Finite Group Databasebeta

← C7×#13967 #13191183

Subgroups — C7×#13967 #13191183

Order 1792.

4478 conjugacy classes of subgroups.

The subgroup lattice has 1062 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C7×#120C211yesmaximal, characteristic
2C22×C4×C7×D4C211yesmaximal, characteristic, complemented
3C23×C7×C22⋊C4C211yesmaximal, characteristic, complemented
4C2×C7×#386C212yesmaximal, complemented
5C2×C7×#386C211yesmaximal, characteristic, complemented
6C2×C7×#379C211yesmaximal, characteristic, complemented
7C7×#1439C212yesmaximal, complemented
8C7×#1438C212yesmaximal, complemented
9C7×#1437C212yesmaximal, complemented
10C7×C22⋊#95C211yesmaximal, characteristic, complemented
11C7×C22⋊#95C211yesmaximal, characteristic, complemented
12C26×C7C2211yescharacteristic
13C23×C7×D4C2212yes—
14C23×C7×D4C2211yescharacteristic
15C24×C4×C7C2211yescharacteristic
16C24×C4×C7C2211yescharacteristic
17C24×C4×C7C2211yescharacteristic, complemented
18C2×C7×#120—24no—
19C2×C7×#120—24no—
20C2×C7×#120C418yescomplemented
21C2×C4×C7×D4—24no—
22C2×C4×C7×D4—24no—
23C2×C4×C7×D4—24no—
24C22×C7×C4⋊C4C2211yescharacteristic, complemented
25C22×C7×C22⋊C4—24no—
26C22×C7×C22⋊C4—28no—
27C22×C7×C22⋊C4C2212yes—
28C22×C7×C22⋊C4C2211yescharacteristic
29C22×C7×C22⋊C4C2212yes—
30C22×C7×C22⋊C4C2212yes—
31C22×C7×C22⋊C4C2211yescharacteristic
32C22×C7×C22⋊C4C2212yes—
33C22×C7×C22⋊C4C2212yes—
34C22×C7×C22⋊C4C2211yescharacteristic
35C22×C7×C22⋊C4C2211yescharacteristic, complemented
36C22×C7×C22⋊C4C2212yescomplemented
37C22×C42×C7C2211yescharacteristic, complemented
38C7×#386—24no—
39C7×#386—28no—
40C7×#379—24no—
41C2×C7×#95C2212yescomplemented
42C2×C7×#95C2212yescomplemented
43C2×C7×#95C2212yescomplemented
44C2×C7×#95C2212yescomplemented
45C2×C7×#95C2212yescomplemented
46#13967C711yesmaximal, characteristic, direct product factor, Sylow
47C25×C7—24no—
48C25×C7—22no—
49C25×C7—24no—
50C25×C7—22no—
51C25×C7—22no—
52C25×C7—22no—
53C25×C7—22no—
54C25×C7—22no—
55C25×C7—42no—
56C25×C7—42no—
57C25×C7C2×C414yescomplemented
58C25×C7C2311yescharacteristic
59C25×C7C2312yes—
60C25×C7C2311yescharacteristic
61C22×C7×D4—22no—
62C22×C7×D4—22no—
63C22×C7×D4—22no—
64C22×C7×D4—22no—
65C22×C7×D4—24no—
66C22×C7×D4—24no—
67C22×C7×D4—24no—
68C22×C7×D4—24no—
69C22×C7×D4—42no—
70C22×C7×D4—42no—
71C22×C7×D4C2×C414yes—
72C22×C7×D4C2×C418yescomplemented
73C22×C7×D4D414yes—
74C22×C7×D4D414yes—
75C23×C4×C7—22no—
76C23×C4×C7—22no—
77C23×C4×C7—22no—
78C23×C4×C7—22no—
79C23×C4×C7—24no—
80C23×C4×C7—24no—
81C23×C4×C7—22no—
82C23×C4×C7—22no—
83C23×C4×C7—22no—
84C23×C4×C7—22no—
85C23×C4×C7—24no—
86C23×C4×C7—42no—
87C23×C4×C7—42no—
88C23×C4×C7—42no—
89C23×C4×C7D414yescomplemented
90C23×C4×C7C2312yes—
91C23×C4×C7C2312yes—
92C23×C4×C7C2311yescharacteristic
93C23×C4×C7C2312yes—
94C23×C4×C7C2311yescharacteristic
95C23×C4×C7C2311yescharacteristic
96C23×C4×C7C2311yescharacteristic
97C23×C4×C7C2311yescharacteristic
98C7×#120—232no—
99C4×C7×D4—232no—
100C2×C7×C4⋊C4—22no—
101C2×C7×C4⋊C4—22no—
102C2×C7×C4⋊C4—22no—
103C2×C7×C22⋊C4—232no—
104C2×C7×C22⋊C4—24no—
105C2×C7×C22⋊C4—22no—
106C2×C7×C22⋊C4—22no—
107C2×C7×C22⋊C4—22no—
108C2×C7×C22⋊C4—22no—
109C2×C7×C22⋊C4—22no—
110C2×C7×C22⋊C4—24no—
111C2×C7×C22⋊C4—24no—
112C2×C7×C22⋊C4—24no—
113C2×C7×C22⋊C4—24no—
114C2×C7×C22⋊C4—24no—
115C2×C7×C22⋊C4—24no—
116C2×C7×C22⋊C4—22no—
117C2×C7×C22⋊C4—22no—
118C2×C7×C22⋊C4—22no—
119C2×C7×C22⋊C4—24no—
120C2×C7×C22⋊C4—22no—
121C2×C7×C22⋊C4—24no—
122C2×C7×C22⋊C4—24no—
123C2×C7×C22⋊C4—22no—
124C2×C7×C22⋊C4—24no—
125C2×C7×C22⋊C4—24no—
126C2×C7×C22⋊C4—24no—
127C2×C7×C22⋊C4—42no—
128C2×C7×C22⋊C4—42no—
129C2×C7×C22⋊C4—42no—
130C2×C7×C22⋊C4C2×C414yescomplemented
131C2×C7×C22⋊C4C2×C418yescomplemented
132C2×C7×C22⋊C4D418yescomplemented
133C2×C7×C22⋊C4D414yescomplemented
134C2×C42×C7—22no—
135C2×C42×C7—22no—
136C2×C42×C7—22no—
137C7×#95—24no—
138C7×#95—24no—
139C7×#95—24no—
140C7×#95—42no—
141C7×#95—42no—
142C22×#120C2×C711yescharacteristic
143C22×C4×D4C2×C711yescharacteristic, complemented
144C23×C22⋊C4C2×C711yescharacteristic, complemented
145C2×#386C2×C712yescomplemented
146C2×#386C2×C711yescharacteristic, complemented
147C2×#379C2×C711yescharacteristic, complemented
148#1439C2×C712yescomplemented
149#1438C2×C712yescomplemented
150#1437C2×C712yescomplemented
151C22⋊#95C2×C711yescharacteristic, complemented
152C22⋊#95C2×C711yescharacteristic, complemented
153C24×C7—22no—
154C24×C7—22no—
155C24×C7—22no—
156C24×C7—22no—
157C24×C7—28no—
158C24×C7—28no—
159C24×C7—216no—
160C24×C7—28no—
161C24×C7—216no—
162C24×C7—22no—
163C24×C7—22no—
164C24×C7—22no—
165C24×C7—21no—
166C24×C7—21no—
167C24×C7—22no—
168C24×C7—22no—
169C24×C7—22no—
170C24×C7—21no—
171C24×C7—21no—
172C24×C7—22no—
173C24×C7—22no—
174C24×C7—22no—
175C24×C7—22no—
176C24×C7—22no—
177C24×C7—22no—
178C24×C7—22no—
179C24×C7—22no—
180C24×C7—22no—
181C24×C7—22no—
182C24×C7—28no—
183C24×C7—28no—
184C24×C7—48no—
185C24×C7—48no—
186C24×C7—48no—
187C24×C7—48no—
188C24×C7—48no—
189C24×C7—48no—
190C24×C7—48no—
191C24×C7—48no—
192C24×C7—48no—
193C24×C7—44no—
194C24×C7—44no—
195C24×C7—48no—
196C24×C7—44no—
197C24×C7—44no—
198C24×C7—44no—
199C24×C7—44no—
200C24×C7C22×C412yes—
201C24×C7C22×C414yes—
202C24×C7C22×C412yes—
203C24×C7C2×D412yes—
204C24×C7C2×D412yes—
205C24×C7C2×D414yes—
206C24×C7C2×D412yes—
207C24×C7C2×D412yes—
208C24×C7C2×D412yes—
209C24×C7C2×D412yes—
210C24×C7#4114yes—
211C24×C7#4112yes—
212C24×C7#4112yes—
213C24×C7C2411yescharacteristic
214C2×C7×D4—28no—
215C2×C7×D4—28no—
216C2×C7×D4—28no—
217C2×C7×D4—28no—
218C2×C7×D4—28no—
219C2×C7×D4—28no—
220C2×C7×D4—216no—
221C2×C7×D4—216no—
222C2×C7×D4—48no—
223C2×C7×D4—48no—
224C2×C7×D4—48no—
225C2×C7×D4—48no—
226C2×C7×D4—48no—
227C2×C7×D4C22⋊C4116yescomplemented
228C22×C4×C7—21no—
229C22×C4×C7—21no—
230C22×C4×C7—21no—
231C22×C4×C7—21no—
232C22×C4×C7—21no—
233C22×C4×C7—21no—
234C22×C4×C7—22no—
235C22×C4×C7—28no—
236C22×C4×C7—28no—
237C22×C4×C7—28no—
238C22×C4×C7—22no—
239C22×C4×C7—22no—
240C22×C4×C7—22no—
241C22×C4×C7—21no—
242C22×C4×C7—21no—
243C22×C4×C7—22no—
244C22×C4×C7—22no—
245C22×C4×C7—22no—
246C22×C4×C7—22no—
247C22×C4×C7—22no—
248C22×C4×C7—21no—
249C22×C4×C7—21no—
250C22×C4×C7—21no—
251C22×C4×C7—21no—
252C22×C4×C7—22no—
253C22×C4×C7—22no—
254C22×C4×C7—22no—
255C22×C4×C7—22no—
256C22×C4×C7—22no—
257C22×C4×C7—22no—
258C22×C4×C7—22no—
259C22×C4×C7—22no—
260C22×C4×C7—22no—
261C22×C4×C7—22no—
262C22×C4×C7—28no—
263C22×C4×C7—22no—
264C22×C4×C7—22no—
265C22×C4×C7—22no—
266C22×C4×C7—22no—
267C22×C4×C7—22no—
268C22×C4×C7—22no—
269C22×C4×C7—22no—
270C22×C4×C7—44no—
271C22×C4×C7—48no—
272C22×C4×C7—48no—
273C22×C4×C7—48no—
274C22×C4×C7—48no—
275C22×C4×C7—48no—
276C22×C4×C7—48no—
277C22×C4×C7—44no—
278C22×C4×C7—44no—
279C22×C4×C7—44no—
280C22×C4×C7—44no—
281C22×C4×C7C22×C414yes—
282C22×C4×C7C22×C412yes—
283C22×C4×C7C2×D414yes—
284C22×C4×C7C2×D412yes—
285C22×C4×C7C2×D412yes—
286C22×C4×C7C2×D412yes—
287C22×C4×C7C2×D412yes—
288C22×C4×C7C2×D412yes—
289C22×C4×C7C2×D414yes—
290C22×C4×C7C2×D412yes—
291C7×C4⋊C4—28no—
292C7×C22⋊C4—216no—
293C7×C22⋊C4—28no—
294C7×C22⋊C4—28no—
295C7×C22⋊C4—28no—
296C7×C22⋊C4—216no—
297C7×C22⋊C4—216no—
298C7×C22⋊C4—48no—
299C7×C22⋊C4—48no—
300C7×C22⋊C4—48no—
301C7×C22⋊C4—44no—
302C42×C7—28no—
303C26C22×C711yescharacteristic
304C23×D4C22×C712yes—
305C23×D4C22×C711yescharacteristic
306C24×C4C22×C711yescharacteristic
307C24×C4C22×C711yescharacteristic
308C24×C4C22×C711yescharacteristic, complemented
309C2×#120—24no—
310C2×#120—24no—
311C2×#120C4×C718yescomplemented
312C2×C4×D4—24no—
313C2×C4×D4—24no—
314C2×C4×D4—24no—
315C22×C4⋊C4C22×C711yescharacteristic, complemented
316C22×C22⋊C4—24no—
317C22×C22⋊C4—28no—
318C22×C22⋊C4C22×C712yes—
319C22×C22⋊C4C22×C711yescharacteristic
320C22×C22⋊C4C22×C712yes—
321C22×C22⋊C4C22×C712yes—
322C22×C22⋊C4C22×C711yescharacteristic
323C22×C22⋊C4C22×C712yes—
324C22×C22⋊C4C22×C712yes—
325C22×C22⋊C4C22×C711yescharacteristic
326C22×C22⋊C4C22×C711yescharacteristic, complemented
327C22×C22⋊C4C22×C712yescomplemented
328C22×C42C22×C711yescharacteristic, complemented
329#386—24no—
330#386—28no—
331#379—24no—
332C2×#95C22×C712yescomplemented
333C2×#95C22×C712yescomplemented
334C2×#95C22×C712yescomplemented
335C2×#95C22×C712yescomplemented
336C2×#95C22×C712yescomplemented
337C23×C7—24no—
338C23×C7—24no—
339C23×C7—22no—
340C23×C7—22no—
341C23×C7—24no—
342C23×C7—22no—
343C23×C7—22no—
344C23×C7—24no—
345C23×C7—24no—
346C23×C7—24no—
347C23×C7—24no—
348C23×C7—24no—
349C23×C7—24no—
350C23×C7—24no—
351C23×C7—24no—
352C23×C7—24no—
353C23×C7—232no—
354C23×C7—24no—
355C23×C7—24no—
356C23×C7—22no—
357C23×C7—22no—
358C23×C7—24no—
359C23×C7—24no—
360C23×C7—24no—
361C23×C7—24no—
362C23×C7—24no—
363C23×C7—24no—
364C23×C7—24no—
365C23×C7—22no—
366C23×C7—22no—
367C23×C7—22no—
368C23×C7—22no—
369C23×C7—24no—
370C23×C7—24no—
371C23×C7—24no—
372C23×C7—24no—
373C23×C7—24no—
374C23×C7—24no—
375C23×C7—24no—
376C23×C7—24no—
377C23×C7—24no—
378C23×C7—24no—
379C23×C7—24no—
380C23×C7—24no—
381C23×C7—24no—
382C23×C7—24no—
383C23×C7—24no—
384C23×C7—432no—
385C23×C7—432no—
386C23×C7—416no—
387C23×C7—416no—
388C23×C7—416no—
389C23×C7—416no—
390C23×C7—432no—
391C23×C7—432no—
392C23×C7—416no—
393C23×C7—41no—
394C23×C7—42no—
395C23×C7—42no—
396C23×C7—42no—
397C23×C7—42no—
398C23×C7—41no—
399C23×C7—42no—
400C23×C7—41no—
401C23×C7—42no—
402C23×C7—41no—
403C23×C7—42no—
404C23×C7—42no—
405C23×C7—42no—
406C23×C7—42no—
407C23×C7—42no—
408C23×C7—42no—
409C23×C7—42no—
410C23×C7—42no—
411C23×C7—42no—
412C23×C7—42no—
413C23×C7—42no—
414C23×C7—42no—
415C23×C7—42no—
416C23×C7—42no—
417C23×C7—42no—
418C23×C7—42no—
419C23×C7—416no—
420C23×C7C2×C22⋊C414yes—
421C23×C7C2×C22⋊C414yescomplemented
422C23×C7C4×D414yes—
423C23×C7C4×D414yes—
424C23×C7C4×D418yescomplemented
425C23×C7#12014yes—
426C23×C7#12114yes—
427C23×C7#12114yes—
428C23×C7#12314yes—
429C23×C7C23×C411yescharacteristic
430C23×C7C22×D411yescharacteristic
431C23×C7C22×D411yescharacteristic
432C23×C7C22×D411yescharacteristic
433C23×C7C22×D411yescharacteristic
434C23×C7C22×D412yes—
435C23×C7C2×#4111yescharacteristic
436C23×C7C2×#4111yescharacteristic
437C23×C7C2×#4112yes—
438C23×C7H(5,𝔽2)12yes—
439C23×C7H(5,𝔽2)12yes—
440C7×D4—232no—
441C7×D4—432no—
442C2×C4×C7—22no—
443C2×C4×C7—22no—
444C2×C4×C7—22no—
445C2×C4×C7—22no—
446C2×C4×C7—22no—
447C2×C4×C7—22no—
448C2×C4×C7—22no—
449C2×C4×C7—22no—
450C2×C4×C7—24no—
451C2×C4×C7—24no—
452C2×C4×C7—24no—
453C2×C4×C7—24no—
454C2×C4×C7—24no—
455C2×C4×C7—22no—
456C2×C4×C7—22no—
457C2×C4×C7—24no—
458C2×C4×C7—22no—
459C2×C4×C7—22no—
460C2×C4×C7—22no—
461C2×C4×C7—24no—
462C2×C4×C7—24no—
463C2×C4×C7—24no—
464C2×C4×C7—24no—
465C2×C4×C7—416no—
466C2×C4×C7—416no—
467C2×C4×C7—416no—
468C2×C4×C7—41no—
469C2×C4×C7—42no—
470C2×C4×C7—41no—
471C2×C4×C7—41no—
472C2×C4×C7—41no—
473C2×C4×C7—42no—
474C2×C4×C7—42no—
475C2×C4×C7—42no—
476C2×C4×C7—42no—
477C2×C4×C7—42no—
478C2×C4×C7—42no—
479C2×C4×C7—42no—
480C2×C4×C7—42no—
481C2×C4×C7—42no—
482C2×C4×C7—42no—
483C2×C4×C7—42no—
484C2×C4×C7—42no—
485C2×C4×C7—42no—
486C2×C4×C7—42no—
487C2×C4×C7—42no—
488C2×C4×C7—42no—
489C2×C4×C7—42no—
490C2×C4×C7—42no—
491C2×C4×C7C2×C22⋊C414yescomplemented
492C2×C4×C7#12014yescomplemented
493C25—24no—
494C25—22no—
495C25—24no—
496C25—22no—
497C25—22no—
498C25—22no—
499C25—22no—
500C25—22no—
501C25—42no—
502C25—42no—
503C25C2×C4×C714yescomplemented
504C25C23×C711yescharacteristic
505C25C23×C712yes—
506C25C23×C711yescharacteristic
507C22×D4—22no—
508C22×D4—22no—
509C22×D4—22no—
510C22×D4—22no—
511C22×D4—24no—
512C22×D4—24no—
513C22×D4—24no—
514C22×D4—24no—
515C22×D4—42no—
516C22×D4—42no—
517C22×D4C2×C4×C714yes—
518C22×D4C2×C4×C718yescomplemented
519C22×D4C7×D414yes—
520C22×D4C7×D414yes—
521C23×C4—22no—
522C23×C4—22no—
523C23×C4—22no—
524C23×C4—22no—
525C23×C4—24no—
526C23×C4—24no—
527C23×C4—22no—
528C23×C4—22no—
529C23×C4—22no—
530C23×C4—22no—
531C23×C4—24no—
532C23×C4—42no—
533C23×C4—42no—
534C23×C4—42no—
535C23×C4C7×D414yescomplemented
536C23×C4C23×C712yes—
537C23×C4C23×C712yes—
538C23×C4C23×C711yescharacteristic
539C23×C4C23×C711yescharacteristic
540C23×C4C23×C711yescharacteristic
541C23×C4C23×C712yes—
542C23×C4C23×C711yescharacteristic
543C23×C4C23×C711yescharacteristic
544#120—232no—
545C4×D4—232no—
546C2×C4⋊C4—22no—
547C2×C4⋊C4—22no—
548C2×C4⋊C4—22no—
549C2×C22⋊C4—232no—
550C2×C22⋊C4—24no—
551C2×C22⋊C4—22no—
552C2×C22⋊C4—22no—
553C2×C22⋊C4—22no—
554C2×C22⋊C4—22no—
555C2×C22⋊C4—22no—
556C2×C22⋊C4—24no—
557C2×C22⋊C4—24no—
558C2×C22⋊C4—24no—
559C2×C22⋊C4—24no—
560C2×C22⋊C4—24no—
561C2×C22⋊C4—24no—
562C2×C22⋊C4—22no—
563C2×C22⋊C4—22no—
564C2×C22⋊C4—22no—
565C2×C22⋊C4—24no—
566C2×C22⋊C4—22no—
567C2×C22⋊C4—24no—
568C2×C22⋊C4—24no—
569C2×C22⋊C4—22no—
570C2×C22⋊C4—24no—
571C2×C22⋊C4—24no—
572C2×C22⋊C4—24no—
573C2×C22⋊C4—42no—
574C2×C22⋊C4—42no—
575C2×C22⋊C4—42no—
576C2×C22⋊C4C2×C4×C714yescomplemented
577C2×C22⋊C4C2×C4×C718yescomplemented
578C2×C22⋊C4C7×D418yescomplemented
579C2×C22⋊C4C7×D414yescomplemented
580C2×C42—22no—
581C2×C42—22no—
582C2×C42—22no—
583#95—24no—
584#95—24no—
585#95—24no—
586#95—42no—
587#95—42no—
588C22×C7—24no—
589C22×C7—28no—
590C22×C7—28no—
591C22×C7—24no—
592C22×C7—24no—
593C22×C7—24no—
594C22×C7—28no—
595C22×C7—28no—
596C22×C7—24no—
597C22×C7—24no—
598C22×C7—28no—
599C22×C7—28no—
600C22×C7—28no—
601C22×C7—24no—
602C22×C7—28no—
603C22×C7—464no—
604C22×C7—42no—
605C22×C7—44no—
606C22×C7—44no—
607C22×C7—44no—
608C22×C7—44no—
609C22×C7—42no—
610C22×C7—44no—
611C22×C7—42no—
612C22×C7—44no—
613C22×C7—42no—
614C22×C7—44no—
615C22×C7—44no—
616C22×C7—44no—
617C22×C7—44no—
618C22×C7—44no—
619C22×C7—44no—
620C22×C7—44no—
621C22×C7—42no—
622C22×C7—44no—
623C22×C7—44no—
624C22×C7—42no—
625C22×C7#38618yescomplemented
626C22×C7C22×C22⋊C411yescharacteristic
627C22×C7C2×C4×D411yescharacteristic
628C22×C7C2×C4×D412yes—
629C22×C7C2×C4×D411yescharacteristic
630C22×C7#51812yes—
631C22×C7C2×#12011yescharacteristic
632C22×C7C2×#12011yescharacteristic
633C22×C7C2×#12111yescharacteristic
634C22×C7C2×#12111yescharacteristic
635C22×C7C2×#12311yescharacteristic
636C22×C7#52511yescharacteristic
637C22×C7#52512yes—
638C22×C7#53411yescharacteristic
639C22×C7#53511yescharacteristic
640C22×C7#53812yes—
641C22×C7D4212yes—
642C22×C7D4212yes—
643C22×C7D4212yes—
644C22×C7#54612yes—
645C22×C7#54612yes—
646C22×C7#54612yes—
647C22×C7#54612yes—
648C22×C7#55112yes—
649C4×C7—24no—
650C4×C7—24no—
651C4×C7—44no—
652C4×C7—42no—
653C4×C7—42no—
654C4×C7—42no—
655C4×C7—44no—
656C4×C7—82no—
657C24—22no—
658C24—22no—
659C24—22no—
660C24—22no—
661C24—28no—
662C24—28no—
663C24—216no—
664C24—28no—
665C24—216no—
666C24—22no—
667C24—22no—
668C24—22no—
669C24—21no—
670C24—21no—
671C24—22no—
672C24—22no—
673C24—22no—
674C24—21no—
675C24—21no—
676C24—22no—
677C24—22no—
678C24—22no—
679C24—22no—
680C24—22no—
681C24—22no—
682C24—22no—
683C24—22no—
684C24—22no—
685C24—22no—
686C24—28no—
687C24—28no—
688C24—48no—
689C24—48no—
690C24—48no—
691C24—48no—
692C24—48no—
693C24—48no—
694C24—48no—
695C24—48no—
696C24—48no—
697C24—44no—
698C24—44no—
699C24—48no—
700C24—44no—
701C24—44no—
702C24—44no—
703C24—44no—
704C24C22×C4×C712yes—
705C24C22×C4×C714yes—
706C24C22×C4×C712yes—
707C24C2×C7×D412yes—
708C24C2×C7×D412yes—
709C24C2×C7×D414yes—
710C24C2×C7×D412yes—
711C24C2×C7×D412yes—
712C24C2×C7×D412yes—
713C24C2×C7×D412yes—
714C24C7×#4114yes—
715C24C7×#4112yes—
716C24C7×#4112yes—
717C24C24×C711yescharacteristic
718C2×D4—28no—
719C2×D4—28no—
720C2×D4—28no—
721C2×D4—28no—
722C2×D4—28no—
723C2×D4—28no—
724C2×D4—216no—
725C2×D4—216no—
726C2×D4—48no—
727C2×D4—48no—
728C2×D4—48no—
729C2×D4—48no—
730C2×D4—48no—
731C2×D4C7×C22⋊C4116yescomplemented
732C22×C4—21no—
733C22×C4—21no—
734C22×C4—21no—
735C22×C4—21no—
736C22×C4—21no—
737C22×C4—21no—
738C22×C4—22no—
739C22×C4—28no—
740C22×C4—28no—
741C22×C4—28no—
742C22×C4—22no—
743C22×C4—22no—
744C22×C4—22no—
745C22×C4—21no—
746C22×C4—21no—
747C22×C4—22no—
748C22×C4—22no—
749C22×C4—22no—
750C22×C4—22no—
751C22×C4—22no—
752C22×C4—21no—
753C22×C4—21no—
754C22×C4—21no—
755C22×C4—21no—
756C22×C4—22no—
757C22×C4—22no—
758C22×C4—22no—
759C22×C4—22no—
760C22×C4—22no—
761C22×C4—22no—
762C22×C4—22no—
763C22×C4—22no—
764C22×C4—22no—
765C22×C4—22no—
766C22×C4—28no—
767C22×C4—22no—
768C22×C4—22no—
769C22×C4—22no—
770C22×C4—22no—
771C22×C4—22no—
772C22×C4—22no—
773C22×C4—22no—
774C22×C4—44no—
775C22×C4—48no—
776C22×C4—48no—
777C22×C4—48no—
778C22×C4—48no—
779C22×C4—48no—
780C22×C4—48no—
781C22×C4—44no—
782C22×C4—44no—
783C22×C4—44no—
784C22×C4—44no—
785C22×C4C22×C4×C714yes—
786C22×C4C22×C4×C712yes—
787C22×C4C2×C7×D414yes—
788C22×C4C2×C7×D412yes—
789C22×C4C2×C7×D412yes—
790C22×C4C2×C7×D412yes—
791C22×C4C2×C7×D412yes—
792C22×C4C2×C7×D412yes—
793C22×C4C2×C7×D414yes—
794C22×C4C2×C7×D412yes—
795C4⋊C4—28no—
796C22⋊C4—216no—
797C22⋊C4—28no—
798C22⋊C4—28no—
799C22⋊C4—28no—
800C22⋊C4—216no—
801C22⋊C4—216no—
802C22⋊C4—48no—
803C22⋊C4—48no—
804C22⋊C4—48no—
805C22⋊C4—44no—
806C42—28no—
807C2×C7—28no—
808C2×C7—44no—
809C2×C7—48no—
810C2×C7C2×#38611yescharacteristic
811C2×C7C4×#12011yescharacteristic
812C2×C7#232111yescharacteristic
813C2×C7D4×C22⋊C412yes—
814C2×C7#235812yes—
815C2×C7#240311yescharacteristic
816C2×C7#240411yescharacteristic
817C2×C7#240811yescharacteristic
818C2×C7#241812yes—
819C2×C7#242412yes—
820C2×C7#253411yescharacteristic
821C23—24no—
822C23—24no—
823C23—22no—
824C23—22no—
825C23—24no—
826C23—22no—
827C23—22no—
828C23—24no—
829C23—24no—
830C23—24no—
831C23—24no—
832C23—24no—
833C23—24no—
834C23—24no—
835C23—24no—
836C23—24no—
837C23—232no—
838C23—24no—
839C23—22no—
840C23—22no—
841C23—24no—
842C23—24no—
843C23—24no—
844C23—24no—
845C23—24no—
846C23—24no—
847C23—24no—
848C23—24no—
849C23—22no—
850C23—22no—
851C23—22no—
852C23—22no—
853C23—24no—
854C23—24no—
855C23—24no—
856C23—24no—
857C23—24no—
858C23—24no—
859C23—24no—
860C23—24no—
861C23—24no—
862C23—24no—
863C23—24no—
864C23—24no—
865C23—24no—
866C23—24no—
867C23—24no—
868C23—432no—
869C23—432no—
870C23—416no—
871C23—416no—
872C23—416no—
873C23—432no—
874C23—432no—
875C23—416no—
876C23—416no—
877C23—41no—
878C23—42no—
879C23—42no—
880C23—42no—
881C23—416no—
882C23—42no—
883C23—41no—
884C23—42no—
885C23—41no—
886C23—42no—
887C23—41no—
888C23—42no—
889C23—42no—
890C23—42no—
891C23—42no—
892C23—42no—
893C23—42no—
894C23—42no—
895C23—42no—
896C23—42no—
897C23—42no—
898C23—42no—
899C23—42no—
900C23—42no—
901C23—42no—
902C23—42no—
903C23—42no—
904C23C2×C7×C22⋊C414yes—
905C23C2×C7×C22⋊C414yescomplemented
906C23C4×C7×D414yes—
907C23C4×C7×D414yes—
908C23C4×C7×D418yescomplemented
909C23C7×#12014yes—
910C23C7×#12114yes—
911C23C7×#12114yes—
912C23C7×#12314yes—
913C23C23×C4×C711yescharacteristic
914C23C22×C7×D411yescharacteristic
915C23C22×C7×D411yescharacteristic
916C23C22×C7×D411yescharacteristic
917C23C22×C7×D411yescharacteristic
918C23C22×C7×D412yes—
919C23C2×C7×#4111yescharacteristic
920C23C2×C7×#4111yescharacteristic
921C23C2×C7×#4112yes—
922C23C7×H(5,𝔽2)12yes—
923C23C7×H(5,𝔽2)12yes—
924D4—232no—
925D4—432no—
926C2×C4—22no—
927C2×C4—22no—
928C2×C4—22no—
929C2×C4—22no—
930C2×C4—22no—
931C2×C4—22no—
932C2×C4—22no—
933C2×C4—22no—
934C2×C4—24no—
935C2×C4—24no—
936C2×C4—24no—
937C2×C4—24no—
938C2×C4—24no—
939C2×C4—22no—
940C2×C4—22no—
941C2×C4—24no—
942C2×C4—22no—
943C2×C4—22no—
944C2×C4—22no—
945C2×C4—24no—
946C2×C4—24no—
947C2×C4—24no—
948C2×C4—24no—
949C2×C4—416no—
950C2×C4—416no—
951C2×C4—416no—
952C2×C4—41no—
953C2×C4—42no—
954C2×C4—41no—
955C2×C4—41no—
956C2×C4—41no—
957C2×C4—42no—
958C2×C4—42no—
959C2×C4—42no—
960C2×C4—42no—
961C2×C4—42no—
962C2×C4—42no—
963C2×C4—42no—
964C2×C4—42no—
965C2×C4—42no—
966C2×C4—42no—
967C2×C4—42no—
968C2×C4—42no—
969C2×C4—42no—
970C2×C4—42no—
971C2×C4—42no—
972C2×C4—42no—
973C2×C4—42no—
974C2×C4—42no—
975C2×C4C2×C7×C22⋊C414yescomplemented
976C2×C4C7×#12014yescomplemented
977C7#1396711yescharacteristic, direct product factor, Sylow
978C22—24no—
979C22—24no—
980C22—24no—
981C22—28no—
982C22—28no—
983C22—24no—
984C22—24no—
985C22—24no—
986C22—28no—
987C22—28no—
988C22—24no—
989C22—28no—
990C22—28no—
991C22—28no—
992C22—28no—
993C22—464no—
994C22—42no—
995C22—44no—
996C22—44no—
997C22—42no—
998C22—44no—
999C22—42no—
1000C22—44no—
1001C22—44no—
1002C22—44no—
1003C22—44no—
1004C22—44no—
1005C22—44no—
1006C22—44no—
1007C22—42no—
1008C22—44no—
1009C22—42no—
1010C22—44no—
1011C22—42no—
1012C22—44no—
1013C22—44no—
1014C22—44no—
1015C22C7×#38618yescomplemented
1016C22C22×C7×C22⋊C411yescharacteristic
1017C22C2×C4×C7×D411yescharacteristic
1018C22C2×C4×C7×D411yescharacteristic
1019C22C2×C4×C7×D412yes—
1020C22C7×#51812yes—
1021C22C2×C7×#12011yescharacteristic
1022C22C2×C7×#12011yescharacteristic
1023C22C2×C7×#12111yescharacteristic
1024C22C2×C7×#12111yescharacteristic
1025C22C2×C7×#12311yescharacteristic
1026C22C7×#52511yescharacteristic
1027C22C7×#52512yes—
1028C22C7×#53411yescharacteristic
1029C22C7×#53511yescharacteristic
1030C22C7×#53812yes—
1031C22C7×D4212yes—
1032C22C7×D4212yes—
1033C22C7×D4212yes—
1034C22C7×#54612yes—
1035C22C7×#54612yes—
1036C22C7×#54612yes—
1037C22C7×#54612yes—
1038C22C7×#55112yes—
1039C4—24no—
1040C4—24no—
1041C4—42no—
1042C4—42no—
1043C4—42no—
1044C4—44no—
1045C4—44no—
1046C4—82no—
1047C2—28no—
1048C2—48no—
1049C2—44no—
1050C2C2×C7×#38611yescharacteristic
1051C2C4×C7×#12011yescharacteristic
1052C2C7×#232111yescharacteristic
1053C2C7×D4×C22⋊C412yes—
1054C2C7×#235812yes—
1055C2C7×#240311yescharacteristic
1056C2C7×#240411yescharacteristic
1057C2C7×#240811yescharacteristic
1058C2C7×#241812yes—
1059C2C7×#242412yes—
1060C2C7×#253411yescharacteristic
subgroupG/H
center, socleC24×C7C24
commutatorC23C23×C4×C7
Frattini, cosocleC24C24×C7
prime radicalC22×C7×#120C2
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. C23×C7×C22⋊C4C2semidirect
4. C2×C7×#386C2semidirect
5. C2×C7×#386C2semidirect
6. C2×C7×#379C2semidirect
7. C7×#1439C2semidirect
8. C7×#1438C2semidirect
9. C7×#1437C2semidirect
10. C7×C22⋊#95C2semidirect
11. C7×C22⋊#95C2semidirect
17. C24×C4×C7C22semidirect
20. C2×C7×#120C4semidirect
24. C22×C7×C4⋊C4C22semidirect
35. C22×C7×C22⋊C4C22semidirect
36. C22×C7×C22⋊C4C22semidirect
37. C22×C42×C7C22semidirect
41. C2×C7×#95C22semidirect
42. C2×C7×#95C22semidirect
43. C2×C7×#95C22semidirect
44. C2×C7×#95C22semidirect
45. C2×C7×#95C22semidirect
46. #13967C7direct (N × H)
57. C25×C7C2×C4semidirect
72. C22×C7×D4C2×C4semidirect
89. C23×C4×C7D4semidirect
130. C2×C7×C22⋊C4C2×C4semidirect
131. C2×C7×C22⋊C4C2×C4semidirect
132. C2×C7×C22⋊C4D4semidirect
133. C2×C7×C22⋊C4D4semidirect
143. C22×C4×D4C2×C7semidirect
144. C23×C22⋊C4C2×C7semidirect
145. C2×#386C2×C7semidirect
146. C2×#386C2×C7semidirect
147. C2×#379C2×C7semidirect
148. #1439C2×C7semidirect
149. #1438C2×C7semidirect
150. #1437C2×C7semidirect
151. C22⋊#95C2×C7semidirect
152. C22⋊#95C2×C7semidirect
227. C2×C7×D4C22⋊C4semidirect
308. C24×C4C22×C7semidirect
311. C2×#120C4×C7semidirect
315. C22×C4⋊C4C22×C7semidirect
326. C22×C22⋊C4C22×C7semidirect
327. C22×C22⋊C4C22×C7semidirect
328. C22×C42C22×C7semidirect
332. C2×#95C22×C7semidirect
333. C2×#95C22×C7semidirect
334. C2×#95C22×C7semidirect
335. C2×#95C22×C7semidirect
336. C2×#95C22×C7semidirect
421. C23×C7C2×C22⋊C4semidirect
424. C23×C7C4×D4semidirect
491. C2×C4×C7C2×C22⋊C4semidirect
492. C2×C4×C7#120semidirect
503. C25C2×C4×C7semidirect
518. C22×D4C2×C4×C7semidirect
535. C23×C4C7×D4semidirect
576. C2×C22⋊C4C2×C4×C7semidirect
577. C2×C22⋊C4C2×C4×C7semidirect
578. C2×C22⋊C4C7×D4semidirect
579. C2×C22⋊C4C7×D4semidirect
625. C22×C7#386semidirect
731. C2×D4C7×C22⋊C4semidirect
905. C23C2×C7×C22⋊C4semidirect
908. C23C4×C7×D4semidirect
975. C2×C4C2×C7×C22⋊C4semidirect
976. C2×C4C7×#120semidirect
977. C7#13967direct (N × H)
1015. C22C7×#386semidirect

Maximal subgroups

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

subgroupindex
C22×C7×#1202
C22×C4×C7×D42
C23×C7×C22⋊C42
C2×C7×#3862
C2×C7×#3792
C7×#14392
C7×#14382
C7×#14372
C7×C22⋊#952
#139677