Finite Group Databasebeta

← C7×#25166 #13202382

Subgroups — C7×#25166 #13202382

Order 1792.

1100 conjugacy classes of subgroups.

The subgroup lattice has 770 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C7×#461C211yesmaximal, characteristic, complemented
2C2×C7×#452C211yesmaximal, characteristic
3C2×C7×#452C211yesmaximal, characteristic
4C2×C7×#440C211yesmaximal, characteristic, complemented
5C7×#2429C211yesmaximal, characteristic, complemented
6C7×#2339C211yesmaximal, characteristic
7C7×#2068C211yesmaximal, characteristic, complemented
8C7×#2036C211yesmaximal, characteristic, complemented
9C7×#2035C211yesmaximal, characteristic, complemented
10C7×#2016C211yesmaximal, characteristic, complemented
11C7×#1971C211yesmaximal, characteristic, complemented
12C7×#1924C211yesmaximal, characteristic, complemented
13C7×#1878C211yesmaximal, characteristic, complemented
14C7×#1877C211yesmaximal, characteristic, complemented
15C7×#1864C211yesmaximal, characteristic, complemented
16C22×C7×#41C2211yescharacteristic
17C22×C7×Q16C2211yescharacteristic
18C22×C7×Q16C2211yescharacteristic
19C22×C7×SD16C2211yescharacteristic
20C22×C7×SD16C2211yescharacteristic
21C2×C7×C4⋊Q8C2211yescharacteristic
22C2×C7×C22⋊Q8C2211yescharacteristic
23C2×C7×C22⋊Q8C2211yescharacteristic
24C2×C4×C7×Q8C2211yescharacteristic
25C2×C4×C7×D4C2211yescharacteristic
26C2×C4×C7×D4C2211yescharacteristic
27C7×#461—24no—
28C7×#452—24no—
29C7×#452—24no—
30C7×#440—24no—
31C2×C7×#107C2211yescharacteristic
32C2×C7×#106C2211yescharacteristic
33C2×C7×C4⋊C8C2211yescharacteristic
34C2×C7×#103C2211yescharacteristic
35C2×C7×#103C2211yescharacteristic
36C2×C7×#103C2211yescharacteristic
37C2×C7×#103C2211yescharacteristic
38C2×C7×#103C2211yescharacteristic
39C2×C7×#103C2211yescharacteristic
40C2×C7×#102C2211yescharacteristic
41C2×C7×#102C2211yescharacteristic
42C2×C7×C22⋊C8C2211yescharacteristic
43C2×C7×C22⋊C8C2211yescharacteristic
44C2×C7×#97C2211yescharacteristic
45C7×#398—21no—
46C7×#396—21no—
47C7×#391C2211yescharacteristic
48C7×#391C2211yescharacteristic
49C7×#391C2211yescharacteristic
50C7×#389—21no—
51C7×#389C2211yescharacteristic
52C7×#388—21no—
53C7×#386—21no—
54C7×#386—21no—
55C7×#381—21no—
56C7×#380C2211yescharacteristic
57C4×C7×C22⋊C4C2211yescharacteristic
58C2×C7×#95—21no—
59C7×#340C2211yescharacteristic
60C7×#340C2211yescharacteristic
61C7×#336C2211yescharacteristic
62C7×#336C2211yescharacteristic
63#25166C711yesmaximal, characteristic, direct product factor, Sylow
64C2×C7×#41—22no—
65C2×C7×#41—22no—
66C2×C7×#41—22no—
67C2×C7×#41—22no—
68C2×C7×#41—41no—
69C2×C7×#41—41no—
70C22×C7×Q8C2311yescharacteristic
71C22×C7×Q8C2311yescharacteristic
72C22×C7×Q8C2311yescharacteristic
73C22×C7×D4—21no—
74C22×C7×D4C2311yescharacteristic
75C23×C4×C7—21no—
76C23×C4×C7—21no—
77C23×C4×C7—21no—
78C23×C4×C7C2311yescharacteristic
79C2×C7×Q16—22no—
80C2×C7×Q16—22no—
81C2×C7×Q16—22no—
82C2×C7×Q16—22no—
83C2×C7×Q16—41no—
84C2×C7×Q16—41no—
85C2×C7×SD16—22no—
86C2×C7×SD16—22no—
87C2×C7×SD16—22no—
88C2×C7×SD16—22no—
89C2×C7×SD16—22no—
90C2×C7×SD16D414yes—
91C22×C7×C8C2311yescharacteristic
92C22×C7×C8C2311yescharacteristic
93C22×C7×C8C2311yescharacteristic
94C22×C7×C8C2311yescharacteristic
95C7×C4⋊Q8—22no—
96C7×C4⋊Q8—41no—
97C7×C22⋊Q8—22no—
98C7×C22⋊Q8—22no—
99C7×C22⋊Q8—41no—
100C7×C22⋊Q8—41no—
101C4×C7×Q8—22no—
102C4×C7×Q8—41no—
103C4×C7×D4—22no—
104C4×C7×D4—22no—
105C4×C7×D4—41no—
106C4×C7×D4—41no—
107C2×C7×C4⋊C4—21no—
108C2×C7×C4⋊C4—21no—
109C2×C7×C4⋊C4—21no—
110C2×C7×C4⋊C4—21no—
111C2×C7×C4⋊C4—21no—
112C2×C7×C4⋊C4—21no—
113C2×C7×C4⋊C4C2311yescharacteristic
114C2×C7×C4⋊C4C2311yescharacteristic
115C2×C7×C4⋊C4C2311yescharacteristic
116C2×C7×C4⋊C4C2311yescharacteristic
117C2×C7×C22⋊C4—21no—
118C2×C7×C22⋊C4—21no—
119C2×C7×C22⋊C4—21no—
120C2×C7×C22⋊C4—21no—
121C2×C7×C22⋊C4—21no—
122C2×C7×C22⋊C4D411yescharacteristic
123C2×C7×C22⋊C4D411yescharacteristic
124C2×C42×C7—21no—
125C2×C42×C7C2311yescharacteristic
126C2×C42×C7C2311yescharacteristic
127C7×#107—22no—
128C7×#106—41no—
129C7×C4⋊C8—22no—
130C7×#103—22no—
131C7×#103—22no—
132C7×#103—22no—
133C7×#103—22no—
134C7×#103—22no—
135C7×#103—41no—
136C7×#102—22no—
137C7×#102D414yes—
138C7×C22⋊C8—22no—
139C7×C22⋊C8—22no—
140C7×#97—22no—
141C7×#95—21no—
142C7×#95—21no—
143C7×#95—21no—
144C7×#95—21no—
145C7×#95—21no—
146C7×#95—21no—
147C7×#95—21no—
148C7×#95—21no—
149C7×#95D411yescharacteristic
150C7×#95D411yescharacteristic
151C2×#461C2×C711yescharacteristic, complemented
152C2×#452C2×C711yescharacteristic
153C2×#452C2×C711yescharacteristic
154C2×#440C2×C711yescharacteristic, complemented
155#2429C2×C711yescharacteristic, complemented
156#2339C2×C711yescharacteristic
157#2068C2×C711yescharacteristic, complemented
158#2036C2×C711yescharacteristic, complemented
159#2035C2×C711yescharacteristic, complemented
160#2016C2×C711yescharacteristic, complemented
161#1971C2×C711yescharacteristic, complemented
162#1924C2×C711yescharacteristic, complemented
163#1878C2×C711yescharacteristic, complemented
164#1877C2×C711yescharacteristic, complemented
165#1864C2×C711yescharacteristic, complemented
166C24×C7—21no—
167C24×C7C2×D411yescharacteristic
168C7×#41—44no—
169C7×#41—44no—
170C7×#41—44no—
171C7×#41—44no—
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—21no—
180C2×C7×Q8—21no—
181C2×C7×Q8—21no—
182C2×C7×Q8—21no—
183C2×C7×Q8—21no—
184C2×C7×Q8—21no—
185C2×C7×Q8—21no—
186C2×C7×Q8—21no—
187C2×C7×Q8—21no—
188C2×C7×Q8C2×D412yes—
189C2×C7×Q8#4112yes—
190C2×C7×D4—24no—
191C2×C7×D4—21no—
192C2×C7×D4—21no—
193C2×C7×D4—21no—
194C2×C7×D4—42no—
195C2×C7×D4—42no—
196C2×C7×D4C2×D412yes—
197C2×C7×D4C2×D412yes—
198C2×C7×D4#4112yes—
199C22×C4×C7—24no—
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—42no—
214C22×C4×C7—42no—
215C22×C4×C7—42no—
216C22×C4×C7—42no—
217C22×C4×C7—42no—
218C22×C4×C7—42no—
219C22×C4×C7—81no—
220C22×C4×C7—81no—
221C22×C4×C7C2×D411yescharacteristic
222C22×C4×C7C2×D411yescharacteristic
223C22×C4×C7C2×D411yescharacteristic
224C22×C4×C7C2×D411yescharacteristic
225C22×C4×C7C2×D411yescharacteristic
226C22×C4×C7C2411yescharacteristic
227C7×Q16—44no—
228C7×Q16—44no—
229C7×SD16—28no—
230C7×SD16—44no—
231C2×C7×C8—21no—
232C2×C7×C8—21no—
233C2×C7×C8—21no—
234C2×C7×C8—21no—
235C2×C7×C8—21no—
236C2×C7×C8—21no—
237C2×C7×C8—21no—
238C2×C7×C8—21no—
239C2×C7×C8—21no—
240C2×C7×C8—21no—
241C2×C7×C8C2×D412yes—
242C2×C7×C8C2×D412yes—
243C7×C4⋊C4—21no—
244C7×C4⋊C4—21no—
245C7×C4⋊C4—21no—
246C7×C4⋊C4—21no—
247C7×C4⋊C4—21no—
248C7×C4⋊C4—21no—
249C7×C4⋊C4—21no—
250C7×C4⋊C4—42no—
251C7×C4⋊C4—42no—
252C7×C4⋊C4—42no—
253C7×C4⋊C4—42no—
254C7×C4⋊C4—42no—
255C7×C4⋊C4—42no—
256C7×C4⋊C4C2×D412yes—
257C7×C22⋊C4—22no—
258C7×C22⋊C4—41no—
259C7×C22⋊C4—42no—
260C7×C22⋊C4—42no—
261C7×C22⋊C4—42no—
262C7×C22⋊C4—42no—
263C7×C22⋊C4—81no—
264C42×C7—21no—
265C42×C7—21no—
266C42×C7—21no—
267C42×C7—21no—
268C42×C7—42no—
269C22×#41C22×C711yescharacteristic
270C22×Q16C22×C711yescharacteristic
271C22×Q16C22×C711yescharacteristic
272C22×SD16C22×C711yescharacteristic
273C22×SD16C22×C711yescharacteristic
274C2×C4⋊Q8C22×C711yescharacteristic
275C2×C22⋊Q8C22×C711yescharacteristic
276C2×C22⋊Q8C22×C711yescharacteristic
277C2×C4×Q8C22×C711yescharacteristic
278C2×C4×D4C22×C711yescharacteristic
279C2×C4×D4C22×C711yescharacteristic
280#461—24no—
281#452—24no—
282#452—24no—
283#440—24no—
284C2×#107C22×C711yescharacteristic
285C2×#106C22×C711yescharacteristic
286C2×C4⋊C8C22×C711yescharacteristic
287C2×#103C22×C711yescharacteristic
288C2×#103C22×C711yescharacteristic
289C2×#103C22×C711yescharacteristic
290C2×#103C22×C711yescharacteristic
291C2×#103C22×C711yescharacteristic
292C2×#103C22×C711yescharacteristic
293C2×#102C22×C711yescharacteristic
294C2×#102C22×C711yescharacteristic
295C2×C22⋊C8C22×C711yescharacteristic
296C2×C22⋊C8C22×C711yescharacteristic
297C2×#97C22×C711yescharacteristic
298#398—21no—
299#396—21no—
300#391C22×C711yescharacteristic
301#391C22×C711yescharacteristic
302#391C22×C711yescharacteristic
303#389—21no—
304#389C22×C711yescharacteristic
305#388—21no—
306#386—21no—
307#386—21no—
308#381—21no—
309#380C22×C711yescharacteristic
310C4×C22⋊C4C22×C711yescharacteristic
311C2×#95—21no—
312#340C22×C711yescharacteristic
313#340C22×C711yescharacteristic
314#336C22×C711yescharacteristic
315#336C22×C711yescharacteristic
316C23×C7—22no—
317C23×C7—22no—
318C23×C7—22no—
319C23×C7—21no—
320C23×C7—21no—
321C23×C7—21no—
322C23×C7—21no—
323C23×C7—21no—
324C23×C7—21no—
325C23×C7—21no—
326C23×C7—41no—
327C23×C7—41no—
328C23×C7—41no—
329C23×C7—41no—
330C23×C7C22×D411yescharacteristic
331C7×Q8—22no—
332C7×Q8—22no—
333C7×Q8—22no—
334C7×Q8—22no—
335C7×Q8—41no—
336C7×Q8—41no—
337C7×Q8—41no—
338C7×Q8—41no—
339C7×Q8—41no—
340C7×Q8—41no—
341C7×Q8—41no—
342C7×Q8—41no—
343C7×D4—22no—
344C7×D4—22no—
345C7×D4—22no—
346C7×D4—48no—
347C7×D4#12114yes—
348C2×C4×C7—21no—
349C2×C4×C7—21no—
350C2×C4×C7—21no—
351C2×C4×C7—22no—
352C2×C4×C7—21no—
353C2×C4×C7—21no—
354C2×C4×C7—21no—
355C2×C4×C7—22no—
356C2×C4×C7—22no—
357C2×C4×C7—21no—
358C2×C4×C7—21no—
359C2×C4×C7—21no—
360C2×C4×C7—21no—
361C2×C4×C7—21no—
362C2×C4×C7—21no—
363C2×C4×C7—21no—
364C2×C4×C7—21no—
365C2×C4×C7—48no—
366C2×C4×C7—41no—
367C2×C4×C7—41no—
368C2×C4×C7—41no—
369C2×C4×C7—41no—
370C2×C4×C7—41no—
371C2×C4×C7—41no—
372C2×C4×C7—41no—
373C2×C4×C7—41no—
374C2×C4×C7—41no—
375C2×C4×C7—41no—
376C2×C4×C7—41no—
377C2×C4×C7—41no—
378C2×C4×C7—41no—
379C2×C4×C7—41no—
380C2×C4×C7—41no—
381C2×C4×C7—41no—
382C2×C4×C7—41no—
383C2×C4×C7—41no—
384C2×C4×C7—41no—
385C2×C4×C7—41no—
386C2×C4×C7—41no—
387C2×C4×C7—41no—
388C2×C4×C7—84no—
389C2×C4×C7—84no—
390C2×C4×C7#13712yes—
391C2×C4×C7C22×D411yescharacteristic
392C2×C4×C7C22×D411yescharacteristic
393C2×C4×C7C2×#4111yescharacteristic
394C2×C4×C7C2×#4111yescharacteristic
395C2×C4×C7H(5,𝔽2)11yescharacteristic
396C2×C4×C7H(5,𝔽2)11yescharacteristic
397C7×C8—22no—
398C7×C8—22no—
399C7×C8—41no—
400C7×C8—41no—
401C2×#41—22no—
402C2×#41—22no—
403C2×#41—22no—
404C2×#41—22no—
405C2×#41—41no—
406C2×#41—41no—
407C22×Q8C23×C711yescharacteristic
408C22×Q8C23×C711yescharacteristic
409C22×Q8C23×C711yescharacteristic
410C22×D4—21no—
411C22×D4C23×C711yescharacteristic
412C23×C4—21no—
413C23×C4—21no—
414C23×C4—21no—
415C23×C4C23×C711yescharacteristic
416C2×Q16—22no—
417C2×Q16—22no—
418C2×Q16—22no—
419C2×Q16—22no—
420C2×Q16—41no—
421C2×Q16—41no—
422C2×SD16—22no—
423C2×SD16—22no—
424C2×SD16—22no—
425C2×SD16—22no—
426C2×SD16—22no—
427C2×SD16C7×D414yes—
428C22×C8C23×C711yescharacteristic
429C22×C8C23×C711yescharacteristic
430C22×C8C23×C711yescharacteristic
431C22×C8C23×C711yescharacteristic
432C4⋊Q8—22no—
433C4⋊Q8—41no—
434C22⋊Q8—22no—
435C22⋊Q8—22no—
436C22⋊Q8—41no—
437C22⋊Q8—41no—
438C4×Q8—22no—
439C4×Q8—41no—
440C4×D4—22no—
441C4×D4—22no—
442C4×D4—41no—
443C4×D4—41no—
444C2×C4⋊C4—21no—
445C2×C4⋊C4—21no—
446C2×C4⋊C4—21no—
447C2×C4⋊C4—21no—
448C2×C4⋊C4—21no—
449C2×C4⋊C4—21no—
450C2×C4⋊C4C23×C711yescharacteristic
451C2×C4⋊C4C23×C711yescharacteristic
452C2×C4⋊C4C23×C711yescharacteristic
453C2×C4⋊C4C23×C711yescharacteristic
454C2×C22⋊C4—21no—
455C2×C22⋊C4—21no—
456C2×C22⋊C4—21no—
457C2×C22⋊C4—21no—
458C2×C22⋊C4—21no—
459C2×C22⋊C4C7×D411yescharacteristic
460C2×C22⋊C4C7×D411yescharacteristic
461C2×C42—21no—
462C2×C42C23×C711yescharacteristic
463C2×C42C23×C711yescharacteristic
464#107—22no—
465#106—41no—
466C4⋊C8—22no—
467#103—22no—
468#103—22no—
469#103—22no—
470#103—22no—
471#103—22no—
472#103—41no—
473#102—22no—
474#102C7×D414yes—
475C22⋊C8—22no—
476C22⋊C8—22no—
477#97—22no—
478#95—21no—
479#95—21no—
480#95—21no—
481#95—21no—
482#95—21no—
483#95—21no—
484#95—21no—
485#95—21no—
486#95C7×D411yescharacteristic
487#95C7×D411yescharacteristic
488C22×C7—24no—
489C22×C7—42no—
490C22×C7—42no—
491C22×C7—42no—
492C22×C7—42no—
493C22×C7—42no—
494C22×C7—42no—
495C22×C7—41no—
496C22×C7—41no—
497C22×C7—41no—
498C22×C7—41no—
499C22×C7—41no—
500C22×C7—41no—
501C22×C7—41no—
502C22×C7#52511yescharacteristic
503C22×C7D4211yescharacteristic
504C22×C7D4211yescharacteristic
505C22×C7C2×#13711yescharacteristic
506C22×C7#57511yescharacteristic
507C22×C7#57711yescharacteristic
508C22×C7#57811yescharacteristic
509C4×C7—22no—
510C4×C7—41no—
511C4×C7—42no—
512C4×C7—42no—
513C4×C7—41no—
514C4×C7—42no—
515C4×C7—41no—
516C4×C7—41no—
517C4×C7—81no—
518C4×C7—81no—
519C4×C7—81no—
520C4×C7—81no—
521C4×C7C2×#12111yescharacteristic
522C4×C7#53811yescharacteristic
523C4×C7#54611yescharacteristic
524C4×C7#54611yescharacteristic
525C24—21no—
526C24C2×C7×D411yescharacteristic
527#41—44no—
528#41—44no—
529#41—44no—
530#41—44no—
531C2×Q8—21no—
532C2×Q8—21no—
533C2×Q8—21no—
534C2×Q8—21no—
535C2×Q8—21no—
536C2×Q8—21no—
537C2×Q8—21no—
538C2×Q8—21no—
539C2×Q8—21no—
540C2×Q8—21no—
541C2×Q8—21no—
542C2×Q8—21no—
543C2×Q8—21no—
544C2×Q8—21no—
545C2×Q8—21no—
546C2×Q8—21no—
547C2×Q8C2×C7×D412yes—
548C2×Q8C7×#4112yes—
549C2×D4—24no—
550C2×D4—21no—
551C2×D4—21no—
552C2×D4—21no—
553C2×D4—42no—
554C2×D4—42no—
555C2×D4C2×C7×D412yes—
556C2×D4C2×C7×D412yes—
557C2×D4C7×#4112yes—
558C22×C4—24no—
559C22×C4—21no—
560C22×C4—21no—
561C22×C4—21no—
562C22×C4—21no—
563C22×C4—21no—
564C22×C4—21no—
565C22×C4—21no—
566C22×C4—21no—
567C22×C4—21no—
568C22×C4—21no—
569C22×C4—21no—
570C22×C4—21no—
571C22×C4—21no—
572C22×C4—42no—
573C22×C4—42no—
574C22×C4—42no—
575C22×C4—42no—
576C22×C4—42no—
577C22×C4—42no—
578C22×C4—81no—
579C22×C4—81no—
580C22×C4C2×C7×D411yescharacteristic
581C22×C4C2×C7×D411yescharacteristic
582C22×C4C2×C7×D411yescharacteristic
583C22×C4C2×C7×D411yescharacteristic
584C22×C4C2×C7×D411yescharacteristic
585C22×C4C24×C711yescharacteristic
586Q16—44no—
587Q16—44no—
588SD16—28no—
589SD16—44no—
590C2×C8—21no—
591C2×C8—21no—
592C2×C8—21no—
593C2×C8—21no—
594C2×C8—21no—
595C2×C8—21no—
596C2×C8—21no—
597C2×C8—21no—
598C2×C8—21no—
599C2×C8—21no—
600C2×C8C2×C7×D412yes—
601C2×C8C2×C7×D412yes—
602C4⋊C4—21no—
603C4⋊C4—21no—
604C4⋊C4—21no—
605C4⋊C4—21no—
606C4⋊C4—21no—
607C4⋊C4—21no—
608C4⋊C4—21no—
609C4⋊C4—42no—
610C4⋊C4—42no—
611C4⋊C4—42no—
612C4⋊C4—42no—
613C4⋊C4—42no—
614C4⋊C4—42no—
615C4⋊C4C2×C7×D412yes—
616C22⋊C4—22no—
617C22⋊C4—41no—
618C22⋊C4—42no—
619C22⋊C4—42no—
620C22⋊C4—42no—
621C22⋊C4—42no—
622C22⋊C4—81no—
623C42—21no—
624C42—21no—
625C42—21no—
626C42—21no—
627C42—42no—
628C2×C7—44no—
629C2×C7—81no—
630C2×C7#242411yescharacteristic
631C2×C7#311611yescharacteristic
632C2×C7#312011yescharacteristic
633C2×C7#326611yescharacteristic
634C2×C7#326711yescharacteristic
635C2×C7#326911yescharacteristic
636C2×C7#327611yescharacteristic
637C23—22no—
638C23—22no—
639C23—22no—
640C23—21no—
641C23—21no—
642C23—21no—
643C23—21no—
644C23—21no—
645C23—21no—
646C23—21no—
647C23—41no—
648C23—41no—
649C23—41no—
650C23—41no—
651C23C22×C7×D411yescharacteristic
652Q8—22no—
653Q8—22no—
654Q8—22no—
655Q8—22no—
656Q8—41no—
657Q8—41no—
658Q8—41no—
659Q8—41no—
660Q8—41no—
661Q8—41no—
662Q8—41no—
663Q8—41no—
664D4—22no—
665D4—22no—
666D4—22no—
667D4—48no—
668D4C7×#12114yes—
669C2×C4—21no—
670C2×C4—21no—
671C2×C4—21no—
672C2×C4—22no—
673C2×C4—21no—
674C2×C4—21no—
675C2×C4—21no—
676C2×C4—22no—
677C2×C4—22no—
678C2×C4—21no—
679C2×C4—21no—
680C2×C4—21no—
681C2×C4—21no—
682C2×C4—21no—
683C2×C4—21no—
684C2×C4—21no—
685C2×C4—21no—
686C2×C4—48no—
687C2×C4—41no—
688C2×C4—41no—
689C2×C4—41no—
690C2×C4—41no—
691C2×C4—41no—
692C2×C4—41no—
693C2×C4—41no—
694C2×C4—41no—
695C2×C4—41no—
696C2×C4—41no—
697C2×C4—41no—
698C2×C4—41no—
699C2×C4—41no—
700C2×C4—41no—
701C2×C4—41no—
702C2×C4—41no—
703C2×C4—41no—
704C2×C4—41no—
705C2×C4—41no—
706C2×C4—41no—
707C2×C4—41no—
708C2×C4—41no—
709C2×C4—84no—
710C2×C4—84no—
711C2×C4C7×#13712yes—
712C2×C4C22×C7×D411yescharacteristic
713C2×C4C22×C7×D411yescharacteristic
714C2×C4C2×C7×#4111yescharacteristic
715C2×C4C2×C7×#4111yescharacteristic
716C2×C4C7×H(5,𝔽2)11yescharacteristic
717C2×C4C7×H(5,𝔽2)11yescharacteristic
718C8—22no—
719C8—22no—
720C8—41no—
721C8—41no—
722C7#2516611yescharacteristic, direct product factor, Sylow
723C22—24no—
724C22—42no—
725C22—42no—
726C22—42no—
727C22—42no—
728C22—42no—
729C22—42no—
730C22—41no—
731C22—41no—
732C22—41no—
733C22—41no—
734C22—41no—
735C22—41no—
736C22—41no—
737C22C7×#52511yescharacteristic
738C22C7×D4211yescharacteristic
739C22C7×D4211yescharacteristic
740C22C2×C7×#13711yescharacteristic
741C22C7×#57511yescharacteristic
742C22C7×#57711yescharacteristic
743C22C7×#57811yescharacteristic
744C4—22no—
745C4—41no—
746C4—42no—
747C4—42no—
748C4—41no—
749C4—42no—
750C4—41no—
751C4—41no—
752C4—81no—
753C4—81no—
754C4—81no—
755C4—81no—
756C4C2×C7×#12111yescharacteristic
757C4C7×#53811yescharacteristic
758C4C7×#54611yescharacteristic
759C4C7×#54611yescharacteristic
760C2—44no—
761C2—81no—
762C2C7×#242411yescharacteristic
763C2C7×#311611yescharacteristic
764C2C7×#312011yescharacteristic
765C2C7×#326611yescharacteristic
766C2C7×#326711yescharacteristic
767C2C7×#326911yescharacteristic
768C2C7×#327611yescharacteristic
subgroupG/H
center, socleC23×C7C22×D4
commutator, Frattini, cosocleC22×C4C24×C7
prime radicalC22×C7×#41C22
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×#461C2semidirect
4. C2×C7×#440C2semidirect
5. C7×#2429C2semidirect
7. C7×#2068C2semidirect
8. C7×#2036C2semidirect
9. C7×#2035C2semidirect
10. C7×#2016C2semidirect
11. C7×#1971C2semidirect
12. C7×#1924C2semidirect
13. C7×#1878C2semidirect
14. C7×#1877C2semidirect
15. C7×#1864C2semidirect
63. #25166C7direct (N × H)
151. C2×#461C2×C7semidirect
154. C2×#440C2×C7semidirect
155. #2429C2×C7semidirect
157. #2068C2×C7semidirect
158. #2036C2×C7semidirect
159. #2035C2×C7semidirect
160. #2016C2×C7semidirect
161. #1971C2×C7semidirect
162. #1924C2×C7semidirect
163. #1878C2×C7semidirect
164. #1877C2×C7semidirect
165. #1864C2×C7semidirect
722. C7#25166direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C7×#4612
C2×C7×#4522
C2×C7×#4402
C7×#24292
C7×#23392
C7×#20682
C7×#20362
C7×#20352
C7×#20162
C7×#19712
C7×#19242
C7×#18782
C7×#18772
C7×#18642
#251667