Finite Group Databasebeta

← C7×#15126 #13192342

Subgroups — C7×#15126 #13192342

Order 1792.

2506 conjugacy classes of subgroups.

The subgroup lattice has 994 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C7×#121C211yesmaximal, characteristic
2C2×C7×#394C212yesmaximal, complemented
3C2×C7×#390C211yesmaximal, characteristic, complemented
4C2×C7×#390C211yesmaximal, characteristic, complemented
5C2×C7×#389C211yesmaximal, characteristic, complemented
6C2×C7×#380C211yesmaximal, characteristic, complemented
7C2×C4×C7×C22⋊C4C211yesmaximal, characteristic, complemented
8C7×#1440C212yesmaximal, complemented
9C7×#1439C212yesmaximal, complemented
10C7×#1438C212yesmaximal, complemented
11C7×C4⋊#95C211yesmaximal, characteristic, complemented
12C23×C7×D4C2211yescharacteristic
13C23×C7×D4C2212yes—
14C24×C4×C7C2211yescharacteristic
15C2×C7×#121—24no—
16C2×C7×#121—24no—
17C2×C7×#121—24no—
18C22×C7×C4⋊C4C2211yescharacteristic
19C22×C7×C4⋊C4C2212yes—
20C22×C7×C4⋊C4C2211yescharacteristic
21C22×C7×C4⋊C4C2211yescharacteristic
22C22×C7×C22⋊C4C2212yes—
23C22×C7×C22⋊C4C2211yescharacteristic
24C22×C7×C22⋊C4C2212yes—
25C22×C7×C22⋊C4C2212yes—
26C22×C7×C22⋊C4C2212yes—
27C22×C7×C22⋊C4C2212yes—
28C22×C7×C22⋊C4C2212yes—
29C22×C7×C22⋊C4C2211yescharacteristic
30C22×C42×C7C2211yescharacteristic
31C22×C42×C7C2211yescharacteristic
32C7×#394—28no—
33C7×#390—24no—
34C7×#390—24no—
35C7×#389—24no—
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—
44#15126C711yesmaximal, characteristic, direct product factor, Sylow
45C25×C7C2312yes—
46C25×C7C2311yescharacteristic
47C22×C7×D4—24no—
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—22no—
57C22×C7×D4—22no—
58C22×C7×D4—42no—
59C22×C7×D4—42no—
60C22×C7×D4D414yes—
61C23×C4×C7—22no—
62C23×C4×C7—22no—
63C23×C4×C7—22no—
64C23×C4×C7—22no—
65C23×C4×C7—22no—
66C23×C4×C7—22no—
67C23×C4×C7D414yes—
68C23×C4×C7C2312yes—
69C23×C4×C7C2312yes—
70C23×C4×C7C2311yescharacteristic
71C23×C4×C7C2311yescharacteristic
72C23×C4×C7C2311yescharacteristic
73C23×C4×C7C2312yes—
74C23×C4×C7C2311yescharacteristic
75C23×C4×C7C2311yescharacteristic
76C23×C4×C7C2311yescharacteristic
77C7×#121—232no—
78C2×C7×C4⋊C4—22no—
79C2×C7×C4⋊C4—22no—
80C2×C7×C4⋊C4—22no—
81C2×C7×C4⋊C4—22no—
82C2×C7×C4⋊C4—22no—
83C2×C7×C4⋊C4—24no—
84C2×C7×C4⋊C4—22no—
85C2×C7×C4⋊C4—24no—
86C2×C7×C4⋊C4—22no—
87C2×C7×C4⋊C4—42no—
88C2×C7×C4⋊C4D414yes—
89C2×C7×C4⋊C4D414yescomplemented
90C2×C7×C22⋊C4—22no—
91C2×C7×C22⋊C4—22no—
92C2×C7×C22⋊C4—24no—
93C2×C7×C22⋊C4—22no—
94C2×C7×C22⋊C4—24no—
95C2×C7×C22⋊C4—24no—
96C2×C7×C22⋊C4—22no—
97C2×C7×C22⋊C4—22no—
98C2×C7×C22⋊C4—24no—
99C2×C7×C22⋊C4—24no—
100C2×C7×C22⋊C4—24no—
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—24no—
108C2×C7×C22⋊C4—42no—
109C2×C7×C22⋊C4—42no—
110C2×C7×C22⋊C4—42no—
111C2×C7×C22⋊C4—42no—
112C2×C7×C22⋊C4—42no—
113C2×C7×C22⋊C4D414yescomplemented
114C2×C42×C7—22no—
115C2×C42×C7—22no—
116C2×C42×C7—22no—
117C2×C42×C7—22no—
118C2×C42×C7—22no—
119C2×C42×C7—22no—
120C7×#95—22no—
121C7×#95—22no—
122C7×#95—24no—
123C7×#95—24no—
124C7×#95—24no—
125C7×#95—42no—
126C22×#121C2×C711yescharacteristic
127C2×#394C2×C712yescomplemented
128C2×#390C2×C711yescharacteristic, complemented
129C2×#390C2×C711yescharacteristic, complemented
130C2×#389C2×C711yescharacteristic, complemented
131C2×#380C2×C711yescharacteristic, complemented
132C2×C4×C22⋊C4C2×C711yescharacteristic, complemented
133#1440C2×C712yescomplemented
134#1439C2×C712yescomplemented
135#1438C2×C712yescomplemented
136C4⋊#95C2×C711yescharacteristic, complemented
137C24×C7—21no—
138C24×C7—21no—
139C24×C7—21no—
140C24×C7—21no—
141C24×C7—21no—
142C24×C7—21no—
143C24×C7—21no—
144C24×C7—21no—
145C24×C7—21no—
146C24×C7—21no—
147C24×C7—21no—
148C24×C7—21no—
149C24×C7—22no—
150C24×C7—22no—
151C24×C7—22no—
152C24×C7—22no—
153C24×C7—22no—
154C24×C7—22no—
155C24×C7—22no—
156C24×C7—22no—
157C24×C7—22no—
158C24×C7—22no—
159C24×C7—22no—
160C24×C7—22no—
161C24×C7—22no—
162C24×C7—22no—
163C24×C7C2×D414yes—
164C24×C7C2×D412yes—
165C24×C7C2×D412yes—
166C24×C7#4112yes—
167C24×C7C2411yescharacteristic
168C2×C7×D4—216no—
169C2×C7×D4—28no—
170C2×C7×D4—28no—
171C2×C7×D4—28no—
172C2×C7×D4—48no—
173C2×C7×D4—48no—
174C2×C7×D4—48no—
175C2×C7×D4—48no—
176C2×C7×D4—48no—
177C2×C7×D4—48no—
178C2×C7×D4—44no—
179C2×C7×D4—44no—
180C2×C7×D4—44no—
181C2×C7×D4—44no—
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—22no—
189C22×C4×C7—22no—
190C22×C4×C7—21no—
191C22×C4×C7—21no—
192C22×C4×C7—21no—
193C22×C4×C7—21no—
194C22×C4×C7—21no—
195C22×C4×C7—22no—
196C22×C4×C7—21no—
197C22×C4×C7—21no—
198C22×C4×C7—22no—
199C22×C4×C7—22no—
200C22×C4×C7—21no—
201C22×C4×C7—21no—
202C22×C4×C7—21no—
203C22×C4×C7—21no—
204C22×C4×C7—21no—
205C22×C4×C7—21no—
206C22×C4×C7—22no—
207C22×C4×C7—22no—
208C22×C4×C7—21no—
209C22×C4×C7—21no—
210C22×C4×C7—21no—
211C22×C4×C7—22no—
212C22×C4×C7—21no—
213C22×C4×C7—22no—
214C22×C4×C7—21no—
215C22×C4×C7—21no—
216C22×C4×C7—22no—
217C22×C4×C7—21no—
218C22×C4×C7—21no—
219C22×C4×C7—22no—
220C22×C4×C7—21no—
221C22×C4×C7—22no—
222C22×C4×C7—21no—
223C22×C4×C7—21no—
224C22×C4×C7—28no—
225C22×C4×C7—28no—
226C22×C4×C7—28no—
227C22×C4×C7—22no—
228C22×C4×C7—22no—
229C22×C4×C7—22no—
230C22×C4×C7—22no—
231C22×C4×C7—22no—
232C22×C4×C7—22no—
233C22×C4×C7—22no—
234C22×C4×C7—44no—
235C22×C4×C7—44no—
236C22×C4×C7—44no—
237C22×C4×C7—44no—
238C22×C4×C7C2×D412yes—
239C22×C4×C7C2×D412yes—
240C22×C4×C7C2×D414yes—
241C22×C4×C7C2×D414yes—
242C22×C4×C7C2×D412yes—
243C22×C4×C7C2×D412yes—
244C22×C4×C7C2×D412yes—
245C22×C4×C7C2×D412yes—
246C22×C4×C7C2×D412yes—
247C22×C4×C7#4112yes—
248C22×C4×C7#4112yes—
249C22×C4×C7#4112yes—
250C22×C4×C7#4112yes—
251C22×C4×C7#4112yes—
252C7×C4⋊C4—28no—
253C7×C4⋊C4—28no—
254C7×C4⋊C4—48no—
255C7×C4⋊C4—44no—
256C7×C22⋊C4—28no—
257C7×C22⋊C4—216no—
258C7×C22⋊C4—28no—
259C7×C22⋊C4—48no—
260C7×C22⋊C4—48no—
261C7×C22⋊C4—48no—
262C7×C22⋊C4—48no—
263C7×C22⋊C4—48no—
264C42×C7—44no—
265C42×C7—44no—
266C23×D4C22×C711yescharacteristic
267C23×D4C22×C712yes—
268C24×C4C22×C711yescharacteristic
269C2×#121—24no—
270C2×#121—24no—
271C2×#121—24no—
272C22×C4⋊C4C22×C711yescharacteristic
273C22×C4⋊C4C22×C712yes—
274C22×C4⋊C4C22×C711yescharacteristic
275C22×C4⋊C4C22×C711yescharacteristic
276C22×C22⋊C4C22×C712yes—
277C22×C22⋊C4C22×C711yescharacteristic
278C22×C22⋊C4C22×C712yes—
279C22×C22⋊C4C22×C712yes—
280C22×C22⋊C4C22×C712yes—
281C22×C22⋊C4C22×C712yes—
282C22×C22⋊C4C22×C712yes—
283C22×C22⋊C4C22×C711yescharacteristic
284C22×C42C22×C711yescharacteristic
285C22×C42C22×C711yescharacteristic
286#394—28no—
287#390—24no—
288#390—24no—
289#389—24no—
290#380—24no—
291C4×C22⋊C4—24no—
292C2×#95C22×C712yes—
293C2×#95C22×C712yes—
294C2×#95C22×C711yescharacteristic
295C2×#95C22×C712yes—
296C2×#95C22×C711yescharacteristic
297C2×#95C22×C712yes—
298C23×C7—22no—
299C23×C7—22no—
300C23×C7—22no—
301C23×C7—22no—
302C23×C7—22no—
303C23×C7—22no—
304C23×C7—22no—
305C23×C7—22no—
306C23×C7—22no—
307C23×C7—22no—
308C23×C7—22no—
309C23×C7—22no—
310C23×C7—22no—
311C23×C7—22no—
312C23×C7—22no—
313C23×C7—22no—
314C23×C7—22no—
315C23×C7—22no—
316C23×C7—24no—
317C23×C7—24no—
318C23×C7—24no—
319C23×C7—24no—
320C23×C7—24no—
321C23×C7—24no—
322C23×C7—24no—
323C23×C7—41no—
324C23×C7—41no—
325C23×C7—41no—
326C23×C7—41no—
327C23×C7—41no—
328C23×C7—41no—
329C23×C7—41no—
330C23×C7—41no—
331C23×C7—41no—
332C23×C7—41no—
333C23×C7—41no—
334C23×C7—41no—
335C23×C7—41no—
336C23×C7—41no—
337C23×C7—41no—
338C23×C7—41no—
339C23×C7—42no—
340C23×C7—42no—
341C23×C7—42no—
342C23×C7—42no—
343C23×C7—42no—
344C23×C7—42no—
345C23×C7—42no—
346C23×C7—42no—
347C23×C7—42no—
348C23×C7—42no—
349C23×C7—42no—
350C23×C7—42no—
351C23×C7—42no—
352C23×C7—42no—
353C23×C7—42no—
354C23×C7—42no—
355C23×C7—42no—
356C23×C7—42no—
357C23×C7—42no—
358C23×C7—42no—
359C23×C7—42no—
360C23×C7—42no—
361C23×C7—42no—
362C23×C7—42no—
363C23×C7—42no—
364C23×C7—42no—
365C23×C7—42no—
366C23×C7—42no—
367C23×C7#12114yes—
368C23×C7C22×D411yescharacteristic
369C23×C7C22×D411yescharacteristic
370C23×C7C22×D411yescharacteristic
371C23×C7C22×D411yescharacteristic
372C23×C7C22×D411yescharacteristic
373C23×C7C2×#4111yescharacteristic
374C23×C7C2×#4111yescharacteristic
375C23×C7C2×#4111yescharacteristic
376C23×C7C2×#4111yescharacteristic
377C23×C7C2×#4111yescharacteristic
378C23×C7C2×#4111yescharacteristic
379C23×C7H(5,𝔽2)11yescharacteristic
380C23×C7H(5,𝔽2)11yescharacteristic
381C23×C7H(5,𝔽2)11yescharacteristic
382C23×C72−1+411yescharacteristic
383C7×D4—432no—
384C7×D4—416no—
385C2×C4×C7—22no—
386C2×C4×C7—24no—
387C2×C4×C7—22no—
388C2×C4×C7—22no—
389C2×C4×C7—24no—
390C2×C4×C7—22no—
391C2×C4×C7—22no—
392C2×C4×C7—22no—
393C2×C4×C7—22no—
394C2×C4×C7—22no—
395C2×C4×C7—22no—
396C2×C4×C7—24no—
397C2×C4×C7—22no—
398C2×C4×C7—24no—
399C2×C4×C7—22no—
400C2×C4×C7—22no—
401C2×C4×C7—24no—
402C2×C4×C7—24no—
403C2×C4×C7—22no—
404C2×C4×C7—22no—
405C2×C4×C7—22no—
406C2×C4×C7—41no—
407C2×C4×C7—41no—
408C2×C4×C7—41no—
409C2×C4×C7—41no—
410C2×C4×C7—41no—
411C2×C4×C7—41no—
412C2×C4×C7—42no—
413C2×C4×C7—41no—
414C2×C4×C7—41no—
415C2×C4×C7—42no—
416C2×C4×C7—41no—
417C2×C4×C7—41no—
418C2×C4×C7—42no—
419C2×C4×C7—41no—
420C2×C4×C7—41no—
421C2×C4×C7—42no—
422C2×C4×C7—42no—
423C2×C4×C7—42no—
424C2×C4×C7—41no—
425C2×C4×C7—41no—
426C2×C4×C7—42no—
427C2×C4×C7—41no—
428C2×C4×C7—41no—
429C2×C4×C7—41no—
430C2×C4×C7—41no—
431C2×C4×C7—42no—
432C2×C4×C7—41no—
433C2×C4×C7—41no—
434C2×C4×C7—416no—
435C2×C4×C7—42no—
436C2×C4×C7—42no—
437C2×C4×C7—42no—
438C2×C4×C7—42no—
439C2×C4×C7—42no—
440C2×C4×C7—42no—
441C2×C4×C7—42no—
442C2×C4×C7#12014yes—
443C2×C4×C7#12114yes—
444C2×C4×C7#12114yes—
445C2×C4×C7#12114yes—
446C2×C4×C7#12314yes—
447C2×C4×C7#12314yes—
448C2×C4×C7#12414yes—
449C25C23×C712yes—
450C25C23×C711yescharacteristic
451C22×D4—24no—
452C22×D4—24no—
453C22×D4—24no—
454C22×D4—24no—
455C22×D4—24no—
456C22×D4—22no—
457C22×D4—22no—
458C22×D4—22no—
459C22×D4—22no—
460C22×D4—22no—
461C22×D4—22no—
462C22×D4—42no—
463C22×D4—42no—
464C22×D4C7×D414yes—
465C23×C4—22no—
466C23×C4—22no—
467C23×C4—22no—
468C23×C4—22no—
469C23×C4—22no—
470C23×C4—22no—
471C23×C4C7×D414yes—
472C23×C4C23×C712yes—
473C23×C4C23×C712yes—
474C23×C4C23×C711yescharacteristic
475C23×C4C23×C711yescharacteristic
476C23×C4C23×C711yescharacteristic
477C23×C4C23×C712yes—
478C23×C4C23×C711yescharacteristic
479C23×C4C23×C711yescharacteristic
480C23×C4C23×C711yescharacteristic
481#121—232no—
482C2×C4⋊C4—22no—
483C2×C4⋊C4—22no—
484C2×C4⋊C4—22no—
485C2×C4⋊C4—22no—
486C2×C4⋊C4—22no—
487C2×C4⋊C4—24no—
488C2×C4⋊C4—22no—
489C2×C4⋊C4—24no—
490C2×C4⋊C4—22no—
491C2×C4⋊C4—42no—
492C2×C4⋊C4C7×D414yes—
493C2×C4⋊C4C7×D414yescomplemented
494C2×C22⋊C4—24no—
495C2×C22⋊C4—22no—
496C2×C22⋊C4—22no—
497C2×C22⋊C4—22no—
498C2×C22⋊C4—24no—
499C2×C22⋊C4—24no—
500C2×C22⋊C4—22no—
501C2×C22⋊C4—22no—
502C2×C22⋊C4—24no—
503C2×C22⋊C4—24no—
504C2×C22⋊C4—24no—
505C2×C22⋊C4—24no—
506C2×C22⋊C4—24no—
507C2×C22⋊C4—24no—
508C2×C22⋊C4—24no—
509C2×C22⋊C4—24no—
510C2×C22⋊C4—24no—
511C2×C22⋊C4—24no—
512C2×C22⋊C4—42no—
513C2×C22⋊C4—42no—
514C2×C22⋊C4—42no—
515C2×C22⋊C4—42no—
516C2×C22⋊C4—42no—
517C2×C22⋊C4C7×D414yescomplemented
518C2×C42—22no—
519C2×C42—22no—
520C2×C42—22no—
521C2×C42—22no—
522C2×C42—22no—
523C2×C42—22no—
524#95—22no—
525#95—22no—
526#95—24no—
527#95—24no—
528#95—24no—
529#95—42no—
530C22×C7—24no—
531C22×C7—24no—
532C22×C7—24no—
533C22×C7—42no—
534C22×C7—42no—
535C22×C7—42no—
536C22×C7—42no—
537C22×C7—42no—
538C22×C7—42no—
539C22×C7—42no—
540C22×C7—42no—
541C22×C7—42no—
542C22×C7—42no—
543C22×C7—42no—
544C22×C7—42no—
545C22×C7—44no—
546C22×C7—44no—
547C22×C7—44no—
548C22×C7—44no—
549C22×C7—44no—
550C22×C7—44no—
551C22×C7—44no—
552C22×C7—82no—
553C22×C7—82no—
554C22×C7—82no—
555C22×C7—82no—
556C22×C7—82no—
557C22×C7—82no—
558C22×C7—82no—
559C22×C7—82no—
560C22×C7C2×#12011yescharacteristic
561C22×C7C2×#12111yescharacteristic
562C22×C7C2×#12111yescharacteristic
563C22×C7C2×#12111yescharacteristic
564C22×C7C2×#12111yescharacteristic
565C22×C7C2×#12311yescharacteristic
566C22×C7C2×#12311yescharacteristic
567C22×C7#52511yescharacteristic
568C22×C7C2×#12411yescharacteristic
569C22×C7#52911yescharacteristic
570C22×C7#52911yescharacteristic
571C22×C7#53211yescharacteristic
572C22×C7#53211yescharacteristic
573C22×C7#53511yescharacteristic
574C22×C7#53711yescharacteristic
575C22×C7#54011yescharacteristic
576C22×C7#54011yescharacteristic
577C22×C7#54211yescharacteristic
578C22×C7#54211yescharacteristic
579C22×C7D4211yescharacteristic
580C22×C7D4211yescharacteristic
581C22×C7D4211yescharacteristic
582C22×C7#54611yescharacteristic
583C22×C7#54611yescharacteristic
584C22×C7#54611yescharacteristic
585C22×C7#54611yescharacteristic
586C22×C7#54711yescharacteristic
587C22×C7#54711yescharacteristic
588C22×C7#54811yescharacteristic
589C22×C7#54811yescharacteristic
590C22×C7#55011yescharacteristic
591C22×C7#55011yescharacteristic
592C22×C7#55311yescharacteristic
593C22×C7#55311yescharacteristic
594C22×C7#55511yescharacteristic
595C4×C7—42no—
596C4×C7—42no—
597C4×C7—42no—
598C4×C7—44no—
599C4×C7—42no—
600C4×C7—42no—
601C4×C7—44no—
602C4×C7—82no—
603C4×C7#39418yescomplemented
604C24—21no—
605C24—21no—
606C24—21no—
607C24—21no—
608C24—21no—
609C24—21no—
610C24—21no—
611C24—21no—
612C24—21no—
613C24—21no—
614C24—21no—
615C24—21no—
616C24—22no—
617C24—22no—
618C24—22no—
619C24—22no—
620C24—22no—
621C24—22no—
622C24—22no—
623C24—22no—
624C24—22no—
625C24—22no—
626C24—22no—
627C24—22no—
628C24—22no—
629C24—22no—
630C24C2×C7×D414yes—
631C24C2×C7×D412yes—
632C24C2×C7×D412yes—
633C24C7×#4112yes—
634C24C24×C711yescharacteristic
635C2×D4—216no—
636C2×D4—28no—
637C2×D4—28no—
638C2×D4—28no—
639C2×D4—48no—
640C2×D4—48no—
641C2×D4—48no—
642C2×D4—48no—
643C2×D4—48no—
644C2×D4—48no—
645C2×D4—44no—
646C2×D4—44no—
647C2×D4—44no—
648C2×D4—44no—
649C22×C4—21no—
650C22×C4—21no—
651C22×C4—21no—
652C22×C4—21no—
653C22×C4—21no—
654C22×C4—21no—
655C22×C4—22no—
656C22×C4—22no—
657C22×C4—21no—
658C22×C4—21no—
659C22×C4—21no—
660C22×C4—21no—
661C22×C4—21no—
662C22×C4—22no—
663C22×C4—21no—
664C22×C4—21no—
665C22×C4—22no—
666C22×C4—22no—
667C22×C4—21no—
668C22×C4—21no—
669C22×C4—21no—
670C22×C4—21no—
671C22×C4—21no—
672C22×C4—21no—
673C22×C4—22no—
674C22×C4—22no—
675C22×C4—21no—
676C22×C4—21no—
677C22×C4—21no—
678C22×C4—22no—
679C22×C4—21no—
680C22×C4—22no—
681C22×C4—21no—
682C22×C4—21no—
683C22×C4—22no—
684C22×C4—21no—
685C22×C4—21no—
686C22×C4—22no—
687C22×C4—21no—
688C22×C4—22no—
689C22×C4—21no—
690C22×C4—21no—
691C22×C4—28no—
692C22×C4—28no—
693C22×C4—28no—
694C22×C4—22no—
695C22×C4—22no—
696C22×C4—22no—
697C22×C4—22no—
698C22×C4—22no—
699C22×C4—22no—
700C22×C4—22no—
701C22×C4—44no—
702C22×C4—44no—
703C22×C4—44no—
704C22×C4—44no—
705C22×C4C2×C7×D412yes—
706C22×C4C2×C7×D412yes—
707C22×C4C2×C7×D414yes—
708C22×C4C2×C7×D414yes—
709C22×C4C2×C7×D412yes—
710C22×C4C2×C7×D412yes—
711C22×C4C2×C7×D412yes—
712C22×C4C2×C7×D412yes—
713C22×C4C2×C7×D412yes—
714C22×C4C7×#4112yes—
715C22×C4C7×#4112yes—
716C22×C4C7×#4112yes—
717C22×C4C7×#4112yes—
718C22×C4C7×#4112yes—
719C4⋊C4—28no—
720C4⋊C4—28no—
721C4⋊C4—48no—
722C4⋊C4—44no—
723C22⋊C4—216no—
724C22⋊C4—28no—
725C22⋊C4—28no—
726C22⋊C4—48no—
727C22⋊C4—48no—
728C22⋊C4—48no—
729C22⋊C4—48no—
730C22⋊C4—48no—
731C42—44no—
732C42—44no—
733C2×C7—44no—
734C2×C7—84no—
735C2×C7C2×#39411yescharacteristic
736C2×C7#240711yescharacteristic
737C2×C7#240811yescharacteristic
738C2×C7#241411yescharacteristic
739C2×C7#241611yescharacteristic
740C2×C7#242011yescharacteristic
741C2×C7#242211yescharacteristic
742C2×C7#242611yescharacteristic
743C2×C7#242711yescharacteristic
744C2×C7#242811yescharacteristic
745C2×C7#242811yescharacteristic
746C2×C7#249011yescharacteristic
747C2×C7#249111yescharacteristic
748C2×C7#262411yescharacteristic
749C2×C7#285411yescharacteristic
750C23—22no—
751C23—22no—
752C23—22no—
753C23—22no—
754C23—22no—
755C23—22no—
756C23—22no—
757C23—22no—
758C23—22no—
759C23—22no—
760C23—22no—
761C23—22no—
762C23—22no—
763C23—22no—
764C23—22no—
765C23—22no—
766C23—22no—
767C23—22no—
768C23—24no—
769C23—24no—
770C23—24no—
771C23—24no—
772C23—24no—
773C23—24no—
774C23—24no—
775C23—41no—
776C23—41no—
777C23—41no—
778C23—41no—
779C23—41no—
780C23—41no—
781C23—41no—
782C23—41no—
783C23—41no—
784C23—41no—
785C23—41no—
786C23—41no—
787C23—41no—
788C23—41no—
789C23—41no—
790C23—41no—
791C23—42no—
792C23—42no—
793C23—42no—
794C23—42no—
795C23—42no—
796C23—42no—
797C23—42no—
798C23—42no—
799C23—42no—
800C23—42no—
801C23—42no—
802C23—42no—
803C23—42no—
804C23—42no—
805C23—42no—
806C23—42no—
807C23—42no—
808C23—42no—
809C23—42no—
810C23—42no—
811C23—42no—
812C23—42no—
813C23—42no—
814C23—42no—
815C23—42no—
816C23—42no—
817C23—42no—
818C23—42no—
819C23C7×#12114yes—
820C23C22×C7×D411yescharacteristic
821C23C22×C7×D411yescharacteristic
822C23C22×C7×D411yescharacteristic
823C23C22×C7×D411yescharacteristic
824C23C22×C7×D411yescharacteristic
825C23C2×C7×#4111yescharacteristic
826C23C2×C7×#4111yescharacteristic
827C23C2×C7×#4111yescharacteristic
828C23C2×C7×#4111yescharacteristic
829C23C2×C7×#4111yescharacteristic
830C23C2×C7×#4111yescharacteristic
831C23C7×H(5,𝔽2)11yescharacteristic
832C23C7×H(5,𝔽2)11yescharacteristic
833C23C7×H(5,𝔽2)11yescharacteristic
834C23C7×2−1+411yescharacteristic
835D4—432no—
836D4—416no—
837C2×C4—22no—
838C2×C4—24no—
839C2×C4—22no—
840C2×C4—22no—
841C2×C4—24no—
842C2×C4—22no—
843C2×C4—22no—
844C2×C4—22no—
845C2×C4—22no—
846C2×C4—22no—
847C2×C4—22no—
848C2×C4—24no—
849C2×C4—22no—
850C2×C4—24no—
851C2×C4—22no—
852C2×C4—22no—
853C2×C4—24no—
854C2×C4—24no—
855C2×C4—22no—
856C2×C4—22no—
857C2×C4—22no—
858C2×C4—41no—
859C2×C4—41no—
860C2×C4—41no—
861C2×C4—41no—
862C2×C4—41no—
863C2×C4—41no—
864C2×C4—42no—
865C2×C4—41no—
866C2×C4—41no—
867C2×C4—42no—
868C2×C4—41no—
869C2×C4—41no—
870C2×C4—42no—
871C2×C4—41no—
872C2×C4—41no—
873C2×C4—42no—
874C2×C4—42no—
875C2×C4—42no—
876C2×C4—41no—
877C2×C4—41no—
878C2×C4—42no—
879C2×C4—41no—
880C2×C4—41no—
881C2×C4—41no—
882C2×C4—41no—
883C2×C4—42no—
884C2×C4—41no—
885C2×C4—41no—
886C2×C4—416no—
887C2×C4—42no—
888C2×C4—42no—
889C2×C4—42no—
890C2×C4—42no—
891C2×C4—42no—
892C2×C4—42no—
893C2×C4—42no—
894C2×C4C7×#12014yes—
895C2×C4C7×#12114yes—
896C2×C4C7×#12114yes—
897C2×C4C7×#12114yes—
898C2×C4C7×#12314yes—
899C2×C4C7×#12314yes—
900C2×C4C7×#12414yes—
901C7#1512611yescharacteristic, direct product factor, Sylow
902C22—24no—
903C22—24no—
904C22—24no—
905C22—42no—
906C22—42no—
907C22—42no—
908C22—42no—
909C22—42no—
910C22—42no—
911C22—42no—
912C22—42no—
913C22—42no—
914C22—42no—
915C22—42no—
916C22—42no—
917C22—44no—
918C22—44no—
919C22—44no—
920C22—44no—
921C22—44no—
922C22—44no—
923C22—44no—
924C22—82no—
925C22—82no—
926C22—82no—
927C22—82no—
928C22—82no—
929C22—82no—
930C22—82no—
931C22—82no—
932C22C2×C7×#12011yescharacteristic
933C22C2×C7×#12111yescharacteristic
934C22C2×C7×#12111yescharacteristic
935C22C2×C7×#12111yescharacteristic
936C22C2×C7×#12111yescharacteristic
937C22C2×C7×#12311yescharacteristic
938C22C2×C7×#12311yescharacteristic
939C22C7×#52511yescharacteristic
940C22C2×C7×#12411yescharacteristic
941C22C7×#52911yescharacteristic
942C22C7×#52911yescharacteristic
943C22C7×#53211yescharacteristic
944C22C7×#53211yescharacteristic
945C22C7×#53511yescharacteristic
946C22C7×#53711yescharacteristic
947C22C7×#54011yescharacteristic
948C22C7×#54011yescharacteristic
949C22C7×#54211yescharacteristic
950C22C7×#54211yescharacteristic
951C22C7×D4211yescharacteristic
952C22C7×D4211yescharacteristic
953C22C7×D4211yescharacteristic
954C22C7×#54611yescharacteristic
955C22C7×#54611yescharacteristic
956C22C7×#54611yescharacteristic
957C22C7×#54611yescharacteristic
958C22C7×#54711yescharacteristic
959C22C7×#54711yescharacteristic
960C22C7×#54811yescharacteristic
961C22C7×#54811yescharacteristic
962C22C7×#55011yescharacteristic
963C22C7×#55011yescharacteristic
964C22C7×#55311yescharacteristic
965C22C7×#55311yescharacteristic
966C22C7×#55511yescharacteristic
967C4—42no—
968C4—44no—
969C4—42no—
970C4—42no—
971C4—42no—
972C4—44no—
973C4—42no—
974C4—82no—
975C4C7×#39418yescomplemented
976C2—44no—
977C2—84no—
978C2C2×C7×#39411yescharacteristic
979C2C7×#240711yescharacteristic
980C2C7×#240811yescharacteristic
981C2C7×#241411yescharacteristic
982C2C7×#241611yescharacteristic
983C2C7×#242011yescharacteristic
984C2C7×#242211yescharacteristic
985C2C7×#242611yescharacteristic
986C2C7×#242711yescharacteristic
987C2C7×#242811yescharacteristic
988C2C7×#242811yescharacteristic
989C2C7×#249011yescharacteristic
990C2C7×#249111yescharacteristic
991C2C7×#262411yescharacteristic
992C2C7×#285411yescharacteristic
subgroupG/H
center, socleC24×C7C24
commutator, Frattini, cosocleC24C24×C7
prime radicalC22×C7×#121C2
LCSG ▷ C24 ▷ C1
UCSC1 ◁ C24×C7 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×C7×#394C2semidirect
3. C2×C7×#390C2semidirect
4. C2×C7×#390C2semidirect
5. C2×C7×#389C2semidirect
6. C2×C7×#380C2semidirect
7. C2×C4×C7×C22⋊C4C2semidirect
8. C7×#1440C2semidirect
9. C7×#1439C2semidirect
10. C7×#1438C2semidirect
11. C7×C4⋊#95C2semidirect
44. #15126C7direct (N × H)
89. C2×C7×C4⋊C4D4semidirect
113. C2×C7×C22⋊C4D4semidirect
127. C2×#394C2×C7semidirect
128. C2×#390C2×C7semidirect
129. C2×#390C2×C7semidirect
130. C2×#389C2×C7semidirect
131. C2×#380C2×C7semidirect
132. C2×C4×C22⋊C4C2×C7semidirect
133. #1440C2×C7semidirect
134. #1439C2×C7semidirect
135. #1438C2×C7semidirect
136. C4⋊#95C2×C7semidirect
493. C2×C4⋊C4C7×D4semidirect
517. C2×C22⋊C4C7×D4semidirect
603. C4×C7#394semidirect
901. C7#15126direct (N × H)
975. C4C7×#394semidirect

Maximal subgroups

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

subgroupindex
C22×C7×#1212
C2×C7×#3942
C2×C7×#3902
C2×C7×#3892
C2×C7×#3802
C2×C4×C7×C22⋊C42
C7×#14402
C7×#14392
C7×#14382
C7×C4⋊#952
#151267