Finite Group Databasebeta

← C7×#15911 #13193127

Subgroups — C7×#15911 #13193127

Order 1792.

1674 conjugacy classes of subgroups.

The subgroup lattice has 1014 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C7×#126C211yesmaximal, characteristic
2C2×C7×#397C211yesmaximal, characteristic
3C2×C7×#397C211yesmaximal, characteristic
4C2×C7×#380C211yesmaximal, characteristic
5C7×#1444C211yesmaximal, characteristic, complemented
6C7×#1444C211yesmaximal, characteristic, complemented
7C7×#1442C211yesmaximal, characteristic, complemented
8C7×#1442C211yesmaximal, characteristic, complemented
9C7×#1441C211yesmaximal, characteristic, complemented
10C7×#1441C211yesmaximal, characteristic, complemented
11C7×#1440C211yesmaximal, characteristic
12C7×#1436C211yesmaximal, characteristic, complemented
13C7×#1436C211yesmaximal, characteristic, complemented
14C7×C22⋊#95C211yesmaximal, characteristic
15C7×C22⋊#95C211yesmaximal, characteristic
16C24×C4×C7C2211yescharacteristic
17C2×C7×#126—24no—
18C2×C7×#126—24no—
19C2×C7×#126—24no—
20C22×C7×C4⋊C4C2211yescharacteristic
21C22×C7×C4⋊C4C2211yescharacteristic
22C22×C7×C4⋊C4C2211yescharacteristic
23C22×C7×C4⋊C4C2211yescharacteristic
24C22×C7×C4⋊C4C2211yescharacteristic
25C22×C7×C4⋊C4C2211yescharacteristic
26C22×C7×C4⋊C4C2211yescharacteristic
27C22×C7×C22⋊C4C2211yescharacteristic
28C22×C7×C22⋊C4C2211yescharacteristic
29C22×C7×C22⋊C4C2211yescharacteristic
30C22×C7×C22⋊C4C2211yescharacteristic
31C22×C7×C22⋊C4C2211yescharacteristic
32C22×C7×C22⋊C4C2211yescharacteristic
33C22×C42×C7C2211yescharacteristic
34C7×#397—24no—
35C7×#397—24no—
36C7×#380—24no—
37C2×C7×#95C2211yescharacteristic
38C2×C7×#95C2211yescharacteristic
39C2×C7×#95C2211yescharacteristic
40C2×C7×#95C2211yescharacteristic
41C2×C7×#95C2211yescharacteristic
42C2×C7×#95C2211yescharacteristic
43C2×C7×#95C2211yescharacteristic
44C2×C7×#95C2211yescharacteristic
45C2×C7×#95C2211yescharacteristic
46C2×C7×#95C2211yescharacteristic
47C2×C7×#95C2211yescharacteristic
48C2×C7×#95C2211yescharacteristic
49C2×C7×#95C2211yescharacteristic
50C2×C7×#95C2211yescharacteristic
51C2×C7×#95C2211yescharacteristic
52C2×C7×#95C2211yescharacteristic
53C2×C7×#95C2211yescharacteristic
54C2×C7×#95C2211yescharacteristic
55C2×C7×#95C2211yescharacteristic
56C2×C7×#95C2211yescharacteristic
57#15911C711yesmaximal, characteristic, direct product factor, Sylow
58C25×C7C2311yescharacteristic
59C23×C4×C7—22no—
60C23×C4×C7—22no—
61C23×C4×C7—22no—
62C23×C4×C7—22no—
63C23×C4×C7—22no—
64C23×C4×C7—41no—
65C23×C4×C7—41no—
66C23×C4×C7C2311yescharacteristic
67C23×C4×C7C2311yescharacteristic
68C23×C4×C7C2311yescharacteristic
69C23×C4×C7C2311yescharacteristic
70C23×C4×C7C2311yescharacteristic
71C23×C4×C7C2311yescharacteristic
72C23×C4×C7C2311yescharacteristic
73C23×C4×C7C2311yescharacteristic
74C23×C4×C7C2311yescharacteristic
75C23×C4×C7C2311yescharacteristic
76C23×C4×C7C2311yescharacteristic
77C23×C4×C7C2311yescharacteristic
78C23×C4×C7C2311yescharacteristic
79C23×C4×C7C2311yescharacteristic
80C7×#126—232no—
81C2×C7×C4⋊C4—22no—
82C2×C7×C4⋊C4—22no—
83C2×C7×C4⋊C4—22no—
84C2×C7×C4⋊C4—22no—
85C2×C7×C4⋊C4—22no—
86C2×C7×C4⋊C4—22no—
87C2×C7×C4⋊C4—22no—
88C2×C7×C4⋊C4—22no—
89C2×C7×C4⋊C4—22no—
90C2×C7×C4⋊C4—22no—
91C2×C7×C4⋊C4—22no—
92C2×C7×C4⋊C4—22no—
93C2×C7×C4⋊C4—22no—
94C2×C7×C4⋊C4—22no—
95C2×C7×C4⋊C4—22no—
96C2×C7×C4⋊C4—22no—
97C2×C7×C4⋊C4—22no—
98C2×C7×C4⋊C4—41no—
99C2×C7×C4⋊C4—41no—
100C2×C7×C4⋊C4—41no—
101C2×C7×C4⋊C4—41no—
102C2×C7×C22⋊C4—22no—
103C2×C7×C22⋊C4—22no—
104C2×C7×C22⋊C4—22no—
105C2×C7×C22⋊C4—22no—
106C2×C7×C22⋊C4—22no—
107C2×C7×C22⋊C4—22no—
108C2×C7×C22⋊C4—22no—
109C2×C7×C22⋊C4—22no—
110C2×C7×C22⋊C4—22no—
111C2×C7×C22⋊C4—22no—
112C2×C7×C22⋊C4—22no—
113C2×C7×C22⋊C4—22no—
114C2×C7×C22⋊C4—22no—
115C2×C7×C22⋊C4—41no—
116C2×C7×C22⋊C4—41no—
117C2×C7×C22⋊C4D414yes—
118C2×C7×C22⋊C4D414yes—
119C2×C7×C22⋊C4D414yes—
120C2×C42×C7—22no—
121C2×C42×C7—22no—
122C2×C42×C7—22no—
123C7×#95—22no—
124C7×#95—22no—
125C7×#95—22no—
126C7×#95—22no—
127C7×#95—22no—
128C7×#95—22no—
129C7×#95—22no—
130C7×#95—22no—
131C7×#95—22no—
132C7×#95—22no—
133C7×#95—22no—
134C7×#95—22no—
135C7×#95—22no—
136C7×#95—22no—
137C7×#95—22no—
138C7×#95—22no—
139C7×#95—41no—
140C7×#95—41no—
141C7×#95—41no—
142C7×#95—41no—
143C22×#126C2×C711yescharacteristic
144C2×#397C2×C711yescharacteristic
145C2×#397C2×C711yescharacteristic
146C2×#380C2×C711yescharacteristic
147#1444C2×C711yescharacteristic, complemented
148#1444C2×C711yescharacteristic, complemented
149#1442C2×C711yescharacteristic, complemented
150#1442C2×C711yescharacteristic, complemented
151#1441C2×C711yescharacteristic, complemented
152#1441C2×C711yescharacteristic, complemented
153#1440C2×C711yescharacteristic
154#1436C2×C711yescharacteristic, complemented
155#1436C2×C711yescharacteristic, complemented
156C22⋊#95C2×C711yescharacteristic
157C22⋊#95C2×C711yescharacteristic
158C24×C7—21no—
159C24×C7—21no—
160C24×C7—21no—
161C24×C7—21no—
162C24×C7—21no—
163C24×C7—21no—
164C24×C7—21no—
165C24×C7—21no—
166C24×C7—21no—
167C24×C7—21no—
168C24×C7—21no—
169C24×C7—21no—
170C24×C7C2×D412yes—
171C24×C7C2×D412yes—
172C24×C7C2×D412yes—
173C24×C7C2411yescharacteristic
174C22×C4×C7—21no—
175C22×C4×C7—21no—
176C22×C4×C7—21no—
177C22×C4×C7—21no—
178C22×C4×C7—28no—
179C22×C4×C7—21no—
180C22×C4×C7—21no—
181C22×C4×C7—21no—
182C22×C4×C7—21no—
183C22×C4×C7—21no—
184C22×C4×C7—21no—
185C22×C4×C7—21no—
186C22×C4×C7—21no—
187C22×C4×C7—21no—
188C22×C4×C7—21no—
189C22×C4×C7—21no—
190C22×C4×C7—21no—
191C22×C4×C7—21no—
192C22×C4×C7—21no—
193C22×C4×C7—21no—
194C22×C4×C7—21no—
195C22×C4×C7—21no—
196C22×C4×C7—21no—
197C22×C4×C7—21no—
198C22×C4×C7—21no—
199C22×C4×C7—21no—
200C22×C4×C7—21no—
201C22×C4×C7—21no—
202C22×C4×C7—21no—
203C22×C4×C7—21no—
204C22×C4×C7—21no—
205C22×C4×C7—21no—
206C22×C4×C7—21no—
207C22×C4×C7—21no—
208C22×C4×C7—21no—
209C22×C4×C7—21no—
210C22×C4×C7—21no—
211C22×C4×C7—21no—
212C22×C4×C7—21no—
213C22×C4×C7—21no—
214C22×C4×C7—21no—
215C22×C4×C7—21no—
216C22×C4×C7—21no—
217C22×C4×C7—21no—
218C22×C4×C7—21no—
219C22×C4×C7—21no—
220C22×C4×C7—21no—
221C22×C4×C7—21no—
222C22×C4×C7—21no—
223C22×C4×C7—21no—
224C22×C4×C7—21no—
225C22×C4×C7—21no—
226C22×C4×C7—21no—
227C22×C4×C7—21no—
228C22×C4×C7—21no—
229C22×C4×C7—21no—
230C22×C4×C7—21no—
231C22×C4×C7—21no—
232C22×C4×C7—21no—
233C22×C4×C7—21no—
234C22×C4×C7—21no—
235C22×C4×C7—21no—
236C22×C4×C7—21no—
237C22×C4×C7—21no—
238C22×C4×C7—21no—
239C22×C4×C7—21no—
240C22×C4×C7—21no—
241C22×C4×C7—21no—
242C22×C4×C7—21no—
243C22×C4×C7—21no—
244C22×C4×C7—21no—
245C22×C4×C7—21no—
246C22×C4×C7—21no—
247C22×C4×C7—21no—
248C22×C4×C7—21no—
249C22×C4×C7—21no—
250C22×C4×C7—21no—
251C22×C4×C7—21no—
252C22×C4×C7—21no—
253C22×C4×C7—21no—
254C22×C4×C7—21no—
255C22×C4×C7—21no—
256C22×C4×C7—21no—
257C22×C4×C7—21no—
258C22×C4×C7—21no—
259C22×C4×C7—21no—
260C22×C4×C7—21no—
261C22×C4×C7—44no—
262C22×C4×C7—44no—
263C22×C4×C7—44no—
264C22×C4×C7—44no—
265C22×C4×C7—44no—
266C22×C4×C7—44no—
267C22×C4×C7C2×D412yes—
268C22×C4×C7C2×D412yes—
269C22×C4×C7C2×D412yes—
270C22×C4×C7C2×D412yes—
271C22×C4×C7C2×D412yes—
272C22×C4×C7C2×D412yes—
273C22×C4×C7#4112yes—
274C22×C4×C7#4112yes—
275C22×C4×C7#4112yes—
276C22×C4×C7#4112yes—
277C22×C4×C7#4112yes—
278C22×C4×C7#4112yes—
279C7×C4⋊C4—28no—
280C7×C4⋊C4—28no—
281C7×C4⋊C4—28no—
282C7×C4⋊C4—44no—
283C7×C4⋊C4—44no—
284C7×C4⋊C4—44no—
285C7×C4⋊C4—44no—
286C7×C22⋊C4—28no—
287C7×C22⋊C4—28no—
288C7×C22⋊C4—28no—
289C7×C22⋊C4—44no—
290C7×C22⋊C4—44no—
291C7×C22⋊C4—44no—
292C42×C7—28no—
293C24×C4C22×C711yescharacteristic
294C2×#126—24no—
295C2×#126—24no—
296C2×#126—24no—
297C22×C4⋊C4C22×C711yescharacteristic
298C22×C4⋊C4C22×C711yescharacteristic
299C22×C4⋊C4C22×C711yescharacteristic
300C22×C4⋊C4C22×C711yescharacteristic
301C22×C4⋊C4C22×C711yescharacteristic
302C22×C4⋊C4C22×C711yescharacteristic
303C22×C4⋊C4C22×C711yescharacteristic
304C22×C22⋊C4C22×C711yescharacteristic
305C22×C22⋊C4C22×C711yescharacteristic
306C22×C22⋊C4C22×C711yescharacteristic
307C22×C22⋊C4C22×C711yescharacteristic
308C22×C22⋊C4C22×C711yescharacteristic
309C22×C22⋊C4C22×C711yescharacteristic
310C22×C42C22×C711yescharacteristic
311#397—24no—
312#397—24no—
313#380—24no—
314C2×#95C22×C711yescharacteristic
315C2×#95C22×C711yescharacteristic
316C2×#95C22×C711yescharacteristic
317C2×#95C22×C711yescharacteristic
318C2×#95C22×C711yescharacteristic
319C2×#95C22×C711yescharacteristic
320C2×#95C22×C711yescharacteristic
321C2×#95C22×C711yescharacteristic
322C2×#95C22×C711yescharacteristic
323C2×#95C22×C711yescharacteristic
324C2×#95C22×C711yescharacteristic
325C2×#95C22×C711yescharacteristic
326C2×#95C22×C711yescharacteristic
327C2×#95C22×C711yescharacteristic
328C2×#95C22×C711yescharacteristic
329C2×#95C22×C711yescharacteristic
330C2×#95C22×C711yescharacteristic
331C2×#95C22×C711yescharacteristic
332C2×#95C22×C711yescharacteristic
333C2×#95C22×C711yescharacteristic
334C23×C7—22no—
335C23×C7—22no—
336C23×C7—22no—
337C23×C7—22no—
338C23×C7—22no—
339C23×C7—22no—
340C23×C7—22no—
341C23×C7—22no—
342C23×C7—22no—
343C23×C7—22no—
344C23×C7—22no—
345C23×C7—22no—
346C23×C7—22no—
347C23×C7—22no—
348C23×C7—22no—
349C23×C7—22no—
350C23×C7—22no—
351C23×C7—22no—
352C23×C7—41no—
353C23×C7—41no—
354C23×C7—41no—
355C23×C7—41no—
356C23×C7—41no—
357C23×C7—41no—
358C23×C7—41no—
359C23×C7—41no—
360C23×C7—41no—
361C23×C7—41no—
362C23×C7—41no—
363C23×C7—41no—
364C23×C7—41no—
365C23×C7—41no—
366C23×C7—41no—
367C23×C7—41no—
368C23×C7#12014yes—
369C23×C7C22×D411yescharacteristic
370C23×C7C22×D411yescharacteristic
371C23×C7C22×D411yescharacteristic
372C23×C7C2×#4111yescharacteristic
373C23×C7C2×#4111yescharacteristic
374C23×C7C2×#4111yescharacteristic
375C23×C7C2×#4111yescharacteristic
376C23×C7C2×#4111yescharacteristic
377C23×C7C2×#4111yescharacteristic
378C23×C7H(5,𝔽2)11yescharacteristic
379C23×C7H(5,𝔽2)11yescharacteristic
380C23×C72−1+411yescharacteristic
381C23×C72−1+411yescharacteristic
382C23×C72−1+411yescharacteristic
383C23×C72−1+411yescharacteristic
384C2×C4×C7—22no—
385C2×C4×C7—22no—
386C2×C4×C7—22no—
387C2×C4×C7—22no—
388C2×C4×C7—22no—
389C2×C4×C7—22no—
390C2×C4×C7—22no—
391C2×C4×C7—22no—
392C2×C4×C7—22no—
393C2×C4×C7—22no—
394C2×C4×C7—22no—
395C2×C4×C7—22no—
396C2×C4×C7—22no—
397C2×C4×C7—22no—
398C2×C4×C7—22no—
399C2×C4×C7—22no—
400C2×C4×C7—22no—
401C2×C4×C7—22no—
402C2×C4×C7—22no—
403C2×C4×C7—22no—
404C2×C4×C7—22no—
405C2×C4×C7—22no—
406C2×C4×C7—22no—
407C2×C4×C7—22no—
408C2×C4×C7—22no—
409C2×C4×C7—22no—
410C2×C4×C7—22no—
411C2×C4×C7—22no—
412C2×C4×C7—22no—
413C2×C4×C7—22no—
414C2×C4×C7—22no—
415C2×C4×C7—22no—
416C2×C4×C7—22no—
417C2×C4×C7—416no—
418C2×C4×C7—41no—
419C2×C4×C7—41no—
420C2×C4×C7—41no—
421C2×C4×C7—41no—
422C2×C4×C7—41no—
423C2×C4×C7—41no—
424C2×C4×C7—41no—
425C2×C4×C7—41no—
426C2×C4×C7—41no—
427C2×C4×C7—41no—
428C2×C4×C7—41no—
429C2×C4×C7—41no—
430C2×C4×C7—41no—
431C2×C4×C7—41no—
432C2×C4×C7—41no—
433C2×C4×C7—41no—
434C2×C4×C7—41no—
435C2×C4×C7—41no—
436C2×C4×C7—41no—
437C2×C4×C7—41no—
438C2×C4×C7—41no—
439C2×C4×C7—41no—
440C2×C4×C7—41no—
441C2×C4×C7—41no—
442C2×C4×C7—41no—
443C2×C4×C7—41no—
444C2×C4×C7—41no—
445C2×C4×C7—41no—
446C2×C4×C7—41no—
447C2×C4×C7—41no—
448C2×C4×C7—41no—
449C2×C4×C7—41no—
450C2×C4×C7—41no—
451C2×C4×C7—41no—
452C2×C4×C7—41no—
453C2×C4×C7—41no—
454C2×C4×C7—41no—
455C2×C4×C7—41no—
456C2×C4×C7—41no—
457C2×C4×C7—41no—
458C2×C4×C7—41no—
459C2×C4×C7—41no—
460C2×C4×C7—41no—
461C2×C4×C7—41no—
462C2×C4×C7—41no—
463C2×C4×C7—41no—
464C2×C4×C7—41no—
465C2×C4×C7—41no—
466C2×C4×C7—41no—
467C2×C4×C7—41no—
468C2×C4×C7—41no—
469C2×C4×C7—41no—
470C2×C4×C7—41no—
471C2×C4×C7—41no—
472C2×C4×C7—41no—
473C2×C4×C7—41no—
474C2×C4×C7—41no—
475C2×C4×C7—41no—
476C2×C4×C7—41no—
477C2×C4×C7—41no—
478C2×C4×C7—41no—
479C2×C4×C7—41no—
480C2×C4×C7—41no—
481C2×C4×C7—41no—
482C2×C4×C7#12614yescomplemented
483C25C23×C711yescharacteristic
484C23×C4—22no—
485C23×C4—22no—
486C23×C4—22no—
487C23×C4—22no—
488C23×C4—22no—
489C23×C4—41no—
490C23×C4—41no—
491C23×C4C23×C711yescharacteristic
492C23×C4C23×C711yescharacteristic
493C23×C4C23×C711yescharacteristic
494C23×C4C23×C711yescharacteristic
495C23×C4C23×C711yescharacteristic
496C23×C4C23×C711yescharacteristic
497C23×C4C23×C711yescharacteristic
498C23×C4C23×C711yescharacteristic
499C23×C4C23×C711yescharacteristic
500C23×C4C23×C711yescharacteristic
501C23×C4C23×C711yescharacteristic
502C23×C4C23×C711yescharacteristic
503C23×C4C23×C711yescharacteristic
504C23×C4C23×C711yescharacteristic
505#126—232no—
506C2×C4⋊C4—22no—
507C2×C4⋊C4—22no—
508C2×C4⋊C4—22no—
509C2×C4⋊C4—22no—
510C2×C4⋊C4—22no—
511C2×C4⋊C4—22no—
512C2×C4⋊C4—22no—
513C2×C4⋊C4—22no—
514C2×C4⋊C4—22no—
515C2×C4⋊C4—22no—
516C2×C4⋊C4—22no—
517C2×C4⋊C4—22no—
518C2×C4⋊C4—22no—
519C2×C4⋊C4—22no—
520C2×C4⋊C4—22no—
521C2×C4⋊C4—22no—
522C2×C4⋊C4—22no—
523C2×C4⋊C4—41no—
524C2×C4⋊C4—41no—
525C2×C4⋊C4—41no—
526C2×C4⋊C4—41no—
527C2×C22⋊C4—22no—
528C2×C22⋊C4—22no—
529C2×C22⋊C4—22no—
530C2×C22⋊C4—22no—
531C2×C22⋊C4—22no—
532C2×C22⋊C4—22no—
533C2×C22⋊C4—22no—
534C2×C22⋊C4—22no—
535C2×C22⋊C4—22no—
536C2×C22⋊C4—22no—
537C2×C22⋊C4—22no—
538C2×C22⋊C4—22no—
539C2×C22⋊C4—22no—
540C2×C22⋊C4—41no—
541C2×C22⋊C4—41no—
542C2×C22⋊C4C7×D414yes—
543C2×C22⋊C4C7×D414yes—
544C2×C22⋊C4C7×D414yes—
545C2×C42—22no—
546C2×C42—22no—
547C2×C42—22no—
548#95—22no—
549#95—22no—
550#95—22no—
551#95—22no—
552#95—22no—
553#95—22no—
554#95—22no—
555#95—22no—
556#95—22no—
557#95—22no—
558#95—22no—
559#95—22no—
560#95—22no—
561#95—22no—
562#95—22no—
563#95—22no—
564#95—41no—
565#95—41no—
566#95—41no—
567#95—41no—
568C22×C7—24no—
569C22×C7—24no—
570C22×C7—24no—
571C22×C7—42no—
572C22×C7—42no—
573C22×C7—42no—
574C22×C7—42no—
575C22×C7—42no—
576C22×C7—42no—
577C22×C7—42no—
578C22×C7—42no—
579C22×C7—42no—
580C22×C7—42no—
581C22×C7—42no—
582C22×C7—42no—
583C22×C7C2×#12011yescharacteristic
584C22×C7#52511yescharacteristic
585C22×C7C2×#12611yescharacteristic
586C22×C7#52911yescharacteristic
587C22×C7#53211yescharacteristic
588C22×C7#53211yescharacteristic
589C22×C7#53611yescharacteristic
590C22×C7#53711yescharacteristic
591C22×C7#53711yescharacteristic
592C22×C7#53811yescharacteristic
593C22×C7#53911yescharacteristic
594C22×C7#54111yescharacteristic
595C22×C7#54111yescharacteristic
596C22×C7#54111yescharacteristic
597C22×C7#54211yescharacteristic
598C22×C7#54611yescharacteristic
599C22×C7#54611yescharacteristic
600C22×C7#54611yescharacteristic
601C22×C7#54611yescharacteristic
602C22×C7#54711yescharacteristic
603C22×C7#54711yescharacteristic
604C22×C7#54711yescharacteristic
605C22×C7#54711yescharacteristic
606C22×C7#54711yescharacteristic
607C22×C7#54711yescharacteristic
608C22×C7#54711yescharacteristic
609C22×C7#54711yescharacteristic
610C22×C7#55111yescharacteristic
611C22×C7#55111yescharacteristic
612C22×C7#55211yescharacteristic
613C22×C7#55211yescharacteristic
614C22×C7#55611yescharacteristic
615C22×C7#55611yescharacteristic
616C22×C7#56311yescharacteristic
617C22×C7#56311yescharacteristic
618C4×C7—24no—
619C4×C7—42no—
620C4×C7—42no—
621C4×C7—42no—
622C4×C7—42no—
623C4×C7—42no—
624C4×C7—42no—
625C4×C7—42no—
626C4×C7—42no—
627C4×C7—42no—
628C4×C7—81no—
629C4×C7—81no—
630C4×C7—81no—
631C4×C7—81no—
632C24—21no—
633C24—21no—
634C24—21no—
635C24—21no—
636C24—21no—
637C24—21no—
638C24—21no—
639C24—21no—
640C24—21no—
641C24—21no—
642C24—21no—
643C24—21no—
644C24C2×C7×D412yes—
645C24C2×C7×D412yes—
646C24C2×C7×D412yes—
647C24C24×C711yescharacteristic
648C22×C4—21no—
649C22×C4—21no—
650C22×C4—21no—
651C22×C4—21no—
652C22×C4—28no—
653C22×C4—21no—
654C22×C4—21no—
655C22×C4—21no—
656C22×C4—21no—
657C22×C4—21no—
658C22×C4—21no—
659C22×C4—21no—
660C22×C4—21no—
661C22×C4—21no—
662C22×C4—21no—
663C22×C4—21no—
664C22×C4—21no—
665C22×C4—21no—
666C22×C4—21no—
667C22×C4—21no—
668C22×C4—21no—
669C22×C4—21no—
670C22×C4—21no—
671C22×C4—21no—
672C22×C4—21no—
673C22×C4—21no—
674C22×C4—21no—
675C22×C4—21no—
676C22×C4—21no—
677C22×C4—21no—
678C22×C4—21no—
679C22×C4—21no—
680C22×C4—21no—
681C22×C4—21no—
682C22×C4—21no—
683C22×C4—21no—
684C22×C4—21no—
685C22×C4—21no—
686C22×C4—21no—
687C22×C4—21no—
688C22×C4—21no—
689C22×C4—21no—
690C22×C4—21no—
691C22×C4—21no—
692C22×C4—21no—
693C22×C4—21no—
694C22×C4—21no—
695C22×C4—21no—
696C22×C4—21no—
697C22×C4—21no—
698C22×C4—21no—
699C22×C4—21no—
700C22×C4—21no—
701C22×C4—21no—
702C22×C4—21no—
703C22×C4—21no—
704C22×C4—21no—
705C22×C4—21no—
706C22×C4—21no—
707C22×C4—21no—
708C22×C4—21no—
709C22×C4—21no—
710C22×C4—21no—
711C22×C4—21no—
712C22×C4—21no—
713C22×C4—21no—
714C22×C4—21no—
715C22×C4—21no—
716C22×C4—21no—
717C22×C4—21no—
718C22×C4—21no—
719C22×C4—21no—
720C22×C4—21no—
721C22×C4—21no—
722C22×C4—21no—
723C22×C4—21no—
724C22×C4—21no—
725C22×C4—21no—
726C22×C4—21no—
727C22×C4—21no—
728C22×C4—21no—
729C22×C4—21no—
730C22×C4—21no—
731C22×C4—21no—
732C22×C4—21no—
733C22×C4—21no—
734C22×C4—21no—
735C22×C4—44no—
736C22×C4—44no—
737C22×C4—44no—
738C22×C4—44no—
739C22×C4—44no—
740C22×C4—44no—
741C22×C4C2×C7×D412yes—
742C22×C4C2×C7×D412yes—
743C22×C4C2×C7×D412yes—
744C22×C4C2×C7×D412yes—
745C22×C4C2×C7×D412yes—
746C22×C4C2×C7×D412yes—
747C22×C4C7×#4112yes—
748C22×C4C7×#4112yes—
749C22×C4C7×#4112yes—
750C22×C4C7×#4112yes—
751C22×C4C7×#4112yes—
752C22×C4C7×#4112yes—
753C4⋊C4—28no—
754C4⋊C4—28no—
755C4⋊C4—28no—
756C4⋊C4—44no—
757C4⋊C4—44no—
758C4⋊C4—44no—
759C4⋊C4—44no—
760C22⋊C4—28no—
761C22⋊C4—28no—
762C22⋊C4—28no—
763C22⋊C4—44no—
764C22⋊C4—44no—
765C22⋊C4—44no—
766C42—28no—
767C2×C7—44no—
768C2×C7#240611yescharacteristic
769C2×C7#243011yescharacteristic
770C2×C7#243011yescharacteristic
771C2×C7#247811yescharacteristic
772C2×C7#248011yescharacteristic
773C2×C7#249611yescharacteristic
774C2×C7#249611yescharacteristic
775C2×C7#252111yescharacteristic
776C2×C7#255311yescharacteristic
777C2×C7#268911yescharacteristic
778C2×C7#269511yescharacteristic
779C2×C7#269811yescharacteristic
780C2×C7#271511yescharacteristic
781C2×C7#272211yescharacteristic
782C2×C7#272211yescharacteristic
783C23—22no—
784C23—22no—
785C23—22no—
786C23—22no—
787C23—22no—
788C23—22no—
789C23—22no—
790C23—22no—
791C23—22no—
792C23—22no—
793C23—22no—
794C23—22no—
795C23—22no—
796C23—22no—
797C23—22no—
798C23—22no—
799C23—22no—
800C23—22no—
801C23—41no—
802C23—41no—
803C23—41no—
804C23—41no—
805C23—41no—
806C23—41no—
807C23—41no—
808C23—41no—
809C23—41no—
810C23—41no—
811C23—41no—
812C23—41no—
813C23—41no—
814C23—41no—
815C23—41no—
816C23—41no—
817C23C7×#12014yes—
818C23C22×C7×D411yescharacteristic
819C23C22×C7×D411yescharacteristic
820C23C22×C7×D411yescharacteristic
821C23C2×C7×#4111yescharacteristic
822C23C2×C7×#4111yescharacteristic
823C23C2×C7×#4111yescharacteristic
824C23C2×C7×#4111yescharacteristic
825C23C2×C7×#4111yescharacteristic
826C23C2×C7×#4111yescharacteristic
827C23C7×H(5,𝔽2)11yescharacteristic
828C23C7×H(5,𝔽2)11yescharacteristic
829C23C7×2−1+411yescharacteristic
830C23C7×2−1+411yescharacteristic
831C23C7×2−1+411yescharacteristic
832C23C7×2−1+411yescharacteristic
833C2×C4—22no—
834C2×C4—22no—
835C2×C4—22no—
836C2×C4—22no—
837C2×C4—22no—
838C2×C4—22no—
839C2×C4—22no—
840C2×C4—22no—
841C2×C4—22no—
842C2×C4—22no—
843C2×C4—22no—
844C2×C4—22no—
845C2×C4—22no—
846C2×C4—22no—
847C2×C4—22no—
848C2×C4—22no—
849C2×C4—22no—
850C2×C4—22no—
851C2×C4—22no—
852C2×C4—22no—
853C2×C4—22no—
854C2×C4—22no—
855C2×C4—22no—
856C2×C4—22no—
857C2×C4—22no—
858C2×C4—22no—
859C2×C4—22no—
860C2×C4—22no—
861C2×C4—22no—
862C2×C4—22no—
863C2×C4—22no—
864C2×C4—22no—
865C2×C4—22no—
866C2×C4—416no—
867C2×C4—41no—
868C2×C4—41no—
869C2×C4—41no—
870C2×C4—41no—
871C2×C4—41no—
872C2×C4—41no—
873C2×C4—41no—
874C2×C4—41no—
875C2×C4—41no—
876C2×C4—41no—
877C2×C4—41no—
878C2×C4—41no—
879C2×C4—41no—
880C2×C4—41no—
881C2×C4—41no—
882C2×C4—41no—
883C2×C4—41no—
884C2×C4—41no—
885C2×C4—41no—
886C2×C4—41no—
887C2×C4—41no—
888C2×C4—41no—
889C2×C4—41no—
890C2×C4—41no—
891C2×C4—41no—
892C2×C4—41no—
893C2×C4—41no—
894C2×C4—41no—
895C2×C4—41no—
896C2×C4—41no—
897C2×C4—41no—
898C2×C4—41no—
899C2×C4—41no—
900C2×C4—41no—
901C2×C4—41no—
902C2×C4—41no—
903C2×C4—41no—
904C2×C4—41no—
905C2×C4—41no—
906C2×C4—41no—
907C2×C4—41no—
908C2×C4—41no—
909C2×C4—41no—
910C2×C4—41no—
911C2×C4—41no—
912C2×C4—41no—
913C2×C4—41no—
914C2×C4—41no—
915C2×C4—41no—
916C2×C4—41no—
917C2×C4—41no—
918C2×C4—41no—
919C2×C4—41no—
920C2×C4—41no—
921C2×C4—41no—
922C2×C4—41no—
923C2×C4—41no—
924C2×C4—41no—
925C2×C4—41no—
926C2×C4—41no—
927C2×C4—41no—
928C2×C4—41no—
929C2×C4—41no—
930C2×C4—41no—
931C2×C4C7×#12614yescomplemented
932C7#1591111yescharacteristic, direct product factor, Sylow
933C22—24no—
934C22—24no—
935C22—24no—
936C22—42no—
937C22—42no—
938C22—42no—
939C22—42no—
940C22—42no—
941C22—42no—
942C22—42no—
943C22—42no—
944C22—42no—
945C22—42no—
946C22—42no—
947C22—42no—
948C22C2×C7×#12011yescharacteristic
949C22C7×#52511yescharacteristic
950C22C2×C7×#12611yescharacteristic
951C22C7×#52911yescharacteristic
952C22C7×#53211yescharacteristic
953C22C7×#53211yescharacteristic
954C22C7×#53611yescharacteristic
955C22C7×#53711yescharacteristic
956C22C7×#53711yescharacteristic
957C22C7×#53811yescharacteristic
958C22C7×#53911yescharacteristic
959C22C7×#54111yescharacteristic
960C22C7×#54111yescharacteristic
961C22C7×#54111yescharacteristic
962C22C7×#54211yescharacteristic
963C22C7×#54611yescharacteristic
964C22C7×#54611yescharacteristic
965C22C7×#54611yescharacteristic
966C22C7×#54611yescharacteristic
967C22C7×#54711yescharacteristic
968C22C7×#54711yescharacteristic
969C22C7×#54711yescharacteristic
970C22C7×#54711yescharacteristic
971C22C7×#54711yescharacteristic
972C22C7×#54711yescharacteristic
973C22C7×#54711yescharacteristic
974C22C7×#54711yescharacteristic
975C22C7×#55111yescharacteristic
976C22C7×#55111yescharacteristic
977C22C7×#55211yescharacteristic
978C22C7×#55211yescharacteristic
979C22C7×#55611yescharacteristic
980C22C7×#55611yescharacteristic
981C22C7×#56311yescharacteristic
982C22C7×#56311yescharacteristic
983C4—24no—
984C4—42no—
985C4—42no—
986C4—42no—
987C4—42no—
988C4—42no—
989C4—42no—
990C4—42no—
991C4—42no—
992C4—42no—
993C4—81no—
994C4—81no—
995C4—81no—
996C4—81no—
997C2—44no—
998C2C7×#240611yescharacteristic
999C2C7×#243011yescharacteristic
1000C2C7×#243011yescharacteristic
1001C2C7×#247811yescharacteristic
1002C2C7×#248011yescharacteristic
1003C2C7×#249611yescharacteristic
1004C2C7×#249611yescharacteristic
1005C2C7×#252111yescharacteristic
1006C2C7×#255311yescharacteristic
1007C2C7×#268911yescharacteristic
1008C2C7×#269511yescharacteristic
1009C2C7×#269811yescharacteristic
1010C2C7×#271511yescharacteristic
1011C2C7×#272211yescharacteristic
1012C2C7×#272211yescharacteristic
subgroupG/H
center, socleC24×C7C24
commutator, Frattini, cosocleC24C24×C7
prime radicalC25×C7C23
LCSG ▷ C24 ▷ C1
UCSC1 ◁ C24×C7 ◁ G

Complements

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

NH ≅ G/Ntype
5. C7×#1444C2semidirect
6. C7×#1444C2semidirect
7. C7×#1442C2semidirect
8. C7×#1442C2semidirect
9. C7×#1441C2semidirect
10. C7×#1441C2semidirect
12. C7×#1436C2semidirect
13. C7×#1436C2semidirect
57. #15911C7direct (N × H)
147. #1444C2×C7semidirect
148. #1444C2×C7semidirect
149. #1442C2×C7semidirect
150. #1442C2×C7semidirect
151. #1441C2×C7semidirect
152. #1441C2×C7semidirect
154. #1436C2×C7semidirect
155. #1436C2×C7semidirect
482. C2×C4×C7#126semidirect
931. C2×C4C7×#126semidirect
932. C7#15911direct (N × H)

Maximal subgroups

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

subgroupindex
C22×C7×#1262
C2×C7×#3972
C2×C7×#3802
C7×#14442
C7×#14422
C7×#14412
C7×#14402
C7×#14362
C7×C22⋊#952
#159117