Finite Group Databasebeta

← C7×#21092 #13198308

Subgroups — C7×#21092 #13198308

Order 1792.

1122 conjugacy classes of subgroups.

The subgroup lattice has 572 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C7×#417C211yesmaximal, characteristic
2C2×C7×#416C211yesmaximal, characteristic
3C2×C7×#405C211yesmaximal, characteristic, complemented
4C7×#2316C211yesmaximal, characteristic, complemented
5C7×#2311C211yesmaximal, characteristic
6C7×#1936C212yesmaximal, complemented
7C7×#1935C212yesmaximal, complemented
8C7×#1934C212yesmaximal, complemented
9C7×#1933C212yesmaximal, complemented
10C7×#1736C211yesmaximal, characteristic, complemented
11C2×C7×#340C211yesmaximal, characteristic, complemented
12C22×C7×#41C2211yescharacteristic
13C22×C7×M16C2211yescharacteristic
14C23×C7×C8C2211yescharacteristic
15C2×C7×#117C2211yescharacteristic
16C2×C7×#117C2211yescharacteristic
17C22×C7×C4⋊C4C2211yescharacteristic
18C22×C7×C4⋊C4C2211yescharacteristic
19C7×#417C418yescomplemented
20C7×#416—24no—
21C2×C7×#103C2211yescharacteristic
22C2×C7×#103C2211yescharacteristic
23C2×C7×#103C2212yes—
24C2×C7×#102C2211yescharacteristic
25C2×C7×#102C2211yescharacteristic
26C2×C7×#102C2212yes—
27C7×#405—24no—
28C2×C7×#97C2212yes—
29C2×C4×C7×C8C2212yes—
30C7×#391C2212yes—
31C7×#390C2212yes—
32C7×#389—21no—
33C7×#389—21no—
34C7×#389C2212yes—
35C7×#389C2212yes—
36C7×#386—22no—
37C7×#380—21no—
38C7×#380—21no—
39C7×#380—22no—
40C7×#340C2212yes—
41C7×#340C2212yes—
42C7×#340C2212yes—
43C7×#340C2212yes—
44#21092C711yesmaximal, characteristic, direct product factor, Sylow
45C2×C7×#41—22no—
46C2×C7×#41—22no—
47C2×C7×#41—22no—
48C2×C7×#41—22no—
49C2×C7×#41—22no—
50C2×C7×#41C2×C414yes—
51C22×C7×Q8C2311yescharacteristic
52C22×C7×D4—21no—
53C22×C7×D4C2311yescharacteristic
54C23×C4×C7—21no—
55C23×C4×C7—21no—
56C23×C4×C7—21no—
57C23×C4×C7C2311yescharacteristic
58C2×C7×M16—22no—
59C2×C7×M16—22no—
60C2×C7×M16C2×C414yes—
61C22×C7×C8—22no—
62C22×C7×C8—22no—
63C22×C7×C8D414yes—
64C22×C7×C8C2312yes—
65C22×C7×C8C2311yescharacteristic
66C22×C7×C8C2311yescharacteristic
67C7×#117—22no—
68C7×#117—22no—
69C7×#117—22no—
70C7×#117—22no—
71C2×C7×C4⋊C4—21no—
72C2×C7×C4⋊C4—22no—
73C2×C7×C4⋊C4—22no—
74C2×C7×C4⋊C4—22no—
75C2×C7×C4⋊C4—21no—
76C2×C7×C4⋊C4—22no—
77C2×C7×C4⋊C4—22no—
78C2×C7×C4⋊C4C2×C414yes—
79C2×C7×C4⋊C4D411yescharacteristic
80C2×C7×C4⋊C4D411yescharacteristic
81C2×C7×C4⋊C4C2312yes—
82C2×C7×C4⋊C4C2311yescharacteristic
83C2×C7×C4⋊C4C2311yescharacteristic
84C2×C7×C4⋊C4C2312yes—
85C2×C7×C22⋊C4—21no—
86C2×C7×C22⋊C4—22no—
87C2×C7×C22⋊C4—22no—
88C2×C7×C22⋊C4D412yes—
89C2×C42×C7—21no—
90C2×C42×C7C2312yes—
91C7×#103—22no—
92C7×#103—22no—
93C7×#103C2×C418yescomplemented
94C7×#102—22no—
95C7×#102—22no—
96C7×#102C2×C418yescomplemented
97C7×#97—24no—
98C4×C7×C8—24no—
99C7×#95—22no—
100C7×#95—22no—
101C7×#95—22no—
102C7×#95—22no—
103C2×#417C2×C711yescharacteristic
104C2×#416C2×C711yescharacteristic
105C2×#405C2×C711yescharacteristic, complemented
106#2316C2×C711yescharacteristic, complemented
107#2311C2×C711yescharacteristic
108#1936C2×C712yescomplemented
109#1935C2×C712yescomplemented
110#1934C2×C712yescomplemented
111#1933C2×C712yescomplemented
112#1736C2×C711yescharacteristic, complemented
113C2×#340C2×C711yescharacteristic, complemented
114C24×C7—21no—
115C24×C7C2×D411yescharacteristic
116C7×#41—28no—
117C7×#41—28no—
118C7×#41—44no—
119C7×#41—44no—
120C2×C7×Q8—21no—
121C2×C7×Q8—21no—
122C2×C7×Q8—21no—
123C2×C7×Q8—21no—
124C2×C7×Q8—21no—
125C2×C7×Q8C22×C412yes—
126C2×C7×D4—24no—
127C2×C7×D4—21no—
128C2×C7×D4—21no—
129C2×C7×D4—21no—
130C2×C7×D4—21no—
131C2×C7×D4—21no—
132C2×C7×D4—42no—
133C2×C7×D4—42no—
134C2×C7×D4C22×C412yes—
135C22×C4×C7—21no—
136C22×C4×C7—22no—
137C22×C4×C7—24no—
138C22×C4×C7—24no—
139C22×C4×C7—21no—
140C22×C4×C7—21no—
141C22×C4×C7—22no—
142C22×C4×C7—42no—
143C22×C4×C7—42no—
144C22×C4×C7—42no—
145C22×C4×C7—81no—
146C22×C4×C7—81no—
147C22×C4×C7—81no—
148C22×C4×C7—81no—
149C22×C4×C7C22×C412yes—
150C22×C4×C7C2×D412yes—
151C22×C4×C7C2×D412yes—
152C22×C4×C7C2×D411yescharacteristic
153C22×C4×C7C2×D412yes—
154C22×C4×C7#4112yes—
155C22×C4×C7#4112yes—
156C22×C4×C7#4112yes—
157C22×C4×C7#4112yes—
158C22×C4×C7C2411yescharacteristic
159C7×M16—28no—
160C2×C7×C8—28no—
161C2×C7×C8—22no—
162C2×C7×C8—21no—
163C2×C7×C8—21no—
164C2×C7×C8—21no—
165C2×C7×C8—21no—
166C2×C7×C8—22no—
167C2×C7×C8C22×C414yes—
168C2×C7×C8C2×D412yes—
169C2×C7×C8C2×D412yes—
170C7×C4⋊C4—24no—
171C7×C4⋊C4—22no—
172C7×C4⋊C4—22no—
173C7×C4⋊C4—22no—
174C7×C4⋊C4—21no—
175C7×C4⋊C4—21no—
176C7×C4⋊C4—22no—
177C7×C4⋊C4—22no—
178C7×C4⋊C4—21no—
179C7×C4⋊C4—21no—
180C7×C4⋊C4—42no—
181C7×C4⋊C4—82no—
182C7×C4⋊C4—82no—
183C7×C4⋊C4C22×C414yes—
184C7×C22⋊C4—24no—
185C7×C22⋊C4—42no—
186C7×C22⋊C4—82no—
187C7×C22⋊C4—82no—
188C42×C7—22no—
189C42×C7—22no—
190C42×C7—42no—
191C22×#41C22×C711yescharacteristic
192C22×M16C22×C711yescharacteristic
193C23×C8C22×C711yescharacteristic
194C2×#117C22×C711yescharacteristic
195C2×#117C22×C711yescharacteristic
196C22×C4⋊C4C22×C711yescharacteristic
197C22×C4⋊C4C22×C711yescharacteristic
198#417C4×C718yescomplemented
199#416—24no—
200C2×#103C22×C711yescharacteristic
201C2×#103C22×C711yescharacteristic
202C2×#103C22×C712yes—
203C2×#102C22×C711yescharacteristic
204C2×#102C22×C711yescharacteristic
205C2×#102C22×C712yes—
206#405—24no—
207C2×#97C22×C712yes—
208C2×C4×C8C22×C712yes—
209#391C22×C712yes—
210#390C22×C712yes—
211#389—21no—
212#389—21no—
213#389C22×C712yes—
214#389C22×C712yes—
215#386—22no—
216#380—21no—
217#380—21no—
218#380—22no—
219#340C22×C712yes—
220#340C22×C712yes—
221#340C22×C712yes—
222#340C22×C712yes—
223C23×C7—21no—
224C23×C7—21no—
225C23×C7—21no—
226C23×C7—21no—
227C23×C7—22no—
228C23×C7—41no—
229C23×C7—41no—
230C23×C7—41no—
231C23×C7—41no—
232C23×C7—41no—
233C23×C7—41no—
234C23×C7C4×D412yes—
235C23×C7#12112yes—
236C23×C7#12412yes—
237C23×C7C22×D411yescharacteristic
238C7×Q8—22no—
239C7×Q8—22no—
240C7×Q8—41no—
241C7×Q8—41no—
242C7×D4—22no—
243C7×D4—22no—
244C7×D4—48no—
245C7×D4—41no—
246C7×D4—41no—
247C2×C4×C7—24no—
248C2×C4×C7—22no—
249C2×C4×C7—22no—
250C2×C4×C7—22no—
251C2×C4×C7—22no—
252C2×C4×C7—22no—
253C2×C4×C7—22no—
254C2×C4×C7—22no—
255C2×C4×C7—41no—
256C2×C4×C7—41no—
257C2×C4×C7—42no—
258C2×C4×C7—42no—
259C2×C4×C7—48no—
260C2×C4×C7—41no—
261C2×C4×C7—41no—
262C2×C4×C7—42no—
263C2×C4×C7—42no—
264C2×C4×C7—41no—
265C2×C4×C7—42no—
266C2×C4×C7—41no—
267C2×C4×C7—41no—
268C2×C4×C7—41no—
269C2×C4×C7—84no—
270C2×C4×C7—84no—
271C2×C4×C7#11714yes—
272C2×C4×C7C4×D414yes—
273C2×C4×C7C4×D412yes—
274C2×C4×C7#12112yes—
275C2×C4×C7#12314yes—
276C2×C4×C7#12412yes—
277C2×C4×C7#12614yes—
278C2×C4×C7C23×C411yescharacteristic
279C2×C4×C7C22×D411yescharacteristic
280C2×C4×C7C2×#4111yescharacteristic
281C2×C4×C7C2×#4111yescharacteristic
282C2×C4×C7C2×#4111yescharacteristic
283C2×C4×C7C2×#4111yescharacteristic
284C7×C8—24no—
285C7×C8—22no—
286C7×C8—22no—
287C2×#41—22no—
288C2×#41—22no—
289C2×#41—22no—
290C2×#41—22no—
291C2×#41—22no—
292C2×#41C2×C4×C714yes—
293C22×Q8C23×C711yescharacteristic
294C22×D4—21no—
295C22×D4C23×C711yescharacteristic
296C23×C4—21no—
297C23×C4—21no—
298C23×C4—21no—
299C23×C4C23×C711yescharacteristic
300C2×M16—22no—
301C2×M16—22no—
302C2×M16C2×C4×C714yes—
303C22×C8—22no—
304C22×C8—22no—
305C22×C8C7×D414yes—
306C22×C8C23×C712yes—
307C22×C8C23×C711yescharacteristic
308C22×C8C23×C711yescharacteristic
309#117—22no—
310#117—22no—
311#117—22no—
312#117—22no—
313C2×C4⋊C4—21no—
314C2×C4⋊C4—22no—
315C2×C4⋊C4—22no—
316C2×C4⋊C4—22no—
317C2×C4⋊C4—21no—
318C2×C4⋊C4—22no—
319C2×C4⋊C4—22no—
320C2×C4⋊C4C2×C4×C714yes—
321C2×C4⋊C4C7×D411yescharacteristic
322C2×C4⋊C4C7×D411yescharacteristic
323C2×C4⋊C4C23×C712yes—
324C2×C4⋊C4C23×C711yescharacteristic
325C2×C4⋊C4C23×C711yescharacteristic
326C2×C4⋊C4C23×C712yes—
327C2×C22⋊C4—21no—
328C2×C22⋊C4—22no—
329C2×C22⋊C4—22no—
330C2×C22⋊C4C7×D412yes—
331C2×C42—21no—
332C2×C42C23×C712yes—
333#103—22no—
334#103—22no—
335#103C2×C4×C718yescomplemented
336#102—22no—
337#102—22no—
338#102C2×C4×C718yescomplemented
339#97—24no—
340C4×C8—24no—
341#95—22no—
342#95—22no—
343#95—22no—
344#95—22no—
345C22×C7—22no—
346C22×C7—22no—
347C22×C7—22no—
348C22×C7—22no—
349C22×C7—22no—
350C22×C7—22no—
351C22×C7—42no—
352C22×C7—42no—
353C22×C7—42no—
354C22×C7—81no—
355C22×C7—81no—
356C22×C7—81no—
357C22×C7—81no—
358C22×C7#38814yes—
359C22×C7C2×C4×D411yescharacteristic
360C22×C7C2×#12111yescharacteristic
361C22×C7C2×#12411yescharacteristic
362C22×C7#57611yescharacteristic
363C22×C7#57711yescharacteristic
364C22×C7#57711yescharacteristic
365C22×C7#57811yescharacteristic
366C4×C7—44no—
367C4×C7—42no—
368C4×C7—42no—
369C4×C7—42no—
370C4×C7—82no—
371C4×C7—81no—
372C4×C7—81no—
373C4×C7#38814yes—
374C4×C7C2×#11711yescharacteristic
375C4×C7C2×C4×D411yescharacteristic
376C4×C7C2×#12311yescharacteristic
377C4×C7C2×#12611yescharacteristic
378C24—21no—
379C24C2×C7×D411yescharacteristic
380#41—28no—
381#41—28no—
382#41—44no—
383#41—44no—
384C2×Q8—21no—
385C2×Q8—21no—
386C2×Q8—21no—
387C2×Q8—21no—
388C2×Q8—21no—
389C2×Q8C22×C4×C712yes—
390C2×D4—24no—
391C2×D4—21no—
392C2×D4—21no—
393C2×D4—21no—
394C2×D4—21no—
395C2×D4—21no—
396C2×D4—42no—
397C2×D4—42no—
398C2×D4C22×C4×C712yes—
399C22×C4—21no—
400C22×C4—22no—
401C22×C4—24no—
402C22×C4—24no—
403C22×C4—21no—
404C22×C4—21no—
405C22×C4—22no—
406C22×C4—42no—
407C22×C4—42no—
408C22×C4—42no—
409C22×C4—81no—
410C22×C4—81no—
411C22×C4—81no—
412C22×C4—81no—
413C22×C4C22×C4×C712yes—
414C22×C4C2×C7×D412yes—
415C22×C4C2×C7×D412yes—
416C22×C4C2×C7×D411yescharacteristic
417C22×C4C2×C7×D412yes—
418C22×C4C7×#4112yes—
419C22×C4C7×#4112yes—
420C22×C4C7×#4112yes—
421C22×C4C7×#4112yes—
422C22×C4C24×C711yescharacteristic
423M16—28no—
424C2×C8—28no—
425C2×C8—22no—
426C2×C8—21no—
427C2×C8—21no—
428C2×C8—21no—
429C2×C8—21no—
430C2×C8—22no—
431C2×C8C22×C4×C714yes—
432C2×C8C2×C7×D412yes—
433C2×C8C2×C7×D412yes—
434C4⋊C4—24no—
435C4⋊C4—22no—
436C4⋊C4—22no—
437C4⋊C4—22no—
438C4⋊C4—21no—
439C4⋊C4—21no—
440C4⋊C4—22no—
441C4⋊C4—22no—
442C4⋊C4—21no—
443C4⋊C4—21no—
444C4⋊C4—42no—
445C4⋊C4—82no—
446C4⋊C4—82no—
447C4⋊C4C22×C4×C714yes—
448C22⋊C4—24no—
449C22⋊C4—42no—
450C22⋊C4—82no—
451C22⋊C4—82no—
452C42—22no—
453C42—22no—
454C42—42no—
455C2×C7—24no—
456C2×C7—82no—
457C2×C7C2×#38811yescharacteristic
458C2×C7#294611yescharacteristic
459C2×C7#294711yescharacteristic
460C2×C7#306011yescharacteristic
461C2×C7#306111yescharacteristic
462C2×C7#313611yescharacteristic
463C2×C7#313711yescharacteristic
464C23—21no—
465C23—21no—
466C23—21no—
467C23—21no—
468C23—22no—
469C23—41no—
470C23—41no—
471C23—41no—
472C23—41no—
473C23—41no—
474C23—41no—
475C23C4×C7×D412yes—
476C23C7×#12112yes—
477C23C7×#12412yes—
478C23C22×C7×D411yescharacteristic
479Q8—22no—
480Q8—22no—
481Q8—41no—
482Q8—41no—
483D4—22no—
484D4—22no—
485D4—48no—
486D4—41no—
487D4—41no—
488C2×C4—24no—
489C2×C4—22no—
490C2×C4—22no—
491C2×C4—22no—
492C2×C4—22no—
493C2×C4—22no—
494C2×C4—22no—
495C2×C4—22no—
496C2×C4—41no—
497C2×C4—41no—
498C2×C4—42no—
499C2×C4—42no—
500C2×C4—48no—
501C2×C4—41no—
502C2×C4—41no—
503C2×C4—42no—
504C2×C4—42no—
505C2×C4—41no—
506C2×C4—42no—
507C2×C4—41no—
508C2×C4—41no—
509C2×C4—41no—
510C2×C4—84no—
511C2×C4—84no—
512C2×C4C7×#11714yes—
513C2×C4C4×C7×D414yes—
514C2×C4C4×C7×D412yes—
515C2×C4C7×#12112yes—
516C2×C4C7×#12314yes—
517C2×C4C7×#12412yes—
518C2×C4C7×#12614yes—
519C2×C4C23×C4×C711yescharacteristic
520C2×C4C22×C7×D411yescharacteristic
521C2×C4C2×C7×#4111yescharacteristic
522C2×C4C2×C7×#4111yescharacteristic
523C2×C4C2×C7×#4111yescharacteristic
524C2×C4C2×C7×#4111yescharacteristic
525C8—24no—
526C8—22no—
527C8—22no—
528C7#2109211yescharacteristic, direct product factor, Sylow
529C22—22no—
530C22—22no—
531C22—22no—
532C22—22no—
533C22—22no—
534C22—22no—
535C22—42no—
536C22—42no—
537C22—42no—
538C22—81no—
539C22—81no—
540C22—81no—
541C22—81no—
542C22C7×#38814yes—
543C22C2×C4×C7×D411yescharacteristic
544C22C2×C7×#12111yescharacteristic
545C22C2×C7×#12411yescharacteristic
546C22C7×#57611yescharacteristic
547C22C7×#57711yescharacteristic
548C22C7×#57711yescharacteristic
549C22C7×#57811yescharacteristic
550C4—44no—
551C4—42no—
552C4—42no—
553C4—42no—
554C4—81no—
555C4—81no—
556C4—82no—
557C4C7×#38814yes—
558C4C2×C7×#11711yescharacteristic
559C4C2×C4×C7×D411yescharacteristic
560C4C2×C7×#12311yescharacteristic
561C4C2×C7×#12611yescharacteristic
562C2—24no—
563C2—82no—
564C2C2×C7×#38811yescharacteristic
565C2C7×#294611yescharacteristic
566C2C7×#294711yescharacteristic
567C2C7×#306011yescharacteristic
568C2C7×#306111yescharacteristic
569C2C7×#313611yescharacteristic
570C2C7×#313711yescharacteristic
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 ◁ C2×C7×#117 ◁ G

Complements

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

NH ≅ G/Ntype
3. C2×C7×#405C2semidirect
4. C7×#2316C2semidirect
6. C7×#1936C2semidirect
7. C7×#1935C2semidirect
8. C7×#1934C2semidirect
9. C7×#1933C2semidirect
10. C7×#1736C2semidirect
11. C2×C7×#340C2semidirect
19. C7×#417C4semidirect
44. #21092C7direct (N × H)
93. C7×#103C2×C4semidirect
96. C7×#102C2×C4semidirect
105. C2×#405C2×C7semidirect
106. #2316C2×C7semidirect
108. #1936C2×C7semidirect
109. #1935C2×C7semidirect
110. #1934C2×C7semidirect
111. #1933C2×C7semidirect
112. #1736C2×C7semidirect
113. C2×#340C2×C7semidirect
198. #417C4×C7semidirect
335. #103C2×C4×C7semidirect
338. #102C2×C4×C7semidirect
528. C7#21092direct (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×C7×#4162
C2×C7×#4052
C7×#23162
C7×#23112
C7×#19362
C7×#19352
C7×#19342
C7×#19332
C7×#17362
C2×C7×#3402
#210927