Finite Group Databasebeta

← C7×#13873 #13191089

Subgroups — C7×#13873 #13191089

Order 1792.

3526 conjugacy classes of subgroups.

The subgroup lattice has 938 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C23×C7×C22⋊C4C211yesmaximal, characteristic
2C2×C7×#388C212yesmaximal, complemented
3C2×C7×#380C211yesmaximal, characteristic, complemented
4C2×C7×#379C211yesmaximal, characteristic
5C2×C7×#379C211yesmaximal, characteristic
6C2×C4×C7×C22⋊C4C211yesmaximal, characteristic, complemented
7C7×#1440C212yesmaximal, complemented
8C7×#1439C212yesmaximal, complemented
9C7×#1437C212yesmaximal, complemented
10C7×C22⋊#95C211yesmaximal, characteristic, complemented
11C7×C22⋊#95C211yesmaximal, characteristic, complemented
12C26×C7C2211yescharacteristic
13C24×C4×C7C2211yescharacteristic
14C24×C4×C7C2211yescharacteristic
15C22×C7×C4⋊C4C2212yescomplemented
16C22×C7×C22⋊C4—28no—
17C22×C7×C22⋊C4C418yescomplemented
18C22×C7×C22⋊C4C2211yescharacteristic
19C22×C7×C22⋊C4C2211yescharacteristic
20C22×C7×C22⋊C4C2212yes—
21C22×C7×C22⋊C4C2212yes—
22C22×C7×C22⋊C4C2212yes—
23C22×C7×C22⋊C4C2212yes—
24C22×C7×C22⋊C4C2211yescharacteristic
25C22×C7×C22⋊C4C2211yescharacteristic
26C22×C7×C22⋊C4C2211yescharacteristic
27C22×C7×C22⋊C4C2211yescharacteristic
28C22×C7×C22⋊C4C2211yescharacteristic
29C22×C7×C22⋊C4C2211yescharacteristic
30C22×C42×C7C2212yescomplemented
31C7×#388—28no—
32C7×#380—24no—
33C7×#379—24no—
34C7×#379—24no—
35C4×C7×C22⋊C4—24no—
36C2×C7×#95C2212yescomplemented
37C2×C7×#95C2212yescomplemented
38C2×C7×#95C2212yescomplemented
39C2×C7×#95C2212yescomplemented
40C2×C7×#95C2212yescomplemented
41C2×C7×#95C2212yescomplemented
42#13873C711yesmaximal, characteristic, direct product factor, Sylow
43C25×C7—24no—
44C25×C7—24no—
45C25×C7—22no—
46C25×C7—22no—
47C25×C7—22no—
48C25×C7—22no—
49C25×C7—22no—
50C25×C7—22no—
51C25×C7—42no—
52C25×C7—42no—
53C25×C7C2×C414yes—
54C25×C7C2311yescharacteristic
55C25×C7C2311yescharacteristic
56C25×C7C2311yescharacteristic
57C23×C4×C7—22no—
58C23×C4×C7—22no—
59C23×C4×C7—22no—
60C23×C4×C7—22no—
61C23×C4×C7—24no—
62C23×C4×C7—24no—
63C23×C4×C7—42no—
64C23×C4×C7—42no—
65C23×C4×C7C2×C414yes—
66C23×C4×C7C2×C414yes—
67C23×C4×C7C2312yes—
68C23×C4×C7C2312yes—
69C23×C4×C7C2311yescharacteristic
70C23×C4×C7C2311yescharacteristic
71C23×C4×C7C2312yes—
72C23×C4×C7C2312yes—
73C23×C4×C7C2311yescharacteristic
74C23×C4×C7C2311yescharacteristic
75C2×C7×C4⋊C4—24no—
76C2×C7×C4⋊C4—24no—
77C2×C7×C4⋊C4—42no—
78C2×C7×C22⋊C4—24no—
79C2×C7×C22⋊C4—22no—
80C2×C7×C22⋊C4—22no—
81C2×C7×C22⋊C4—22no—
82C2×C7×C22⋊C4—22no—
83C2×C7×C22⋊C4—24no—
84C2×C7×C22⋊C4—24no—
85C2×C7×C22⋊C4—232no—
86C2×C7×C22⋊C4—22no—
87C2×C7×C22⋊C4—22no—
88C2×C7×C22⋊C4—22no—
89C2×C7×C22⋊C4—24no—
90C2×C7×C22⋊C4—24no—
91C2×C7×C22⋊C4—24no—
92C2×C7×C22⋊C4—24no—
93C2×C7×C22⋊C4—22no—
94C2×C7×C22⋊C4—22no—
95C2×C7×C22⋊C4—22no—
96C2×C7×C22⋊C4—24no—
97C2×C7×C22⋊C4—24no—
98C2×C7×C22⋊C4—24no—
99C2×C7×C22⋊C4—24no—
100C2×C7×C22⋊C4—42no—
101C2×C7×C22⋊C4—42no—
102C2×C7×C22⋊C4—42no—
103C2×C7×C22⋊C4—42no—
104C2×C7×C22⋊C4C2×C414yes—
105C2×C7×C22⋊C4C2×C414yes—
106C2×C7×C22⋊C4C2×C414yes—
107C2×C7×C22⋊C4C2×C414yes—
108C2×C7×C22⋊C4D414yes—
109C2×C7×C22⋊C4D414yes—
110C2×C7×C22⋊C4D418yes—
111C2×C42×C7—24no—
112C2×C42×C7—24no—
113C2×C42×C7—42no—
114C7×#95—24no—
115C7×#95—24no—
116C7×#95—24no—
117C7×#95—24no—
118C7×#95—42no—
119C7×#95—42no—
120C23×C22⋊C4C2×C711yescharacteristic
121C2×#388C2×C712yescomplemented
122C2×#380C2×C711yescharacteristic, complemented
123C2×#379C2×C711yescharacteristic
124C2×#379C2×C711yescharacteristic
125C2×C4×C22⋊C4C2×C711yescharacteristic, complemented
126#1440C2×C712yescomplemented
127#1439C2×C712yescomplemented
128#1437C2×C712yescomplemented
129C22⋊#95C2×C711yescharacteristic, complemented
130C22⋊#95C2×C711yescharacteristic, complemented
131C24×C7—22no—
132C24×C7—22no—
133C24×C7—22no—
134C24×C7—22no—
135C24×C7—216no—
136C24×C7—216no—
137C24×C7—28no—
138C24×C7—28no—
139C24×C7—28no—
140C24×C7—22no—
141C24×C7—21no—
142C24×C7—21no—
143C24×C7—21no—
144C24×C7—21no—
145C24×C7—21no—
146C24×C7—21no—
147C24×C7—22no—
148C24×C7—21no—
149C24×C7—21no—
150C24×C7—21no—
151C24×C7—21no—
152C24×C7—21no—
153C24×C7—21no—
154C24×C7—22no—
155C24×C7—22no—
156C24×C7—22no—
157C24×C7—22no—
158C24×C7—28no—
159C24×C7—28no—
160C24×C7—44no—
161C24×C7—44no—
162C24×C7—48no—
163C24×C7—48no—
164C24×C7—48no—
165C24×C7—48no—
166C24×C7—48no—
167C24×C7—48no—
168C24×C7—48no—
169C24×C7—48no—
170C24×C7—48no—
171C24×C7—48no—
172C24×C7—44no—
173C24×C7—44no—
174C24×C7—44no—
175C24×C7—44no—
176C24×C7C22×C412yes—
177C24×C7C22×C412yes—
178C24×C7C22×C412yes—
179C24×C7C2×D414yes—
180C24×C7C2×D412yes—
181C24×C7C2×D412yes—
182C24×C7#4114yes—
183C24×C7#4112yes—
184C24×C7#4112yes—
185C24×C7#4112yes—
186C24×C7#4112yes—
187C24×C7C2411yescharacteristic
188C22×C4×C7—21no—
189C22×C4×C7—21no—
190C22×C4×C7—21no—
191C22×C4×C7—21no—
192C22×C4×C7—22no—
193C22×C4×C7—22no—
194C22×C4×C7—28no—
195C22×C4×C7—28no—
196C22×C4×C7—21no—
197C22×C4×C7—21no—
198C22×C4×C7—22no—
199C22×C4×C7—22no—
200C22×C4×C7—22no—
201C22×C4×C7—22no—
202C22×C4×C7—22no—
203C22×C4×C7—22no—
204C22×C4×C7—22no—
205C22×C4×C7—22no—
206C22×C4×C7—22no—
207C22×C4×C7—22no—
208C22×C4×C7—21no—
209C22×C4×C7—21no—
210C22×C4×C7—22no—
211C22×C4×C7—22no—
212C22×C4×C7—22no—
213C22×C4×C7—22no—
214C22×C4×C7—22no—
215C22×C4×C7—22no—
216C22×C4×C7—28no—
217C22×C4×C7—28no—
218C22×C4×C7—22no—
219C22×C4×C7—22no—
220C22×C4×C7—22no—
221C22×C4×C7—22no—
222C22×C4×C7—22no—
223C22×C4×C7—22no—
224C22×C4×C7—22no—
225C22×C4×C7—22no—
226C22×C4×C7—22no—
227C22×C4×C7—22no—
228C22×C4×C7—22no—
229C22×C4×C7—22no—
230C22×C4×C7—22no—
231C22×C4×C7—22no—
232C22×C4×C7—44no—
233C22×C4×C7—44no—
234C22×C4×C7—48no—
235C22×C4×C7—48no—
236C22×C4×C7—48no—
237C22×C4×C7—48no—
238C22×C4×C7C22×C412yes—
239C22×C4×C7C22×C412yes—
240C22×C4×C7C22×C412yes—
241C22×C4×C7C22×C412yes—
242C22×C4×C7C2×D414yes—
243C22×C4×C7C2×D414yes—
244C22×C4×C7C2×D414yes—
245C22×C4×C7C2×D414yes—
246C7×C4⋊C4—48no—
247C7×C22⋊C4—28no—
248C7×C22⋊C4—28no—
249C7×C22⋊C4—28no—
250C7×C22⋊C4—28no—
251C7×C22⋊C4—28no—
252C7×C22⋊C4—48no—
253C7×C22⋊C4—48no—
254C7×C22⋊C4—48no—
255C7×C22⋊C4—48no—
256C7×C22⋊C4—44no—
257C7×C22⋊C4—44no—
258C7×C22⋊C4C22⋊C4116yescomplemented
259C42×C7—48no—
260C26C22×C711yescharacteristic
261C24×C4C22×C711yescharacteristic
262C24×C4C22×C711yescharacteristic
263C22×C4⋊C4C22×C712yescomplemented
264C22×C22⋊C4—28no—
265C22×C22⋊C4C4×C718yescomplemented
266C22×C22⋊C4C22×C711yescharacteristic
267C22×C22⋊C4C22×C711yescharacteristic
268C22×C22⋊C4C22×C712yes—
269C22×C22⋊C4C22×C712yes—
270C22×C22⋊C4C22×C712yes—
271C22×C22⋊C4C22×C712yes—
272C22×C22⋊C4C22×C711yescharacteristic
273C22×C22⋊C4C22×C711yescharacteristic
274C22×C22⋊C4C22×C711yescharacteristic
275C22×C22⋊C4C22×C711yescharacteristic
276C22×C22⋊C4C22×C711yescharacteristic
277C22×C22⋊C4C22×C711yescharacteristic
278C22×C42C22×C712yescomplemented
279#388—28no—
280#380—24no—
281#379—24no—
282#379—24no—
283C4×C22⋊C4—24no—
284C2×#95C22×C712yescomplemented
285C2×#95C22×C712yescomplemented
286C2×#95C22×C712yescomplemented
287C2×#95C22×C712yescomplemented
288C2×#95C22×C712yescomplemented
289C2×#95C22×C712yescomplemented
290C23×C7—22no—
291C23×C7—22no—
292C23×C7—22no—
293C23×C7—22no—
294C23×C7—24no—
295C23×C7—24no—
296C23×C7—24no—
297C23×C7—24no—
298C23×C7—24no—
299C23×C7—24no—
300C23×C7—24no—
301C23×C7—24no—
302C23×C7—24no—
303C23×C7—24no—
304C23×C7—24no—
305C23×C7—24no—
306C23×C7—232no—
307C23×C7—22no—
308C23×C7—22no—
309C23×C7—22no—
310C23×C7—22no—
311C23×C7—22no—
312C23×C7—22no—
313C23×C7—22no—
314C23×C7—22no—
315C23×C7—22no—
316C23×C7—22no—
317C23×C7—22no—
318C23×C7—22no—
319C23×C7—24no—
320C23×C7—24no—
321C23×C7—24no—
322C23×C7—24no—
323C23×C7—24no—
324C23×C7—24no—
325C23×C7—24no—
326C23×C7—24no—
327C23×C7—24no—
328C23×C7—24no—
329C23×C7—24no—
330C23×C7—24no—
331C23×C7—416no—
332C23×C7—416no—
333C23×C7—416no—
334C23×C7—416no—
335C23×C7—416no—
336C23×C7—432no—
337C23×C7—432no—
338C23×C7—432no—
339C23×C7—432no—
340C23×C7—41no—
341C23×C7—41no—
342C23×C7—41no—
343C23×C7—41no—
344C23×C7—41no—
345C23×C7—41no—
346C23×C7—41no—
347C23×C7—41no—
348C23×C7—42no—
349C23×C7—42no—
350C23×C7—42no—
351C23×C7—42no—
352C23×C7—42no—
353C23×C7—42no—
354C23×C7—42no—
355C23×C7—42no—
356C23×C7—42no—
357C23×C7—42no—
358C23×C7—42no—
359C23×C7—42no—
360C23×C7—416no—
361C23×C7C2×C22⋊C414yes—
362C23×C7#11714yes—
363C23×C7#11714yes—
364C23×C7C4×D414yes—
365C23×C7C4×D414yes—
366C23×C7#12114yes—
367C23×C7#12314yes—
368C23×C7#12414yes—
369C23×C7#12614yes—
370C23×C7C23×C411yescharacteristic
371C23×C7C22×D412yes—
372C23×C7C22×D411yescharacteristic
373C23×C7C22×D411yescharacteristic
374C23×C7C2×#4111yescharacteristic
375C23×C7C2×#4111yescharacteristic
376C23×C7C2×#4112yes—
377C23×C7C2×#4111yescharacteristic
378C23×C7C2×#4111yescharacteristic
379C23×C7H(5,𝔽2)12yes—
380C23×C7H(5,𝔽2)12yes—
381C2×C4×C7—22no—
382C2×C4×C7—22no—
383C2×C4×C7—22no—
384C2×C4×C7—22no—
385C2×C4×C7—24no—
386C2×C4×C7—24no—
387C2×C4×C7—24no—
388C2×C4×C7—24no—
389C2×C4×C7—22no—
390C2×C4×C7—22no—
391C2×C4×C7—22no—
392C2×C4×C7—22no—
393C2×C4×C7—22no—
394C2×C4×C7—22no—
395C2×C4×C7—24no—
396C2×C4×C7—24no—
397C2×C4×C7—24no—
398C2×C4×C7—24no—
399C2×C4×C7—24no—
400C2×C4×C7—24no—
401C2×C4×C7—416no—
402C2×C4×C7—416no—
403C2×C4×C7—42no—
404C2×C4×C7—42no—
405C2×C4×C7—42no—
406C2×C4×C7—42no—
407C2×C4×C7—42no—
408C2×C4×C7—42no—
409C2×C4×C7—42no—
410C2×C4×C7—42no—
411C2×C4×C7—42no—
412C2×C4×C7—42no—
413C2×C4×C7—42no—
414C2×C4×C7—42no—
415C2×C4×C7—42no—
416C2×C4×C7—42no—
417C2×C4×C7—42no—
418C2×C4×C7—42no—
419C2×C4×C7—42no—
420C2×C4×C7—42no—
421C2×C4×C7—42no—
422C2×C4×C7—42no—
423C2×C4×C7—42no—
424C2×C4×C7—42no—
425C2×C4×C7—42no—
426C2×C4×C7—42no—
427C2×C4×C7—42no—
428C2×C4×C7—42no—
429C2×C4×C7C2×C22⋊C414yes—
430C2×C4×C7C2×C22⋊C414yes—
431C25—24no—
432C25—24no—
433C25—22no—
434C25—22no—
435C25—22no—
436C25—22no—
437C25—22no—
438C25—22no—
439C25—42no—
440C25—42no—
441C25C2×C4×C714yes—
442C25C23×C711yescharacteristic
443C25C23×C711yescharacteristic
444C25C23×C711yescharacteristic
445C23×C4—22no—
446C23×C4—22no—
447C23×C4—22no—
448C23×C4—22no—
449C23×C4—24no—
450C23×C4—24no—
451C23×C4—42no—
452C23×C4—42no—
453C23×C4C2×C4×C714yes—
454C23×C4C2×C4×C714yes—
455C23×C4C23×C712yes—
456C23×C4C23×C712yes—
457C23×C4C23×C711yescharacteristic
458C23×C4C23×C711yescharacteristic
459C23×C4C23×C712yes—
460C23×C4C23×C712yes—
461C23×C4C23×C711yescharacteristic
462C23×C4C23×C711yescharacteristic
463C2×C4⋊C4—24no—
464C2×C4⋊C4—24no—
465C2×C4⋊C4—42no—
466C2×C22⋊C4—24no—
467C2×C22⋊C4—22no—
468C2×C22⋊C4—22no—
469C2×C22⋊C4—22no—
470C2×C22⋊C4—22no—
471C2×C22⋊C4—24no—
472C2×C22⋊C4—24no—
473C2×C22⋊C4—232no—
474C2×C22⋊C4—22no—
475C2×C22⋊C4—22no—
476C2×C22⋊C4—22no—
477C2×C22⋊C4—24no—
478C2×C22⋊C4—24no—
479C2×C22⋊C4—24no—
480C2×C22⋊C4—24no—
481C2×C22⋊C4—22no—
482C2×C22⋊C4—22no—
483C2×C22⋊C4—22no—
484C2×C22⋊C4—24no—
485C2×C22⋊C4—24no—
486C2×C22⋊C4—24no—
487C2×C22⋊C4—24no—
488C2×C22⋊C4—42no—
489C2×C22⋊C4—42no—
490C2×C22⋊C4—42no—
491C2×C22⋊C4—42no—
492C2×C22⋊C4C2×C4×C714yes—
493C2×C22⋊C4C2×C4×C714yes—
494C2×C22⋊C4C2×C4×C714yes—
495C2×C22⋊C4C2×C4×C714yes—
496C2×C22⋊C4C7×D414yes—
497C2×C22⋊C4C7×D414yes—
498C2×C22⋊C4C7×D418yes—
499C2×C42—24no—
500C2×C42—24no—
501C2×C42—42no—
502#95—24no—
503#95—24no—
504#95—24no—
505#95—24no—
506#95—42no—
507#95—42no—
508C22×C7—24no—
509C22×C7—24no—
510C22×C7—24no—
511C22×C7—24no—
512C22×C7—24no—
513C22×C7—28no—
514C22×C7—28no—
515C22×C7—28no—
516C22×C7—28no—
517C22×C7—24no—
518C22×C7—24no—
519C22×C7—24no—
520C22×C7—24no—
521C22×C7—24no—
522C22×C7—24no—
523C22×C7—24no—
524C22×C7—464no—
525C22×C7—42no—
526C22×C7—42no—
527C22×C7—42no—
528C22×C7—42no—
529C22×C7—42no—
530C22×C7—42no—
531C22×C7—44no—
532C22×C7—44no—
533C22×C7—44no—
534C22×C7—44no—
535C22×C7—44no—
536C22×C7—44no—
537C22×C7—44no—
538C22×C7—44no—
539C22×C7—42no—
540C22×C7—42no—
541C22×C7#38818yescomplemented
542C22×C7C22×C22⋊C411yescharacteristic
543C22×C7C2×#11711yescharacteristic
544C22×C7C2×#11711yescharacteristic
545C22×C7C2×C4×D411yescharacteristic
546C22×C7C2×C4×D411yescharacteristic
547C22×C7#51811yescharacteristic
548C22×C7#51811yescharacteristic
549C22×C7C2×#12111yescharacteristic
550C22×C7C2×#12311yescharacteristic
551C22×C7#52512yes—
552C22×C7#52512yes—
553C22×C7C2×#12411yescharacteristic
554C22×C7C2×#12611yescharacteristic
555C22×C7#53812yes—
556C22×C7#53812yes—
557C22×C7D4212yes—
558C22×C7D4212yes—
559C22×C7#54612yes—
560C22×C7#54612yes—
561C22×C7#54612yes—
562C22×C7#54612yes—
563C22×C7#55112yes—
564C22×C7#55112yes—
565C4×C7—24no—
566C4×C7—24no—
567C4×C7—42no—
568C4×C7—42no—
569C4×C7—44no—
570C4×C7—44no—
571C4×C7—82no—
572C4×C7—82no—
573C24—22no—
574C24—22no—
575C24—22no—
576C24—22no—
577C24—216no—
578C24—216no—
579C24—28no—
580C24—28no—
581C24—28no—
582C24—22no—
583C24—21no—
584C24—21no—
585C24—21no—
586C24—21no—
587C24—21no—
588C24—21no—
589C24—22no—
590C24—21no—
591C24—21no—
592C24—21no—
593C24—21no—
594C24—21no—
595C24—21no—
596C24—22no—
597C24—22no—
598C24—22no—
599C24—22no—
600C24—28no—
601C24—28no—
602C24—44no—
603C24—44no—
604C24—48no—
605C24—48no—
606C24—48no—
607C24—48no—
608C24—48no—
609C24—48no—
610C24—48no—
611C24—48no—
612C24—48no—
613C24—48no—
614C24—44no—
615C24—44no—
616C24—44no—
617C24—44no—
618C24C22×C4×C712yes—
619C24C22×C4×C712yes—
620C24C22×C4×C712yes—
621C24C2×C7×D414yes—
622C24C2×C7×D412yes—
623C24C2×C7×D412yes—
624C24C7×#4114yes—
625C24C7×#4112yes—
626C24C7×#4112yes—
627C24C7×#4112yes—
628C24C7×#4112yes—
629C24C24×C711yescharacteristic
630C22×C4—21no—
631C22×C4—21no—
632C22×C4—21no—
633C22×C4—21no—
634C22×C4—22no—
635C22×C4—22no—
636C22×C4—28no—
637C22×C4—28no—
638C22×C4—21no—
639C22×C4—21no—
640C22×C4—22no—
641C22×C4—22no—
642C22×C4—22no—
643C22×C4—22no—
644C22×C4—22no—
645C22×C4—22no—
646C22×C4—22no—
647C22×C4—22no—
648C22×C4—22no—
649C22×C4—22no—
650C22×C4—21no—
651C22×C4—21no—
652C22×C4—22no—
653C22×C4—22no—
654C22×C4—22no—
655C22×C4—22no—
656C22×C4—22no—
657C22×C4—22no—
658C22×C4—28no—
659C22×C4—28no—
660C22×C4—22no—
661C22×C4—22no—
662C22×C4—22no—
663C22×C4—22no—
664C22×C4—22no—
665C22×C4—22no—
666C22×C4—22no—
667C22×C4—22no—
668C22×C4—22no—
669C22×C4—22no—
670C22×C4—22no—
671C22×C4—22no—
672C22×C4—22no—
673C22×C4—22no—
674C22×C4—44no—
675C22×C4—44no—
676C22×C4—48no—
677C22×C4—48no—
678C22×C4—48no—
679C22×C4—48no—
680C22×C4C22×C4×C712yes—
681C22×C4C22×C4×C712yes—
682C22×C4C22×C4×C712yes—
683C22×C4C22×C4×C712yes—
684C22×C4C2×C7×D414yes—
685C22×C4C2×C7×D414yes—
686C22×C4C2×C7×D414yes—
687C22×C4C2×C7×D414yes—
688C4⋊C4—48no—
689C22⋊C4—28no—
690C22⋊C4—28no—
691C22⋊C4—28no—
692C22⋊C4—28no—
693C22⋊C4—28no—
694C22⋊C4—48no—
695C22⋊C4—48no—
696C22⋊C4—48no—
697C22⋊C4—48no—
698C22⋊C4—44no—
699C22⋊C4—44no—
700C22⋊C4C7×C22⋊C4116yescomplemented
701C42—48no—
702C2×C7—28no—
703C2×C7—44no—
704C2×C7—44no—
705C2×C7#228011yescharacteristic
706C2×C7C2×#38811yescharacteristic
707C2×C7#231211yescharacteristic
708C2×C7D4×C22⋊C411yescharacteristic
709C2×C7D4×C22⋊C411yescharacteristic
710C2×C7#234211yescharacteristic
711C2×C7#234211yescharacteristic
712C2×C7#241812yes—
713C2×C7#242412yes—
714C2×C7#247212yes—
715C2×C7#248012yes—
716C23—22no—
717C23—22no—
718C23—22no—
719C23—22no—
720C23—24no—
721C23—24no—
722C23—24no—
723C23—24no—
724C23—24no—
725C23—24no—
726C23—24no—
727C23—24no—
728C23—24no—
729C23—24no—
730C23—24no—
731C23—24no—
732C23—232no—
733C23—22no—
734C23—22no—
735C23—22no—
736C23—22no—
737C23—22no—
738C23—22no—
739C23—22no—
740C23—22no—
741C23—22no—
742C23—22no—
743C23—22no—
744C23—22no—
745C23—24no—
746C23—24no—
747C23—24no—
748C23—24no—
749C23—24no—
750C23—24no—
751C23—24no—
752C23—24no—
753C23—24no—
754C23—24no—
755C23—24no—
756C23—24no—
757C23—416no—
758C23—416no—
759C23—416no—
760C23—416no—
761C23—432no—
762C23—432no—
763C23—432no—
764C23—432no—
765C23—416no—
766C23—41no—
767C23—41no—
768C23—41no—
769C23—41no—
770C23—416no—
771C23—41no—
772C23—41no—
773C23—41no—
774C23—41no—
775C23—42no—
776C23—42no—
777C23—42no—
778C23—42no—
779C23—42no—
780C23—42no—
781C23—42no—
782C23—42no—
783C23—42no—
784C23—42no—
785C23—42no—
786C23—42no—
787C23C2×C7×C22⋊C414yes—
788C23C7×#11714yes—
789C23C7×#11714yes—
790C23C4×C7×D414yes—
791C23C4×C7×D414yes—
792C23C7×#12114yes—
793C23C7×#12314yes—
794C23C7×#12414yes—
795C23C7×#12614yes—
796C23C23×C4×C711yescharacteristic
797C23C22×C7×D412yes—
798C23C22×C7×D411yescharacteristic
799C23C22×C7×D411yescharacteristic
800C23C2×C7×#4111yescharacteristic
801C23C2×C7×#4111yescharacteristic
802C23C2×C7×#4112yes—
803C23C2×C7×#4111yescharacteristic
804C23C2×C7×#4111yescharacteristic
805C23C7×H(5,𝔽2)12yes—
806C23C7×H(5,𝔽2)12yes—
807C2×C4—22no—
808C2×C4—22no—
809C2×C4—22no—
810C2×C4—22no—
811C2×C4—24no—
812C2×C4—24no—
813C2×C4—24no—
814C2×C4—24no—
815C2×C4—22no—
816C2×C4—22no—
817C2×C4—22no—
818C2×C4—22no—
819C2×C4—22no—
820C2×C4—22no—
821C2×C4—24no—
822C2×C4—24no—
823C2×C4—24no—
824C2×C4—24no—
825C2×C4—24no—
826C2×C4—24no—
827C2×C4—416no—
828C2×C4—416no—
829C2×C4—42no—
830C2×C4—42no—
831C2×C4—42no—
832C2×C4—42no—
833C2×C4—42no—
834C2×C4—42no—
835C2×C4—42no—
836C2×C4—42no—
837C2×C4—42no—
838C2×C4—42no—
839C2×C4—42no—
840C2×C4—42no—
841C2×C4—42no—
842C2×C4—42no—
843C2×C4—42no—
844C2×C4—42no—
845C2×C4—42no—
846C2×C4—42no—
847C2×C4—42no—
848C2×C4—42no—
849C2×C4—42no—
850C2×C4—42no—
851C2×C4—42no—
852C2×C4—42no—
853C2×C4—42no—
854C2×C4—42no—
855C2×C4C2×C7×C22⋊C414yes—
856C2×C4C2×C7×C22⋊C414yes—
857C7#1387311yescharacteristic, direct product factor, Sylow
858C22—28no—
859C22—28no—
860C22—28no—
861C22—28no—
862C22—24no—
863C22—24no—
864C22—24no—
865C22—24no—
866C22—24no—
867C22—24no—
868C22—24no—
869C22—24no—
870C22—24no—
871C22—24no—
872C22—24no—
873C22—24no—
874C22—464no—
875C22—44no—
876C22—44no—
877C22—44no—
878C22—44no—
879C22—44no—
880C22—44no—
881C22—44no—
882C22—44no—
883C22—42no—
884C22—42no—
885C22—42no—
886C22—42no—
887C22—42no—
888C22—42no—
889C22—42no—
890C22—42no—
891C22C7×#38818yescomplemented
892C22C22×C7×C22⋊C411yescharacteristic
893C22C2×C7×#11711yescharacteristic
894C22C2×C7×#11711yescharacteristic
895C22C2×C4×C7×D411yescharacteristic
896C22C2×C4×C7×D411yescharacteristic
897C22C7×#51811yescharacteristic
898C22C7×#51811yescharacteristic
899C22C2×C7×#12111yescharacteristic
900C22C2×C7×#12311yescharacteristic
901C22C7×#52512yes—
902C22C7×#52512yes—
903C22C2×C7×#12411yescharacteristic
904C22C2×C7×#12611yescharacteristic
905C22C7×#53812yes—
906C22C7×#53812yes—
907C22C7×D4212yes—
908C22C7×D4212yes—
909C22C7×#54612yes—
910C22C7×#54612yes—
911C22C7×#54612yes—
912C22C7×#54612yes—
913C22C7×#55112yes—
914C22C7×#55112yes—
915C4—24no—
916C4—24no—
917C4—44no—
918C4—44no—
919C4—42no—
920C4—42no—
921C4—82no—
922C4—82no—
923C2—28no—
924C2—44no—
925C2—44no—
926C2C7×#228011yescharacteristic
927C2C2×C7×#38811yescharacteristic
928C2C7×#231211yescharacteristic
929C2C7×D4×C22⋊C411yescharacteristic
930C2C7×D4×C22⋊C411yescharacteristic
931C2C7×#234211yescharacteristic
932C2C7×#234211yescharacteristic
933C2C7×#241812yes—
934C2C7×#242412yes—
935C2C7×#247212yes—
936C2C7×#248012yes—
subgroupG/H
center, socleC24×C7C24
commutatorC23C23×C4×C7
Frattini, cosocleC24C24×C7
prime radicalC26×C7C22
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C24×C7 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×C7×#388C2semidirect
3. C2×C7×#380C2semidirect
6. C2×C4×C7×C22⋊C4C2semidirect
7. C7×#1440C2semidirect
8. C7×#1439C2semidirect
9. C7×#1437C2semidirect
10. C7×C22⋊#95C2semidirect
11. C7×C22⋊#95C2semidirect
15. C22×C7×C4⋊C4C22semidirect
17. C22×C7×C22⋊C4C4semidirect
30. C22×C42×C7C22semidirect
36. C2×C7×#95C22semidirect
37. C2×C7×#95C22semidirect
38. C2×C7×#95C22semidirect
39. C2×C7×#95C22semidirect
40. C2×C7×#95C22semidirect
41. C2×C7×#95C22semidirect
42. #13873C7direct (N × H)
121. C2×#388C2×C7semidirect
122. C2×#380C2×C7semidirect
125. C2×C4×C22⋊C4C2×C7semidirect
126. #1440C2×C7semidirect
127. #1439C2×C7semidirect
128. #1437C2×C7semidirect
129. C22⋊#95C2×C7semidirect
130. C22⋊#95C2×C7semidirect
258. C7×C22⋊C4C22⋊C4semidirect
263. C22×C4⋊C4C22×C7semidirect
265. C22×C22⋊C4C4×C7semidirect
278. C22×C42C22×C7semidirect
284. C2×#95C22×C7semidirect
285. C2×#95C22×C7semidirect
286. C2×#95C22×C7semidirect
287. C2×#95C22×C7semidirect
288. C2×#95C22×C7semidirect
289. C2×#95C22×C7semidirect
541. C22×C7#388semidirect
700. C22⋊C4C7×C22⋊C4semidirect
857. C7#13873direct (N × H)
891. C22C7×#388semidirect

Maximal subgroups

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

subgroupindex
C23×C7×C22⋊C42
C2×C7×#3882
C2×C7×#3802
C2×C7×#3792
C2×C4×C7×C22⋊C42
C7×#14402
C7×#14392
C7×#14372
C7×C22⋊#952
#138737