Finite Group Databasebeta

← C2×C7×#1603 #13195315

Subgroups — C2×C7×#1603 #13195315

Order 1792.

1232 conjugacy classes of subgroups.

The subgroup lattice has 584 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C7×#539C211yesmaximal, characteristic
2C2×C7×#451C211yesmaximal, characteristic, complemented
3C2×C7×#448C211yesmaximal, characteristic
4C2×C7×#395C211yesmaximal, characteristic, complemented
5C7×#1603C218yesmaximal, direct product factor
6C2×C7×#328C211yesmaximal, characteristic, complemented
7C2×C7×#327C211yesmaximal, characteristic
8C2×C7×#324C211yesmaximal, characteristic, complemented
9C23×C7×Q8C2211yescharacteristic
10C22×C7×Q16—21no—
11C22×C7×SD16—21no—
12C7×#539—22no—
13C7×#539—22no—
14C7×#539—22no—
15C7×#539C2214yes—
16C2×C7×#126—21no—
17C2×C7×#125—21no—
18C2×C7×#123—21no—
19C2×C7×#123—21no—
20C2×C7×C22⋊Q8—21no—
21C2×C7×C22⋊Q8C2211yescharacteristic
22C2×C7×#121C2211yescharacteristic
23C2×C4×C7×D4—21no—
24C22×C7×C4⋊C4—21no—
25C22×C7×C4⋊C4C2211yescharacteristic
26C7×#451—22no—
27C7×#451C2214yescomplemented
28C7×#448—22no—
29C7×#448C2214yes—
30C2×C7×#103—21no—
31C2×C7×#103—21no—
32C2×C7×C22⋊C8C2211yescharacteristic
33C2×C7×C22⋊C8C2211yescharacteristic
34C7×#395—22no—
35C7×#395C2214yescomplemented
36C2×C7×#95—21no—
37C2×C7×#95C2211yescharacteristic
38C7×#328C2214yescomplemented
39C7×#327C2214yes—
40C7×#324C2214yescomplemented
41C2×#1603C711yesmaximal, characteristic, direct product factor, Sylow
42C22×C7×Q8—21no—
43C22×C7×Q8—21no—
44C22×C7×Q8—21no—
45C22×C7×Q8—21no—
46C22×C7×Q8—21no—
47C22×C7×Q8—44no—
48C22×C7×Q8D411yescharacteristic
49C22×C7×Q8C2312yes—
50C22×C7×D4—21no—
51C22×C7×D4D411yescharacteristic
52C23×C4×C7—21no—
53C23×C4×C7—21no—
54C23×C4×C7—21no—
55C23×C4×C7D411yescharacteristic
56C23×C4×C7D411yescharacteristic
57C23×C4×C7C2311yescharacteristic
58C2×C7×Q16—24no—
59C2×C7×Q16—44no—
60C2×C7×SD16—24no—
61C2×C7×SD16—44no—
62C22×C7×C8—21no—
63C22×C7×C8—21no—
64C7×#126—24no—
65C7×#126—24no—
66C7×#125—24no—
67C7×#125—24no—
68C7×#123—24no—
69C7×#123—24no—
70C7×#123—24no—
71C7×#123—24no—
72C7×C22⋊Q8—24no—
73C7×C22⋊Q8—24no—
74C7×C22⋊Q8—21no—
75C7×C22⋊Q8—21no—
76C7×C22⋊Q8D412yes—
77C7×C22⋊Q8C2312yes—
78C7×#121—21no—
79C7×#121—21no—
80C7×#121D412yes—
81C7×#121C2312yes—
82C4×C7×D4—24no—
83C4×C7×D4—24no—
84C2×C7×C4⋊C4—21no—
85C2×C7×C4⋊C4—21no—
86C2×C7×C4⋊C4—21no—
87C2×C7×C4⋊C4—21no—
88C2×C7×C4⋊C4—21no—
89C2×C7×C4⋊C4—21no—
90C2×C7×C4⋊C4—21no—
91C2×C7×C4⋊C4—21no—
92C2×C7×C4⋊C4—24no—
93C2×C7×C4⋊C4—44no—
94C2×C7×C4⋊C4D412yes—
95C2×C7×C4⋊C4D411yescharacteristic
96C2×C7×C4⋊C4D411yescharacteristic
97C2×C7×C4⋊C4C2312yes—
98C2×C7×C22⋊C4—21no—
99C2×C7×C22⋊C4—21no—
100C2×C7×C22⋊C4—21no—
101C2×C7×C22⋊C4—21no—
102C2×C7×C22⋊C4—21no—
103C2×C42×C7—21no—
104C7×#103—24no—
105C7×#103—24no—
106C7×C22⋊C8—21no—
107C7×C22⋊C8—21no—
108C7×C22⋊C8C2312yes—
109C7×C22⋊C8C2312yes—
110C7×#95—24no—
111C7×#95—21no—
112C7×#95C2312yes—
113C2×#539C2×C711yescharacteristic
114C2×#451C2×C711yescharacteristic, complemented
115C2×#448C2×C711yescharacteristic
116C2×#395C2×C711yescharacteristic, complemented
117#1603C2×C718yesdirect product factor
118C2×#328C2×C711yescharacteristic, complemented
119C2×#327C2×C711yescharacteristic
120C2×#324C2×C711yescharacteristic, complemented
121C24×C7—21no—
122C24×C7C2×D411yescharacteristic
123C2×C7×Q8—21no—
124C2×C7×Q8—24no—
125C2×C7×Q8—24no—
126C2×C7×Q8—22no—
127C2×C7×Q8—22no—
128C2×C7×Q8—44no—
129C2×C7×Q8—42no—
130C2×C7×Q8—42no—
131C2×C7×Q8—44no—
132C2×C7×Q8—42no—
133C2×C7×Q8—44no—
134C2×C7×Q8—44no—
135C2×C7×Q8—41no—
136C2×C7×Q8—41no—
137C2×C7×Q8C2×D412yes—
138C2×C7×D4—22no—
139C2×C7×D4—22no—
140C2×C7×D4—21no—
141C2×C7×D4—42no—
142C2×C7×D4—42no—
143C2×C7×D4—42no—
144C2×C7×D4C2×D412yes—
145C22×C4×C7—24no—
146C22×C4×C7—24no—
147C22×C4×C7—21no—
148C22×C4×C7—21no—
149C22×C4×C7—21no—
150C22×C4×C7—21no—
151C22×C4×C7—21no—
152C22×C4×C7—21no—
153C22×C4×C7—22no—
154C22×C4×C7—22no—
155C22×C4×C7—22no—
156C22×C4×C7—22no—
157C22×C4×C7—24no—
158C22×C4×C7—21no—
159C22×C4×C7—42no—
160C22×C4×C7—42no—
161C22×C4×C7—42no—
162C22×C4×C7—41no—
163C22×C4×C7—41no—
164C22×C4×C7—42no—
165C22×C4×C7—42no—
166C22×C4×C7—82no—
167C22×C4×C7C2×D412yes—
168C22×C4×C7C2×D411yescharacteristic
169C22×C4×C7C2×D411yescharacteristic
170C22×C4×C7C2×D412yes—
171C22×C4×C7C2×D411yescharacteristic
172C22×C4×C7C2×D411yescharacteristic
173C22×C4×C7C2×D411yescharacteristic
174C22×C4×C7C2411yescharacteristic
175C7×Q16—48no—
176C7×SD16—48no—
177C2×C7×C8—22no—
178C2×C7×C8—22no—
179C2×C7×C8—42no—
180C2×C7×C8—42no—
181C7×C4⋊C4—24no—
182C7×C4⋊C4—24no—
183C7×C4⋊C4—24no—
184C7×C4⋊C4—22no—
185C7×C4⋊C4—22no—
186C7×C4⋊C4—22no—
187C7×C4⋊C4—21no—
188C7×C4⋊C4—21no—
189C7×C4⋊C4—22no—
190C7×C4⋊C4—22no—
191C7×C4⋊C4—22no—
192C7×C4⋊C4—48no—
193C7×C4⋊C4C2×D412yes—
194C7×C4⋊C4C2×D412yes—
195C7×C22⋊C4—24no—
196C7×C22⋊C4—24no—
197C7×C22⋊C4—24no—
198C7×C22⋊C4—22no—
199C7×C22⋊C4—22no—
200C7×C22⋊C4—22no—
201C7×C22⋊C4—22no—
202C42×C7—24no—
203C23×Q8C22×C711yescharacteristic
204C22×Q16—21no—
205C22×SD16—21no—
206#539—22no—
207#539—22no—
208#539—22no—
209#539C22×C714yes—
210C2×#126—21no—
211C2×#125—21no—
212C2×#123—21no—
213C2×#123—21no—
214C2×C22⋊Q8—21no—
215C2×C22⋊Q8C22×C711yescharacteristic
216C2×#121C22×C711yescharacteristic
217C2×C4×D4—21no—
218C22×C4⋊C4—21no—
219C22×C4⋊C4C22×C711yescharacteristic
220#451—22no—
221#451C22×C714yescomplemented
222#448—22no—
223#448C22×C714yes—
224C2×#103—21no—
225C2×#103—21no—
226C2×C22⋊C8C22×C711yescharacteristic
227C2×C22⋊C8C22×C711yescharacteristic
228#395—22no—
229#395C22×C714yescomplemented
230C2×#95—21no—
231C2×#95C22×C711yescharacteristic
232#328C22×C714yescomplemented
233#327C22×C714yes—
234#324C22×C714yescomplemented
235C23×C7—22no—
236C23×C7—22no—
237C23×C7—22no—
238C23×C7—42no—
239C23×C7—42no—
240C23×C7—42no—
241C23×C7#12011yescharacteristic
242C23×C7#12011yescharacteristic
243C23×C7#13512yes—
244C23×C7#13712yes—
245C23×C7C22×D411yescharacteristic
246C7×Q8—24no—
247C7×Q8—24no—
248C7×Q8—42no—
249C7×Q8—42no—
250C7×Q8—42no—
251C7×Q8—44no—
252C7×Q8—44no—
253C7×Q8—81no—
254C7×D4—42no—
255C7×D4—42no—
256C7×D4—42no—
257C7×D4—44no—
258C7×D4—81no—
259C2×C4×C7—22no—
260C2×C4×C7—22no—
261C2×C4×C7—24no—
262C2×C4×C7—24no—
263C2×C4×C7—22no—
264C2×C4×C7—22no—
265C2×C4×C7—22no—
266C2×C4×C7—22no—
267C2×C4×C7—22no—
268C2×C4×C7—22no—
269C2×C4×C7—22no—
270C2×C4×C7—41no—
271C2×C4×C7—41no—
272C2×C4×C7—41no—
273C2×C4×C7—41no—
274C2×C4×C7—42no—
275C2×C4×C7—48no—
276C2×C4×C7—42no—
277C2×C4×C7—44no—
278C2×C4×C7—42no—
279C2×C4×C7—42no—
280C2×C4×C7—42no—
281C2×C4×C7—42no—
282C2×C4×C7—42no—
283C2×C4×C7—42no—
284C2×C4×C7—44no—
285C2×C4×C7—42no—
286C2×C4×C7—42no—
287C2×C4×C7—42no—
288C2×C4×C7—81no—
289C2×C4×C7—84no—
290C2×C4×C7#12011yescharacteristic
291C2×C4×C7#12011yescharacteristic
292C2×C4×C7C22×D411yescharacteristic
293C2×C4×C7C22×D411yescharacteristic
294C7×C8—42no—
295C7×C8—42no—
296C22×Q8—21no—
297C22×Q8—21no—
298C22×Q8—21no—
299C22×Q8—21no—
300C22×Q8—21no—
301C22×Q8—44no—
302C22×Q8C7×D411yescharacteristic
303C22×Q8C23×C712yes—
304C22×D4—21no—
305C22×D4C7×D411yescharacteristic
306C23×C4—21no—
307C23×C4—21no—
308C23×C4—21no—
309C23×C4C7×D411yescharacteristic
310C23×C4C7×D411yescharacteristic
311C23×C4C23×C711yescharacteristic
312C2×Q16—24no—
313C2×Q16—44no—
314C2×SD16—24no—
315C2×SD16—44no—
316C22×C8—21no—
317C22×C8—21no—
318#126—24no—
319#126—24no—
320#125—24no—
321#125—24no—
322#123—24no—
323#123—24no—
324#123—24no—
325#123—24no—
326C22⋊Q8—24no—
327C22⋊Q8—24no—
328C22⋊Q8—21no—
329C22⋊Q8—21no—
330C22⋊Q8C7×D412yes—
331C22⋊Q8C23×C712yes—
332#121—21no—
333#121—21no—
334#121C7×D412yes—
335#121C23×C712yes—
336C4×D4—24no—
337C4×D4—24no—
338C2×C4⋊C4—21no—
339C2×C4⋊C4—21no—
340C2×C4⋊C4—21no—
341C2×C4⋊C4—21no—
342C2×C4⋊C4—21no—
343C2×C4⋊C4—21no—
344C2×C4⋊C4—21no—
345C2×C4⋊C4—21no—
346C2×C4⋊C4—24no—
347C2×C4⋊C4—44no—
348C2×C4⋊C4C7×D412yes—
349C2×C4⋊C4C7×D411yescharacteristic
350C2×C4⋊C4C7×D411yescharacteristic
351C2×C4⋊C4C23×C712yes—
352C2×C22⋊C4—21no—
353C2×C22⋊C4—21no—
354C2×C22⋊C4—21no—
355C2×C22⋊C4—21no—
356C2×C22⋊C4—21no—
357C2×C42—21no—
358#103—24no—
359#103—24no—
360C22⋊C8—21no—
361C22⋊C8—21no—
362C22⋊C8C23×C712yes—
363C22⋊C8C23×C712yes—
364#95—24no—
365#95—21no—
366#95C23×C712yes—
367C22×C7—24no—
368C22×C7—24no—
369C22×C7—21no—
370C22×C7—21no—
371C22×C7—21no—
372C22×C7—21no—
373C22×C7—42no—
374C22×C7—42no—
375C22×C7—42no—
376C22×C7—84no—
377C22×C7#45212yes—
378C22×C7#45212yes—
379C22×C7#45612yes—
380C22×C7B(4,𝔽2)12yes—
381C22×C7C2×#12011yescharacteristic
382C22×C7C2×#13511yescharacteristic
383C22×C7C2×#13711yescharacteristic
384C4×C7—21no—
385C4×C7—21no—
386C4×C7—21no—
387C4×C7—21no—
388C4×C7—44no—
389C4×C7—42no—
390C4×C7—42no—
391C4×C7—42no—
392C4×C7—44no—
393C4×C7—42no—
394C4×C7—42no—
395C24—21no—
396C24C2×C7×D411yescharacteristic
397C2×Q8—21no—
398C2×Q8—24no—
399C2×Q8—24no—
400C2×Q8—22no—
401C2×Q8—22no—
402C2×Q8—44no—
403C2×Q8—42no—
404C2×Q8—42no—
405C2×Q8—44no—
406C2×Q8—42no—
407C2×Q8—44no—
408C2×Q8—44no—
409C2×Q8—41no—
410C2×Q8—41no—
411C2×Q8C2×C7×D412yes—
412C2×D4—22no—
413C2×D4—22no—
414C2×D4—21no—
415C2×D4—42no—
416C2×D4—42no—
417C2×D4—42no—
418C2×D4C2×C7×D412yes—
419C22×C4—24no—
420C22×C4—24no—
421C22×C4—21no—
422C22×C4—21no—
423C22×C4—21no—
424C22×C4—21no—
425C22×C4—21no—
426C22×C4—21no—
427C22×C4—22no—
428C22×C4—22no—
429C22×C4—22no—
430C22×C4—22no—
431C22×C4—24no—
432C22×C4—21no—
433C22×C4—42no—
434C22×C4—42no—
435C22×C4—42no—
436C22×C4—41no—
437C22×C4—41no—
438C22×C4—42no—
439C22×C4—42no—
440C22×C4—82no—
441C22×C4C2×C7×D412yes—
442C22×C4C2×C7×D411yescharacteristic
443C22×C4C2×C7×D411yescharacteristic
444C22×C4C2×C7×D412yes—
445C22×C4C2×C7×D411yescharacteristic
446C22×C4C2×C7×D411yescharacteristic
447C22×C4C2×C7×D411yescharacteristic
448C22×C4C24×C711yescharacteristic
449Q16—48no—
450SD16—48no—
451C2×C8—22no—
452C2×C8—22no—
453C2×C8—42no—
454C2×C8—42no—
455C4⋊C4—24no—
456C4⋊C4—24no—
457C4⋊C4—24no—
458C4⋊C4—22no—
459C4⋊C4—22no—
460C4⋊C4—22no—
461C4⋊C4—21no—
462C4⋊C4—21no—
463C4⋊C4—22no—
464C4⋊C4—22no—
465C4⋊C4—22no—
466C4⋊C4—48no—
467C4⋊C4C2×C7×D412yes—
468C4⋊C4C2×C7×D412yes—
469C22⋊C4—24no—
470C22⋊C4—24no—
471C22⋊C4—24no—
472C22⋊C4—22no—
473C22⋊C4—22no—
474C22⋊C4—22no—
475C22⋊C4—22no—
476C42—24no—
477C2×C7—21no—
478C2×C7—21no—
479C2×C7—22no—
480C2×C7—82no—
481C2×C7#160314yesdirect product factor
482C2×C7C2×#45211yescharacteristic
483C2×C7C2×#45611yescharacteristic
484C2×C7C2×B(4,𝔽2)11yescharacteristic
485C23—22no—
486C23—22no—
487C23—22no—
488C23—42no—
489C23—42no—
490C23—42no—
491C23C7×#12011yescharacteristic
492C23C7×#12011yescharacteristic
493C23C7×#13512yes—
494C23C7×#13712yes—
495C23C22×C7×D411yescharacteristic
496Q8—24no—
497Q8—24no—
498Q8—42no—
499Q8—42no—
500Q8—42no—
501Q8—44no—
502Q8—44no—
503Q8—81no—
504D4—42no—
505D4—42no—
506D4—42no—
507D4—44no—
508D4—81no—
509C2×C4—22no—
510C2×C4—22no—
511C2×C4—24no—
512C2×C4—24no—
513C2×C4—22no—
514C2×C4—22no—
515C2×C4—22no—
516C2×C4—22no—
517C2×C4—22no—
518C2×C4—22no—
519C2×C4—22no—
520C2×C4—41no—
521C2×C4—41no—
522C2×C4—41no—
523C2×C4—41no—
524C2×C4—42no—
525C2×C4—48no—
526C2×C4—42no—
527C2×C4—44no—
528C2×C4—42no—
529C2×C4—42no—
530C2×C4—42no—
531C2×C4—42no—
532C2×C4—42no—
533C2×C4—42no—
534C2×C4—44no—
535C2×C4—42no—
536C2×C4—42no—
537C2×C4—42no—
538C2×C4—81no—
539C2×C4—84no—
540C2×C4C7×#12011yescharacteristic
541C2×C4C7×#12011yescharacteristic
542C2×C4C22×C7×D411yescharacteristic
543C2×C4C22×C7×D411yescharacteristic
544C8—42no—
545C8—42no—
546C7C2×#160311yescharacteristic, direct product factor, Sylow
547C22—21no—
548C22—21no—
549C22—21no—
550C22—21no—
551C22—24no—
552C22—24no—
553C22—42no—
554C22—42no—
555C22—42no—
556C22—84no—
557C22C7×#45212yes—
558C22C7×#45212yes—
559C22C7×#45612yes—
560C22C7×B(4,𝔽2)12yes—
561C22C2×C7×#12011yescharacteristic
562C22C2×C7×#13511yescharacteristic
563C22C2×C7×#13711yescharacteristic
564C4—21no—
565C4—21no—
566C4—21no—
567C4—21no—
568C4—44no—
569C4—42no—
570C4—42no—
571C4—42no—
572C4—44no—
573C4—42no—
574C4—42no—
575C2—21no—
576C2—21no—
577C2—22no—
578C2—82no—
579C2C7×#160314yesdirect product factor
580C2C2×C7×#45211yescharacteristic
581C2C2×C7×#45611yescharacteristic
582C2C2×C7×B(4,𝔽2)11yescharacteristic
subgroupG/H
center, socleC23×C7#120
commutator, Frattini, cosocleC22×C4C24×C7
prime radicalC2×C7×#121C22
LCSG ▷ C22×C4 ▷ C22 ▷ C1
UCSC1 ◁ C23×C7 ◁ C23×C4×C7 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×C7×#451C2semidirect
4. C2×C7×#395C2semidirect
5. C7×#1603C2direct (N × H)
6. C2×C7×#328C2semidirect
8. C2×C7×#324C2semidirect
27. C7×#451C22semidirect
35. C7×#395C22semidirect
38. C7×#328C22semidirect
40. C7×#324C22semidirect
41. C2×#1603C7direct (N × H)
114. C2×#451C2×C7semidirect
116. C2×#395C2×C7semidirect
117. #1603C2×C7direct (N × H)
118. C2×#328C2×C7semidirect
120. C2×#324C2×C7semidirect
221. #451C22×C7semidirect
229. #395C22×C7semidirect
232. #328C22×C7semidirect
234. #324C22×C7semidirect
481. C2×C7#1603direct (N × H)
546. C7C2×#1603direct (N × H)
579. C2C7×#1603direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C7×#5392
C2×C7×#4512
C2×C7×#4482
C2×C7×#3952
C7×#16032
C2×C7×#3282
C2×C7×#3272
C2×C7×#3242
C2×#16037