Finite Group Databasebeta

← C7×#24451 #13201667

Subgroups — C7×#24451 #13201667

Order 1792.

1580 conjugacy classes of subgroups.

The subgroup lattice has 958 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C7×#550C211yesmaximal, characteristic, complemented
2C2×C7×#469C211yesmaximal, characteristic, complemented
3C2×C7×#449C211yesmaximal, characteristic, complemented
4C2×C7×#449C211yesmaximal, characteristic, complemented
5C2×C7×#417C211yesmaximal, characteristic, complemented
6C7×#2416C211yesmaximal, characteristic, complemented
7C7×#2041C211yesmaximal, characteristic, complemented
8C7×#2034C211yesmaximal, characteristic, complemented
9C7×#2011C211yesmaximal, characteristic, complemented
10C7×#1999C211yesmaximal, characteristic, complemented
11C7×#1880C211yesmaximal, characteristic, complemented
12C7×#1874C211yesmaximal, characteristic, complemented
13C7×#1870C211yesmaximal, characteristic, complemented
14C7×#1865C211yesmaximal, characteristic, complemented
15C7×#1788C211yesmaximal, characteristic, complemented
16C22×C7×#41C2211yescharacteristic
17C22×C7×#41C2211yescharacteristic
18C22×C7×SD16C2211yescharacteristic
19C22×C7×D8C2211yescharacteristic
20C22×C7×D8C2211yescharacteristic
21C22×C7×M16C2211yescharacteristic
22C7×#550—24no—
23C7×#550—24no—
24C2×C7×#127—21no—
25C2×C7×#127C2211yescharacteristic
26C2×C7×#121—21no—
27C2×C7×#121—21no—
28C2×C7×#121—21no—
29C2×C7×#121C2211yescharacteristic
30C2×C7×#121C2211yescharacteristic
31C2×C7×#121C2211yescharacteristic
32C2×C7×#121C2211yescharacteristic
33C2×C4×C7×Q8C2211yescharacteristic
34C2×C4×C7×D4—21no—
35C2×C4×C7×D4C2211yescharacteristic
36C22×C7×C4⋊C4C2211yescharacteristic
37C7×#469—24no—
38C7×#449—24no—
39C7×#449—24no—
40C2×C7×#106C2211yescharacteristic
41C7×#417—24no—
42C2×C7×#103C2211yescharacteristic
43C2×C7×#103C2211yescharacteristic
44C2×C7×#103C2211yescharacteristic
45C2×C7×#102C2211yescharacteristic
46C2×C7×#102C2211yescharacteristic
47C2×C7×#102C2211yescharacteristic
48C2×C7×#102C2211yescharacteristic
49C2×C7×#102C2211yescharacteristic
50C2×C7×#102C2211yescharacteristic
51C2×C7×#102C2211yescharacteristic
52C2×C7×C22⋊C8C2211yescharacteristic
53C2×C7×C22⋊C8C2211yescharacteristic
54C2×C7×C22⋊C8C2211yescharacteristic
55C7×#396—21no—
56C7×#394—21no—
57C7×#390C2211yescharacteristic
58C7×#389C2211yescharacteristic
59C7×#386—21no—
60C7×#380C2211yescharacteristic
61C7×#340C2211yescharacteristic
62C7×#340C2211yescharacteristic
63C7×#336C2211yescharacteristic
64C7×#336C2211yescharacteristic
65#24451C711yesmaximal, characteristic, direct product factor, Sylow
66C2×C7×#41—22no—
67C2×C7×#41—22no—
68C2×C7×#41—22no—
69C2×C7×#41—22no—
70C2×C7×#41—22no—
71C2×C7×#41—22no—
72C2×C7×#41—22no—
73C2×C7×#41—41no—
74C2×C7×#41—41no—
75C2×C7×#41—41no—
76C2×C7×#41—41no—
77C2×C7×#41D414yescomplemented
78C22×C7×Q8C2311yescharacteristic
79C22×C7×D4—21no—
80C22×C7×D4—21no—
81C22×C7×D4—21no—
82C22×C7×D4—21no—
83C22×C7×D4—21no—
84C22×C7×D4—21no—
85C22×C7×D4—21no—
86C22×C7×D4—21no—
87C22×C7×D4D411yescharacteristic
88C22×C7×D4C2311yescharacteristic
89C22×C7×D4C2311yescharacteristic
90C22×C7×D4C2311yescharacteristic
91C23×C4×C7—21no—
92C23×C4×C7—21no—
93C23×C4×C7—21no—
94C23×C4×C7C2311yescharacteristic
95C23×C4×C7C2311yescharacteristic
96C2×C7×SD16—22no—
97C2×C7×SD16—22no—
98C2×C7×SD16—22no—
99C2×C7×D8—22no—
100C2×C7×D8—22no—
101C2×C7×D8—22no—
102C2×C7×D8—41no—
103C2×C7×D8—41no—
104C2×C7×D8—41no—
105C2×C7×M16—22no—
106C2×C7×M16—22no—
107C2×C7×M16—41no—
108C22×C7×C8C2311yescharacteristic
109C22×C7×C8C2311yescharacteristic
110C22×C7×C8C2311yescharacteristic
111C22×C7×C8C2311yescharacteristic
112C7×#127—28no—
113C7×#127—22no—
114C7×#127—22no—
115C7×#121—28no—
116C7×#121—28no—
117C7×#121—22no—
118C7×#121—22no—
119C7×#121—22no—
120C7×#121—22no—
121C7×#121—22no—
122C7×#121—22no—
123C7×#121—41no—
124C7×#121—44no—
125C7×#121D414yescomplemented
126C4×C7×Q8—22no—
127C4×C7×Q8—22no—
128C4×C7×D4—28no—
129C4×C7×D4—22no—
130C4×C7×D4—22no—
131C2×C7×C4⋊C4—21no—
132C2×C7×C4⋊C4—22no—
133C2×C7×C4⋊C4—21no—
134C2×C7×C4⋊C4—21no—
135C2×C7×C4⋊C4—41no—
136C2×C7×C4⋊C4D411yescharacteristic
137C2×C7×C4⋊C4C2311yescharacteristic
138C2×C7×C4⋊C4C2311yescharacteristic
139C2×C7×C4⋊C4C2311yescharacteristic
140C2×C7×C4⋊C4C2311yescharacteristic
141C2×C7×C22⋊C4—21no—
142C2×C7×C22⋊C4—21no—
143C2×C7×C22⋊C4—21no—
144C2×C7×C22⋊C4—21no—
145C2×C7×C22⋊C4—21no—
146C2×C7×C22⋊C4—21no—
147C2×C7×C22⋊C4—21no—
148C2×C7×C22⋊C4D411yescharacteristic
149C2×C7×C22⋊C4D411yescharacteristic
150C2×C42×C7—21no—
151C2×C42×C7C2311yescharacteristic
152C7×#106—22no—
153C7×#103—22no—
154C7×#103—22no—
155C7×#103D414yescomplemented
156C7×#102—22no—
157C7×#102—22no—
158C7×#102—22no—
159C7×#102—22no—
160C7×#102—22no—
161C7×#102—22no—
162C7×#102—41no—
163C7×C22⋊C8—22no—
164C7×C22⋊C8—22no—
165C7×C22⋊C8—41no—
166C7×#95—21no—
167C7×#95—21no—
168C2×#550C2×C711yescharacteristic, complemented
169C2×#469C2×C711yescharacteristic, complemented
170C2×#449C2×C711yescharacteristic, complemented
171C2×#449C2×C711yescharacteristic, complemented
172C2×#417C2×C711yescharacteristic, complemented
173#2416C2×C711yescharacteristic, complemented
174#2041C2×C711yescharacteristic, complemented
175#2034C2×C711yescharacteristic, complemented
176#2011C2×C711yescharacteristic, complemented
177#1999C2×C711yescharacteristic, complemented
178#1880C2×C711yescharacteristic, complemented
179#1874C2×C711yescharacteristic, complemented
180#1870C2×C711yescharacteristic, complemented
181#1865C2×C711yescharacteristic, complemented
182#1788C2×C711yescharacteristic, complemented
183C24×C7—21no—
184C24×C7—21no—
185C24×C7—21no—
186C24×C7C2×D411yescharacteristic
187C24×C7C2×D411yescharacteristic
188C7×#41—28no—
189C7×#41—44no—
190C7×#41—44no—
191C7×#41—44no—
192C7×#41—44no—
193C7×#41—44no—
194C7×#41—44no—
195C7×#41—44no—
196C2×C7×Q8—21no—
197C2×C7×Q8—21no—
198C2×C7×Q8—21no—
199C2×C7×Q8C2×D412yes—
200C2×C7×Q8C2×D412yes—
201C2×C7×Q8#4112yes—
202C2×C7×D4—24no—
203C2×C7×D4—24no—
204C2×C7×D4—22no—
205C2×C7×D4—24no—
206C2×C7×D4—24no—
207C2×C7×D4—24no—
208C2×C7×D4—24no—
209C2×C7×D4—22no—
210C2×C7×D4—21no—
211C2×C7×D4—21no—
212C2×C7×D4—21no—
213C2×C7×D4—21no—
214C2×C7×D4—21no—
215C2×C7×D4—21no—
216C2×C7×D4—21no—
217C2×C7×D4—21no—
218C2×C7×D4—21no—
219C2×C7×D4—21no—
220C2×C7×D4—21no—
221C2×C7×D4—21no—
222C2×C7×D4—21no—
223C2×C7×D4—21no—
224C2×C7×D4—21no—
225C2×C7×D4—21no—
226C2×C7×D4—41no—
227C2×C7×D4—42no—
228C2×C7×D4—42no—
229C2×C7×D4—42no—
230C2×C7×D4—42no—
231C2×C7×D4—42no—
232C2×C7×D4—42no—
233C2×C7×D4—42no—
234C2×C7×D4—42no—
235C2×C7×D4—42no—
236C2×C7×D4—42no—
237C2×C7×D4—42no—
238C2×C7×D4—81no—
239C2×C7×D4—81no—
240C2×C7×D4—81no—
241C2×C7×D4—81no—
242C2×C7×D4—81no—
243C2×C7×D4—81no—
244C2×C7×D4—81no—
245C2×C7×D4C2×D412yes—
246C2×C7×D4C2×D412yes—
247C22×C4×C7—21no—
248C22×C4×C7—21no—
249C22×C4×C7—21no—
250C22×C4×C7—21no—
251C22×C4×C7—21no—
252C22×C4×C7—24no—
253C22×C4×C7—21no—
254C22×C4×C7—21no—
255C22×C4×C7—24no—
256C22×C4×C7—21no—
257C22×C4×C7—21no—
258C22×C4×C7—21no—
259C22×C4×C7—21no—
260C22×C4×C7—21no—
261C22×C4×C7—21no—
262C22×C4×C7—21no—
263C22×C4×C7—21no—
264C22×C4×C7—42no—
265C22×C4×C7—42no—
266C22×C4×C7—42no—
267C22×C4×C7—42no—
268C22×C4×C7—42no—
269C22×C4×C7—42no—
270C22×C4×C7—81no—
271C22×C4×C7C2×D411yescharacteristic
272C22×C4×C7C2×D411yescharacteristic
273C22×C4×C7C2×D411yescharacteristic
274C22×C4×C7C2×D412yes—
275C22×C4×C7C2×D412yes—
276C22×C4×C7C2×D411yescharacteristic
277C22×C4×C7C2411yescharacteristic
278C7×SD16—44no—
279C7×D8—44no—
280C7×D8—44no—
281C7×M16—44no—
282C2×C7×C8—21no—
283C2×C7×C8—21no—
284C2×C7×C8—21no—
285C2×C7×C8—21no—
286C2×C7×C8—21no—
287C2×C7×C8—21no—
288C2×C7×C8—21no—
289C2×C7×C8—21no—
290C2×C7×C8—21no—
291C2×C7×C8—21no—
292C2×C7×C8—21no—
293C2×C7×C8C2×D412yes—
294C7×C4⋊C4—24no—
295C7×C4⋊C4—22no—
296C7×C4⋊C4—21no—
297C7×C4⋊C4—21no—
298C7×C4⋊C4—21no—
299C7×C4⋊C4—21no—
300C7×C4⋊C4—21no—
301C7×C4⋊C4—21no—
302C7×C4⋊C4—42no—
303C7×C4⋊C4—42no—
304C7×C4⋊C4C2×D412yes—
305C7×C4⋊C4C2×D412yes—
306C7×C22⋊C4—24no—
307C7×C22⋊C4—22no—
308C7×C22⋊C4—24no—
309C7×C22⋊C4—22no—
310C7×C22⋊C4—42no—
311C7×C22⋊C4—42no—
312C7×C22⋊C4—42no—
313C7×C22⋊C4—42no—
314C7×C22⋊C4—81no—
315C42×C7—24no—
316C42×C7—21no—
317C42×C7—21no—
318C22×#41C22×C711yescharacteristic
319C22×#41C22×C711yescharacteristic
320C22×SD16C22×C711yescharacteristic
321C22×D8C22×C711yescharacteristic
322C22×D8C22×C711yescharacteristic
323C22×M16C22×C711yescharacteristic
324#550—24no—
325#550—24no—
326C2×#127—21no—
327C2×#127C22×C711yescharacteristic
328C2×#121—21no—
329C2×#121—21no—
330C2×#121—21no—
331C2×#121C22×C711yescharacteristic
332C2×#121C22×C711yescharacteristic
333C2×#121C22×C711yescharacteristic
334C2×#121C22×C711yescharacteristic
335C2×C4×Q8C22×C711yescharacteristic
336C2×C4×D4—21no—
337C2×C4×D4C22×C711yescharacteristic
338C22×C4⋊C4C22×C711yescharacteristic
339#469—24no—
340#449—24no—
341#449—24no—
342C2×#106C22×C711yescharacteristic
343#417—24no—
344C2×#103C22×C711yescharacteristic
345C2×#103C22×C711yescharacteristic
346C2×#103C22×C711yescharacteristic
347C2×#102C22×C711yescharacteristic
348C2×#102C22×C711yescharacteristic
349C2×#102C22×C711yescharacteristic
350C2×#102C22×C711yescharacteristic
351C2×#102C22×C711yescharacteristic
352C2×#102C22×C711yescharacteristic
353C2×#102C22×C711yescharacteristic
354C2×C22⋊C8C22×C711yescharacteristic
355C2×C22⋊C8C22×C711yescharacteristic
356C2×C22⋊C8C22×C711yescharacteristic
357#396—21no—
358#394—21no—
359#390C22×C711yescharacteristic
360#389C22×C711yescharacteristic
361#386—21no—
362#380C22×C711yescharacteristic
363#340C22×C711yescharacteristic
364#340C22×C711yescharacteristic
365#336C22×C711yescharacteristic
366#336C22×C711yescharacteristic
367C23×C7—21no—
368C23×C7—21no—
369C23×C7—21no—
370C23×C7—21no—
371C23×C7—21no—
372C23×C7—21no—
373C23×C7—21no—
374C23×C7—22no—
375C23×C7—22no—
376C23×C7—21no—
377C23×C7—21no—
378C23×C7—21no—
379C23×C7—21no—
380C23×C7—21no—
381C23×C7—21no—
382C23×C7—41no—
383C23×C7—41no—
384C23×C7—41no—
385C23×C7—41no—
386C23×C7—41no—
387C23×C7—41no—
388C23×C7—41no—
389C23×C7—41no—
390C23×C7—41no—
391C23×C7—41no—
392C23×C7—41no—
393C23×C7—41no—
394C23×C7—41no—
395C23×C7—41no—
396C23×C7—41no—
397C23×C7—41no—
398C23×C7—41no—
399C23×C7—41no—
400C23×C7—41no—
401C23×C7#12012yes—
402C23×C7C22×D411yescharacteristic
403C7×Q8—22no—
404C7×Q8—22no—
405C7×Q8—22no—
406C7×Q8#12114yescomplemented
407C7×D4—22no—
408C7×D4—22no—
409C7×D4—22no—
410C7×D4—22no—
411C7×D4—44no—
412C7×D4—48no—
413C7×D4—48no—
414C7×D4—48no—
415C7×D4—41no—
416C7×D4—41no—
417C7×D4—41no—
418C7×D4—41no—
419C7×D4—41no—
420C7×D4—41no—
421C7×D4—41no—
422C7×D4—41no—
423C7×D4—84no—
424C7×D4—84no—
425C7×D4—84no—
426C7×D4—84no—
427C7×D4—84no—
428C2×C4×C7—21no—
429C2×C4×C7—22no—
430C2×C4×C7—21no—
431C2×C4×C7—22no—
432C2×C4×C7—21no—
433C2×C4×C7—22no—
434C2×C4×C7—21no—
435C2×C4×C7—22no—
436C2×C4×C7—22no—
437C2×C4×C7—22no—
438C2×C4×C7—22no—
439C2×C4×C7—21no—
440C2×C4×C7—22no—
441C2×C4×C7—21no—
442C2×C4×C7—21no—
443C2×C4×C7—22no—
444C2×C4×C7—21no—
445C2×C4×C7—21no—
446C2×C4×C7—21no—
447C2×C4×C7—48no—
448C2×C4×C7—48no—
449C2×C4×C7—41no—
450C2×C4×C7—41no—
451C2×C4×C7—41no—
452C2×C4×C7—41no—
453C2×C4×C7—41no—
454C2×C4×C7—41no—
455C2×C4×C7—41no—
456C2×C4×C7—41no—
457C2×C4×C7—41no—
458C2×C4×C7—41no—
459C2×C4×C7—41no—
460C2×C4×C7—41no—
461C2×C4×C7—41no—
462C2×C4×C7—41no—
463C2×C4×C7—84no—
464C2×C4×C7#12012yes—
465C2×C4×C7AGL(1,ℤ/8)12yes—
466C2×C4×C7C22×D411yescharacteristic
467C2×C4×C7C22×D411yescharacteristic
468C2×C4×C7C22×D411yescharacteristic
469C2×C4×C7C2×#4111yescharacteristic
470C2×C4×C7H(5,𝔽2)11yescharacteristic
471C2×C4×C7H(5,𝔽2)11yescharacteristic
472C7×C8—22no—
473C7×C8—41no—
474C7×C8—41no—
475C7×C8—41no—
476C2×#41—22no—
477C2×#41—22no—
478C2×#41—22no—
479C2×#41—22no—
480C2×#41—22no—
481C2×#41—22no—
482C2×#41—22no—
483C2×#41—41no—
484C2×#41—41no—
485C2×#41—41no—
486C2×#41—41no—
487C2×#41C7×D414yescomplemented
488C22×Q8C23×C711yescharacteristic
489C22×D4—21no—
490C22×D4—21no—
491C22×D4—21no—
492C22×D4—21no—
493C22×D4—21no—
494C22×D4—21no—
495C22×D4—21no—
496C22×D4—21no—
497C22×D4C7×D411yescharacteristic
498C22×D4C23×C711yescharacteristic
499C22×D4C23×C711yescharacteristic
500C22×D4C23×C711yescharacteristic
501C23×C4—21no—
502C23×C4—21no—
503C23×C4—21no—
504C23×C4C23×C711yescharacteristic
505C23×C4C23×C711yescharacteristic
506C2×SD16—22no—
507C2×SD16—22no—
508C2×SD16—22no—
509C2×D8—22no—
510C2×D8—22no—
511C2×D8—22no—
512C2×D8—41no—
513C2×D8—41no—
514C2×D8—41no—
515C2×M16—22no—
516C2×M16—22no—
517C2×M16—41no—
518C22×C8C23×C711yescharacteristic
519C22×C8C23×C711yescharacteristic
520C22×C8C23×C711yescharacteristic
521C22×C8C23×C711yescharacteristic
522#127—28no—
523#127—22no—
524#127—22no—
525#121—28no—
526#121—28no—
527#121—22no—
528#121—22no—
529#121—22no—
530#121—22no—
531#121—22no—
532#121—22no—
533#121—41no—
534#121—44no—
535#121C7×D414yescomplemented
536C4×Q8—22no—
537C4×Q8—22no—
538C4×D4—28no—
539C4×D4—22no—
540C4×D4—22no—
541C2×C4⋊C4—21no—
542C2×C4⋊C4—22no—
543C2×C4⋊C4—21no—
544C2×C4⋊C4—21no—
545C2×C4⋊C4—41no—
546C2×C4⋊C4C7×D411yescharacteristic
547C2×C4⋊C4C23×C711yescharacteristic
548C2×C4⋊C4C23×C711yescharacteristic
549C2×C4⋊C4C23×C711yescharacteristic
550C2×C4⋊C4C23×C711yescharacteristic
551C2×C22⋊C4—21no—
552C2×C22⋊C4—21no—
553C2×C22⋊C4—21no—
554C2×C22⋊C4—21no—
555C2×C22⋊C4—21no—
556C2×C22⋊C4—21no—
557C2×C22⋊C4—21no—
558C2×C22⋊C4C7×D411yescharacteristic
559C2×C22⋊C4C7×D411yescharacteristic
560C2×C42—21no—
561C2×C42C23×C711yescharacteristic
562#106—22no—
563#103—22no—
564#103—22no—
565#103C7×D414yescomplemented
566#102—22no—
567#102—22no—
568#102—22no—
569#102—22no—
570#102—22no—
571#102—22no—
572#102—41no—
573C22⋊C8—22no—
574C22⋊C8—22no—
575C22⋊C8—41no—
576#95—21no—
577#95—21no—
578C22×C7—22no—
579C22×C7—22no—
580C22×C7—22no—
581C22×C7—41no—
582C22×C7—41no—
583C22×C7—41no—
584C22×C7—41no—
585C22×C7—41no—
586C22×C7—42no—
587C22×C7—42no—
588C22×C7—41no—
589C22×C7—41no—
590C22×C7—42no—
591C22×C7—42no—
592C22×C7—41no—
593C22×C7—42no—
594C22×C7—42no—
595C22×C7—41no—
596C22×C7—41no—
597C22×C7—41no—
598C22×C7—81no—
599C22×C7—81no—
600C22×C7—81no—
601C22×C7—81no—
602C22×C7—81no—
603C22×C7—81no—
604C22×C7—81no—
605C22×C7—81no—
606C22×C7—81no—
607C22×C7—81no—
608C22×C7—81no—
609C22×C7—81no—
610C22×C7—81no—
611C22×C7—81no—
612C22×C7—81no—
613C22×C7C2×#12011yescharacteristic
614C22×C7D4211yescharacteristic
615C22×C7#54611yescharacteristic
616C22×C7C2×AGL(1,ℤ/8)11yescharacteristic
617C22×C7#57511yescharacteristic
618C22×C7#57611yescharacteristic
619C22×C7#57711yescharacteristic
620C4×C7—22no—
621C4×C7—24no—
622C4×C7—22no—
623C4×C7—41no—
624C4×C7—41no—
625C4×C7—42no—
626C4×C7—42no—
627C4×C7—81no—
628C4×C7—81no—
629C4×C7C2×#12111yescharacteristic
630C4×C7#53411yescharacteristic
631C4×C7D4211yescharacteristic
632C4×C7#54611yescharacteristic
633C24—21no—
634C24—21no—
635C24—21no—
636C24C2×C7×D411yescharacteristic
637C24C2×C7×D411yescharacteristic
638#41—28no—
639#41—44no—
640#41—44no—
641#41—44no—
642#41—44no—
643#41—44no—
644#41—44no—
645#41—44no—
646C2×Q8—21no—
647C2×Q8—21no—
648C2×Q8—21no—
649C2×Q8C2×C7×D412yes—
650C2×Q8C2×C7×D412yes—
651C2×Q8C7×#4112yes—
652C2×D4—24no—
653C2×D4—24no—
654C2×D4—22no—
655C2×D4—24no—
656C2×D4—24no—
657C2×D4—24no—
658C2×D4—24no—
659C2×D4—22no—
660C2×D4—21no—
661C2×D4—21no—
662C2×D4—21no—
663C2×D4—21no—
664C2×D4—21no—
665C2×D4—21no—
666C2×D4—21no—
667C2×D4—21no—
668C2×D4—21no—
669C2×D4—21no—
670C2×D4—21no—
671C2×D4—21no—
672C2×D4—21no—
673C2×D4—21no—
674C2×D4—21no—
675C2×D4—21no—
676C2×D4—41no—
677C2×D4—42no—
678C2×D4—42no—
679C2×D4—42no—
680C2×D4—42no—
681C2×D4—42no—
682C2×D4—42no—
683C2×D4—42no—
684C2×D4—42no—
685C2×D4—42no—
686C2×D4—42no—
687C2×D4—42no—
688C2×D4—81no—
689C2×D4—81no—
690C2×D4—81no—
691C2×D4—81no—
692C2×D4—81no—
693C2×D4—81no—
694C2×D4—81no—
695C2×D4C2×C7×D412yes—
696C2×D4C2×C7×D412yes—
697C22×C4—21no—
698C22×C4—21no—
699C22×C4—21no—
700C22×C4—21no—
701C22×C4—21no—
702C22×C4—24no—
703C22×C4—21no—
704C22×C4—21no—
705C22×C4—24no—
706C22×C4—21no—
707C22×C4—21no—
708C22×C4—21no—
709C22×C4—21no—
710C22×C4—21no—
711C22×C4—21no—
712C22×C4—21no—
713C22×C4—21no—
714C22×C4—42no—
715C22×C4—42no—
716C22×C4—42no—
717C22×C4—42no—
718C22×C4—42no—
719C22×C4—42no—
720C22×C4—81no—
721C22×C4C2×C7×D411yescharacteristic
722C22×C4C2×C7×D411yescharacteristic
723C22×C4C2×C7×D411yescharacteristic
724C22×C4C2×C7×D412yes—
725C22×C4C2×C7×D412yes—
726C22×C4C2×C7×D411yescharacteristic
727C22×C4C24×C711yescharacteristic
728SD16—44no—
729D8—44no—
730D8—44no—
731M16—44no—
732C2×C8—21no—
733C2×C8—21no—
734C2×C8—21no—
735C2×C8—21no—
736C2×C8—21no—
737C2×C8—21no—
738C2×C8—21no—
739C2×C8—21no—
740C2×C8—21no—
741C2×C8—21no—
742C2×C8—21no—
743C2×C8C2×C7×D412yes—
744C4⋊C4—24no—
745C4⋊C4—22no—
746C4⋊C4—21no—
747C4⋊C4—21no—
748C4⋊C4—21no—
749C4⋊C4—21no—
750C4⋊C4—21no—
751C4⋊C4—21no—
752C4⋊C4—42no—
753C4⋊C4—42no—
754C4⋊C4C2×C7×D412yes—
755C4⋊C4C2×C7×D412yes—
756C22⋊C4—24no—
757C22⋊C4—22no—
758C22⋊C4—24no—
759C22⋊C4—22no—
760C22⋊C4—42no—
761C22⋊C4—42no—
762C22⋊C4—42no—
763C22⋊C4—42no—
764C22⋊C4—81no—
765C42—24no—
766C42—21no—
767C42—21no—
768C2×C7—42no—
769C2×C7—81no—
770C2×C7—82no—
771C2×C7—82no—
772C2×C7—161no—
773C2×C7#241011yescharacteristic
774C2×C7#300611yescharacteristic
775C2×C7#301211yescharacteristic
776C2×C7#327111yescharacteristic
777C2×C7#327411yescharacteristic
778C2×C7#330911yescharacteristic
779C2×C7#333211yescharacteristic
780C23—21no—
781C23—21no—
782C23—21no—
783C23—21no—
784C23—21no—
785C23—21no—
786C23—21no—
787C23—22no—
788C23—22no—
789C23—21no—
790C23—21no—
791C23—21no—
792C23—21no—
793C23—21no—
794C23—21no—
795C23—41no—
796C23—41no—
797C23—41no—
798C23—41no—
799C23—41no—
800C23—41no—
801C23—41no—
802C23—41no—
803C23—41no—
804C23—41no—
805C23—41no—
806C23—41no—
807C23—41no—
808C23—41no—
809C23—41no—
810C23—41no—
811C23—41no—
812C23—41no—
813C23—41no—
814C23C7×#12012yes—
815C23C22×C7×D411yescharacteristic
816Q8—22no—
817Q8—22no—
818Q8—22no—
819Q8C7×#12114yescomplemented
820D4—22no—
821D4—22no—
822D4—22no—
823D4—22no—
824D4—44no—
825D4—48no—
826D4—48no—
827D4—48no—
828D4—41no—
829D4—41no—
830D4—41no—
831D4—41no—
832D4—41no—
833D4—41no—
834D4—41no—
835D4—41no—
836D4—84no—
837D4—84no—
838D4—84no—
839D4—84no—
840D4—84no—
841C2×C4—21no—
842C2×C4—22no—
843C2×C4—21no—
844C2×C4—22no—
845C2×C4—21no—
846C2×C4—22no—
847C2×C4—21no—
848C2×C4—22no—
849C2×C4—22no—
850C2×C4—22no—
851C2×C4—22no—
852C2×C4—21no—
853C2×C4—22no—
854C2×C4—21no—
855C2×C4—21no—
856C2×C4—22no—
857C2×C4—21no—
858C2×C4—21no—
859C2×C4—21no—
860C2×C4—48no—
861C2×C4—48no—
862C2×C4—41no—
863C2×C4—41no—
864C2×C4—41no—
865C2×C4—41no—
866C2×C4—41no—
867C2×C4—41no—
868C2×C4—41no—
869C2×C4—41no—
870C2×C4—41no—
871C2×C4—41no—
872C2×C4—41no—
873C2×C4—41no—
874C2×C4—41no—
875C2×C4—41no—
876C2×C4—84no—
877C2×C4C7×#12012yes—
878C2×C4C7×AGL(1,ℤ/8)12yes—
879C2×C4C22×C7×D411yescharacteristic
880C2×C4C22×C7×D411yescharacteristic
881C2×C4C22×C7×D411yescharacteristic
882C2×C4C2×C7×#4111yescharacteristic
883C2×C4C7×H(5,𝔽2)11yescharacteristic
884C2×C4C7×H(5,𝔽2)11yescharacteristic
885C8—22no—
886C8—41no—
887C8—41no—
888C8—41no—
889C7#2445111yescharacteristic, direct product factor, Sylow
890C22—22no—
891C22—22no—
892C22—22no—
893C22—41no—
894C22—41no—
895C22—41no—
896C22—41no—
897C22—42no—
898C22—42no—
899C22—41no—
900C22—41no—
901C22—42no—
902C22—42no—
903C22—41no—
904C22—42no—
905C22—42no—
906C22—41no—
907C22—41no—
908C22—41no—
909C22—41no—
910C22—81no—
911C22—81no—
912C22—81no—
913C22—81no—
914C22—81no—
915C22—81no—
916C22—81no—
917C22—81no—
918C22—81no—
919C22—81no—
920C22—81no—
921C22—81no—
922C22—81no—
923C22—81no—
924C22—81no—
925C22C2×C7×#12011yescharacteristic
926C22C7×D4211yescharacteristic
927C22C7×#54611yescharacteristic
928C22C2×C7×AGL(1,ℤ/8)11yescharacteristic
929C22C7×#57511yescharacteristic
930C22C7×#57611yescharacteristic
931C22C7×#57711yescharacteristic
932C4—22no—
933C4—24no—
934C4—22no—
935C4—41no—
936C4—41no—
937C4—42no—
938C4—42no—
939C4—81no—
940C4—81no—
941C4C2×C7×#12111yescharacteristic
942C4C7×#53411yescharacteristic
943C4C7×D4211yescharacteristic
944C4C7×#54611yescharacteristic
945C2—42no—
946C2—81no—
947C2—82no—
948C2—82no—
949C2—161no—
950C2C7×#241011yescharacteristic
951C2C7×#300611yescharacteristic
952C2C7×#301211yescharacteristic
953C2C7×#327111yescharacteristic
954C2C7×#327411yescharacteristic
955C2C7×#330911yescharacteristic
956C2C7×#333211yescharacteristic
subgroupG/H
center, socleC23×C7C22×D4
commutator, Frattini, cosocleC22×C4C24×C7
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
1. C2×C7×#550C2semidirect
2. C2×C7×#469C2semidirect
3. C2×C7×#449C2semidirect
4. C2×C7×#449C2semidirect
5. C2×C7×#417C2semidirect
6. C7×#2416C2semidirect
7. C7×#2041C2semidirect
8. C7×#2034C2semidirect
9. C7×#2011C2semidirect
10. C7×#1999C2semidirect
11. C7×#1880C2semidirect
12. C7×#1874C2semidirect
13. C7×#1870C2semidirect
14. C7×#1865C2semidirect
15. C7×#1788C2semidirect
65. #24451C7direct (N × H)
77. C2×C7×#41D4semidirect
125. C7×#121D4semidirect
155. C7×#103D4semidirect
168. C2×#550C2×C7semidirect
169. C2×#469C2×C7semidirect
170. C2×#449C2×C7semidirect
171. C2×#449C2×C7semidirect
172. C2×#417C2×C7semidirect
173. #2416C2×C7semidirect
174. #2041C2×C7semidirect
175. #2034C2×C7semidirect
176. #2011C2×C7semidirect
177. #1999C2×C7semidirect
178. #1880C2×C7semidirect
179. #1874C2×C7semidirect
180. #1870C2×C7semidirect
181. #1865C2×C7semidirect
182. #1788C2×C7semidirect
406. C7×Q8#121semidirect
487. C2×#41C7×D4semidirect
535. #121C7×D4semidirect
565. #103C7×D4semidirect
819. Q8C7×#121semidirect
889. C7#24451direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C7×#5502
C2×C7×#4692
C2×C7×#4492
C2×C7×#4172
C7×#24162
C7×#20412
C7×#20342
C7×#20112
C7×#19992
C7×#18802
C7×#18742
C7×#18702
C7×#18652
C7×#17882
#244517