Finite Group Databasebeta

← C7×#24109 #13201325

Subgroups — C7×#24109 #13201325

Order 1792.

1084 conjugacy classes of subgroups.

The subgroup lattice has 718 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C7×#554C211yesmaximal, characteristic
2C2×C7×#485C211yesmaximal, characteristic, complemented
3C2×C7×#428C211yesmaximal, characteristic, complemented
4C7×#2485C211yesmaximal, characteristic
5C7×#2058C211yesmaximal, characteristic, complemented
6C7×#2057C211yesmaximal, characteristic, complemented
7C7×#2036C211yesmaximal, characteristic, complemented
8C7×#2035C211yesmaximal, characteristic, complemented
9C7×#1894C211yesmaximal, characteristic, complemented
10C7×#1870C211yesmaximal, characteristic
11C7×#1865C211yesmaximal, characteristic, complemented
12C7×#1863C211yesmaximal, characteristic, complemented
13C7×#1853C211yesmaximal, characteristic, complemented
14C7×#1852C211yesmaximal, characteristic, complemented
15C7×#1823C211yesmaximal, characteristic, complemented
16C22×C7×M16C2211yescharacteristic
17C7×#554—24no—
18C7×#554—24no—
19C2×C7×C4⋊Q8C2211yescharacteristic
20C2×C7×#125—21no—
21C2×C7×C22⋊Q8—21no—
22C2×C7×C22⋊Q8—21no—
23C2×C7×C22⋊Q8C2211yescharacteristic
24C2×C7×C22⋊Q8C2211yescharacteristic
25C2×C4×C7×Q8C2211yescharacteristic
26C2×C4×C7×D4—21no—
27C2×C4×C7×D4C2211yescharacteristic
28C2×C7×#117C2211yescharacteristic
29C22×C7×C4⋊C4C2211yescharacteristic
30C22×C7×C4⋊C4C2211yescharacteristic
31C7×#485—24no—
32C7×#428—24no—
33C2×C7×#107C2211yescharacteristic
34C2×C7×#107C2211yescharacteristic
35C2×C7×#107C2211yescharacteristic
36C2×C7×#106C2211yescharacteristic
37C2×C7×#106C2211yescharacteristic
38C2×C7×#106C2211yescharacteristic
39C2×C7×#103C2211yescharacteristic
40C2×C7×#103C2211yescharacteristic
41C2×C7×#103C2211yescharacteristic
42C2×C7×#103C2211yescharacteristic
43C2×C7×C22⋊C8C2211yescharacteristic
44C2×C7×C22⋊C8C2211yescharacteristic
45C2×C7×C22⋊C8C2211yescharacteristic
46C7×#397—21no—
47C7×#394—21no—
48C7×#389C2211yescharacteristic
49C7×#389C2211yescharacteristic
50C7×#388—21no—
51C7×#387—21no—
52C7×#380C2211yescharacteristic
53C7×#380C2211yescharacteristic
54C7×#380C2211yescharacteristic
55C7×#340C2211yescharacteristic
56C7×#340C2211yescharacteristic
57C7×#340C2211yescharacteristic
58C7×#340C2211yescharacteristic
59C7×#340C2211yescharacteristic
60C7×#340C2211yescharacteristic
61C7×#336C2211yescharacteristic
62C7×#336C2211yescharacteristic
63#24109C711yesmaximal, characteristic, direct product factor, Sylow
64C22×C7×Q8—21no—
65C22×C7×Q8C2311yescharacteristic
66C22×C7×D4D411yescharacteristic
67C23×C4×C7—21no—
68C23×C4×C7—21no—
69C23×C4×C7C2311yescharacteristic
70C23×C4×C7C2311yescharacteristic
71C2×C7×M16—22no—
72C2×C7×M16—22no—
73C2×C7×M16—22no—
74C22×C7×C8C2311yescharacteristic
75C22×C7×C8C2311yescharacteristic
76C22×C7×C8C2311yescharacteristic
77C22×C7×C8C2311yescharacteristic
78C7×C4⋊Q8—22no—
79C7×C4⋊Q8—22no—
80C7×#125—28no—
81C7×C22⋊Q8—28no—
82C7×C22⋊Q8—28no—
83C7×C22⋊Q8—22no—
84C7×C22⋊Q8—22no—
85C7×C22⋊Q8—22no—
86C7×C22⋊Q8D414yes—
87C4×C7×Q8—22no—
88C4×C7×Q8—22no—
89C4×C7×D4—28no—
90C4×C7×D4—22no—
91C4×C7×D4—22no—
92C7×#117—22no—
93C7×#117—22no—
94C2×C7×C4⋊C4—21no—
95C2×C7×C4⋊C4—21no—
96C2×C7×C4⋊C4—22no—
97C2×C7×C4⋊C4—21no—
98C2×C7×C4⋊C4—21no—
99C2×C7×C4⋊C4—21no—
100C2×C7×C4⋊C4—21no—
101C2×C7×C4⋊C4—22no—
102C2×C7×C4⋊C4—22no—
103C2×C7×C4⋊C4—21no—
104C2×C7×C4⋊C4—21no—
105C2×C7×C4⋊C4D411yescharacteristic
106C2×C7×C4⋊C4D414yes—
107C2×C7×C4⋊C4C2311yescharacteristic
108C2×C7×C4⋊C4C2311yescharacteristic
109C2×C7×C4⋊C4C2311yescharacteristic
110C2×C7×C4⋊C4C2311yescharacteristic
111C2×C7×C4⋊C4C2311yescharacteristic
112C2×C7×C4⋊C4C2311yescharacteristic
113C2×C7×C4⋊C4C2311yescharacteristic
114C2×C7×C22⋊C4—21no—
115C2×C7×C22⋊C4—21no—
116C2×C7×C22⋊C4—21no—
117C2×C7×C22⋊C4—21no—
118C2×C7×C22⋊C4—21no—
119C2×C7×C22⋊C4—21no—
120C2×C7×C22⋊C4D411yescharacteristic
121C2×C7×C22⋊C4D411yescharacteristic
122C2×C42×C7—21no—
123C2×C42×C7—21no—
124C2×C42×C7C2311yescharacteristic
125C7×#107—22no—
126C7×#107—22no—
127C7×#107—22no—
128C7×#106—22no—
129C7×#106—22no—
130C7×#106—22no—
131C7×#103—22no—
132C7×#103—22no—
133C7×#103—22no—
134C7×#103—22no—
135C7×C22⋊C8—22no—
136C7×C22⋊C8—22no—
137C7×C22⋊C8—22no—
138C7×#95—21no—
139C7×#95—21no—
140C7×#95—21no—
141C7×#95—21no—
142C7×#95—21no—
143C2×#554C2×C711yescharacteristic
144C2×#485C2×C711yescharacteristic, complemented
145C2×#428C2×C711yescharacteristic, complemented
146#2485C2×C711yescharacteristic
147#2058C2×C711yescharacteristic, complemented
148#2057C2×C711yescharacteristic, complemented
149#2036C2×C711yescharacteristic, complemented
150#2035C2×C711yescharacteristic, complemented
151#1894C2×C711yescharacteristic, complemented
152#1870C2×C711yescharacteristic
153#1865C2×C711yescharacteristic, complemented
154#1863C2×C711yescharacteristic, complemented
155#1853C2×C711yescharacteristic, complemented
156#1852C2×C711yescharacteristic, complemented
157#1823C2×C711yescharacteristic, complemented
158C24×C7C2×D411yescharacteristic
159C24×C7C2×D411yescharacteristic
160C2×C7×Q8—24no—
161C2×C7×Q8—21no—
162C2×C7×Q8—21no—
163C2×C7×Q8—21no—
164C2×C7×Q8—21no—
165C2×C7×Q8—21no—
166C2×C7×Q8—81no—
167C2×C7×Q8—81no—
168C2×C7×Q8C2×D412yes—
169C2×C7×D4—22no—
170C2×C7×D4—22no—
171C2×C7×D4—22no—
172C22×C4×C7—21no—
173C22×C4×C7—21no—
174C22×C4×C7—21no—
175C22×C4×C7—21no—
176C22×C4×C7—21no—
177C22×C4×C7—21no—
178C22×C4×C7—21no—
179C22×C4×C7—21no—
180C22×C4×C7—24no—
181C22×C4×C7—24no—
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—81no—
193C22×C4×C7—81no—
194C22×C4×C7—81no—
195C22×C4×C7—81no—
196C22×C4×C7C2×D411yescharacteristic
197C22×C4×C7C2×D411yescharacteristic
198C22×C4×C7C2×D411yescharacteristic
199C22×C4×C7C2×D412yes—
200C22×C4×C7C2×D412yes—
201C22×C4×C7C2×D411yescharacteristic
202C22×C4×C7C2411yescharacteristic
203C7×M16—28no—
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×C8—21no—
213C2×C7×C8—21no—
214C2×C7×C8#4112yes—
215C2×C7×C8#4112yes—
216C7×C4⋊C4—24no—
217C7×C4⋊C4—24no—
218C7×C4⋊C4—24no—
219C7×C4⋊C4—24no—
220C7×C4⋊C4—24no—
221C7×C4⋊C4—24no—
222C7×C4⋊C4—22no—
223C7×C4⋊C4—21no—
224C7×C4⋊C4—21no—
225C7×C4⋊C4—21no—
226C7×C4⋊C4—21no—
227C7×C4⋊C4—21no—
228C7×C4⋊C4—21no—
229C7×C4⋊C4—21no—
230C7×C4⋊C4—21no—
231C7×C4⋊C4—21no—
232C7×C4⋊C4—21no—
233C7×C4⋊C4—21no—
234C7×C4⋊C4—42no—
235C7×C4⋊C4—81no—
236C7×C4⋊C4C2×D412yes—
237C7×C4⋊C4C2×D412yes—
238C7×C4⋊C4C2×D412yes—
239C7×C22⋊C4—24no—
240C7×C22⋊C4—24no—
241C7×C22⋊C4—22no—
242C7×C22⋊C4—22no—
243C7×C22⋊C4—42no—
244C7×C22⋊C4—42no—
245C7×C22⋊C4—81no—
246C7×C22⋊C4—81no—
247C42×C7—24no—
248C42×C7—21no—
249C42×C7—21no—
250C42×C7—42no—
251C22×M16C22×C711yescharacteristic
252#554—24no—
253#554—24no—
254C2×C4⋊Q8C22×C711yescharacteristic
255C2×#125—21no—
256C2×C22⋊Q8—21no—
257C2×C22⋊Q8—21no—
258C2×C22⋊Q8C22×C711yescharacteristic
259C2×C22⋊Q8C22×C711yescharacteristic
260C2×C4×Q8C22×C711yescharacteristic
261C2×C4×D4—21no—
262C2×C4×D4C22×C711yescharacteristic
263C2×#117C22×C711yescharacteristic
264C22×C4⋊C4C22×C711yescharacteristic
265C22×C4⋊C4C22×C711yescharacteristic
266#485—24no—
267#428—24no—
268C2×#107C22×C711yescharacteristic
269C2×#107C22×C711yescharacteristic
270C2×#107C22×C711yescharacteristic
271C2×#106C22×C711yescharacteristic
272C2×#106C22×C711yescharacteristic
273C2×#106C22×C711yescharacteristic
274C2×#103C22×C711yescharacteristic
275C2×#103C22×C711yescharacteristic
276C2×#103C22×C711yescharacteristic
277C2×#103C22×C711yescharacteristic
278C2×C22⋊C8C22×C711yescharacteristic
279C2×C22⋊C8C22×C711yescharacteristic
280C2×C22⋊C8C22×C711yescharacteristic
281#397—21no—
282#394—21no—
283#389C22×C711yescharacteristic
284#389C22×C711yescharacteristic
285#388—21no—
286#387—21no—
287#380C22×C711yescharacteristic
288#380C22×C711yescharacteristic
289#380C22×C711yescharacteristic
290#340C22×C711yescharacteristic
291#340C22×C711yescharacteristic
292#340C22×C711yescharacteristic
293#340C22×C711yescharacteristic
294#340C22×C711yescharacteristic
295#340C22×C711yescharacteristic
296#336C22×C711yescharacteristic
297#336C22×C711yescharacteristic
298C23×C7—21no—
299C23×C7—21no—
300C23×C7—21no—
301C23×C7—21no—
302C23×C7—21no—
303C23×C7—21no—
304C23×C7—21no—
305C23×C7—21no—
306C23×C7—21no—
307C23×C7—21no—
308C23×C7—21no—
309C23×C7—21no—
310C23×C7#12012yes—
311C23×C7#13712yes—
312C23×C7C22×D411yescharacteristic
313C7×Q8—22no—
314C7×Q8—22no—
315C7×Q8—41no—
316C7×Q8—41no—
317C7×Q8—84no—
318C7×D4—28no—
319C2×C4×C7—21no—
320C2×C4×C7—21no—
321C2×C4×C7—21no—
322C2×C4×C7—21no—
323C2×C4×C7—22no—
324C2×C4×C7—22no—
325C2×C4×C7—22no—
326C2×C4×C7—22no—
327C2×C4×C7—22no—
328C2×C4×C7—21no—
329C2×C4×C7—22no—
330C2×C4×C7—21no—
331C2×C4×C7—22no—
332C2×C4×C7—22no—
333C2×C4×C7—21no—
334C2×C4×C7—21no—
335C2×C4×C7—21no—
336C2×C4×C7—21no—
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—41no—
360C2×C4×C7—41no—
361C2×C4×C7—84no—
362C2×C4×C7—84no—
363C2×C4×C7#12012yes—
364C2×C4×C7#13712yes—
365C2×C4×C7C22×D411yescharacteristic
366C2×C4×C7C22×D411yescharacteristic
367C2×C4×C7C2×#4111yescharacteristic
368C2×C4×C7C2×#4111yescharacteristic
369C2×C4×C72−1+411yescharacteristic
370C2×C4×C72−1+411yescharacteristic
371C7×C8—22no—
372C7×C8—22no—
373C7×C8—41no—
374C7×C8—41no—
375C22×Q8—21no—
376C22×Q8C23×C711yescharacteristic
377C22×D4C7×D411yescharacteristic
378C23×C4—21no—
379C23×C4—21no—
380C23×C4C23×C711yescharacteristic
381C23×C4C23×C711yescharacteristic
382C2×M16—22no—
383C2×M16—22no—
384C2×M16—22no—
385C22×C8C23×C711yescharacteristic
386C22×C8C23×C711yescharacteristic
387C22×C8C23×C711yescharacteristic
388C22×C8C23×C711yescharacteristic
389C4⋊Q8—22no—
390C4⋊Q8—22no—
391#125—28no—
392C22⋊Q8—28no—
393C22⋊Q8—28no—
394C22⋊Q8—22no—
395C22⋊Q8—22no—
396C22⋊Q8—22no—
397C22⋊Q8C7×D414yes—
398C4×Q8—22no—
399C4×Q8—22no—
400C4×D4—28no—
401C4×D4—22no—
402C4×D4—22no—
403#117—22no—
404#117—22no—
405C2×C4⋊C4—21no—
406C2×C4⋊C4—21no—
407C2×C4⋊C4—22no—
408C2×C4⋊C4—21no—
409C2×C4⋊C4—21no—
410C2×C4⋊C4—21no—
411C2×C4⋊C4—21no—
412C2×C4⋊C4—22no—
413C2×C4⋊C4—22no—
414C2×C4⋊C4—21no—
415C2×C4⋊C4—21no—
416C2×C4⋊C4C7×D411yescharacteristic
417C2×C4⋊C4C7×D414yes—
418C2×C4⋊C4C23×C711yescharacteristic
419C2×C4⋊C4C23×C711yescharacteristic
420C2×C4⋊C4C23×C711yescharacteristic
421C2×C4⋊C4C23×C711yescharacteristic
422C2×C4⋊C4C23×C711yescharacteristic
423C2×C4⋊C4C23×C711yescharacteristic
424C2×C4⋊C4C23×C711yescharacteristic
425C2×C22⋊C4—21no—
426C2×C22⋊C4—21no—
427C2×C22⋊C4—21no—
428C2×C22⋊C4—21no—
429C2×C22⋊C4—21no—
430C2×C22⋊C4—21no—
431C2×C22⋊C4C7×D411yescharacteristic
432C2×C22⋊C4C7×D411yescharacteristic
433C2×C42—21no—
434C2×C42—21no—
435C2×C42C23×C711yescharacteristic
436#107—22no—
437#107—22no—
438#107—22no—
439#106—22no—
440#106—22no—
441#106—22no—
442#103—22no—
443#103—22no—
444#103—22no—
445#103—22no—
446C22⋊C8—22no—
447C22⋊C8—22no—
448C22⋊C8—22no—
449#95—21no—
450#95—21no—
451#95—21no—
452#95—21no—
453#95—21no—
454C22×C7—22no—
455C22×C7—22no—
456C22×C7—22no—
457C22×C7—22no—
458C22×C7—22no—
459C22×C7—22no—
460C22×C7—41no—
461C22×C7—41no—
462C22×C7—41no—
463C22×C7—41no—
464C22×C7—41no—
465C22×C7—41no—
466C22×C7—41no—
467C22×C7—41no—
468C22×C7C2×#12011yescharacteristic
469C22×C7#54711yescharacteristic
470C22×C7#54711yescharacteristic
471C22×C7C2×#13711yescharacteristic
472C22×C7C2×#13711yescharacteristic
473C22×C7#57611yescharacteristic
474C22×C7#57711yescharacteristic
475C4×C7—22no—
476C4×C7—22no—
477C4×C7—41no—
478C4×C7—42no—
479C4×C7—41no—
480C4×C7—42no—
481C4×C7—42no—
482C4×C7—42no—
483C4×C7—81no—
484C4×C7—81no—
485C4×C7—81no—
486C4×C7—81no—
487C4×C7#52511yescharacteristic
488C4×C7#53611yescharacteristic
489C4×C7#54711yescharacteristic
490C4×C7#54711yescharacteristic
491C24C2×C7×D411yescharacteristic
492C24C2×C7×D411yescharacteristic
493C2×Q8—24no—
494C2×Q8—21no—
495C2×Q8—21no—
496C2×Q8—21no—
497C2×Q8—21no—
498C2×Q8—21no—
499C2×Q8—81no—
500C2×Q8—81no—
501C2×Q8C2×C7×D412yes—
502C2×D4—22no—
503C2×D4—22no—
504C2×D4—22no—
505C22×C4—21no—
506C22×C4—21no—
507C22×C4—21no—
508C22×C4—21no—
509C22×C4—21no—
510C22×C4—21no—
511C22×C4—21no—
512C22×C4—21no—
513C22×C4—24no—
514C22×C4—24no—
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—21no—
524C22×C4—21no—
525C22×C4—81no—
526C22×C4—81no—
527C22×C4—81no—
528C22×C4—81no—
529C22×C4C2×C7×D411yescharacteristic
530C22×C4C2×C7×D411yescharacteristic
531C22×C4C2×C7×D411yescharacteristic
532C22×C4C2×C7×D412yes—
533C22×C4C2×C7×D412yes—
534C22×C4C2×C7×D411yescharacteristic
535C22×C4C24×C711yescharacteristic
536M16—28no—
537C2×C8—21no—
538C2×C8—21no—
539C2×C8—21no—
540C2×C8—21no—
541C2×C8—21no—
542C2×C8—21no—
543C2×C8—21no—
544C2×C8—21no—
545C2×C8—21no—
546C2×C8—21no—
547C2×C8C7×#4112yes—
548C2×C8C7×#4112yes—
549C4⋊C4—24no—
550C4⋊C4—24no—
551C4⋊C4—24no—
552C4⋊C4—24no—
553C4⋊C4—24no—
554C4⋊C4—24no—
555C4⋊C4—22no—
556C4⋊C4—21no—
557C4⋊C4—21no—
558C4⋊C4—21no—
559C4⋊C4—21no—
560C4⋊C4—21no—
561C4⋊C4—21no—
562C4⋊C4—21no—
563C4⋊C4—21no—
564C4⋊C4—21no—
565C4⋊C4—21no—
566C4⋊C4—21no—
567C4⋊C4—42no—
568C4⋊C4—81no—
569C4⋊C4C2×C7×D412yes—
570C4⋊C4C2×C7×D412yes—
571C4⋊C4C2×C7×D412yes—
572C22⋊C4—24no—
573C22⋊C4—24no—
574C22⋊C4—22no—
575C22⋊C4—22no—
576C22⋊C4—42no—
577C22⋊C4—42no—
578C22⋊C4—81no—
579C22⋊C4—81no—
580C42—24no—
581C42—21no—
582C42—21no—
583C42—42no—
584C2×C7—42no—
585C2×C7—42no—
586C2×C7#240611yescharacteristic
587C2×C7#300411yescharacteristic
588C2×C7#301211yescharacteristic
589C2×C7#334411yescharacteristic
590C2×C7#334611yescharacteristic
591C2×C7#335611yescharacteristic
592C2×C7#335711yescharacteristic
593C23—21no—
594C23—21no—
595C23—21no—
596C23—21no—
597C23—21no—
598C23—21no—
599C23—21no—
600C23—21no—
601C23—21no—
602C23—21no—
603C23—21no—
604C23—21no—
605C23C7×#12012yes—
606C23C7×#13712yes—
607C23C22×C7×D411yescharacteristic
608Q8—22no—
609Q8—22no—
610Q8—41no—
611Q8—41no—
612Q8—84no—
613D4—28no—
614C2×C4—21no—
615C2×C4—21no—
616C2×C4—21no—
617C2×C4—21no—
618C2×C4—22no—
619C2×C4—22no—
620C2×C4—22no—
621C2×C4—22no—
622C2×C4—22no—
623C2×C4—21no—
624C2×C4—22no—
625C2×C4—21no—
626C2×C4—22no—
627C2×C4—22no—
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—41no—
656C2×C4—84no—
657C2×C4—84no—
658C2×C4C7×#12012yes—
659C2×C4C7×#13712yes—
660C2×C4C22×C7×D411yescharacteristic
661C2×C4C22×C7×D411yescharacteristic
662C2×C4C2×C7×#4111yescharacteristic
663C2×C4C2×C7×#4111yescharacteristic
664C2×C4C7×2−1+411yescharacteristic
665C2×C4C7×2−1+411yescharacteristic
666C8—22no—
667C8—22no—
668C8—41no—
669C8—41no—
670C7#2410911yescharacteristic, direct product factor, Sylow
671C22—22no—
672C22—22no—
673C22—22no—
674C22—22no—
675C22—22no—
676C22—22no—
677C22—41no—
678C22—41no—
679C22—41no—
680C22—41no—
681C22—41no—
682C22—41no—
683C22—41no—
684C22—41no—
685C22C2×C7×#12011yescharacteristic
686C22C7×#54711yescharacteristic
687C22C7×#54711yescharacteristic
688C22C2×C7×#13711yescharacteristic
689C22C2×C7×#13711yescharacteristic
690C22C7×#57611yescharacteristic
691C22C7×#57711yescharacteristic
692C4—22no—
693C4—22no—
694C4—41no—
695C4—42no—
696C4—41no—
697C4—42no—
698C4—42no—
699C4—42no—
700C4—81no—
701C4—81no—
702C4—81no—
703C4—81no—
704C4C7×#52511yescharacteristic
705C4C7×#53611yescharacteristic
706C4C7×#54711yescharacteristic
707C4C7×#54711yescharacteristic
708C2—42no—
709C2—42no—
710C2C7×#240611yescharacteristic
711C2C7×#300411yescharacteristic
712C2C7×#301211yescharacteristic
713C2C7×#334411yescharacteristic
714C2C7×#334611yescharacteristic
715C2C7×#335611yescharacteristic
716C2C7×#335711yescharacteristic
subgroupG/H
center, socleC23×C7C22×D4
commutator, Frattini, cosocleC22×C4C24×C7
prime radicalC22×C7×D4D4
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C7 ◁ C2×C4×C7×D4 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×C7×#485C2semidirect
3. C2×C7×#428C2semidirect
5. C7×#2058C2semidirect
6. C7×#2057C2semidirect
7. C7×#2036C2semidirect
8. C7×#2035C2semidirect
9. C7×#1894C2semidirect
11. C7×#1865C2semidirect
12. C7×#1863C2semidirect
13. C7×#1853C2semidirect
14. C7×#1852C2semidirect
15. C7×#1823C2semidirect
63. #24109C7direct (N × H)
144. C2×#485C2×C7semidirect
145. C2×#428C2×C7semidirect
147. #2058C2×C7semidirect
148. #2057C2×C7semidirect
149. #2036C2×C7semidirect
150. #2035C2×C7semidirect
151. #1894C2×C7semidirect
153. #1865C2×C7semidirect
154. #1863C2×C7semidirect
155. #1853C2×C7semidirect
156. #1852C2×C7semidirect
157. #1823C2×C7semidirect
670. C7#24109direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C7×#5542
C2×C7×#4852
C2×C7×#4282
C7×#24852
C7×#20582
C7×#20572
C7×#20362
C7×#20352
C7×#18942
C7×#18702
C7×#18652
C7×#18632
C7×#18532
C7×#18522
C7×#18232
#241097