Finite Group Databasebeta

← C7×#15939 #13193155

Subgroups — C7×#15939 #13193155

Order 1792.

1826 conjugacy classes of subgroups.

The subgroup lattice has 1152 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C7×#126C211yesmaximal, characteristic, complemented
2C2×C7×#399C211yesmaximal, characteristic, complemented
3C2×C7×#394C211yesmaximal, characteristic
4C2×C7×#388C211yesmaximal, characteristic, complemented
5C7×#1441C211yesmaximal, characteristic, complemented
6C7×#1441C211yesmaximal, characteristic, complemented
7C7×#1439C211yesmaximal, characteristic, complemented
8C7×#1439C211yesmaximal, characteristic, complemented
9C7×#1439C211yesmaximal, characteristic, complemented
10C7×#1438C211yesmaximal, characteristic
11C7×#1438C211yesmaximal, characteristic
12C7×#1437C211yesmaximal, characteristic, complemented
13C7×#1437C211yesmaximal, characteristic, complemented
14C7×#1436C211yesmaximal, characteristic, complemented
15C7×C4⋊#95C211yesmaximal, characteristic, complemented
16C23×C7×D4C2211yescharacteristic
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×C22⋊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×C7×C22⋊C4C2211yescharacteristic
34C22×C7×C22⋊C4C2211yescharacteristic
35C22×C7×C22⋊C4C2211yescharacteristic
36C22×C7×C22⋊C4C2211yescharacteristic
37C22×C7×C22⋊C4C2211yescharacteristic
38C22×C42×C7C2211yescharacteristic
39C22×C42×C7C2211yescharacteristic
40C7×#399—24no—
41C7×#394—24no—
42C7×#388—24no—
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#15939C711yesmaximal, characteristic, direct product factor, Sylow
58C25×C7C2311yescharacteristic
59C25×C7C2311yescharacteristic
60C22×C7×D4—22no—
61C22×C7×D4—22no—
62C22×C7×D4—22no—
63C22×C7×D4—41no—
64C22×C7×D4—41no—
65C22×C7×D4—41no—
66C22×C7×D4—41no—
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—41no—
95C2×C7×C4⋊C4—41no—
96C2×C7×C4⋊C4—41no—
97C2×C7×C4⋊C4D414yescomplemented
98C2×C7×C4⋊C4D414yescomplemented
99C2×C7×C22⋊C4—22no—
100C2×C7×C22⋊C4—22no—
101C2×C7×C22⋊C4—22no—
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—22no—
116C2×C7×C22⋊C4—22no—
117C2×C7×C22⋊C4—22no—
118C2×C7×C22⋊C4—22no—
119C2×C7×C22⋊C4—22no—
120C2×C7×C22⋊C4—22no—
121C2×C7×C22⋊C4—22no—
122C2×C7×C22⋊C4—22no—
123C2×C7×C22⋊C4—22no—
124C2×C7×C22⋊C4—22no—
125C2×C7×C22⋊C4—22no—
126C2×C7×C22⋊C4—41no—
127C2×C7×C22⋊C4—41no—
128C2×C7×C22⋊C4—41no—
129C2×C7×C22⋊C4—41no—
130C2×C7×C22⋊C4—41no—
131C2×C7×C22⋊C4—41no—
132C2×C7×C22⋊C4—41no—
133C2×C7×C22⋊C4—41no—
134C2×C7×C22⋊C4D414yes—
135C2×C42×C7—22no—
136C2×C42×C7—22no—
137C2×C42×C7—22no—
138C2×C42×C7—22no—
139C2×C42×C7—22no—
140C2×C42×C7—41no—
141C7×#95—22no—
142C7×#95—22no—
143C7×#95—22no—
144C7×#95—22no—
145C7×#95—22no—
146C7×#95—22no—
147C7×#95—41no—
148C7×#95—41no—
149C7×#95—41no—
150C7×#95—41no—
151C7×#95—41no—
152C7×#95—41no—
153C7×#95—41no—
154C7×#95—41no—
155C22×#126C2×C711yescharacteristic, complemented
156C2×#399C2×C711yescharacteristic, complemented
157C2×#394C2×C711yescharacteristic
158C2×#388C2×C711yescharacteristic, complemented
159#1441C2×C711yescharacteristic, complemented
160#1441C2×C711yescharacteristic, complemented
161#1439C2×C711yescharacteristic, complemented
162#1439C2×C711yescharacteristic, complemented
163#1439C2×C711yescharacteristic, complemented
164#1438C2×C711yescharacteristic
165#1438C2×C711yescharacteristic
166#1437C2×C711yescharacteristic, complemented
167#1437C2×C711yescharacteristic, complemented
168#1436C2×C711yescharacteristic, complemented
169C4⋊#95C2×C711yescharacteristic, complemented
170C24×C7—21no—
171C24×C7—21no—
172C24×C7—21no—
173C24×C7—21no—
174C24×C7—21no—
175C24×C7—21no—
176C24×C7—21no—
177C24×C7—21no—
178C24×C7—21no—
179C24×C7—21no—
180C24×C7—21no—
181C24×C7—21no—
182C24×C7—21no—
183C24×C7—21no—
184C24×C7—21no—
185C24×C7—21no—
186C24×C7—21no—
187C24×C7—21no—
188C24×C7—21no—
189C24×C7—21no—
190C24×C7—21no—
191C24×C7—21no—
192C24×C7—21no—
193C24×C7—21no—
194C24×C7—21no—
195C24×C7—21no—
196C24×C7—21no—
197C24×C7—21no—
198C24×C7C2×D412yes—
199C24×C7#4112yes—
200C24×C7C2411yescharacteristic
201C2×C7×D4—44no—
202C2×C7×D4—44no—
203C2×C7×D4—44no—
204C2×C7×D4—44no—
205C2×C7×D4—44no—
206C2×C7×D4—44no—
207C2×C7×D4—44no—
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—21no—
262C22×C4×C7—21no—
263C22×C4×C7—21no—
264C22×C4×C7—21no—
265C22×C4×C7—21no—
266C22×C4×C7—21no—
267C22×C4×C7—21no—
268C22×C4×C7—21no—
269C22×C4×C7—21no—
270C22×C4×C7—21no—
271C22×C4×C7—21no—
272C22×C4×C7—21no—
273C22×C4×C7—21no—
274C22×C4×C7—21no—
275C22×C4×C7—21no—
276C22×C4×C7—21no—
277C22×C4×C7—21no—
278C22×C4×C7—21no—
279C22×C4×C7—21no—
280C22×C4×C7—21no—
281C22×C4×C7—21no—
282C22×C4×C7—21no—
283C22×C4×C7—21no—
284C22×C4×C7—21no—
285C22×C4×C7—21no—
286C22×C4×C7C2×D412yes—
287C22×C4×C7C2×D412yes—
288C22×C4×C7C2×D412yes—
289C22×C4×C7C2×D412yes—
290C22×C4×C7C2×D412yes—
291C22×C4×C7C2×D412yes—
292C22×C4×C7C2×D412yes—
293C22×C4×C7C2×D412yes—
294C22×C4×C7#4112yes—
295C22×C4×C7#4112yes—
296C22×C4×C7#4112yes—
297C22×C4×C7#4112yes—
298C22×C4×C7#4112yes—
299C7×C4⋊C4—28no—
300C7×C4⋊C4—28no—
301C7×C4⋊C4—28no—
302C7×C4⋊C4—44no—
303C7×C4⋊C4—44no—
304C7×C4⋊C4—44no—
305C7×C22⋊C4—28no—
306C7×C22⋊C4—28no—
307C7×C22⋊C4—28no—
308C7×C22⋊C4—28no—
309C7×C22⋊C4—44no—
310C7×C22⋊C4—44no—
311C7×C22⋊C4—44no—
312C7×C22⋊C4—44no—
313C7×C22⋊C4—44no—
314C7×C22⋊C4—44no—
315C7×C22⋊C4—44no—
316C7×C22⋊C4—44no—
317C42×C7—28no—
318C42×C7—44no—
319C23×D4C22×C711yescharacteristic
320C2×#126—24no—
321C2×#126—24no—
322C2×#126—24no—
323C22×C4⋊C4C22×C711yescharacteristic
324C22×C4⋊C4C22×C711yescharacteristic
325C22×C4⋊C4C22×C711yescharacteristic
326C22×C4⋊C4C22×C711yescharacteristic
327C22×C4⋊C4C22×C711yescharacteristic
328C22×C4⋊C4C22×C711yescharacteristic
329C22×C22⋊C4C22×C711yescharacteristic
330C22×C22⋊C4C22×C711yescharacteristic
331C22×C22⋊C4C22×C711yescharacteristic
332C22×C22⋊C4C22×C711yescharacteristic
333C22×C22⋊C4C22×C711yescharacteristic
334C22×C22⋊C4C22×C711yescharacteristic
335C22×C22⋊C4C22×C711yescharacteristic
336C22×C22⋊C4C22×C711yescharacteristic
337C22×C22⋊C4C22×C711yescharacteristic
338C22×C22⋊C4C22×C711yescharacteristic
339C22×C22⋊C4C22×C711yescharacteristic
340C22×C22⋊C4C22×C711yescharacteristic
341C22×C42C22×C711yescharacteristic
342C22×C42C22×C711yescharacteristic
343#399—24no—
344#394—24no—
345#388—24no—
346C2×#95C22×C711yescharacteristic
347C2×#95C22×C711yescharacteristic
348C2×#95C22×C711yescharacteristic
349C2×#95C22×C711yescharacteristic
350C2×#95C22×C711yescharacteristic
351C2×#95C22×C711yescharacteristic
352C2×#95C22×C711yescharacteristic
353C2×#95C22×C711yescharacteristic
354C2×#95C22×C711yescharacteristic
355C2×#95C22×C711yescharacteristic
356C2×#95C22×C711yescharacteristic
357C2×#95C22×C711yescharacteristic
358C2×#95C22×C711yescharacteristic
359C2×#95C22×C711yescharacteristic
360C23×C7—22no—
361C23×C7—22no—
362C23×C7—22no—
363C23×C7—22no—
364C23×C7—22no—
365C23×C7—22no—
366C23×C7—22no—
367C23×C7—22no—
368C23×C7—22no—
369C23×C7—22no—
370C23×C7—22no—
371C23×C7—22no—
372C23×C7—22no—
373C23×C7—22no—
374C23×C7—41no—
375C23×C7—41no—
376C23×C7—41no—
377C23×C7—41no—
378C23×C7—41no—
379C23×C7—41no—
380C23×C7—41no—
381C23×C7—41no—
382C23×C7—41no—
383C23×C7—41no—
384C23×C7—41no—
385C23×C7—41no—
386C23×C7—41no—
387C23×C7—41no—
388C23×C7—41no—
389C23×C7—41no—
390C23×C7—41no—
391C23×C7—41no—
392C23×C7—41no—
393C23×C7—41no—
394C23×C7—41no—
395C23×C7—41no—
396C23×C7—41no—
397C23×C7—41no—
398C23×C7—41no—
399C23×C7—41no—
400C23×C7—41no—
401C23×C7—41no—
402C23×C7—41no—
403C23×C7—41no—
404C23×C7—41no—
405C23×C7—41no—
406C23×C7—41no—
407C23×C7—41no—
408C23×C7—41no—
409C23×C7—41no—
410C23×C7—41no—
411C23×C7—41no—
412C23×C7—41no—
413C23×C7—41no—
414C23×C7—41no—
415C23×C7—41no—
416C23×C7—41no—
417C23×C7—41no—
418C23×C7—41no—
419C23×C7—41no—
420C23×C7—41no—
421C23×C7—41no—
422C23×C7—41no—
423C23×C7—41no—
424C23×C7—41no—
425C23×C7—41no—
426C23×C7—41no—
427C23×C7—41no—
428C23×C7—41no—
429C23×C7—41no—
430C23×C7C22×D411yescharacteristic
431C23×C7C22×D411yescharacteristic
432C23×C7C22×D411yescharacteristic
433C23×C7C2×#4111yescharacteristic
434C23×C7C2×#4111yescharacteristic
435C23×C7C2×#4111yescharacteristic
436C23×C7C2×#4111yescharacteristic
437C23×C7C2×#4111yescharacteristic
438C23×C7C2×#4111yescharacteristic
439C23×C7H(5,𝔽2)11yescharacteristic
440C23×C7H(5,𝔽2)11yescharacteristic
441C23×C7H(5,𝔽2)11yescharacteristic
442C23×C7H(5,𝔽2)11yescharacteristic
443C23×C72−1+411yescharacteristic
444C23×C72−1+411yescharacteristic
445C7×D4—416no—
446C2×C4×C7—22no—
447C2×C4×C7—22no—
448C2×C4×C7—22no—
449C2×C4×C7—22no—
450C2×C4×C7—22no—
451C2×C4×C7—22no—
452C2×C4×C7—22no—
453C2×C4×C7—22no—
454C2×C4×C7—22no—
455C2×C4×C7—22no—
456C2×C4×C7—22no—
457C2×C4×C7—22no—
458C2×C4×C7—22no—
459C2×C4×C7—22no—
460C2×C4×C7—22no—
461C2×C4×C7—22no—
462C2×C4×C7—22no—
463C2×C4×C7—22no—
464C2×C4×C7—22no—
465C2×C4×C7—22no—
466C2×C4×C7—22no—
467C2×C4×C7—22no—
468C2×C4×C7—22no—
469C2×C4×C7—22no—
470C2×C4×C7—22no—
471C2×C4×C7—22no—
472C2×C4×C7—22no—
473C2×C4×C7—22no—
474C2×C4×C7—22no—
475C2×C4×C7—22no—
476C2×C4×C7—22no—
477C2×C4×C7—22no—
478C2×C4×C7—22no—
479C2×C4×C7—22no—
480C2×C4×C7—22no—
481C2×C4×C7—22no—
482C2×C4×C7—41no—
483C2×C4×C7—41no—
484C2×C4×C7—41no—
485C2×C4×C7—41no—
486C2×C4×C7—41no—
487C2×C4×C7—41no—
488C2×C4×C7—41no—
489C2×C4×C7—41no—
490C2×C4×C7—41no—
491C2×C4×C7—41no—
492C2×C4×C7—41no—
493C2×C4×C7—41no—
494C2×C4×C7—41no—
495C2×C4×C7—41no—
496C2×C4×C7—41no—
497C2×C4×C7—41no—
498C2×C4×C7—41no—
499C2×C4×C7—41no—
500C2×C4×C7—41no—
501C2×C4×C7—41no—
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—41no—
515C2×C4×C7—41no—
516C2×C4×C7—41no—
517C2×C4×C7—41no—
518C2×C4×C7—41no—
519C2×C4×C7—41no—
520C2×C4×C7—41no—
521C2×C4×C7—41no—
522C2×C4×C7—41no—
523C2×C4×C7—41no—
524C2×C4×C7—41no—
525C2×C4×C7—41no—
526C2×C4×C7—41no—
527C2×C4×C7—41no—
528C2×C4×C7—41no—
529C2×C4×C7—41no—
530C2×C4×C7—41no—
531C2×C4×C7—41no—
532C2×C4×C7—41no—
533C2×C4×C7—41no—
534C2×C4×C7—41no—
535C2×C4×C7—41no—
536C2×C4×C7#12014yes—
537C25C23×C711yescharacteristic
538C25C23×C711yescharacteristic
539C22×D4—22no—
540C22×D4—22no—
541C22×D4—22no—
542C22×D4—41no—
543C22×D4—41no—
544C22×D4—41no—
545C22×D4—41no—
546C23×C4C23×C711yescharacteristic
547C23×C4C23×C711yescharacteristic
548C23×C4C23×C711yescharacteristic
549C23×C4C23×C711yescharacteristic
550C23×C4C23×C711yescharacteristic
551C23×C4C23×C711yescharacteristic
552C23×C4C23×C711yescharacteristic
553C23×C4C23×C711yescharacteristic
554C23×C4C23×C711yescharacteristic
555C23×C4C23×C711yescharacteristic
556C23×C4C23×C711yescharacteristic
557C23×C4C23×C711yescharacteristic
558C23×C4C23×C711yescharacteristic
559#126—232no—
560C2×C4⋊C4—22no—
561C2×C4⋊C4—22no—
562C2×C4⋊C4—22no—
563C2×C4⋊C4—22no—
564C2×C4⋊C4—22no—
565C2×C4⋊C4—22no—
566C2×C4⋊C4—22no—
567C2×C4⋊C4—22no—
568C2×C4⋊C4—22no—
569C2×C4⋊C4—22no—
570C2×C4⋊C4—22no—
571C2×C4⋊C4—22no—
572C2×C4⋊C4—22no—
573C2×C4⋊C4—41no—
574C2×C4⋊C4—41no—
575C2×C4⋊C4—41no—
576C2×C4⋊C4C7×D414yescomplemented
577C2×C4⋊C4C7×D414yescomplemented
578C2×C22⋊C4—22no—
579C2×C22⋊C4—22no—
580C2×C22⋊C4—22no—
581C2×C22⋊C4—22no—
582C2×C22⋊C4—22no—
583C2×C22⋊C4—22no—
584C2×C22⋊C4—22no—
585C2×C22⋊C4—22no—
586C2×C22⋊C4—22no—
587C2×C22⋊C4—22no—
588C2×C22⋊C4—22no—
589C2×C22⋊C4—22no—
590C2×C22⋊C4—22no—
591C2×C22⋊C4—22no—
592C2×C22⋊C4—22no—
593C2×C22⋊C4—22no—
594C2×C22⋊C4—22no—
595C2×C22⋊C4—22no—
596C2×C22⋊C4—22no—
597C2×C22⋊C4—22no—
598C2×C22⋊C4—22no—
599C2×C22⋊C4—22no—
600C2×C22⋊C4—22no—
601C2×C22⋊C4—22no—
602C2×C22⋊C4—22no—
603C2×C22⋊C4—22no—
604C2×C22⋊C4—22no—
605C2×C22⋊C4—41no—
606C2×C22⋊C4—41no—
607C2×C22⋊C4—41no—
608C2×C22⋊C4—41no—
609C2×C22⋊C4—41no—
610C2×C22⋊C4—41no—
611C2×C22⋊C4—41no—
612C2×C22⋊C4—41no—
613C2×C22⋊C4C7×D414yes—
614C2×C42—22no—
615C2×C42—22no—
616C2×C42—22no—
617C2×C42—22no—
618C2×C42—22no—
619C2×C42—41no—
620#95—22no—
621#95—22no—
622#95—22no—
623#95—22no—
624#95—22no—
625#95—22no—
626#95—41no—
627#95—41no—
628#95—41no—
629#95—41no—
630#95—41no—
631#95—41no—
632#95—41no—
633#95—41no—
634C22×C7—42no—
635C22×C7—42no—
636C22×C7—42no—
637C22×C7—42no—
638C22×C7—42no—
639C22×C7—42no—
640C22×C7—42no—
641C22×C7—42no—
642C22×C7—42no—
643C22×C7—42no—
644C22×C7—42no—
645C22×C7—42no—
646C22×C7—42no—
647C22×C7—42no—
648C22×C7—81no—
649C22×C7—81no—
650C22×C7—81no—
651C22×C7—81no—
652C22×C7—81no—
653C22×C7—81no—
654C22×C7—81no—
655C22×C7—81no—
656C22×C7—81no—
657C22×C7—81no—
658C22×C7—81no—
659C22×C7—81no—
660C22×C7—81no—
661C22×C7—81no—
662C22×C7—81no—
663C22×C7—81no—
664C22×C7C2×#12011yescharacteristic
665C22×C7#52511yescharacteristic
666C22×C7#52911yescharacteristic
667C22×C7#52911yescharacteristic
668C22×C7#53211yescharacteristic
669C22×C7#53211yescharacteristic
670C22×C7#53511yescharacteristic
671C22×C7#53711yescharacteristic
672C22×C7#53711yescharacteristic
673C22×C7#53811yescharacteristic
674C22×C7#53811yescharacteristic
675C22×C7#53911yescharacteristic
676C22×C7#53911yescharacteristic
677C22×C7#54211yescharacteristic
678C22×C7#54211yescharacteristic
679C22×C7#54611yescharacteristic
680C22×C7#54611yescharacteristic
681C22×C7#54611yescharacteristic
682C22×C7#54611yescharacteristic
683C22×C7#54611yescharacteristic
684C22×C7#54711yescharacteristic
685C22×C7#54711yescharacteristic
686C22×C7#54711yescharacteristic
687C22×C7#54811yescharacteristic
688C22×C7#55011yescharacteristic
689C22×C7#55011yescharacteristic
690C22×C7#55011yescharacteristic
691C22×C7#55111yescharacteristic
692C22×C7#55111yescharacteristic
693C22×C7#55111yescharacteristic
694C22×C7#55211yescharacteristic
695C22×C7#55311yescharacteristic
696C22×C7#55611yescharacteristic
697C22×C7#56011yescharacteristic
698C22×C7#56311yescharacteristic
699C4×C7—24no—
700C4×C7—42no—
701C4×C7—42no—
702C4×C7—42no—
703C4×C7—42no—
704C4×C7—42no—
705C4×C7—42no—
706C4×C7—42no—
707C4×C7—42no—
708C4×C7—42no—
709C4×C7—42no—
710C4×C7—81no—
711C4×C7—81no—
712C24—21no—
713C24—21no—
714C24—21no—
715C24—21no—
716C24—21no—
717C24—21no—
718C24—21no—
719C24—21no—
720C24—21no—
721C24—21no—
722C24—21no—
723C24—21no—
724C24—21no—
725C24—21no—
726C24—21no—
727C24—21no—
728C24—21no—
729C24—21no—
730C24—21no—
731C24—21no—
732C24—21no—
733C24—21no—
734C24—21no—
735C24—21no—
736C24—21no—
737C24—21no—
738C24—21no—
739C24—21no—
740C24C2×C7×D412yes—
741C24C7×#4112yes—
742C24C24×C711yescharacteristic
743C2×D4—44no—
744C2×D4—44no—
745C2×D4—44no—
746C2×D4—44no—
747C2×D4—44no—
748C2×D4—44no—
749C2×D4—44no—
750C22×C4—21no—
751C22×C4—21no—
752C22×C4—21no—
753C22×C4—21no—
754C22×C4—21no—
755C22×C4—21no—
756C22×C4—21no—
757C22×C4—21no—
758C22×C4—21no—
759C22×C4—21no—
760C22×C4—21no—
761C22×C4—21no—
762C22×C4—21no—
763C22×C4—21no—
764C22×C4—21no—
765C22×C4—21no—
766C22×C4—21no—
767C22×C4—21no—
768C22×C4—21no—
769C22×C4—21no—
770C22×C4—21no—
771C22×C4—21no—
772C22×C4—21no—
773C22×C4—21no—
774C22×C4—21no—
775C22×C4—21no—
776C22×C4—21no—
777C22×C4—21no—
778C22×C4—21no—
779C22×C4—21no—
780C22×C4—21no—
781C22×C4—21no—
782C22×C4—21no—
783C22×C4—21no—
784C22×C4—21no—
785C22×C4—21no—
786C22×C4—21no—
787C22×C4—21no—
788C22×C4—21no—
789C22×C4—21no—
790C22×C4—21no—
791C22×C4—21no—
792C22×C4—21no—
793C22×C4—21no—
794C22×C4—21no—
795C22×C4—21no—
796C22×C4—21no—
797C22×C4—21no—
798C22×C4—21no—
799C22×C4—21no—
800C22×C4—21no—
801C22×C4—21no—
802C22×C4—21no—
803C22×C4—21no—
804C22×C4—21no—
805C22×C4—21no—
806C22×C4—21no—
807C22×C4—21no—
808C22×C4—21no—
809C22×C4—21no—
810C22×C4—21no—
811C22×C4—21no—
812C22×C4—21no—
813C22×C4—21no—
814C22×C4—21no—
815C22×C4—21no—
816C22×C4—21no—
817C22×C4—21no—
818C22×C4—21no—
819C22×C4—21no—
820C22×C4—21no—
821C22×C4—21no—
822C22×C4—21no—
823C22×C4—21no—
824C22×C4—21no—
825C22×C4—21no—
826C22×C4—21no—
827C22×C4—21no—
828C22×C4C2×C7×D412yes—
829C22×C4C2×C7×D412yes—
830C22×C4C2×C7×D412yes—
831C22×C4C2×C7×D412yes—
832C22×C4C2×C7×D412yes—
833C22×C4C2×C7×D412yes—
834C22×C4C2×C7×D412yes—
835C22×C4C2×C7×D412yes—
836C22×C4C7×#4112yes—
837C22×C4C7×#4112yes—
838C22×C4C7×#4112yes—
839C22×C4C7×#4112yes—
840C22×C4C7×#4112yes—
841C4⋊C4—28no—
842C4⋊C4—28no—
843C4⋊C4—28no—
844C4⋊C4—44no—
845C4⋊C4—44no—
846C4⋊C4—44no—
847C22⋊C4—28no—
848C22⋊C4—28no—
849C22⋊C4—28no—
850C22⋊C4—28no—
851C22⋊C4—44no—
852C22⋊C4—44no—
853C22⋊C4—44no—
854C22⋊C4—44no—
855C22⋊C4—44no—
856C22⋊C4—44no—
857C22⋊C4—44no—
858C22⋊C4—44no—
859C42—28no—
860C42—44no—
861C2×C7—82no—
862C2×C7—82no—
863C2×C7#240711yescharacteristic
864C2×C7#243011yescharacteristic
865C2×C7#243111yescharacteristic
866C2×C7#246711yescharacteristic
867C2×C7#247911yescharacteristic
868C2×C7#252111yescharacteristic
869C2×C7#255311yescharacteristic
870C2×C7#255411yescharacteristic
871C2×C7#256011yescharacteristic
872C2×C7#268511yescharacteristic
873C2×C7#270211yescharacteristic
874C2×C7#270511yescharacteristic
875C2×C7#270511yescharacteristic
876C2×C7#271811yescharacteristic
877C2×C7#272711yescharacteristic
878C23—22no—
879C23—22no—
880C23—22no—
881C23—22no—
882C23—22no—
883C23—22no—
884C23—22no—
885C23—22no—
886C23—22no—
887C23—22no—
888C23—22no—
889C23—22no—
890C23—22no—
891C23—22no—
892C23—41no—
893C23—41no—
894C23—41no—
895C23—41no—
896C23—41no—
897C23—41no—
898C23—41no—
899C23—41no—
900C23—41no—
901C23—41no—
902C23—41no—
903C23—41no—
904C23—41no—
905C23—41no—
906C23—41no—
907C23—41no—
908C23—41no—
909C23—41no—
910C23—41no—
911C23—41no—
912C23—41no—
913C23—41no—
914C23—41no—
915C23—41no—
916C23—41no—
917C23—41no—
918C23—41no—
919C23—41no—
920C23—41no—
921C23—41no—
922C23—41no—
923C23—41no—
924C23—41no—
925C23—41no—
926C23—41no—
927C23—41no—
928C23—41no—
929C23—41no—
930C23—41no—
931C23—41no—
932C23—41no—
933C23—41no—
934C23—41no—
935C23—41no—
936C23—41no—
937C23—41no—
938C23—41no—
939C23—41no—
940C23—41no—
941C23—41no—
942C23—41no—
943C23—41no—
944C23—41no—
945C23—41no—
946C23—41no—
947C23—41no—
948C23C22×C7×D411yescharacteristic
949C23C22×C7×D411yescharacteristic
950C23C22×C7×D411yescharacteristic
951C23C2×C7×#4111yescharacteristic
952C23C2×C7×#4111yescharacteristic
953C23C2×C7×#4111yescharacteristic
954C23C2×C7×#4111yescharacteristic
955C23C2×C7×#4111yescharacteristic
956C23C2×C7×#4111yescharacteristic
957C23C7×H(5,𝔽2)11yescharacteristic
958C23C7×H(5,𝔽2)11yescharacteristic
959C23C7×H(5,𝔽2)11yescharacteristic
960C23C7×H(5,𝔽2)11yescharacteristic
961C23C7×2−1+411yescharacteristic
962C23C7×2−1+411yescharacteristic
963D4—416no—
964C2×C4—22no—
965C2×C4—22no—
966C2×C4—22no—
967C2×C4—22no—
968C2×C4—22no—
969C2×C4—22no—
970C2×C4—22no—
971C2×C4—22no—
972C2×C4—22no—
973C2×C4—22no—
974C2×C4—22no—
975C2×C4—22no—
976C2×C4—22no—
977C2×C4—22no—
978C2×C4—22no—
979C2×C4—22no—
980C2×C4—22no—
981C2×C4—22no—
982C2×C4—22no—
983C2×C4—22no—
984C2×C4—22no—
985C2×C4—22no—
986C2×C4—22no—
987C2×C4—22no—
988C2×C4—22no—
989C2×C4—22no—
990C2×C4—22no—
991C2×C4—22no—
992C2×C4—22no—
993C2×C4—22no—
994C2×C4—22no—
995C2×C4—22no—
996C2×C4—22no—
997C2×C4—22no—
998C2×C4—22no—
999C2×C4—22no—
1000C2×C4—41no—
1001C2×C4—41no—
1002C2×C4—41no—
1003C2×C4—41no—
1004C2×C4—41no—
1005C2×C4—41no—
1006C2×C4—41no—
1007C2×C4—41no—
1008C2×C4—41no—
1009C2×C4—41no—
1010C2×C4—41no—
1011C2×C4—41no—
1012C2×C4—41no—
1013C2×C4—41no—
1014C2×C4—41no—
1015C2×C4—41no—
1016C2×C4—41no—
1017C2×C4—41no—
1018C2×C4—41no—
1019C2×C4—41no—
1020C2×C4—41no—
1021C2×C4—41no—
1022C2×C4—41no—
1023C2×C4—41no—
1024C2×C4—41no—
1025C2×C4—41no—
1026C2×C4—41no—
1027C2×C4—41no—
1028C2×C4—41no—
1029C2×C4—41no—
1030C2×C4—41no—
1031C2×C4—41no—
1032C2×C4—41no—
1033C2×C4—41no—
1034C2×C4—41no—
1035C2×C4—41no—
1036C2×C4—41no—
1037C2×C4—41no—
1038C2×C4—41no—
1039C2×C4—41no—
1040C2×C4—41no—
1041C2×C4—41no—
1042C2×C4—41no—
1043C2×C4—41no—
1044C2×C4—41no—
1045C2×C4—41no—
1046C2×C4—41no—
1047C2×C4—41no—
1048C2×C4—41no—
1049C2×C4—41no—
1050C2×C4—41no—
1051C2×C4—41no—
1052C2×C4—41no—
1053C2×C4—41no—
1054C2×C4C7×#12014yes—
1055C7#1593911yescharacteristic, direct product factor, Sylow
1056C22—42no—
1057C22—42no—
1058C22—42no—
1059C22—42no—
1060C22—42no—
1061C22—42no—
1062C22—42no—
1063C22—42no—
1064C22—42no—
1065C22—42no—
1066C22—42no—
1067C22—42no—
1068C22—42no—
1069C22—42no—
1070C22—81no—
1071C22—81no—
1072C22—81no—
1073C22—81no—
1074C22—81no—
1075C22—81no—
1076C22—81no—
1077C22—81no—
1078C22—81no—
1079C22—81no—
1080C22—81no—
1081C22—81no—
1082C22—81no—
1083C22—81no—
1084C22—81no—
1085C22—81no—
1086C22C2×C7×#12011yescharacteristic
1087C22C7×#52511yescharacteristic
1088C22C7×#52911yescharacteristic
1089C22C7×#52911yescharacteristic
1090C22C7×#53211yescharacteristic
1091C22C7×#53211yescharacteristic
1092C22C7×#53511yescharacteristic
1093C22C7×#53711yescharacteristic
1094C22C7×#53711yescharacteristic
1095C22C7×#53811yescharacteristic
1096C22C7×#53811yescharacteristic
1097C22C7×#53911yescharacteristic
1098C22C7×#53911yescharacteristic
1099C22C7×#54211yescharacteristic
1100C22C7×#54211yescharacteristic
1101C22C7×#54611yescharacteristic
1102C22C7×#54611yescharacteristic
1103C22C7×#54611yescharacteristic
1104C22C7×#54611yescharacteristic
1105C22C7×#54611yescharacteristic
1106C22C7×#54711yescharacteristic
1107C22C7×#54711yescharacteristic
1108C22C7×#54711yescharacteristic
1109C22C7×#54811yescharacteristic
1110C22C7×#55011yescharacteristic
1111C22C7×#55011yescharacteristic
1112C22C7×#55011yescharacteristic
1113C22C7×#55111yescharacteristic
1114C22C7×#55111yescharacteristic
1115C22C7×#55111yescharacteristic
1116C22C7×#55211yescharacteristic
1117C22C7×#55311yescharacteristic
1118C22C7×#55611yescharacteristic
1119C22C7×#56011yescharacteristic
1120C22C7×#56311yescharacteristic
1121C4—24no—
1122C4—42no—
1123C4—42no—
1124C4—42no—
1125C4—42no—
1126C4—42no—
1127C4—42no—
1128C4—42no—
1129C4—42no—
1130C4—42no—
1131C4—42no—
1132C4—81no—
1133C4—81no—
1134C2—82no—
1135C2—82no—
1136C2C7×#240711yescharacteristic
1137C2C7×#243011yescharacteristic
1138C2C7×#243111yescharacteristic
1139C2C7×#246711yescharacteristic
1140C2C7×#247911yescharacteristic
1141C2C7×#252111yescharacteristic
1142C2C7×#255311yescharacteristic
1143C2C7×#255411yescharacteristic
1144C2C7×#256011yescharacteristic
1145C2C7×#268511yescharacteristic
1146C2C7×#270211yescharacteristic
1147C2C7×#270511yescharacteristic
1148C2C7×#270511yescharacteristic
1149C2C7×#271811yescharacteristic
1150C2C7×#272711yescharacteristic
subgroupG/H
center, socleC24×C7C24
commutator, Frattini, cosocleC24C24×C7
prime radicalC23×C7×D4C22
LCSG ▷ C24 ▷ C1
UCSC1 ◁ C24×C7 ◁ G

Complements

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

NH ≅ G/Ntype
1. C22×C7×#126C2semidirect
2. C2×C7×#399C2semidirect
4. C2×C7×#388C2semidirect
5. C7×#1441C2semidirect
6. C7×#1441C2semidirect
7. C7×#1439C2semidirect
8. C7×#1439C2semidirect
9. C7×#1439C2semidirect
12. C7×#1437C2semidirect
13. C7×#1437C2semidirect
14. C7×#1436C2semidirect
15. C7×C4⋊#95C2semidirect
57. #15939C7direct (N × H)
97. C2×C7×C4⋊C4D4semidirect
98. C2×C7×C4⋊C4D4semidirect
155. C22×#126C2×C7semidirect
156. C2×#399C2×C7semidirect
158. C2×#388C2×C7semidirect
159. #1441C2×C7semidirect
160. #1441C2×C7semidirect
161. #1439C2×C7semidirect
162. #1439C2×C7semidirect
163. #1439C2×C7semidirect
166. #1437C2×C7semidirect
167. #1437C2×C7semidirect
168. #1436C2×C7semidirect
169. C4⋊#95C2×C7semidirect
576. C2×C4⋊C4C7×D4semidirect
577. C2×C4⋊C4C7×D4semidirect
1055. C7#15939direct (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×#3992
C2×C7×#3942
C2×C7×#3882
C7×#14412
C7×#14392
C7×#14382
C7×#14372
C7×#14362
C7×C4⋊#952
#159397