Finite Group Databasebeta

← C7×#13877 #13191093

Subgroups — C7×#13877 #13191093

Order 1792.

4046 conjugacy classes of subgroups.

The subgroup lattice has 650 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C23×C7×C22⋊C4C211yesmaximal, characteristic
2C23×C7×C22⋊C4C211yesmaximal, characteristic
3C2×C7×#385C212yesmaximal, complemented
4C2×C7×#380C212yesmaximal, complemented
5C2×C7×#379C211yesmaximal, characteristic
6C7×#1439C214yesmaximal, complemented
7C7×C22⋊#95C212yesmaximal, complemented
8C7×C22⋊#95C212yesmaximal, complemented
9C26×C7C2211yescharacteristic
10C24×C4×C7C2212yes—
11C24×C4×C7C2212yes—
12C22×C7×C4⋊C4C2214yescomplemented
13C22×C7×C22⋊C4—24no—
14C22×C7×C22⋊C4—28no—
15C22×C7×C22⋊C4—28no—
16C22×C7×C22⋊C4C418yescomplemented
17C22×C7×C22⋊C4C2212yes—
18C22×C7×C22⋊C4C2211yescharacteristic
19C22×C7×C22⋊C4C2212yes—
20C22×C7×C22⋊C4C2211yescharacteristic
21C22×C7×C22⋊C4C2211yescharacteristic
22C22×C7×C22⋊C4C2212yes—
23C22×C7×C22⋊C4C2212yes—
24C22×C7×C22⋊C4C2212yes—
25C22×C7×C22⋊C4C2211yescharacteristic
26C7×#385—28no—
27C7×#380—28no—
28C7×#379—24no—
29C2×C7×#95C2214yescomplemented
30C2×C7×#95C2214yescomplemented
31C2×C7×#95C2214yescomplemented
32#13877C711yesmaximal, characteristic, direct product factor, Sylow
33C25×C7—24no—
34C25×C7—24no—
35C25×C7—24no—
36C25×C7—24no—
37C25×C7—44no—
38C25×C7C2×C414yes—
39C25×C7D414yes—
40C25×C7Q814yes—
41C25×C7C2311yescharacteristic
42C25×C7C2311yescharacteristic
43C25×C7C2311yescharacteristic
44C23×C4×C7—24no—
45C23×C4×C7—24no—
46C23×C4×C7—24no—
47C23×C4×C7—28no—
48C23×C4×C7—28no—
49C23×C4×C7—24no—
50C23×C4×C7—24no—
51C23×C4×C7—44no—
52C23×C4×C7—44no—
53C23×C4×C7C2×C418yescomplemented
54C23×C4×C7C2312yes—
55C23×C4×C7C2312yes—
56C23×C4×C7C2312yes—
57C23×C4×C7C2314yes—
58C23×C4×C7C2312yes—
59C2×C7×C4⋊C4—28no—
60C2×C7×C4⋊C4—28no—
61C2×C7×C4⋊C4—44no—
62C2×C7×C22⋊C4—232no—
63C2×C7×C22⋊C4—24no—
64C2×C7×C22⋊C4—24no—
65C2×C7×C22⋊C4—24no—
66C2×C7×C22⋊C4—24no—
67C2×C7×C22⋊C4—28no—
68C2×C7×C22⋊C4—28no—
69C2×C7×C22⋊C4—232no—
70C2×C7×C22⋊C4—24no—
71C2×C7×C22⋊C4—22no—
72C2×C7×C22⋊C4—24no—
73C2×C7×C22⋊C4—22no—
74C2×C7×C22⋊C4—24no—
75C2×C7×C22⋊C4—24no—
76C2×C7×C22⋊C4—24no—
77C2×C7×C22⋊C4—24no—
78C2×C7×C22⋊C4—44no—
79C2×C7×C22⋊C4C2×C414yes—
80C2×C7×C22⋊C4C2×C414yes—
81C2×C7×C22⋊C4C2×C418yescomplemented
82C2×C7×C22⋊C4D418yes—
83C2×C7×C22⋊C4D418yes—
84C7×#95—28no—
85C7×#95—28no—
86C7×#95—44no—
87C23×C22⋊C4C2×C711yescharacteristic
88C23×C22⋊C4C2×C711yescharacteristic
89C2×#385C2×C712yescomplemented
90C2×#380C2×C712yescomplemented
91C2×#379C2×C711yescharacteristic
92#1439C2×C714yescomplemented
93C22⋊#95C2×C712yescomplemented
94C22⋊#95C2×C712yescomplemented
95C24×C7—22no—
96C24×C7—22no—
97C24×C7—22no—
98C24×C7—22no—
99C24×C7—24no—
100C24×C7—24no—
101C24×C7—28no—
102C24×C7—28no—
103C24×C7—216no—
104C24×C7—28no—
105C24×C7—216no—
106C24×C7—216no—
107C24×C7—216no—
108C24×C7—28no—
109C24×C7—22no—
110C24×C7—22no—
111C24×C7—22no—
112C24×C7—22no—
113C24×C7—24no—
114C24×C7—48no—
115C24×C7—48no—
116C24×C7—48no—
117C24×C7—416no—
118C24×C7—416no—
119C24×C7—416no—
120C24×C7—416no—
121C24×C7C4⋊C4116yescomplemented
122C24×C7C22×C412yes—
123C24×C7C22×C412yes—
124C24×C7C22×C412yes—
125C24×C7C2×D412yes—
126C24×C7C2×D414yes—
127C24×C7C2×D412yes—
128C24×C7C2×D412yes—
129C24×C7C2×D414yes—
130C24×C7C2×Q812yes—
131C24×C7C2×Q812yes—
132C24×C7C2×Q812yes—
133C24×C7#4114yes—
134C24×C7#4114yes—
135C24×C7C2411yescharacteristic
136C22×C4×C7—22no—
137C22×C4×C7—22no—
138C22×C4×C7—24no—
139C22×C4×C7—216no—
140C22×C4×C7—216no—
141C22×C4×C7—22no—
142C22×C4×C7—24no—
143C22×C4×C7—24no—
144C22×C4×C7—24no—
145C22×C4×C7—24no—
146C22×C4×C7—22no—
147C22×C4×C7—24no—
148C22×C4×C7—24no—
149C22×C4×C7—24no—
150C22×C4×C7—24no—
151C22×C4×C7—216no—
152C22×C4×C7—22no—
153C22×C4×C7—24no—
154C22×C4×C7—22no—
155C22×C4×C7—22no—
156C22×C4×C7—22no—
157C22×C4×C7—22no—
158C22×C4×C7—22no—
159C22×C4×C7—24no—
160C22×C4×C7—24no—
161C22×C4×C7—24no—
162C22×C4×C7—48no—
163C22×C4×C7—416no—
164C22×C4×C7—416no—
165C22×C4×C7—416no—
166C22×C4×C7—416no—
167C22×C4×C7—48no—
168C22×C4×C7—48no—
169C22×C4×C7C22×C414yes—
170C22×C4×C7C22×C414yes—
171C22×C4×C7C2×D418yes—
172C22×C4×C7C2×D418yes—
173C7×C4⋊C4—416no—
174C7×C22⋊C4—216no—
175C7×C22⋊C4—28no—
176C7×C22⋊C4—216no—
177C7×C22⋊C4—216no—
178C7×C22⋊C4—48no—
179C7×C22⋊C4—44no—
180C7×C22⋊C4—48no—
181C7×C22⋊C4—44no—
182C7×C22⋊C4C22⋊C4116yescomplemented
183C26C22×C711yescharacteristic
184C24×C4C22×C712yes—
185C24×C4C22×C712yes—
186C22×C4⋊C4C22×C714yescomplemented
187C22×C22⋊C4—24no—
188C22×C22⋊C4—28no—
189C22×C22⋊C4—28no—
190C22×C22⋊C4C4×C718yescomplemented
191C22×C22⋊C4C22×C712yes—
192C22×C22⋊C4C22×C711yescharacteristic
193C22×C22⋊C4C22×C712yes—
194C22×C22⋊C4C22×C711yescharacteristic
195C22×C22⋊C4C22×C711yescharacteristic
196C22×C22⋊C4C22×C712yes—
197C22×C22⋊C4C22×C712yes—
198C22×C22⋊C4C22×C712yes—
199C22×C22⋊C4C22×C711yescharacteristic
200#385—28no—
201#380—28no—
202#379—24no—
203C2×#95C22×C714yescomplemented
204C2×#95C22×C714yescomplemented
205C2×#95C22×C714yescomplemented
206C23×C7—22no—
207C23×C7—22no—
208C23×C7—24no—
209C23×C7—24no—
210C23×C7—24no—
211C23×C7—22no—
212C23×C7—24no—
213C23×C7—24no—
214C23×C7—24no—
215C23×C7—22no—
216C23×C7—24no—
217C23×C7—24no—
218C23×C7—24no—
219C23×C7—24no—
220C23×C7—28no—
221C23×C7—28no—
222C23×C7—28no—
223C23×C7—28no—
224C23×C7—28no—
225C23×C7—28no—
226C23×C7—28no—
227C23×C7—28no—
228C23×C7—22no—
229C23×C7—22no—
230C23×C7—24no—
231C23×C7—24no—
232C23×C7—22no—
233C23×C7—24no—
234C23×C7—24no—
235C23×C7—24no—
236C23×C7—22no—
237C23×C7—24no—
238C23×C7—24no—
239C23×C7—232no—
240C23×C7—232no—
241C23×C7—416no—
242C23×C7—432no—
243C23×C7—432no—
244C23×C7—432no—
245C23×C7—432no—
246C23×C7—464no—
247C23×C7—44no—
248C23×C7—44no—
249C23×C7—44no—
250C23×C7—44no—
251C23×C7C2×C22⋊C414yes—
252C23×C7C2×C4⋊C414yes—
253C23×C7C2×C4⋊C414yes—
254C23×C7C2×C4⋊C414yes—
255C23×C7#11714yes—
256C23×C7C4×D418yes—
257C23×C7#12014yes—
258C23×C7#12118yes—
259C23×C7C22⋊Q818yes—
260C23×C7C22⋊Q818yes—
261C23×C7#12314yes—
262C23×C7C23×C411yescharacteristic
263C23×C7C22×D412yes—
264C23×C7C22×D411yescharacteristic
265C23×C7C22×D412yes—
266C23×C7C22×Q811yescharacteristic
267C23×C7C2×#4112yes—
268C23×C7C2×#4112yes—
269C23×C7H(5,𝔽2)14yes—
270C2×C4×C7—24no—
271C2×C4×C7—24no—
272C2×C4×C7—28no—
273C2×C4×C7—28no—
274C2×C4×C7—24no—
275C2×C4×C7—24no—
276C2×C4×C7—24no—
277C2×C4×C7—28no—
278C2×C4×C7—28no—
279C2×C4×C7—28no—
280C2×C4×C7—432no—
281C2×C4×C7—432no—
282C2×C4×C7—44no—
283C2×C4×C7—44no—
284C2×C4×C7—44no—
285C2×C4×C7—44no—
286C2×C4×C7—44no—
287C2×C4×C7—44no—
288C2×C4×C7—42no—
289C2×C4×C7—42no—
290C2×C4×C7—42no—
291C2×C4×C7—42no—
292C2×C4×C7—42no—
293C2×C4×C7—42no—
294C2×C4×C7—44no—
295C2×C4×C7—44no—
296C2×C4×C7—44no—
297C2×C4×C7—44no—
298C2×C4×C7C2×C22⋊C418yescomplemented
299C25—24no—
300C25—24no—
301C25—24no—
302C25—24no—
303C25—44no—
304C25C2×C4×C714yes—
305C25C7×D414yes—
306C25C7×Q814yes—
307C25C23×C711yescharacteristic
308C25C23×C711yescharacteristic
309C25C23×C711yescharacteristic
310C23×C4—24no—
311C23×C4—24no—
312C23×C4—24no—
313C23×C4—28no—
314C23×C4—28no—
315C23×C4—24no—
316C23×C4—24no—
317C23×C4—44no—
318C23×C4—44no—
319C23×C4C2×C4×C718yescomplemented
320C23×C4C23×C712yes—
321C23×C4C23×C712yes—
322C23×C4C23×C712yes—
323C23×C4C23×C714yes—
324C23×C4C23×C712yes—
325C2×C4⋊C4—28no—
326C2×C4⋊C4—28no—
327C2×C4⋊C4—44no—
328C2×C22⋊C4—232no—
329C2×C22⋊C4—24no—
330C2×C22⋊C4—24no—
331C2×C22⋊C4—24no—
332C2×C22⋊C4—24no—
333C2×C22⋊C4—28no—
334C2×C22⋊C4—28no—
335C2×C22⋊C4—232no—
336C2×C22⋊C4—24no—
337C2×C22⋊C4—22no—
338C2×C22⋊C4—24no—
339C2×C22⋊C4—22no—
340C2×C22⋊C4—24no—
341C2×C22⋊C4—24no—
342C2×C22⋊C4—24no—
343C2×C22⋊C4—24no—
344C2×C22⋊C4—44no—
345C2×C22⋊C4C2×C4×C714yes—
346C2×C22⋊C4C2×C4×C714yes—
347C2×C22⋊C4C2×C4×C718yescomplemented
348C2×C22⋊C4C7×D418yes—
349C2×C22⋊C4C7×D418yes—
350#95—28no—
351#95—28no—
352#95—44no—
353C22×C7—24no—
354C22×C7—24no—
355C22×C7—28no—
356C22×C7—28no—
357C22×C7—28no—
358C22×C7—28no—
359C22×C7—28no—
360C22×C7—28no—
361C22×C7—28no—
362C22×C7—28no—
363C22×C7—216no—
364C22×C7—216no—
365C22×C7—24no—
366C22×C7—24no—
367C22×C7—24no—
368C22×C7—24no—
369C22×C7—24no—
370C22×C7—464no—
371C22×C7—44no—
372C22×C7—44no—
373C22×C7—44no—
374C22×C7—44no—
375C22×C7—48no—
376C22×C7#38018yescomplemented
377C22×C7#38518yescomplemented
378C22×C7C22×C22⋊C411yescharacteristic
379C22×C7C22×C4⋊C411yescharacteristic
380C22×C7C2×#11711yescharacteristic
381C22×C7C2×C4×D412yes—
382C22×C7#51812yes—
383C22×C7C2×#12011yescharacteristic
384C22×C7C2×#12112yes—
385C22×C7C2×C22⋊Q812yes—
386C22×C7C2×C22⋊Q812yes—
387C22×C7C2×#12311yescharacteristic
388C22×C7#53412yes—
389C22×C7#54312yes—
390C22×C7D4214yes—
391C22×C7#54614yes—
392C22×C7#54614yes—
393C22×C7#55114yes—
394C4×C7—28no—
395C4×C7—44no—
396C4×C7—48no—
397C4×C7—82no—
398C4×C7—82no—
399C24—22no—
400C24—22no—
401C24—22no—
402C24—22no—
403C24—24no—
404C24—24no—
405C24—28no—
406C24—28no—
407C24—216no—
408C24—28no—
409C24—216no—
410C24—216no—
411C24—216no—
412C24—28no—
413C24—22no—
414C24—22no—
415C24—22no—
416C24—22no—
417C24—24no—
418C24—48no—
419C24—48no—
420C24—48no—
421C24—416no—
422C24—416no—
423C24—416no—
424C24—416no—
425C24C7×C4⋊C4116yescomplemented
426C24C22×C4×C712yes—
427C24C22×C4×C712yes—
428C24C22×C4×C712yes—
429C24C2×C7×D412yes—
430C24C2×C7×D414yes—
431C24C2×C7×D412yes—
432C24C2×C7×D412yes—
433C24C2×C7×D414yes—
434C24C2×C7×Q812yes—
435C24C2×C7×Q812yes—
436C24C2×C7×Q812yes—
437C24C7×#4114yes—
438C24C7×#4114yes—
439C24C24×C711yescharacteristic
440C22×C4—22no—
441C22×C4—22no—
442C22×C4—24no—
443C22×C4—216no—
444C22×C4—216no—
445C22×C4—22no—
446C22×C4—24no—
447C22×C4—24no—
448C22×C4—24no—
449C22×C4—24no—
450C22×C4—22no—
451C22×C4—24no—
452C22×C4—24no—
453C22×C4—24no—
454C22×C4—24no—
455C22×C4—216no—
456C22×C4—22no—
457C22×C4—24no—
458C22×C4—22no—
459C22×C4—22no—
460C22×C4—22no—
461C22×C4—22no—
462C22×C4—22no—
463C22×C4—24no—
464C22×C4—24no—
465C22×C4—24no—
466C22×C4—48no—
467C22×C4—416no—
468C22×C4—416no—
469C22×C4—416no—
470C22×C4—416no—
471C22×C4—48no—
472C22×C4—48no—
473C22×C4C22×C4×C714yes—
474C22×C4C22×C4×C714yes—
475C22×C4C2×C7×D418yes—
476C22×C4C2×C7×D418yes—
477C4⋊C4—416no—
478C22⋊C4—216no—
479C22⋊C4—28no—
480C22⋊C4—216no—
481C22⋊C4—216no—
482C22⋊C4—48no—
483C22⋊C4—44no—
484C22⋊C4—48no—
485C22⋊C4—44no—
486C22⋊C4C7×C22⋊C4116yescomplemented
487C2×C7—28no—
488C2×C7—28no—
489C2×C7—44no—
490C2×C7C2×#38011yescharacteristic
491C2×C7C2×#38511yescharacteristic
492C2×C7#231511yescharacteristic
493C2×C7D4×C22⋊C412yes—
494C2×C7#234212yes—
495C2×C7#241012yes—
496C2×C7#241212yes—
497C2×C7#243714yes—
498C23—22no—
499C23—22no—
500C23—24no—
501C23—24no—
502C23—24no—
503C23—22no—
504C23—24no—
505C23—24no—
506C23—24no—
507C23—22no—
508C23—24no—
509C23—24no—
510C23—24no—
511C23—24no—
512C23—28no—
513C23—28no—
514C23—28no—
515C23—28no—
516C23—28no—
517C23—28no—
518C23—28no—
519C23—28no—
520C23—22no—
521C23—22no—
522C23—24no—
523C23—232no—
524C23—24no—
525C23—22no—
526C23—232no—
527C23—24no—
528C23—24no—
529C23—24no—
530C23—22no—
531C23—24no—
532C23—24no—
533C23—416no—
534C23—432no—
535C23—432no—
536C23—464no—
537C23—432no—
538C23—432no—
539C23—44no—
540C23—44no—
541C23—44no—
542C23—44no—
543C23C2×C7×C22⋊C414yes—
544C23C2×C7×C4⋊C414yes—
545C23C2×C7×C4⋊C414yes—
546C23C2×C7×C4⋊C414yes—
547C23C7×#11714yes—
548C23C4×C7×D418yes—
549C23C7×#12014yes—
550C23C7×#12118yes—
551C23C7×C22⋊Q818yes—
552C23C7×C22⋊Q818yes—
553C23C7×#12314yes—
554C23C23×C4×C711yescharacteristic
555C23C22×C7×D412yes—
556C23C22×C7×D411yescharacteristic
557C23C22×C7×D412yes—
558C23C22×C7×Q811yescharacteristic
559C23C2×C7×#4112yes—
560C23C2×C7×#4112yes—
561C23C7×H(5,𝔽2)14yes—
562C2×C4—24no—
563C2×C4—24no—
564C2×C4—28no—
565C2×C4—28no—
566C2×C4—24no—
567C2×C4—24no—
568C2×C4—24no—
569C2×C4—28no—
570C2×C4—28no—
571C2×C4—28no—
572C2×C4—432no—
573C2×C4—432no—
574C2×C4—44no—
575C2×C4—44no—
576C2×C4—44no—
577C2×C4—44no—
578C2×C4—44no—
579C2×C4—44no—
580C2×C4—42no—
581C2×C4—42no—
582C2×C4—42no—
583C2×C4—42no—
584C2×C4—42no—
585C2×C4—42no—
586C2×C4—44no—
587C2×C4—44no—
588C2×C4—44no—
589C2×C4—44no—
590C2×C4C2×C7×C22⋊C418yescomplemented
591C7#1387711yescharacteristic, direct product factor, Sylow
592C22—28no—
593C22—28no—
594C22—28no—
595C22—28no—
596C22—216no—
597C22—216no—
598C22—24no—
599C22—24no—
600C22—24no—
601C22—24no—
602C22—28no—
603C22—28no—
604C22—28no—
605C22—28no—
606C22—24no—
607C22—24no—
608C22—24no—
609C22—464no—
610C22—44no—
611C22—44no—
612C22—48no—
613C22—44no—
614C22—44no—
615C22C7×#38018yescomplemented
616C22C7×#38518yescomplemented
617C22C22×C7×C22⋊C411yescharacteristic
618C22C22×C7×C4⋊C411yescharacteristic
619C22C2×C7×#11711yescharacteristic
620C22C2×C4×C7×D412yes—
621C22C7×#51812yes—
622C22C2×C7×#12011yescharacteristic
623C22C2×C7×#12112yes—
624C22C2×C7×C22⋊Q812yes—
625C22C2×C7×C22⋊Q812yes—
626C22C2×C7×#12311yescharacteristic
627C22C7×#53412yes—
628C22C7×#54312yes—
629C22C7×D4214yes—
630C22C7×#54614yes—
631C22C7×#54614yes—
632C22C7×#55114yes—
633C4—28no—
634C4—48no—
635C4—44no—
636C4—82no—
637C4—82no—
638C2—28no—
639C2—28no—
640C2—44no—
641C2C2×C7×#38011yescharacteristic
642C2C2×C7×#38511yescharacteristic
643C2C7×#231511yescharacteristic
644C2C7×D4×C22⋊C412yes—
645C2C7×#234212yes—
646C2C7×#241012yes—
647C2C7×#241212yes—
648C2C7×#243714yes—
subgroupG/H
center, socleC24×C7C24
commutatorC23C23×C4×C7
Frattini, cosocleC24C24×C7
prime radicalC26×C7C22
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C24×C7 ◁ G

Complements

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

NH ≅ G/Ntype
3. C2×C7×#385C2semidirect
4. C2×C7×#380C2semidirect
6. C7×#1439C2semidirect
7. C7×C22⋊#95C2semidirect
8. C7×C22⋊#95C2semidirect
12. C22×C7×C4⋊C4C22semidirect
16. C22×C7×C22⋊C4C4semidirect
29. C2×C7×#95C22semidirect
30. C2×C7×#95C22semidirect
31. C2×C7×#95C22semidirect
32. #13877C7direct (N × H)
53. C23×C4×C7C2×C4semidirect
81. C2×C7×C22⋊C4C2×C4semidirect
89. C2×#385C2×C7semidirect
90. C2×#380C2×C7semidirect
92. #1439C2×C7semidirect
93. C22⋊#95C2×C7semidirect
94. C22⋊#95C2×C7semidirect
121. C24×C7C4⋊C4semidirect
182. C7×C22⋊C4C22⋊C4semidirect
186. C22×C4⋊C4C22×C7semidirect
190. C22×C22⋊C4C4×C7semidirect
203. C2×#95C22×C7semidirect
204. C2×#95C22×C7semidirect
205. C2×#95C22×C7semidirect
298. C2×C4×C7C2×C22⋊C4semidirect
319. C23×C4C2×C4×C7semidirect
347. C2×C22⋊C4C2×C4×C7semidirect
376. C22×C7#380semidirect
377. C22×C7#385semidirect
425. C24C7×C4⋊C4semidirect
486. C22⋊C4C7×C22⋊C4semidirect
590. C2×C4C2×C7×C22⋊C4semidirect
591. C7#13877direct (N × H)
615. C22C7×#380semidirect
616. C22C7×#385semidirect

Maximal subgroups

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

subgroupindex
C23×C7×C22⋊C42
C2×C7×#3852
C2×C7×#3802
C2×C7×#3792
C7×#14392
C7×C22⋊#952
#138777