Finite Group Databasebeta

← C7×#24469 #13201685

Subgroups — C7×#24469 #13201685

Order 1792.

1402 conjugacy classes of subgroups.

The subgroup lattice has 1052 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C7×#3489C211yesmaximal, characteristic, complemented
2C7×#3055C211yesmaximal, characteristic, complemented
3C2×C7×#454C211yesmaximal, characteristic, complemented
4C7×#3006C211yesmaximal, characteristic, complemented
5C2×C7×#421C211yesmaximal, characteristic, complemented
6C7×#2620C211yesmaximal, characteristic, complemented
7C7×#2039C211yesmaximal, characteristic, complemented
8C7×#2038C211yesmaximal, characteristic, complemented
9C7×#2006C211yesmaximal, characteristic, complemented
10C7×#2003C211yesmaximal, characteristic, complemented
11C7×#1901C211yesmaximal, characteristic, complemented
12C7×#1897C211yesmaximal, characteristic, complemented
13C7×#1883C211yesmaximal, characteristic, complemented
14C7×#1859C211yesmaximal, characteristic, complemented
15C7×#1793C211yesmaximal, characteristic, complemented
16C2×C7×2−1+4C2211yescharacteristic
17C22×C7×#41C2211yescharacteristic
18C2×C7×AGL(1,ℤ/8)C2211yescharacteristic
19C2×C7×AGL(1,ℤ/8)C2211yescharacteristic
20C2×C7×AGL(1,ℤ/8)C2211yescharacteristic, complemented
21C22×C7×M16C2211yescharacteristic
22C7×D4×Q8—21no—
23C7×#548—21no—
24C7×#547—21no—
25C7×#547—22no—
26C7×#546—21no—
27C7×#546—22no—
28C7×#537—21no—
29C7×#537C2211yescharacteristic
30C7×#536—21no—
31C7×#536C2211yescharacteristic
32C2×C7×#124C2211yescharacteristic, complemented
33C7×#525—21no—
34C7×#525C2211yescharacteristic
35C2×C7×C22⋊Q8—21no—
36C2×C7×C22⋊Q8C2211yescharacteristic
37C2×C7×#121C2211yescharacteristic
38C7×#520C2211yescharacteristic
39C2×C7×#117C2211yescharacteristic
40C7×#469—21no—
41C7×#468—21no—
42C7×#466—21no—
43C7×#465—21no—
44C7×#454—24no—
45C7×#449—21no—
46C7×#449—21no—
47C7×#448—21no—
48C7×#447—21no—
49C7×#428C2211yescharacteristic, complemented
50C7×#421—24no—
51C2×C7×#104C2211yescharacteristic
52C2×C7×#104C2211yescharacteristic
53C2×C7×#104C2211yescharacteristic
54C2×C7×#104C2211yescharacteristic
55C2×C7×#104C2211yescharacteristic, complemented
56C2×C7×#104C2211yescharacteristic, complemented
57C7×#418C2211yescharacteristic, complemented
58C7×#417C2211yescharacteristic
59C7×#417C2211yescharacteristic
60C7×#417C2211yescharacteristic, complemented
61C2×C7×#101C2211yescharacteristic, complemented
62C2×C7×#101C2211yescharacteristic, complemented
63C7×#407C2211yescharacteristic
64C7×#396—22no—
65C7×#394—22no—
66C7×#391C2211yescharacteristic, complemented
67C7×#390C2211yescharacteristic, complemented
68C7×#384C2211yescharacteristic, complemented
69C7×#343C2211yescharacteristic, complemented
70C7×#343C2211yescharacteristic, complemented
71C7×#339C2211yescharacteristic, complemented
72C7×#339C2211yescharacteristic, complemented
73#24469C711yesmaximal, characteristic, direct product factor, Sylow
74C7×2−1+4—22no—
75C7×2−1+4—22no—
76C7×2−1+4—41no—
77C7×2−1+4—41no—
78C2×C7×#41—21no—
79C2×C7×#41—21no—
80C2×C7×#41—21no—
81C2×C7×#41—21no—
82C2×C7×#41—22no—
83C2×C7×#41—22no—
84C2×C7×#41—22no—
85C2×C7×#41—41no—
86C2×C7×#41—41no—
87C2×C7×#41D411yescharacteristic
88C2×C7×#41D411yescharacteristic
89C2×C7×#41C2311yescharacteristic
90C2×C7×#41C2311yescharacteristic
91C2×C7×#41C2311yescharacteristic
92C22×C7×Q8—21no—
93C22×C7×Q8—21no—
94C22×C7×Q8D411yescharacteristic
95C22×C7×Q8C2311yescharacteristic
96C22×C7×D4—21no—
97C22×C7×D4—21no—
98C22×C7×D4D411yescharacteristic
99C22×C7×D4C2311yescharacteristic
100C23×C4×C7—21no—
101C23×C4×C7C2311yescharacteristic
102C7×AGL(1,ℤ/8)—22no—
103C7×AGL(1,ℤ/8)—22no—
104C7×AGL(1,ℤ/8)—22no—
105C7×AGL(1,ℤ/8)—41no—
106C7×AGL(1,ℤ/8)—41no—
107C7×AGL(1,ℤ/8)—41no—
108C2×C7×SD16—21no—
109C2×C7×SD16—21no—
110C2×C7×SD16—21no—
111C2×C7×D8—21no—
112C2×C7×D8—21no—
113C2×C7×D8—21no—
114C2×C7×M16—21no—
115C2×C7×M16—22no—
116C2×C7×M16—41no—
117C2×C7×M16C2311yescharacteristic
118C2×C7×M16C2311yescharacteristic
119C2×C7×M16C2311yescharacteristic
120C2×C7×M16C2311yescharacteristic
121C22×C7×C8—21no—
122C7×C4⋊Q8—22no—
123C7×C4⋊Q8—21no—
124C7×#124—22no—
125C7×#124—21no—
126C7×#124—22no—
127C7×#124—41no—
128C7×#123—22no—
129C7×#123—22no—
130C7×#123—22no—
131C7×#123—21no—
132C7×#123—22no—
133C7×C22⋊Q8—22no—
134C7×C22⋊Q8—22no—
135C7×C22⋊Q8—22no—
136C7×C22⋊Q8—21no—
137C7×C22⋊Q8—21no—
138C7×C22⋊Q8—21no—
139C7×C22⋊Q8—21no—
140C7×C22⋊Q8—21no—
141C7×C22⋊Q8—21no—
142C7×C22⋊Q8—21no—
143C7×C22⋊Q8—21no—
144C7×C22⋊Q8D411yescharacteristic
145C7×C22⋊Q8D411yescharacteristic
146C7×#121—22no—
147C7×#121—22no—
148C7×#121—22no—
149C7×#121—21no—
150C7×#121—21no—
151C7×#121—22no—
152C7×#121—21no—
153C7×#121—21no—
154C7×#121—21no—
155C7×#121—21no—
156C7×#121D411yescharacteristic
157C7×#121D411yescharacteristic
158C7×#120—22no—
159C7×#120—21no—
160C4×C7×Q8—21no—
161C4×C7×D4—22no—
162C4×C7×D4—22no—
163C4×C7×D4—21no—
164C4×C7×D4—22no—
165C4×C7×D4—21no—
166C4×C7×D4—21no—
167C7×#117—21no—
168C7×#117—22no—
169C7×#117—41no—
170C7×#117C2311yescharacteristic
171C2×C7×C4⋊C4—22no—
172C2×C7×C4⋊C4—21no—
173C2×C7×C4⋊C4—21no—
174C2×C7×C4⋊C4—22no—
175C2×C7×C4⋊C4D412yes—
176C2×C7×C4⋊C4C2311yescharacteristic
177C2×C7×C4⋊C4C2311yescharacteristic
178C2×C7×C22⋊C4—22no—
179C2×C7×C22⋊C4—21no—
180C2×C7×C22⋊C4—21no—
181C2×C7×C22⋊C4—22no—
182C2×C7×C22⋊C4—22no—
183C2×C7×C22⋊C4D412yes—
184C2×C42×C7C2311yescharacteristic
185C2×C42×C7C2311yescharacteristic
186C7×#107—21no—
187C7×#106—21no—
188C7×#104—22no—
189C7×#104—22no—
190C7×#104—22no—
191C7×#104—22no—
192C7×#104—41no—
193C7×#104D414yescomplemented
194C7×#103—21no—
195C7×#103—21no—
196C7×#103—21no—
197C7×#102—21no—
198C7×#102—21no—
199C7×#102—21no—
200C7×#102—21no—
201C7×#102—21no—
202C7×#101—22no—
203C7×#101—41no—
204C7×C22⋊C8—21no—
205C7×C22⋊C8—21no—
206C7×#95—22no—
207#3489C2×C711yescharacteristic, complemented
208#3055C2×C711yescharacteristic, complemented
209C2×#454C2×C711yescharacteristic, complemented
210#3006C2×C711yescharacteristic, complemented
211C2×#421C2×C711yescharacteristic, complemented
212#2620C2×C711yescharacteristic, complemented
213#2039C2×C711yescharacteristic, complemented
214#2038C2×C711yescharacteristic, complemented
215#2006C2×C711yescharacteristic, complemented
216#2003C2×C711yescharacteristic, complemented
217#1901C2×C711yescharacteristic, complemented
218#1897C2×C711yescharacteristic, complemented
219#1883C2×C711yescharacteristic, complemented
220#1859C2×C711yescharacteristic, complemented
221#1793C2×C711yescharacteristic, complemented
222C24×C7—21no—
223C24×C7—21no—
224C24×C7C2×D411yescharacteristic
225C7×#41—21no—
226C7×#41—21no—
227C7×#41—22no—
228C7×#41—22no—
229C7×#41—21no—
230C7×#41—21no—
231C7×#41—21no—
232C7×#41—21no—
233C7×#41—21no—
234C7×#41—21no—
235C7×#41—21no—
236C7×#41—21no—
237C7×#41—42no—
238C7×#41—42no—
239C7×#41—41no—
240C7×#41—41no—
241C7×#41—42no—
242C7×#41—42no—
243C7×#41—42no—
244C7×#41—42no—
245C7×#41—44no—
246C7×#41—44no—
247C7×#41—42no—
248C7×#41—42no—
249C7×#41C2×D412yes—
250C7×#41#4112yes—
251C2×C7×Q8—22no—
252C2×C7×Q8—21no—
253C2×C7×Q8—21no—
254C2×C7×Q8—21no—
255C2×C7×Q8—21no—
256C2×C7×Q8—21no—
257C2×C7×Q8—21no—
258C2×C7×Q8—21no—
259C2×C7×Q8—22no—
260C2×C7×Q8—41no—
261C2×C7×Q8—42no—
262C2×C7×Q8—42no—
263C2×C7×Q8—42no—
264C2×C7×Q8—42no—
265C2×C7×Q8C2×D411yescharacteristic
266C2×C7×Q8C2×D411yescharacteristic
267C2×C7×Q8C2×D411yescharacteristic
268C2×C7×D4—21no—
269C2×C7×D4—22no—
270C2×C7×D4—22no—
271C2×C7×D4—21no—
272C2×C7×D4—21no—
273C2×C7×D4—21no—
274C2×C7×D4—21no—
275C2×C7×D4—21no—
276C2×C7×D4—22no—
277C2×C7×D4—21no—
278C2×C7×D4—21no—
279C2×C7×D4—21no—
280C2×C7×D4—21no—
281C2×C7×D4—21no—
282C2×C7×D4—21no—
283C2×C7×D4—21no—
284C2×C7×D4—21no—
285C2×C7×D4—41no—
286C2×C7×D4—42no—
287C2×C7×D4—42no—
288C2×C7×D4—41no—
289C2×C7×D4—41no—
290C2×C7×D4—82no—
291C2×C7×D4C2×D411yescharacteristic
292C2×C7×D4C2×D411yescharacteristic
293C2×C7×D4C2×D411yescharacteristic
294C22×C4×C7—21no—
295C22×C4×C7—21no—
296C22×C4×C7—21no—
297C22×C4×C7—21no—
298C22×C4×C7—21no—
299C22×C4×C7—22no—
300C22×C4×C7—22no—
301C22×C4×C7—21no—
302C22×C4×C7—21no—
303C22×C4×C7—22no—
304C22×C4×C7—21no—
305C22×C4×C7—21no—
306C22×C4×C7—21no—
307C22×C4×C7—21no—
308C22×C4×C7—21no—
309C22×C4×C7—21no—
310C22×C4×C7—42no—
311C22×C4×C7—42no—
312C22×C4×C7C2×D412yes—
313C22×C4×C7C2×D411yescharacteristic
314C22×C4×C7C2×D411yescharacteristic
315C22×C4×C7C2×D411yescharacteristic
316C22×C4×C7C2×D411yescharacteristic
317C22×C4×C7C2×D411yescharacteristic
318C22×C4×C7C2×D412yes—
319C22×C4×C7C2411yescharacteristic
320C7×SD16—42no—
321C7×SD16—42no—
322C7×SD16—42no—
323C7×D8—42no—
324C7×D8—42no—
325C7×D8—42no—
326C7×M16—21no—
327C7×M16—21no—
328C7×M16—21no—
329C7×M16—21no—
330C7×M16—21no—
331C7×M16—21no—
332C7×M16—21no—
333C7×M16—42no—
334C7×M16C2×D412yes—
335C2×C7×C8—21no—
336C2×C7×C8—21no—
337C2×C7×C8—21no—
338C2×C7×C8—21no—
339C2×C7×C8—42no—
340C7×C4⋊C4—22no—
341C7×C4⋊C4—22no—
342C7×C4⋊C4—22no—
343C7×C4⋊C4—22no—
344C7×C4⋊C4—21no—
345C7×C4⋊C4—22no—
346C7×C4⋊C4—22no—
347C7×C4⋊C4—21no—
348C7×C4⋊C4—21no—
349C7×C4⋊C4—21no—
350C7×C4⋊C4—21no—
351C7×C4⋊C4—21no—
352C7×C4⋊C4—42no—
353C7×C4⋊C4—82no—
354C7×C4⋊C4C2×D411yescharacteristic
355C7×C4⋊C4C2×D411yescharacteristic
356C7×C22⋊C4—22no—
357C7×C22⋊C4—22no—
358C7×C22⋊C4—22no—
359C7×C22⋊C4—22no—
360C7×C22⋊C4—22no—
361C7×C22⋊C4—21no—
362C7×C22⋊C4—22no—
363C7×C22⋊C4—22no—
364C7×C22⋊C4—21no—
365C7×C22⋊C4—21no—
366C7×C22⋊C4—21no—
367C7×C22⋊C4—21no—
368C7×C22⋊C4—44no—
369C7×C22⋊C4—42no—
370C7×C22⋊C4—41no—
371C7×C22⋊C4—41no—
372C7×C22⋊C4—82no—
373C42×C7—22no—
374C42×C7—21no—
375C42×C7—21no—
376C42×C7—21no—
377C42×C7—21no—
378C42×C7C2×D412yes—
379C2×2−1+4C22×C711yescharacteristic
380C22×#41C22×C711yescharacteristic
381C2×AGL(1,ℤ/8)C22×C711yescharacteristic
382C2×AGL(1,ℤ/8)C22×C711yescharacteristic
383C2×AGL(1,ℤ/8)C22×C711yescharacteristic, complemented
384C22×M16C22×C711yescharacteristic
385D4×Q8—21no—
386#548—21no—
387#547—21no—
388#547—22no—
389#546—21no—
390#546—22no—
391#537—21no—
392#537C22×C711yescharacteristic
393#536—21no—
394#536C22×C711yescharacteristic
395C2×#124C22×C711yescharacteristic, complemented
396#525—21no—
397#525C22×C711yescharacteristic
398C2×C22⋊Q8—21no—
399C2×C22⋊Q8C22×C711yescharacteristic
400C2×#121C22×C711yescharacteristic
401#520C22×C711yescharacteristic
402C2×#117C22×C711yescharacteristic
403#469—21no—
404#468—21no—
405#466—21no—
406#465—21no—
407#454—24no—
408#449—21no—
409#449—21no—
410#448—21no—
411#447—21no—
412#428C22×C711yescharacteristic, complemented
413#421—24no—
414C2×#104C22×C711yescharacteristic
415C2×#104C22×C711yescharacteristic
416C2×#104C22×C711yescharacteristic
417C2×#104C22×C711yescharacteristic
418C2×#104C22×C711yescharacteristic, complemented
419C2×#104C22×C711yescharacteristic, complemented
420#418C22×C711yescharacteristic, complemented
421#417C22×C711yescharacteristic
422#417C22×C711yescharacteristic
423#417C22×C711yescharacteristic, complemented
424C2×#101C22×C711yescharacteristic, complemented
425C2×#101C22×C711yescharacteristic, complemented
426#407C22×C711yescharacteristic
427#396—22no—
428#394—22no—
429#391C22×C711yescharacteristic, complemented
430#390C22×C711yescharacteristic, complemented
431#384C22×C711yescharacteristic, complemented
432#343C22×C711yescharacteristic, complemented
433#343C22×C711yescharacteristic, complemented
434#339C22×C711yescharacteristic, complemented
435#339C22×C711yescharacteristic, complemented
436C23×C7—21no—
437C23×C7—21no—
438C23×C7—21no—
439C23×C7—21no—
440C23×C7—21no—
441C23×C7—41no—
442C23×C7—41no—
443C23×C7—42no—
444C23×C7—42no—
445C23×C7—42no—
446C23×C7—42no—
447C23×C7—41no—
448C23×C7—41no—
449C23×C7—41no—
450C23×C7—81no—
451C23×C7#12011yescharacteristic
452C23×C7#12011yescharacteristic
453C23×C7C22×D411yescharacteristic
454C7×Q8—21no—
455C7×Q8—21no—
456C7×Q8—21no—
457C7×Q8—21no—
458C7×Q8—21no—
459C7×Q8—42no—
460C7×Q8—44no—
461C7×Q8—41no—
462C7×Q8—41no—
463C7×Q8—41no—
464C7×Q8—41no—
465C7×Q8#12112yes—
466C7×D4—22no—
467C7×D4—22no—
468C7×D4—21no—
469C7×D4—21no—
470C7×D4—21no—
471C7×D4—21no—
472C7×D4—21no—
473C7×D4—42no—
474C7×D4—42no—
475C7×D4—42no—
476C7×D4—42no—
477C7×D4—44no—
478C7×D4—41no—
479C7×D4—41no—
480C7×D4—41no—
481C7×D4—41no—
482C7×D4—41no—
483C7×D4—41no—
484C7×D4—41no—
485C7×D4—41no—
486C7×D4—81no—
487C7×D4—82no—
488C7×D4—82no—
489C7×D4—82no—
490C7×D4#12112yes—
491C2×C4×C7—21no—
492C2×C4×C7—21no—
493C2×C4×C7—21no—
494C2×C4×C7—21no—
495C2×C4×C7—21no—
496C2×C4×C7—21no—
497C2×C4×C7—21no—
498C2×C4×C7—21no—
499C2×C4×C7—21no—
500C2×C4×C7—22no—
501C2×C4×C7—21no—
502C2×C4×C7—21no—
503C2×C4×C7—22no—
504C2×C4×C7—21no—
505C2×C4×C7—22no—
506C2×C4×C7—21no—
507C2×C4×C7—21no—
508C2×C4×C7—22no—
509C2×C4×C7—21no—
510C2×C4×C7—22no—
511C2×C4×C7—22no—
512C2×C4×C7—22no—
513C2×C4×C7—42no—
514C2×C4×C7—42no—
515C2×C4×C7—42no—
516C2×C4×C7—44no—
517C2×C4×C7—41no—
518C2×C4×C7—41no—
519C2×C4×C7—44no—
520C2×C4×C7—41no—
521C2×C4×C7—41no—
522C2×C4×C7—41no—
523C2×C4×C7—41no—
524C2×C4×C7—42no—
525C2×C4×C7—41no—
526C2×C4×C7—42no—
527C2×C4×C7—41no—
528C2×C4×C7—41no—
529C2×C4×C7—41no—
530C2×C4×C7—82no—
531C2×C4×C7#12011yescharacteristic
532C2×C4×C7#12011yescharacteristic
533C2×C4×C7C22×D411yescharacteristic
534C2×C4×C7C22×D411yescharacteristic
535C2×C4×C7C22×D411yescharacteristic
536C2×C4×C7C2×#4111yescharacteristic
537C2×C4×C7H(5,𝔽2)11yescharacteristic
538C2×C4×C7H(5,𝔽2)11yescharacteristic
539C7×C8—22no—
540C7×C8—41no—
541C7×C8—41no—
542C7×C8—41no—
5432−1+4—22no—
5442−1+4—22no—
5452−1+4—41no—
5462−1+4—41no—
547C2×#41—21no—
548C2×#41—21no—
549C2×#41—21no—
550C2×#41—22no—
551C2×#41—21no—
552C2×#41—22no—
553C2×#41—22no—
554C2×#41—41no—
555C2×#41—41no—
556C2×#41C7×D411yescharacteristic
557C2×#41C7×D411yescharacteristic
558C2×#41C23×C711yescharacteristic
559C2×#41C23×C711yescharacteristic
560C2×#41C23×C711yescharacteristic
561C22×Q8—21no—
562C22×Q8—21no—
563C22×Q8C7×D411yescharacteristic
564C22×Q8C23×C711yescharacteristic
565C22×D4—21no—
566C22×D4—21no—
567C22×D4C7×D411yescharacteristic
568C22×D4C23×C711yescharacteristic
569C23×C4—21no—
570C23×C4C23×C711yescharacteristic
571AGL(1,ℤ/8)—22no—
572AGL(1,ℤ/8)—22no—
573AGL(1,ℤ/8)—22no—
574AGL(1,ℤ/8)—41no—
575AGL(1,ℤ/8)—41no—
576AGL(1,ℤ/8)—41no—
577C2×SD16—21no—
578C2×SD16—21no—
579C2×SD16—21no—
580C2×D8—21no—
581C2×D8—21no—
582C2×D8—21no—
583C2×M16—21no—
584C2×M16—22no—
585C2×M16—41no—
586C2×M16C23×C711yescharacteristic
587C2×M16C23×C711yescharacteristic
588C2×M16C23×C711yescharacteristic
589C2×M16C23×C711yescharacteristic
590C22×C8—21no—
591C4⋊Q8—22no—
592C4⋊Q8—21no—
593#124—22no—
594#124—21no—
595#124—22no—
596#124—41no—
597#123—22no—
598#123—22no—
599#123—22no—
600#123—21no—
601#123—22no—
602C22⋊Q8—22no—
603C22⋊Q8—22no—
604C22⋊Q8—22no—
605C22⋊Q8—21no—
606C22⋊Q8—21no—
607C22⋊Q8—21no—
608C22⋊Q8—21no—
609C22⋊Q8—21no—
610C22⋊Q8—21no—
611C22⋊Q8—21no—
612C22⋊Q8—21no—
613C22⋊Q8C7×D411yescharacteristic
614C22⋊Q8C7×D411yescharacteristic
615#121—22no—
616#121—22no—
617#121—22no—
618#121—21no—
619#121—21no—
620#121—22no—
621#121—21no—
622#121—21no—
623#121—21no—
624#121—21no—
625#121C7×D411yescharacteristic
626#121C7×D411yescharacteristic
627#120—22no—
628#120—21no—
629C4×Q8—21no—
630C4×D4—22no—
631C4×D4—22no—
632C4×D4—21no—
633C4×D4—22no—
634C4×D4—21no—
635C4×D4—21no—
636#117—21no—
637#117—22no—
638#117—41no—
639#117C23×C711yescharacteristic
640C2×C4⋊C4—22no—
641C2×C4⋊C4—21no—
642C2×C4⋊C4—21no—
643C2×C4⋊C4—22no—
644C2×C4⋊C4C7×D412yes—
645C2×C4⋊C4C23×C711yescharacteristic
646C2×C4⋊C4C23×C711yescharacteristic
647C2×C22⋊C4—22no—
648C2×C22⋊C4—21no—
649C2×C22⋊C4—21no—
650C2×C22⋊C4—22no—
651C2×C22⋊C4—22no—
652C2×C22⋊C4C7×D412yes—
653C2×C42C23×C711yescharacteristic
654C2×C42C23×C711yescharacteristic
655#107—21no—
656#106—21no—
657#104—22no—
658#104—22no—
659#104—22no—
660#104—22no—
661#104—41no—
662#104C7×D414yescomplemented
663#103—21no—
664#103—21no—
665#103—21no—
666#102—21no—
667#102—21no—
668#102—21no—
669#102—21no—
670#102—21no—
671#101—22no—
672#101—41no—
673C22⋊C8—21no—
674C22⋊C8—21no—
675#95—22no—
676C22×C7—21no—
677C22×C7—21no—
678C22×C7—21no—
679C22×C7—21no—
680C22×C7—22no—
681C22×C7—21no—
682C22×C7—21no—
683C22×C7—21no—
684C22×C7—21no—
685C22×C7—41no—
686C22×C7—41no—
687C22×C7—41no—
688C22×C7—41no—
689C22×C7—41no—
690C22×C7—41no—
691C22×C7—41no—
692C22×C7—41no—
693C22×C7—81no—
694C22×C7—81no—
695C22×C7—82no—
696C22×C7—82no—
697C22×C7—84no—
698C22×C7—81no—
699C22×C7—81no—
700C22×C7—81no—
701C22×C7C2×#12011yescharacteristic
702C22×C7D4211yescharacteristic
703C22×C7#54611yescharacteristic
704C4×C7—21no—
705C4×C7—21no—
706C4×C7—22no—
707C4×C7—42no—
708C4×C7—42no—
709C4×C7—41no—
710C4×C7—41no—
711C4×C7—41no—
712C4×C7—42no—
713C4×C7—41no—
714C4×C7—81no—
715C4×C7—81no—
716C4×C7C2×#12111yescharacteristic
717C4×C7#53411yescharacteristic
718C4×C7D4211yescharacteristic
719C4×C7#54611yescharacteristic
720C24—21no—
721C24—21no—
722C24C2×C7×D411yescharacteristic
723#41—21no—
724#41—21no—
725#41—22no—
726#41—22no—
727#41—21no—
728#41—21no—
729#41—21no—
730#41—21no—
731#41—21no—
732#41—21no—
733#41—21no—
734#41—21no—
735#41—42no—
736#41—42no—
737#41—41no—
738#41—41no—
739#41—42no—
740#41—42no—
741#41—42no—
742#41—42no—
743#41—44no—
744#41—44no—
745#41—42no—
746#41—42no—
747#41C2×C7×D412yes—
748#41C7×#4112yes—
749C2×Q8—22no—
750C2×Q8—21no—
751C2×Q8—21no—
752C2×Q8—21no—
753C2×Q8—21no—
754C2×Q8—21no—
755C2×Q8—21no—
756C2×Q8—21no—
757C2×Q8—22no—
758C2×Q8—41no—
759C2×Q8—42no—
760C2×Q8—42no—
761C2×Q8—42no—
762C2×Q8—42no—
763C2×Q8C2×C7×D411yescharacteristic
764C2×Q8C2×C7×D411yescharacteristic
765C2×Q8C2×C7×D411yescharacteristic
766C2×D4—21no—
767C2×D4—22no—
768C2×D4—22no—
769C2×D4—21no—
770C2×D4—21no—
771C2×D4—21no—
772C2×D4—21no—
773C2×D4—21no—
774C2×D4—22no—
775C2×D4—21no—
776C2×D4—21no—
777C2×D4—21no—
778C2×D4—21no—
779C2×D4—21no—
780C2×D4—21no—
781C2×D4—21no—
782C2×D4—21no—
783C2×D4—41no—
784C2×D4—42no—
785C2×D4—42no—
786C2×D4—41no—
787C2×D4—41no—
788C2×D4—82no—
789C2×D4C2×C7×D411yescharacteristic
790C2×D4C2×C7×D411yescharacteristic
791C2×D4C2×C7×D411yescharacteristic
792C22×C4—21no—
793C22×C4—21no—
794C22×C4—21no—
795C22×C4—21no—
796C22×C4—21no—
797C22×C4—22no—
798C22×C4—22no—
799C22×C4—21no—
800C22×C4—21no—
801C22×C4—22no—
802C22×C4—21no—
803C22×C4—21no—
804C22×C4—21no—
805C22×C4—21no—
806C22×C4—21no—
807C22×C4—21no—
808C22×C4—42no—
809C22×C4—42no—
810C22×C4C2×C7×D412yes—
811C22×C4C2×C7×D411yescharacteristic
812C22×C4C2×C7×D411yescharacteristic
813C22×C4C2×C7×D411yescharacteristic
814C22×C4C2×C7×D411yescharacteristic
815C22×C4C2×C7×D411yescharacteristic
816C22×C4C2×C7×D412yes—
817C22×C4C24×C711yescharacteristic
818SD16—42no—
819SD16—42no—
820SD16—42no—
821D8—42no—
822D8—42no—
823D8—42no—
824M16—21no—
825M16—21no—
826M16—21no—
827M16—21no—
828M16—21no—
829M16—21no—
830M16—21no—
831M16—42no—
832M16C2×C7×D412yes—
833C2×C8—21no—
834C2×C8—21no—
835C2×C8—21no—
836C2×C8—21no—
837C2×C8—42no—
838C4⋊C4—22no—
839C4⋊C4—22no—
840C4⋊C4—22no—
841C4⋊C4—22no—
842C4⋊C4—21no—
843C4⋊C4—22no—
844C4⋊C4—22no—
845C4⋊C4—21no—
846C4⋊C4—21no—
847C4⋊C4—21no—
848C4⋊C4—21no—
849C4⋊C4—21no—
850C4⋊C4—42no—
851C4⋊C4—82no—
852C4⋊C4C2×C7×D411yescharacteristic
853C4⋊C4C2×C7×D411yescharacteristic
854C22⋊C4—22no—
855C22⋊C4—22no—
856C22⋊C4—22no—
857C22⋊C4—22no—
858C22⋊C4—22no—
859C22⋊C4—21no—
860C22⋊C4—22no—
861C22⋊C4—22no—
862C22⋊C4—21no—
863C22⋊C4—21no—
864C22⋊C4—21no—
865C22⋊C4—21no—
866C22⋊C4—44no—
867C22⋊C4—42no—
868C22⋊C4—41no—
869C22⋊C4—41no—
870C22⋊C4—82no—
871C42—22no—
872C42—21no—
873C42—21no—
874C42—21no—
875C42—21no—
876C42C2×C7×D412yes—
877C2×C7—21no—
878C2×C7—21no—
879C2×C7—41no—
880C2×C7—41no—
881C2×C7—42no—
882C2×C7—81no—
883C2×C7—81no—
884C2×C7—161no—
885C2×C7#241011yescharacteristic
886C2×C7#302011yescharacteristic
887C2×C7#302111yescharacteristic
888C23—21no—
889C23—21no—
890C23—21no—
891C23—21no—
892C23—21no—
893C23—41no—
894C23—41no—
895C23—42no—
896C23—42no—
897C23—42no—
898C23—42no—
899C23—41no—
900C23—41no—
901C23—41no—
902C23—81no—
903C23C7×#12011yescharacteristic
904C23C7×#12011yescharacteristic
905C23C22×C7×D411yescharacteristic
906Q8—21no—
907Q8—21no—
908Q8—21no—
909Q8—21no—
910Q8—21no—
911Q8—42no—
912Q8—44no—
913Q8—41no—
914Q8—41no—
915Q8—41no—
916Q8—41no—
917Q8C7×#12112yes—
918D4—22no—
919D4—22no—
920D4—21no—
921D4—21no—
922D4—21no—
923D4—21no—
924D4—21no—
925D4—42no—
926D4—42no—
927D4—42no—
928D4—42no—
929D4—44no—
930D4—41no—
931D4—41no—
932D4—41no—
933D4—41no—
934D4—41no—
935D4—41no—
936D4—41no—
937D4—41no—
938D4—81no—
939D4—82no—
940D4—82no—
941D4—82no—
942D4C7×#12112yes—
943C2×C4—21no—
944C2×C4—21no—
945C2×C4—21no—
946C2×C4—21no—
947C2×C4—21no—
948C2×C4—21no—
949C2×C4—21no—
950C2×C4—21no—
951C2×C4—21no—
952C2×C4—22no—
953C2×C4—21no—
954C2×C4—21no—
955C2×C4—22no—
956C2×C4—21no—
957C2×C4—22no—
958C2×C4—21no—
959C2×C4—21no—
960C2×C4—22no—
961C2×C4—21no—
962C2×C4—22no—
963C2×C4—22no—
964C2×C4—22no—
965C2×C4—42no—
966C2×C4—42no—
967C2×C4—42no—
968C2×C4—44no—
969C2×C4—41no—
970C2×C4—41no—
971C2×C4—44no—
972C2×C4—41no—
973C2×C4—41no—
974C2×C4—41no—
975C2×C4—41no—
976C2×C4—42no—
977C2×C4—41no—
978C2×C4—42no—
979C2×C4—41no—
980C2×C4—41no—
981C2×C4—41no—
982C2×C4—82no—
983C2×C4C7×#12011yescharacteristic
984C2×C4C7×#12011yescharacteristic
985C2×C4C22×C7×D411yescharacteristic
986C2×C4C22×C7×D411yescharacteristic
987C2×C4C22×C7×D411yescharacteristic
988C2×C4C2×C7×#4111yescharacteristic
989C2×C4C7×H(5,𝔽2)11yescharacteristic
990C2×C4C7×H(5,𝔽2)11yescharacteristic
991C8—22no—
992C8—41no—
993C8—41no—
994C8—41no—
995C7#2446911yescharacteristic, direct product factor, Sylow
996C22—21no—
997C22—21no—
998C22—21no—
999C22—21no—
1000C22—22no—
1001C22—21no—
1002C22—21no—
1003C22—21no—
1004C22—21no—
1005C22—41no—
1006C22—41no—
1007C22—41no—
1008C22—41no—
1009C22—41no—
1010C22—41no—
1011C22—41no—
1012C22—41no—
1013C22—81no—
1014C22—81no—
1015C22—82no—
1016C22—82no—
1017C22—84no—
1018C22—81no—
1019C22—81no—
1020C22—81no—
1021C22C2×C7×#12011yescharacteristic
1022C22C7×D4211yescharacteristic
1023C22C7×#54611yescharacteristic
1024C4—21no—
1025C4—21no—
1026C4—22no—
1027C4—42no—
1028C4—42no—
1029C4—41no—
1030C4—41no—
1031C4—41no—
1032C4—42no—
1033C4—41no—
1034C4—81no—
1035C4—81no—
1036C4C2×C7×#12111yescharacteristic
1037C4C7×#53411yescharacteristic
1038C4C7×D4211yescharacteristic
1039C4C7×#54611yescharacteristic
1040C2—21no—
1041C2—21no—
1042C2—41no—
1043C2—41no—
1044C2—42no—
1045C2—81no—
1046C2—81no—
1047C2—161no—
1048C2C7×#241011yescharacteristic
1049C2C7×#302011yescharacteristic
1050C2C7×#302111yescharacteristic
subgroupG/H
center, socleC22×C7C2×#120
commutator, Frattini, cosocleC22×C4C24×C7
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C7 ◁ C23×C4×C7 ◁ G

Complements

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

NH ≅ G/Ntype
1. C7×#3489C2semidirect
2. C7×#3055C2semidirect
3. C2×C7×#454C2semidirect
4. C7×#3006C2semidirect
5. C2×C7×#421C2semidirect
6. C7×#2620C2semidirect
7. C7×#2039C2semidirect
8. C7×#2038C2semidirect
9. C7×#2006C2semidirect
10. C7×#2003C2semidirect
11. C7×#1901C2semidirect
12. C7×#1897C2semidirect
13. C7×#1883C2semidirect
14. C7×#1859C2semidirect
15. C7×#1793C2semidirect
20. C2×C7×AGL(1,ℤ/8)C22semidirect
32. C2×C7×#124C22semidirect
49. C7×#428C22semidirect
55. C2×C7×#104C22semidirect
56. C2×C7×#104C22semidirect
57. C7×#418C22semidirect
60. C7×#417C22semidirect
61. C2×C7×#101C22semidirect
62. C2×C7×#101C22semidirect
66. C7×#391C22semidirect
67. C7×#390C22semidirect
68. C7×#384C22semidirect
69. C7×#343C22semidirect
70. C7×#343C22semidirect
71. C7×#339C22semidirect
72. C7×#339C22semidirect
73. #24469C7direct (N × H)
193. C7×#104D4semidirect
207. #3489C2×C7semidirect
208. #3055C2×C7semidirect
209. C2×#454C2×C7semidirect
210. #3006C2×C7semidirect
211. C2×#421C2×C7semidirect
212. #2620C2×C7semidirect
213. #2039C2×C7semidirect
214. #2038C2×C7semidirect
215. #2006C2×C7semidirect
216. #2003C2×C7semidirect
217. #1901C2×C7semidirect
218. #1897C2×C7semidirect
219. #1883C2×C7semidirect
220. #1859C2×C7semidirect
221. #1793C2×C7semidirect
383. C2×AGL(1,ℤ/8)C22×C7semidirect
395. C2×#124C22×C7semidirect
412. #428C22×C7semidirect
418. C2×#104C22×C7semidirect
419. C2×#104C22×C7semidirect
420. #418C22×C7semidirect
423. #417C22×C7semidirect
424. C2×#101C22×C7semidirect
425. C2×#101C22×C7semidirect
429. #391C22×C7semidirect
430. #390C22×C7semidirect
431. #384C22×C7semidirect
432. #343C22×C7semidirect
433. #343C22×C7semidirect
434. #339C22×C7semidirect
435. #339C22×C7semidirect
662. #104C7×D4semidirect
995. C7#24469direct (N × H)

Maximal subgroups

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

subgroupindex
C7×#34892
C7×#30552
C2×C7×#4542
C7×#30062
C2×C7×#4212
C7×#26202
C7×#20392
C7×#20382
C7×#20062
C7×#20032
C7×#19012
C7×#18972
C7×#18832
C7×#18592
C7×#17932
#244697