Finite Group Databasebeta

← C7×#24103 #13201319

Subgroups — C7×#24103 #13201319

Order 1792.

1110 conjugacy classes of subgroups.

The subgroup lattice has 746 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C7×#553C211yesmaximal, characteristic
2C2×C7×#482C211yesmaximal, characteristic, complemented
3C2×C7×#428C211yesmaximal, characteristic, complemented
4C7×#2485C211yesmaximal, characteristic, complemented
5C7×#2059C211yesmaximal, characteristic, complemented
6C7×#2059C211yesmaximal, characteristic, complemented
7C7×#2034C211yesmaximal, characteristic, complemented
8C7×#2033C211yesmaximal, characteristic, complemented
9C7×#1895C211yesmaximal, characteristic, complemented
10C7×#1870C211yesmaximal, characteristic, complemented
11C7×#1864C211yesmaximal, characteristic, complemented
12C7×#1862C211yesmaximal, characteristic, complemented
13C7×#1854C211yesmaximal, characteristic, complemented
14C7×#1854C211yesmaximal, characteristic, complemented
15C7×#1823C211yesmaximal, characteristic, complemented
16C22×C7×M16C2211yescharacteristic
17C7×#553—24no—
18C7×#553—24no—
19C2×C7×#126—21no—
20C2×C7×#125C2211yescharacteristic
21C2×C7×#123—21no—
22C2×C7×#121—21no—
23C2×C7×#121C2211yescharacteristic
24C2×C7×#121C2211yescharacteristic
25C2×C4×C7×D4—21no—
26C2×C4×C7×D4C2211yescharacteristic
27C2×C4×C7×D4C2211yescharacteristic
28C2×C7×#117C2211yescharacteristic
29C2×C7×#117C2211yescharacteristic
30C22×C7×C4⋊C4C2211yescharacteristic
31C7×#482—24no—
32C7×#428—24no—
33C2×C7×#107C2211yescharacteristic
34C2×C7×#107C2211yescharacteristic
35C2×C7×#107C2211yescharacteristic
36C2×C7×#106C2211yescharacteristic
37C2×C7×#106C2211yescharacteristic
38C2×C7×#106C2211yescharacteristic
39C2×C7×#102C2211yescharacteristic
40C2×C7×#102C2211yescharacteristic
41C2×C7×#102C2211yescharacteristic
42C2×C7×#102C2211yescharacteristic
43C2×C7×C22⋊C8C2211yescharacteristic
44C2×C7×C22⋊C8C2211yescharacteristic
45C2×C7×C22⋊C8C2211yescharacteristic
46C7×#397—21no—
47C7×#394—21no—
48C7×#389C2211yescharacteristic
49C7×#389C2211yescharacteristic
50C7×#388—21no—
51C7×#387—21no—
52C7×#380C2211yescharacteristic
53C7×#380C2211yescharacteristic
54C7×#380C2211yescharacteristic
55C7×#340C2211yescharacteristic
56C7×#340C2211yescharacteristic
57C7×#340C2211yescharacteristic
58C7×#340C2211yescharacteristic
59C7×#340C2211yescharacteristic
60C7×#340C2211yescharacteristic
61C7×#336C2211yescharacteristic
62C7×#336C2211yescharacteristic
63#24103C711yesmaximal, characteristic, direct product factor, Sylow
64C22×C7×D4—21no—
65C22×C7×D4—21no—
66C22×C7×D4D411yescharacteristic
67C22×C7×D4C2311yescharacteristic
68C23×C4×C7—21no—
69C23×C4×C7—21no—
70C23×C4×C7C2311yescharacteristic
71C23×C4×C7C2311yescharacteristic
72C2×C7×M16—22no—
73C2×C7×M16—22no—
74C2×C7×M16—22no—
75C22×C7×C8C2311yescharacteristic
76C22×C7×C8C2311yescharacteristic
77C22×C7×C8C2311yescharacteristic
78C22×C7×C8C2311yescharacteristic
79C7×#126—28no—
80C7×#125—22no—
81C7×#125—22no—
82C7×#123—28no—
83C7×#121—28no—
84C7×#121—22no—
85C7×#121—22no—
86C7×#121—22no—
87C7×#121D414yes—
88C4×C7×D4—28no—
89C4×C7×D4—22no—
90C4×C7×D4—22no—
91C4×C7×D4—22no—
92C4×C7×D4—22no—
93C7×#117—22no—
94C7×#117—22no—
95C7×#117—22no—
96C7×#117—22no—
97C2×C7×C4⋊C4—21no—
98C2×C7×C4⋊C4—22no—
99C2×C7×C4⋊C4—21no—
100C2×C7×C4⋊C4—21no—
101C2×C7×C4⋊C4—21no—
102C2×C7×C4⋊C4—21no—
103C2×C7×C4⋊C4D411yescharacteristic
104C2×C7×C4⋊C4D414yes—
105C2×C7×C4⋊C4C2311yescharacteristic
106C2×C7×C4⋊C4C2311yescharacteristic
107C2×C7×C4⋊C4C2311yescharacteristic
108C2×C7×C4⋊C4C2311yescharacteristic
109C2×C7×C4⋊C4C2311yescharacteristic
110C2×C7×C4⋊C4C2311yescharacteristic
111C2×C7×C4⋊C4C2311yescharacteristic
112C2×C7×C22⋊C4—21no—
113C2×C7×C22⋊C4—21no—
114C2×C7×C22⋊C4—21no—
115C2×C7×C22⋊C4—21no—
116C2×C7×C22⋊C4—21no—
117C2×C7×C22⋊C4—21no—
118C2×C7×C22⋊C4—21no—
119C2×C7×C22⋊C4—21no—
120C2×C7×C22⋊C4D411yescharacteristic
121C2×C7×C22⋊C4D411yescharacteristic
122C2×C42×C7—21no—
123C2×C42×C7—21no—
124C2×C42×C7C2311yescharacteristic
125C7×#107—22no—
126C7×#107—22no—
127C7×#107—22no—
128C7×#106—22no—
129C7×#106—22no—
130C7×#106—22no—
131C7×#102—22no—
132C7×#102—22no—
133C7×#102—22no—
134C7×#102—22no—
135C7×C22⋊C8—22no—
136C7×C22⋊C8—22no—
137C7×C22⋊C8—22no—
138C7×#95—21no—
139C7×#95—21no—
140C7×#95—21no—
141C7×#95—21no—
142C7×#95—21no—
143C2×#553C2×C711yescharacteristic
144C2×#482C2×C711yescharacteristic, complemented
145C2×#428C2×C711yescharacteristic, complemented
146#2485C2×C711yescharacteristic, complemented
147#2059C2×C711yescharacteristic, complemented
148#2059C2×C711yescharacteristic, complemented
149#2034C2×C711yescharacteristic, complemented
150#2033C2×C711yescharacteristic, complemented
151#1895C2×C711yescharacteristic, complemented
152#1870C2×C711yescharacteristic, complemented
153#1864C2×C711yescharacteristic, complemented
154#1862C2×C711yescharacteristic, complemented
155#1854C2×C711yescharacteristic, complemented
156#1854C2×C711yescharacteristic, complemented
157#1823C2×C711yescharacteristic, complemented
158C24×C7—21no—
159C24×C7C2×D411yescharacteristic
160C24×C7C2×D411yescharacteristic
161C2×C7×D4—22no—
162C2×C7×D4—24no—
163C2×C7×D4—24no—
164C2×C7×D4—21no—
165C2×C7×D4—21no—
166C2×C7×D4—21no—
167C2×C7×D4—21no—
168C2×C7×D4—21no—
169C2×C7×D4—41no—
170C2×C7×D4—41no—
171C2×C7×D4—42no—
172C2×C7×D4—42no—
173C2×C7×D4—81no—
174C2×C7×D4—81no—
175C2×C7×D4C2×D412yes—
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—24no—
184C22×C4×C7—24no—
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—81no—
196C22×C4×C7—81no—
197C22×C4×C7—81no—
198C22×C4×C7—81no—
199C22×C4×C7C2×D411yescharacteristic
200C22×C4×C7C2×D411yescharacteristic
201C22×C4×C7C2×D411yescharacteristic
202C22×C4×C7C2×D411yescharacteristic
203C22×C4×C7C2×D412yes—
204C22×C4×C7C2×D412yes—
205C22×C4×C7C2411yescharacteristic
206C7×M16—28no—
207C2×C7×C8—21no—
208C2×C7×C8—21no—
209C2×C7×C8—21no—
210C2×C7×C8—21no—
211C2×C7×C8—21no—
212C2×C7×C8—21no—
213C2×C7×C8—21no—
214C2×C7×C8—21no—
215C2×C7×C8—21no—
216C2×C7×C8—21no—
217C2×C7×C8#4112yes—
218C2×C7×C8#4112yes—
219C7×C4⋊C4—24no—
220C7×C4⋊C4—24no—
221C7×C4⋊C4—24no—
222C7×C4⋊C4—22no—
223C7×C4⋊C4—21no—
224C7×C4⋊C4—21no—
225C7×C4⋊C4—21no—
226C7×C4⋊C4—21no—
227C7×C4⋊C4—21no—
228C7×C4⋊C4—21no—
229C7×C4⋊C4—21no—
230C7×C4⋊C4—21no—
231C7×C4⋊C4—21no—
232C7×C4⋊C4—21no—
233C7×C4⋊C4—21no—
234C7×C4⋊C4—42no—
235C7×C4⋊C4—81no—
236C7×C4⋊C4C2×D412yes—
237C7×C4⋊C4C2×D412yes—
238C7×C4⋊C4C2×D412yes—
239C7×C22⋊C4—24no—
240C7×C22⋊C4—24no—
241C7×C22⋊C4—24no—
242C7×C22⋊C4—22no—
243C7×C22⋊C4—24no—
244C7×C22⋊C4—22no—
245C7×C22⋊C4—42no—
246C7×C22⋊C4—42no—
247C7×C22⋊C4—81no—
248C7×C22⋊C4—81no—
249C42×C7—24no—
250C42×C7—21no—
251C42×C7—21no—
252C42×C7—42no—
253C22×M16C22×C711yescharacteristic
254#553—24no—
255#553—24no—
256C2×#126—21no—
257C2×#125C22×C711yescharacteristic
258C2×#123—21no—
259C2×#121—21no—
260C2×#121C22×C711yescharacteristic
261C2×#121C22×C711yescharacteristic
262C2×C4×D4—21no—
263C2×C4×D4C22×C711yescharacteristic
264C2×C4×D4C22×C711yescharacteristic
265C2×#117C22×C711yescharacteristic
266C2×#117C22×C711yescharacteristic
267C22×C4⋊C4C22×C711yescharacteristic
268#482—24no—
269#428—24no—
270C2×#107C22×C711yescharacteristic
271C2×#107C22×C711yescharacteristic
272C2×#107C22×C711yescharacteristic
273C2×#106C22×C711yescharacteristic
274C2×#106C22×C711yescharacteristic
275C2×#106C22×C711yescharacteristic
276C2×#102C22×C711yescharacteristic
277C2×#102C22×C711yescharacteristic
278C2×#102C22×C711yescharacteristic
279C2×#102C22×C711yescharacteristic
280C2×C22⋊C8C22×C711yescharacteristic
281C2×C22⋊C8C22×C711yescharacteristic
282C2×C22⋊C8C22×C711yescharacteristic
283#397—21no—
284#394—21no—
285#389C22×C711yescharacteristic
286#389C22×C711yescharacteristic
287#388—21no—
288#387—21no—
289#380C22×C711yescharacteristic
290#380C22×C711yescharacteristic
291#380C22×C711yescharacteristic
292#340C22×C711yescharacteristic
293#340C22×C711yescharacteristic
294#340C22×C711yescharacteristic
295#340C22×C711yescharacteristic
296#340C22×C711yescharacteristic
297#340C22×C711yescharacteristic
298#336C22×C711yescharacteristic
299#336C22×C711yescharacteristic
300C23×C7—21no—
301C23×C7—21no—
302C23×C7—21no—
303C23×C7—21no—
304C23×C7—21no—
305C23×C7—21no—
306C23×C7—21no—
307C23×C7—22no—
308C23×C7—21no—
309C23×C7—21no—
310C23×C7—21no—
311C23×C7—21no—
312C23×C7—21no—
313C23×C7—21no—
314C23×C7—41no—
315C23×C7—41no—
316C23×C7—41no—
317C23×C7—41no—
318C23×C7—41no—
319C23×C7—41no—
320C23×C7#12012yes—
321C23×C7C22×D411yescharacteristic
322C7×D4—22no—
323C7×D4—22no—
324C7×D4—44no—
325C7×D4—48no—
326C7×D4—41no—
327C7×D4—41no—
328C7×D4—84no—
329C2×C4×C7—21no—
330C2×C4×C7—21no—
331C2×C4×C7—22no—
332C2×C4×C7—22no—
333C2×C4×C7—22no—
334C2×C4×C7—22no—
335C2×C4×C7—21no—
336C2×C4×C7—21no—
337C2×C4×C7—22no—
338C2×C4×C7—21no—
339C2×C4×C7—22no—
340C2×C4×C7—22no—
341C2×C4×C7—21no—
342C2×C4×C7—21no—
343C2×C4×C7—21no—
344C2×C4×C7—21no—
345C2×C4×C7—21no—
346C2×C4×C7—21no—
347C2×C4×C7—41no—
348C2×C4×C7—41no—
349C2×C4×C7—41no—
350C2×C4×C7—41no—
351C2×C4×C7—41no—
352C2×C4×C7—41no—
353C2×C4×C7—41no—
354C2×C4×C7—41no—
355C2×C4×C7—41no—
356C2×C4×C7—41no—
357C2×C4×C7—41no—
358C2×C4×C7—41no—
359C2×C4×C7—41no—
360C2×C4×C7—41no—
361C2×C4×C7—41no—
362C2×C4×C7—41no—
363C2×C4×C7—41no—
364C2×C4×C7—41no—
365C2×C4×C7—41no—
366C2×C4×C7—41no—
367C2×C4×C7—41no—
368C2×C4×C7—41no—
369C2×C4×C7—84no—
370C2×C4×C7—84no—
371C2×C4×C7#12012yes—
372C2×C4×C7C22×D411yescharacteristic
373C2×C4×C7C22×D411yescharacteristic
374C2×C4×C7C2×#4111yescharacteristic
375C2×C4×C7C2×#4111yescharacteristic
376C2×C4×C72−1+411yescharacteristic
377C2×C4×C72−1+411yescharacteristic
378C7×C8—22no—
379C7×C8—22no—
380C7×C8—41no—
381C7×C8—41no—
382C22×D4—21no—
383C22×D4—21no—
384C22×D4C7×D411yescharacteristic
385C22×D4C23×C711yescharacteristic
386C23×C4—21no—
387C23×C4—21no—
388C23×C4C23×C711yescharacteristic
389C23×C4C23×C711yescharacteristic
390C2×M16—22no—
391C2×M16—22no—
392C2×M16—22no—
393C22×C8C23×C711yescharacteristic
394C22×C8C23×C711yescharacteristic
395C22×C8C23×C711yescharacteristic
396C22×C8C23×C711yescharacteristic
397#126—28no—
398#125—22no—
399#125—22no—
400#123—28no—
401#121—28no—
402#121—22no—
403#121—22no—
404#121—22no—
405#121C7×D414yes—
406C4×D4—28no—
407C4×D4—22no—
408C4×D4—22no—
409C4×D4—22no—
410C4×D4—22no—
411#117—22no—
412#117—22no—
413#117—22no—
414#117—22no—
415C2×C4⋊C4—21no—
416C2×C4⋊C4—22no—
417C2×C4⋊C4—21no—
418C2×C4⋊C4—21no—
419C2×C4⋊C4—21no—
420C2×C4⋊C4—21no—
421C2×C4⋊C4C7×D411yescharacteristic
422C2×C4⋊C4C7×D414yes—
423C2×C4⋊C4C23×C711yescharacteristic
424C2×C4⋊C4C23×C711yescharacteristic
425C2×C4⋊C4C23×C711yescharacteristic
426C2×C4⋊C4C23×C711yescharacteristic
427C2×C4⋊C4C23×C711yescharacteristic
428C2×C4⋊C4C23×C711yescharacteristic
429C2×C4⋊C4C23×C711yescharacteristic
430C2×C22⋊C4—21no—
431C2×C22⋊C4—21no—
432C2×C22⋊C4—21no—
433C2×C22⋊C4—21no—
434C2×C22⋊C4—21no—
435C2×C22⋊C4—21no—
436C2×C22⋊C4—21no—
437C2×C22⋊C4—21no—
438C2×C22⋊C4C7×D411yescharacteristic
439C2×C22⋊C4C7×D411yescharacteristic
440C2×C42—21no—
441C2×C42—21no—
442C2×C42C23×C711yescharacteristic
443#107—22no—
444#107—22no—
445#107—22no—
446#106—22no—
447#106—22no—
448#106—22no—
449#102—22no—
450#102—22no—
451#102—22no—
452#102—22no—
453C22⋊C8—22no—
454C22⋊C8—22no—
455C22⋊C8—22no—
456#95—21no—
457#95—21no—
458#95—21no—
459#95—21no—
460#95—21no—
461C22×C7—22no—
462C22×C7—22no—
463C22×C7—22no—
464C22×C7—41no—
465C22×C7—41no—
466C22×C7—41no—
467C22×C7—41no—
468C22×C7—41no—
469C22×C7—41no—
470C22×C7—41no—
471C22×C7—41no—
472C22×C7—41no—
473C22×C7—42no—
474C22×C7—41no—
475C22×C7—42no—
476C22×C7—42no—
477C22×C7—41no—
478C22×C7—81no—
479C22×C7—81no—
480C22×C7—81no—
481C22×C7—81no—
482C22×C7C2×#12011yescharacteristic
483C22×C7#54711yescharacteristic
484C22×C7#54711yescharacteristic
485C22×C7#57511yescharacteristic
486C22×C7#57511yescharacteristic
487C22×C7#57611yescharacteristic
488C22×C7#57711yescharacteristic
489C4×C7—22no—
490C4×C7—41no—
491C4×C7—41no—
492C4×C7—42no—
493C4×C7—41no—
494C4×C7—42no—
495C4×C7—42no—
496C4×C7—81no—
497C4×C7—81no—
498C4×C7—81no—
499C4×C7—81no—
500C4×C7#52511yescharacteristic
501C4×C7#53611yescharacteristic
502C4×C7#54711yescharacteristic
503C4×C7#54711yescharacteristic
504C24—21no—
505C24C2×C7×D411yescharacteristic
506C24C2×C7×D411yescharacteristic
507C2×D4—22no—
508C2×D4—24no—
509C2×D4—24no—
510C2×D4—21no—
511C2×D4—21no—
512C2×D4—21no—
513C2×D4—21no—
514C2×D4—21no—
515C2×D4—41no—
516C2×D4—41no—
517C2×D4—42no—
518C2×D4—42no—
519C2×D4—81no—
520C2×D4—81no—
521C2×D4C2×C7×D412yes—
522C22×C4—21no—
523C22×C4—21no—
524C22×C4—21no—
525C22×C4—21no—
526C22×C4—21no—
527C22×C4—21no—
528C22×C4—21no—
529C22×C4—24no—
530C22×C4—24no—
531C22×C4—21no—
532C22×C4—21no—
533C22×C4—21no—
534C22×C4—21no—
535C22×C4—21no—
536C22×C4—21no—
537C22×C4—21no—
538C22×C4—21no—
539C22×C4—21no—
540C22×C4—21no—
541C22×C4—81no—
542C22×C4—81no—
543C22×C4—81no—
544C22×C4—81no—
545C22×C4C2×C7×D411yescharacteristic
546C22×C4C2×C7×D411yescharacteristic
547C22×C4C2×C7×D411yescharacteristic
548C22×C4C2×C7×D411yescharacteristic
549C22×C4C2×C7×D412yes—
550C22×C4C2×C7×D412yes—
551C22×C4C24×C711yescharacteristic
552M16—28no—
553C2×C8—21no—
554C2×C8—21no—
555C2×C8—21no—
556C2×C8—21no—
557C2×C8—21no—
558C2×C8—21no—
559C2×C8—21no—
560C2×C8—21no—
561C2×C8—21no—
562C2×C8—21no—
563C2×C8C7×#4112yes—
564C2×C8C7×#4112yes—
565C4⋊C4—24no—
566C4⋊C4—24no—
567C4⋊C4—24no—
568C4⋊C4—22no—
569C4⋊C4—21no—
570C4⋊C4—21no—
571C4⋊C4—21no—
572C4⋊C4—21no—
573C4⋊C4—21no—
574C4⋊C4—21no—
575C4⋊C4—21no—
576C4⋊C4—21no—
577C4⋊C4—21no—
578C4⋊C4—21no—
579C4⋊C4—21no—
580C4⋊C4—42no—
581C4⋊C4—81no—
582C4⋊C4C2×C7×D412yes—
583C4⋊C4C2×C7×D412yes—
584C4⋊C4C2×C7×D412yes—
585C22⋊C4—24no—
586C22⋊C4—24no—
587C22⋊C4—24no—
588C22⋊C4—22no—
589C22⋊C4—24no—
590C22⋊C4—22no—
591C22⋊C4—42no—
592C22⋊C4—42no—
593C22⋊C4—81no—
594C22⋊C4—81no—
595C42—24no—
596C42—21no—
597C42—21no—
598C42—42no—
599C2×C7—42no—
600C2×C7—81no—
601C2×C7—82no—
602C2×C7#240611yescharacteristic
603C2×C7#300511yescharacteristic
604C2×C7#301211yescharacteristic
605C2×C7#334711yescharacteristic
606C2×C7#335011yescharacteristic
607C2×C7#335111yescharacteristic
608C2×C7#335511yescharacteristic
609C23—21no—
610C23—21no—
611C23—21no—
612C23—21no—
613C23—21no—
614C23—21no—
615C23—21no—
616C23—22no—
617C23—21no—
618C23—21no—
619C23—21no—
620C23—21no—
621C23—21no—
622C23—21no—
623C23—41no—
624C23—41no—
625C23—41no—
626C23—41no—
627C23—41no—
628C23—41no—
629C23C7×#12012yes—
630C23C22×C7×D411yescharacteristic
631D4—22no—
632D4—22no—
633D4—44no—
634D4—48no—
635D4—41no—
636D4—41no—
637D4—84no—
638C2×C4—21no—
639C2×C4—21no—
640C2×C4—22no—
641C2×C4—22no—
642C2×C4—22no—
643C2×C4—22no—
644C2×C4—21no—
645C2×C4—21no—
646C2×C4—22no—
647C2×C4—21no—
648C2×C4—22no—
649C2×C4—22no—
650C2×C4—21no—
651C2×C4—21no—
652C2×C4—21no—
653C2×C4—21no—
654C2×C4—21no—
655C2×C4—21no—
656C2×C4—41no—
657C2×C4—41no—
658C2×C4—41no—
659C2×C4—41no—
660C2×C4—41no—
661C2×C4—41no—
662C2×C4—41no—
663C2×C4—41no—
664C2×C4—41no—
665C2×C4—41no—
666C2×C4—41no—
667C2×C4—41no—
668C2×C4—41no—
669C2×C4—41no—
670C2×C4—41no—
671C2×C4—41no—
672C2×C4—41no—
673C2×C4—41no—
674C2×C4—41no—
675C2×C4—41no—
676C2×C4—41no—
677C2×C4—41no—
678C2×C4—84no—
679C2×C4—84no—
680C2×C4C7×#12012yes—
681C2×C4C22×C7×D411yescharacteristic
682C2×C4C22×C7×D411yescharacteristic
683C2×C4C2×C7×#4111yescharacteristic
684C2×C4C2×C7×#4111yescharacteristic
685C2×C4C7×2−1+411yescharacteristic
686C2×C4C7×2−1+411yescharacteristic
687C8—22no—
688C8—22no—
689C8—41no—
690C8—41no—
691C7#2410311yescharacteristic, direct product factor, Sylow
692C22—22no—
693C22—22no—
694C22—22no—
695C22—41no—
696C22—41no—
697C22—41no—
698C22—41no—
699C22—41no—
700C22—42no—
701C22—41no—
702C22—42no—
703C22—42no—
704C22—41no—
705C22—41no—
706C22—41no—
707C22—41no—
708C22—41no—
709C22—81no—
710C22—81no—
711C22—81no—
712C22—81no—
713C22C2×C7×#12011yescharacteristic
714C22C7×#54711yescharacteristic
715C22C7×#54711yescharacteristic
716C22C7×#57511yescharacteristic
717C22C7×#57511yescharacteristic
718C22C7×#57611yescharacteristic
719C22C7×#57711yescharacteristic
720C4—22no—
721C4—41no—
722C4—41no—
723C4—42no—
724C4—41no—
725C4—42no—
726C4—42no—
727C4—81no—
728C4—81no—
729C4—81no—
730C4—81no—
731C4C7×#52511yescharacteristic
732C4C7×#53611yescharacteristic
733C4C7×#54711yescharacteristic
734C4C7×#54711yescharacteristic
735C2—42no—
736C2—81no—
737C2—82no—
738C2C7×#240611yescharacteristic
739C2C7×#300511yescharacteristic
740C2C7×#301211yescharacteristic
741C2C7×#334711yescharacteristic
742C2C7×#335011yescharacteristic
743C2C7×#335111yescharacteristic
744C2C7×#335511yescharacteristic
subgroupG/H
center, socleC23×C7C22×D4
commutator, Frattini, cosocleC22×C4C24×C7
prime radicalC2×C7×#553C2
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C7 ◁ C2×C4×C7×D4 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×C7×#482C2semidirect
3. C2×C7×#428C2semidirect
4. C7×#2485C2semidirect
5. C7×#2059C2semidirect
6. C7×#2059C2semidirect
7. C7×#2034C2semidirect
8. C7×#2033C2semidirect
9. C7×#1895C2semidirect
10. C7×#1870C2semidirect
11. C7×#1864C2semidirect
12. C7×#1862C2semidirect
13. C7×#1854C2semidirect
14. C7×#1854C2semidirect
15. C7×#1823C2semidirect
63. #24103C7direct (N × H)
144. C2×#482C2×C7semidirect
145. C2×#428C2×C7semidirect
146. #2485C2×C7semidirect
147. #2059C2×C7semidirect
148. #2059C2×C7semidirect
149. #2034C2×C7semidirect
150. #2033C2×C7semidirect
151. #1895C2×C7semidirect
152. #1870C2×C7semidirect
153. #1864C2×C7semidirect
154. #1862C2×C7semidirect
155. #1854C2×C7semidirect
156. #1854C2×C7semidirect
157. #1823C2×C7semidirect
691. C7#24103direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C7×#5532
C2×C7×#4822
C2×C7×#4282
C7×#24852
C7×#20592
C7×#20342
C7×#20332
C7×#18952
C7×#18702
C7×#18642
C7×#18622
C7×#18542
C7×#18232
#241037