Finite Group Databasebeta

← C7×#14032 #13191248

Subgroups — C7×#14032 #13191248

Order 1792.

1702 conjugacy classes of subgroups.

The subgroup lattice has 1010 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C7×#388C211yesmaximal, characteristic
2C2×C7×#387C211yesmaximal, characteristic, complemented
3C2×C7×#385C211yesmaximal, characteristic
4C2×C4×C7×C4⋊C4C211yesmaximal, characteristic, complemented
5C2×C4×C7×C22⋊C4C211yesmaximal, characteristic
6C7×#1442C211yesmaximal, characteristic, complemented
7C7×#1442C211yesmaximal, characteristic, complemented
8C7×#1440C211yesmaximal, characteristic
9C7×#1439C211yesmaximal, characteristic
10C7×#1437C211yesmaximal, characteristic
11C7×#1436C211yesmaximal, characteristic, complemented
12C7×#1436C211yesmaximal, characteristic, complemented
13C7×#1434C211yesmaximal, characteristic, complemented
14C7×#1434C211yesmaximal, characteristic, complemented
15C7×C22⋊#95C211yesmaximal, characteristic
16C24×C4×C7C2211yescharacteristic
17C22×C7×C4⋊C4C2211yescharacteristic
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×C42×C7C2211yescharacteristic
28C22×C42×C7C2211yescharacteristic
29C22×C42×C7C2211yescharacteristic
30C22×C42×C7C2211yescharacteristic
31C7×#388C418yescomplemented
32C7×#387—24no—
33C7×#385—24no—
34C4×C7×C4⋊C4—24no—
35C4×C7×C22⋊C4—24no—
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
53C2×C7×#95C2211yescharacteristic
54C2×C7×#95C2211yescharacteristic
55C2×C7×#95C2211yescharacteristic
56#14032C711yesmaximal, characteristic, direct product factor, Sylow
57C25×C7C2311yescharacteristic
58C23×C4×C7—22no—
59C23×C4×C7—22no—
60C23×C4×C7—22no—
61C23×C4×C7—22no—
62C23×C4×C7—22no—
63C23×C4×C7—41no—
64C23×C4×C7—41no—
65C23×C4×C7C2311yescharacteristic
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
79C2×C7×C4⋊C4—22no—
80C2×C7×C4⋊C4—22no—
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—41no—
89C2×C7×C4⋊C4C2×C414yescomplemented
90C2×C7×C4⋊C4D414yes—
91C2×C7×C22⋊C4—22no—
92C2×C7×C22⋊C4—22no—
93C2×C7×C22⋊C4—22no—
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—41no—
105C2×C7×C22⋊C4—41no—
106C2×C7×C22⋊C4C2×C414yes—
107C2×C7×C22⋊C4C2×C414yes—
108C2×C7×C22⋊C4C2×C414yes—
109C2×C42×C7—22no—
110C2×C42×C7—22no—
111C2×C42×C7—22no—
112C2×C42×C7—22no—
113C2×C42×C7—22no—
114C2×C42×C7—22no—
115C2×C42×C7—22no—
116C2×C42×C7—22no—
117C2×C42×C7—41no—
118C2×C42×C7—41no—
119C2×C42×C7—41no—
120C2×C42×C7C2×C414yescomplemented
121C7×#95—22no—
122C7×#95—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—41no—
135C7×#95—41no—
136C7×#95—41no—
137C7×#95—41no—
138C7×#95C2×C414yescomplemented
139C7×#95C2×C414yescomplemented
140C7×#95D414yes—
141C2×#388C2×C711yescharacteristic
142C2×#387C2×C711yescharacteristic, complemented
143C2×#385C2×C711yescharacteristic
144C2×C4×C4⋊C4C2×C711yescharacteristic, complemented
145C2×C4×C22⋊C4C2×C711yescharacteristic
146#1442C2×C711yescharacteristic, complemented
147#1442C2×C711yescharacteristic, complemented
148#1440C2×C711yescharacteristic
149#1439C2×C711yescharacteristic
150#1437C2×C711yescharacteristic
151#1436C2×C711yescharacteristic, complemented
152#1436C2×C711yescharacteristic, complemented
153#1434C2×C711yescharacteristic, complemented
154#1434C2×C711yescharacteristic, complemented
155C22⋊#95C2×C711yescharacteristic
156C24×C7—21no—
157C24×C7—21no—
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×C7C22×C412yes—
169C24×C7#4112yes—
170C24×C7#4112yes—
171C24×C7C2411yescharacteristic
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—28no—
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—44no—
254C22×C4×C7—44no—
255C22×C4×C7—44no—
256C22×C4×C7—44no—
257C22×C4×C7—44no—
258C22×C4×C7—44no—
259C22×C4×C7C22×C412yes—
260C22×C4×C7C22×C412yes—
261C22×C4×C7C22×C412yes—
262C22×C4×C7C22×C412yes—
263C22×C4×C7C22×C412yes—
264C22×C4×C7C22×C412yes—
265C22×C4×C7C2×D412yes—
266C22×C4×C7C2×D412yes—
267C22×C4×C7C2×D412yes—
268C22×C4×C7C2×D412yes—
269C22×C4×C7C2×D412yes—
270C22×C4×C7C2×D412yes—
271C22×C4×C7#4112yes—
272C22×C4×C7#4112yes—
273C22×C4×C7#4112yes—
274C22×C4×C7#4112yes—
275C22×C4×C7#4112yes—
276C22×C4×C7#4112yes—
277C7×C4⋊C4—28no—
278C7×C4⋊C4—28no—
279C7×C4⋊C4—28no—
280C7×C4⋊C4—44no—
281C7×C22⋊C4—28no—
282C7×C22⋊C4—28no—
283C7×C22⋊C4—28no—
284C7×C22⋊C4—28no—
285C7×C22⋊C4—44no—
286C7×C22⋊C4—44no—
287C42×C7—28no—
288C42×C7—44no—
289C42×C7—44no—
290C42×C7—44no—
291C24×C4C22×C711yescharacteristic
292C22×C4⋊C4C22×C711yescharacteristic
293C22×C4⋊C4C22×C711yescharacteristic
294C22×C4⋊C4C22×C711yescharacteristic
295C22×C4⋊C4C22×C711yescharacteristic
296C22×C22⋊C4C22×C711yescharacteristic
297C22×C22⋊C4C22×C711yescharacteristic
298C22×C22⋊C4C22×C711yescharacteristic
299C22×C22⋊C4C22×C711yescharacteristic
300C22×C22⋊C4C22×C711yescharacteristic
301C22×C22⋊C4C22×C711yescharacteristic
302C22×C42C22×C711yescharacteristic
303C22×C42C22×C711yescharacteristic
304C22×C42C22×C711yescharacteristic
305C22×C42C22×C711yescharacteristic
306#388C4×C718yescomplemented
307#387—24no—
308#385—24no—
309C4×C4⋊C4—24no—
310C4×C22⋊C4—24no—
311C2×#95C22×C711yescharacteristic
312C2×#95C22×C711yescharacteristic
313C2×#95C22×C711yescharacteristic
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
331C23×C7—22no—
332C23×C7—22no—
333C23×C7—22no—
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—41no—
350C23×C7—41no—
351C23×C7—41no—
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#11714yes—
366C23×C7C23×C411yescharacteristic
367C23×C7C22×D411yescharacteristic
368C23×C7C22×D411yescharacteristic
369C23×C7C2×#4111yescharacteristic
370C23×C7C2×#4111yescharacteristic
371C23×C7C2×#4111yescharacteristic
372C23×C7C2×#4111yescharacteristic
373C23×C7C2×#4111yescharacteristic
374C23×C7C2×#4111yescharacteristic
375C23×C7C2×#4111yescharacteristic
376C23×C7C2×#4111yescharacteristic
377C23×C7H(5,𝔽2)11yescharacteristic
378C23×C7H(5,𝔽2)11yescharacteristic
379C23×C72−1+411yescharacteristic
380C23×C72−1+411yescharacteristic
381C2×C4×C7—22no—
382C2×C4×C7—22no—
383C2×C4×C7—22no—
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—22no—
418C2×C4×C7—22no—
419C2×C4×C7—22no—
420C2×C4×C7—22no—
421C2×C4×C7—22no—
422C2×C4×C7—22no—
423C2×C4×C7—22no—
424C2×C4×C7—22no—
425C2×C4×C7—22no—
426C2×C4×C7—416no—
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×C7C4×D414yes—
478C2×C4×C7C4×D414yes—
479C2×C4×C7#12314yes—
480C25C23×C711yescharacteristic
481C23×C4—22no—
482C23×C4—22no—
483C23×C4—22no—
484C23×C4—22no—
485C23×C4—22no—
486C23×C4—41no—
487C23×C4—41no—
488C23×C4C23×C711yescharacteristic
489C23×C4C23×C711yescharacteristic
490C23×C4C23×C711yescharacteristic
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
502C2×C4⋊C4—22no—
503C2×C4⋊C4—22no—
504C2×C4⋊C4—22no—
505C2×C4⋊C4—22no—
506C2×C4⋊C4—22no—
507C2×C4⋊C4—22no—
508C2×C4⋊C4—22no—
509C2×C4⋊C4—22no—
510C2×C4⋊C4—22no—
511C2×C4⋊C4—41no—
512C2×C4⋊C4C2×C4×C714yescomplemented
513C2×C4⋊C4C7×D414yes—
514C2×C22⋊C4—22no—
515C2×C22⋊C4—22no—
516C2×C22⋊C4—22no—
517C2×C22⋊C4—22no—
518C2×C22⋊C4—22no—
519C2×C22⋊C4—22no—
520C2×C22⋊C4—22no—
521C2×C22⋊C4—22no—
522C2×C22⋊C4—22no—
523C2×C22⋊C4—22no—
524C2×C22⋊C4—22no—
525C2×C22⋊C4—22no—
526C2×C22⋊C4—22no—
527C2×C22⋊C4—41no—
528C2×C22⋊C4—41no—
529C2×C22⋊C4C2×C4×C714yes—
530C2×C22⋊C4C2×C4×C714yes—
531C2×C22⋊C4C2×C4×C714yes—
532C2×C42—22no—
533C2×C42—22no—
534C2×C42—22no—
535C2×C42—22no—
536C2×C42—22no—
537C2×C42—22no—
538C2×C42—22no—
539C2×C42—22no—
540C2×C42—41no—
541C2×C42—41no—
542C2×C42—41no—
543C2×C42C2×C4×C714yescomplemented
544#95—22no—
545#95—22no—
546#95—22no—
547#95—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—41no—
558#95—41no—
559#95—41no—
560#95—41no—
561#95C2×C4×C714yescomplemented
562#95C2×C4×C714yescomplemented
563#95C7×D414yes—
564C22×C7—24no—
565C22×C7—24no—
566C22×C7—24no—
567C22×C7—42no—
568C22×C7—42no—
569C22×C7—42no—
570C22×C7—42no—
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×C7C2×#11711yescharacteristic
580C22×C7C2×C4×D411yescharacteristic
581C22×C7C2×C4×D411yescharacteristic
582C22×C7C4×#4111yescharacteristic
583C22×C7C4×#4111yescharacteristic
584C22×C7#52011yescharacteristic
585C22×C7#52011yescharacteristic
586C22×C7C2×#12311yescharacteristic
587C22×C7#52511yescharacteristic
588C22×C7#52511yescharacteristic
589C22×C7#52511yescharacteristic
590C22×C7#52911yescharacteristic
591C22×C7#52911yescharacteristic
592C22×C7#52911yescharacteristic
593C22×C7#52911yescharacteristic
594C22×C7#53811yescharacteristic
595C22×C7#53911yescharacteristic
596C22×C7#54111yescharacteristic
597C22×C7#54211yescharacteristic
598C22×C7D4211yescharacteristic
599C22×C7#54611yescharacteristic
600C22×C7#54611yescharacteristic
601C22×C7#54711yescharacteristic
602C22×C7#54811yescharacteristic
603C22×C7#54811yescharacteristic
604C22×C7#54811yescharacteristic
605C22×C7#55111yescharacteristic
606C22×C7#55111yescharacteristic
607C22×C7#55211yescharacteristic
608C22×C7#55211yescharacteristic
609C22×C7#55211yescharacteristic
610C22×C7#55311yescharacteristic
611C22×C7#55311yescharacteristic
612C22×C7#55611yescharacteristic
613C22×C7#55911yescharacteristic
614C4×C7—24no—
615C4×C7—24no—
616C4×C7—24no—
617C4×C7—42no—
618C4×C7—42no—
619C4×C7—42no—
620C4×C7—42no—
621C4×C7—42no—
622C4×C7—42no—
623C4×C7—42no—
624C4×C7—42no—
625C4×C7—42no—
626C4×C7—81no—
627C4×C7—81no—
628C24—21no—
629C24—21no—
630C24—21no—
631C24—21no—
632C24—21no—
633C24—21no—
634C24—21no—
635C24—21no—
636C24—21no—
637C24—21no—
638C24—21no—
639C24—21no—
640C24C22×C4×C712yes—
641C24C7×#4112yes—
642C24C7×#4112yes—
643C24C24×C711yescharacteristic
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—28no—
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—44no—
726C22×C4—44no—
727C22×C4—44no—
728C22×C4—44no—
729C22×C4—44no—
730C22×C4—44no—
731C22×C4C22×C4×C712yes—
732C22×C4C22×C4×C712yes—
733C22×C4C22×C4×C712yes—
734C22×C4C22×C4×C712yes—
735C22×C4C22×C4×C712yes—
736C22×C4C22×C4×C712yes—
737C22×C4C2×C7×D412yes—
738C22×C4C2×C7×D412yes—
739C22×C4C2×C7×D412yes—
740C22×C4C2×C7×D412yes—
741C22×C4C2×C7×D412yes—
742C22×C4C2×C7×D412yes—
743C22×C4C7×#4112yes—
744C22×C4C7×#4112yes—
745C22×C4C7×#4112yes—
746C22×C4C7×#4112yes—
747C22×C4C7×#4112yes—
748C22×C4C7×#4112yes—
749C4⋊C4—28no—
750C4⋊C4—28no—
751C4⋊C4—28no—
752C4⋊C4—44no—
753C22⋊C4—28no—
754C22⋊C4—28no—
755C22⋊C4—28no—
756C22⋊C4—28no—
757C22⋊C4—44no—
758C22⋊C4—44no—
759C42—28no—
760C42—44no—
761C42—44no—
762C42—44no—
763C2×C7—44no—
764C2×C7#229011yescharacteristic
765C2×C7C4×#12311yescharacteristic
766C2×C7#233411yescharacteristic
767C2×C7#234311yescharacteristic
768C2×C7#235211yescharacteristic
769C2×C7#236111yescharacteristic
770C2×C7#236711yescharacteristic
771C2×C7#241811yescharacteristic
772C2×C7#242111yescharacteristic
773C2×C7#245811yescharacteristic
774C2×C7#246311yescharacteristic
775C2×C7#246811yescharacteristic
776C2×C7#247511yescharacteristic
777C2×C7#257311yescharacteristic
778C2×C7#259511yescharacteristic
779C23—22no—
780C23—22no—
781C23—22no—
782C23—22no—
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—41no—
798C23—41no—
799C23—41no—
800C23—41no—
801C23—41no—
802C23—41no—
803C23—41no—
804C23—41no—
805C23—41no—
806C23—41no—
807C23—41no—
808C23—41no—
809C23—41no—
810C23—41no—
811C23—41no—
812C23—41no—
813C23C7×#11714yes—
814C23C23×C4×C711yescharacteristic
815C23C22×C7×D411yescharacteristic
816C23C22×C7×D411yescharacteristic
817C23C2×C7×#4111yescharacteristic
818C23C2×C7×#4111yescharacteristic
819C23C2×C7×#4111yescharacteristic
820C23C2×C7×#4111yescharacteristic
821C23C2×C7×#4111yescharacteristic
822C23C2×C7×#4111yescharacteristic
823C23C2×C7×#4111yescharacteristic
824C23C2×C7×#4111yescharacteristic
825C23C7×H(5,𝔽2)11yescharacteristic
826C23C7×H(5,𝔽2)11yescharacteristic
827C23C7×2−1+411yescharacteristic
828C23C7×2−1+411yescharacteristic
829C2×C4—22no—
830C2×C4—22no—
831C2×C4—22no—
832C2×C4—22no—
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—22no—
867C2×C4—22no—
868C2×C4—22no—
869C2×C4—22no—
870C2×C4—22no—
871C2×C4—22no—
872C2×C4—22no—
873C2×C4—22no—
874C2×C4—416no—
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×C4C4×C7×D414yes—
926C2×C4C4×C7×D414yes—
927C2×C4C7×#12314yes—
928C7#1403211yescharacteristic, direct product factor, Sylow
929C22—24no—
930C22—24no—
931C22—24no—
932C22—42no—
933C22—42no—
934C22—42no—
935C22—42no—
936C22—42no—
937C22—42no—
938C22—42no—
939C22—42no—
940C22—42no—
941C22—42no—
942C22—42no—
943C22—42no—
944C22C2×C7×#11711yescharacteristic
945C22C2×C4×C7×D411yescharacteristic
946C22C2×C4×C7×D411yescharacteristic
947C22C4×C7×#4111yescharacteristic
948C22C4×C7×#4111yescharacteristic
949C22C7×#52011yescharacteristic
950C22C7×#52011yescharacteristic
951C22C2×C7×#12311yescharacteristic
952C22C7×#52511yescharacteristic
953C22C7×#52511yescharacteristic
954C22C7×#52511yescharacteristic
955C22C7×#52911yescharacteristic
956C22C7×#52911yescharacteristic
957C22C7×#52911yescharacteristic
958C22C7×#52911yescharacteristic
959C22C7×#53811yescharacteristic
960C22C7×#53911yescharacteristic
961C22C7×#54111yescharacteristic
962C22C7×#54211yescharacteristic
963C22C7×D4211yescharacteristic
964C22C7×#54611yescharacteristic
965C22C7×#54611yescharacteristic
966C22C7×#54711yescharacteristic
967C22C7×#54811yescharacteristic
968C22C7×#54811yescharacteristic
969C22C7×#54811yescharacteristic
970C22C7×#55111yescharacteristic
971C22C7×#55111yescharacteristic
972C22C7×#55211yescharacteristic
973C22C7×#55211yescharacteristic
974C22C7×#55211yescharacteristic
975C22C7×#55311yescharacteristic
976C22C7×#55311yescharacteristic
977C22C7×#55611yescharacteristic
978C22C7×#55911yescharacteristic
979C4—24no—
980C4—24no—
981C4—24no—
982C4—42no—
983C4—42no—
984C4—42no—
985C4—42no—
986C4—42no—
987C4—42no—
988C4—42no—
989C4—42no—
990C4—42no—
991C4—81no—
992C4—81no—
993C2—44no—
994C2C7×#229011yescharacteristic
995C2C4×C7×#12311yescharacteristic
996C2C7×#233411yescharacteristic
997C2C7×#234311yescharacteristic
998C2C7×#235211yescharacteristic
999C2C7×#236111yescharacteristic
1000C2C7×#236711yescharacteristic
1001C2C7×#241811yescharacteristic
1002C2C7×#242111yescharacteristic
1003C2C7×#245811yescharacteristic
1004C2C7×#246311yescharacteristic
1005C2C7×#246811yescharacteristic
1006C2C7×#247511yescharacteristic
1007C2C7×#257311yescharacteristic
1008C2C7×#259511yescharacteristic
subgroupG/H
center, socleC24×C7C24
commutatorC23C23×C4×C7
Frattini, cosocleC24C24×C7
prime radicalC25×C7C23
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C24×C7 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×C7×#387C2semidirect
4. C2×C4×C7×C4⋊C4C2semidirect
6. C7×#1442C2semidirect
7. C7×#1442C2semidirect
11. C7×#1436C2semidirect
12. C7×#1436C2semidirect
13. C7×#1434C2semidirect
14. C7×#1434C2semidirect
31. C7×#388C4semidirect
56. #14032C7direct (N × H)
89. C2×C7×C4⋊C4C2×C4semidirect
120. C2×C42×C7C2×C4semidirect
138. C7×#95C2×C4semidirect
139. C7×#95C2×C4semidirect
142. C2×#387C2×C7semidirect
144. C2×C4×C4⋊C4C2×C7semidirect
146. #1442C2×C7semidirect
147. #1442C2×C7semidirect
151. #1436C2×C7semidirect
152. #1436C2×C7semidirect
153. #1434C2×C7semidirect
154. #1434C2×C7semidirect
306. #388C4×C7semidirect
512. C2×C4⋊C4C2×C4×C7semidirect
543. C2×C42C2×C4×C7semidirect
561. #95C2×C4×C7semidirect
562. #95C2×C4×C7semidirect
928. C7#14032direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C7×#3882
C2×C7×#3872
C2×C7×#3852
C2×C4×C7×C4⋊C42
C2×C4×C7×C22⋊C42
C7×#14422
C7×#14402
C7×#14392
C7×#14372
C7×#14362
C7×#14342
C7×C22⋊#952
#140327