Finite Group Databasebeta

← C7×#15921 #13193137

Subgroups — C7×#15921 #13193137

Order 1792.

1746 conjugacy classes of subgroups.

The subgroup lattice has 1144 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C7×#394C211yesmaximal, characteristic
2C2×C7×#388C211yesmaximal, characteristic, complemented
3C2×C7×#386C211yesmaximal, characteristic
4C2×C7×#381C211yesmaximal, characteristic, complemented
5C7×#1443C211yesmaximal, characteristic, complemented
6C7×#1441C211yesmaximal, characteristic, complemented
7C7×#1441C211yesmaximal, characteristic, complemented
8C7×#1440C211yesmaximal, characteristic, complemented
9C7×#1439C211yesmaximal, characteristic, complemented
10C7×#1439C211yesmaximal, characteristic, complemented
11C7×#1439C211yesmaximal, characteristic, complemented
12C7×#1438C211yesmaximal, characteristic
13C7×#1437C211yesmaximal, characteristic, complemented
14C7×#1434C211yesmaximal, characteristic, complemented
15C7×C22⋊#95C211yesmaximal, characteristic, complemented
16C23×C7×D4C2211yescharacteristic
17C24×C4×C7C2211yescharacteristic
18C22×C7×C4⋊C4C2211yescharacteristic
19C22×C7×C4⋊C4C2211yescharacteristic
20C22×C7×C4⋊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×C7×C22⋊C4C2211yescharacteristic
28C22×C7×C22⋊C4C2211yescharacteristic
29C22×C7×C22⋊C4C2211yescharacteristic
30C22×C7×C22⋊C4C2211yescharacteristic
31C22×C7×C22⋊C4C2211yescharacteristic
32C22×C42×C7C2211yescharacteristic
33C7×#394—24no—
34C7×#388—24no—
35C7×#386—24no—
36C7×#381—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
55#15921C711yesmaximal, characteristic, direct product factor, Sylow
56C25×C7C2311yescharacteristic
57C25×C7C2311yescharacteristic
58C22×C7×D4—22no—
59C22×C7×D4—22no—
60C22×C7×D4—22no—
61C22×C7×D4—22no—
62C22×C7×D4—22no—
63C22×C7×D4—41no—
64C22×C7×D4—41no—
65C23×C4×C7—22no—
66C23×C4×C7—22no—
67C23×C4×C7—22no—
68C23×C4×C7—22no—
69C23×C4×C7—22no—
70C23×C4×C7—41no—
71C23×C4×C7—41no—
72C23×C4×C7C2311yescharacteristic
73C23×C4×C7C2311yescharacteristic
74C23×C4×C7C2311yescharacteristic
75C23×C4×C7C2311yescharacteristic
76C23×C4×C7C2311yescharacteristic
77C23×C4×C7C2311yescharacteristic
78C23×C4×C7C2311yescharacteristic
79C23×C4×C7C2311yescharacteristic
80C23×C4×C7C2311yescharacteristic
81C23×C4×C7C2311yescharacteristic
82C23×C4×C7C2311yescharacteristic
83C23×C4×C7C2311yescharacteristic
84C23×C4×C7C2311yescharacteristic
85C2×C7×C4⋊C4—22no—
86C2×C7×C4⋊C4—22no—
87C2×C7×C4⋊C4—22no—
88C2×C7×C4⋊C4—22no—
89C2×C7×C4⋊C4—41no—
90C2×C7×C4⋊C4—41no—
91C2×C7×C4⋊C4—41no—
92C2×C7×C4⋊C4—41no—
93C2×C7×C4⋊C4—41no—
94C2×C7×C22⋊C4—22no—
95C2×C7×C22⋊C4—22no—
96C2×C7×C22⋊C4—22no—
97C2×C7×C22⋊C4—22no—
98C2×C7×C22⋊C4—22no—
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—41no—
112C2×C7×C22⋊C4—41no—
113C2×C7×C22⋊C4—41no—
114C2×C7×C22⋊C4—41no—
115C2×C7×C22⋊C4—41no—
116C2×C7×C22⋊C4—41no—
117C2×C7×C22⋊C4—41no—
118C2×C7×C22⋊C4—41no—
119C2×C7×C22⋊C4—41no—
120C2×C7×C22⋊C4—41no—
121C2×C7×C22⋊C4—41no—
122C2×C7×C22⋊C4—41no—
123C2×C7×C22⋊C4—41no—
124C2×C7×C22⋊C4—41no—
125C2×C7×C22⋊C4D414yes—
126C2×C7×C22⋊C4D414yes—
127C2×C42×C7—22no—
128C2×C42×C7—22no—
129C2×C42×C7—41no—
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—22no—
140C7×#95—22no—
141C7×#95—22no—
142C7×#95—41no—
143C7×#95—41no—
144C7×#95—41no—
145C7×#95—41no—
146C7×#95—41no—
147C7×#95—41no—
148C2×#394C2×C711yescharacteristic
149C2×#388C2×C711yescharacteristic, complemented
150C2×#386C2×C711yescharacteristic
151C2×#381C2×C711yescharacteristic, complemented
152#1443C2×C711yescharacteristic, complemented
153#1441C2×C711yescharacteristic, complemented
154#1441C2×C711yescharacteristic, complemented
155#1440C2×C711yescharacteristic, complemented
156#1439C2×C711yescharacteristic, complemented
157#1439C2×C711yescharacteristic, complemented
158#1439C2×C711yescharacteristic, complemented
159#1438C2×C711yescharacteristic
160#1437C2×C711yescharacteristic, complemented
161#1434C2×C711yescharacteristic, complemented
162C22⋊#95C2×C711yescharacteristic, complemented
163C24×C7—21no—
164C24×C7—21no—
165C24×C7—21no—
166C24×C7—21no—
167C24×C7—21no—
168C24×C7—21no—
169C24×C7—21no—
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×C7C2×D412yes—
190C24×C7C2×D412yes—
191C24×C7#4112yes—
192C24×C7#4112yes—
193C24×C7C2411yescharacteristic
194C2×C7×D4—28no—
195C2×C7×D4—44no—
196C2×C7×D4—44no—
197C2×C7×D4—44no—
198C2×C7×D4—44no—
199C2×C7×D4—44no—
200C2×C7×D4—44no—
201C22×C4×C7—28no—
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—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—44no—
285C22×C4×C7—44no—
286C22×C4×C7—44no—
287C22×C4×C7—44no—
288C22×C4×C7—44no—
289C22×C4×C7—44no—
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—44no—
300C7×C4⋊C4—44no—
301C7×C4⋊C4—44no—
302C7×C22⋊C4—28no—
303C7×C22⋊C4—44no—
304C7×C22⋊C4—44no—
305C7×C22⋊C4—44no—
306C7×C22⋊C4—44no—
307C7×C22⋊C4—44no—
308C7×C22⋊C4—44no—
309C7×C22⋊C4—44no—
310C7×C22⋊C4—44no—
311C7×C22⋊C4—44no—
312C7×C22⋊C4—44no—
313C42×C7—44no—
314C23×D4C22×C711yescharacteristic
315C24×C4C22×C711yescharacteristic
316C22×C4⋊C4C22×C711yescharacteristic
317C22×C4⋊C4C22×C711yescharacteristic
318C22×C4⋊C4C22×C711yescharacteristic
319C22×C22⋊C4C22×C711yescharacteristic
320C22×C22⋊C4C22×C711yescharacteristic
321C22×C22⋊C4C22×C711yescharacteristic
322C22×C22⋊C4C22×C711yescharacteristic
323C22×C22⋊C4C22×C711yescharacteristic
324C22×C22⋊C4C22×C711yescharacteristic
325C22×C22⋊C4C22×C711yescharacteristic
326C22×C22⋊C4C22×C711yescharacteristic
327C22×C22⋊C4C22×C711yescharacteristic
328C22×C22⋊C4C22×C711yescharacteristic
329C22×C22⋊C4C22×C711yescharacteristic
330C22×C42C22×C711yescharacteristic
331#394—24no—
332#388—24no—
333#386—24no—
334#381—24no—
335C2×#95C22×C711yescharacteristic
336C2×#95C22×C711yescharacteristic
337C2×#95C22×C711yescharacteristic
338C2×#95C22×C711yescharacteristic
339C2×#95C22×C711yescharacteristic
340C2×#95C22×C711yescharacteristic
341C2×#95C22×C711yescharacteristic
342C2×#95C22×C711yescharacteristic
343C2×#95C22×C711yescharacteristic
344C2×#95C22×C711yescharacteristic
345C2×#95C22×C711yescharacteristic
346C2×#95C22×C711yescharacteristic
347C2×#95C22×C711yescharacteristic
348C2×#95C22×C711yescharacteristic
349C2×#95C22×C711yescharacteristic
350C2×#95C22×C711yescharacteristic
351C2×#95C22×C711yescharacteristic
352C2×#95C22×C711yescharacteristic
353C23×C7—22no—
354C23×C7—22no—
355C23×C7—22no—
356C23×C7—22no—
357C23×C7—22no—
358C23×C7—22no—
359C23×C7—22no—
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—22no—
375C23×C7—22no—
376C23×C7—22no—
377C23×C7—22no—
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#12114yes—
423C23×C7C22×D411yescharacteristic
424C23×C7C22×D411yescharacteristic
425C23×C7C2×#4111yescharacteristic
426C23×C7C2×#4111yescharacteristic
427C23×C7C2×#4111yescharacteristic
428C23×C7C2×#4111yescharacteristic
429C23×C7C2×#4111yescharacteristic
430C23×C7C2×#4111yescharacteristic
431C23×C7C2×#4111yescharacteristic
432C23×C7H(5,𝔽2)11yescharacteristic
433C23×C7H(5,𝔽2)11yescharacteristic
434C23×C7H(5,𝔽2)11yescharacteristic
435C23×C7H(5,𝔽2)11yescharacteristic
436C23×C7H(5,𝔽2)11yescharacteristic
437C23×C72−1+411yescharacteristic
438C7×D4—416no—
439C2×C4×C7—22no—
440C2×C4×C7—22no—
441C2×C4×C7—22no—
442C2×C4×C7—22no—
443C2×C4×C7—22no—
444C2×C4×C7—22no—
445C2×C4×C7—22no—
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—416no—
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—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—
531C25C23×C711yescharacteristic
532C25C23×C711yescharacteristic
533C22×D4—22no—
534C22×D4—22no—
535C22×D4—22no—
536C22×D4—22no—
537C22×D4—22no—
538C22×D4—41no—
539C22×D4—41no—
540C23×C4—22no—
541C23×C4—22no—
542C23×C4—22no—
543C23×C4—22no—
544C23×C4—22no—
545C23×C4—41no—
546C23×C4—41no—
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
559C23×C4C23×C711yescharacteristic
560C2×C4⋊C4—22no—
561C2×C4⋊C4—22no—
562C2×C4⋊C4—22no—
563C2×C4⋊C4—22no—
564C2×C4⋊C4—41no—
565C2×C4⋊C4—41no—
566C2×C4⋊C4—41no—
567C2×C4⋊C4—41no—
568C2×C4⋊C4—41no—
569C2×C22⋊C4—22no—
570C2×C22⋊C4—22no—
571C2×C22⋊C4—22no—
572C2×C22⋊C4—22no—
573C2×C22⋊C4—22no—
574C2×C22⋊C4—22no—
575C2×C22⋊C4—22no—
576C2×C22⋊C4—22no—
577C2×C22⋊C4—22no—
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—41no—
587C2×C22⋊C4—41no—
588C2×C22⋊C4—41no—
589C2×C22⋊C4—41no—
590C2×C22⋊C4—41no—
591C2×C22⋊C4—41no—
592C2×C22⋊C4—41no—
593C2×C22⋊C4—41no—
594C2×C22⋊C4—41no—
595C2×C22⋊C4—41no—
596C2×C22⋊C4—41no—
597C2×C22⋊C4—41no—
598C2×C22⋊C4—41no—
599C2×C22⋊C4—41no—
600C2×C22⋊C4C7×D414yes—
601C2×C22⋊C4C7×D414yes—
602C2×C42—22no—
603C2×C42—22no—
604C2×C42—41no—
605#95—22no—
606#95—22no—
607#95—22no—
608#95—22no—
609#95—22no—
610#95—22no—
611#95—22no—
612#95—22no—
613#95—22no—
614#95—22no—
615#95—22no—
616#95—22no—
617#95—41no—
618#95—41no—
619#95—41no—
620#95—41no—
621#95—41no—
622#95—41no—
623C22×C7—24no—
624C22×C7—24no—
625C22×C7—24no—
626C22×C7—42no—
627C22×C7—42no—
628C22×C7—42no—
629C22×C7—42no—
630C22×C7—42no—
631C22×C7—42no—
632C22×C7—42no—
633C22×C7—42no—
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—81no—
646C22×C7—81no—
647C22×C7—81no—
648C22×C7—81no—
649C22×C7—81no—
650C22×C7—81no—
651C22×C7—81no—
652C22×C7—81no—
653C22×C7C2×#12111yescharacteristic
654C22×C7#52511yescharacteristic
655C22×C7#52511yescharacteristic
656C22×C7#52911yescharacteristic
657C22×C7#52911yescharacteristic
658C22×C7#52911yescharacteristic
659C22×C7#53411yescharacteristic
660C22×C7#53511yescharacteristic
661C22×C7#53811yescharacteristic
662C22×C7#53911yescharacteristic
663C22×C7#53911yescharacteristic
664C22×C7#54011yescharacteristic
665C22×C7#54011yescharacteristic
666C22×C7#54011yescharacteristic
667C22×C7#54211yescharacteristic
668C22×C7#54611yescharacteristic
669C22×C7#54611yescharacteristic
670C22×C7#54611yescharacteristic
671C22×C7#54611yescharacteristic
672C22×C7#54611yescharacteristic
673C22×C7#54611yescharacteristic
674C22×C7#54711yescharacteristic
675C22×C7#54711yescharacteristic
676C22×C7#55111yescharacteristic
677C22×C7#55111yescharacteristic
678C22×C7#55111yescharacteristic
679C22×C7#55111yescharacteristic
680C22×C7#55111yescharacteristic
681C22×C7#55311yescharacteristic
682C22×C7#55311yescharacteristic
683C22×C7#55511yescharacteristic
684C22×C7#55511yescharacteristic
685C22×C7#55611yescharacteristic
686C22×C7#56011yescharacteristic
687C22×C7#56211yescharacteristic
688C4×C7—42no—
689C4×C7—42no—
690C4×C7—42no—
691C4×C7—42no—
692C4×C7—42no—
693C4×C7—42no—
694C4×C7—42no—
695C4×C7—42no—
696C4×C7—42no—
697C4×C7—81no—
698C4×C7—81no—
699C4×C7—81no—
700C4×C7—81no—
701C24—21no—
702C24—21no—
703C24—21no—
704C24—21no—
705C24—21no—
706C24—21no—
707C24—21no—
708C24—21no—
709C24—21no—
710C24—21no—
711C24—21no—
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—
727C24C2×C7×D412yes—
728C24C2×C7×D412yes—
729C24C7×#4112yes—
730C24C7×#4112yes—
731C24C24×C711yescharacteristic
732C2×D4—28no—
733C2×D4—44no—
734C2×D4—44no—
735C2×D4—44no—
736C2×D4—44no—
737C2×D4—44no—
738C2×D4—44no—
739C22×C4—28no—
740C22×C4—21no—
741C22×C4—21no—
742C22×C4—21no—
743C22×C4—21no—
744C22×C4—21no—
745C22×C4—21no—
746C22×C4—21no—
747C22×C4—21no—
748C22×C4—21no—
749C22×C4—21no—
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—44no—
823C22×C4—44no—
824C22×C4—44no—
825C22×C4—44no—
826C22×C4—44no—
827C22×C4—44no—
828C22×C4C2×C7×D412yes—
829C22×C4C2×C7×D412yes—
830C22×C4C2×C7×D412yes—
831C22×C4C2×C7×D412yes—
832C22×C4C7×#4112yes—
833C22×C4C7×#4112yes—
834C22×C4C7×#4112yes—
835C22×C4C7×#4112yes—
836C22×C4C7×#4112yes—
837C4⋊C4—44no—
838C4⋊C4—44no—
839C4⋊C4—44no—
840C22⋊C4—28no—
841C22⋊C4—44no—
842C22⋊C4—44no—
843C22⋊C4—44no—
844C22⋊C4—44no—
845C22⋊C4—44no—
846C22⋊C4—44no—
847C22⋊C4—44no—
848C22⋊C4—44no—
849C22⋊C4—44no—
850C22⋊C4—44no—
851C42—44no—
852C2×C7—44no—
853C2×C7—82no—
854C2×C7#241111yescharacteristic
855C2×C7#242511yescharacteristic
856C2×C7#245711yescharacteristic
857C2×C7#246611yescharacteristic
858C2×C7#247411yescharacteristic
859C2×C7#247611yescharacteristic
860C2×C7#252611yescharacteristic
861C2×C7#253411yescharacteristic
862C2×C7#257211yescharacteristic
863C2×C7#268611yescharacteristic
864C2×C7#269911yescharacteristic
865C2×C7#270311yescharacteristic
866C2×C7#270611yescharacteristic
867C2×C7#274011yescharacteristic
868C2×C7#274611yescharacteristic
869C23—22no—
870C23—22no—
871C23—22no—
872C23—22no—
873C23—22no—
874C23—22no—
875C23—22no—
876C23—22no—
877C23—22no—
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—22no—
893C23—22no—
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—
938C23C7×#12114yes—
939C23C22×C7×D411yescharacteristic
940C23C22×C7×D411yescharacteristic
941C23C2×C7×#4111yescharacteristic
942C23C2×C7×#4111yescharacteristic
943C23C2×C7×#4111yescharacteristic
944C23C2×C7×#4111yescharacteristic
945C23C2×C7×#4111yescharacteristic
946C23C2×C7×#4111yescharacteristic
947C23C2×C7×#4111yescharacteristic
948C23C7×H(5,𝔽2)11yescharacteristic
949C23C7×H(5,𝔽2)11yescharacteristic
950C23C7×H(5,𝔽2)11yescharacteristic
951C23C7×H(5,𝔽2)11yescharacteristic
952C23C7×H(5,𝔽2)11yescharacteristic
953C23C7×2−1+411yescharacteristic
954D4—416no—
955C2×C4—22no—
956C2×C4—22no—
957C2×C4—22no—
958C2×C4—22no—
959C2×C4—22no—
960C2×C4—22no—
961C2×C4—22no—
962C2×C4—22no—
963C2×C4—22no—
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—416no—
983C2×C4—41no—
984C2×C4—41no—
985C2×C4—41no—
986C2×C4—41no—
987C2×C4—41no—
988C2×C4—41no—
989C2×C4—41no—
990C2×C4—41no—
991C2×C4—41no—
992C2×C4—41no—
993C2×C4—41no—
994C2×C4—41no—
995C2×C4—41no—
996C2×C4—41no—
997C2×C4—41no—
998C2×C4—41no—
999C2×C4—41no—
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—
1047C7#1592111yescharacteristic, direct product factor, Sylow
1048C22—24no—
1049C22—24no—
1050C22—24no—
1051C22—42no—
1052C22—42no—
1053C22—42no—
1054C22—42no—
1055C22—42no—
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—
1078C22C2×C7×#12111yescharacteristic
1079C22C7×#52511yescharacteristic
1080C22C7×#52511yescharacteristic
1081C22C7×#52911yescharacteristic
1082C22C7×#52911yescharacteristic
1083C22C7×#52911yescharacteristic
1084C22C7×#53411yescharacteristic
1085C22C7×#53511yescharacteristic
1086C22C7×#53811yescharacteristic
1087C22C7×#53911yescharacteristic
1088C22C7×#53911yescharacteristic
1089C22C7×#54011yescharacteristic
1090C22C7×#54011yescharacteristic
1091C22C7×#54011yescharacteristic
1092C22C7×#54211yescharacteristic
1093C22C7×#54611yescharacteristic
1094C22C7×#54611yescharacteristic
1095C22C7×#54611yescharacteristic
1096C22C7×#54611yescharacteristic
1097C22C7×#54611yescharacteristic
1098C22C7×#54611yescharacteristic
1099C22C7×#54711yescharacteristic
1100C22C7×#54711yescharacteristic
1101C22C7×#55111yescharacteristic
1102C22C7×#55111yescharacteristic
1103C22C7×#55111yescharacteristic
1104C22C7×#55111yescharacteristic
1105C22C7×#55111yescharacteristic
1106C22C7×#55311yescharacteristic
1107C22C7×#55311yescharacteristic
1108C22C7×#55511yescharacteristic
1109C22C7×#55511yescharacteristic
1110C22C7×#55611yescharacteristic
1111C22C7×#56011yescharacteristic
1112C22C7×#56211yescharacteristic
1113C4—42no—
1114C4—42no—
1115C4—42no—
1116C4—42no—
1117C4—42no—
1118C4—42no—
1119C4—42no—
1120C4—42no—
1121C4—42no—
1122C4—81no—
1123C4—81no—
1124C4—81no—
1125C4—81no—
1126C2—44no—
1127C2—82no—
1128C2C7×#241111yescharacteristic
1129C2C7×#242511yescharacteristic
1130C2C7×#245711yescharacteristic
1131C2C7×#246611yescharacteristic
1132C2C7×#247411yescharacteristic
1133C2C7×#247611yescharacteristic
1134C2C7×#252611yescharacteristic
1135C2C7×#253411yescharacteristic
1136C2C7×#257211yescharacteristic
1137C2C7×#268611yescharacteristic
1138C2C7×#269911yescharacteristic
1139C2C7×#270311yescharacteristic
1140C2C7×#270611yescharacteristic
1141C2C7×#274011yescharacteristic
1142C2C7×#274611yescharacteristic
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
2. C2×C7×#388C2semidirect
4. C2×C7×#381C2semidirect
5. C7×#1443C2semidirect
6. C7×#1441C2semidirect
7. C7×#1441C2semidirect
8. C7×#1440C2semidirect
9. C7×#1439C2semidirect
10. C7×#1439C2semidirect
11. C7×#1439C2semidirect
13. C7×#1437C2semidirect
14. C7×#1434C2semidirect
15. C7×C22⋊#95C2semidirect
55. #15921C7direct (N × H)
149. C2×#388C2×C7semidirect
151. C2×#381C2×C7semidirect
152. #1443C2×C7semidirect
153. #1441C2×C7semidirect
154. #1441C2×C7semidirect
155. #1440C2×C7semidirect
156. #1439C2×C7semidirect
157. #1439C2×C7semidirect
158. #1439C2×C7semidirect
160. #1437C2×C7semidirect
161. #1434C2×C7semidirect
162. C22⋊#95C2×C7semidirect
1047. C7#15921direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C7×#3942
C2×C7×#3882
C2×C7×#3862
C2×C7×#3812
C7×#14432
C7×#14412
C7×#14402
C7×#14392
C7×#14382
C7×#14372
C7×#14342
C7×C22⋊#952
#159217