Finite Group Databasebeta

← C7×#15943 #13193159

Subgroups — C7×#15943 #13193159

Order 1792.

1278 conjugacy classes of subgroups.

The subgroup lattice has 970 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C7×#396C211yesmaximal, characteristic
2C2×C7×#382C211yesmaximal, characteristic, complemented
3C7×#1445C211yesmaximal, characteristic, complemented
4C7×#1443C211yesmaximal, characteristic, complemented
5C7×#1442C211yesmaximal, characteristic, complemented
6C7×#1441C211yesmaximal, characteristic, complemented
7C7×#1440C211yesmaximal, characteristic
8C7×#1440C211yesmaximal, characteristic
9C7×#1440C211yesmaximal, characteristic
10C7×#1439C211yesmaximal, characteristic
11C7×#1437C211yesmaximal, characteristic
12C7×#1437C211yesmaximal, characteristic
13C7×#1436C211yesmaximal, characteristic, complemented
14C7×#1436C211yesmaximal, characteristic, complemented
15C7×#1434C211yesmaximal, characteristic, complemented
16C22×C7×C4⋊C4C2211yescharacteristic
17C22×C7×C4⋊C4C2211yescharacteristic
18C22×C7×C4⋊C4C2211yescharacteristic
19C22×C7×C4⋊C4C2211yescharacteristic
20C22×C7×C22⋊C4C2211yescharacteristic
21C22×C7×C22⋊C4C2211yescharacteristic
22C22×C7×C22⋊C4C2211yescharacteristic
23C22×C7×C22⋊C4C2211yescharacteristic
24C22×C7×C22⋊C4C2211yescharacteristic
25C22×C7×C22⋊C4C2211yescharacteristic
26C22×C7×C22⋊C4C2211yescharacteristic
27C22×C42×C7C2211yescharacteristic
28C22×C42×C7C2211yescharacteristic
29C7×#396—24no—
30C7×#382—24no—
31C2×C7×#95C2211yescharacteristic
32C2×C7×#95C2211yescharacteristic
33C2×C7×#95C2211yescharacteristic
34C2×C7×#95C2211yescharacteristic
35C2×C7×#95C2211yescharacteristic
36C2×C7×#95C2211yescharacteristic
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
53#15943C711yesmaximal, characteristic, direct product factor, Sylow
54C25×C7C2311yescharacteristic
55C23×C4×C7C2311yescharacteristic
56C23×C4×C7C2311yescharacteristic
57C23×C4×C7C2311yescharacteristic
58C23×C4×C7C2311yescharacteristic
59C23×C4×C7C2311yescharacteristic
60C23×C4×C7C2311yescharacteristic
61C23×C4×C7C2311yescharacteristic
62C23×C4×C7C2311yescharacteristic
63C23×C4×C7C2311yescharacteristic
64C23×C4×C7C2311yescharacteristic
65C23×C4×C7C2311yescharacteristic
66C23×C4×C7C2311yescharacteristic
67C23×C4×C7C2311yescharacteristic
68C23×C4×C7C2311yescharacteristic
69C2×C7×C4⋊C4—22no—
70C2×C7×C4⋊C4—22no—
71C2×C7×C4⋊C4—22no—
72C2×C7×C4⋊C4—22no—
73C2×C7×C4⋊C4—22no—
74C2×C7×C4⋊C4—22no—
75C2×C7×C4⋊C4—41no—
76C2×C7×C4⋊C4—41no—
77C2×C7×C4⋊C4—41no—
78C2×C7×C4⋊C4—41no—
79C2×C7×C4⋊C4—41no—
80C2×C7×C4⋊C4D414yes—
81C2×C7×C22⋊C4—22no—
82C2×C7×C22⋊C4—22no—
83C2×C7×C22⋊C4—22no—
84C2×C7×C22⋊C4—22no—
85C2×C7×C22⋊C4—22no—
86C2×C7×C22⋊C4—22no—
87C2×C7×C22⋊C4—22no—
88C2×C7×C22⋊C4—22no—
89C2×C7×C22⋊C4—22no—
90C2×C7×C22⋊C4—22no—
91C2×C7×C22⋊C4—22no—
92C2×C7×C22⋊C4—22no—
93C2×C7×C22⋊C4—22no—
94C2×C7×C22⋊C4—41no—
95C2×C7×C22⋊C4—41no—
96C2×C7×C22⋊C4—41no—
97C2×C7×C22⋊C4—41no—
98C2×C7×C22⋊C4—41no—
99C2×C7×C22⋊C4—41no—
100C2×C7×C22⋊C4—41no—
101C2×C7×C22⋊C4—41no—
102C2×C42×C7—22no—
103C2×C42×C7—22no—
104C2×C42×C7—22no—
105C2×C42×C7—22no—
106C2×C42×C7—41no—
107C2×C42×C7—41no—
108C7×#95—22no—
109C7×#95—22no—
110C7×#95—22no—
111C7×#95—22no—
112C7×#95—22no—
113C7×#95—22no—
114C7×#95—22no—
115C7×#95—22no—
116C7×#95—22no—
117C7×#95—22no—
118C7×#95—22no—
119C7×#95—22no—
120C7×#95—22no—
121C7×#95—41no—
122C7×#95—41no—
123C7×#95—41no—
124C7×#95—41no—
125C7×#95—41no—
126C7×#95—41no—
127C7×#95—41no—
128C7×#95—41no—
129C7×#95—41no—
130C2×#396C2×C711yescharacteristic
131C2×#382C2×C711yescharacteristic, complemented
132#1445C2×C711yescharacteristic, complemented
133#1443C2×C711yescharacteristic, complemented
134#1442C2×C711yescharacteristic, complemented
135#1441C2×C711yescharacteristic, complemented
136#1440C2×C711yescharacteristic
137#1440C2×C711yescharacteristic
138#1440C2×C711yescharacteristic
139#1439C2×C711yescharacteristic
140#1437C2×C711yescharacteristic
141#1437C2×C711yescharacteristic
142#1436C2×C711yescharacteristic, complemented
143#1436C2×C711yescharacteristic, complemented
144#1434C2×C711yescharacteristic, complemented
145C24×C7—21no—
146C24×C7—21no—
147C24×C7—21no—
148C24×C7—21no—
149C24×C7—21no—
150C24×C7—21no—
151C24×C7—21no—
152C24×C7—21no—
153C24×C7—21no—
154C24×C7—21no—
155C24×C7—21no—
156C24×C7—21no—
157C24×C7—21no—
158C24×C7—21no—
159C24×C7#4112yes—
160C24×C7C2411yescharacteristic
161C22×C4×C7—21no—
162C22×C4×C7—21no—
163C22×C4×C7—21no—
164C22×C4×C7—21no—
165C22×C4×C7—21no—
166C22×C4×C7—21no—
167C22×C4×C7—21no—
168C22×C4×C7—21no—
169C22×C4×C7—21no—
170C22×C4×C7—21no—
171C22×C4×C7—21no—
172C22×C4×C7—21no—
173C22×C4×C7—21no—
174C22×C4×C7—21no—
175C22×C4×C7—21no—
176C22×C4×C7—21no—
177C22×C4×C7—21no—
178C22×C4×C7—21no—
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×C7C2×D412yes—
250C22×C4×C7C2×D412yes—
251C22×C4×C7C2×D412yes—
252C22×C4×C7#4112yes—
253C22×C4×C7#4112yes—
254C22×C4×C7#4112yes—
255C22×C4×C7#4112yes—
256C22×C4×C7#4112yes—
257C22×C4×C7#4112yes—
258C22×C4×C7#4112yes—
259C7×C4⋊C4—44no—
260C7×C4⋊C4—44no—
261C7×C4⋊C4—44no—
262C7×C4⋊C4—44no—
263C7×C22⋊C4—44no—
264C7×C22⋊C4—44no—
265C7×C22⋊C4—44no—
266C7×C22⋊C4—44no—
267C7×C22⋊C4—44no—
268C7×C22⋊C4—44no—
269C7×C22⋊C4—44no—
270C42×C7—28no—
271C42×C7—44no—
272C22×C4⋊C4C22×C711yescharacteristic
273C22×C4⋊C4C22×C711yescharacteristic
274C22×C4⋊C4C22×C711yescharacteristic
275C22×C4⋊C4C22×C711yescharacteristic
276C22×C22⋊C4C22×C711yescharacteristic
277C22×C22⋊C4C22×C711yescharacteristic
278C22×C22⋊C4C22×C711yescharacteristic
279C22×C22⋊C4C22×C711yescharacteristic
280C22×C22⋊C4C22×C711yescharacteristic
281C22×C22⋊C4C22×C711yescharacteristic
282C22×C22⋊C4C22×C711yescharacteristic
283C22×C42C22×C711yescharacteristic
284C22×C42C22×C711yescharacteristic
285#396—24no—
286#382—24no—
287C2×#95C22×C711yescharacteristic
288C2×#95C22×C711yescharacteristic
289C2×#95C22×C711yescharacteristic
290C2×#95C22×C711yescharacteristic
291C2×#95C22×C711yescharacteristic
292C2×#95C22×C711yescharacteristic
293C2×#95C22×C711yescharacteristic
294C2×#95C22×C711yescharacteristic
295C2×#95C22×C711yescharacteristic
296C2×#95C22×C711yescharacteristic
297C2×#95C22×C711yescharacteristic
298C2×#95C22×C711yescharacteristic
299C2×#95C22×C711yescharacteristic
300C2×#95C22×C711yescharacteristic
301C2×#95C22×C711yescharacteristic
302C2×#95C22×C711yescharacteristic
303C2×#95C22×C711yescharacteristic
304C2×#95C22×C711yescharacteristic
305C2×#95C22×C711yescharacteristic
306C2×#95C22×C711yescharacteristic
307C2×#95C22×C711yescharacteristic
308C2×#95C22×C711yescharacteristic
309C23×C7—22no—
310C23×C7—22no—
311C23×C7—22no—
312C23×C7—22no—
313C23×C7—22no—
314C23×C7—22no—
315C23×C7—22no—
316C23×C7—41no—
317C23×C7—41no—
318C23×C7—41no—
319C23×C7—41no—
320C23×C7—41no—
321C23×C7—41no—
322C23×C7—41no—
323C23×C7—41no—
324C23×C7—41no—
325C23×C7—41no—
326C23×C7—41no—
327C23×C7—41no—
328C23×C7—41no—
329C23×C7—41no—
330C23×C7—41no—
331C23×C7—41no—
332C23×C7—41no—
333C23×C7—41no—
334C23×C7—41no—
335C23×C7—41no—
336C23×C7—41no—
337C23×C7—41no—
338C23×C7—41no—
339C23×C7—41no—
340C23×C7—41no—
341C23×C7—41no—
342C23×C7—41no—
343C23×C7—41no—
344C23×C7C22×D411yescharacteristic
345C23×C7C2×#4111yescharacteristic
346C23×C7C2×#4111yescharacteristic
347C23×C7C2×#4111yescharacteristic
348C23×C7C2×#4111yescharacteristic
349C23×C7C2×#4111yescharacteristic
350C23×C7C2×#4111yescharacteristic
351C23×C7C2×#4111yescharacteristic
352C23×C7C2×#4111yescharacteristic
353C23×C7H(5,𝔽2)11yescharacteristic
354C23×C7H(5,𝔽2)11yescharacteristic
355C23×C7H(5,𝔽2)11yescharacteristic
356C23×C7H(5,𝔽2)11yescharacteristic
357C23×C72−1+411yescharacteristic
358C23×C72−1+411yescharacteristic
359C2×C4×C7—22no—
360C2×C4×C7—22no—
361C2×C4×C7—22no—
362C2×C4×C7—22no—
363C2×C4×C7—22no—
364C2×C4×C7—22no—
365C2×C4×C7—22no—
366C2×C4×C7—22no—
367C2×C4×C7—22no—
368C2×C4×C7—22no—
369C2×C4×C7—22no—
370C2×C4×C7—22no—
371C2×C4×C7—22no—
372C2×C4×C7—22no—
373C2×C4×C7—22no—
374C2×C4×C7—22no—
375C2×C4×C7—22no—
376C2×C4×C7—22no—
377C2×C4×C7—22no—
378C2×C4×C7—22no—
379C2×C4×C7—22no—
380C2×C4×C7—22no—
381C2×C4×C7—22no—
382C2×C4×C7—22no—
383C2×C4×C7—22no—
384C2×C4×C7—22no—
385C2×C4×C7—22no—
386C2×C4×C7—41no—
387C2×C4×C7—41no—
388C2×C4×C7—41no—
389C2×C4×C7—41no—
390C2×C4×C7—41no—
391C2×C4×C7—41no—
392C2×C4×C7—41no—
393C2×C4×C7—41no—
394C2×C4×C7—41no—
395C2×C4×C7—41no—
396C2×C4×C7—41no—
397C2×C4×C7—41no—
398C2×C4×C7—41no—
399C2×C4×C7—41no—
400C2×C4×C7—41no—
401C2×C4×C7—41no—
402C2×C4×C7—41no—
403C2×C4×C7—41no—
404C2×C4×C7—41no—
405C2×C4×C7—41no—
406C2×C4×C7—41no—
407C2×C4×C7—41no—
408C2×C4×C7—41no—
409C2×C4×C7—41no—
410C2×C4×C7—41no—
411C2×C4×C7—41no—
412C2×C4×C7—41no—
413C2×C4×C7—41no—
414C2×C4×C7—41no—
415C2×C4×C7—41no—
416C2×C4×C7—41no—
417C2×C4×C7—41no—
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#12414yes—
457C25C23×C711yescharacteristic
458C23×C4C23×C711yescharacteristic
459C23×C4C23×C711yescharacteristic
460C23×C4C23×C711yescharacteristic
461C23×C4C23×C711yescharacteristic
462C23×C4C23×C711yescharacteristic
463C23×C4C23×C711yescharacteristic
464C23×C4C23×C711yescharacteristic
465C23×C4C23×C711yescharacteristic
466C23×C4C23×C711yescharacteristic
467C23×C4C23×C711yescharacteristic
468C23×C4C23×C711yescharacteristic
469C23×C4C23×C711yescharacteristic
470C23×C4C23×C711yescharacteristic
471C23×C4C23×C711yescharacteristic
472C2×C4⋊C4—22no—
473C2×C4⋊C4—22no—
474C2×C4⋊C4—22no—
475C2×C4⋊C4—22no—
476C2×C4⋊C4—22no—
477C2×C4⋊C4—22no—
478C2×C4⋊C4—41no—
479C2×C4⋊C4—41no—
480C2×C4⋊C4—41no—
481C2×C4⋊C4—41no—
482C2×C4⋊C4—41no—
483C2×C4⋊C4C7×D414yes—
484C2×C22⋊C4—22no—
485C2×C22⋊C4—22no—
486C2×C22⋊C4—22no—
487C2×C22⋊C4—22no—
488C2×C22⋊C4—22no—
489C2×C22⋊C4—22no—
490C2×C22⋊C4—22no—
491C2×C22⋊C4—22no—
492C2×C22⋊C4—22no—
493C2×C22⋊C4—22no—
494C2×C22⋊C4—22no—
495C2×C22⋊C4—22no—
496C2×C22⋊C4—22no—
497C2×C22⋊C4—41no—
498C2×C22⋊C4—41no—
499C2×C22⋊C4—41no—
500C2×C22⋊C4—41no—
501C2×C22⋊C4—41no—
502C2×C22⋊C4—41no—
503C2×C22⋊C4—41no—
504C2×C22⋊C4—41no—
505C2×C42—22no—
506C2×C42—22no—
507C2×C42—22no—
508C2×C42—22no—
509C2×C42—41no—
510C2×C42—41no—
511#95—22no—
512#95—22no—
513#95—22no—
514#95—22no—
515#95—22no—
516#95—22no—
517#95—22no—
518#95—22no—
519#95—22no—
520#95—22no—
521#95—22no—
522#95—22no—
523#95—22no—
524#95—41no—
525#95—41no—
526#95—41no—
527#95—41no—
528#95—41no—
529#95—41no—
530#95—41no—
531#95—41no—
532#95—41no—
533C22×C7—42no—
534C22×C7—42no—
535C22×C7—42no—
536C22×C7—42no—
537C22×C7—42no—
538C22×C7—42no—
539C22×C7—42no—
540C22×C7—81no—
541C22×C7—81no—
542C22×C7—81no—
543C22×C7—81no—
544C22×C7—81no—
545C22×C7—81no—
546C22×C7—81no—
547C22×C7—81no—
548C22×C7#52511yescharacteristic
549C22×C7C2×#12411yescharacteristic
550C22×C7#52911yescharacteristic
551C22×C7#52911yescharacteristic
552C22×C7#52911yescharacteristic
553C22×C7#52911yescharacteristic
554C22×C7#53411yescharacteristic
555C22×C7#53811yescharacteristic
556C22×C7#53811yescharacteristic
557C22×C7#54011yescharacteristic
558C22×C7#54111yescharacteristic
559C22×C7#54211yescharacteristic
560C22×C7#54211yescharacteristic
561C22×C7#54211yescharacteristic
562C22×C7#54211yescharacteristic
563C22×C7#54611yescharacteristic
564C22×C7#54711yescharacteristic
565C22×C7#54811yescharacteristic
566C22×C7#55011yescharacteristic
567C22×C7#55111yescharacteristic
568C22×C7#55111yescharacteristic
569C22×C7#55111yescharacteristic
570C22×C7#55211yescharacteristic
571C22×C7#55211yescharacteristic
572C22×C7#55211yescharacteristic
573C22×C7#55211yescharacteristic
574C22×C7#55311yescharacteristic
575C22×C7#55311yescharacteristic
576C22×C7#55311yescharacteristic
577C22×C7#55311yescharacteristic
578C22×C7#55311yescharacteristic
579C22×C7#55311yescharacteristic
580C22×C7#55511yescharacteristic
581C22×C7#56211yescharacteristic
582C22×C7#56211yescharacteristic
583C4×C7—24no—
584C4×C7—42no—
585C4×C7—42no—
586C4×C7—42no—
587C4×C7—42no—
588C4×C7—42no—
589C4×C7—42no—
590C4×C7—42no—
591C4×C7—81no—
592C4×C7—81no—
593C4×C7—81no—
594C4×C7—81no—
595C4×C7—81no—
596C4×C7—81no—
597C24—21no—
598C24—21no—
599C24—21no—
600C24—21no—
601C24—21no—
602C24—21no—
603C24—21no—
604C24—21no—
605C24—21no—
606C24—21no—
607C24—21no—
608C24—21no—
609C24—21no—
610C24—21no—
611C24C7×#4112yes—
612C24C24×C711yescharacteristic
613C22×C4—21no—
614C22×C4—21no—
615C22×C4—21no—
616C22×C4—21no—
617C22×C4—21no—
618C22×C4—21no—
619C22×C4—21no—
620C22×C4—21no—
621C22×C4—21no—
622C22×C4—21no—
623C22×C4—21no—
624C22×C4—21no—
625C22×C4—21no—
626C22×C4—21no—
627C22×C4—21no—
628C22×C4—21no—
629C22×C4—21no—
630C22×C4—21no—
631C22×C4—21no—
632C22×C4—21no—
633C22×C4—21no—
634C22×C4—21no—
635C22×C4—21no—
636C22×C4—21no—
637C22×C4—21no—
638C22×C4—21no—
639C22×C4—21no—
640C22×C4—21no—
641C22×C4—21no—
642C22×C4—21no—
643C22×C4—21no—
644C22×C4—21no—
645C22×C4—21no—
646C22×C4—21no—
647C22×C4—21no—
648C22×C4—21no—
649C22×C4—21no—
650C22×C4—21no—
651C22×C4—21no—
652C22×C4—21no—
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×C4C2×C7×D412yes—
702C22×C4C2×C7×D412yes—
703C22×C4C2×C7×D412yes—
704C22×C4C7×#4112yes—
705C22×C4C7×#4112yes—
706C22×C4C7×#4112yes—
707C22×C4C7×#4112yes—
708C22×C4C7×#4112yes—
709C22×C4C7×#4112yes—
710C22×C4C7×#4112yes—
711C4⋊C4—44no—
712C4⋊C4—44no—
713C4⋊C4—44no—
714C4⋊C4—44no—
715C22⋊C4—44no—
716C22⋊C4—44no—
717C22⋊C4—44no—
718C22⋊C4—44no—
719C22⋊C4—44no—
720C22⋊C4—44no—
721C22⋊C4—44no—
722C42—28no—
723C42—44no—
724C2×C7—82no—
725C2×C7#247711yescharacteristic
726C2×C7#247911yescharacteristic
727C2×C7#248911yescharacteristic
728C2×C7#249011yescharacteristic
729C2×C7#251511yescharacteristic
730C2×C7#251811yescharacteristic
731C2×C7#252911yescharacteristic
732C2×C7#257611yescharacteristic
733C2×C7#259111yescharacteristic
734C2×C7#268611yescharacteristic
735C2×C7#273011yescharacteristic
736C2×C7#276111yescharacteristic
737C2×C7#276111yescharacteristic
738C2×C7#277211yescharacteristic
739C2×C7#277211yescharacteristic
740C23—22no—
741C23—22no—
742C23—22no—
743C23—22no—
744C23—22no—
745C23—22no—
746C23—22no—
747C23—41no—
748C23—41no—
749C23—41no—
750C23—41no—
751C23—41no—
752C23—41no—
753C23—41no—
754C23—41no—
755C23—41no—
756C23—41no—
757C23—41no—
758C23—41no—
759C23—41no—
760C23—41no—
761C23—41no—
762C23—41no—
763C23—41no—
764C23—41no—
765C23—41no—
766C23—41no—
767C23—41no—
768C23—41no—
769C23—41no—
770C23—41no—
771C23—41no—
772C23—41no—
773C23—41no—
774C23—41no—
775C23C22×C7×D411yescharacteristic
776C23C2×C7×#4111yescharacteristic
777C23C2×C7×#4111yescharacteristic
778C23C2×C7×#4111yescharacteristic
779C23C2×C7×#4111yescharacteristic
780C23C2×C7×#4111yescharacteristic
781C23C2×C7×#4111yescharacteristic
782C23C2×C7×#4111yescharacteristic
783C23C2×C7×#4111yescharacteristic
784C23C7×H(5,𝔽2)11yescharacteristic
785C23C7×H(5,𝔽2)11yescharacteristic
786C23C7×H(5,𝔽2)11yescharacteristic
787C23C7×H(5,𝔽2)11yescharacteristic
788C23C7×2−1+411yescharacteristic
789C23C7×2−1+411yescharacteristic
790C2×C4—22no—
791C2×C4—22no—
792C2×C4—22no—
793C2×C4—22no—
794C2×C4—22no—
795C2×C4—22no—
796C2×C4—22no—
797C2×C4—22no—
798C2×C4—22no—
799C2×C4—22no—
800C2×C4—22no—
801C2×C4—22no—
802C2×C4—22no—
803C2×C4—22no—
804C2×C4—22no—
805C2×C4—22no—
806C2×C4—22no—
807C2×C4—22no—
808C2×C4—22no—
809C2×C4—22no—
810C2×C4—22no—
811C2×C4—22no—
812C2×C4—22no—
813C2×C4—22no—
814C2×C4—22no—
815C2×C4—22no—
816C2×C4—22no—
817C2×C4—41no—
818C2×C4—41no—
819C2×C4—41no—
820C2×C4—41no—
821C2×C4—41no—
822C2×C4—41no—
823C2×C4—41no—
824C2×C4—41no—
825C2×C4—41no—
826C2×C4—41no—
827C2×C4—41no—
828C2×C4—41no—
829C2×C4—41no—
830C2×C4—41no—
831C2×C4—41no—
832C2×C4—41no—
833C2×C4—41no—
834C2×C4—41no—
835C2×C4—41no—
836C2×C4—41no—
837C2×C4—41no—
838C2×C4—41no—
839C2×C4—41no—
840C2×C4—41no—
841C2×C4—41no—
842C2×C4—41no—
843C2×C4—41no—
844C2×C4—41no—
845C2×C4—41no—
846C2×C4—41no—
847C2×C4—41no—
848C2×C4—41no—
849C2×C4—41no—
850C2×C4—41no—
851C2×C4—41no—
852C2×C4—41no—
853C2×C4—41no—
854C2×C4—41no—
855C2×C4—41no—
856C2×C4—41no—
857C2×C4—41no—
858C2×C4—41no—
859C2×C4—41no—
860C2×C4—41no—
861C2×C4—41no—
862C2×C4—41no—
863C2×C4—41no—
864C2×C4—41no—
865C2×C4—41no—
866C2×C4—41no—
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×C4C7×#12414yes—
888C7#1594311yescharacteristic, direct product factor, Sylow
889C22—42no—
890C22—42no—
891C22—42no—
892C22—42no—
893C22—42no—
894C22—42no—
895C22—42no—
896C22—81no—
897C22—81no—
898C22—81no—
899C22—81no—
900C22—81no—
901C22—81no—
902C22—81no—
903C22—81no—
904C22C7×#52511yescharacteristic
905C22C2×C7×#12411yescharacteristic
906C22C7×#52911yescharacteristic
907C22C7×#52911yescharacteristic
908C22C7×#52911yescharacteristic
909C22C7×#52911yescharacteristic
910C22C7×#53411yescharacteristic
911C22C7×#53811yescharacteristic
912C22C7×#53811yescharacteristic
913C22C7×#54011yescharacteristic
914C22C7×#54111yescharacteristic
915C22C7×#54211yescharacteristic
916C22C7×#54211yescharacteristic
917C22C7×#54211yescharacteristic
918C22C7×#54211yescharacteristic
919C22C7×#54611yescharacteristic
920C22C7×#54711yescharacteristic
921C22C7×#54811yescharacteristic
922C22C7×#55011yescharacteristic
923C22C7×#55111yescharacteristic
924C22C7×#55111yescharacteristic
925C22C7×#55111yescharacteristic
926C22C7×#55211yescharacteristic
927C22C7×#55211yescharacteristic
928C22C7×#55211yescharacteristic
929C22C7×#55211yescharacteristic
930C22C7×#55311yescharacteristic
931C22C7×#55311yescharacteristic
932C22C7×#55311yescharacteristic
933C22C7×#55311yescharacteristic
934C22C7×#55311yescharacteristic
935C22C7×#55311yescharacteristic
936C22C7×#55511yescharacteristic
937C22C7×#56211yescharacteristic
938C22C7×#56211yescharacteristic
939C4—24no—
940C4—42no—
941C4—42no—
942C4—42no—
943C4—42no—
944C4—42no—
945C4—42no—
946C4—42no—
947C4—81no—
948C4—81no—
949C4—81no—
950C4—81no—
951C4—81no—
952C4—81no—
953C2—82no—
954C2C7×#247711yescharacteristic
955C2C7×#247911yescharacteristic
956C2C7×#248911yescharacteristic
957C2C7×#249011yescharacteristic
958C2C7×#251511yescharacteristic
959C2C7×#251811yescharacteristic
960C2C7×#252911yescharacteristic
961C2C7×#257611yescharacteristic
962C2C7×#259111yescharacteristic
963C2C7×#268611yescharacteristic
964C2C7×#273011yescharacteristic
965C2C7×#276111yescharacteristic
966C2C7×#276111yescharacteristic
967C2C7×#277211yescharacteristic
968C2C7×#277211yescharacteristic
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
2. C2×C7×#382C2semidirect
3. C7×#1445C2semidirect
4. C7×#1443C2semidirect
5. C7×#1442C2semidirect
6. C7×#1441C2semidirect
13. C7×#1436C2semidirect
14. C7×#1436C2semidirect
15. C7×#1434C2semidirect
53. #15943C7direct (N × H)
131. C2×#382C2×C7semidirect
132. #1445C2×C7semidirect
133. #1443C2×C7semidirect
134. #1442C2×C7semidirect
135. #1441C2×C7semidirect
142. #1436C2×C7semidirect
143. #1436C2×C7semidirect
144. #1434C2×C7semidirect
888. C7#15943direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C7×#3962
C2×C7×#3822
C7×#14452
C7×#14432
C7×#14422
C7×#14412
C7×#14402
C7×#14392
C7×#14372
C7×#14362
C7×#14342
#159437