Finite Group Databasebeta

← C7×#13995 #13191211

Subgroups — C7×#13995 #13191211

Order 1792.

4210 conjugacy classes of subgroups.

The subgroup lattice has 1042 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C7×#120C211yesmaximal, characteristic
2C23×C7×C22⋊C4C211yesmaximal, characteristic, complemented
3C2×C7×#390C212yesmaximal, complemented
4C2×C7×#386C211yesmaximal, characteristic, complemented
5C2×C7×#386C211yesmaximal, characteristic, complemented
6C2×C7×#385C211yesmaximal, characteristic, complemented
7C2×C7×#379C211yesmaximal, characteristic, complemented
8C2×C4×C7×C22⋊C4C211yesmaximal, characteristic, complemented
9C7×#1439C212yesmaximal, complemented
10C7×#1438C212yesmaximal, complemented
11C7×#1437C212yesmaximal, complemented
12C26×C7C2211yescharacteristic
13C23×C7×D4C2211yescharacteristic
14C23×C7×D4C2212yes—
15C24×C4×C7C2211yescharacteristic
16C24×C4×C7C2211yescharacteristic
17C2×C7×#120—24no—
18C2×C7×#120—24no—
19C2×C7×#120C418yescomplemented
20C22×C7×C4⋊C4C2212yescomplemented
21C22×C7×C22⋊C4—24no—
22C22×C7×C22⋊C4—28no—
23C22×C7×C22⋊C4C2212yes—
24C22×C7×C22⋊C4C2211yescharacteristic
25C22×C7×C22⋊C4C2212yes—
26C22×C7×C22⋊C4C2212yes—
27C22×C7×C22⋊C4C2212yes—
28C22×C7×C22⋊C4C2212yes—
29C22×C7×C22⋊C4C2211yescharacteristic
30C22×C7×C22⋊C4C2211yescharacteristic
31C22×C7×C22⋊C4C2211yescharacteristic, complemented
32C22×C7×C22⋊C4C2212yescomplemented
33C22×C7×C22⋊C4C2211yescharacteristic, complemented
34C22×C42×C7C2212yescomplemented
35C7×#390—28no—
36C7×#386—24no—
37C7×#386—24no—
38C7×#385—24no—
39C7×#379—24no—
40C4×C7×C22⋊C4—24no—
41C2×C7×#95C2212yescomplemented
42C2×C7×#95C2212yescomplemented
43C2×C7×#95C2211yescharacteristic, complemented
44C2×C7×#95C2212yescomplemented
45C2×C7×#95C2211yescharacteristic, complemented
46#13995C711yesmaximal, 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×C414yes—
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—22no—
68C22×C7×D4—22no—
69C22×C7×D4—24no—
70C22×C7×D4—24no—
71C22×C7×D4—42no—
72C22×C7×D4—42no—
73C22×C7×D4C2×C414yes—
74C22×C7×D4C2×C418yescomplemented
75C23×C4×C7—22no—
76C23×C4×C7—22no—
77C23×C4×C7—22no—
78C23×C4×C7—24no—
79C23×C4×C7—24no—
80C23×C4×C7—22no—
81C23×C4×C7—22no—
82C23×C4×C7—42no—
83C23×C4×C7—42no—
84C23×C4×C7D414yescomplemented
85C23×C4×C7C2311yescharacteristic
86C23×C4×C7C2311yescharacteristic
87C23×C4×C7C2311yescharacteristic
88C23×C4×C7C2312yes—
89C23×C4×C7C2311yescharacteristic
90C23×C4×C7C2312yes—
91C23×C4×C7C2312yes—
92C23×C4×C7C2311yescharacteristic
93C7×#120—232no—
94C2×C7×C4⋊C4—24no—
95C2×C7×C4⋊C4—24no—
96C2×C7×C4⋊C4—42no—
97C2×C7×C22⋊C4—232no—
98C2×C7×C22⋊C4—24no—
99C2×C7×C22⋊C4—22no—
100C2×C7×C22⋊C4—22no—
101C2×C7×C22⋊C4—24no—
102C2×C7×C22⋊C4—24no—
103C2×C7×C22⋊C4—24no—
104C2×C7×C22⋊C4—24no—
105C2×C7×C22⋊C4—24no—
106C2×C7×C22⋊C4—24no—
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—22no—
116C2×C7×C22⋊C4—22no—
117C2×C7×C22⋊C4—24no—
118C2×C7×C22⋊C4—24no—
119C2×C7×C22⋊C4—42no—
120C2×C7×C22⋊C4—42no—
121C2×C7×C22⋊C4—42no—
122C2×C7×C22⋊C4—42no—
123C2×C7×C22⋊C4C2×C414yes—
124C2×C7×C22⋊C4C2×C418yescomplemented
125C2×C7×C22⋊C4D414yes—
126C2×C7×C22⋊C4D414yes—
127C2×C7×C22⋊C4D418yescomplemented
128C2×C7×C22⋊C4D414yescomplemented
129C2×C42×C7—24no—
130C2×C42×C7—24no—
131C2×C42×C7—42no—
132C7×#95—24no—
133C7×#95—24no—
134C7×#95—24no—
135C7×#95—22no—
136C7×#95—22no—
137C22×#120C2×C711yescharacteristic
138C23×C22⋊C4C2×C711yescharacteristic, complemented
139C2×#390C2×C712yescomplemented
140C2×#386C2×C711yescharacteristic, complemented
141C2×#386C2×C711yescharacteristic, complemented
142C2×#385C2×C711yescharacteristic, complemented
143C2×#379C2×C711yescharacteristic, complemented
144C2×C4×C22⋊C4C2×C711yescharacteristic, complemented
145#1439C2×C712yescomplemented
146#1438C2×C712yescomplemented
147#1437C2×C712yescomplemented
148C24×C7—22no—
149C24×C7—22no—
150C24×C7—22no—
151C24×C7—22no—
152C24×C7—28no—
153C24×C7—28no—
154C24×C7—216no—
155C24×C7—216no—
156C24×C7—28no—
157C24×C7—22no—
158C24×C7—22no—
159C24×C7—22no—
160C24×C7—22no—
161C24×C7—22no—
162C24×C7—22no—
163C24×C7—22no—
164C24×C7—22no—
165C24×C7—22no—
166C24×C7—22no—
167C24×C7—22no—
168C24×C7—22no—
169C24×C7—28no—
170C24×C7—28no—
171C24×C7—21no—
172C24×C7—22no—
173C24×C7—21no—
174C24×C7—21no—
175C24×C7—21no—
176C24×C7—21no—
177C24×C7—21no—
178C24×C7—22no—
179C24×C7—22no—
180C24×C7—22no—
181C24×C7—48no—
182C24×C7—48no—
183C24×C7—48no—
184C24×C7—48no—
185C24×C7—48no—
186C24×C7—48no—
187C24×C7—48no—
188C24×C7—48no—
189C24×C7—48no—
190C24×C7—44no—
191C24×C7—44no—
192C24×C7—48no—
193C24×C7—44no—
194C24×C7—44no—
195C24×C7—44no—
196C24×C7—44no—
197C24×C7C22×C412yes—
198C24×C7C22×C414yes—
199C24×C7C22×C412yes—
200C24×C7C2×D414yes—
201C24×C7C2×D412yes—
202C24×C7C2×D412yes—
203C24×C7C2×D412yes—
204C24×C7C2×D412yes—
205C24×C7#4114yes—
206C24×C7#4112yes—
207C24×C7#4112yes—
208C24×C7C2411yescharacteristic
209C2×C7×D4—28no—
210C2×C7×D4—28no—
211C2×C7×D4—28no—
212C2×C7×D4—216no—
213C2×C7×D4—216no—
214C2×C7×D4—48no—
215C2×C7×D4—48no—
216C2×C7×D4—48no—
217C2×C7×D4—48no—
218C2×C7×D4—48no—
219C2×C7×D4—44no—
220C2×C7×D4—44no—
221C2×C7×D4—44no—
222C2×C7×D4—44no—
223C22×C4×C7—21no—
224C22×C4×C7—22no—
225C22×C4×C7—21no—
226C22×C4×C7—22no—
227C22×C4×C7—22no—
228C22×C4×C7—22no—
229C22×C4×C7—22no—
230C22×C4×C7—28no—
231C22×C4×C7—28no—
232C22×C4×C7—21no—
233C22×C4×C7—21no—
234C22×C4×C7—21no—
235C22×C4×C7—22no—
236C22×C4×C7—22no—
237C22×C4×C7—22no—
238C22×C4×C7—22no—
239C22×C4×C7—22no—
240C22×C4×C7—22no—
241C22×C4×C7—22no—
242C22×C4×C7—21no—
243C22×C4×C7—21no—
244C22×C4×C7—22no—
245C22×C4×C7—22no—
246C22×C4×C7—21no—
247C22×C4×C7—21no—
248C22×C4×C7—21no—
249C22×C4×C7—22no—
250C22×C4×C7—22no—
251C22×C4×C7—22no—
252C22×C4×C7—22no—
253C22×C4×C7—22no—
254C22×C4×C7—28no—
255C22×C4×C7—21no—
256C22×C4×C7—21no—
257C22×C4×C7—21no—
258C22×C4×C7—21no—
259C22×C4×C7—21no—
260C22×C4×C7—22no—
261C22×C4×C7—21no—
262C22×C4×C7—22no—
263C22×C4×C7—22no—
264C22×C4×C7—22no—
265C22×C4×C7—44no—
266C22×C4×C7—48no—
267C22×C4×C7—48no—
268C22×C4×C7—48no—
269C22×C4×C7—48no—
270C22×C4×C7—44no—
271C22×C4×C7—44no—
272C22×C4×C7C22×C412yes—
273C22×C4×C7C22×C414yes—
274C22×C4×C7C2×D414yes—
275C22×C4×C7C2×D412yes—
276C22×C4×C7C2×D414yes—
277C22×C4×C7C2×D414yes—
278C22×C4×C7C2×D414yes—
279C22×C4×C7C2×D412yes—
280C22×C4×C7C2×D414yes—
281C7×C4⋊C4—48no—
282C7×C22⋊C4—216no—
283C7×C22⋊C4—28no—
284C7×C22⋊C4—216no—
285C7×C22⋊C4—216no—
286C7×C22⋊C4—48no—
287C7×C22⋊C4—48no—
288C7×C22⋊C4—48no—
289C7×C22⋊C4—44no—
290C7×C22⋊C4—44no—
291C7×C22⋊C4—44no—
292C7×C22⋊C4C22⋊C4116yescomplemented
293C42×C7—48no—
294C26C22×C711yescharacteristic
295C23×D4C22×C711yescharacteristic
296C23×D4C22×C712yes—
297C24×C4C22×C711yescharacteristic
298C24×C4C22×C711yescharacteristic
299C2×#120—24no—
300C2×#120—24no—
301C2×#120C4×C718yescomplemented
302C22×C4⋊C4C22×C712yescomplemented
303C22×C22⋊C4—24no—
304C22×C22⋊C4—28no—
305C22×C22⋊C4C22×C712yes—
306C22×C22⋊C4C22×C711yescharacteristic
307C22×C22⋊C4C22×C712yes—
308C22×C22⋊C4C22×C712yes—
309C22×C22⋊C4C22×C712yes—
310C22×C22⋊C4C22×C712yes—
311C22×C22⋊C4C22×C711yescharacteristic
312C22×C22⋊C4C22×C711yescharacteristic
313C22×C22⋊C4C22×C711yescharacteristic, complemented
314C22×C22⋊C4C22×C712yescomplemented
315C22×C22⋊C4C22×C711yescharacteristic, complemented
316C22×C42C22×C712yescomplemented
317#390—28no—
318#386—24no—
319#386—24no—
320#385—24no—
321#379—24no—
322C4×C22⋊C4—24no—
323C2×#95C22×C711yescharacteristic, complemented
324C2×#95C22×C712yescomplemented
325C2×#95C22×C712yescomplemented
326C2×#95C22×C712yescomplemented
327C2×#95C22×C711yescharacteristic, complemented
328C23×C7—24no—
329C23×C7—24no—
330C23×C7—22no—
331C23×C7—22no—
332C23×C7—24no—
333C23×C7—22no—
334C23×C7—22no—
335C23×C7—24no—
336C23×C7—24no—
337C23×C7—24no—
338C23×C7—24no—
339C23×C7—24no—
340C23×C7—24no—
341C23×C7—24no—
342C23×C7—24no—
343C23×C7—24no—
344C23×C7—232no—
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—24no—
354C23×C7—24no—
355C23×C7—24no—
356C23×C7—24no—
357C23×C7—24no—
358C23×C7—24no—
359C23×C7—24no—
360C23×C7—24no—
361C23×C7—24no—
362C23×C7—24no—
363C23×C7—22no—
364C23×C7—22no—
365C23×C7—24no—
366C23×C7—22no—
367C23×C7—24no—
368C23×C7—432no—
369C23×C7—432no—
370C23×C7—416no—
371C23×C7—416no—
372C23×C7—416no—
373C23×C7—432no—
374C23×C7—416no—
375C23×C7—432no—
376C23×C7—416no—
377C23×C7—42no—
378C23×C7—42no—
379C23×C7—42no—
380C23×C7—42no—
381C23×C7—42no—
382C23×C7—42no—
383C23×C7—42no—
384C23×C7—42no—
385C23×C7—42no—
386C23×C7—42no—
387C23×C7—42no—
388C23×C7—42no—
389C23×C7—42no—
390C23×C7—42no—
391C23×C7—42no—
392C23×C7—42no—
393C23×C7—416no—
394C23×C7—41no—
395C23×C7—41no—
396C23×C7—41no—
397C23×C7—41no—
398C23×C7—42no—
399C23×C7—41no—
400C23×C7—41no—
401C23×C7—41no—
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×C7C2×C22⋊C414yes—
413C23×C7C4×D418yes—
414C23×C7C4×D414yes—
415C23×C7C4×D414yes—
416C23×C7#12114yes—
417C23×C7#12114yes—
418C23×C7#12414yes—
419C23×C7#12714yes—
420C23×C7C23×C411yescharacteristic
421C23×C7C22×D411yescharacteristic
422C23×C7C22×D411yescharacteristic
423C23×C7C22×D411yescharacteristic
424C23×C7C22×D412yes—
425C23×C7C22×D411yescharacteristic
426C23×C7C2×#4111yescharacteristic
427C23×C7C2×#4111yescharacteristic
428C23×C7C2×#4112yes—
429C23×C7H(5,𝔽2)12yes—
430C23×C7H(5,𝔽2)12yes—
431C7×D4—432no—
432C7×D4—416no—
433C2×C4×C7—24no—
434C2×C4×C7—24no—
435C2×C4×C7—22no—
436C2×C4×C7—22no—
437C2×C4×C7—24no—
438C2×C4×C7—24no—
439C2×C4×C7—24no—
440C2×C4×C7—24no—
441C2×C4×C7—24no—
442C2×C4×C7—24no—
443C2×C4×C7—22no—
444C2×C4×C7—22no—
445C2×C4×C7—22no—
446C2×C4×C7—22no—
447C2×C4×C7—24no—
448C2×C4×C7—24no—
449C2×C4×C7—22no—
450C2×C4×C7—22no—
451C2×C4×C7—24no—
452C2×C4×C7—24no—
453C2×C4×C7—24no—
454C2×C4×C7—24no—
455C2×C4×C7—416no—
456C2×C4×C7—416no—
457C2×C4×C7—41no—
458C2×C4×C7—41no—
459C2×C4×C7—42no—
460C2×C4×C7—41no—
461C2×C4×C7—42no—
462C2×C4×C7—41no—
463C2×C4×C7—42no—
464C2×C4×C7—42no—
465C2×C4×C7—42no—
466C2×C4×C7—42no—
467C2×C4×C7—42no—
468C2×C4×C7—42no—
469C2×C4×C7—42no—
470C2×C4×C7—42no—
471C2×C4×C7—41no—
472C2×C4×C7—41no—
473C2×C4×C7—41no—
474C2×C4×C7—41no—
475C2×C4×C7—41no—
476C2×C4×C7—41no—
477C2×C4×C7—42no—
478C2×C4×C7—42no—
479C2×C4×C7—42no—
480C2×C4×C7—42no—
481C2×C4×C7C2×C22⋊C418yescomplemented
482C2×C4×C7#12014yescomplemented
483C25—24no—
484C25—22no—
485C25—24no—
486C25—22no—
487C25—22no—
488C25—22no—
489C25—22no—
490C25—22no—
491C25—42no—
492C25—42no—
493C25C2×C4×C714yes—
494C25C23×C711yescharacteristic
495C25C23×C712yes—
496C25C23×C711yescharacteristic
497C22×D4—22no—
498C22×D4—22no—
499C22×D4—22no—
500C22×D4—22no—
501C22×D4—24no—
502C22×D4—24no—
503C22×D4—22no—
504C22×D4—22no—
505C22×D4—24no—
506C22×D4—24no—
507C22×D4—42no—
508C22×D4—42no—
509C22×D4C2×C4×C714yes—
510C22×D4C2×C4×C718yescomplemented
511C23×C4—22no—
512C23×C4—22no—
513C23×C4—22no—
514C23×C4—24no—
515C23×C4—24no—
516C23×C4—22no—
517C23×C4—22no—
518C23×C4—42no—
519C23×C4—42no—
520C23×C4C7×D414yescomplemented
521C23×C4C23×C711yescharacteristic
522C23×C4C23×C711yescharacteristic
523C23×C4C23×C711yescharacteristic
524C23×C4C23×C712yes—
525C23×C4C23×C712yes—
526C23×C4C23×C711yescharacteristic
527C23×C4C23×C712yes—
528C23×C4C23×C711yescharacteristic
529#120—232no—
530C2×C4⋊C4—24no—
531C2×C4⋊C4—24no—
532C2×C4⋊C4—42no—
533C2×C22⋊C4—232no—
534C2×C22⋊C4—24no—
535C2×C22⋊C4—22no—
536C2×C22⋊C4—22no—
537C2×C22⋊C4—24no—
538C2×C22⋊C4—24no—
539C2×C22⋊C4—24no—
540C2×C22⋊C4—24no—
541C2×C22⋊C4—24no—
542C2×C22⋊C4—24no—
543C2×C22⋊C4—22no—
544C2×C22⋊C4—22no—
545C2×C22⋊C4—22no—
546C2×C22⋊C4—24no—
547C2×C22⋊C4—24no—
548C2×C22⋊C4—24no—
549C2×C22⋊C4—24no—
550C2×C22⋊C4—24no—
551C2×C22⋊C4—22no—
552C2×C22⋊C4—22no—
553C2×C22⋊C4—24no—
554C2×C22⋊C4—24no—
555C2×C22⋊C4—42no—
556C2×C22⋊C4—42no—
557C2×C22⋊C4—42no—
558C2×C22⋊C4—42no—
559C2×C22⋊C4C2×C4×C714yes—
560C2×C22⋊C4C2×C4×C718yescomplemented
561C2×C22⋊C4C7×D414yes—
562C2×C22⋊C4C7×D414yes—
563C2×C22⋊C4C7×D418yescomplemented
564C2×C22⋊C4C7×D414yescomplemented
565C2×C42—24no—
566C2×C42—24no—
567C2×C42—42no—
568#95—24no—
569#95—24no—
570#95—24no—
571#95—22no—
572#95—22no—
573C22×C7—24no—
574C22×C7—28no—
575C22×C7—28no—
576C22×C7—24no—
577C22×C7—24no—
578C22×C7—28no—
579C22×C7—24no—
580C22×C7—28no—
581C22×C7—24no—
582C22×C7—24no—
583C22×C7—28no—
584C22×C7—28no—
585C22×C7—28no—
586C22×C7—464no—
587C22×C7—44no—
588C22×C7—44no—
589C22×C7—44no—
590C22×C7—44no—
591C22×C7—44no—
592C22×C7—44no—
593C22×C7—44no—
594C22×C7—44no—
595C22×C7—44no—
596C22×C7—44no—
597C22×C7—44no—
598C22×C7—44no—
599C22×C7—42no—
600C22×C7—44no—
601C22×C7—44no—
602C22×C7—42no—
603C22×C7—42no—
604C22×C7—81no—
605C22×C7—81no—
606C22×C7—82no—
607C22×C7—81no—
608C22×C7—82no—
609C22×C7—81no—
610C22×C7#39018yescomplemented
611C22×C7C22×C22⋊C411yescharacteristic
612C22×C7C2×C4×D411yescharacteristic
613C22×C7C2×C4×D412yes—
614C22×C7C2×C4×D411yescharacteristic
615C22×C7#51812yes—
616C22×C7C2×#12011yescharacteristic
617C22×C7C2×#12111yescharacteristic
618C22×C7C2×#12111yescharacteristic
619C22×C7#52511yescharacteristic
620C22×C7#52512yes—
621C22×C7C2×#12411yescharacteristic
622C22×C7C2×#12711yescharacteristic
623C22×C7#53411yescharacteristic
624C22×C7#53511yescharacteristic
625C22×C7#53812yes—
626C22×C7D4212yes—
627C22×C7D4212yes—
628C22×C7D4212yes—
629C22×C7#54612yes—
630C22×C7#54612yes—
631C22×C7#54612yes—
632C22×C7#54612yes—
633C22×C7#55112yes—
634C4×C7—28no—
635C4×C7—24no—
636C4×C7—42no—
637C4×C7—44no—
638C4×C7—44no—
639C4×C7—42no—
640C4×C7—81no—
641C4×C7—81no—
642C24—22no—
643C24—22no—
644C24—22no—
645C24—22no—
646C24—28no—
647C24—28no—
648C24—216no—
649C24—216no—
650C24—28no—
651C24—22no—
652C24—22no—
653C24—22no—
654C24—22no—
655C24—22no—
656C24—22no—
657C24—22no—
658C24—22no—
659C24—22no—
660C24—22no—
661C24—22no—
662C24—22no—
663C24—28no—
664C24—28no—
665C24—21no—
666C24—22no—
667C24—21no—
668C24—21no—
669C24—21no—
670C24—21no—
671C24—21no—
672C24—22no—
673C24—22no—
674C24—22no—
675C24—48no—
676C24—48no—
677C24—48no—
678C24—48no—
679C24—48no—
680C24—48no—
681C24—48no—
682C24—48no—
683C24—48no—
684C24—44no—
685C24—44no—
686C24—48no—
687C24—44no—
688C24—44no—
689C24—44no—
690C24—44no—
691C24C22×C4×C712yes—
692C24C22×C4×C714yes—
693C24C22×C4×C712yes—
694C24C2×C7×D414yes—
695C24C2×C7×D412yes—
696C24C2×C7×D412yes—
697C24C2×C7×D412yes—
698C24C2×C7×D412yes—
699C24C7×#4114yes—
700C24C7×#4112yes—
701C24C7×#4112yes—
702C24C24×C711yescharacteristic
703C2×D4—28no—
704C2×D4—28no—
705C2×D4—28no—
706C2×D4—216no—
707C2×D4—216no—
708C2×D4—48no—
709C2×D4—48no—
710C2×D4—48no—
711C2×D4—48no—
712C2×D4—48no—
713C2×D4—44no—
714C2×D4—44no—
715C2×D4—44no—
716C2×D4—44no—
717C22×C4—21no—
718C22×C4—22no—
719C22×C4—21no—
720C22×C4—22no—
721C22×C4—22no—
722C22×C4—22no—
723C22×C4—22no—
724C22×C4—28no—
725C22×C4—28no—
726C22×C4—21no—
727C22×C4—21no—
728C22×C4—21no—
729C22×C4—22no—
730C22×C4—22no—
731C22×C4—22no—
732C22×C4—22no—
733C22×C4—22no—
734C22×C4—22no—
735C22×C4—22no—
736C22×C4—21no—
737C22×C4—21no—
738C22×C4—22no—
739C22×C4—22no—
740C22×C4—21no—
741C22×C4—21no—
742C22×C4—21no—
743C22×C4—22no—
744C22×C4—22no—
745C22×C4—22no—
746C22×C4—22no—
747C22×C4—22no—
748C22×C4—28no—
749C22×C4—21no—
750C22×C4—21no—
751C22×C4—21no—
752C22×C4—21no—
753C22×C4—21no—
754C22×C4—22no—
755C22×C4—21no—
756C22×C4—22no—
757C22×C4—22no—
758C22×C4—22no—
759C22×C4—44no—
760C22×C4—48no—
761C22×C4—48no—
762C22×C4—48no—
763C22×C4—48no—
764C22×C4—44no—
765C22×C4—44no—
766C22×C4C22×C4×C712yes—
767C22×C4C22×C4×C714yes—
768C22×C4C2×C7×D414yes—
769C22×C4C2×C7×D412yes—
770C22×C4C2×C7×D414yes—
771C22×C4C2×C7×D414yes—
772C22×C4C2×C7×D414yes—
773C22×C4C2×C7×D412yes—
774C22×C4C2×C7×D414yes—
775C4⋊C4—48no—
776C22⋊C4—216no—
777C22⋊C4—28no—
778C22⋊C4—216no—
779C22⋊C4—216no—
780C22⋊C4—48no—
781C22⋊C4—48no—
782C22⋊C4—48no—
783C22⋊C4—44no—
784C22⋊C4—44no—
785C22⋊C4—44no—
786C22⋊C4C7×C22⋊C4116yescomplemented
787C42—48no—
788C2×C7—28no—
789C2×C7—48no—
790C2×C7—82no—
791C2×C7C2×#39011yescharacteristic
792C2×C7C4×#12011yescharacteristic
793C2×C7#232111yescharacteristic
794C2×C7D4×C22⋊C412yes—
795C2×C7#235812yes—
796C2×C7#241011yescharacteristic
797C2×C7#241111yescharacteristic
798C2×C7#242412yes—
799C2×C7#243311yescharacteristic
800C2×C7#247212yes—
801C2×C7#253911yescharacteristic
802C23—24no—
803C23—24no—
804C23—22no—
805C23—22no—
806C23—24no—
807C23—22no—
808C23—22no—
809C23—24no—
810C23—24no—
811C23—24no—
812C23—24no—
813C23—24no—
814C23—24no—
815C23—24no—
816C23—24no—
817C23—24no—
818C23—232no—
819C23—24no—
820C23—24no—
821C23—24no—
822C23—24no—
823C23—24no—
824C23—24no—
825C23—24no—
826C23—24no—
827C23—24no—
828C23—24no—
829C23—24no—
830C23—24no—
831C23—24no—
832C23—24no—
833C23—24no—
834C23—24no—
835C23—24no—
836C23—24no—
837C23—22no—
838C23—22no—
839C23—22no—
840C23—24no—
841C23—24no—
842C23—432no—
843C23—432no—
844C23—416no—
845C23—416no—
846C23—432no—
847C23—416no—
848C23—432no—
849C23—416no—
850C23—416no—
851C23—42no—
852C23—42no—
853C23—42no—
854C23—416no—
855C23—42no—
856C23—42no—
857C23—42no—
858C23—42no—
859C23—42no—
860C23—42no—
861C23—42no—
862C23—42no—
863C23—42no—
864C23—42no—
865C23—42no—
866C23—42no—
867C23—42no—
868C23—41no—
869C23—41no—
870C23—41no—
871C23—41no—
872C23—42no—
873C23—41no—
874C23—41no—
875C23—41no—
876C23—41no—
877C23—42no—
878C23—42no—
879C23—42no—
880C23—42no—
881C23—42no—
882C23—42no—
883C23—42no—
884C23—42no—
885C23—42no—
886C23C2×C7×C22⋊C414yes—
887C23C4×C7×D418yes—
888C23C4×C7×D414yes—
889C23C4×C7×D414yes—
890C23C7×#12114yes—
891C23C7×#12114yes—
892C23C7×#12414yes—
893C23C7×#12714yes—
894C23C23×C4×C711yescharacteristic
895C23C22×C7×D411yescharacteristic
896C23C22×C7×D411yescharacteristic
897C23C22×C7×D411yescharacteristic
898C23C22×C7×D412yes—
899C23C22×C7×D411yescharacteristic
900C23C2×C7×#4111yescharacteristic
901C23C2×C7×#4111yescharacteristic
902C23C2×C7×#4112yes—
903C23C7×H(5,𝔽2)12yes—
904C23C7×H(5,𝔽2)12yes—
905D4—432no—
906D4—416no—
907C2×C4—24no—
908C2×C4—24no—
909C2×C4—22no—
910C2×C4—22no—
911C2×C4—24no—
912C2×C4—24no—
913C2×C4—24no—
914C2×C4—24no—
915C2×C4—24no—
916C2×C4—24no—
917C2×C4—22no—
918C2×C4—22no—
919C2×C4—22no—
920C2×C4—22no—
921C2×C4—24no—
922C2×C4—24no—
923C2×C4—22no—
924C2×C4—22no—
925C2×C4—24no—
926C2×C4—24no—
927C2×C4—24no—
928C2×C4—24no—
929C2×C4—416no—
930C2×C4—416no—
931C2×C4—41no—
932C2×C4—41no—
933C2×C4—42no—
934C2×C4—41no—
935C2×C4—42no—
936C2×C4—41no—
937C2×C4—42no—
938C2×C4—42no—
939C2×C4—42no—
940C2×C4—42no—
941C2×C4—42no—
942C2×C4—42no—
943C2×C4—42no—
944C2×C4—42no—
945C2×C4—41no—
946C2×C4—41no—
947C2×C4—41no—
948C2×C4—41no—
949C2×C4—41no—
950C2×C4—41no—
951C2×C4—42no—
952C2×C4—42no—
953C2×C4—42no—
954C2×C4—42no—
955C2×C4C2×C7×C22⋊C418yescomplemented
956C2×C4C7×#12014yescomplemented
957C7#1399511yescharacteristic, direct product factor, Sylow
958C22—24no—
959C22—24no—
960C22—28no—
961C22—24no—
962C22—28no—
963C22—24no—
964C22—24no—
965C22—24no—
966C22—28no—
967C22—28no—
968C22—28no—
969C22—28no—
970C22—28no—
971C22—464no—
972C22—44no—
973C22—44no—
974C22—44no—
975C22—44no—
976C22—44no—
977C22—44no—
978C22—44no—
979C22—44no—
980C22—44no—
981C22—44no—
982C22—44no—
983C22—44no—
984C22—42no—
985C22—42no—
986C22—42no—
987C22—44no—
988C22—44no—
989C22—81no—
990C22—81no—
991C22—82no—
992C22—81no—
993C22—82no—
994C22—81no—
995C22C7×#39018yescomplemented
996C22C22×C7×C22⋊C411yescharacteristic
997C22C2×C4×C7×D411yescharacteristic
998C22C2×C4×C7×D411yescharacteristic
999C22C2×C4×C7×D412yes—
1000C22C7×#51812yes—
1001C22C2×C7×#12011yescharacteristic
1002C22C2×C7×#12111yescharacteristic
1003C22C2×C7×#12111yescharacteristic
1004C22C7×#52511yescharacteristic
1005C22C7×#52512yes—
1006C22C2×C7×#12411yescharacteristic
1007C22C2×C7×#12711yescharacteristic
1008C22C7×#53411yescharacteristic
1009C22C7×#53511yescharacteristic
1010C22C7×#53812yes—
1011C22C7×D4212yes—
1012C22C7×D4212yes—
1013C22C7×D4212yes—
1014C22C7×#54612yes—
1015C22C7×#54612yes—
1016C22C7×#54612yes—
1017C22C7×#54612yes—
1018C22C7×#55112yes—
1019C4—24no—
1020C4—28no—
1021C4—42no—
1022C4—44no—
1023C4—44no—
1024C4—42no—
1025C4—81no—
1026C4—81no—
1027C2—28no—
1028C2—48no—
1029C2—82no—
1030C2C2×C7×#39011yescharacteristic
1031C2C4×C7×#12011yescharacteristic
1032C2C7×#232111yescharacteristic
1033C2C7×D4×C22⋊C412yes—
1034C2C7×#235812yes—
1035C2C7×#241011yescharacteristic
1036C2C7×#241111yescharacteristic
1037C2C7×#242412yes—
1038C2C7×#243311yescharacteristic
1039C2C7×#247212yes—
1040C2C7×#253911yescharacteristic
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. C23×C7×C22⋊C4C2semidirect
3. C2×C7×#390C2semidirect
4. C2×C7×#386C2semidirect
5. C2×C7×#386C2semidirect
6. C2×C7×#385C2semidirect
7. C2×C7×#379C2semidirect
8. C2×C4×C7×C22⋊C4C2semidirect
9. C7×#1439C2semidirect
10. C7×#1438C2semidirect
11. C7×#1437C2semidirect
19. C2×C7×#120C4semidirect
20. C22×C7×C4⋊C4C22semidirect
31. C22×C7×C22⋊C4C22semidirect
32. C22×C7×C22⋊C4C22semidirect
33. C22×C7×C22⋊C4C22semidirect
34. C22×C42×C7C22semidirect
41. C2×C7×#95C22semidirect
42. C2×C7×#95C22semidirect
43. C2×C7×#95C22semidirect
44. C2×C7×#95C22semidirect
45. C2×C7×#95C22semidirect
46. #13995C7direct (N × H)
74. C22×C7×D4C2×C4semidirect
84. C23×C4×C7D4semidirect
124. C2×C7×C22⋊C4C2×C4semidirect
127. C2×C7×C22⋊C4D4semidirect
128. C2×C7×C22⋊C4D4semidirect
138. C23×C22⋊C4C2×C7semidirect
139. C2×#390C2×C7semidirect
140. C2×#386C2×C7semidirect
141. C2×#386C2×C7semidirect
142. C2×#385C2×C7semidirect
143. C2×#379C2×C7semidirect
144. C2×C4×C22⋊C4C2×C7semidirect
145. #1439C2×C7semidirect
146. #1438C2×C7semidirect
147. #1437C2×C7semidirect
292. C7×C22⋊C4C22⋊C4semidirect
301. C2×#120C4×C7semidirect
302. C22×C4⋊C4C22×C7semidirect
313. C22×C22⋊C4C22×C7semidirect
314. C22×C22⋊C4C22×C7semidirect
315. C22×C22⋊C4C22×C7semidirect
316. C22×C42C22×C7semidirect
323. C2×#95C22×C7semidirect
324. C2×#95C22×C7semidirect
325. C2×#95C22×C7semidirect
326. C2×#95C22×C7semidirect
327. C2×#95C22×C7semidirect
481. C2×C4×C7C2×C22⋊C4semidirect
482. C2×C4×C7#120semidirect
510. C22×D4C2×C4×C7semidirect
520. C23×C4C7×D4semidirect
560. C2×C22⋊C4C2×C4×C7semidirect
563. C2×C22⋊C4C7×D4semidirect
564. C2×C22⋊C4C7×D4semidirect
610. C22×C7#390semidirect
786. C22⋊C4C7×C22⋊C4semidirect
955. C2×C4C2×C7×C22⋊C4semidirect
956. C2×C4C7×#120semidirect
957. C7#13995direct (N × H)
995. C22C7×#390semidirect

Maximal subgroups

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

subgroupindex
C22×C7×#1202
C23×C7×C22⋊C42
C2×C7×#3902
C2×C7×#3862
C2×C7×#3852
C2×C7×#3792
C2×C4×C7×C22⋊C42
C7×#14392
C7×#14382
C7×#14372
#139957