Finite Group Databasebeta

← C7×#25165 #13202381

Subgroups — C7×#25165 #13202381

Order 1792.

1180 conjugacy classes of subgroups.

The subgroup lattice has 816 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C7×#460C211yesmaximal, characteristic, complemented
2C2×C7×#448C211yesmaximal, characteristic, complemented
3C2×C7×#448C211yesmaximal, characteristic, complemented
4C2×C7×#440C211yesmaximal, characteristic, complemented
5C7×#2428C211yesmaximal, characteristic
6C7×Q8×C22⋊C4C211yesmaximal, characteristic, complemented
7C7×#2068C211yesmaximal, characteristic, complemented
8C7×#2033C211yesmaximal, characteristic, complemented
9C7×#2033C211yesmaximal, characteristic, complemented
10C7×#2014C211yesmaximal, characteristic, complemented
11C7×#1973C211yesmaximal, characteristic, complemented
12C7×#1924C211yesmaximal, characteristic, complemented
13C7×#1880C211yesmaximal, characteristic, complemented
14C7×#1877C211yesmaximal, characteristic, complemented
15C7×#1863C211yesmaximal, characteristic, complemented
16C23×C7×Q8C2211yescharacteristic
17C22×C7×SD16C2211yescharacteristic
18C22×C7×SD16C2211yescharacteristic
19C22×C7×SD16C2211yescharacteristic
20C22×C7×SD16C2211yescharacteristic
21C2×C7×#127C2211yescharacteristic
22C2×C7×#121—21no—
23C2×C7×#121C2211yescharacteristic
24C2×C7×#121C2211yescharacteristic
25C2×C4×C7×Q8C2211yescharacteristic
26C2×C4×C7×Q8C2211yescharacteristic
27C2×C4×C7×D4C2211yescharacteristic
28C7×#460—24no—
29C7×#448—24no—
30C7×#448—24no—
31C7×#440—24no—
32C2×C7×#107C2211yescharacteristic
33C2×C7×#107C2211yescharacteristic
34C2×C7×C4⋊C8C2211yescharacteristic
35C2×C7×#103C2211yescharacteristic
36C2×C7×#103C2211yescharacteristic
37C2×C7×#103C2211yescharacteristic
38C2×C7×#103C2211yescharacteristic
39C2×C7×#102C2211yescharacteristic
40C2×C7×#102C2211yescharacteristic
41C2×C7×#102C2211yescharacteristic
42C2×C7×#102C2211yescharacteristic
43C2×C7×C22⋊C8C2211yescharacteristic
44C2×C7×C22⋊C8C2211yescharacteristic
45C2×C7×#97C2211yescharacteristic
46C7×#394—21no—
47C7×#392—21no—
48C7×#391—21no—
49C7×#391—21no—
50C7×#391C2211yescharacteristic
51C7×#391C2211yescharacteristic
52C7×#390C2211yescharacteristic
53C7×#389C2211yescharacteristic
54C7×#386—21no—
55C7×#380—21no—
56C7×#380C2211yescharacteristic
57C4×C7×C22⋊C4—21no—
58C4×C7×C22⋊C4C2211yescharacteristic
59C7×#340C2211yescharacteristic
60C7×#340C2211yescharacteristic
61C7×#336C2211yescharacteristic
62C7×#336C2211yescharacteristic
63#25165C711yesmaximal, characteristic, direct product factor, Sylow
64C22×C7×Q8—22no—
65C22×C7×Q8—22no—
66C22×C7×Q8—21no—
67C22×C7×Q8—22no—
68C22×C7×Q8—22no—
69C22×C7×Q8—41no—
70C22×C7×Q8—41no—
71C22×C7×Q8C2311yescharacteristic
72C22×C7×Q8C2311yescharacteristic
73C22×C7×D4—21no—
74C22×C7×D4—21no—
75C22×C7×D4—21no—
76C22×C7×D4—21no—
77C22×C7×D4C2311yescharacteristic
78C22×C7×D4C2311yescharacteristic
79C23×C4×C7—21no—
80C23×C4×C7—21no—
81C23×C4×C7C2311yescharacteristic
82C2×C7×SD16—22no—
83C2×C7×SD16—22no—
84C2×C7×SD16—22no—
85C2×C7×SD16—22no—
86C2×C7×SD16—22no—
87C2×C7×SD16—22no—
88C2×C7×SD16—22no—
89C2×C7×SD16—22no—
90C2×C7×SD16—22no—
91C2×C7×SD16—41no—
92C2×C7×SD16—41no—
93C2×C7×SD16D414yescomplemented
94C22×C7×C8C2311yescharacteristic
95C22×C7×C8C2311yescharacteristic
96C22×C7×C8C2311yescharacteristic
97C22×C7×C8C2311yescharacteristic
98C7×#127—22no—
99C7×#127—41no—
100C7×#121—22no—
101C7×#121—22no—
102C7×#121—44no—
103C7×#121—41no—
104C7×#121—41no—
105C4×C7×Q8—22no—
106C4×C7×Q8—22no—
107C4×C7×Q8—41no—
108C4×C7×Q8—41no—
109C4×C7×D4—22no—
110C4×C7×D4—41no—
111C2×C7×C4⋊C4—21no—
112C2×C7×C4⋊C4—21no—
113C2×C7×C4⋊C4—21no—
114C2×C7×C4⋊C4C2311yescharacteristic
115C2×C7×C4⋊C4C2311yescharacteristic
116C2×C7×C4⋊C4C2311yescharacteristic
117C2×C7×C4⋊C4C2311yescharacteristic
118C2×C7×C22⋊C4—21no—
119C2×C7×C22⋊C4—21no—
120C2×C7×C22⋊C4—21no—
121C2×C7×C22⋊C4—21no—
122C2×C7×C22⋊C4—21no—
123C2×C7×C22⋊C4—21no—
124C2×C7×C22⋊C4D411yescharacteristic
125C2×C7×C22⋊C4D411yescharacteristic
126C2×C42×C7—21no—
127C2×C42×C7—21no—
128C2×C42×C7C2311yescharacteristic
129C2×C42×C7C2311yescharacteristic
130C7×#107—22no—
131C7×#107—41no—
132C7×C4⋊C8—22no—
133C7×#103—22no—
134C7×#103—22no—
135C7×#103—22no—
136C7×#103D414yescomplemented
137C7×#102—22no—
138C7×#102—22no—
139C7×#102—22no—
140C7×#102—41no—
141C7×C22⋊C8—22no—
142C7×C22⋊C8—22no—
143C7×#97—22no—
144C7×#95—21no—
145C7×#95—21no—
146C7×#95—21no—
147C7×#95—21no—
148C7×#95—21no—
149C7×#95—21no—
150C7×#95D411yescharacteristic
151C7×#95D411yescharacteristic
152C2×#460C2×C711yescharacteristic, complemented
153C2×#448C2×C711yescharacteristic, complemented
154C2×#448C2×C711yescharacteristic, complemented
155C2×#440C2×C711yescharacteristic, complemented
156#2428C2×C711yescharacteristic
157Q8×C22⋊C4C2×C711yescharacteristic, complemented
158#2068C2×C711yescharacteristic, complemented
159#2033C2×C711yescharacteristic, complemented
160#2033C2×C711yescharacteristic, complemented
161#2014C2×C711yescharacteristic, complemented
162#1973C2×C711yescharacteristic, complemented
163#1924C2×C711yescharacteristic, complemented
164#1880C2×C711yescharacteristic, complemented
165#1877C2×C711yescharacteristic, complemented
166#1863C2×C711yescharacteristic, complemented
167C24×C7—21no—
168C24×C7—21no—
169C24×C7C2×D411yescharacteristic
170C2×C7×Q8—24no—
171C2×C7×Q8—21no—
172C2×C7×Q8—21no—
173C2×C7×Q8—21no—
174C2×C7×Q8—21no—
175C2×C7×Q8—21no—
176C2×C7×Q8—21no—
177C2×C7×Q8—21no—
178C2×C7×Q8—21no—
179C2×C7×Q8—42no—
180C2×C7×Q8—42no—
181C2×C7×Q8—44no—
182C2×C7×Q8—44no—
183C2×C7×Q8—44no—
184C2×C7×Q8—44no—
185C2×C7×Q8C2×D412yes—
186C2×C7×Q8C2×D412yes—
187C2×C7×Q8#4112yes—
188C2×C7×Q8#4112yes—
189C2×C7×D4—21no—
190C2×C7×D4—21no—
191C2×C7×D4—21no—
192C2×C7×D4—21no—
193C2×C7×D4—21no—
194C2×C7×D4—21no—
195C2×C7×D4—21no—
196C2×C7×D4—21no—
197C2×C7×D4—21no—
198C2×C7×D4—21no—
199C2×C7×D4—21no—
200C2×C7×D4—42no—
201C2×C7×D4—42no—
202C2×C7×D4—42no—
203C2×C7×D4—42no—
204C2×C7×D4—42no—
205C2×C7×D4—42no—
206C2×C7×D4—42no—
207C2×C7×D4—42no—
208C2×C7×D4—81no—
209C2×C7×D4—81no—
210C2×C7×D4—81no—
211C2×C7×D4—81no—
212C2×C7×D4C2×D412yes—
213C22×C4×C7—21no—
214C22×C4×C7—24no—
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—42no—
227C22×C4×C7—42no—
228C22×C4×C7—42no—
229C22×C4×C7—42no—
230C22×C4×C7—81no—
231C22×C4×C7C2×D411yescharacteristic
232C22×C4×C7C2×D411yescharacteristic
233C22×C4×C7C2×D411yescharacteristic
234C22×C4×C7C2×D411yescharacteristic
235C22×C4×C7C2×D411yescharacteristic
236C22×C4×C7C2411yescharacteristic
237C7×SD16—28no—
238C7×SD16—44no—
239C7×SD16—44no—
240C7×SD16—44no—
241C2×C7×C8—21no—
242C2×C7×C8—21no—
243C2×C7×C8—21no—
244C2×C7×C8—21no—
245C2×C7×C8—21no—
246C2×C7×C8—21no—
247C2×C7×C8—21no—
248C2×C7×C8—21no—
249C2×C7×C8—21no—
250C2×C7×C8—21no—
251C2×C7×C8C2×D412yes—
252C2×C7×C8C2×D412yes—
253C7×C4⋊C4—21no—
254C7×C4⋊C4—21no—
255C7×C4⋊C4—21no—
256C7×C4⋊C4—21no—
257C7×C4⋊C4—21no—
258C7×C4⋊C4—21no—
259C7×C4⋊C4—21no—
260C7×C4⋊C4—42no—
261C7×C4⋊C4—42no—
262C7×C4⋊C4—42no—
263C7×C4⋊C4C2×D412yes—
264C7×C22⋊C4—22no—
265C7×C22⋊C4—22no—
266C7×C22⋊C4—42no—
267C7×C22⋊C4—42no—
268C7×C22⋊C4—42no—
269C7×C22⋊C4—42no—
270C7×C22⋊C4—42no—
271C7×C22⋊C4—81no—
272C42×C7—21no—
273C42×C7—21no—
274C42×C7—21no—
275C42×C7—21no—
276C42×C7—42no—
277C42×C7—42no—
278C23×Q8C22×C711yescharacteristic
279C22×SD16C22×C711yescharacteristic
280C22×SD16C22×C711yescharacteristic
281C22×SD16C22×C711yescharacteristic
282C22×SD16C22×C711yescharacteristic
283C2×#127C22×C711yescharacteristic
284C2×#121—21no—
285C2×#121C22×C711yescharacteristic
286C2×#121C22×C711yescharacteristic
287C2×C4×Q8C22×C711yescharacteristic
288C2×C4×Q8C22×C711yescharacteristic
289C2×C4×D4C22×C711yescharacteristic
290#460—24no—
291#448—24no—
292#448—24no—
293#440—24no—
294C2×#107C22×C711yescharacteristic
295C2×#107C22×C711yescharacteristic
296C2×C4⋊C8C22×C711yescharacteristic
297C2×#103C22×C711yescharacteristic
298C2×#103C22×C711yescharacteristic
299C2×#103C22×C711yescharacteristic
300C2×#103C22×C711yescharacteristic
301C2×#102C22×C711yescharacteristic
302C2×#102C22×C711yescharacteristic
303C2×#102C22×C711yescharacteristic
304C2×#102C22×C711yescharacteristic
305C2×C22⋊C8C22×C711yescharacteristic
306C2×C22⋊C8C22×C711yescharacteristic
307C2×#97C22×C711yescharacteristic
308#394—21no—
309#392—21no—
310#391—21no—
311#391—21no—
312#391C22×C711yescharacteristic
313#391C22×C711yescharacteristic
314#390C22×C711yescharacteristic
315#389C22×C711yescharacteristic
316#386—21no—
317#380—21no—
318#380C22×C711yescharacteristic
319C4×C22⋊C4—21no—
320C4×C22⋊C4C22×C711yescharacteristic
321#340C22×C711yescharacteristic
322#340C22×C711yescharacteristic
323#336C22×C711yescharacteristic
324#336C22×C711yescharacteristic
325C23×C7—21no—
326C23×C7—21no—
327C23×C7—21no—
328C23×C7—21no—
329C23×C7—21no—
330C23×C7—21no—
331C23×C7—22no—
332C23×C7—41no—
333C23×C7—41no—
334C23×C7—41no—
335C23×C7—41no—
336C23×C7—41no—
337C23×C7—41no—
338C23×C7—41no—
339C23×C7—41no—
340C23×C7—41no—
341C23×C7—41no—
342C23×C7—41no—
343C23×C7—41no—
344C23×C7—41no—
345C23×C7AGL(1,ℤ/8)12yes—
346C23×C7C22×D411yescharacteristic
347C7×Q8—22no—
348C7×Q8—22no—
349C7×Q8—22no—
350C7×Q8—22no—
351C7×Q8—22no—
352C7×Q8—48no—
353C7×Q8—41no—
354C7×Q8—41no—
355C7×Q8#12114yescomplemented
356C7×D4—22no—
357C7×D4—22no—
358C7×D4—41no—
359C7×D4—41no—
360C7×D4—41no—
361C7×D4—41no—
362C7×D4—41no—
363C7×D4—41no—
364C7×D4—84no—
365C7×D4—84no—
366C7×D4—84no—
367C7×D4—84no—
368C2×C4×C7—22no—
369C2×C4×C7—21no—
370C2×C4×C7—22no—
371C2×C4×C7—22no—
372C2×C4×C7—21no—
373C2×C4×C7—22no—
374C2×C4×C7—21no—
375C2×C4×C7—21no—
376C2×C4×C7—21no—
377C2×C4×C7—21no—
378C2×C4×C7—22no—
379C2×C4×C7—21no—
380C2×C4×C7—21no—
381C2×C4×C7—21no—
382C2×C4×C7—21no—
383C2×C4×C7—21no—
384C2×C4×C7—21no—
385C2×C4×C7—21no—
386C2×C4×C7—21no—
387C2×C4×C7—48no—
388C2×C4×C7—41no—
389C2×C4×C7—41no—
390C2×C4×C7—41no—
391C2×C4×C7—41no—
392C2×C4×C7—41no—
393C2×C4×C7—41no—
394C2×C4×C7—41no—
395C2×C4×C7—41no—
396C2×C4×C7—41no—
397C2×C4×C7—41no—
398C2×C4×C7—41no—
399C2×C4×C7—41no—
400C2×C4×C7—41no—
401C2×C4×C7—41no—
402C2×C4×C7—41no—
403C2×C4×C7—41no—
404C2×C4×C7—41no—
405C2×C4×C7—84no—
406C2×C4×C7#13712yes—
407C2×C4×C7C22×D411yescharacteristic
408C2×C4×C7C22×D411yescharacteristic
409C2×C4×C7C2×#4111yescharacteristic
410C2×C4×C7C2×#4111yescharacteristic
411C2×C4×C7H(5,𝔽2)11yescharacteristic
412C2×C4×C7H(5,𝔽2)11yescharacteristic
413C7×C8—22no—
414C7×C8—22no—
415C7×C8—41no—
416C7×C8—41no—
417C22×Q8—22no—
418C22×Q8—22no—
419C22×Q8—21no—
420C22×Q8—22no—
421C22×Q8—22no—
422C22×Q8—41no—
423C22×Q8—41no—
424C22×Q8C23×C711yescharacteristic
425C22×Q8C23×C711yescharacteristic
426C22×D4—21no—
427C22×D4—21no—
428C22×D4—21no—
429C22×D4—21no—
430C22×D4C23×C711yescharacteristic
431C22×D4C23×C711yescharacteristic
432C23×C4—21no—
433C23×C4—21no—
434C23×C4C23×C711yescharacteristic
435C2×SD16—22no—
436C2×SD16—22no—
437C2×SD16—22no—
438C2×SD16—22no—
439C2×SD16—22no—
440C2×SD16—22no—
441C2×SD16—22no—
442C2×SD16—22no—
443C2×SD16—22no—
444C2×SD16—41no—
445C2×SD16—41no—
446C2×SD16C7×D414yescomplemented
447C22×C8C23×C711yescharacteristic
448C22×C8C23×C711yescharacteristic
449C22×C8C23×C711yescharacteristic
450C22×C8C23×C711yescharacteristic
451#127—22no—
452#127—41no—
453#121—22no—
454#121—22no—
455#121—44no—
456#121—41no—
457#121—41no—
458C4×Q8—22no—
459C4×Q8—22no—
460C4×Q8—41no—
461C4×Q8—41no—
462C4×D4—22no—
463C4×D4—41no—
464C2×C4⋊C4—21no—
465C2×C4⋊C4—21no—
466C2×C4⋊C4—21no—
467C2×C4⋊C4C23×C711yescharacteristic
468C2×C4⋊C4C23×C711yescharacteristic
469C2×C4⋊C4C23×C711yescharacteristic
470C2×C4⋊C4C23×C711yescharacteristic
471C2×C22⋊C4—21no—
472C2×C22⋊C4—21no—
473C2×C22⋊C4—21no—
474C2×C22⋊C4—21no—
475C2×C22⋊C4—21no—
476C2×C22⋊C4—21no—
477C2×C22⋊C4C7×D411yescharacteristic
478C2×C22⋊C4C7×D411yescharacteristic
479C2×C42—21no—
480C2×C42—21no—
481C2×C42C23×C711yescharacteristic
482C2×C42C23×C711yescharacteristic
483#107—22no—
484#107—41no—
485C4⋊C8—22no—
486#103—22no—
487#103—22no—
488#103—22no—
489#103C7×D414yescomplemented
490#102—22no—
491#102—22no—
492#102—22no—
493#102—41no—
494C22⋊C8—22no—
495C22⋊C8—22no—
496#97—22no—
497#95—21no—
498#95—21no—
499#95—21no—
500#95—21no—
501#95—21no—
502#95—21no—
503#95C7×D411yescharacteristic
504#95C7×D411yescharacteristic
505C22×C7—22no—
506C22×C7—22no—
507C22×C7—22no—
508C22×C7—41no—
509C22×C7—41no—
510C22×C7—41no—
511C22×C7—41no—
512C22×C7—42no—
513C22×C7—42no—
514C22×C7—42no—
515C22×C7—81no—
516C22×C7—81no—
517C22×C7—81no—
518C22×C7—81no—
519C22×C7—81no—
520C22×C7—81no—
521C22×C7—81no—
522C22×C7—81no—
523C22×C7—81no—
524C22×C7—81no—
525C22×C7—81no—
526C22×C7#52511yescharacteristic
527C22×C7D4211yescharacteristic
528C22×C7D4211yescharacteristic
529C22×C7C2×AGL(1,ℤ/8)11yescharacteristic
530C22×C7C2×#13711yescharacteristic
531C22×C7#57711yescharacteristic
532C22×C7#57711yescharacteristic
533C4×C7—24no—
534C4×C7—22no—
535C4×C7—41no—
536C4×C7—42no—
537C4×C7—41no—
538C4×C7—41no—
539C4×C7—42no—
540C4×C7—41no—
541C4×C7—81no—
542C4×C7—81no—
543C4×C7—81no—
544C4×C7C2×#12111yescharacteristic
545C4×C7#53811yescharacteristic
546C4×C7#54611yescharacteristic
547C4×C7#54611yescharacteristic
548C24—21no—
549C24—21no—
550C24C2×C7×D411yescharacteristic
551C2×Q8—24no—
552C2×Q8—21no—
553C2×Q8—21no—
554C2×Q8—21no—
555C2×Q8—21no—
556C2×Q8—21no—
557C2×Q8—21no—
558C2×Q8—21no—
559C2×Q8—21no—
560C2×Q8—42no—
561C2×Q8—42no—
562C2×Q8—44no—
563C2×Q8—44no—
564C2×Q8—44no—
565C2×Q8—44no—
566C2×Q8C2×C7×D412yes—
567C2×Q8C2×C7×D412yes—
568C2×Q8C7×#4112yes—
569C2×Q8C7×#4112yes—
570C2×D4—21no—
571C2×D4—21no—
572C2×D4—21no—
573C2×D4—21no—
574C2×D4—21no—
575C2×D4—21no—
576C2×D4—21no—
577C2×D4—21no—
578C2×D4—21no—
579C2×D4—21no—
580C2×D4—21no—
581C2×D4—42no—
582C2×D4—42no—
583C2×D4—42no—
584C2×D4—42no—
585C2×D4—42no—
586C2×D4—42no—
587C2×D4—42no—
588C2×D4—42no—
589C2×D4—81no—
590C2×D4—81no—
591C2×D4—81no—
592C2×D4—81no—
593C2×D4C2×C7×D412yes—
594C22×C4—21no—
595C22×C4—24no—
596C22×C4—21no—
597C22×C4—21no—
598C22×C4—21no—
599C22×C4—21no—
600C22×C4—21no—
601C22×C4—21no—
602C22×C4—21no—
603C22×C4—21no—
604C22×C4—21no—
605C22×C4—21no—
606C22×C4—21no—
607C22×C4—42no—
608C22×C4—42no—
609C22×C4—42no—
610C22×C4—42no—
611C22×C4—81no—
612C22×C4C2×C7×D411yescharacteristic
613C22×C4C2×C7×D411yescharacteristic
614C22×C4C2×C7×D411yescharacteristic
615C22×C4C2×C7×D411yescharacteristic
616C22×C4C2×C7×D411yescharacteristic
617C22×C4C24×C711yescharacteristic
618SD16—28no—
619SD16—44no—
620SD16—44no—
621SD16—44no—
622C2×C8—21no—
623C2×C8—21no—
624C2×C8—21no—
625C2×C8—21no—
626C2×C8—21no—
627C2×C8—21no—
628C2×C8—21no—
629C2×C8—21no—
630C2×C8—21no—
631C2×C8—21no—
632C2×C8C2×C7×D412yes—
633C2×C8C2×C7×D412yes—
634C4⋊C4—21no—
635C4⋊C4—21no—
636C4⋊C4—21no—
637C4⋊C4—21no—
638C4⋊C4—21no—
639C4⋊C4—21no—
640C4⋊C4—21no—
641C4⋊C4—42no—
642C4⋊C4—42no—
643C4⋊C4—42no—
644C4⋊C4C2×C7×D412yes—
645C22⋊C4—22no—
646C22⋊C4—22no—
647C22⋊C4—42no—
648C22⋊C4—42no—
649C22⋊C4—42no—
650C22⋊C4—42no—
651C22⋊C4—42no—
652C22⋊C4—81no—
653C42—21no—
654C42—21no—
655C42—21no—
656C42—21no—
657C42—42no—
658C42—42no—
659C2×C7—42no—
660C2×C7—82no—
661C2×C7—161no—
662C2×C7#242411yescharacteristic
663C2×C7#311211yescharacteristic
664C2×C7#312611yescharacteristic
665C2×C7#326511yescharacteristic
666C2×C7#326511yescharacteristic
667C2×C7#326611yescharacteristic
668C2×C7#327811yescharacteristic
669C23—21no—
670C23—21no—
671C23—21no—
672C23—21no—
673C23—21no—
674C23—21no—
675C23—22no—
676C23—41no—
677C23—41no—
678C23—41no—
679C23—41no—
680C23—41no—
681C23—41no—
682C23—41no—
683C23—41no—
684C23—41no—
685C23—41no—
686C23—41no—
687C23—41no—
688C23—41no—
689C23C7×AGL(1,ℤ/8)12yes—
690C23C22×C7×D411yescharacteristic
691Q8—22no—
692Q8—22no—
693Q8—22no—
694Q8—22no—
695Q8—22no—
696Q8—48no—
697Q8—41no—
698Q8—41no—
699Q8C7×#12114yescomplemented
700D4—22no—
701D4—22no—
702D4—41no—
703D4—41no—
704D4—41no—
705D4—41no—
706D4—41no—
707D4—41no—
708D4—84no—
709D4—84no—
710D4—84no—
711D4—84no—
712C2×C4—22no—
713C2×C4—21no—
714C2×C4—22no—
715C2×C4—22no—
716C2×C4—21no—
717C2×C4—22no—
718C2×C4—21no—
719C2×C4—21no—
720C2×C4—21no—
721C2×C4—21no—
722C2×C4—22no—
723C2×C4—21no—
724C2×C4—21no—
725C2×C4—21no—
726C2×C4—21no—
727C2×C4—21no—
728C2×C4—21no—
729C2×C4—21no—
730C2×C4—21no—
731C2×C4—48no—
732C2×C4—41no—
733C2×C4—41no—
734C2×C4—41no—
735C2×C4—41no—
736C2×C4—41no—
737C2×C4—41no—
738C2×C4—41no—
739C2×C4—41no—
740C2×C4—41no—
741C2×C4—41no—
742C2×C4—41no—
743C2×C4—41no—
744C2×C4—41no—
745C2×C4—41no—
746C2×C4—41no—
747C2×C4—41no—
748C2×C4—41no—
749C2×C4—84no—
750C2×C4C7×#13712yes—
751C2×C4C22×C7×D411yescharacteristic
752C2×C4C22×C7×D411yescharacteristic
753C2×C4C2×C7×#4111yescharacteristic
754C2×C4C2×C7×#4111yescharacteristic
755C2×C4C7×H(5,𝔽2)11yescharacteristic
756C2×C4C7×H(5,𝔽2)11yescharacteristic
757C8—22no—
758C8—22no—
759C8—41no—
760C8—41no—
761C7#2516511yescharacteristic, direct product factor, Sylow
762C22—22no—
763C22—22no—
764C22—22no—
765C22—41no—
766C22—41no—
767C22—41no—
768C22—41no—
769C22—42no—
770C22—42no—
771C22—42no—
772C22—81no—
773C22—81no—
774C22—81no—
775C22—81no—
776C22—81no—
777C22—81no—
778C22—81no—
779C22—81no—
780C22—81no—
781C22—81no—
782C22—81no—
783C22C7×#52511yescharacteristic
784C22C7×D4211yescharacteristic
785C22C7×D4211yescharacteristic
786C22C2×C7×AGL(1,ℤ/8)11yescharacteristic
787C22C2×C7×#13711yescharacteristic
788C22C7×#57711yescharacteristic
789C22C7×#57711yescharacteristic
790C4—24no—
791C4—22no—
792C4—41no—
793C4—42no—
794C4—41no—
795C4—41no—
796C4—42no—
797C4—41no—
798C4—81no—
799C4—81no—
800C4—81no—
801C4C2×C7×#12111yescharacteristic
802C4C7×#53811yescharacteristic
803C4C7×#54611yescharacteristic
804C4C7×#54611yescharacteristic
805C2—42no—
806C2—82no—
807C2—161no—
808C2C7×#242411yescharacteristic
809C2C7×#311211yescharacteristic
810C2C7×#312611yescharacteristic
811C2C7×#326511yescharacteristic
812C2C7×#326511yescharacteristic
813C2C7×#326611yescharacteristic
814C2C7×#327811yescharacteristic
subgroupG/H
center, socleC23×C7C22×D4
commutator, Frattini, cosocleC22×C4C24×C7
prime radicalC7×#2428C2
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C7 ◁ C4×C7×C22⋊C4 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×C7×#460C2semidirect
2. C2×C7×#448C2semidirect
3. C2×C7×#448C2semidirect
4. C2×C7×#440C2semidirect
6. C7×Q8×C22⋊C4C2semidirect
7. C7×#2068C2semidirect
8. C7×#2033C2semidirect
9. C7×#2033C2semidirect
10. C7×#2014C2semidirect
11. C7×#1973C2semidirect
12. C7×#1924C2semidirect
13. C7×#1880C2semidirect
14. C7×#1877C2semidirect
15. C7×#1863C2semidirect
63. #25165C7direct (N × H)
93. C2×C7×SD16D4semidirect
136. C7×#103D4semidirect
152. C2×#460C2×C7semidirect
153. C2×#448C2×C7semidirect
154. C2×#448C2×C7semidirect
155. C2×#440C2×C7semidirect
157. Q8×C22⋊C4C2×C7semidirect
158. #2068C2×C7semidirect
159. #2033C2×C7semidirect
160. #2033C2×C7semidirect
161. #2014C2×C7semidirect
162. #1973C2×C7semidirect
163. #1924C2×C7semidirect
164. #1880C2×C7semidirect
165. #1877C2×C7semidirect
166. #1863C2×C7semidirect
355. C7×Q8#121semidirect
446. C2×SD16C7×D4semidirect
489. #103C7×D4semidirect
699. Q8C7×#121semidirect
761. C7#25165direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C7×#4602
C2×C7×#4482
C2×C7×#4402
C7×#24282
C7×Q8×C22⋊C42
C7×#20682
C7×#20332
C7×#20142
C7×#19732
C7×#19242
C7×#18802
C7×#18772
C7×#18632
#251657