Finite Group Databasebeta

← C7×#15110 #13192326

Subgroups — C7×#15110 #13192326

Order 1792.

1334 conjugacy classes of subgroups.

The subgroup lattice has 640 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C7×#388C211yesmaximal, characteristic
2C2×C4×C7×C4⋊C4C211yesmaximal, characteristic, complemented
3C7×#1443C212yesmaximal, complemented
4C7×#1442C211yesmaximal, characteristic, complemented
5C7×#1442C211yesmaximal, characteristic, complemented
6C7×#1440C212yesmaximal
7C7×#1439C211yesmaximal, characteristic
8C7×#1439C211yesmaximal, characteristic
9C7×#1437C212yesmaximal
10C7×#1436C212yesmaximal, complemented
11C7×#1434C211yesmaximal, characteristic, complemented
12C22×C7×C4⋊C4C2211yescharacteristic
13C22×C7×C4⋊C4C2211yescharacteristic
14C22×C7×C4⋊C4C2211yescharacteristic
15C22×C7×C22⋊C4C2211yescharacteristic
16C22×C7×C22⋊C4C2211yescharacteristic
17C22×C7×C22⋊C4C2211yescharacteristic
18C22×C7×C22⋊C4C2212yes—
19C22×C7×C22⋊C4C2212yes—
20C22×C42×C7C2211yescharacteristic
21C22×C42×C7C2212yes—
22C7×#388—24no—
23C4×C7×C4⋊C4—24no—
24C2×C7×#95C2212yes—
25C2×C7×#95C2211yescharacteristic
26C2×C7×#95C2211yescharacteristic
27C2×C7×#95C2212yes—
28C2×C7×#95C2211yescharacteristic
29C2×C7×#95C2211yescharacteristic
30C2×C7×#95C2212yes—
31C2×C7×#95C2212yes—
32C2×C7×#95C2212yes—
33C2×C7×#95C2212yes—
34C2×C7×#95C2212yes—
35C2×C7×#95C2212yes—
36C2×C7×#95C2212yes—
37#15110C711yesmaximal, characteristic, direct product factor, Sylow
38C25×C7C2311yescharacteristic
39C23×C4×C7C2311yescharacteristic
40C23×C4×C7C2312yes—
41C23×C4×C7C2312yes—
42C23×C4×C7C2311yescharacteristic
43C23×C4×C7C2311yescharacteristic
44C23×C4×C7C2312yes—
45C23×C4×C7C2312yes—
46C23×C4×C7C2311yescharacteristic
47C23×C4×C7C2311yescharacteristic
48C23×C4×C7C2311yescharacteristic
49C2×C7×C4⋊C4—22no—
50C2×C7×C4⋊C4—22no—
51C2×C7×C4⋊C4—24no—
52C2×C7×C4⋊C4—24no—
53C2×C7×C4⋊C4—22no—
54C2×C7×C4⋊C4—24no—
55C2×C7×C22⋊C4—22no—
56C2×C7×C22⋊C4—22no—
57C2×C7×C22⋊C4—22no—
58C2×C7×C22⋊C4—24no—
59C2×C7×C22⋊C4—22no—
60C2×C7×C22⋊C4—22no—
61C2×C7×C22⋊C4—24no—
62C2×C7×C22⋊C4—24no—
63C2×C7×C22⋊C4—22no—
64C2×C7×C22⋊C4—22no—
65C2×C7×C22⋊C4—24no—
66C2×C7×C22⋊C4—42no—
67C2×C7×C22⋊C4—42no—
68C2×C7×C22⋊C4—42no—
69C2×C42×C7—22no—
70C2×C42×C7—22no—
71C2×C42×C7—24no—
72C2×C42×C7—42no—
73C2×C42×C7—42no—
74C2×C42×C7D414yes—
75C7×#95—24no—
76C7×#95—22no—
77C7×#95—22no—
78C7×#95—24no—
79C7×#95—24no—
80C7×#95—24no—
81C7×#95—22no—
82C7×#95—22no—
83C7×#95—24no—
84C7×#95—42no—
85C7×#95—42no—
86C7×#95—42no—
87C7×#95—42no—
88C2×#388C2×C711yescharacteristic
89C2×C4×C4⋊C4C2×C711yescharacteristic, complemented
90#1443C2×C712yescomplemented
91#1442C2×C711yescharacteristic, complemented
92#1442C2×C711yescharacteristic, complemented
93#1440C2×C712yes—
94#1439C2×C711yescharacteristic
95#1439C2×C711yescharacteristic
96#1437C2×C712yes—
97#1436C2×C712yescomplemented
98#1434C2×C711yescharacteristic, complemented
99C24×C7—21no—
100C24×C7—21no—
101C24×C7—22no—
102C24×C7—22no—
103C24×C7—22no—
104C24×C7—21no—
105C24×C7—21no—
106C24×C7—22no—
107C24×C7—21no—
108C24×C7—21no—
109C24×C7#4112yes—
110C24×C7C2411yescharacteristic
111C22×C4×C7—21no—
112C22×C4×C7—21no—
113C22×C4×C7—22no—
114C22×C4×C7—22no—
115C22×C4×C7—22no—
116C22×C4×C7—22no—
117C22×C4×C7—22no—
118C22×C4×C7—21no—
119C22×C4×C7—22no—
120C22×C4×C7—22no—
121C22×C4×C7—21no—
122C22×C4×C7—21no—
123C22×C4×C7—21no—
124C22×C4×C7—21no—
125C22×C4×C7—21no—
126C22×C4×C7—22no—
127C22×C4×C7—22no—
128C22×C4×C7—22no—
129C22×C4×C7—22no—
130C22×C4×C7—21no—
131C22×C4×C7—22no—
132C22×C4×C7—22no—
133C22×C4×C7—22no—
134C22×C4×C7—22no—
135C22×C4×C7—22no—
136C22×C4×C7—21no—
137C22×C4×C7—22no—
138C22×C4×C7—21no—
139C22×C4×C7—21no—
140C22×C4×C7—22no—
141C22×C4×C7—22no—
142C22×C4×C7—22no—
143C22×C4×C7—22no—
144C22×C4×C7—22no—
145C22×C4×C7—22no—
146C22×C4×C7—22no—
147C22×C4×C7—22no—
148C22×C4×C7—21no—
149C22×C4×C7—21no—
150C22×C4×C7—22no—
151C22×C4×C7—22no—
152C22×C4×C7—22no—
153C22×C4×C7—22no—
154C22×C4×C7—22no—
155C22×C4×C7—22no—
156C22×C4×C7—21no—
157C22×C4×C7—22no—
158C22×C4×C7—22no—
159C22×C4×C7—22no—
160C22×C4×C7—22no—
161C22×C4×C7—21no—
162C22×C4×C7C2×D412yes—
163C22×C4×C7C2×D412yes—
164C22×C4×C7C2×D412yes—
165C22×C4×C7#4112yes—
166C22×C4×C7#4114yes—
167C22×C4×C7#4114yes—
168C22×C4×C7#4112yes—
169C22×C4×C7#4112yes—
170C22×C4×C7#4114yes—
171C7×C4⋊C4—28no—
172C7×C4⋊C4—28no—
173C7×C4⋊C4—44no—
174C7×C22⋊C4—28no—
175C7×C22⋊C4—48no—
176C7×C22⋊C4—48no—
177C7×C22⋊C4—44no—
178C7×C22⋊C4—44no—
179C42×C7—28no—
180C42×C7—48no—
181C22×C4⋊C4C22×C711yescharacteristic
182C22×C4⋊C4C22×C711yescharacteristic
183C22×C4⋊C4C22×C711yescharacteristic
184C22×C22⋊C4C22×C711yescharacteristic
185C22×C22⋊C4C22×C711yescharacteristic
186C22×C22⋊C4C22×C711yescharacteristic
187C22×C22⋊C4C22×C712yes—
188C22×C22⋊C4C22×C712yes—
189C22×C42C22×C711yescharacteristic
190C22×C42C22×C712yes—
191#388—24no—
192C4×C4⋊C4—24no—
193C2×#95C22×C712yes—
194C2×#95C22×C711yescharacteristic
195C2×#95C22×C711yescharacteristic
196C2×#95C22×C712yes—
197C2×#95C22×C712yes—
198C2×#95C22×C712yes—
199C2×#95C22×C712yes—
200C2×#95C22×C711yescharacteristic
201C2×#95C22×C711yescharacteristic
202C2×#95C22×C712yes—
203C2×#95C22×C712yes—
204C2×#95C22×C712yes—
205C2×#95C22×C712yes—
206C23×C7—22no—
207C23×C7—24no—
208C23×C7—24no—
209C23×C7—22no—
210C23×C7—22no—
211C23×C7—41no—
212C23×C7—41no—
213C23×C7—41no—
214C23×C7—41no—
215C23×C7—42no—
216C23×C7—42no—
217C23×C7—42no—
218C23×C7—41no—
219C23×C7—41no—
220C23×C7—42no—
221C23×C7—42no—
222C23×C7—42no—
223C23×C7—42no—
224C23×C7—42no—
225C23×C7—41no—
226C23×C7—42no—
227C23×C7—41no—
228C23×C7—42no—
229C23×C7C22×D411yescharacteristic
230C23×C7C2×#4111yescharacteristic
231C23×C7C2×#4111yescharacteristic
232C23×C7C2×#4112yes—
233C23×C7C2×#4111yescharacteristic
234C23×C7C2×#4112yes—
235C23×C7C2×#4111yescharacteristic
236C23×C7C2×#4112yes—
237C23×C7H(5,𝔽2)12yes—
238C23×C7H(5,𝔽2)11yescharacteristic
239C23×C72−1+411yescharacteristic
240C2×C4×C7—22no—
241C2×C4×C7—22no—
242C2×C4×C7—22no—
243C2×C4×C7—24no—
244C2×C4×C7—24no—
245C2×C4×C7—22no—
246C2×C4×C7—24no—
247C2×C4×C7—24no—
248C2×C4×C7—22no—
249C2×C4×C7—22no—
250C2×C4×C7—22no—
251C2×C4×C7—24no—
252C2×C4×C7—24no—
253C2×C4×C7—24no—
254C2×C4×C7—22no—
255C2×C4×C7—24no—
256C2×C4×C7—24no—
257C2×C4×C7—24no—
258C2×C4×C7—24no—
259C2×C4×C7—42no—
260C2×C4×C7—41no—
261C2×C4×C7—41no—
262C2×C4×C7—42no—
263C2×C4×C7—42no—
264C2×C4×C7—42no—
265C2×C4×C7—42no—
266C2×C4×C7—42no—
267C2×C4×C7—42no—
268C2×C4×C7—42no—
269C2×C4×C7—41no—
270C2×C4×C7—42no—
271C2×C4×C7—41no—
272C2×C4×C7—41no—
273C2×C4×C7—41no—
274C2×C4×C7—41no—
275C2×C4×C7—41no—
276C2×C4×C7—41no—
277C2×C4×C7—41no—
278C2×C4×C7—42no—
279C2×C4×C7—42no—
280C2×C4×C7—42no—
281C2×C4×C7—42no—
282C2×C4×C7—41no—
283C2×C4×C7—41no—
284C2×C4×C7—42no—
285C2×C4×C7—42no—
286C2×C4×C7—42no—
287C2×C4×C7—42no—
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—42no—
295C2×C4×C7—42no—
296C2×C4×C7—42no—
297C2×C4×C7—42no—
298C2×C4×C7#12314yes—
299C2×C4×C7#12414yes—
300C25C23×C711yescharacteristic
301C23×C4C23×C711yescharacteristic
302C23×C4C23×C711yescharacteristic
303C23×C4C23×C712yes—
304C23×C4C23×C712yes—
305C23×C4C23×C711yescharacteristic
306C23×C4C23×C711yescharacteristic
307C23×C4C23×C712yes—
308C23×C4C23×C712yes—
309C23×C4C23×C711yescharacteristic
310C23×C4C23×C711yescharacteristic
311C2×C4⋊C4—22no—
312C2×C4⋊C4—22no—
313C2×C4⋊C4—24no—
314C2×C4⋊C4—24no—
315C2×C4⋊C4—22no—
316C2×C4⋊C4—24no—
317C2×C22⋊C4—22no—
318C2×C22⋊C4—22no—
319C2×C22⋊C4—22no—
320C2×C22⋊C4—24no—
321C2×C22⋊C4—22no—
322C2×C22⋊C4—22no—
323C2×C22⋊C4—24no—
324C2×C22⋊C4—24no—
325C2×C22⋊C4—22no—
326C2×C22⋊C4—22no—
327C2×C22⋊C4—24no—
328C2×C22⋊C4—42no—
329C2×C22⋊C4—42no—
330C2×C22⋊C4—42no—
331C2×C42—22no—
332C2×C42—22no—
333C2×C42—24no—
334C2×C42—42no—
335C2×C42—42no—
336C2×C42C7×D414yes—
337#95—24no—
338#95—22no—
339#95—22no—
340#95—24no—
341#95—24no—
342#95—24no—
343#95—22no—
344#95—22no—
345#95—24no—
346#95—42no—
347#95—42no—
348#95—42no—
349#95—42no—
350C22×C7—44no—
351C22×C7—44no—
352C22×C7—42no—
353C22×C7—42no—
354C22×C7—42no—
355C22×C7—81no—
356C22×C7—82no—
357C22×C7—82no—
358C22×C7—81no—
359C22×C7—81no—
360C22×C7—81no—
361C22×C7C2×#12311yescharacteristic
362C22×C7#52511yescharacteristic
363C22×C7#52511yescharacteristic
364C22×C7#52511yescharacteristic
365C22×C7C2×#12411yescharacteristic
366C22×C7#52912yes—
367C22×C7#52912yes—
368C22×C7#52912yes—
369C22×C7#52912yes—
370C22×C7#53511yescharacteristic
371C22×C7#53711yescharacteristic
372C22×C7#53812yes—
373C22×C7#53912yes—
374C22×C7#55112yes—
375C22×C7#55211yescharacteristic
376C22×C7#55312yes—
377C22×C7#55312yes—
378C22×C7#55312yes—
379C22×C7#55311yescharacteristic
380C22×C7#55511yescharacteristic
381C22×C7#55612yes—
382C22×C7#55611yescharacteristic
383C22×C7#55912yes—
384C4×C7—24no—
385C4×C7—24no—
386C4×C7—44no—
387C4×C7—44no—
388C4×C7—42no—
389C4×C7—42no—
390C4×C7—81no—
391C4×C7—82no—
392C4×C7—82no—
393C4×C7—81no—
394C24—21no—
395C24—21no—
396C24—22no—
397C24—22no—
398C24—22no—
399C24—21no—
400C24—21no—
401C24—22no—
402C24—21no—
403C24—21no—
404C24C7×#4112yes—
405C24C24×C711yescharacteristic
406C22×C4—21no—
407C22×C4—21no—
408C22×C4—22no—
409C22×C4—22no—
410C22×C4—22no—
411C22×C4—22no—
412C22×C4—22no—
413C22×C4—21no—
414C22×C4—22no—
415C22×C4—22no—
416C22×C4—21no—
417C22×C4—21no—
418C22×C4—21no—
419C22×C4—21no—
420C22×C4—21no—
421C22×C4—22no—
422C22×C4—22no—
423C22×C4—22no—
424C22×C4—22no—
425C22×C4—21no—
426C22×C4—22no—
427C22×C4—22no—
428C22×C4—22no—
429C22×C4—22no—
430C22×C4—22no—
431C22×C4—21no—
432C22×C4—22no—
433C22×C4—21no—
434C22×C4—21no—
435C22×C4—22no—
436C22×C4—22no—
437C22×C4—22no—
438C22×C4—22no—
439C22×C4—22no—
440C22×C4—22no—
441C22×C4—22no—
442C22×C4—22no—
443C22×C4—21no—
444C22×C4—21no—
445C22×C4—22no—
446C22×C4—22no—
447C22×C4—22no—
448C22×C4—22no—
449C22×C4—22no—
450C22×C4—22no—
451C22×C4—21no—
452C22×C4—22no—
453C22×C4—22no—
454C22×C4—22no—
455C22×C4—22no—
456C22×C4—21no—
457C22×C4C2×C7×D412yes—
458C22×C4C2×C7×D412yes—
459C22×C4C2×C7×D412yes—
460C22×C4C7×#4112yes—
461C22×C4C7×#4114yes—
462C22×C4C7×#4114yes—
463C22×C4C7×#4112yes—
464C22×C4C7×#4112yes—
465C22×C4C7×#4114yes—
466C4⋊C4—28no—
467C4⋊C4—28no—
468C4⋊C4—44no—
469C22⋊C4—28no—
470C22⋊C4—48no—
471C22⋊C4—48no—
472C22⋊C4—44no—
473C22⋊C4—44no—
474C42—28no—
475C42—48no—
476C2×C7—82no—
477C2×C7#239811yescharacteristic
478C2×C7#248511yescharacteristic
479C2×C7#250411yescharacteristic
480C2×C7#257312yes—
481C2×C7#259211yescharacteristic
482C2×C7#259312yes—
483C2×C7#259412yes—
484C2×C7#259512yes—
485C2×C7#259811yescharacteristic
486C2×C7#263611yescharacteristic
487C2×C7#285311yescharacteristic
488C23—22no—
489C23—24no—
490C23—24no—
491C23—22no—
492C23—22no—
493C23—41no—
494C23—41no—
495C23—41no—
496C23—41no—
497C23—42no—
498C23—42no—
499C23—42no—
500C23—41no—
501C23—41no—
502C23—42no—
503C23—42no—
504C23—42no—
505C23—42no—
506C23—42no—
507C23—41no—
508C23—41no—
509C23—42no—
510C23—42no—
511C23C22×C7×D411yescharacteristic
512C23C2×C7×#4111yescharacteristic
513C23C2×C7×#4111yescharacteristic
514C23C2×C7×#4112yes—
515C23C2×C7×#4111yescharacteristic
516C23C2×C7×#4112yes—
517C23C2×C7×#4111yescharacteristic
518C23C2×C7×#4112yes—
519C23C7×H(5,𝔽2)12yes—
520C23C7×H(5,𝔽2)11yescharacteristic
521C23C7×2−1+411yescharacteristic
522C2×C4—22no—
523C2×C4—22no—
524C2×C4—22no—
525C2×C4—24no—
526C2×C4—24no—
527C2×C4—22no—
528C2×C4—24no—
529C2×C4—24no—
530C2×C4—22no—
531C2×C4—22no—
532C2×C4—22no—
533C2×C4—24no—
534C2×C4—24no—
535C2×C4—24no—
536C2×C4—22no—
537C2×C4—24no—
538C2×C4—24no—
539C2×C4—24no—
540C2×C4—24no—
541C2×C4—41no—
542C2×C4—42no—
543C2×C4—41no—
544C2×C4—42no—
545C2×C4—42no—
546C2×C4—42no—
547C2×C4—42no—
548C2×C4—42no—
549C2×C4—42no—
550C2×C4—42no—
551C2×C4—41no—
552C2×C4—41no—
553C2×C4—42no—
554C2×C4—41no—
555C2×C4—41no—
556C2×C4—41no—
557C2×C4—41no—
558C2×C4—41no—
559C2×C4—41no—
560C2×C4—42no—
561C2×C4—42no—
562C2×C4—42no—
563C2×C4—42no—
564C2×C4—41no—
565C2×C4—41no—
566C2×C4—42no—
567C2×C4—42no—
568C2×C4—42no—
569C2×C4—42no—
570C2×C4—42no—
571C2×C4—42no—
572C2×C4—42no—
573C2×C4—42no—
574C2×C4—42no—
575C2×C4—42no—
576C2×C4—42no—
577C2×C4—42no—
578C2×C4—42no—
579C2×C4—42no—
580C2×C4C7×#12314yes—
581C2×C4C7×#12414yes—
582C7#1511011yescharacteristic, direct product factor, Sylow
583C22—42no—
584C22—42no—
585C22—44no—
586C22—44no—
587C22—42no—
588C22—81no—
589C22—81no—
590C22—82no—
591C22—82no—
592C22—81no—
593C22—81no—
594C22C2×C7×#12311yescharacteristic
595C22C7×#52511yescharacteristic
596C22C7×#52511yescharacteristic
597C22C7×#52511yescharacteristic
598C22C2×C7×#12411yescharacteristic
599C22C7×#52912yes—
600C22C7×#52912yes—
601C22C7×#52912yes—
602C22C7×#52912yes—
603C22C7×#53511yescharacteristic
604C22C7×#53711yescharacteristic
605C22C7×#53812yes—
606C22C7×#53912yes—
607C22C7×#55112yes—
608C22C7×#55211yescharacteristic
609C22C7×#55311yescharacteristic
610C22C7×#55312yes—
611C22C7×#55312yes—
612C22C7×#55312yes—
613C22C7×#55511yescharacteristic
614C22C7×#55611yescharacteristic
615C22C7×#55612yes—
616C22C7×#55912yes—
617C4—24no—
618C4—24no—
619C4—42no—
620C4—42no—
621C4—44no—
622C4—44no—
623C4—81no—
624C4—81no—
625C4—82no—
626C4—82no—
627C2—82no—
628C2C7×#239811yescharacteristic
629C2C7×#248511yescharacteristic
630C2C7×#250411yescharacteristic
631C2C7×#257312yes—
632C2C7×#259211yescharacteristic
633C2C7×#259312yes—
634C2C7×#259412yes—
635C2C7×#259512yes—
636C2C7×#259811yescharacteristic
637C2C7×#263611yescharacteristic
638C2C7×#285311yescharacteristic
subgroupG/H
center, socleC24×C7C24
commutator, Frattini, cosocleC24C24×C7
prime radicalC25×C7C23
LCSG ▷ C24 ▷ C1
UCSC1 ◁ C24×C7 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×C4×C7×C4⋊C4C2semidirect
3. C7×#1443C2semidirect
4. C7×#1442C2semidirect
5. C7×#1442C2semidirect
10. C7×#1436C2semidirect
11. C7×#1434C2semidirect
37. #15110C7direct (N × H)
89. C2×C4×C4⋊C4C2×C7semidirect
90. #1443C2×C7semidirect
91. #1442C2×C7semidirect
92. #1442C2×C7semidirect
97. #1436C2×C7semidirect
98. #1434C2×C7semidirect
582. C7#15110direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C7×#3882
C2×C4×C7×C4⋊C42
C7×#14432
C7×#14422
C7×#14402
C7×#14392
C7×#14372
C7×#14362
C7×#14342
#151107