Finite Group Databasebeta

← C7×#26983 #13204199

Subgroups — C7×#26983 #13204199

Order 1792.

916 conjugacy classes of subgroups.

The subgroup lattice has 716 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C7×#468C211yesmaximal, characteristic
2C2×C7×#440C211yesmaximal, characteristic, complemented
3C7×#2429C211yesmaximal, characteristic, complemented
4C7×#2422C211yesmaximal, characteristic
5C7×#2083C211yesmaximal, characteristic, complemented
6C7×#2036C211yesmaximal, characteristic, complemented
7C7×#2013C211yesmaximal, characteristic, complemented
8C7×#2000C211yesmaximal, characteristic
9C7×#1956C211yesmaximal, characteristic, complemented
10C7×#1935C211yesmaximal, characteristic, complemented
11C7×#1934C211yesmaximal, characteristic, complemented
12C7×#1894C211yesmaximal, characteristic, complemented
13C7×#1877C211yesmaximal, characteristic, complemented
14C7×#1863C211yesmaximal, characteristic, complemented
15C7×#1753C211yesmaximal, characteristic, complemented
16C22×C7×SD16C2211yescharacteristic
17C22×C7×SD16C2211yescharacteristic
18C22×C7×M16C2211yescharacteristic
19C2×C7×C4⋊Q8C2211yescharacteristic
20C2×C7×#123—21no—
21C2×C7×C22⋊Q8C2211yescharacteristic
22C2×C7×C22⋊Q8C2211yescharacteristic
23C2×C7×#121C2211yescharacteristic
24C2×C4×C7×Q8C2211yescharacteristic
25C2×C4×C7×D4C2211yescharacteristic
26C7×#468—24no—
27C7×#440—24no—
28C2×C7×#107C2211yescharacteristic
29C2×C7×#107C2211yescharacteristic
30C2×C7×#103C2211yescharacteristic
31C2×C7×#103C2211yescharacteristic
32C2×C7×#103C2211yescharacteristic
33C2×C7×#103C2211yescharacteristic
34C2×C7×#103C2211yescharacteristic
35C2×C7×#103C2211yescharacteristic
36C2×C7×#102C2211yescharacteristic
37C2×C7×#102C2211yescharacteristic
38C2×C7×C22⋊C8C2211yescharacteristic
39C2×C7×#97C2211yescharacteristic
40C2×C4×C7×C8C2211yescharacteristic
41C7×#398—21no—
42C7×#397—21no—
43C7×#396—21no—
44C7×#394—21no—
45C7×#391C2211yescharacteristic
46C7×#390C2211yescharacteristic
47C7×#389—21no—
48C7×#389C2211yescharacteristic
49C7×#389C2211yescharacteristic
50C7×#388—21no—
51C7×#385—21no—
52C7×#384C2211yescharacteristic
53C7×#380C2211yescharacteristic
54C4×C7×C22⋊C4C2211yescharacteristic
55C7×#340C2211yescharacteristic
56C7×#340C2211yescharacteristic
57C7×#340C2211yescharacteristic
58C7×#340C2211yescharacteristic
59C7×#336C2211yescharacteristic
60C7×#336C2211yescharacteristic
61#26983C711yesmaximal, characteristic, direct product factor, Sylow
62C22×C7×Q8C2311yescharacteristic
63C22×C7×Q8C2311yescharacteristic
64C22×C7×D4—21no—
65C22×C7×D4C2311yescharacteristic
66C23×C4×C7—21no—
67C23×C4×C7C2311yescharacteristic
68C2×C7×SD16—22no—
69C2×C7×SD16—22no—
70C2×C7×SD16—22no—
71C2×C7×SD16—22no—
72C2×C7×SD16—22no—
73C2×C7×SD16—41no—
74C2×C7×M16—22no—
75C2×C7×M16—22no—
76C2×C7×M16—41no—
77C22×C7×C8C2311yescharacteristic
78C22×C7×C8C2311yescharacteristic
79C22×C7×C8C2311yescharacteristic
80C22×C7×C8C2311yescharacteristic
81C7×C4⋊Q8—22no—
82C7×C4⋊Q8—41no—
83C7×#123—44no—
84C7×C22⋊Q8—22no—
85C7×C22⋊Q8—22no—
86C7×C22⋊Q8—41no—
87C7×C22⋊Q8—41no—
88C7×#121—22no—
89C7×#121—41no—
90C4×C7×Q8—22no—
91C4×C7×Q8—41no—
92C4×C7×D4—22no—
93C4×C7×D4—41no—
94C2×C7×C4⋊C4—21no—
95C2×C7×C4⋊C4—21no—
96C2×C7×C4⋊C4—21no—
97C2×C7×C4⋊C4—21no—
98C2×C7×C4⋊C4—21no—
99C2×C7×C4⋊C4—21no—
100C2×C7×C4⋊C4—21no—
101C2×C7×C4⋊C4—21no—
102C2×C7×C4⋊C4—21no—
103C2×C7×C4⋊C4C2311yescharacteristic
104C2×C7×C4⋊C4C2311yescharacteristic
105C2×C7×C4⋊C4C2311yescharacteristic
106C2×C7×C4⋊C4C2311yescharacteristic
107C2×C7×C4⋊C4C2311yescharacteristic
108C2×C7×C22⋊C4—21no—
109C2×C7×C22⋊C4—21no—
110C2×C7×C22⋊C4—21no—
111C2×C7×C22⋊C4—21no—
112C2×C7×C22⋊C4—21no—
113C2×C7×C22⋊C4—21no—
114C2×C7×C22⋊C4—21no—
115C2×C7×C22⋊C4D411yescharacteristic
116C2×C7×C22⋊C4D411yescharacteristic
117C2×C42×C7—21no—
118C2×C42×C7C2311yescharacteristic
119C2×C42×C7C2311yescharacteristic
120C7×#107—22no—
121C7×#107—22no—
122C7×#103—22no—
123C7×#103—22no—
124C7×#103—22no—
125C7×#103—22no—
126C7×#103—41no—
127C7×#103—41no—
128C7×#102—41no—
129C7×#102D414yes—
130C7×C22⋊C8—22no—
131C7×#97—22no—
132C4×C7×C8—41no—
133C7×#95—21no—
134C7×#95—21no—
135C7×#95—21no—
136C7×#95—21no—
137C7×#95—21no—
138C7×#95D411yescharacteristic
139C7×#95D411yescharacteristic
140C2×#468C2×C711yescharacteristic
141C2×#440C2×C711yescharacteristic, complemented
142#2429C2×C711yescharacteristic, complemented
143#2422C2×C711yescharacteristic
144#2083C2×C711yescharacteristic, complemented
145#2036C2×C711yescharacteristic, complemented
146#2013C2×C711yescharacteristic, complemented
147#2000C2×C711yescharacteristic
148#1956C2×C711yescharacteristic, complemented
149#1935C2×C711yescharacteristic, complemented
150#1934C2×C711yescharacteristic, complemented
151#1894C2×C711yescharacteristic, complemented
152#1877C2×C711yescharacteristic, complemented
153#1863C2×C711yescharacteristic, complemented
154#1753C2×C711yescharacteristic, complemented
155C24×C7—21no—
156C24×C7C2×D411yescharacteristic
157C2×C7×Q8—21no—
158C2×C7×Q8—21no—
159C2×C7×Q8—21no—
160C2×C7×Q8—21no—
161C2×C7×Q8—21no—
162C2×C7×Q8—21no—
163C2×C7×Q8—21no—
164C2×C7×Q8—21no—
165C2×C7×Q8—21no—
166C2×C7×Q8—21no—
167C2×C7×Q8—21no—
168C2×C7×Q8#4112yes—
169C2×C7×D4—21no—
170C2×C7×D4—21no—
171C2×C7×D4—21no—
172C2×C7×D4—21no—
173C2×C7×D4—21no—
174C2×C7×D4—42no—
175C2×C7×D4—42no—
176C2×C7×D4—81no—
177C2×C7×D4C2×D412yes—
178C22×C4×C7—21no—
179C22×C4×C7—21no—
180C22×C4×C7—21no—
181C22×C4×C7—21no—
182C22×C4×C7—21no—
183C22×C4×C7—21no—
184C22×C4×C7—21no—
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—42no—
192C22×C4×C7—42no—
193C22×C4×C7—81no—
194C22×C4×C7C2×D411yescharacteristic
195C22×C4×C7C2×D411yescharacteristic
196C22×C4×C7C2×D411yescharacteristic
197C22×C4×C7C2×D411yescharacteristic
198C22×C4×C7C2×D411yescharacteristic
199C22×C4×C7C2411yescharacteristic
200C7×SD16—28no—
201C7×SD16—44no—
202C7×M16—44no—
203C2×C7×C8—21no—
204C2×C7×C8—21no—
205C2×C7×C8—21no—
206C2×C7×C8—21no—
207C2×C7×C8—21no—
208C2×C7×C8—21no—
209C2×C7×C8—21no—
210C2×C7×C8—21no—
211C2×C7×C8—21no—
212C2×C7×C8C2×D412yes—
213C2×C7×C8#4112yes—
214C2×C7×C8#4112yes—
215C7×C4⋊C4—21no—
216C7×C4⋊C4—21no—
217C7×C4⋊C4—21no—
218C7×C4⋊C4—21no—
219C7×C4⋊C4—21no—
220C7×C4⋊C4—21no—
221C7×C4⋊C4—21no—
222C7×C4⋊C4—21no—
223C7×C4⋊C4—21no—
224C7×C4⋊C4—42no—
225C7×C4⋊C4—42no—
226C7×C4⋊C4—42no—
227C7×C4⋊C4—42no—
228C7×C4⋊C4—42no—
229C7×C4⋊C4—42no—
230C7×C4⋊C4—42no—
231C7×C4⋊C4—42no—
232C7×C4⋊C4—81no—
233C7×C4⋊C4C2×D412yes—
234C7×C22⋊C4—22no—
235C7×C22⋊C4—22no—
236C7×C22⋊C4—42no—
237C7×C22⋊C4—42no—
238C7×C22⋊C4—42no—
239C7×C22⋊C4—42no—
240C7×C22⋊C4—42no—
241C7×C22⋊C4—42no—
242C7×C22⋊C4—42no—
243C42×C7—21no—
244C42×C7—21no—
245C42×C7—21no—
246C42×C7—21no—
247C42×C7—42no—
248C22×SD16C22×C711yescharacteristic
249C22×SD16C22×C711yescharacteristic
250C22×M16C22×C711yescharacteristic
251C2×C4⋊Q8C22×C711yescharacteristic
252C2×#123—21no—
253C2×C22⋊Q8C22×C711yescharacteristic
254C2×C22⋊Q8C22×C711yescharacteristic
255C2×#121C22×C711yescharacteristic
256C2×C4×Q8C22×C711yescharacteristic
257C2×C4×D4C22×C711yescharacteristic
258#468—24no—
259#440—24no—
260C2×#107C22×C711yescharacteristic
261C2×#107C22×C711yescharacteristic
262C2×#103C22×C711yescharacteristic
263C2×#103C22×C711yescharacteristic
264C2×#103C22×C711yescharacteristic
265C2×#103C22×C711yescharacteristic
266C2×#103C22×C711yescharacteristic
267C2×#103C22×C711yescharacteristic
268C2×#102C22×C711yescharacteristic
269C2×#102C22×C711yescharacteristic
270C2×C22⋊C8C22×C711yescharacteristic
271C2×#97C22×C711yescharacteristic
272C2×C4×C8C22×C711yescharacteristic
273#398—21no—
274#397—21no—
275#396—21no—
276#394—21no—
277#391C22×C711yescharacteristic
278#390C22×C711yescharacteristic
279#389—21no—
280#389C22×C711yescharacteristic
281#389C22×C711yescharacteristic
282#388—21no—
283#385—21no—
284#384C22×C711yescharacteristic
285#380C22×C711yescharacteristic
286C4×C22⋊C4C22×C711yescharacteristic
287#340C22×C711yescharacteristic
288#340C22×C711yescharacteristic
289#340C22×C711yescharacteristic
290#340C22×C711yescharacteristic
291#336C22×C711yescharacteristic
292#336C22×C711yescharacteristic
293C23×C7—21no—
294C23×C7—21no—
295C23×C7—22no—
296C23×C7—21no—
297C23×C7—21no—
298C23×C7—21no—
299C23×C7—21no—
300C23×C7—21no—
301C23×C7—41no—
302C23×C7—41no—
303C23×C7—41no—
304C23×C7—41no—
305C23×C7—41no—
306C23×C7—41no—
307C23×C7C22×D411yescharacteristic
308C7×Q8—22no—
309C7×Q8—22no—
310C7×Q8—41no—
311C7×Q8—41no—
312C7×Q8—41no—
313C7×Q8—41no—
314C7×Q8—41no—
315C7×Q8—41no—
316C7×D4—22no—
317C7×D4—22no—
318C7×D4—41no—
319C7×D4—41no—
320C7×D4—84no—
321C2×C4×C7—21no—
322C2×C4×C7—21no—
323C2×C4×C7—21no—
324C2×C4×C7—21no—
325C2×C4×C7—21no—
326C2×C4×C7—21no—
327C2×C4×C7—21no—
328C2×C4×C7—22no—
329C2×C4×C7—21no—
330C2×C4×C7—22no—
331C2×C4×C7—21no—
332C2×C4×C7—21no—
333C2×C4×C7—21no—
334C2×C4×C7—21no—
335C2×C4×C7—21no—
336C2×C4×C7—41no—
337C2×C4×C7—41no—
338C2×C4×C7—41no—
339C2×C4×C7—41no—
340C2×C4×C7—41no—
341C2×C4×C7—41no—
342C2×C4×C7—41no—
343C2×C4×C7—41no—
344C2×C4×C7—41no—
345C2×C4×C7—41no—
346C2×C4×C7—41no—
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—84no—
360C2×C4×C7AGL(1,ℤ/8)12yes—
361C2×C4×C7#13712yes—
362C2×C4×C7C22×D411yescharacteristic
363C2×C4×C7C2×#4111yescharacteristic
364C2×C4×C7C2×#4111yescharacteristic
365C2×C4×C7C2×#4111yescharacteristic
366C2×C4×C7H(5,𝔽2)11yescharacteristic
367C2×C4×C7H(5,𝔽2)11yescharacteristic
368C7×C8—22no—
369C7×C8—22no—
370C7×C8—22no—
371C7×C8—41no—
372C22×Q8C23×C711yescharacteristic
373C22×Q8C23×C711yescharacteristic
374C22×D4—21no—
375C22×D4C23×C711yescharacteristic
376C23×C4—21no—
377C23×C4C23×C711yescharacteristic
378C2×SD16—22no—
379C2×SD16—22no—
380C2×SD16—22no—
381C2×SD16—22no—
382C2×SD16—22no—
383C2×SD16—41no—
384C2×M16—22no—
385C2×M16—22no—
386C2×M16—41no—
387C22×C8C23×C711yescharacteristic
388C22×C8C23×C711yescharacteristic
389C22×C8C23×C711yescharacteristic
390C22×C8C23×C711yescharacteristic
391C4⋊Q8—22no—
392C4⋊Q8—41no—
393#123—44no—
394C22⋊Q8—22no—
395C22⋊Q8—22no—
396C22⋊Q8—41no—
397C22⋊Q8—41no—
398#121—22no—
399#121—41no—
400C4×Q8—22no—
401C4×Q8—41no—
402C4×D4—22no—
403C4×D4—41no—
404C2×C4⋊C4—21no—
405C2×C4⋊C4—21no—
406C2×C4⋊C4—21no—
407C2×C4⋊C4—21no—
408C2×C4⋊C4—21no—
409C2×C4⋊C4—21no—
410C2×C4⋊C4—21no—
411C2×C4⋊C4—21no—
412C2×C4⋊C4—21no—
413C2×C4⋊C4C23×C711yescharacteristic
414C2×C4⋊C4C23×C711yescharacteristic
415C2×C4⋊C4C23×C711yescharacteristic
416C2×C4⋊C4C23×C711yescharacteristic
417C2×C4⋊C4C23×C711yescharacteristic
418C2×C22⋊C4—21no—
419C2×C22⋊C4—21no—
420C2×C22⋊C4—21no—
421C2×C22⋊C4—21no—
422C2×C22⋊C4—21no—
423C2×C22⋊C4—21no—
424C2×C22⋊C4—21no—
425C2×C22⋊C4C7×D411yescharacteristic
426C2×C22⋊C4C7×D411yescharacteristic
427C2×C42—21no—
428C2×C42C23×C711yescharacteristic
429C2×C42C23×C711yescharacteristic
430#107—22no—
431#107—22no—
432#103—22no—
433#103—22no—
434#103—22no—
435#103—22no—
436#103—41no—
437#103—41no—
438#102—41no—
439#102C7×D414yes—
440C22⋊C8—22no—
441#97—22no—
442C4×C8—41no—
443#95—21no—
444#95—21no—
445#95—21no—
446#95—21no—
447#95—21no—
448#95C7×D411yescharacteristic
449#95C7×D411yescharacteristic
450C22×C7—41no—
451C22×C7—41no—
452C22×C7—41no—
453C22×C7—42no—
454C22×C7—42no—
455C22×C7—41no—
456C22×C7—41no—
457C22×C7—42no—
458C22×C7—41no—
459C22×C7—41no—
460C22×C7—81no—
461C22×C7—81no—
462C22×C7—81no—
463C22×C7—81no—
464C22×C7#53211yescharacteristic
465C22×C7D4211yescharacteristic
466C22×C7#54611yescharacteristic
467C22×C7C2×AGL(1,ℤ/8)11yescharacteristic
468C22×C7C2×#13711yescharacteristic
469C22×C7#57711yescharacteristic
470C22×C7#57811yescharacteristic
471C4×C7—22no—
472C4×C7—22no—
473C4×C7—41no—
474C4×C7—42no—
475C4×C7—41no—
476C4×C7—42no—
477C4×C7—41no—
478C4×C7—81no—
479C4×C7—81no—
480C4×C7—81no—
481C4×C7—81no—
482C4×C7—81no—
483C4×C7#52511yescharacteristic
484C4×C7#54011yescharacteristic
485C4×C7#54611yescharacteristic
486C4×C7#55311yescharacteristic
487C24—21no—
488C24C2×C7×D411yescharacteristic
489C2×Q8—21no—
490C2×Q8—21no—
491C2×Q8—21no—
492C2×Q8—21no—
493C2×Q8—21no—
494C2×Q8—21no—
495C2×Q8—21no—
496C2×Q8—21no—
497C2×Q8—21no—
498C2×Q8—21no—
499C2×Q8—21no—
500C2×Q8C7×#4112yes—
501C2×D4—21no—
502C2×D4—21no—
503C2×D4—21no—
504C2×D4—21no—
505C2×D4—21no—
506C2×D4—42no—
507C2×D4—42no—
508C2×D4—81no—
509C2×D4C2×C7×D412yes—
510C22×C4—21no—
511C22×C4—21no—
512C22×C4—21no—
513C22×C4—21no—
514C22×C4—21no—
515C22×C4—21no—
516C22×C4—21no—
517C22×C4—21no—
518C22×C4—21no—
519C22×C4—21no—
520C22×C4—21no—
521C22×C4—21no—
522C22×C4—21no—
523C22×C4—42no—
524C22×C4—42no—
525C22×C4—81no—
526C22×C4C2×C7×D411yescharacteristic
527C22×C4C2×C7×D411yescharacteristic
528C22×C4C2×C7×D411yescharacteristic
529C22×C4C2×C7×D411yescharacteristic
530C22×C4C2×C7×D411yescharacteristic
531C22×C4C24×C711yescharacteristic
532SD16—28no—
533SD16—44no—
534M16—44no—
535C2×C8—21no—
536C2×C8—21no—
537C2×C8—21no—
538C2×C8—21no—
539C2×C8—21no—
540C2×C8—21no—
541C2×C8—21no—
542C2×C8—21no—
543C2×C8—21no—
544C2×C8C2×C7×D412yes—
545C2×C8C7×#4112yes—
546C2×C8C7×#4112yes—
547C4⋊C4—21no—
548C4⋊C4—21no—
549C4⋊C4—21no—
550C4⋊C4—21no—
551C4⋊C4—21no—
552C4⋊C4—21no—
553C4⋊C4—21no—
554C4⋊C4—21no—
555C4⋊C4—21no—
556C4⋊C4—42no—
557C4⋊C4—42no—
558C4⋊C4—42no—
559C4⋊C4—42no—
560C4⋊C4—42no—
561C4⋊C4—42no—
562C4⋊C4—42no—
563C4⋊C4—42no—
564C4⋊C4—81no—
565C4⋊C4C2×C7×D412yes—
566C22⋊C4—22no—
567C22⋊C4—22no—
568C22⋊C4—42no—
569C22⋊C4—42no—
570C22⋊C4—42no—
571C22⋊C4—42no—
572C22⋊C4—42no—
573C22⋊C4—42no—
574C22⋊C4—42no—
575C42—21no—
576C42—21no—
577C42—21no—
578C42—21no—
579C42—42no—
580C2×C7—81no—
581C2×C7—82no—
582C2×C7#246411yescharacteristic
583C2×C7#317811yescharacteristic
584C2×C7#318211yescharacteristic
585C2×C7#327211yescharacteristic
586C2×C7#327611yescharacteristic
587C2×C7#330811yescharacteristic
588C2×C7#332011yescharacteristic
589C23—21no—
590C23—21no—
591C23—22no—
592C23—21no—
593C23—21no—
594C23—21no—
595C23—21no—
596C23—21no—
597C23—41no—
598C23—41no—
599C23—41no—
600C23—41no—
601C23—41no—
602C23—41no—
603C23C22×C7×D411yescharacteristic
604Q8—22no—
605Q8—22no—
606Q8—41no—
607Q8—41no—
608Q8—41no—
609Q8—41no—
610Q8—41no—
611Q8—41no—
612D4—22no—
613D4—22no—
614D4—41no—
615D4—41no—
616D4—84no—
617C2×C4—21no—
618C2×C4—21no—
619C2×C4—21no—
620C2×C4—21no—
621C2×C4—21no—
622C2×C4—21no—
623C2×C4—21no—
624C2×C4—22no—
625C2×C4—21no—
626C2×C4—22no—
627C2×C4—21no—
628C2×C4—21no—
629C2×C4—21no—
630C2×C4—21no—
631C2×C4—21no—
632C2×C4—41no—
633C2×C4—41no—
634C2×C4—41no—
635C2×C4—41no—
636C2×C4—41no—
637C2×C4—41no—
638C2×C4—41no—
639C2×C4—41no—
640C2×C4—41no—
641C2×C4—41no—
642C2×C4—41no—
643C2×C4—41no—
644C2×C4—41no—
645C2×C4—41no—
646C2×C4—41no—
647C2×C4—41no—
648C2×C4—41no—
649C2×C4—41no—
650C2×C4—41no—
651C2×C4—41no—
652C2×C4—41no—
653C2×C4—41no—
654C2×C4—41no—
655C2×C4—84no—
656C2×C4C7×AGL(1,ℤ/8)12yes—
657C2×C4C7×#13712yes—
658C2×C4C22×C7×D411yescharacteristic
659C2×C4C2×C7×#4111yescharacteristic
660C2×C4C2×C7×#4111yescharacteristic
661C2×C4C2×C7×#4111yescharacteristic
662C2×C4C7×H(5,𝔽2)11yescharacteristic
663C2×C4C7×H(5,𝔽2)11yescharacteristic
664C8—22no—
665C8—22no—
666C8—22no—
667C8—41no—
668C7#2698311yescharacteristic, direct product factor, Sylow
669C22—41no—
670C22—41no—
671C22—41no—
672C22—42no—
673C22—42no—
674C22—41no—
675C22—41no—
676C22—42no—
677C22—41no—
678C22—41no—
679C22—81no—
680C22—81no—
681C22—81no—
682C22—81no—
683C22C7×#53211yescharacteristic
684C22C7×D4211yescharacteristic
685C22C7×#54611yescharacteristic
686C22C2×C7×AGL(1,ℤ/8)11yescharacteristic
687C22C2×C7×#13711yescharacteristic
688C22C7×#57711yescharacteristic
689C22C7×#57811yescharacteristic
690C4—22no—
691C4—22no—
692C4—41no—
693C4—42no—
694C4—41no—
695C4—42no—
696C4—41no—
697C4—81no—
698C4—81no—
699C4—81no—
700C4—81no—
701C4—81no—
702C4C7×#52511yescharacteristic
703C4C7×#54011yescharacteristic
704C4C7×#54611yescharacteristic
705C4C7×#55311yescharacteristic
706C2—81no—
707C2—82no—
708C2C7×#246411yescharacteristic
709C2C7×#317811yescharacteristic
710C2C7×#318211yescharacteristic
711C2C7×#327211yescharacteristic
712C2C7×#327611yescharacteristic
713C2C7×#330811yescharacteristic
714C2C7×#332011yescharacteristic
subgroupG/H
center, socleC23×C7C22×D4
commutator, Frattini, cosocleC22×C4C24×C7
prime radicalC2×C7×#121C22
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
2. C2×C7×#440C2semidirect
3. C7×#2429C2semidirect
5. C7×#2083C2semidirect
6. C7×#2036C2semidirect
7. C7×#2013C2semidirect
9. C7×#1956C2semidirect
10. C7×#1935C2semidirect
11. C7×#1934C2semidirect
12. C7×#1894C2semidirect
13. C7×#1877C2semidirect
14. C7×#1863C2semidirect
15. C7×#1753C2semidirect
61. #26983C7direct (N × H)
141. C2×#440C2×C7semidirect
142. #2429C2×C7semidirect
144. #2083C2×C7semidirect
145. #2036C2×C7semidirect
146. #2013C2×C7semidirect
148. #1956C2×C7semidirect
149. #1935C2×C7semidirect
150. #1934C2×C7semidirect
151. #1894C2×C7semidirect
152. #1877C2×C7semidirect
153. #1863C2×C7semidirect
154. #1753C2×C7semidirect
668. C7#26983direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C7×#4682
C2×C7×#4402
C7×#24292
C7×#24222
C7×#20832
C7×#20362
C7×#20132
C7×#20002
C7×#19562
C7×#19352
C7×#19342
C7×#18942
C7×#18772
C7×#18632
C7×#17532
#269837