Finite Group Databasebeta

← C7×#26982 #13204198

Subgroups — C7×#26982 #13204198

Order 1792.

922 conjugacy classes of subgroups.

The subgroup lattice has 742 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C7×#469C211yesmaximal, characteristic
2C2×C7×#440C211yesmaximal, characteristic, complemented
3C7×#2426C211yesmaximal, characteristic, complemented
4C7×#2420C211yesmaximal, characteristic, complemented
5C7×#2085C211yesmaximal, characteristic, complemented
6C7×#2033C211yesmaximal, characteristic, complemented
7C7×#2012C211yesmaximal, characteristic, complemented
8C7×#2000C211yesmaximal, characteristic, complemented
9C7×#1958C211yesmaximal, characteristic, complemented
10C7×#1936C211yesmaximal, characteristic, complemented
11C7×#1934C211yesmaximal, characteristic, complemented
12C7×#1894C211yesmaximal, characteristic, complemented
13C7×#1879C211yesmaximal, characteristic, complemented
14C7×#1865C211yesmaximal, characteristic, complemented
15C7×#1753C211yesmaximal, characteristic, complemented
16C22×C7×SD16C2211yescharacteristic
17C22×C7×D8C2211yescharacteristic
18C22×C7×M16C2211yescharacteristic
19C2×C7×#124C2211yescharacteristic
20C2×C7×C22⋊Q8C2211yescharacteristic
21C2×C7×#121C2211yescharacteristic
22C2×C7×#121C2211yescharacteristic
23C2×C4×C7×Q8C2211yescharacteristic
24C2×C4×C7×D4C2211yescharacteristic
25C7×#469—24no—
26C7×#440—24no—
27C2×C7×#107C2211yescharacteristic
28C2×C7×#106C2211yescharacteristic
29C2×C7×#103C2211yescharacteristic
30C2×C7×#103C2211yescharacteristic
31C2×C7×#103C2211yescharacteristic
32C2×C7×#102C2211yescharacteristic
33C2×C7×#102C2211yescharacteristic
34C2×C7×#102C2211yescharacteristic
35C2×C7×#102C2211yescharacteristic
36C2×C7×#102C2211yescharacteristic
37C2×C7×C22⋊C8C2211yescharacteristic
38C2×C7×#97C2211yescharacteristic
39C2×C4×C7×C8C2211yescharacteristic
40C7×#397—21no—
41C7×#396—21no—
42C7×#394—21no—
43C7×#394—21no—
44C7×#390—21no—
45C7×#390C2211yescharacteristic
46C7×#390C2211yescharacteristic
47C7×#389C2211yescharacteristic
48C7×#389C2211yescharacteristic
49C7×#388—21no—
50C7×#386—21no—
51C7×#382C2211yescharacteristic
52C7×#381—21no—
53C7×#380C2211yescharacteristic
54C4×C7×C22⋊C4C2211yescharacteristic
55C7×#340C2211yescharacteristic
56C7×#340C2211yescharacteristic
57C7×#340C2211yescharacteristic
58C7×#340C2211yescharacteristic
59C7×#336C2211yescharacteristic
60C7×#336C2211yescharacteristic
61#26982C711yesmaximal, characteristic, direct product factor, Sylow
62C22×C7×Q8C2311yescharacteristic
63C22×C7×D4—21no—
64C22×C7×D4—21no—
65C22×C7×D4C2311yescharacteristic
66C22×C7×D4C2311yescharacteristic
67C23×C4×C7—21no—
68C23×C4×C7C2311yescharacteristic
69C2×C7×SD16—22no—
70C2×C7×SD16—22no—
71C2×C7×SD16—22no—
72C2×C7×D8—22no—
73C2×C7×D8—22no—
74C2×C7×D8—41no—
75C2×C7×M16—22no—
76C2×C7×M16—22no—
77C2×C7×M16—41no—
78C22×C7×C8C2311yescharacteristic
79C22×C7×C8C2311yescharacteristic
80C22×C7×C8C2311yescharacteristic
81C22×C7×C8C2311yescharacteristic
82C7×#124—22no—
83C7×#124—41no—
84C7×C22⋊Q8—22no—
85C7×C22⋊Q8—41no—
86C7×#121—22no—
87C7×#121—22no—
88C7×#121—41no—
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⋊C4C2311yescharacteristic
99C2×C7×C4⋊C4C2311yescharacteristic
100C2×C7×C4⋊C4C2311yescharacteristic
101C2×C7×C4⋊C4C2311yescharacteristic
102C2×C7×C4⋊C4C2311yescharacteristic
103C2×C7×C22⋊C4—21no—
104C2×C7×C22⋊C4—21no—
105C2×C7×C22⋊C4—21no—
106C2×C7×C22⋊C4—21no—
107C2×C7×C22⋊C4—21no—
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⋊C4D411yescharacteristic
115C2×C7×C22⋊C4D411yescharacteristic
116C2×C42×C7—21no—
117C2×C42×C7C2311yescharacteristic
118C2×C42×C7C2311yescharacteristic
119C7×#107—22no—
120C7×#106—22no—
121C7×#103—22no—
122C7×#103—22no—
123C7×#103—41no—
124C7×#102—22no—
125C7×#102—22no—
126C7×#102—41no—
127C7×#102—41no—
128C7×#102D414yes—
129C7×C22⋊C8—22no—
130C7×#97—22no—
131C4×C7×C8—41no—
132C7×#95—21no—
133C7×#95—21no—
134C7×#95—21no—
135C7×#95—21no—
136C7×#95—21no—
137C7×#95D411yescharacteristic
138C7×#95D411yescharacteristic
139C2×#469C2×C711yescharacteristic
140C2×#440C2×C711yescharacteristic, complemented
141#2426C2×C711yescharacteristic, complemented
142#2420C2×C711yescharacteristic, complemented
143#2085C2×C711yescharacteristic, complemented
144#2033C2×C711yescharacteristic, complemented
145#2012C2×C711yescharacteristic, complemented
146#2000C2×C711yescharacteristic, complemented
147#1958C2×C711yescharacteristic, complemented
148#1936C2×C711yescharacteristic, complemented
149#1934C2×C711yescharacteristic, complemented
150#1894C2×C711yescharacteristic, complemented
151#1879C2×C711yescharacteristic, complemented
152#1865C2×C711yescharacteristic, complemented
153#1753C2×C711yescharacteristic, complemented
154C24×C7—21no—
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#4112yes—
163C2×C7×D4—21no—
164C2×C7×D4—21no—
165C2×C7×D4—21no—
166C2×C7×D4—21no—
167C2×C7×D4—21no—
168C2×C7×D4—21no—
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—42no—
177C2×C7×D4—42no—
178C2×C7×D4—81no—
179C2×C7×D4—81no—
180C2×C7×D4C2×D412yes—
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—21no—
192C22×C4×C7—21no—
193C22×C4×C7—42no—
194C22×C4×C7—42no—
195C22×C4×C7—81no—
196C22×C4×C7C2×D411yescharacteristic
197C22×C4×C7C2×D411yescharacteristic
198C22×C4×C7C2×D411yescharacteristic
199C22×C4×C7C2×D411yescharacteristic
200C22×C4×C7C2×D411yescharacteristic
201C22×C4×C7C2411yescharacteristic
202C7×SD16—28no—
203C7×D8—44no—
204C7×M16—44no—
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×C8—21no—
213C2×C7×C8—21no—
214C2×C7×C8C2×D412yes—
215C2×C7×C8#4112yes—
216C2×C7×C8#4112yes—
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—21no—
225C7×C4⋊C4—21no—
226C7×C4⋊C4—42no—
227C7×C4⋊C4—42no—
228C7×C4⋊C4—81no—
229C7×C4⋊C4—81no—
230C7×C4⋊C4C2×D412yes—
231C7×C22⋊C4—41no—
232C7×C22⋊C4—41no—
233C7×C22⋊C4—42no—
234C7×C22⋊C4—42no—
235C7×C22⋊C4—42no—
236C7×C22⋊C4—42no—
237C7×C22⋊C4—42no—
238C7×C22⋊C4—42no—
239C7×C22⋊C4—42no—
240C7×C22⋊C4—81no—
241C7×C22⋊C4—81no—
242C7×C22⋊C4—81no—
243C7×C22⋊C4—81no—
244C42×C7—21no—
245C42×C7—21no—
246C42×C7—21no—
247C42×C7—21no—
248C42×C7—42no—
249C22×SD16C22×C711yescharacteristic
250C22×D8C22×C711yescharacteristic
251C22×M16C22×C711yescharacteristic
252C2×#124C22×C711yescharacteristic
253C2×C22⋊Q8C22×C711yescharacteristic
254C2×#121C22×C711yescharacteristic
255C2×#121C22×C711yescharacteristic
256C2×C4×Q8C22×C711yescharacteristic
257C2×C4×D4C22×C711yescharacteristic
258#469—24no—
259#440—24no—
260C2×#107C22×C711yescharacteristic
261C2×#106C22×C711yescharacteristic
262C2×#103C22×C711yescharacteristic
263C2×#103C22×C711yescharacteristic
264C2×#103C22×C711yescharacteristic
265C2×#102C22×C711yescharacteristic
266C2×#102C22×C711yescharacteristic
267C2×#102C22×C711yescharacteristic
268C2×#102C22×C711yescharacteristic
269C2×#102C22×C711yescharacteristic
270C2×C22⋊C8C22×C711yescharacteristic
271C2×#97C22×C711yescharacteristic
272C2×C4×C8C22×C711yescharacteristic
273#397—21no—
274#396—21no—
275#394—21no—
276#394—21no—
277#390—21no—
278#390C22×C711yescharacteristic
279#390C22×C711yescharacteristic
280#389C22×C711yescharacteristic
281#389C22×C711yescharacteristic
282#388—21no—
283#386—21no—
284#382C22×C711yescharacteristic
285#381—21no—
286#380C22×C711yescharacteristic
287C4×C22⋊C4C22×C711yescharacteristic
288#340C22×C711yescharacteristic
289#340C22×C711yescharacteristic
290#340C22×C711yescharacteristic
291#340C22×C711yescharacteristic
292#336C22×C711yescharacteristic
293#336C22×C711yescharacteristic
294C23×C7—21no—
295C23×C7—22no—
296C23×C7—21no—
297C23×C7—21no—
298C23×C7—21no—
299C23×C7—21no—
300C23×C7—21no—
301C23×C7—21no—
302C23×C7—41no—
303C23×C7—41no—
304C23×C7—41no—
305C23×C7—41no—
306C23×C7—41no—
307C23×C7—41no—
308C23×C7—41no—
309C23×C7—41no—
310C23×C7—41no—
311C23×C7—41no—
312C23×C7—41no—
313C23×C7—41no—
314C23×C7—41no—
315C23×C7C22×D411yescharacteristic
316C7×Q8—22no—
317C7×Q8—22no—
318C7×Q8—41no—
319C7×Q8—41no—
320C7×D4—22no—
321C7×D4—22no—
322C7×D4—41no—
323C7×D4—41no—
324C7×D4—41no—
325C7×D4—41no—
326C7×D4—41no—
327C7×D4—41no—
328C7×D4—84no—
329C7×D4—84no—
330C2×C4×C7—21no—
331C2×C4×C7—21no—
332C2×C4×C7—21no—
333C2×C4×C7—22no—
334C2×C4×C7—21no—
335C2×C4×C7—21no—
336C2×C4×C7—21no—
337C2×C4×C7—22no—
338C2×C4×C7—21no—
339C2×C4×C7—21no—
340C2×C4×C7—21no—
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—84no—
368C2×C4×C7C22×D411yescharacteristic
369C2×C4×C7C2×#4111yescharacteristic
370C2×C4×C7C2×#4111yescharacteristic
371C2×C4×C7C2×#4111yescharacteristic
372C2×C4×C7H(5,𝔽2)11yescharacteristic
373C2×C4×C7H(5,𝔽2)11yescharacteristic
374C7×C8—22no—
375C7×C8—22no—
376C7×C8—22no—
377C7×C8—41no—
378C22×Q8C23×C711yescharacteristic
379C22×D4—21no—
380C22×D4—21no—
381C22×D4C23×C711yescharacteristic
382C22×D4C23×C711yescharacteristic
383C23×C4—21no—
384C23×C4C23×C711yescharacteristic
385C2×SD16—22no—
386C2×SD16—22no—
387C2×SD16—22no—
388C2×D8—22no—
389C2×D8—22no—
390C2×D8—41no—
391C2×M16—22no—
392C2×M16—22no—
393C2×M16—41no—
394C22×C8C23×C711yescharacteristic
395C22×C8C23×C711yescharacteristic
396C22×C8C23×C711yescharacteristic
397C22×C8C23×C711yescharacteristic
398#124—22no—
399#124—41no—
400C22⋊Q8—22no—
401C22⋊Q8—41no—
402#121—22no—
403#121—22no—
404#121—41no—
405#121—41no—
406C4×Q8—22no—
407C4×Q8—41no—
408C4×D4—22no—
409C4×D4—41no—
410C2×C4⋊C4—21no—
411C2×C4⋊C4—21no—
412C2×C4⋊C4—21no—
413C2×C4⋊C4—21no—
414C2×C4⋊C4C23×C711yescharacteristic
415C2×C4⋊C4C23×C711yescharacteristic
416C2×C4⋊C4C23×C711yescharacteristic
417C2×C4⋊C4C23×C711yescharacteristic
418C2×C4⋊C4C23×C711yescharacteristic
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⋊C4—21no—
426C2×C22⋊C4—21no—
427C2×C22⋊C4—21no—
428C2×C22⋊C4—21no—
429C2×C22⋊C4—21no—
430C2×C22⋊C4C7×D411yescharacteristic
431C2×C22⋊C4C7×D411yescharacteristic
432C2×C42—21no—
433C2×C42C23×C711yescharacteristic
434C2×C42C23×C711yescharacteristic
435#107—22no—
436#106—22no—
437#103—22no—
438#103—22no—
439#103—41no—
440#102—22no—
441#102—22no—
442#102—41no—
443#102—41no—
444#102C7×D414yes—
445C22⋊C8—22no—
446#97—22no—
447C4×C8—41no—
448#95—21no—
449#95—21no—
450#95—21no—
451#95—21no—
452#95—21no—
453#95C7×D411yescharacteristic
454#95C7×D411yescharacteristic
455C22×C7—41no—
456C22×C7—41no—
457C22×C7—41no—
458C22×C7—42no—
459C22×C7—42no—
460C22×C7—41no—
461C22×C7—41no—
462C22×C7—42no—
463C22×C7—41no—
464C22×C7—41no—
465C22×C7—81no—
466C22×C7—81no—
467C22×C7—81no—
468C22×C7—81no—
469C22×C7—81no—
470C22×C7—81no—
471C22×C7—81no—
472C22×C7—81no—
473C22×C7—81no—
474C22×C7—81no—
475C22×C7—81no—
476C22×C7#53211yescharacteristic
477C22×C7D4211yescharacteristic
478C22×C7#54611yescharacteristic
479C22×C7#57511yescharacteristic
480C22×C7#57511yescharacteristic
481C22×C7#57611yescharacteristic
482C22×C7#57711yescharacteristic
483C4×C7—41no—
484C4×C7—42no—
485C4×C7—41no—
486C4×C7—42no—
487C4×C7—41no—
488C4×C7—41no—
489C4×C7—41no—
490C4×C7—81no—
491C4×C7—81no—
492C4×C7—81no—
493C4×C7—81no—
494C4×C7#52511yescharacteristic
495C4×C7#54011yescharacteristic
496C4×C7#54611yescharacteristic
497C4×C7#55311yescharacteristic
498C24—21no—
499C24—21no—
500C24C2×C7×D411yescharacteristic
501C2×Q8—21no—
502C2×Q8—21no—
503C2×Q8—21no—
504C2×Q8—21no—
505C2×Q8—21no—
506C2×Q8C7×#4112yes—
507C2×D4—21no—
508C2×D4—21no—
509C2×D4—21no—
510C2×D4—21no—
511C2×D4—21no—
512C2×D4—21no—
513C2×D4—21no—
514C2×D4—21no—
515C2×D4—21no—
516C2×D4—21no—
517C2×D4—21no—
518C2×D4—42no—
519C2×D4—42no—
520C2×D4—42no—
521C2×D4—42no—
522C2×D4—81no—
523C2×D4—81no—
524C2×D4C2×C7×D412yes—
525C22×C4—21no—
526C22×C4—21no—
527C22×C4—21no—
528C22×C4—21no—
529C22×C4—21no—
530C22×C4—21no—
531C22×C4—21no—
532C22×C4—21no—
533C22×C4—21no—
534C22×C4—21no—
535C22×C4—21no—
536C22×C4—21no—
537C22×C4—42no—
538C22×C4—42no—
539C22×C4—81no—
540C22×C4C2×C7×D411yescharacteristic
541C22×C4C2×C7×D411yescharacteristic
542C22×C4C2×C7×D411yescharacteristic
543C22×C4C2×C7×D411yescharacteristic
544C22×C4C2×C7×D411yescharacteristic
545C22×C4C24×C711yescharacteristic
546SD16—28no—
547D8—44no—
548M16—44no—
549C2×C8—21no—
550C2×C8—21no—
551C2×C8—21no—
552C2×C8—21no—
553C2×C8—21no—
554C2×C8—21no—
555C2×C8—21no—
556C2×C8—21no—
557C2×C8—21no—
558C2×C8C2×C7×D412yes—
559C2×C8C7×#4112yes—
560C2×C8C7×#4112yes—
561C4⋊C4—21no—
562C4⋊C4—21no—
563C4⋊C4—21no—
564C4⋊C4—21no—
565C4⋊C4—21no—
566C4⋊C4—21no—
567C4⋊C4—21no—
568C4⋊C4—21no—
569C4⋊C4—21no—
570C4⋊C4—42no—
571C4⋊C4—42no—
572C4⋊C4—81no—
573C4⋊C4—81no—
574C4⋊C4C2×C7×D412yes—
575C22⋊C4—41no—
576C22⋊C4—41no—
577C22⋊C4—42no—
578C22⋊C4—42no—
579C22⋊C4—42no—
580C22⋊C4—42no—
581C22⋊C4—42no—
582C22⋊C4—42no—
583C22⋊C4—42no—
584C22⋊C4—81no—
585C22⋊C4—81no—
586C22⋊C4—81no—
587C22⋊C4—81no—
588C42—21no—
589C42—21no—
590C42—21no—
591C42—21no—
592C42—42no—
593C2×C7—81no—
594C2×C7—82no—
595C2×C7—161no—
596C2×C7#246411yescharacteristic
597C2×C7#317911yescharacteristic
598C2×C7#318311yescharacteristic
599C2×C7#327311yescharacteristic
600C2×C7#327511yescharacteristic
601C2×C7#330911yescharacteristic
602C2×C7#332111yescharacteristic
603C23—21no—
604C23—22no—
605C23—21no—
606C23—21no—
607C23—21no—
608C23—21no—
609C23—21no—
610C23—21no—
611C23—41no—
612C23—41no—
613C23—41no—
614C23—41no—
615C23—41no—
616C23—41no—
617C23—41no—
618C23—41no—
619C23—41no—
620C23—41no—
621C23—41no—
622C23—41no—
623C23—41no—
624C23C22×C7×D411yescharacteristic
625Q8—22no—
626Q8—22no—
627Q8—41no—
628Q8—41no—
629D4—22no—
630D4—22no—
631D4—41no—
632D4—41no—
633D4—41no—
634D4—41no—
635D4—41no—
636D4—41no—
637D4—84no—
638D4—84no—
639C2×C4—21no—
640C2×C4—21no—
641C2×C4—21no—
642C2×C4—22no—
643C2×C4—21no—
644C2×C4—21no—
645C2×C4—21no—
646C2×C4—22no—
647C2×C4—21no—
648C2×C4—21no—
649C2×C4—21no—
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—84no—
677C2×C4C22×C7×D411yescharacteristic
678C2×C4C2×C7×#4111yescharacteristic
679C2×C4C2×C7×#4111yescharacteristic
680C2×C4C2×C7×#4111yescharacteristic
681C2×C4C7×H(5,𝔽2)11yescharacteristic
682C2×C4C7×H(5,𝔽2)11yescharacteristic
683C8—22no—
684C8—22no—
685C8—22no—
686C8—41no—
687C7#2698211yescharacteristic, direct product factor, Sylow
688C22—41no—
689C22—41no—
690C22—41no—
691C22—42no—
692C22—42no—
693C22—41no—
694C22—41no—
695C22—42no—
696C22—41no—
697C22—41no—
698C22—81no—
699C22—81no—
700C22—81no—
701C22—81no—
702C22—81no—
703C22—81no—
704C22—81no—
705C22—81no—
706C22—81no—
707C22—81no—
708C22—81no—
709C22C7×#53211yescharacteristic
710C22C7×D4211yescharacteristic
711C22C7×#54611yescharacteristic
712C22C7×#57511yescharacteristic
713C22C7×#57511yescharacteristic
714C22C7×#57611yescharacteristic
715C22C7×#57711yescharacteristic
716C4—41no—
717C4—42no—
718C4—41no—
719C4—42no—
720C4—41no—
721C4—41no—
722C4—41no—
723C4—81no—
724C4—81no—
725C4—81no—
726C4—81no—
727C4C7×#52511yescharacteristic
728C4C7×#54011yescharacteristic
729C4C7×#54611yescharacteristic
730C4C7×#55311yescharacteristic
731C2—81no—
732C2—82no—
733C2—161no—
734C2C7×#246411yescharacteristic
735C2C7×#317911yescharacteristic
736C2C7×#318311yescharacteristic
737C2C7×#327311yescharacteristic
738C2C7×#327511yescharacteristic
739C2C7×#330911yescharacteristic
740C2C7×#332111yescharacteristic
subgroupG/H
center, socleC23×C7C22×D4
commutator, Frattini, cosocleC22×C4C24×C7
prime radicalC2×C7×#469C2
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×#2426C2semidirect
4. C7×#2420C2semidirect
5. C7×#2085C2semidirect
6. C7×#2033C2semidirect
7. C7×#2012C2semidirect
8. C7×#2000C2semidirect
9. C7×#1958C2semidirect
10. C7×#1936C2semidirect
11. C7×#1934C2semidirect
12. C7×#1894C2semidirect
13. C7×#1879C2semidirect
14. C7×#1865C2semidirect
15. C7×#1753C2semidirect
61. #26982C7direct (N × H)
140. C2×#440C2×C7semidirect
141. #2426C2×C7semidirect
142. #2420C2×C7semidirect
143. #2085C2×C7semidirect
144. #2033C2×C7semidirect
145. #2012C2×C7semidirect
146. #2000C2×C7semidirect
147. #1958C2×C7semidirect
148. #1936C2×C7semidirect
149. #1934C2×C7semidirect
150. #1894C2×C7semidirect
151. #1879C2×C7semidirect
152. #1865C2×C7semidirect
153. #1753C2×C7semidirect
687. C7#26982direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C7×#4692
C2×C7×#4402
C7×#24262
C7×#24202
C7×#20852
C7×#20332
C7×#20122
C7×#20002
C7×#19582
C7×#19362
C7×#19342
C7×#18942
C7×#18792
C7×#18652
C7×#17532
#269827