Finite Group Databasebeta

← C7×#21093 #13198309

Subgroups — C7×#21093 #13198309

Order 1792.

1198 conjugacy classes of subgroups.

The subgroup lattice has 618 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C7×#417C211yesmaximal, characteristic
2C2×C7×#417C211yesmaximal, characteristic
3C2×C4×C7×M16C211yesmaximal, characteristic, complemented
4C7×#2297C211yesmaximal, characteristic
5C2×C7×#389C211yesmaximal, characteristic, complemented
6C7×#1936C212yesmaximal, complemented
7C7×#1935C212yesmaximal, complemented
8C7×#1934C212yesmaximal, complemented
9C7×#1933C212yesmaximal, complemented
10C7×#1736C211yesmaximal, characteristic, complemented
11C7×#1736C211yesmaximal, characteristic, complemented
12C22×C7×#41C2211yescharacteristic
13C22×C7×M16C2211yescharacteristic
14C22×C7×M16C2211yescharacteristic
15C2×C7×#117C2211yescharacteristic
16C22×C7×C4⋊C4—21no—
17C22×C7×C4⋊C4C2211yescharacteristic
18C22×C7×C4⋊C4C2211yescharacteristic
19C22×C42×C7C2211yescharacteristic
20C7×#417—24no—
21C7×#417C418yescomplemented
22C2×C7×#103C2212yes—
23C2×C7×#103C2212yes—
24C2×C7×#102C2212yes—
25C2×C7×#102C2212yes—
26C4×C7×M16—24no—
27C2×C7×#97C2212yes—
28C2×C4×C7×C8C2212yes—
29C7×#391C2211yescharacteristic
30C7×#391C2211yescharacteristic
31C7×#390C2211yescharacteristic
32C7×#390C2211yescharacteristic
33C7×#389—21no—
34C7×#389—21no—
35C7×#389C2212yes—
36C7×#389C2212yes—
37C7×#386—21no—
38C7×#386—21no—
39C4×C7×C22⋊C4—21no—
40C4×C7×C22⋊C4—21no—
41C2×C7×#95—21no—
42C7×#340C2212yes—
43C7×#340C2212yes—
44C7×#340C2212yes—
45C7×#340C2212yes—
46#21093C711yesmaximal, characteristic, direct product factor, Sylow
47C2×C7×#41—22no—
48C2×C7×#41—22no—
49C2×C7×#41—22no—
50C2×C7×#41—22no—
51C2×C7×#41—22no—
52C2×C7×#41C2×C414yes—
53C22×C7×Q8C2311yescharacteristic
54C22×C7×D4—21no—
55C22×C7×D4C2311yescharacteristic
56C23×C4×C7—21no—
57C23×C4×C7—21no—
58C23×C4×C7—21no—
59C23×C4×C7D411yescharacteristic
60C23×C4×C7D411yescharacteristic
61C23×C4×C7C2311yescharacteristic
62C2×C7×M16—22no—
63C2×C7×M16—22no—
64C2×C7×M16—22no—
65C2×C7×M16—22no—
66C2×C7×M16C2×C414yes—
67C2×C7×M16D414yes—
68C22×C7×C8C2312yes—
69C22×C7×C8C2312yes—
70C7×#117—22no—
71C7×#117—22no—
72C2×C7×C4⋊C4—21no—
73C2×C7×C4⋊C4—22no—
74C2×C7×C4⋊C4—22no—
75C2×C7×C4⋊C4—22no—
76C2×C7×C4⋊C4—22no—
77C2×C7×C4⋊C4—22no—
78C2×C7×C4⋊C4—21no—
79C2×C7×C4⋊C4—44no—
80C2×C7×C4⋊C4C2×C414yes—
81C2×C7×C4⋊C4C2311yescharacteristic
82C2×C7×C4⋊C4C2311yescharacteristic
83C2×C7×C4⋊C4C2312yes—
84C2×C7×C4⋊C4C2312yes—
85C2×C7×C22⋊C4—21no—
86C2×C7×C22⋊C4—21no—
87C2×C7×C22⋊C4—21no—
88C2×C7×C22⋊C4—21no—
89C2×C7×C22⋊C4—21no—
90C2×C42×C7—22no—
91C2×C42×C7—22no—
92C2×C42×C7—21no—
93C2×C42×C7D411yescharacteristic
94C2×C42×C7D411yescharacteristic
95C2×C42×C7C2311yescharacteristic
96C2×C42×C7C2311yescharacteristic
97C7×#103—24no—
98C7×#103C2×C418yescomplemented
99C7×#102—24no—
100C7×#102C2×C418yescomplemented
101C7×#97—24no—
102C4×C7×C8—24no—
103C7×#95—22no—
104C7×#95—22no—
105C7×#95—21no—
106C7×#95—21no—
107C7×#95—21no—
108C7×#95—21no—
109C2×#417C2×C711yescharacteristic
110C2×#417C2×C711yescharacteristic
111C2×C4×M16C2×C711yescharacteristic, complemented
112#2297C2×C711yescharacteristic
113C2×#389C2×C711yescharacteristic, complemented
114#1936C2×C712yescomplemented
115#1935C2×C712yescomplemented
116#1934C2×C712yescomplemented
117#1933C2×C712yescomplemented
118#1736C2×C711yescharacteristic, complemented
119#1736C2×C711yescharacteristic, complemented
120C24×C7—21no—
121C24×C7C2×D411yescharacteristic
122C7×#41—28no—
123C7×#41—28no—
124C7×#41—44no—
125C7×#41—44no—
126C2×C7×Q8—21no—
127C2×C7×Q8—21no—
128C2×C7×Q8—21no—
129C2×C7×Q8—21no—
130C2×C7×Q8—21no—
131C2×C7×Q8C22×C412yes—
132C2×C7×D4—24no—
133C2×C7×D4—21no—
134C2×C7×D4—21no—
135C2×C7×D4—21no—
136C2×C7×D4—21no—
137C2×C7×D4—21no—
138C2×C7×D4—42no—
139C2×C7×D4—42no—
140C2×C7×D4C22×C412yes—
141C22×C4×C7—24no—
142C22×C4×C7—22no—
143C22×C4×C7—22no—
144C22×C4×C7—21no—
145C22×C4×C7—22no—
146C22×C4×C7—24no—
147C22×C4×C7—22no—
148C22×C4×C7—22no—
149C22×C4×C7—21no—
150C22×C4×C7—21no—
151C22×C4×C7—22no—
152C22×C4×C7—41no—
153C22×C4×C7—41no—
154C22×C4×C7—42no—
155C22×C4×C7—42no—
156C22×C4×C7—42no—
157C22×C4×C7—42no—
158C22×C4×C7—42no—
159C22×C4×C7—42no—
160C22×C4×C7—42no—
161C22×C4×C7C22×C412yes—
162C22×C4×C7C2×D411yescharacteristic
163C22×C4×C7C2×D411yescharacteristic
164C22×C4×C7C2×D411yescharacteristic
165C22×C4×C7C2×D411yescharacteristic
166C22×C4×C7C2×D411yescharacteristic
167C22×C4×C7C2×D412yes—
168C22×C4×C7#4112yes—
169C22×C4×C7#4112yes—
170C22×C4×C7#4112yes—
171C22×C4×C7#4112yes—
172C22×C4×C7C2411yescharacteristic
173C7×M16—28no—
174C7×M16—28no—
175C2×C7×C8—22no—
176C2×C7×C8—22no—
177C2×C7×C8—22no—
178C2×C7×C8—22no—
179C2×C7×C8C22×C414yes—
180C2×C7×C8C2×D414yes—
181C7×C4⋊C4—24no—
182C7×C4⋊C4—22no—
183C7×C4⋊C4—22no—
184C7×C4⋊C4—22no—
185C7×C4⋊C4—21no—
186C7×C4⋊C4—21no—
187C7×C4⋊C4—21no—
188C7×C4⋊C4—21no—
189C7×C4⋊C4—44no—
190C7×C4⋊C4—42no—
191C7×C4⋊C4—44no—
192C7×C4⋊C4C22×C414yes—
193C7×C22⋊C4—42no—
194C7×C22⋊C4—42no—
195C7×C22⋊C4—42no—
196C7×C22⋊C4—42no—
197C7×C22⋊C4—42no—
198C42×C7—22no—
199C42×C7—22no—
200C42×C7—21no—
201C42×C7—21no—
202C42×C7—21no—
203C42×C7—21no—
204C42×C7—42no—
205C22×#41C22×C711yescharacteristic
206C22×M16C22×C711yescharacteristic
207C22×M16C22×C711yescharacteristic
208C2×#117C22×C711yescharacteristic
209C22×C4⋊C4—21no—
210C22×C4⋊C4C22×C711yescharacteristic
211C22×C4⋊C4C22×C711yescharacteristic
212C22×C42C22×C711yescharacteristic
213#417—24no—
214#417C4×C718yescomplemented
215C2×#103C22×C712yes—
216C2×#103C22×C712yes—
217C2×#102C22×C712yes—
218C2×#102C22×C712yes—
219C4×M16—24no—
220C2×#97C22×C712yes—
221C2×C4×C8C22×C712yes—
222#391C22×C711yescharacteristic
223#391C22×C711yescharacteristic
224#390C22×C711yescharacteristic
225#390C22×C711yescharacteristic
226#389—21no—
227#389—21no—
228#389C22×C712yes—
229#389C22×C712yes—
230#386—21no—
231#386—21no—
232C4×C22⋊C4—21no—
233C4×C22⋊C4—21no—
234C2×#95—21no—
235#340C22×C712yes—
236#340C22×C712yes—
237#340C22×C712yes—
238#340C22×C712yes—
239C23×C7—21no—
240C23×C7—21no—
241C23×C7—21no—
242C23×C7—21no—
243C23×C7—22no—
244C23×C7—41no—
245C23×C7—41no—
246C23×C7—41no—
247C23×C7—41no—
248C23×C7—41no—
249C23×C7—41no—
250C23×C7C4×D412yes—
251C23×C7#12112yes—
252C23×C7#12412yes—
253C23×C7C22×D411yescharacteristic
254C7×Q8—22no—
255C7×Q8—22no—
256C7×Q8—41no—
257C7×Q8—41no—
258C7×D4—22no—
259C7×D4—22no—
260C7×D4—48no—
261C7×D4—41no—
262C7×D4—41no—
263C2×C4×C7—21no—
264C2×C4×C7—21no—
265C2×C4×C7—21no—
266C2×C4×C7—21no—
267C2×C4×C7—24no—
268C2×C4×C7—22no—
269C2×C4×C7—21no—
270C2×C4×C7—21no—
271C2×C4×C7—21no—
272C2×C4×C7—21no—
273C2×C4×C7—21no—
274C2×C4×C7—21no—
275C2×C4×C7—44no—
276C2×C4×C7—44no—
277C2×C4×C7—48no—
278C2×C4×C7—41no—
279C2×C4×C7—41no—
280C2×C4×C7—42no—
281C2×C4×C7—42no—
282C2×C4×C7—48no—
283C2×C4×C7—42no—
284C2×C4×C7—41no—
285C2×C4×C7—41no—
286C2×C4×C7—41no—
287C2×C4×C7—42no—
288C2×C4×C7—41no—
289C2×C4×C7—41no—
290C2×C4×C7—41no—
291C2×C4×C7—42no—
292C2×C4×C7—84no—
293C2×C4×C7#11714yes—
294C2×C4×C7C4×D414yes—
295C2×C4×C7C4×D412yes—
296C2×C4×C7#12112yes—
297C2×C4×C7#12314yes—
298C2×C4×C7#12412yes—
299C2×C4×C7#12614yes—
300C2×C4×C7AGL(1,ℤ/8)12yes—
301C2×C4×C7#13712yes—
302C2×C4×C7C23×C411yescharacteristic
303C2×C4×C7C22×D411yescharacteristic
304C2×C4×C7C2×#4111yescharacteristic
305C2×C4×C7C2×#4111yescharacteristic
306C2×C4×C7C2×#4111yescharacteristic
307C2×C4×C7C2×#4111yescharacteristic
308C7×C8—24no—
309C7×C8—24no—
310C2×#41—22no—
311C2×#41—22no—
312C2×#41—22no—
313C2×#41—22no—
314C2×#41—22no—
315C2×#41C2×C4×C714yes—
316C22×Q8C23×C711yescharacteristic
317C22×D4—21no—
318C22×D4C23×C711yescharacteristic
319C23×C4—21no—
320C23×C4—21no—
321C23×C4—21no—
322C23×C4C7×D411yescharacteristic
323C23×C4C7×D411yescharacteristic
324C23×C4C23×C711yescharacteristic
325C2×M16—22no—
326C2×M16—22no—
327C2×M16—22no—
328C2×M16—22no—
329C2×M16C2×C4×C714yes—
330C2×M16C7×D414yes—
331C22×C8C23×C712yes—
332C22×C8C23×C712yes—
333#117—22no—
334#117—22no—
335C2×C4⋊C4—21no—
336C2×C4⋊C4—22no—
337C2×C4⋊C4—22no—
338C2×C4⋊C4—22no—
339C2×C4⋊C4—22no—
340C2×C4⋊C4—22no—
341C2×C4⋊C4—21no—
342C2×C4⋊C4—44no—
343C2×C4⋊C4C2×C4×C714yes—
344C2×C4⋊C4C23×C712yes—
345C2×C4⋊C4C23×C711yescharacteristic
346C2×C4⋊C4C23×C711yescharacteristic
347C2×C4⋊C4C23×C712yes—
348C2×C22⋊C4—21no—
349C2×C22⋊C4—21no—
350C2×C22⋊C4—21no—
351C2×C22⋊C4—21no—
352C2×C22⋊C4—21no—
353C2×C42—22no—
354C2×C42—22no—
355C2×C42—21no—
356C2×C42C7×D411yescharacteristic
357C2×C42C7×D411yescharacteristic
358C2×C42C23×C711yescharacteristic
359C2×C42C23×C711yescharacteristic
360#103—24no—
361#103C2×C4×C718yescomplemented
362#102—24no—
363#102C2×C4×C718yescomplemented
364#97—24no—
365C4×C8—24no—
366#95—22no—
367#95—22no—
368#95—21no—
369#95—21no—
370#95—21no—
371#95—21no—
372C22×C7—22no—
373C22×C7—22no—
374C22×C7—22no—
375C22×C7—22no—
376C22×C7—22no—
377C22×C7—22no—
378C22×C7—42no—
379C22×C7—42no—
380C22×C7—42no—
381C22×C7—81no—
382C22×C7—81no—
383C22×C7—81no—
384C22×C7—81no—
385C22×C7#38814yes—
386C22×C7C2×C4×D411yescharacteristic
387C22×C7C2×#12111yescharacteristic
388C22×C7C2×#12411yescharacteristic
389C22×C7C2×AGL(1,ℤ/8)11yescharacteristic
390C22×C7C2×#13711yescharacteristic
391C22×C7#57511yescharacteristic
392C22×C7#57511yescharacteristic
393C4×C7—22no—
394C4×C7—22no—
395C4×C7—44no—
396C4×C7—41no—
397C4×C7—41no—
398C4×C7—42no—
399C4×C7—81no—
400C4×C7—81no—
401C4×C7—82no—
402C4×C7#38814yes—
403C4×C7C2×#11711yescharacteristic
404C4×C7C2×C4×D411yescharacteristic
405C4×C7C2×#12311yescharacteristic
406C4×C7C2×#12611yescharacteristic
407C24—21no—
408C24C2×C7×D411yescharacteristic
409#41—28no—
410#41—28no—
411#41—44no—
412#41—44no—
413C2×Q8—21no—
414C2×Q8—21no—
415C2×Q8—21no—
416C2×Q8—21no—
417C2×Q8—21no—
418C2×Q8C22×C4×C712yes—
419C2×D4—24no—
420C2×D4—21no—
421C2×D4—21no—
422C2×D4—21no—
423C2×D4—21no—
424C2×D4—21no—
425C2×D4—42no—
426C2×D4—42no—
427C2×D4C22×C4×C712yes—
428C22×C4—24no—
429C22×C4—22no—
430C22×C4—22no—
431C22×C4—21no—
432C22×C4—22no—
433C22×C4—24no—
434C22×C4—22no—
435C22×C4—22no—
436C22×C4—21no—
437C22×C4—21no—
438C22×C4—22no—
439C22×C4—41no—
440C22×C4—41no—
441C22×C4—42no—
442C22×C4—42no—
443C22×C4—42no—
444C22×C4—42no—
445C22×C4—42no—
446C22×C4—42no—
447C22×C4—42no—
448C22×C4C22×C4×C712yes—
449C22×C4C2×C7×D411yescharacteristic
450C22×C4C2×C7×D411yescharacteristic
451C22×C4C2×C7×D411yescharacteristic
452C22×C4C2×C7×D411yescharacteristic
453C22×C4C2×C7×D411yescharacteristic
454C22×C4C2×C7×D412yes—
455C22×C4C7×#4112yes—
456C22×C4C7×#4112yes—
457C22×C4C7×#4112yes—
458C22×C4C7×#4112yes—
459C22×C4C24×C711yescharacteristic
460M16—28no—
461M16—28no—
462C2×C8—22no—
463C2×C8—22no—
464C2×C8—22no—
465C2×C8—22no—
466C2×C8C22×C4×C714yes—
467C2×C8C2×C7×D414yes—
468C4⋊C4—24no—
469C4⋊C4—22no—
470C4⋊C4—22no—
471C4⋊C4—22no—
472C4⋊C4—21no—
473C4⋊C4—21no—
474C4⋊C4—21no—
475C4⋊C4—21no—
476C4⋊C4—44no—
477C4⋊C4—42no—
478C4⋊C4—44no—
479C4⋊C4C22×C4×C714yes—
480C22⋊C4—42no—
481C22⋊C4—42no—
482C22⋊C4—42no—
483C22⋊C4—42no—
484C22⋊C4—42no—
485C42—22no—
486C42—22no—
487C42—21no—
488C42—21no—
489C42—21no—
490C42—21no—
491C42—42no—
492C2×C7—24no—
493C2×C7—82no—
494C2×C7C2×#38811yescharacteristic
495C2×C7C4×AGL(1,ℤ/8)11yescharacteristic
496C2×C7C4×#13711yescharacteristic
497C2×C7#305511yescharacteristic
498C2×C7#305611yescharacteristic
499C2×C7#314111yescharacteristic
500C2×C7#314211yescharacteristic
501C23—21no—
502C23—21no—
503C23—21no—
504C23—21no—
505C23—22no—
506C23—41no—
507C23—41no—
508C23—41no—
509C23—41no—
510C23—41no—
511C23—41no—
512C23C4×C7×D412yes—
513C23C7×#12112yes—
514C23C7×#12412yes—
515C23C22×C7×D411yescharacteristic
516Q8—22no—
517Q8—22no—
518Q8—41no—
519Q8—41no—
520D4—22no—
521D4—22no—
522D4—48no—
523D4—41no—
524D4—41no—
525C2×C4—21no—
526C2×C4—21no—
527C2×C4—21no—
528C2×C4—21no—
529C2×C4—24no—
530C2×C4—22no—
531C2×C4—21no—
532C2×C4—21no—
533C2×C4—21no—
534C2×C4—21no—
535C2×C4—21no—
536C2×C4—21no—
537C2×C4—44no—
538C2×C4—44no—
539C2×C4—48no—
540C2×C4—41no—
541C2×C4—41no—
542C2×C4—42no—
543C2×C4—42no—
544C2×C4—48no—
545C2×C4—42no—
546C2×C4—41no—
547C2×C4—41no—
548C2×C4—41no—
549C2×C4—42no—
550C2×C4—41no—
551C2×C4—41no—
552C2×C4—41no—
553C2×C4—42no—
554C2×C4—84no—
555C2×C4C7×#11714yes—
556C2×C4C4×C7×D414yes—
557C2×C4C4×C7×D412yes—
558C2×C4C7×#12112yes—
559C2×C4C7×#12314yes—
560C2×C4C7×#12412yes—
561C2×C4C7×#12614yes—
562C2×C4C7×AGL(1,ℤ/8)12yes—
563C2×C4C7×#13712yes—
564C2×C4C23×C4×C711yescharacteristic
565C2×C4C22×C7×D411yescharacteristic
566C2×C4C2×C7×#4111yescharacteristic
567C2×C4C2×C7×#4111yescharacteristic
568C2×C4C2×C7×#4111yescharacteristic
569C2×C4C2×C7×#4111yescharacteristic
570C8—24no—
571C8—24no—
572C7#2109311yescharacteristic, direct product factor, Sylow
573C22—22no—
574C22—22no—
575C22—22no—
576C22—22no—
577C22—22no—
578C22—22no—
579C22—42no—
580C22—42no—
581C22—42no—
582C22—81no—
583C22—81no—
584C22—81no—
585C22—81no—
586C22C7×#38814yes—
587C22C2×C4×C7×D411yescharacteristic
588C22C2×C7×#12111yescharacteristic
589C22C2×C7×#12411yescharacteristic
590C22C2×C7×AGL(1,ℤ/8)11yescharacteristic
591C22C2×C7×#13711yescharacteristic
592C22C7×#57511yescharacteristic
593C22C7×#57511yescharacteristic
594C4—22no—
595C4—22no—
596C4—44no—
597C4—41no—
598C4—41no—
599C4—42no—
600C4—82no—
601C4—81no—
602C4—81no—
603C4C7×#38814yes—
604C4C2×C7×#11711yescharacteristic
605C4C2×C4×C7×D411yescharacteristic
606C4C2×C7×#12311yescharacteristic
607C4C2×C7×#12611yescharacteristic
608C2—24no—
609C2—82no—
610C2C2×C7×#38811yescharacteristic
611C2C4×C7×AGL(1,ℤ/8)11yescharacteristic
612C2C4×C7×#13711yescharacteristic
613C2C7×#305511yescharacteristic
614C2C7×#305611yescharacteristic
615C2C7×#314111yescharacteristic
616C2C7×#314211yescharacteristic
subgroupG/H
center, socleC23×C7C22×D4
commutatorC2×C4C23×C4×C7
Frattini, cosocleC22×C4C24×C7
prime radicalC22×C7×#41C22
LCSG ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C7 ◁ C22×C42×C7 ◁ G

Complements

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

NH ≅ G/Ntype
3. C2×C4×C7×M16C2semidirect
5. C2×C7×#389C2semidirect
6. C7×#1936C2semidirect
7. C7×#1935C2semidirect
8. C7×#1934C2semidirect
9. C7×#1933C2semidirect
10. C7×#1736C2semidirect
11. C7×#1736C2semidirect
21. C7×#417C4semidirect
46. #21093C7direct (N × H)
98. C7×#103C2×C4semidirect
100. C7×#102C2×C4semidirect
111. C2×C4×M16C2×C7semidirect
113. C2×#389C2×C7semidirect
114. #1936C2×C7semidirect
115. #1935C2×C7semidirect
116. #1934C2×C7semidirect
117. #1933C2×C7semidirect
118. #1736C2×C7semidirect
119. #1736C2×C7semidirect
214. #417C4×C7semidirect
361. #103C2×C4×C7semidirect
363. #102C2×C4×C7semidirect
572. C7#21093direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C7×#4172
C2×C4×C7×M162
C7×#22972
C2×C7×#3892
C7×#19362
C7×#19352
C7×#19342
C7×#19332
C7×#17362
#210937