Finite Group Databasebeta

← C7×#13970 #13191186

Subgroups — C7×#13970 #13191186

Order 1792.

3058 conjugacy classes of subgroups.

The subgroup lattice has 1014 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C7×#121C211yesmaximal, characteristic
2C22×C4×C7×D4C211yesmaximal, characteristic, complemented
3C2×C7×#390C211yesmaximal, characteristic, complemented
4C2×C7×#386C212yesmaximal, complemented
5C2×C7×#380C211yesmaximal, characteristic, complemented
6C2×C4×C7×C22⋊C4C211yesmaximal, characteristic, complemented
7C7×#1440C212yesmaximal, complemented
8C7×#1438C212yesmaximal, complemented
9C7×C4⋊#95C211yesmaximal, characteristic, complemented
10C7×C4⋊#95C211yesmaximal, characteristic, complemented
11C7×C22⋊#95C212yesmaximal, complemented
12C23×C7×D4C2212yes—
13C23×C7×D4C2211yescharacteristic
14C24×C4×C7C2211yescharacteristic
15C24×C4×C7C2212yes—
16C2×C7×#121—24no—
17C2×C7×#121—24no—
18C2×C7×#121C418yescomplemented
19C2×C4×C7×D4—24no—
20C2×C4×C7×D4—24no—
21C2×C4×C7×D4—24no—
22C22×C7×C4⋊C4C2211yescharacteristic
23C22×C7×C4⋊C4C2211yescharacteristic
24C22×C7×C4⋊C4C2211yescharacteristic
25C22×C7×C22⋊C4C2212yes—
26C22×C7×C22⋊C4C2211yescharacteristic
27C22×C7×C22⋊C4C2212yes—
28C22×C7×C22⋊C4C2212yes—
29C22×C7×C22⋊C4C2212yes—
30C22×C7×C22⋊C4C2212yes—
31C22×C7×C22⋊C4C2211yescharacteristic
32C22×C42×C7C2211yescharacteristic
33C22×C42×C7C2211yescharacteristic
34C7×#390—24no—
35C7×#386—28no—
36C7×#380—24no—
37C4×C7×C22⋊C4—24no—
38C2×C7×#95C2211yescharacteristic
39C2×C7×#95C2211yescharacteristic
40C2×C7×#95C2212yes—
41C2×C7×#95C2212yes—
42C2×C7×#95C2212yes—
43C2×C7×#95C2212yes—
44C2×C7×#95C2212yes—
45#13970C711yesmaximal, characteristic, direct product factor, Sylow
46C25×C7C2312yes—
47C25×C7C2311yescharacteristic
48C22×C7×D4—24no—
49C22×C7×D4—24no—
50C22×C7×D4—24no—
51C22×C7×D4—24no—
52C22×C7×D4—22no—
53C22×C7×D4—22no—
54C22×C7×D4—22no—
55C22×C7×D4—22no—
56C22×C7×D4—42no—
57C22×C7×D4—42no—
58C22×C7×D4C2×C414yes—
59C22×C7×D4C2×C418yescomplemented
60C22×C7×D4D414yes—
61C22×C7×D4D414yes—
62C23×C4×C7—24no—
63C23×C4×C7—22no—
64C23×C4×C7—24no—
65C23×C4×C7—24no—
66C23×C4×C7—22no—
67C23×C4×C7—22no—
68C23×C4×C7—22no—
69C23×C4×C7—22no—
70C23×C4×C7—22no—
71C23×C4×C7—24no—
72C23×C4×C7—24no—
73C23×C4×C7—42no—
74C23×C4×C7—42no—
75C23×C4×C7C2×C414yescomplemented
76C23×C4×C7C2312yes—
77C23×C4×C7C2312yes—
78C23×C4×C7C2311yescharacteristic
79C23×C4×C7C2311yescharacteristic
80C23×C4×C7C2311yescharacteristic
81C23×C4×C7C2312yes—
82C23×C4×C7C2311yescharacteristic
83C23×C4×C7C2311yescharacteristic
84C23×C4×C7C2311yescharacteristic
85C7×#121—232no—
86C4×C7×D4—232no—
87C2×C7×C4⋊C4—22no—
88C2×C7×C4⋊C4—22no—
89C2×C7×C4⋊C4—22no—
90C2×C7×C4⋊C4—22no—
91C2×C7×C4⋊C4—22no—
92C2×C7×C4⋊C4—22no—
93C2×C7×C4⋊C4—22no—
94C2×C7×C4⋊C4C2×C414yescomplemented
95C2×C7×C4⋊C4D414yescomplemented
96C2×C7×C22⋊C4—24no—
97C2×C7×C22⋊C4—24no—
98C2×C7×C22⋊C4—24no—
99C2×C7×C22⋊C4—22no—
100C2×C7×C22⋊C4—22no—
101C2×C7×C22⋊C4—22no—
102C2×C7×C22⋊C4—24no—
103C2×C7×C22⋊C4—24no—
104C2×C7×C22⋊C4—22no—
105C2×C7×C22⋊C4—22no—
106C2×C7×C22⋊C4—24no—
107C2×C7×C22⋊C4—24no—
108C2×C7×C22⋊C4—24no—
109C2×C7×C22⋊C4—24no—
110C2×C7×C22⋊C4—24no—
111C2×C7×C22⋊C4—24no—
112C2×C7×C22⋊C4—42no—
113C2×C7×C22⋊C4—42no—
114C2×C7×C22⋊C4—42no—
115C2×C7×C22⋊C4C2×C418yescomplemented
116C2×C7×C22⋊C4D414yescomplemented
117C2×C42×C7—22no—
118C2×C42×C7—22no—
119C2×C42×C7—22no—
120C2×C42×C7—22no—
121C2×C42×C7—22no—
122C2×C42×C7D414yescomplemented
123C7×#95—22no—
124C7×#95—22no—
125C7×#95—24no—
126C7×#95—24no—
127C7×#95—24no—
128C7×#95—42no—
129C7×#95—42no—
130C22×#121C2×C711yescharacteristic
131C22×C4×D4C2×C711yescharacteristic, complemented
132C2×#390C2×C711yescharacteristic, complemented
133C2×#386C2×C712yescomplemented
134C2×#380C2×C711yescharacteristic, complemented
135C2×C4×C22⋊C4C2×C711yescharacteristic, complemented
136#1440C2×C712yescomplemented
137#1438C2×C712yescomplemented
138C4⋊#95C2×C711yescharacteristic, complemented
139C4⋊#95C2×C711yescharacteristic, complemented
140C22⋊#95C2×C712yescomplemented
141C24×C7—21no—
142C24×C7—21no—
143C24×C7—22no—
144C24×C7—22no—
145C24×C7—22no—
146C24×C7—21no—
147C24×C7—21no—
148C24×C7—21no—
149C24×C7—21no—
150C24×C7—22no—
151C24×C7—21no—
152C24×C7—21no—
153C24×C7—22no—
154C24×C7—22no—
155C24×C7—22no—
156C24×C7—22no—
157C24×C7—21no—
158C24×C7—22no—
159C24×C7—22no—
160C24×C7—22no—
161C24×C7—21no—
162C24×C7—21no—
163C24×C7—22no—
164C24×C7—21no—
165C24×C7C22×C414yes—
166C24×C7C22×C412yes—
167C24×C7C2×D414yes—
168C24×C7C2×D414yes—
169C24×C7C2×D412yes—
170C24×C7#4112yes—
171C24×C7C2411yescharacteristic
172C2×C7×D4—216no—
173C2×C7×D4—216no—
174C2×C7×D4—28no—
175C2×C7×D4—28no—
176C2×C7×D4—28no—
177C2×C7×D4—28no—
178C2×C7×D4—28no—
179C2×C7×D4—28no—
180C2×C7×D4—48no—
181C2×C7×D4—48no—
182C2×C7×D4—48no—
183C2×C7×D4—48no—
184C2×C7×D4—48no—
185C2×C7×D4C22⋊C4116yescomplemented
186C22×C4×C7—21no—
187C22×C4×C7—21no—
188C22×C4×C7—21no—
189C22×C4×C7—21no—
190C22×C4×C7—216no—
191C22×C4×C7—21no—
192C22×C4×C7—21no—
193C22×C4×C7—22no—
194C22×C4×C7—21no—
195C22×C4×C7—21no—
196C22×C4×C7—22no—
197C22×C4×C7—21no—
198C22×C4×C7—21no—
199C22×C4×C7—21no—
200C22×C4×C7—21no—
201C22×C4×C7—21no—
202C22×C4×C7—21no—
203C22×C4×C7—22no—
204C22×C4×C7—22no—
205C22×C4×C7—22no—
206C22×C4×C7—22no—
207C22×C4×C7—21no—
208C22×C4×C7—21no—
209C22×C4×C7—21no—
210C22×C4×C7—21no—
211C22×C4×C7—21no—
212C22×C4×C7—21no—
213C22×C4×C7—21no—
214C22×C4×C7—21no—
215C22×C4×C7—22no—
216C22×C4×C7—22no—
217C22×C4×C7—21no—
218C22×C4×C7—21no—
219C22×C4×C7—22no—
220C22×C4×C7—22no—
221C22×C4×C7—22no—
222C22×C4×C7—21no—
223C22×C4×C7—21no—
224C22×C4×C7—22no—
225C22×C4×C7—21no—
226C22×C4×C7—21no—
227C22×C4×C7—28no—
228C22×C4×C7—28no—
229C22×C4×C7—28no—
230C22×C4×C7—22no—
231C22×C4×C7—22no—
232C22×C4×C7—22no—
233C22×C4×C7—22no—
234C22×C4×C7—22no—
235C22×C4×C7—22no—
236C22×C4×C7—22no—
237C22×C4×C7—48no—
238C22×C4×C7—48no—
239C22×C4×C7—48no—
240C22×C4×C7—48no—
241C22×C4×C7—48no—
242C22×C4×C7—44no—
243C22×C4×C7—44no—
244C22×C4×C7—44no—
245C22×C4×C7—48no—
246C22×C4×C7—44no—
247C22×C4×C7C22×C412yes—
248C22×C4×C7C22×C414yes—
249C22×C4×C7C22×C412yes—
250C22×C4×C7C2×D412yes—
251C22×C4×C7C2×D412yes—
252C22×C4×C7C2×D414yes—
253C22×C4×C7C2×D412yes—
254C22×C4×C7C2×D412yes—
255C22×C4×C7C2×D412yes—
256C22×C4×C7C2×D412yes—
257C22×C4×C7C2×D412yes—
258C22×C4×C7C2×D412yes—
259C22×C4×C7#4112yes—
260C22×C4×C7#4112yes—
261C22×C4×C7#4112yes—
262C22×C4×C7#4112yes—
263C7×C4⋊C4—28no—
264C7×C4⋊C4—28no—
265C7×C4⋊C4—44no—
266C7×C22⋊C4—28no—
267C7×C22⋊C4—216no—
268C7×C22⋊C4—216no—
269C7×C22⋊C4—28no—
270C7×C22⋊C4—48no—
271C7×C22⋊C4—48no—
272C7×C22⋊C4—48no—
273C42×C7—28no—
274C42×C7—44no—
275C23×D4C22×C712yes—
276C23×D4C22×C711yescharacteristic
277C24×C4C22×C711yescharacteristic
278C24×C4C22×C712yes—
279C2×#121—24no—
280C2×#121—24no—
281C2×#121C4×C718yescomplemented
282C2×C4×D4—24no—
283C2×C4×D4—24no—
284C2×C4×D4—24no—
285C22×C4⋊C4C22×C711yescharacteristic
286C22×C4⋊C4C22×C711yescharacteristic
287C22×C4⋊C4C22×C711yescharacteristic
288C22×C22⋊C4C22×C712yes—
289C22×C22⋊C4C22×C711yescharacteristic
290C22×C22⋊C4C22×C712yes—
291C22×C22⋊C4C22×C712yes—
292C22×C22⋊C4C22×C712yes—
293C22×C22⋊C4C22×C712yes—
294C22×C22⋊C4C22×C711yescharacteristic
295C22×C42C22×C711yescharacteristic
296C22×C42C22×C711yescharacteristic
297#390—24no—
298#386—28no—
299#380—24no—
300C4×C22⋊C4—24no—
301C2×#95C22×C711yescharacteristic
302C2×#95C22×C712yes—
303C2×#95C22×C712yes—
304C2×#95C22×C712yes—
305C2×#95C22×C711yescharacteristic
306C2×#95C22×C712yes—
307C2×#95C22×C712yes—
308C23×C7—22no—
309C23×C7—22no—
310C23×C7—22no—
311C23×C7—24no—
312C23×C7—24no—
313C23×C7—24no—
314C23×C7—24no—
315C23×C7—22no—
316C23×C7—22no—
317C23×C7—24no—
318C23×C7—24no—
319C23×C7—22no—
320C23×C7—24no—
321C23×C7—22no—
322C23×C7—24no—
323C23×C7—24no—
324C23×C7—24no—
325C23×C7—22no—
326C23×C7—22no—
327C23×C7—22no—
328C23×C7—22no—
329C23×C7—24no—
330C23×C7—24no—
331C23×C7—22no—
332C23×C7—22no—
333C23×C7—24no—
334C23×C7—24no—
335C23×C7—22no—
336C23×C7—22no—
337C23×C7—24no—
338C23×C7—24no—
339C23×C7—24no—
340C23×C7—24no—
341C23×C7—22no—
342C23×C7—22no—
343C23×C7—22no—
344C23×C7—41no—
345C23×C7—42no—
346C23×C7—41no—
347C23×C7—41no—
348C23×C7—41no—
349C23×C7—42no—
350C23×C7—42no—
351C23×C7—42no—
352C23×C7—42no—
353C23×C7—41no—
354C23×C7—41no—
355C23×C7—42no—
356C23×C7—41no—
357C23×C7—42no—
358C23×C7—41no—
359C23×C7—42no—
360C23×C7—42no—
361C23×C7—42no—
362C23×C7—41no—
363C23×C7—41no—
364C23×C7—41no—
365C23×C7—41no—
366C23×C7—41no—
367C23×C7—42no—
368C23×C7—42no—
369C23×C7—41no—
370C23×C7—42no—
371C23×C7—42no—
372C23×C7—41no—
373C23×C7—42no—
374C23×C7—41no—
375C23×C7—42no—
376C23×C7C2×C22⋊C418yes—
377C23×C7C4×D414yescomplemented
378C23×C7C23×C411yescharacteristic
379C23×C7C22×D411yescharacteristic
380C23×C7C22×D411yescharacteristic
381C23×C7C22×D411yescharacteristic
382C23×C7C22×D411yescharacteristic
383C23×C7C22×D411yescharacteristic
384C23×C7C2×#4111yescharacteristic
385C23×C7C2×#4111yescharacteristic
386C23×C7C2×#4111yescharacteristic
387C23×C7C2×#4111yescharacteristic
388C23×C7C2×#4111yescharacteristic
389C23×C7H(5,𝔽2)11yescharacteristic
390C23×C7H(5,𝔽2)11yescharacteristic
391C23×C7H(5,𝔽2)11yescharacteristic
392C23×C72−1+411yescharacteristic
393C7×D4—232no—
394C7×D4—432no—
395C2×C4×C7—22no—
396C2×C4×C7—22no—
397C2×C4×C7—22no—
398C2×C4×C7—22no—
399C2×C4×C7—22no—
400C2×C4×C7—22no—
401C2×C4×C7—22no—
402C2×C4×C7—24no—
403C2×C4×C7—22no—
404C2×C4×C7—22no—
405C2×C4×C7—24no—
406C2×C4×C7—24no—
407C2×C4×C7—22no—
408C2×C4×C7—24no—
409C2×C4×C7—22no—
410C2×C4×C7—22no—
411C2×C4×C7—22no—
412C2×C4×C7—22no—
413C2×C4×C7—22no—
414C2×C4×C7—24no—
415C2×C4×C7—22no—
416C2×C4×C7—24no—
417C2×C4×C7—22no—
418C2×C4×C7—22no—
419C2×C4×C7—432no—
420C2×C4×C7—41no—
421C2×C4×C7—41no—
422C2×C4×C7—41no—
423C2×C4×C7—42no—
424C2×C4×C7—41no—
425C2×C4×C7—41no—
426C2×C4×C7—41no—
427C2×C4×C7—41no—
428C2×C4×C7—42no—
429C2×C4×C7—41no—
430C2×C4×C7—42no—
431C2×C4×C7—42no—
432C2×C4×C7—42no—
433C2×C4×C7—41no—
434C2×C4×C7—41no—
435C2×C4×C7—42no—
436C2×C4×C7—42no—
437C2×C4×C7—42no—
438C2×C4×C7—41no—
439C2×C4×C7—41no—
440C2×C4×C7—41no—
441C2×C4×C7—41no—
442C2×C4×C7—41no—
443C2×C4×C7—41no—
444C2×C4×C7—416no—
445C2×C4×C7—42no—
446C2×C4×C7—42no—
447C2×C4×C7—42no—
448C2×C4×C7—42no—
449C2×C4×C7—42no—
450C2×C4×C7—42no—
451C2×C4×C7—42no—
452C2×C4×C7C2×C22⋊C414yes—
453C2×C4×C7C4×D414yes—
454C2×C4×C7C4×D414yes—
455C2×C4×C7#12014yes—
456C2×C4×C7#12114yes—
457C2×C4×C7#12114yes—
458C2×C4×C7#12114yescomplemented
459C2×C4×C7#12314yes—
460C25C23×C712yes—
461C25C23×C711yescharacteristic
462C22×D4—24no—
463C22×D4—24no—
464C22×D4—24no—
465C22×D4—24no—
466C22×D4—22no—
467C22×D4—22no—
468C22×D4—22no—
469C22×D4—22no—
470C22×D4—42no—
471C22×D4—42no—
472C22×D4C2×C4×C714yes—
473C22×D4C2×C4×C718yescomplemented
474C22×D4C7×D414yes—
475C22×D4C7×D414yes—
476C23×C4—24no—
477C23×C4—24no—
478C23×C4—24no—
479C23×C4—22no—
480C23×C4—22no—
481C23×C4—22no—
482C23×C4—22no—
483C23×C4—22no—
484C23×C4—22no—
485C23×C4—24no—
486C23×C4—24no—
487C23×C4—42no—
488C23×C4—42no—
489C23×C4C2×C4×C714yescomplemented
490C23×C4C23×C712yes—
491C23×C4C23×C711yescharacteristic
492C23×C4C23×C712yes—
493C23×C4C23×C711yescharacteristic
494C23×C4C23×C711yescharacteristic
495C23×C4C23×C712yes—
496C23×C4C23×C711yescharacteristic
497C23×C4C23×C711yescharacteristic
498C23×C4C23×C711yescharacteristic
499#121—232no—
500C4×D4—232no—
501C2×C4⋊C4—22no—
502C2×C4⋊C4—22no—
503C2×C4⋊C4—22no—
504C2×C4⋊C4—22no—
505C2×C4⋊C4—22no—
506C2×C4⋊C4—22no—
507C2×C4⋊C4—22no—
508C2×C4⋊C4C2×C4×C714yescomplemented
509C2×C4⋊C4C7×D414yescomplemented
510C2×C22⋊C4—24no—
511C2×C22⋊C4—24no—
512C2×C22⋊C4—24no—
513C2×C22⋊C4—22no—
514C2×C22⋊C4—24no—
515C2×C22⋊C4—24no—
516C2×C22⋊C4—22no—
517C2×C22⋊C4—22no—
518C2×C22⋊C4—22no—
519C2×C22⋊C4—22no—
520C2×C22⋊C4—24no—
521C2×C22⋊C4—24no—
522C2×C22⋊C4—24no—
523C2×C22⋊C4—24no—
524C2×C22⋊C4—24no—
525C2×C22⋊C4—24no—
526C2×C22⋊C4—42no—
527C2×C22⋊C4—42no—
528C2×C22⋊C4—42no—
529C2×C22⋊C4C2×C4×C718yescomplemented
530C2×C22⋊C4C7×D414yescomplemented
531C2×C42—22no—
532C2×C42—22no—
533C2×C42—22no—
534C2×C42—22no—
535C2×C42—22no—
536C2×C42C7×D414yescomplemented
537#95—22no—
538#95—22no—
539#95—24no—
540#95—24no—
541#95—24no—
542#95—42no—
543#95—42no—
544C22×C7—24no—
545C22×C7—28no—
546C22×C7—28no—
547C22×C7—24no—
548C22×C7—28no—
549C22×C7—24no—
550C22×C7—42no—
551C22×C7—44no—
552C22×C7—42no—
553C22×C7—44no—
554C22×C7—42no—
555C22×C7—44no—
556C22×C7—44no—
557C22×C7—42no—
558C22×C7—44no—
559C22×C7—42no—
560C22×C7—44no—
561C22×C7—42no—
562C22×C7—44no—
563C22×C7—42no—
564C22×C7—44no—
565C22×C7—42no—
566C22×C7—44no—
567C22×C7—42no—
568C22×C7—44no—
569C22×C7—42no—
570C22×C7—42no—
571C22×C7—44no—
572C22×C7—42no—
573C22×C7—44no—
574C22×C7C22×C22⋊C411yescharacteristic
575C22×C7C2×C4×D411yescharacteristic
576C22×C7C2×C4×D411yescharacteristic
577C22×C7C2×C4×D411yescharacteristic
578C22×C7C4×#4111yescharacteristic
579C22×C7#51811yescharacteristic
580C22×C7#52011yescharacteristic
581C22×C7C2×#12011yescharacteristic
582C22×C7C2×#12111yescharacteristic
583C22×C7C2×#12111yescharacteristic
584C22×C7C2×#12111yescharacteristic
585C22×C7C2×#12311yescharacteristic
586C22×C7#52511yescharacteristic
587C22×C7#52911yescharacteristic
588C22×C7#53211yescharacteristic
589C22×C7#53511yescharacteristic
590C22×C7#53711yescharacteristic
591C22×C7#54011yescharacteristic
592C22×C7#54211yescharacteristic
593C22×C7D4211yescharacteristic
594C22×C7D4211yescharacteristic
595C22×C7D4211yescharacteristic
596C22×C7#54611yescharacteristic
597C22×C7#54611yescharacteristic
598C22×C7#54611yescharacteristic
599C22×C7#54611yescharacteristic
600C22×C7#54611yescharacteristic
601C22×C7#54711yescharacteristic
602C22×C7#54711yescharacteristic
603C22×C7#54711yescharacteristic
604C22×C7#54811yescharacteristic
605C22×C7#55011yescharacteristic
606C22×C7#55311yescharacteristic
607C22×C7#55311yescharacteristic
608C22×C7#55511yescharacteristic
609C4×C7—24no—
610C4×C7—44no—
611C4×C7—42no—
612C4×C7—44no—
613C4×C7—42no—
614C4×C7—42no—
615C4×C7—42no—
616C4×C7—82no—
617C4×C7#38618yescomplemented
618C24—21no—
619C24—21no—
620C24—22no—
621C24—22no—
622C24—22no—
623C24—21no—
624C24—21no—
625C24—21no—
626C24—21no—
627C24—22no—
628C24—21no—
629C24—21no—
630C24—22no—
631C24—22no—
632C24—22no—
633C24—22no—
634C24—21no—
635C24—22no—
636C24—22no—
637C24—22no—
638C24—21no—
639C24—21no—
640C24—22no—
641C24—21no—
642C24C22×C4×C714yes—
643C24C22×C4×C712yes—
644C24C2×C7×D414yes—
645C24C2×C7×D414yes—
646C24C2×C7×D412yes—
647C24C7×#4112yes—
648C24C24×C711yescharacteristic
649C2×D4—216no—
650C2×D4—216no—
651C2×D4—28no—
652C2×D4—28no—
653C2×D4—28no—
654C2×D4—28no—
655C2×D4—28no—
656C2×D4—28no—
657C2×D4—48no—
658C2×D4—48no—
659C2×D4—48no—
660C2×D4—48no—
661C2×D4—48no—
662C2×D4C7×C22⋊C4116yescomplemented
663C22×C4—21no—
664C22×C4—21no—
665C22×C4—21no—
666C22×C4—21no—
667C22×C4—216no—
668C22×C4—21no—
669C22×C4—21no—
670C22×C4—22no—
671C22×C4—21no—
672C22×C4—21no—
673C22×C4—22no—
674C22×C4—21no—
675C22×C4—21no—
676C22×C4—21no—
677C22×C4—21no—
678C22×C4—21no—
679C22×C4—21no—
680C22×C4—22no—
681C22×C4—22no—
682C22×C4—22no—
683C22×C4—22no—
684C22×C4—21no—
685C22×C4—21no—
686C22×C4—21no—
687C22×C4—21no—
688C22×C4—21no—
689C22×C4—21no—
690C22×C4—21no—
691C22×C4—21no—
692C22×C4—22no—
693C22×C4—22no—
694C22×C4—21no—
695C22×C4—21no—
696C22×C4—22no—
697C22×C4—22no—
698C22×C4—22no—
699C22×C4—21no—
700C22×C4—21no—
701C22×C4—22no—
702C22×C4—21no—
703C22×C4—21no—
704C22×C4—28no—
705C22×C4—28no—
706C22×C4—28no—
707C22×C4—22no—
708C22×C4—22no—
709C22×C4—22no—
710C22×C4—22no—
711C22×C4—22no—
712C22×C4—22no—
713C22×C4—22no—
714C22×C4—48no—
715C22×C4—48no—
716C22×C4—48no—
717C22×C4—48no—
718C22×C4—48no—
719C22×C4—44no—
720C22×C4—44no—
721C22×C4—44no—
722C22×C4—48no—
723C22×C4—44no—
724C22×C4C22×C4×C712yes—
725C22×C4C22×C4×C714yes—
726C22×C4C22×C4×C712yes—
727C22×C4C2×C7×D412yes—
728C22×C4C2×C7×D412yes—
729C22×C4C2×C7×D414yes—
730C22×C4C2×C7×D412yes—
731C22×C4C2×C7×D412yes—
732C22×C4C2×C7×D412yes—
733C22×C4C2×C7×D412yes—
734C22×C4C2×C7×D412yes—
735C22×C4C2×C7×D412yes—
736C22×C4C7×#4112yes—
737C22×C4C7×#4112yes—
738C22×C4C7×#4112yes—
739C22×C4C7×#4112yes—
740C4⋊C4—28no—
741C4⋊C4—28no—
742C4⋊C4—44no—
743C22⋊C4—216no—
744C22⋊C4—28no—
745C22⋊C4—216no—
746C22⋊C4—28no—
747C22⋊C4—48no—
748C22⋊C4—48no—
749C22⋊C4—48no—
750C42—28no—
751C42—44no—
752C2×C7—44no—
753C2×C7—48no—
754C2×C7C2×#38611yescharacteristic
755C2×C7C4×#12111yescharacteristic
756C2×C7#232411yescharacteristic
757C2×C7D4×C22⋊C411yescharacteristic
758C2×C7#233911yescharacteristic
759C2×C7#236111yescharacteristic
760C2×C7#236311yescharacteristic
761C2×C7#240711yescharacteristic
762C2×C7#240811yescharacteristic
763C2×C7#242011yescharacteristic
764C2×C7#242211yescharacteristic
765C2×C7#242711yescharacteristic
766C2×C7#242811yescharacteristic
767C2×C7#253511yescharacteristic
768C2×C7#253711yescharacteristic
769C23—22no—
770C23—22no—
771C23—22no—
772C23—24no—
773C23—24no—
774C23—24no—
775C23—22no—
776C23—24no—
777C23—22no—
778C23—24no—
779C23—24no—
780C23—22no—
781C23—24no—
782C23—22no—
783C23—24no—
784C23—24no—
785C23—24no—
786C23—22no—
787C23—22no—
788C23—22no—
789C23—22no—
790C23—24no—
791C23—24no—
792C23—22no—
793C23—22no—
794C23—24no—
795C23—24no—
796C23—22no—
797C23—22no—
798C23—24no—
799C23—24no—
800C23—24no—
801C23—24no—
802C23—22no—
803C23—22no—
804C23—22no—
805C23—41no—
806C23—42no—
807C23—41no—
808C23—41no—
809C23—41no—
810C23—42no—
811C23—42no—
812C23—42no—
813C23—42no—
814C23—41no—
815C23—41no—
816C23—42no—
817C23—41no—
818C23—42no—
819C23—41no—
820C23—42no—
821C23—42no—
822C23—42no—
823C23—41no—
824C23—41no—
825C23—41no—
826C23—41no—
827C23—42no—
828C23—41no—
829C23—42no—
830C23—41no—
831C23—42no—
832C23—42no—
833C23—41no—
834C23—42no—
835C23—41no—
836C23—42no—
837C23C2×C7×C22⋊C418yes—
838C23C4×C7×D414yescomplemented
839C23C23×C4×C711yescharacteristic
840C23C22×C7×D411yescharacteristic
841C23C22×C7×D411yescharacteristic
842C23C22×C7×D411yescharacteristic
843C23C22×C7×D411yescharacteristic
844C23C22×C7×D411yescharacteristic
845C23C2×C7×#4111yescharacteristic
846C23C2×C7×#4111yescharacteristic
847C23C2×C7×#4111yescharacteristic
848C23C2×C7×#4111yescharacteristic
849C23C2×C7×#4111yescharacteristic
850C23C7×H(5,𝔽2)11yescharacteristic
851C23C7×H(5,𝔽2)11yescharacteristic
852C23C7×H(5,𝔽2)11yescharacteristic
853C23C7×2−1+411yescharacteristic
854D4—232no—
855D4—432no—
856C2×C4—22no—
857C2×C4—22no—
858C2×C4—22no—
859C2×C4—22no—
860C2×C4—22no—
861C2×C4—22no—
862C2×C4—22no—
863C2×C4—24no—
864C2×C4—22no—
865C2×C4—22no—
866C2×C4—24no—
867C2×C4—24no—
868C2×C4—22no—
869C2×C4—24no—
870C2×C4—22no—
871C2×C4—22no—
872C2×C4—22no—
873C2×C4—22no—
874C2×C4—22no—
875C2×C4—24no—
876C2×C4—22no—
877C2×C4—24no—
878C2×C4—22no—
879C2×C4—22no—
880C2×C4—432no—
881C2×C4—41no—
882C2×C4—41no—
883C2×C4—41no—
884C2×C4—42no—
885C2×C4—41no—
886C2×C4—41no—
887C2×C4—41no—
888C2×C4—41no—
889C2×C4—42no—
890C2×C4—41no—
891C2×C4—42no—
892C2×C4—42no—
893C2×C4—42no—
894C2×C4—41no—
895C2×C4—41no—
896C2×C4—42no—
897C2×C4—42no—
898C2×C4—42no—
899C2×C4—41no—
900C2×C4—41no—
901C2×C4—41no—
902C2×C4—41no—
903C2×C4—41no—
904C2×C4—41no—
905C2×C4—416no—
906C2×C4—42no—
907C2×C4—42no—
908C2×C4—42no—
909C2×C4—42no—
910C2×C4—42no—
911C2×C4—42no—
912C2×C4—42no—
913C2×C4C2×C7×C22⋊C414yes—
914C2×C4C4×C7×D414yes—
915C2×C4C4×C7×D414yes—
916C2×C4C7×#12014yes—
917C2×C4C7×#12114yes—
918C2×C4C7×#12114yes—
919C2×C4C7×#12114yescomplemented
920C2×C4C7×#12314yes—
921C7#1397011yescharacteristic, direct product factor, Sylow
922C22—28no—
923C22—24no—
924C22—24no—
925C22—28no—
926C22—28no—
927C22—24no—
928C22—44no—
929C22—42no—
930C22—44no—
931C22—42no—
932C22—44no—
933C22—42no—
934C22—44no—
935C22—42no—
936C22—44no—
937C22—42no—
938C22—44no—
939C22—42no—
940C22—44no—
941C22—42no—
942C22—42no—
943C22—44no—
944C22—42no—
945C22—44no—
946C22—42no—
947C22—44no—
948C22—42no—
949C22—44no—
950C22—42no—
951C22—44no—
952C22C22×C7×C22⋊C411yescharacteristic
953C22C2×C4×C7×D411yescharacteristic
954C22C2×C4×C7×D411yescharacteristic
955C22C2×C4×C7×D411yescharacteristic
956C22C4×C7×#4111yescharacteristic
957C22C7×#51811yescharacteristic
958C22C7×#52011yescharacteristic
959C22C2×C7×#12011yescharacteristic
960C22C2×C7×#12111yescharacteristic
961C22C2×C7×#12111yescharacteristic
962C22C2×C7×#12111yescharacteristic
963C22C2×C7×#12311yescharacteristic
964C22C7×#52511yescharacteristic
965C22C7×#52911yescharacteristic
966C22C7×#53211yescharacteristic
967C22C7×#53511yescharacteristic
968C22C7×#53711yescharacteristic
969C22C7×#54011yescharacteristic
970C22C7×#54211yescharacteristic
971C22C7×D4211yescharacteristic
972C22C7×D4211yescharacteristic
973C22C7×D4211yescharacteristic
974C22C7×#54611yescharacteristic
975C22C7×#54611yescharacteristic
976C22C7×#54611yescharacteristic
977C22C7×#54611yescharacteristic
978C22C7×#54611yescharacteristic
979C22C7×#54711yescharacteristic
980C22C7×#54711yescharacteristic
981C22C7×#54711yescharacteristic
982C22C7×#54811yescharacteristic
983C22C7×#55011yescharacteristic
984C22C7×#55311yescharacteristic
985C22C7×#55311yescharacteristic
986C22C7×#55511yescharacteristic
987C4—24no—
988C4—42no—
989C4—44no—
990C4—42no—
991C4—42no—
992C4—42no—
993C4—44no—
994C4—82no—
995C4C7×#38618yescomplemented
996C2—48no—
997C2—44no—
998C2C2×C7×#38611yescharacteristic
999C2C4×C7×#12111yescharacteristic
1000C2C7×#232411yescharacteristic
1001C2C7×D4×C22⋊C411yescharacteristic
1002C2C7×#233911yescharacteristic
1003C2C7×#236111yescharacteristic
1004C2C7×#236311yescharacteristic
1005C2C7×#240711yescharacteristic
1006C2C7×#240811yescharacteristic
1007C2C7×#242011yescharacteristic
1008C2C7×#242211yescharacteristic
1009C2C7×#242711yescharacteristic
1010C2C7×#242811yescharacteristic
1011C2C7×#253511yescharacteristic
1012C2C7×#253711yescharacteristic
subgroupG/H
center, socleC24×C7C24
commutatorC23C23×C4×C7
Frattini, cosocleC24C24×C7
prime radicalC22×C7×#121C2
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C24×C7 ◁ G

Complements

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

NH ≅ G/Ntype
2. C22×C4×C7×D4C2semidirect
3. C2×C7×#390C2semidirect
4. C2×C7×#386C2semidirect
5. C2×C7×#380C2semidirect
6. C2×C4×C7×C22⋊C4C2semidirect
7. C7×#1440C2semidirect
8. C7×#1438C2semidirect
9. C7×C4⋊#95C2semidirect
10. C7×C4⋊#95C2semidirect
11. C7×C22⋊#95C2semidirect
18. C2×C7×#121C4semidirect
45. #13970C7direct (N × H)
59. C22×C7×D4C2×C4semidirect
75. C23×C4×C7C2×C4semidirect
94. C2×C7×C4⋊C4C2×C4semidirect
95. C2×C7×C4⋊C4D4semidirect
115. C2×C7×C22⋊C4C2×C4semidirect
116. C2×C7×C22⋊C4D4semidirect
122. C2×C42×C7D4semidirect
131. C22×C4×D4C2×C7semidirect
132. C2×#390C2×C7semidirect
133. C2×#386C2×C7semidirect
134. C2×#380C2×C7semidirect
135. C2×C4×C22⋊C4C2×C7semidirect
136. #1440C2×C7semidirect
137. #1438C2×C7semidirect
138. C4⋊#95C2×C7semidirect
139. C4⋊#95C2×C7semidirect
140. C22⋊#95C2×C7semidirect
185. C2×C7×D4C22⋊C4semidirect
281. C2×#121C4×C7semidirect
377. C23×C7C4×D4semidirect
458. C2×C4×C7#121semidirect
473. C22×D4C2×C4×C7semidirect
489. C23×C4C2×C4×C7semidirect
508. C2×C4⋊C4C2×C4×C7semidirect
509. C2×C4⋊C4C7×D4semidirect
529. C2×C22⋊C4C2×C4×C7semidirect
530. C2×C22⋊C4C7×D4semidirect
536. C2×C42C7×D4semidirect
617. C4×C7#386semidirect
662. C2×D4C7×C22⋊C4semidirect
838. C23C4×C7×D4semidirect
919. C2×C4C7×#121semidirect
921. C7#13970direct (N × H)
995. C4C7×#386semidirect

Maximal subgroups

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

subgroupindex
C22×C7×#1212
C22×C4×C7×D42
C2×C7×#3902
C2×C7×#3862
C2×C7×#3802
C2×C4×C7×C22⋊C42
C7×#14402
C7×#14382
C7×C4⋊#952
C7×C22⋊#952
#139707