—
364C2×C7×D4C2×D411yescharacteristic
365C2×C7×D4C2×D411yescharacteristic
366C2×C7×D4C2×D412yes—
367C2×C7×D4C2×D412yes—
368C2×C7×D4C2411yescharacteristic
369C2×C7×D4C2412yes—
370C22×C4×C7—21no—
371C22×C4×C7—21no—
372C22×C4×C7—21no—
373C22×C4×C7—22no—
374C22×C4×C7—22no—
375C22×C4×C7—22no—
376C22×C4×C7—22no—
377C22×C4×C7—21no—
378C22×C4×C7—22no—
379C22×C4×C7—21no—
380C22×C4×C7—21no—
381C22×C4×C7—22no—
382C22×C4×C7—82no—
383C22×C4×C7C2×D411yescharacteristic
384C22×C4×C7C2×D411yescharacteristic
385C22×C4×C7C2412yes—
386C22×C4×C7C2412yes—
387C22×C4×C7C2411yescharacteristic
388C7×SD16—24no—
389C7×D8—24no—
390C7×M16—22no—
391C7×M16—24no—
392C7×M16—24no—
393C7×M16#4114yescomplemented
394C2×C7×C8—22no—
395C2×C7×C8—22no—
396C2×C7×C8—24no—
397C2×C7×C8—24no—
398C2×C7×C8C2412yes—
399C2×C7×C8C2411yescharacteristic
400C2×C7×C8C2411yescharacteristic
401C2×C7×C8C2411yescharacteristic
402C2×C7×C8C2411yescharacteristic
403C2×C7×C8C2412yes—
404C7×C4⋊C4—22no—
405C7×C4⋊C4—22no—
406C7×C4⋊C4—22no—
407C7×C4⋊C4—22no—
408C7×C4⋊C4—21no—
409C7×C4⋊C4—21no—
410C7×C4⋊C4—21no—
411C7×C4⋊C4—22no—
412C7×C4⋊C4—22no—
413C7×C4⋊C4—22no—
414C7×C4⋊C4—22no—
415C7×C4⋊C4—21no—
416C7×C4⋊C4—21no—
417C7×C4⋊C4—21no—
418C7×C4⋊C4—22no—
419C7×C4⋊C4—22no—
420C7×C4⋊C4—21no—
421C7×C4⋊C4—21no—
422C7×C4⋊C4—21no—
423C7×C4⋊C4—21no—
424C7×C4⋊C4—21no—
425C7×C4⋊C4C2×D412yes—
426C7×C4⋊C4C2×D412yes—
427C7×C4⋊C4C2411yescharacteristic
428C7×C4⋊C4C2412yes—
429C7×C4⋊C4C2411yescharacteristic
430C7×C4⋊C4C2412yes—
431C7×C4⋊C4C2412yes—
432C7×C4⋊C4C2411yescharacteristic
433C7×C4⋊C4C2411yescharacteristic
434C7×C4⋊C4C2411yescharacteristic
435C7×C4⋊C4C2411yescharacteristic
436C7×C22⋊C4—22no—
437C7×C22⋊C4—22no—
438C7×C22⋊C4—21no—
439C7×C22⋊C4—21no—
440C7×C22⋊C4—21no—
441C7×C22⋊C4—22no—
442C7×C22⋊C4—22no—
443C7×C22⋊C4—22no—
444C7×C22⋊C4—22no—
445C7×C22⋊C4—22no—
446C7×C22⋊C4—22no—
447C7×C22⋊C4—21no—
448C7×C22⋊C4—21no—
449C7×C22⋊C4—22no—
450C7×C22⋊C4—22no—
451C7×C22⋊C4—22no—
452C7×C22⋊C4—22no—
453C7×C22⋊C4—22no—
454C7×C22⋊C4—22no—
455C7×C22⋊C4C2×D412yes—
456C7×C22⋊C4C2×D412yes—
457C7×C22⋊C4C2×D412yes—
458C7×C22⋊C4C2×D412yes—
459C42×C7—21no—
460C42×C7—21no—
461C42×C7—21no—
462C42×C7—22no—
463C42×C7—22no—
464C42×C7—22no—
465C42×C7—22no—
466C42×C7—21no—
467C42×C7—21no—
468C42×C7C2×D411yescharacteristic
469C42×C7C2×D411yescharacteristic
470C42×C7C2411yescharacteristic
471C42×C7C2411yescharacteristic
472C2×AGL(1,ℤ/8)C22×C711yescharacteristic
473C2×#131C22×C711yescharacteristic
474C2×#131C22×C711yescharacteristic
475#559—21no—
476#559—21no—
477#556—21no—
478#555C22×C712yes—
479#553—22no—
480#553—22no—
481#553C22×C712yes—
482#553C22×C712yes—
483#553C22×C712yescomplemented
484#553C22×C712yescomplemented
485#552C22×C712yescomplemented
486#552C22×C712yescomplemented
487#550—21no—
488#547C22×C712yes—
489#541—21no—
490#540—21no—
491#538—22no—
492#537C22×C711yescharacteristic
493#537C22×C711yescharacteristic
494#535C22×C711yescharacteristic
495#535C22×C711yescharacteristic
496#533C22×C711yescharacteristic
497#532C22×C711yescharacteristic
498#529—21no—
499#529—21no—
500C2×#125C22×C711yescharacteristic
501#525—22no—
502#520C22×C711yescharacteristic
503#520C22×C711yescharacteristic
504#520C22×C711yescharacteristic
505#520C22×C711yescharacteristic
506C4×#41C22×C711yescharacteristic
507C2×C4×D4C22×C711yescharacteristic
508#501C22×C712yescomplemented
509#501C22×C712yescomplemented
510#499C22×C712yescomplemented
511#499C22×C712yescomplemented
512#485C22×C712yescomplemented
513#485C22×C712yescomplemented
514#484C22×C712yescomplemented
515#483C22×C712yescomplemented
516#482C22×C712yes—
517#482C22×C712yes—
518#482C22×C712yes—
519#482C22×C712yes—
520#482C22×C712yescomplemented
521#482C22×C712yescomplemented
522#481C22×C712yes—
523#481C22×C712yes—
524#481C22×C712yescomplemented
525#480C22×C712yes—
526#480C22×C712yes—
527#480C22×C712yescomplemented
528#479C22×C711yescharacteristic, complemented
529#479C22×C711yescharacteristic, complemented
530#478C22×C712yes—
531#478C22×C712yes—
532#478C22×C712yes—
533#478C22×C712yes—
534#478C22×C711yescharacteristic, complemented
535#478C22×C711yescharacteristic, complemented
536#477C22×C711yescharacteristic, complemented
537#476C22×C711yescharacteristic, complemented
538#475C22×C711yescharacteristic, complemented
539#474C22×C711yescharacteristic, complemented
540#469C22×C712yes—
541#469C22×C712yes—
542#468C22×C712yes—
543#468C22×C712yes—
544#466C22×C712yes—
545#466C22×C712yes—
546#465C22×C712yes—
547#465C22×C712yes—
548#442C22×C712yes—
549#440C22×C712yes—
550C4×SD16C22×C712yes—
551C4×D8C22×C712yes—
552#436C22×C712yescomplemented
553#435C22×C712yescomplemented
554#435C22×C712yescomplemented
555C8×D4C22×C712yescomplemented
556#428C22×C711yescharacteristic
557#428C22×C711yescharacteristic
558#428C22×C711yescharacteristic
559#428C22×C711yescharacteristic
560#428C22×C711yescharacteristic
561#428C22×C712yescomplemented
562#428C22×C712yescomplemented
563#428C22×C712yescomplemented
564#428C22×C712yescomplemented
565#427C22×C711yescharacteristic
566#427C22×C711yescharacteristic
567#427C22×C712yescomplemented
568#427C22×C712yescomplemented
569C2×#107C22×C711yescharacteristic
570C2×#107C22×C712yescomplemented
571C2×#106C22×C711yescharacteristic
572C2×#106C22×C712yescomplemented
573C2×C4⋊C8C22×C711yescharacteristic
574#418C22×C711yescharacteristic
575#417C22×C711yescharacteristic
576#416C22×C711yescharacteristic
577#416C22×C711yescharacteristic
578C2×#102C22×C711yescharacteristic
579C2×#102C22×C711yescharacteristic
580#408C22×C711yescharacteristic
581#408C22×C711yescharacteristic
582C4×M16C22×C711yescharacteristic
583C23×C7—21no—
584C23×C7—22no—
585C23×C7—42no—
586C23×C7—81no—
587C23×C7—81no—
588C23×C7C22×D412yes—
589C23×C7C22×D412yes—
590C23×C7C22×D411yescharacteristic
591C7×Q8—22no—
592C7×Q8—22no—
593C7×Q8—21no—
594C7×Q8—21no—
595C7×Q8—42no—
596C7×Q8—81no—
597C7×D4—24no—
598C7×D4—24no—
599C7×D4—22no—
600C7×D4—22no—
601C7×D4—21no—
602C7×D4—22no—
603C7×D4—22no—
604C7×D4—21no—
605C7×D4—42no—
606C7×D4—42no—
607C7×D4—42no—
608C7×D4—42no—
609C7×D4—82no—
610C7×D4—82no—
611C7×D4—82no—
612C7×D4—82no—
613C7×D4—82no—
614C7×D4—82no—
615C2×C4×C7—22no—
616C2×C4×C7—22no—
617C2×C4×C7—22no—
618C2×C4×C7—22no—
619C2×C4×C7—21no—
620C2×C4×C7—21no—
621C2×C4×C7—21no—
622C2×C4×C7—21no—
623C2×C4×C7—21no—
624C2×C4×C7—22no—
625C2×C4×C7—22no—
626C2×C4×C7—22no—
627C2×C4×C7—21no—
628C2×C4×C7—21no—
629C2×C4×C7—41no—
630C2×C4×C7—41no—
631C2×C4×C7—44no—
632C2×C4×C7—42no—
633C2×C4×C7—81no—
634C2×C4×C7—81no—
635C2×C4×C7—82no—
636C2×C4×C7—82no—
637C2×C4×C7—81no—
638C2×C4×C7—82no—
639C2×C4×C7—81no—
640C2×C4×C7—81no—
641C2×C4×C7—82no—
642C2×C4×C7—82no—
643C2×C4×C7C22×D412yes—
644C2×C4×C7C22×D412yes—
645C2×C4×C7C22×D411yescharacteristic
646C2×C4×C7C22×D411yescharacteristic
647C2×C4×C7C22×D411yescharacteristic
648C2×C4×C7C22×D411yescharacteristic
649C2×C4×C7C22×D411yescharacteristic
650C2×C4×C7C2×#4112yes—
651C2×C4×C72−1+412yes—
652C2×C4×C7C2511yescharacteristic
653C7×C8—21no—
654C7×C8—21no—
655C7×C8—21no—
656C7×C8—21no—
657C7×C8—22no—
658C7×C8C2×#4114yes—
659C2×#41—22no—
660C2×#41C23×C711yescharacteristic
661C2×#41C23×C711yescharacteristic
662C2×#41C23×C711yescharacteristic
663C22×D4C23×C711yescharacteristic
664C23×C4—21no—
665AGL(1,ℤ/8)—24no—
666C2×SD16C23×C712yes—
667C2×D8C23×C712yes—
668#131—24no—
669#131—24no—
670C2×M16C23×C712yes—
671C2×M16C23×C712yes—
672C2×M16C23×C711yescharacteristic
673C2×M16C23×C711yescharacteristic
674C22×C8C23×C711yescharacteristic
675C22×C8C23×C711yescharacteristic
676C22×C8C23×C712yes—
677C22×C8C23×C712yes—
678C4⋊Q8C7×D411yescharacteristic
679C4⋊Q8C23×C711yescharacteristic
680C4⋊Q8C23×C711yescharacteristic
681#127—21no—
682#127—21no—
683#127C7×D411yescharacteristic
684#126—22no—
685#126—22no—
686#126—22no—
687#126—22no—
688#126—22no—
689#126—22no—
690#125—22no—
691#125—22no—
692#125—21no—
693#125—21no—
694#125C23×C712yes—
695#125C23×C712yes—
696#125C23×C711yescharacteristic
697#125C23×C711yescharacteristic
698#124—21no—
699#124—21no—
700#124—22no—
701#124—22no—
702#124C7×D411yescharacteristic
703#124C7×D411yescharacteristic
704#123—22no—
705#123—22no—
706#123—22no—
707#123—22no—
708#123—22no—
709#123—22no—
710#123—22no—
711#123—22no—
712C22⋊Q8—21no—
713C22⋊Q8—21no—
714C22⋊Q8—21no—
715C22⋊Q8—21no—
716C22⋊Q8—22no—
717C22⋊Q8C23×C712yes—
718C22⋊Q8C23×C712yes—
719#121—22no—
720#121—21no—
721#121—21no—
722#121—22no—
723#121—22no—
724#121—22no—
725#121—22no—
726#121—22no—
727#121—22no—
728#121C7×D412yes—
729#121C7×D412yes—
730#121C23×C712yes—
731#121C23×C712yes—
732#121C23×C712yes—
733#121C23×C712yes—
734#121C23×C712yes—
735#121C23×C712yes—
736#120—22no—
737#120—22no—
738C4×Q8—21no—
739C4×Q8—21no—
740C4×Q8—21no—
741C4×Q8—21no—
742C4×Q8—21no—
743C4×Q8—21no—
744C4×Q8C23×C711yescharacteristic
745C4×Q8C23×C711yescharacteristic
746C4×D4—22no—
747C4×D4—22no—
748C4×D4—21no—
749C4×D4—21no—
750C4×D4—21no—
751C4×D4—21no—
752C4×D4—22no—
753C4×D4—22no—
754C4×D4—21no—
755C4×D4—21no—
756C4×D4—22no—
757C4×D4—22no—
758C4×D4—22no—
759C4×D4—22no—
760C4×D4—21no—
761C4×D4—21no—
762C4×D4C23×C712yes—
763C4×D4C23×C712yes—
764C4×D4C23×C711yescharacteristic
765C4×D4C23×C711yescharacteristic
766C4×D4C23×C712yes—
767C4×D4C23×C712yes—
768#117—22no—
769#117—22no—
770#117—22no—
771#117—21no—
772#117C23×C711yescharacteristic
773#117C23×C711yescharacteristic
774#117C23×C711yescharacteristic
775#117C23×C712yes—
776#117C23×C712yes—
777#117C23×C712yes—
778#117C23×C712yes—
779C2×C4⋊C4—21no—
780C2×C4⋊C4—21no—
781C2×C4⋊C4C23×C711yescharacteristic
782C2×C4⋊C4C23×C711yescharacteristic
783C2×C4⋊C4C23×C711yescharacteristic
784C2×C4⋊C4C23×C712yes—
785C2×C4⋊C4C23×C712yes—
786C2×C4⋊C4C23×C712yes—
787C2×C4⋊C4C23×C712yes—
788C2×C22⋊C4—21no—
789C2×C42—21no—
790C2×C42C23×C711yescharacteristic
791#107C23×C712yes—
792#107C23×C712yes—
793#107C23×C711yescharacteristic
794#107C23×C712yes—
795#107C23×C712yes—
796#107C23×C711yescharacteristic
797#107C23×C711yescharacteristic
798#107C23×C711yescharacteristic
799#107C23×C712yes—
800#107C23×C712yes—
801#107C23×C712yes—
802#106C23×C712yes—
803#106C23×C712yes—
804#106C23×C711yescharacteristic
805#106C23×C712yes—
806#106C23×C712yes—
807#106C23×C711yescharacteristic
808#106C23×C711yescharacteristic
809#106C23×C711yescharacteristic
810#106C23×C712yes—
811#106C23×C712yes—
812#106C23×C712yes—
813C4⋊C8C23×C711yescharacteristic
814C4⋊C8C23×C711yescharacteristic
815C4⋊C8C23×C711yescharacteristic
816C4⋊C8C23×C711yescharacteristic
817#103C23×C711yescharacteristic
818#103C23×C711yescharacteristic
819#103C23×C711yescharacteristic
820#103C23×C711yescharacteristic
821#103C23×C712yes—
822#102C23×C712yes—
823#102C23×C712yes—
824#102C23×C712yes—
825#102C23×C712yes—
826#102C23×C711yescharacteristic
827#102C23×C711yescharacteristic
828#102C23×C711yescharacteristic
829#102C23×C711yescharacteristic
830#102C23×C712yes—
831#102C23×C712yes—
832#102C23×C712yes—
833C22⋊C8C23×C712yes—
834C22⋊C8C23×C712yes—
835C22⋊C8C23×C712yes—
836C22⋊C8C23×C712yes—
837#97C23×C712yes—
838C4×C8C23×C712yes—
839C22×C7—21no—
840C22×C7—21no—
841C22×C7—22no—
842C22×C7—22no—
843C22×C7—22no—
844C22×C7—22no—
845C22×C7—22no—
846C22×C7—22no—
847C22×C7—41no—
848C22×C7—42no—
849C22×C7—42no—
850C22×C7—41no—
851C22×C7—41no—
852C22×C7—42no—
853C22×C7—84no—
854C22×C7#54712yes—
855C22×C7C23×D411yescharacteristic
856C4×C7—21no—
857C4×C7—21no—
858C4×C7—21no—
859C4×C7—21no—
860C4×C7—22no—
861C4×C7—22no—
862C4×C7—41no—
863C4×C7—42no—
864C4×C7—41no—
865C4×C7—41no—
866C4×C7—42no—
867C4×C7—41no—
868C4×C7—42no—
869C4×C7—41no—
870C4×C7—41no—
871C4×C7—41no—
872C4×C7#54712yes—
873C4×C7C22×#4111yescharacteristic
874C4×C7C2×2−1+411yescharacteristic
875C24—21no—
876#41—22no—
877#41—22no—
878#41—22no—
879#41—22no—
880#41—22no—
881#41—22no—
882#41—84no—
883C2×Q8—21no—
884C2×Q8—21no—
885C2×Q8C2×C7×D411yescharacteristic
886C2×Q8C2×C7×D411yescharacteristic
887C2×Q8C24×C711yescharacteristic
888C2×D4—21no—
889C2×D4—22no—
890C2×D4—22no—
891C2×D4—22no—
892C2×D4—22no—
893C2×D4—22no—
894C2×D4—22no—
895C2×D4—21no—
896C2×D4—22no—
897C2×D4—22no—
898C2×D4C2×C7×D412yes—
899C2×D4C2×C7×D412yes—
900C2×D4C2×C7×D411yescharacteristic
901C2×D4C2×C7×D411yescharacteristic
902C2×D4C2×C7×D412yes—
903C2×D4C2×C7×D412yes—
904C2×D4C24×C711yescharacteristic
905C2×D4C24×C712yes—
906C22×C4—21no—
907C22×C4—21no—
908C22×C4—21no—
909C22×C4—22no—
910C22×C4—22no—
911C22×C4—22no—
912C22×C4—22no—
913C22×C4—21no—
914C22×C4—22no—
915C22×C4—21no—
916C22×C4—21no—
917C22×C4—22no—
918C22×C4—82no—
919C22×C4C2×C7×D411yescharacteristic
920C22×C4C2×C7×D411yescharacteristic
921C22×C4C24×C712yes—
922C22×C4C24×C712yes—
923C22×C4C24×C711yescharacteristic
924SD16—24no—
925D8—24no—
926M16—22no—
927M16—24no—
928M16—24no—
929M16C7×#4114yescomplemented
930C2×C8—22no—
931C2×C8—22no—
932C2×C8—24no—
933C2×C8—24no—
934C2×C8C24×C712yes—
935C2×C8C24×C711yescharacteristic
936C2×C8C24×C711yescharacteristic
937C2×C8C24×C711yescharacteristic
938C2×C8C24×C711yescharacteristic
939C2×C8C24×C712yes—
940C4⋊C4—22no—
941C4⋊C4—22no—
942C4⋊C4—22no—
943C4⋊C4—22no—
944C4⋊C4—21no—
945C4⋊C4—21no—
946C4⋊C4—21no—
947C4⋊C4—22no—
948C4⋊C4—22no—
949C4⋊C4—22no—
950C4⋊C4—22no—
951C4⋊C4—21no—
952C4⋊C4—21no—
953C4⋊C4—21no—
954C4⋊C4—22no—
955C4⋊C4—22no—
956C4⋊C4—21no—
957C4⋊C4—21no—
958C4⋊C4—21no—
959C4⋊C4—21no—
960C4⋊C4—21no—
961C4⋊C4C2×C7×D412yes—
962C4⋊C4C2×C7×D412yes—
963C4⋊C4C24×C711yescharacteristic
964C4⋊C4C24×C712yes—
965C4⋊C4C24×C711yescharacteristic
966C4⋊C4C24×C712yes—
967C4⋊C4C24×C712yes—
968C4⋊C4C24×C711yescharacteristic
969C4⋊C4C24×C711yescharacteristic
970C4⋊C4C24×C711yescharacteristic
971C4⋊C4C24×C711yescharacteristic
972C22⋊C4—22no—
973C22⋊C4—22no—
974C22⋊C4—21no—
975C22⋊C4—21no—
976C22⋊C4—21no—
977C22⋊C4—22no—
978C22⋊C4—22no—
979C22⋊C4—22no—
980C22⋊C4—22no—
981C22⋊C4—22no—
982C22⋊C4—22no—
983C22⋊C4—21no—
984C22⋊C4—21no—
985C22⋊C4—22no—
986C22⋊C4—22no—
987C22⋊C4—22no—
988C22⋊C4—22no—
989C22⋊C4—22no—
990C22⋊C4—22no—
991C22⋊C4C2×C7×D412yes—
992C22⋊C4C2×C7×D412yes—
993C22⋊C4C2×C7×D412yes—
994C22⋊C4C2×C7×D412yes—
995C42—21no—
996C42—21no—
997C42—21no—
998C42—22no—
999C42—22no—
1000C42—22no—
1001C42—22no—
1002C42—21no—
1003C42—21no—
1004C42C2×C7×D411yescharacteristic
1005C42C2×C7×D411yescharacteristic
1006C42C24×C711yescharacteristic
1007C42C24×C711yescharacteristic
1008C2×C7—22no—
1009C2×C7—42no—
1010C2×C7—42no—
1011C2×C7—81no—
1012C2×C7—82no—
1013C2×C7C2×#54711yescharacteristic
1014C2×C7#358411yescharacteristic
1015C2×C7#358511yescharacteristic
1016C23—21no—
1017C23—22no—
1018C23—42no—
1019C23—81no—
1020C23—81no—
1021C23C22×C7×D412yes—
1022C23C22×C7×D412yes—
1023C23C22×C7×D411yescharacteristic
1024Q8—22no—
1025Q8—22no—
1026Q8—21no—
1027Q8—21no—
1028Q8—42no—
1029Q8—81no—
1030D4—24no—
1031D4—24no—
1032D4—21no—
1033D4—22no—
1034D4—22no—
1035D4—21no—
1036D4—22no—
1037D4—22no—
1038D4—42no—
1039D4—42no—
1040D4—42no—
1041D4—42no—
1042D4—82no—
1043D4—82no—
1044D4—82no—
1045D4—82no—
1046D4—82no—
1047D4—82no—
1048C2×C4—22no—
1049C2×C4—22no—
1050C2×C4—22no—
1051C2×C4—22no—
1052C2×C4—21no—
1053C2×C4—21no—
1054C2×C4—21no—
1055C2×C4—21no—
1056C2×C4—21no—
1057C2×C4—22no—
1058C2×C4—22no—
1059C2×C4—22no—
1060C2×C4—21no—
1061C2×C4—21no—
1062C2×C4—41no—
1063C2×C4—41no—
1064C2×C4—44no—
1065C2×C4—42no—
1066C2×C4—81no—
1067C2×C4—81no—
1068C2×C4—82no—
1069C2×C4—82no—
1070C2×C4—81no—
1071C2×C4—82no—
1072C2×C4—81no—
1073C2×C4—81no—
1074C2×C4—82no—
1075C2×C4—82no—
1076C2×C4C22×C7×D412yes—
1077C2×C4C22×C7×D412yes—
1078C2×C4C22×C7×D411yescharacteristic
1079C2×C4C22×C7×D411yescharacteristic
1080C2×C4C22×C7×D411yescharacteristic
1081C2×C4C22×C7×D411yescharacteristic
1082C2×C4C22×C7×D411yescharacteristic
1083C2×C4C2×C7×#4112yes—
1084C2×C4C7×2−1+412yes—
1085C2×C4C25×C711yescharacteristic
1086C8—21no—
1087C8—21no—
1088C8—21no—
1089C8—21no—
1090C8—22no—
1091C8C2×C7×#4114yes—
1092C7#6128311yescharacteristic, direct product factor, Sylow
1093C22—21no—
1094C22—21no—
1095C22—22no—
1096C22—22no—
1097C22—22no—
1098C22—22no—
1099C22—22no—
1100C22—22no—
1101C22—41no—
1102C22—42no—
1103C22—42no—
1104C22—41no—
1105C22—41no—
1106C22—42no—
1107C22—84no—
1108C22C7×#54712yes—
1109C22C23×C7×D411yescharacteristic
1110C4—21no—
1111C4—21no—
1112C4—21no—
1113C4—21no—
1114C4—22no—
1115C4—22no—
1116C4—41no—
1117C4—42no—
1118C4—41no—
1119C4—41no—
1120C4—42no—
1121C4—41no—
1122C4—41no—
1123C4—41no—
1124C4—42no—
1125C4—41no—
1126C4C7×#54712yes—
1127C4C22×C7×#4111yescharacteristic
1128C4C2×C7×2−1+411yescharacteristic
1129C2—22no—
1130C2—42no—
1131C2—42no—
1132C2—82no—
1133C2—81no—
1134C2C2×C7×#54711yescharacteristic
1135C2C7×#358411yescharacteristic
1136C2C7×#358511yescharacteristic
subgroupG/H
center, socleC22×C7C23×D4
commutator, Frattini, cosocleC2×C4C25×C7
LCSG ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C7 ◁ C7×#532 ◁ G

Complements

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

NH ≅ G/Ntype
1. C7×#3512C2semidirect
2. C7×#3506C2semidirect
3. C7×#3355C2semidirect
4. C7×#3351C2semidirect
5. C7×#3348C2semidirect
6. C7×#3347C2semidirect
7. C7×#3345C2semidirect
8. C7×#3343C2semidirect
9. C7×#3339C2semidirect
10. C7×#3337C2semidirect
11. C7×#3166C2semidirect
12. C7×#3099C2semidirect
13. C7×#3098C2semidirect
14. C7×#3096C2semidirect
15. C7×#3096C2semidirect
16. C7×#3076C2semidirect
17. C2×C7×#478C2semidirect
18. C7×#3062C2semidirect
19. C7×#3062C2semidirect
20. C4×C7×AGL(1,ℤ/8)C2semidirect
21. C7×#2935C2semidirect
22. C7×#2913C2semidirect
23. C7×#2912C2semidirect
35. C7×#553C22semidirect
36. C7×#553C22semidirect
37. C7×#552C22semidirect
38. C7×#552C22semidirect
60. C7×#501C22semidirect
61. C7×#501C22semidirect
62. C7×#499C22semidirect
63. C7×#499C22semidirect
64. C7×#485C22semidirect
65. C7×#485C22semidirect
66. C7×#484C22semidirect
67. C7×#483C22semidirect
72. C7×#482C22semidirect
73. C7×#482C22semidirect
76. C7×#481C22semidirect
79. C7×#480C22semidirect
80. C7×#479C22semidirect
81. C7×#479C22semidirect
86. C7×#478C22semidirect
87. C7×#478C22semidirect
88. C7×#477C22semidirect
89. C7×#476C22semidirect
90. C7×#475C22semidirect
91. C7×#474C22semidirect
104. C7×#436C22semidirect
105. C7×#435C22semidirect
106. C7×#435C22semidirect
107. C7×C8×D4C22semidirect
113. C7×#428C22semidirect
114. C7×#428C22semidirect
115. C7×#428C22semidirect
116. C7×#428C22semidirect
119. C7×#427C22semidirect
120. C7×#427C22semidirect
122. C2×C7×#107C22semidirect
124. C2×C7×#106C22semidirect
135. #61283C7direct (N × H)
316. #3512C2×C7semidirect
317. #3506C2×C7semidirect
318. #3355C2×C7semidirect
319. #3351C2×C7semidirect
320. #3348C2×C7semidirect
321. #3347C2×C7semidirect
322. #3345C2×C7semidirect
323. #3343C2×C7semidirect
324. #3339C2×C7semidirect
325. #3337C2×C7semidirect
326. #3166C2×C7semidirect
327. #3099C2×C7semidirect
328. #3098C2×C7semidirect
329. #3096C2×C7semidirect
330. #3096C2×C7semidirect
331. #3076C2×C7semidirect
332. C2×#478C2×C7semidirect
333. #3062C2×C7semidirect
334. #3062C2×C7semidirect
335. C4×AGL(1,ℤ/8)C2×C7semidirect
336. #2935C2×C7semidirect
337. #2913C2×C7semidirect
338. #2912C2×C7semidirect
393. C7×M16#41semidirect
483. #553C22×C7semidirect
484. #553C22×C7semidirect
485. #552C22×C7semidirect
486. #552C22×C7semidirect
508. #501C22×C7semidirect
509. #501C22×C7semidirect
510. #499C22×C7semidirect
511. #499C22×C7semidirect
512. #485C22×C7semidirect
513. #485C22×C7semidirect
514. #484C22×C7semidirect
515. #483C22×C7semidirect
520. #482C22×C7semidirect
521. #482C22×C7semidirect
524. #481C22×C7semidirect
527. #480C22×C7semidirect
528. #479C22×C7semidirect
529. #479C22×C7semidirect
534. #478C22×C7semidirect
535. #478C22×C7semidirect
536. #477C22×C7semidirect
537. #476C22×C7semidirect
538. #475C22×C7semidirect
539. #474C22×C7semidirect
552. #436C22×C7semidirect
553. #435C22×C7semidirect
554. #435C22×C7semidirect
555. C8×D4C22×C7semidirect
561. #428C22×C7semidirect
562. #428C22×C7semidirect
563. #428C22×C7semidirect
564. #428C22×C7semidirect
567. #427C22×C7semidirect
568. #427C22×C7semidirect
570. C2×#107C22×C7semidirect
572. C2×#106C22×C7semidirect
929. M16C7×#41semidirect
1092. C7#61283direct (N × H)

Maximal subgroups

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

subgroupindex
C7×#35122
C7×#35062
C7×#33552
C7×#33512
C7×#33482
C7×#33472
C7×#33452
C7×#33432
C7×#33392
C7×#33372
C7×#31662
C7×#30992
C7×#30982
C7×#30962
C7×#30762
C2×C7×#4782
C7×#30622
C4×C7×AGL(1,ℤ/8)2
C7×#29352
C7×#29132
C7×#29122
#612837