Finite Group Databasebeta

← C7×#14429 #13191645

Subgroups — C7×#14429 #13191645

Order 1792.

1866 conjugacy classes of subgroups.

The subgroup lattice has 1158 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C7×#390C211yesmaximal, characteristic
2C2×C7×#388C211yesmaximal, characteristic, complemented
3C2×C7×#387C211yesmaximal, characteristic, complemented
4C2×C7×#386C211yesmaximal, characteristic
5C2×C7×#385C211yesmaximal, characteristic, complemented
6C7×#1445C211yesmaximal, characteristic, complemented
7C7×#1440C211yesmaximal, characteristic, complemented
8C7×#1439C211yesmaximal, characteristic, complemented
9C7×#1439C211yesmaximal, characteristic, complemented
10C7×#1439C211yesmaximal, characteristic, complemented
11C7×#1438C211yesmaximal, characteristic
12C7×#1437C211yesmaximal, characteristic, complemented
13C7×C4⋊#95C211yesmaximal, 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×C4⋊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×C7×C22⋊C4C2211yescharacteristic
33C22×C42×C7C2211yescharacteristic
34C22×C42×C7C2211yescharacteristic
35C7×#390C418yescomplemented
36C7×#388—24no—
37C7×#387—24no—
38C7×#386—24no—
39C7×#385—24no—
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#14429C711yesmaximal, characteristic, direct product factor, Sylow
57C25×C7C2311yescharacteristic
58C25×C7C2311yescharacteristic
59C22×C7×D4—22no—
60C22×C7×D4—22no—
61C22×C7×D4—22no—
62C22×C7×D4—22no—
63C22×C7×D4—41no—
64C22×C7×D4—41no—
65C22×C7×D4C2×C414yes—
66C23×C4×C7—22no—
67C23×C4×C7—22no—
68C23×C4×C7—22no—
69C23×C4×C7—41no—
70C23×C4×C7—41no—
71C23×C4×C7—41no—
72C23×C4×C7—41no—
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
85C23×C4×C7C2311yescharacteristic
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—41no—
92C2×C7×C4⋊C4—41no—
93C2×C7×C4⋊C4—41no—
94C2×C7×C4⋊C4—41no—
95C2×C7×C4⋊C4—41no—
96C2×C7×C4⋊C4C2×C414yescomplemented
97C2×C7×C4⋊C4D414yescomplemented
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⋊C4—41no—
126C2×C7×C22⋊C4—41no—
127C2×C7×C22⋊C4C2×C414yes—
128C2×C7×C22⋊C4C2×C414yes—
129C2×C7×C22⋊C4C2×C414yescomplemented
130C2×C7×C22⋊C4C2×C414yescomplemented
131C2×C42×C7—22no—
132C2×C42×C7—22no—
133C2×C42×C7—41no—
134C2×C42×C7—41no—
135C2×C42×C7—41no—
136C2×C42×C7C2×C414yescomplemented
137C7×#95—22no—
138C7×#95—22no—
139C7×#95—22no—
140C7×#95—22no—
141C7×#95—22no—
142C7×#95—22no—
143C7×#95—22no—
144C7×#95—22no—
145C7×#95—22no—
146C7×#95—41no—
147C7×#95—41no—
148C7×#95—41no—
149C7×#95—41no—
150C7×#95—41no—
151C7×#95—41no—
152C7×#95D414yes—
153C2×#390C2×C711yescharacteristic
154C2×#388C2×C711yescharacteristic, complemented
155C2×#387C2×C711yescharacteristic, complemented
156C2×#386C2×C711yescharacteristic
157C2×#385C2×C711yescharacteristic, complemented
158#1445C2×C711yescharacteristic, complemented
159#1440C2×C711yescharacteristic, complemented
160#1439C2×C711yescharacteristic, complemented
161#1439C2×C711yescharacteristic, complemented
162#1439C2×C711yescharacteristic, complemented
163#1438C2×C711yescharacteristic
164#1437C2×C711yescharacteristic, complemented
165C4⋊#95C2×C711yescharacteristic, complemented
166#1434C2×C711yescharacteristic, complemented
167C22⋊#95C2×C711yescharacteristic, complemented
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×C7—21no—
190C24×C7—21no—
191C24×C7—21no—
192C24×C7—21no—
193C24×C7—21no—
194C24×C7C22×C412yes—
195C24×C7C22×C412yes—
196C24×C7#4112yes—
197C24×C7#4112yes—
198C24×C7C2411yescharacteristic
199C2×C7×D4—28no—
200C2×C7×D4—28no—
201C2×C7×D4—44no—
202C2×C7×D4—44no—
203C2×C7×D4—44no—
204C2×C7×D4—44no—
205C2×C7×D4—44no—
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×C7—44no—
291C22×C4×C7C22×C412yes—
292C22×C4×C7C22×C412yes—
293C22×C4×C7C22×C412yes—
294C22×C4×C7C22×C412yes—
295C22×C4×C7C22×C412yes—
296C22×C4×C7C2×D412yes—
297C22×C4×C7C2×D412yes—
298C22×C4×C7C2×D412yes—
299C22×C4×C7C2×D412yes—
300C22×C4×C7C2×D412yes—
301C22×C4×C7C2×D412yes—
302C22×C4×C7#4112yes—
303C22×C4×C7#4112yes—
304C7×C4⋊C4—28no—
305C7×C4⋊C4—44no—
306C7×C4⋊C4—44no—
307C7×C4⋊C4—44no—
308C7×C22⋊C4—28no—
309C7×C22⋊C4—28no—
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—
317C7×C22⋊C4—44no—
318C7×C22⋊C4—44no—
319C42×C7—44no—
320C42×C7—44no—
321C23×D4C22×C711yescharacteristic
322C24×C4C22×C711yescharacteristic
323C22×C4⋊C4C22×C711yescharacteristic
324C22×C4⋊C4C22×C711yescharacteristic
325C22×C4⋊C4C22×C711yescharacteristic
326C22×C4⋊C4C22×C711yescharacteristic
327C22×C22⋊C4C22×C711yescharacteristic
328C22×C22⋊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×C42C22×C711yescharacteristic
339C22×C42C22×C711yescharacteristic
340#390C4×C718yescomplemented
341#388—24no—
342#387—24no—
343#386—24no—
344#385—24no—
345C2×#95C22×C711yescharacteristic
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
360C2×#95C22×C711yescharacteristic
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—22no—
379C23×C7—22no—
380C23×C7—22no—
381C23×C7—22no—
382C23×C7—22no—
383C23×C7—22no—
384C23×C7—22no—
385C23×C7—22no—
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×C7#11714yes—
431C23×C7C23×C411yescharacteristic
432C23×C7C22×D411yescharacteristic
433C23×C7C22×D411yescharacteristic
434C23×C7C2×#4111yescharacteristic
435C23×C7C2×#4111yescharacteristic
436C23×C7C2×#4111yescharacteristic
437C23×C7C2×#4111yescharacteristic
438C23×C7H(5,𝔽2)11yescharacteristic
439C23×C7H(5,𝔽2)11yescharacteristic
440C23×C7H(5,𝔽2)11yescharacteristic
441C23×C7H(5,𝔽2)11yescharacteristic
442C23×C7H(5,𝔽2)11yescharacteristic
443C23×C7H(5,𝔽2)11yescharacteristic
444C23×C72−1+411yescharacteristic
445C23×C72−1+411yescharacteristic
446C7×D4—416no—
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—416no—
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—
531C2×C4×C7—41no—
532C2×C4×C7—41no—
533C2×C4×C7—41no—
534C2×C4×C7—41no—
535C2×C4×C7—41no—
536C2×C4×C7—41no—
537C2×C4×C7C4×D414yes—
538C2×C4×C7C4×D414yes—
539C25C23×C711yescharacteristic
540C25C23×C711yescharacteristic
541C22×D4—22no—
542C22×D4—22no—
543C22×D4—22no—
544C22×D4—22no—
545C22×D4—41no—
546C22×D4—41no—
547C22×D4C2×C4×C714yes—
548C23×C4—22no—
549C23×C4—22no—
550C23×C4—22no—
551C23×C4—41no—
552C23×C4—41no—
553C23×C4—41no—
554C23×C4—41no—
555C23×C4C23×C711yescharacteristic
556C23×C4C23×C711yescharacteristic
557C23×C4C23×C711yescharacteristic
558C23×C4C23×C711yescharacteristic
559C23×C4C23×C711yescharacteristic
560C23×C4C23×C711yescharacteristic
561C23×C4C23×C711yescharacteristic
562C23×C4C23×C711yescharacteristic
563C23×C4C23×C711yescharacteristic
564C23×C4C23×C711yescharacteristic
565C23×C4C23×C711yescharacteristic
566C23×C4C23×C711yescharacteristic
567C23×C4C23×C711yescharacteristic
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⋊C4—41no—
577C2×C4⋊C4—41no—
578C2×C4⋊C4C2×C4×C714yescomplemented
579C2×C4⋊C4C7×D414yescomplemented
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—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⋊C4—41no—
601C2×C22⋊C4—41no—
602C2×C22⋊C4—41no—
603C2×C22⋊C4—41no—
604C2×C22⋊C4—41no—
605C2×C22⋊C4—41no—
606C2×C22⋊C4—41no—
607C2×C22⋊C4—41no—
608C2×C22⋊C4—41no—
609C2×C22⋊C4C2×C4×C714yes—
610C2×C22⋊C4C2×C4×C714yes—
611C2×C22⋊C4C2×C4×C714yescomplemented
612C2×C22⋊C4C2×C4×C714yescomplemented
613C2×C42—22no—
614C2×C42—22no—
615C2×C42—41no—
616C2×C42—41no—
617C2×C42—41no—
618C2×C42C2×C4×C714yescomplemented
619#95—22no—
620#95—22no—
621#95—22no—
622#95—22no—
623#95—22no—
624#95—22no—
625#95—22no—
626#95—22no—
627#95—22no—
628#95—41no—
629#95—41no—
630#95—41no—
631#95—41no—
632#95—41no—
633#95—41no—
634#95C7×D414yes—
635C22×C7—24no—
636C22×C7—24no—
637C22×C7—24no—
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—42no—
649C22×C7—42no—
650C22×C7—42no—
651C22×C7—42no—
652C22×C7—42no—
653C22×C7—42no—
654C22×C7—42no—
655C22×C7—42no—
656C22×C7—42no—
657C22×C7—81no—
658C22×C7—81no—
659C22×C7—81no—
660C22×C7—81no—
661C22×C7—81no—
662C22×C7—81no—
663C22×C7—81no—
664C22×C7—81no—
665C22×C7C2×#11711yescharacteristic
666C22×C7C2×C4×D411yescharacteristic
667C22×C7C2×C4×D411yescharacteristic
668C22×C7#51811yescharacteristic
669C22×C7#51811yescharacteristic
670C22×C7#52011yescharacteristic
671C22×C7#52011yescharacteristic
672C22×C7#53411yescharacteristic
673C22×C7#53511yescharacteristic
674C22×C7#53611yescharacteristic
675C22×C7#53711yescharacteristic
676C22×C7#53811yescharacteristic
677C22×C7#53811yescharacteristic
678C22×C7#53811yescharacteristic
679C22×C7#53911yescharacteristic
680C22×C7#53911yescharacteristic
681C22×C7#53911yescharacteristic
682C22×C7#54211yescharacteristic
683C22×C7#54211yescharacteristic
684C22×C7D4211yescharacteristic
685C22×C7#54611yescharacteristic
686C22×C7#54611yescharacteristic
687C22×C7#54611yescharacteristic
688C22×C7#54811yescharacteristic
689C22×C7#55011yescharacteristic
690C22×C7#55011yescharacteristic
691C22×C7#55111yescharacteristic
692C22×C7#55111yescharacteristic
693C22×C7#55211yescharacteristic
694C22×C7#55311yescharacteristic
695C22×C7#55911yescharacteristic
696C22×C7#56011yescharacteristic
697C22×C7#56011yescharacteristic
698C22×C7#56211yescharacteristic
699C22×C7#56211yescharacteristic
700C4×C7—24no—
701C4×C7—24no—
702C4×C7—42no—
703C4×C7—42no—
704C4×C7—42no—
705C4×C7—42no—
706C4×C7—42no—
707C4×C7—42no—
708C4×C7—42no—
709C4×C7—81no—
710C4×C7—81no—
711C4×C7—81no—
712C4×C7—81no—
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—
739C24C22×C4×C712yes—
740C24C22×C4×C712yes—
741C24C7×#4112yes—
742C24C7×#4112yes—
743C24C24×C711yescharacteristic
744C2×D4—28no—
745C2×D4—28no—
746C2×D4—44no—
747C2×D4—44no—
748C2×D4—44no—
749C2×D4—44no—
750C2×D4—44no—
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×C4—21no—
829C22×C4—44no—
830C22×C4—44no—
831C22×C4—44no—
832C22×C4—44no—
833C22×C4—44no—
834C22×C4—44no—
835C22×C4—44no—
836C22×C4C22×C4×C712yes—
837C22×C4C22×C4×C712yes—
838C22×C4C22×C4×C712yes—
839C22×C4C22×C4×C712yes—
840C22×C4C22×C4×C712yes—
841C22×C4C2×C7×D412yes—
842C22×C4C2×C7×D412yes—
843C22×C4C2×C7×D412yes—
844C22×C4C2×C7×D412yes—
845C22×C4C2×C7×D412yes—
846C22×C4C2×C7×D412yes—
847C22×C4C7×#4112yes—
848C22×C4C7×#4112yes—
849C4⋊C4—28no—
850C4⋊C4—44no—
851C4⋊C4—44no—
852C4⋊C4—44no—
853C22⋊C4—28no—
854C22⋊C4—28no—
855C22⋊C4—44no—
856C22⋊C4—44no—
857C22⋊C4—44no—
858C22⋊C4—44no—
859C22⋊C4—44no—
860C22⋊C4—44no—
861C22⋊C4—44no—
862C22⋊C4—44no—
863C22⋊C4—44no—
864C42—44no—
865C42—44no—
866C2×C7—44no—
867C2×C7—82no—
868C2×C7#231811yescharacteristic
869C2×C7#232511yescharacteristic
870C2×C7#232611yescharacteristic
871C2×C7#234211yescharacteristic
872C2×C7#235211yescharacteristic
873C2×C7#236611yescharacteristic
874C2×C7#237711yescharacteristic
875C2×C7#267811yescharacteristic
876C2×C7#268111yescharacteristic
877C2×C7#269411yescharacteristic
878C2×C7#270511yescharacteristic
879C2×C7#271411yescharacteristic
880C2×C7#273011yescharacteristic
881C2×C7#275111yescharacteristic
882C2×C7#279611yescharacteristic
883C23—22no—
884C23—22no—
885C23—22no—
886C23—22no—
887C23—22no—
888C23—22no—
889C23—22no—
890C23—22no—
891C23—22no—
892C23—22no—
893C23—22no—
894C23—22no—
895C23—22no—
896C23—22no—
897C23—22no—
898C23—22no—
899C23—22no—
900C23—22no—
901C23—22no—
902C23—22no—
903C23—22no—
904C23—22no—
905C23—22no—
906C23—22no—
907C23—22no—
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—
948C23—41no—
949C23—41no—
950C23—41no—
951C23—41no—
952C23C7×#11714yes—
953C23C23×C4×C711yescharacteristic
954C23C22×C7×D411yescharacteristic
955C23C22×C7×D411yescharacteristic
956C23C2×C7×#4111yescharacteristic
957C23C2×C7×#4111yescharacteristic
958C23C2×C7×#4111yescharacteristic
959C23C2×C7×#4111yescharacteristic
960C23C7×H(5,𝔽2)11yescharacteristic
961C23C7×H(5,𝔽2)11yescharacteristic
962C23C7×H(5,𝔽2)11yescharacteristic
963C23C7×H(5,𝔽2)11yescharacteristic
964C23C7×H(5,𝔽2)11yescharacteristic
965C23C7×H(5,𝔽2)11yescharacteristic
966C23C7×2−1+411yescharacteristic
967C23C7×2−1+411yescharacteristic
968D4—416no—
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—22no—
1001C2×C4—22no—
1002C2×C4—416no—
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×C4—41no—
1055C2×C4—41no—
1056C2×C4—41no—
1057C2×C4—41no—
1058C2×C4—41no—
1059C2×C4C4×C7×D414yes—
1060C2×C4C4×C7×D414yes—
1061C7#1442911yescharacteristic, direct product factor, Sylow
1062C22—24no—
1063C22—24no—
1064C22—24no—
1065C22—42no—
1066C22—42no—
1067C22—42no—
1068C22—42no—
1069C22—42no—
1070C22—42no—
1071C22—42no—
1072C22—42no—
1073C22—42no—
1074C22—42no—
1075C22—42no—
1076C22—42no—
1077C22—42no—
1078C22—42no—
1079C22—42no—
1080C22—42no—
1081C22—42no—
1082C22—42no—
1083C22—42no—
1084C22—81no—
1085C22—81no—
1086C22—81no—
1087C22—81no—
1088C22—81no—
1089C22—81no—
1090C22—81no—
1091C22—81no—
1092C22C2×C7×#11711yescharacteristic
1093C22C2×C4×C7×D411yescharacteristic
1094C22C2×C4×C7×D411yescharacteristic
1095C22C7×#51811yescharacteristic
1096C22C7×#51811yescharacteristic
1097C22C7×#52011yescharacteristic
1098C22C7×#52011yescharacteristic
1099C22C7×#53411yescharacteristic
1100C22C7×#53511yescharacteristic
1101C22C7×#53611yescharacteristic
1102C22C7×#53711yescharacteristic
1103C22C7×#53811yescharacteristic
1104C22C7×#53811yescharacteristic
1105C22C7×#53811yescharacteristic
1106C22C7×#53911yescharacteristic
1107C22C7×#53911yescharacteristic
1108C22C7×#53911yescharacteristic
1109C22C7×#54211yescharacteristic
1110C22C7×#54211yescharacteristic
1111C22C7×D4211yescharacteristic
1112C22C7×#54611yescharacteristic
1113C22C7×#54611yescharacteristic
1114C22C7×#54611yescharacteristic
1115C22C7×#54811yescharacteristic
1116C22C7×#55011yescharacteristic
1117C22C7×#55011yescharacteristic
1118C22C7×#55111yescharacteristic
1119C22C7×#55111yescharacteristic
1120C22C7×#55211yescharacteristic
1121C22C7×#55311yescharacteristic
1122C22C7×#55911yescharacteristic
1123C22C7×#56011yescharacteristic
1124C22C7×#56011yescharacteristic
1125C22C7×#56211yescharacteristic
1126C22C7×#56211yescharacteristic
1127C4—24no—
1128C4—24no—
1129C4—42no—
1130C4—42no—
1131C4—42no—
1132C4—42no—
1133C4—42no—
1134C4—42no—
1135C4—42no—
1136C4—81no—
1137C4—81no—
1138C4—81no—
1139C4—81no—
1140C2—44no—
1141C2—82no—
1142C2C7×#231811yescharacteristic
1143C2C7×#232511yescharacteristic
1144C2C7×#232611yescharacteristic
1145C2C7×#234211yescharacteristic
1146C2C7×#235211yescharacteristic
1147C2C7×#236611yescharacteristic
1148C2C7×#237711yescharacteristic
1149C2C7×#267811yescharacteristic
1150C2C7×#268111yescharacteristic
1151C2C7×#269411yescharacteristic
1152C2C7×#270511yescharacteristic
1153C2C7×#271411yescharacteristic
1154C2C7×#273011yescharacteristic
1155C2C7×#275111yescharacteristic
1156C2C7×#279611yescharacteristic
subgroupG/H
center, socleC24×C7C24
commutatorC23C23×C4×C7
Frattini, cosocleC24C24×C7
prime radicalC23×C7×D4C22
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C24×C7 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×C7×#388C2semidirect
3. C2×C7×#387C2semidirect
5. C2×C7×#385C2semidirect
6. C7×#1445C2semidirect
7. C7×#1440C2semidirect
8. C7×#1439C2semidirect
9. C7×#1439C2semidirect
10. C7×#1439C2semidirect
12. C7×#1437C2semidirect
13. C7×C4⋊#95C2semidirect
14. C7×#1434C2semidirect
15. C7×C22⋊#95C2semidirect
35. C7×#390C4semidirect
56. #14429C7direct (N × H)
96. C2×C7×C4⋊C4C2×C4semidirect
97. C2×C7×C4⋊C4D4semidirect
129. C2×C7×C22⋊C4C2×C4semidirect
130. C2×C7×C22⋊C4C2×C4semidirect
136. C2×C42×C7C2×C4semidirect
154. C2×#388C2×C7semidirect
155. C2×#387C2×C7semidirect
157. C2×#385C2×C7semidirect
158. #1445C2×C7semidirect
159. #1440C2×C7semidirect
160. #1439C2×C7semidirect
161. #1439C2×C7semidirect
162. #1439C2×C7semidirect
164. #1437C2×C7semidirect
165. C4⋊#95C2×C7semidirect
166. #1434C2×C7semidirect
167. C22⋊#95C2×C7semidirect
340. #390C4×C7semidirect
578. C2×C4⋊C4C2×C4×C7semidirect
579. C2×C4⋊C4C7×D4semidirect
611. C2×C22⋊C4C2×C4×C7semidirect
612. C2×C22⋊C4C2×C4×C7semidirect
618. C2×C42C2×C4×C7semidirect
1061. C7#14429direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C7×#3902
C2×C7×#3882
C2×C7×#3872
C2×C7×#3862
C2×C7×#3852
C7×#14452
C7×#14402
C7×#14392
C7×#14382
C7×#14372
C7×C4⋊#952
C7×#14342
C7×C22⋊#952
#144297