Finite Group Databasebeta

← C2×C7×#1931 #13198290

Subgroups — C2×C7×#1931 #13198290

Order 1792.

1154 conjugacy classes of subgroups.

The subgroup lattice has 528 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C7×#428C211yesmaximal, characteristic, complemented
2C2×C7×#418C211yesmaximal, characteristic
3C22×C7×#102C211yesmaximal, characteristic
4C22×C7×#100C211yesmaximal, characteristic
5C2×C7×#405C211yesmaximal, characteristic, complemented
6C7×#1931C218yesmaximal, direct product factor
7C2×C7×#343C211yesmaximal, characteristic, complemented
8C2×C7×#341C211yesmaximal, characteristic, complemented
9C23×C7×D4C2211yescharacteristic
10C22×C7×M16C2211yescharacteristic
11C22×C7×M16C2211yescharacteristic
12C22×C7×M16C2211yescharacteristic
13C23×C7×C8C2211yescharacteristic
14C2×C7×#117C2211yescharacteristic
15C22×C7×C4⋊C4C2211yescharacteristic
16C7×#428—22no—
17C7×#428C2214yescomplemented
18C2×C7×#107—21no—
19C2×C7×#106—21no—
20C7×#418—22no—
21C7×#418C2214yes—
22C2×C7×#102—21no—
23C2×C7×#102—21no—
24C2×C7×#102—22no—
25C2×C7×#102—21no—
26C2×C7×#102—21no—
27C2×C7×#102C2214yes—
28C2×C7×#100C418yescomplemented
29C2×C7×#100C2214yes—
30C7×#405—22no—
31C7×#405C2214yescomplemented
32C2×C7×#97—21no—
33C2×C4×C7×C8—21no—
34C7×#343C2214yescomplemented
35C7×#341C2214yescomplemented
36C2×#1931C711yesmaximal, characteristic, direct product factor, Sylow
37C25×C7—21no—
38C22×C7×D4—21no—
39C22×C7×D4—21no—
40C22×C7×D4—21no—
41C22×C7×D4—21no—
42C22×C7×D4—22no—
43C22×C7×D4—22no—
44C22×C7×D4—21no—
45C22×C7×D4—22no—
46C22×C7×D4C2×C414yes—
47C22×C7×D4C2312yes—
48C23×C4×C7—21no—
49C23×C4×C7C2311yescharacteristic
50C2×C7×M16—21no—
51C2×C7×M16—21no—
52C2×C7×M16—22no—
53C2×C7×M16—22no—
54C2×C7×M16—21no—
55C2×C7×M16—22no—
56C2×C7×M16—22no—
57C2×C7×M16C2×C414yes—
58C2×C7×M16C2×C414yes—
59C2×C7×M16C2312yes—
60C2×C7×M16C2312yes—
61C2×C7×M16C2312yes—
62C22×C7×C8—21no—
63C22×C7×C8—21no—
64C22×C7×C8—22no—
65C22×C7×C8—22no—
66C22×C7×C8—21no—
67C22×C7×C8D411yescharacteristic
68C22×C7×C8D411yescharacteristic
69C22×C7×C8D412yes—
70C22×C7×C8C2312yes—
71C7×#117—21no—
72C7×#117—21no—
73C7×#117D412yes—
74C7×#117C2312yes—
75C2×C7×C4⋊C4—21no—
76C2×C7×C4⋊C4—21no—
77C2×C7×C4⋊C4—21no—
78C2×C7×C4⋊C4—21no—
79C2×C7×C4⋊C4—21no—
80C2×C7×C4⋊C4D411yescharacteristic
81C2×C7×C4⋊C4D411yescharacteristic
82C2×C7×C4⋊C4C2312yes—
83C2×C7×C22⋊C4—21no—
84C2×C42×C7—21no—
85C7×#107—24no—
86C7×#106—24no—
87C7×#102—24no—
88C7×#102—24no—
89C7×#102—24no—
90C7×#102—24no—
91C7×#100C2×C4116yescomplemented
92C7×#97—24no—
93C4×C7×C8—24no—
94C2×#428C2×C711yescharacteristic, complemented
95C2×#418C2×C711yescharacteristic
96C22×#102C2×C711yescharacteristic
97C22×#100C2×C711yescharacteristic
98C2×#405C2×C711yescharacteristic, complemented
99#1931C2×C718yesdirect product factor
100C2×#343C2×C711yescharacteristic, complemented
101C2×#341C2×C711yescharacteristic, complemented
102C24×C7—24no—
103C24×C7—22no—
104C24×C7—41no—
105C24×C7—41no—
106C24×C7—42no—
107C24×C7—82no—
108C24×C7—82no—
109C24×C7#4111yescharacteristic
110C2×C7×D4—24no—
111C2×C7×D4—24no—
112C2×C7×D4—24no—
113C2×C7×D4—24no—
114C2×C7×D4—24no—
115C2×C7×D4—22no—
116C2×C7×D4—22no—
117C2×C7×D4—22no—
118C2×C7×D4—22no—
119C2×C7×D4—22no—
120C2×C7×D4—41no—
121C2×C7×D4—41no—
122C2×C7×D4—42no—
123C2×C7×D4—42no—
124C2×C7×D4—42no—
125C2×C7×D4—42no—
126C2×C7×D4—42no—
127C2×C7×D4C22×C414yes—
128C22×C4×C7—21no—
129C22×C4×C7—21no—
130C22×C4×C7—22no—
131C22×C4×C7—41no—
132C22×C4×C7—41no—
133C22×C4×C7—82no—
134C22×C4×C7C22×C412yes—
135C22×C4×C7C2×D411yescharacteristic
136C22×C4×C7C2×D411yescharacteristic
137C22×C4×C7C2×D411yescharacteristic
138C22×C4×C7C2×D411yescharacteristic
139C22×C4×C7#4111yescharacteristic
140C22×C4×C7#4112yes—
141C22×C4×C7#4112yes—
142C22×C4×C7#4112yes—
143C22×C4×C7C2411yescharacteristic
144C7×M16—24no—
145C7×M16—24no—
146C7×M16—22no—
147C7×M16—22no—
148C7×M16—22no—
149C7×M16—22no—
150C7×M16—42no—
151C7×M16C22×C414yes—
152C7×M16C22×C414yes—
153C2×C7×C8—24no—
154C2×C7×C8—24no—
155C2×C7×C8—22no—
156C2×C7×C8—22no—
157C2×C7×C8—24no—
158C2×C7×C8—22no—
159C2×C7×C8—22no—
160C2×C7×C8—22no—
161C2×C7×C8—22no—
162C2×C7×C8—22no—
163C2×C7×C8—42no—
164C2×C7×C8C2×D412yes—
165C2×C7×C8C2×D412yes—
166C7×C4⋊C4—21no—
167C7×C4⋊C4—21no—
168C7×C4⋊C4—22no—
169C7×C4⋊C4—22no—
170C7×C4⋊C4—41no—
171C7×C4⋊C4—41no—
172C7×C4⋊C4C2×D412yes—
173C7×C4⋊C4C2×D412yes—
174C7×C22⋊C4—22no—
175C7×C22⋊C4—22no—
176C42×C7—22no—
177C42×C7—22no—
178C23×D4C22×C711yescharacteristic
179C22×M16C22×C711yescharacteristic
180C22×M16C22×C711yescharacteristic
181C22×M16C22×C711yescharacteristic
182C23×C8C22×C711yescharacteristic
183C2×#117C22×C711yescharacteristic
184C22×C4⋊C4C22×C711yescharacteristic
185#428—22no—
186#428C22×C714yescomplemented
187C2×#107—21no—
188C2×#106—21no—
189#418—22no—
190#418C22×C714yes—
191C2×#102—21no—
192C2×#102—21no—
193C2×#102—22no—
194C2×#102—21no—
195C2×#102—21no—
196C2×#102C22×C714yes—
197C2×#100C4×C718yescomplemented
198C2×#100C22×C714yes—
199#405—22no—
200#405C22×C714yescomplemented
201C2×#97—21no—
202C2×C4×C8—21no—
203#343C22×C714yescomplemented
204#341C22×C714yescomplemented
205C23×C7—22no—
206C23×C7—22no—
207C23×C7—24no—
208C23×C7—42no—
209C23×C7—42no—
210C23×C7—44no—
211C23×C7—44no—
212C23×C7—88no—
213C23×C7—82no—
214C23×C7—82no—
215C23×C7—88no—
216C23×C7—82no—
217C23×C7—82no—
218C23×C7—82no—
219C23×C7—82no—
220C23×C7#11712yes—
221C23×C7#12111yescharacteristic
222C23×C7#12111yescharacteristic
223C23×C7#12612yes—
224C23×C7C2×#4111yescharacteristic
225C7×D4—24no—
226C7×D4—24no—
227C7×D4—42no—
228C7×D4—42no—
229C7×D4—44no—
230C7×D4—44no—
231C2×C4×C7—22no—
232C2×C4×C7—22no—
233C2×C4×C7—42no—
234C2×C4×C7—42no—
235C2×C4×C7—42no—
236C2×C4×C7—82no—
237C2×C4×C7—82no—
238C2×C4×C7—82no—
239C2×C4×C7#11712yes—
240C2×C4×C7C4×D412yes—
241C2×C4×C7C4×D412yes—
242C2×C4×C7C4×D412yes—
243C2×C4×C7C4×D412yes—
244C2×C4×C7#12111yescharacteristic
245C2×C4×C7#12111yescharacteristic
246C2×C4×C7#12312yes—
247C2×C4×C7#12312yes—
248C2×C4×C7#12412yes—
249C2×C4×C7#12412yes—
250C2×C4×C7#12612yes—
251C2×C4×C7C23×C411yescharacteristic
252C2×C4×C7C22×D411yescharacteristic
253C2×C4×C7C22×D411yescharacteristic
254C2×C4×C7C2×#4111yescharacteristic
255C2×C4×C7C2×#4111yescharacteristic
256C2×C4×C7C2×#4111yescharacteristic
257C7×C8—24no—
258C7×C8—24no—
259C7×C8—22no—
260C7×C8—22no—
261C7×C8—42no—
262C25—21no—
263C22×D4—21no—
264C22×D4—21no—
265C22×D4—21no—
266C22×D4—21no—
267C22×D4—22no—
268C22×D4—22no—
269C22×D4—21no—
270C22×D4—22no—
271C22×D4C2×C4×C714yes—
272C22×D4C23×C712yes—
273C23×C4—21no—
274C23×C4C23×C711yescharacteristic
275C2×M16—21no—
276C2×M16—21no—
277C2×M16—22no—
278C2×M16—22no—
279C2×M16—21no—
280C2×M16—22no—
281C2×M16—22no—
282C2×M16C2×C4×C714yes—
283C2×M16C2×C4×C714yes—
284C2×M16C23×C712yes—
285C2×M16C23×C712yes—
286C2×M16C23×C712yes—
287C22×C8—21no—
288C22×C8—21no—
289C22×C8—22no—
290C22×C8—22no—
291C22×C8—21no—
292C22×C8C7×D411yescharacteristic
293C22×C8C7×D411yescharacteristic
294C22×C8C7×D412yes—
295C22×C8C23×C712yes—
296#117—21no—
297#117—21no—
298#117C7×D412yes—
299#117C23×C712yes—
300C2×C4⋊C4—21no—
301C2×C4⋊C4—21no—
302C2×C4⋊C4—21no—
303C2×C4⋊C4—21no—
304C2×C4⋊C4—21no—
305C2×C4⋊C4C7×D411yescharacteristic
306C2×C4⋊C4C7×D411yescharacteristic
307C2×C4⋊C4C23×C712yes—
308C2×C22⋊C4—21no—
309C2×C42—21no—
310#107—24no—
311#106—24no—
312#102—24no—
313#102—24no—
314#102—24no—
315#102—24no—
316#100C2×C4×C7116yescomplemented
317#97—24no—
318C4×C8—24no—
319C22×C7—24no—
320C22×C7—24no—
321C22×C7—21no—
322C22×C7—21no—
323C22×C7—21no—
324C22×C7—21no—
325C22×C7—44no—
326C22×C7—84no—
327C22×C7—84no—
328C22×C7—88no—
329C22×C7—88no—
330C22×C7—82no—
331C22×C7—82no—
332C22×C7#38812yes—
333C22×C7#38812yes—
334C22×C7#47112yes—
335C22×C7#47212yes—
336C22×C7C2×#11711yescharacteristic
337C22×C7C2×#12111yescharacteristic
338C22×C7C2×#12611yescharacteristic
339C4×C7—42no—
340C4×C7—42no—
341C4×C7—82no—
342C4×C7#38812yes—
343C4×C7#38812yes—
344C4×C7C2×C4×D411yescharacteristic
345C4×C7C2×C4×D411yescharacteristic
346C4×C7C2×#12311yescharacteristic
347C4×C7C2×#12411yescharacteristic
348C24—24no—
349C24—22no—
350C24—41no—
351C24—41no—
352C24—42no—
353C24—82no—
354C24—82no—
355C24C7×#4111yescharacteristic
356C2×D4—24no—
357C2×D4—24no—
358C2×D4—24no—
359C2×D4—24no—
360C2×D4—24no—
361C2×D4—22no—
362C2×D4—22no—
363C2×D4—22no—
364C2×D4—22no—
365C2×D4—22no—
366C2×D4—41no—
367C2×D4—41no—
368C2×D4—42no—
369C2×D4—42no—
370C2×D4—42no—
371C2×D4—42no—
372C2×D4—42no—
373C2×D4C22×C4×C714yes—
374C22×C4—21no—
375C22×C4—21no—
376C22×C4—22no—
377C22×C4—41no—
378C22×C4—41no—
379C22×C4—82no—
380C22×C4C22×C4×C712yes—
381C22×C4C2×C7×D411yescharacteristic
382C22×C4C2×C7×D411yescharacteristic
383C22×C4C2×C7×D411yescharacteristic
384C22×C4C2×C7×D411yescharacteristic
385C22×C4C7×#4111yescharacteristic
386C22×C4C7×#4112yes—
387C22×C4C7×#4112yes—
388C22×C4C7×#4112yes—
389C22×C4C24×C711yescharacteristic
390M16—24no—
391M16—24no—
392M16—22no—
393M16—22no—
394M16—22no—
395M16—22no—
396M16—42no—
397M16C22×C4×C714yes—
398M16C22×C4×C714yes—
399C2×C8—24no—
400C2×C8—24no—
401C2×C8—22no—
402C2×C8—22no—
403C2×C8—24no—
404C2×C8—22no—
405C2×C8—22no—
406C2×C8—22no—
407C2×C8—22no—
408C2×C8—22no—
409C2×C8—42no—
410C2×C8C2×C7×D412yes—
411C2×C8C2×C7×D412yes—
412C4⋊C4—21no—
413C4⋊C4—21no—
414C4⋊C4—22no—
415C4⋊C4—22no—
416C4⋊C4—41no—
417C4⋊C4—41no—
418C4⋊C4C2×C7×D412yes—
419C4⋊C4C2×C7×D412yes—
420C22⋊C4—22no—
421C22⋊C4—22no—
422C42—22no—
423C42—22no—
424C2×C7—21no—
425C2×C7—21no—
426C2×C7—22no—
427C2×C7—84no—
428C2×C7#193114yesdirect product factor
429C2×C7C2×#38811yescharacteristic
430C2×C7C2×#47111yescharacteristic
431C2×C7C2×#47211yescharacteristic
432C23—22no—
433C23—22no—
434C23—24no—
435C23—42no—
436C23—44no—
437C23—44no—
438C23—42no—
439C23—82no—
440C23—82no—
441C23—88no—
442C23—82no—
443C23—82no—
444C23—88no—
445C23—82no—
446C23—82no—
447C23C7×#11712yes—
448C23C7×#12111yescharacteristic
449C23C7×#12111yescharacteristic
450C23C7×#12612yes—
451C23C2×C7×#4111yescharacteristic
452D4—24no—
453D4—24no—
454D4—42no—
455D4—44no—
456D4—44no—
457D4—42no—
458C2×C4—22no—
459C2×C4—22no—
460C2×C4—42no—
461C2×C4—42no—
462C2×C4—42no—
463C2×C4—82no—
464C2×C4—82no—
465C2×C4—82no—
466C2×C4C7×#11712yes—
467C2×C4C4×C7×D412yes—
468C2×C4C4×C7×D412yes—
469C2×C4C4×C7×D412yes—
470C2×C4C4×C7×D412yes—
471C2×C4C7×#12111yescharacteristic
472C2×C4C7×#12111yescharacteristic
473C2×C4C7×#12312yes—
474C2×C4C7×#12312yes—
475C2×C4C7×#12412yes—
476C2×C4C7×#12412yes—
477C2×C4C7×#12612yes—
478C2×C4C23×C4×C711yescharacteristic
479C2×C4C22×C7×D411yescharacteristic
480C2×C4C22×C7×D411yescharacteristic
481C2×C4C2×C7×#4111yescharacteristic
482C2×C4C2×C7×#4111yescharacteristic
483C2×C4C2×C7×#4111yescharacteristic
484C8—24no—
485C8—24no—
486C8—22no—
487C8—22no—
488C8—42no—
489C7C2×#193111yescharacteristic, direct product factor, Sylow
490C22—21no—
491C22—21no—
492C22—21no—
493C22—21no—
494C22—24no—
495C22—24no—
496C22—44no—
497C22—84no—
498C22—88no—
499C22—84no—
500C22—82no—
501C22—82no—
502C22—88no—
503C22C7×#38812yes—
504C22C7×#38812yes—
505C22C7×#47112yes—
506C22C7×#47212yes—
507C22C2×C7×#11711yescharacteristic
508C22C2×C7×#12111yescharacteristic
509C22C2×C7×#12611yescharacteristic
510C4—42no—
511C4—42no—
512C4—82no—
513C4C7×#38812yes—
514C4C7×#38812yes—
515C4C2×C4×C7×D411yescharacteristic
516C4C2×C4×C7×D411yescharacteristic
517C4C2×C7×#12311yescharacteristic
518C4C2×C7×#12411yescharacteristic
519C2—21no—
520C2—22no—
521C2—21no—
522C2—84no—
523C2C7×#193114yesdirect product factor
524C2C2×C7×#38811yescharacteristic
525C2C2×C7×#47111yescharacteristic
526C2C2×C7×#47211yescharacteristic
subgroupG/H
center, socleC23×C7#121
commutatorC2×C4C23×C4×C7
Frattini, cosocleC22×C4C24×C7
prime radicalC23×C7×D4C22
LCSG ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C7 ◁ C23×C4×C7 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×C7×#428C2semidirect
5. C2×C7×#405C2semidirect
6. C7×#1931C2direct (N × H)
7. C2×C7×#343C2semidirect
8. C2×C7×#341C2semidirect
17. C7×#428C22semidirect
28. C2×C7×#100C4semidirect
31. C7×#405C22semidirect
34. C7×#343C22semidirect
35. C7×#341C22semidirect
36. C2×#1931C7direct (N × H)
91. C7×#100C2×C4semidirect
94. C2×#428C2×C7semidirect
98. C2×#405C2×C7semidirect
99. #1931C2×C7direct (N × H)
100. C2×#343C2×C7semidirect
101. C2×#341C2×C7semidirect
186. #428C22×C7semidirect
197. C2×#100C4×C7semidirect
200. #405C22×C7semidirect
203. #343C22×C7semidirect
204. #341C22×C7semidirect
316. #100C2×C4×C7semidirect
428. C2×C7#1931direct (N × H)
489. C7C2×#1931direct (N × H)
523. C2C7×#1931direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C7×#4282
C2×C7×#4182
C22×C7×#1022
C22×C7×#1002
C2×C7×#4052
C7×#19312
C2×C7×#3432
C2×C7×#3412
C2×#19317