Finite Group Databasebeta

← C2×C7×#3044 #13237635

Subgroups — C2×C7×#3044 #13237635

Order 1792.

2666 conjugacy classes of subgroups.

The subgroup lattice has 502 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C7×#137C211yesmaximal, characteristic
2C23×C7×Q16C211yesmaximal, characteristic, complemented
3C2×C7×#536C211yesmaximal, characteristic
4C2×C7×#519C211yesmaximal, characteristic, complemented
5C7×#3044C2116yesmaximal, direct product factor
6C2×C7×#464C214yesmaximal, complemented
7C2×C7×#462C214yesmaximal, complemented
8C2×C7×#424C211yesmaximal, characteristic, complemented
9C2×C7×#419C211yesmaximal, characteristic, complemented
10C2×C7×#416C211yesmaximal, characteristic
11C22×C7×#41C2211yescharacteristic
12C23×C7×Q8C2211yescharacteristic
13C23×C7×Q8C2211yescharacteristic
14C2×C7×#137—28no—
15C2×C7×#137C2218yes—
16C22×C7×Q16—28no—
17C22×C7×Q16C2214yes—
18C22×C7×Q16C2212yes—
19C22×C7×Q16C2218yescomplemented
20C22×C7×SD16C2212yes—
21C22×C7×M16C2211yescharacteristic
22C23×C7×C8C2211yescharacteristic
23C7×#536—24no—
24C7×#536C2218yes—
25C2×C7×C4⋊Q8C2212yes—
26C2×C7×#124C2212yes—
27C2×C7×#123—22no—
28C2×C7×C22⋊Q8—22no—
29C7×#519—24no—
30C7×#519C2218yescomplemented
31C2×C4×C7×Q8—22no—
32C2×C4×C7×Q8C2214yes—
33C2×C7×#117—22no—
34C2×C7×#117C2211yescharacteristic
35C2×C7×#117C2211yescharacteristic
36C7×#464C22132yescomplemented
37C7×#462C22132yescomplemented
38C7×#424C2218yescomplemented
39C2×C7×C4⋊C8C2214yes—
40C7×#419C2218yescomplemented
41C7×#416C2218yes—
42C2×C7×#103C2212yes—
43C2×C7×#103C2214yes—
44C2×C7×#102C2212yes—
45C2×#3044C711yesmaximal, characteristic, direct product factor, Sylow
46C2×C7×#41—22no—
47C2×C7×#41—24no—
48C2×C7×#41—24no—
49C2×C7×#41C2314yes—
50C22×C7×Q8—21no—
51C22×C7×Q8—22no—
52C22×C7×Q8—21no—
53C22×C7×Q8—22no—
54C22×C7×Q8—24no—
55C22×C7×Q8—24no—
56C22×C7×Q8—24no—
57C22×C7×Q8D418yes—
58C22×C7×Q8C2312yes—
59C22×C7×Q8C2314yes—
60C22×C7×Q8C2311yescharacteristic
61C22×C7×Q8C2312yes—
62C22×C7×Q8C2314yes—
63C22×C7×D4—21no—
64C22×C7×D4C2311yescharacteristic
65C23×C4×C7—21no—
66C23×C4×C7—21no—
67C23×C4×C7—21no—
68C23×C4×C7C2311yescharacteristic
69C7×#137—232no—
70C2×C7×Q16—216no—
71C2×C7×Q16—232no—
72C2×C7×Q16—28no—
73C2×C7×Q16C23116yes—
74C2×C7×Q16C2318yes—
75C2×C7×SD16—28no—
76C2×C7×SD16C2318yes—
77C2×C7×M16—24no—
78C2×C7×M16C2314yes—
79C22×C7×C8—24no—
80C22×C7×C8C2312yes—
81C22×C7×C8C2312yes—
82C22×C7×C8C2314yes—
83C7×C4⋊Q8—24no—
84C7×C4⋊Q8C2318yes—
85C7×#124—24no—
86C7×#124C2318yes—
87C7×#123—216no—
88C7×C22⋊Q8—216no—
89C4×C7×Q8—216no—
90C4×C7×Q8—28no—
91C4×C7×Q8C23116yes—
92C7×#117—22no—
93C7×#117—216no—
94C7×#117D414yes—
95C7×#117C2314yes—
96C7×#117C2314yes—
97C2×C7×C4⋊C4—24no—
98C2×C7×C4⋊C4—24no—
99C2×C7×C4⋊C4D412yes—
100C2×C7×C4⋊C4C2312yes—
101C2×C7×C22⋊C4—21no—
102C2×C7×C22⋊C4—24no—
103C2×C7×C22⋊C4D412yes—
104C2×C42×C7—24no—
105C2×C42×C7—21no—
106C2×C42×C7C2312yes—
107C7×C4⋊C8C23116yes—
108C7×#103C2318yes—
109C7×#103C23116yes—
110C7×#102C2318yes—
111C22×#137C2×C711yescharacteristic
112C23×Q16C2×C711yescharacteristic, complemented
113C2×#536C2×C711yescharacteristic
114C2×#519C2×C711yescharacteristic, complemented
115#3044C2×C7116yesdirect product factor
116C2×#464C2×C714yescomplemented
117C2×#462C2×C714yescomplemented
118C2×#424C2×C711yescharacteristic, complemented
119C2×#419C2×C711yescharacteristic, complemented
120C2×#416C2×C711yescharacteristic
121C24×C7—21no—
122C24×C7C2×D411yescharacteristic
123C7×#41—28no—
124C7×#41—28no—
125C7×#41—48no—
126C2×C7×Q8—28no—
127C2×C7×Q8—216no—
128C2×C7×Q8—24no—
129C2×C7×Q8—22no—
130C2×C7×Q8—24no—
131C2×C7×Q8—22no—
132C2×C7×Q8—21no—
133C2×C7×Q8—24no—
134C2×C7×Q8—28no—
135C2×C7×Q8—24no—
136C2×C7×Q8—28no—
137C2×C7×Q8—22no—
138C2×C7×Q8—24no—
139C2×C7×Q8—28no—
140C2×C7×Q8—22no—
141C2×C7×Q8—44no—
142C2×C7×Q8—48no—
143C2×C7×Q8C2×D418yes—
144C2×C7×Q8C2×D4116yes—
145C2×C7×Q8C2414yes—
146C2×C7×Q8C2412yes—
147C2×C7×Q8C2414yes—
148C2×C7×D4—24no—
149C2×C7×D4—22no—
150C2×C7×D4—21no—
151C2×C7×D4—22no—
152C2×C7×D4—44no—
153C2×C7×D4C2412yes—
154C22×C4×C7—28no—
155C22×C4×C7—24no—
156C22×C4×C7—22no—
157C22×C4×C7—24no—
158C22×C4×C7—22no—
159C22×C4×C7—22no—
160C22×C4×C7—21no—
161C22×C4×C7—24no—
162C22×C4×C7—44no—
163C22×C4×C7—44no—
164C22×C4×C7C2×D414yes—
165C22×C4×C7C2×D412yes—
166C22×C4×C7C2×D411yescharacteristic
167C22×C4×C7C2×D414yes—
168C22×C4×C7#4114yes—
169C22×C4×C7C2412yes—
170C22×C4×C7C2411yescharacteristic
171C7×Q16—232no—
172C7×Q16—216no—
173C7×SD16—216no—
174C7×M16—28no—
175C2×C7×C8—24no—
176C2×C7×C8—28no—
177C2×C7×C8—24no—
178C2×C7×C8C2414yes—
179C2×C7×C8C2414yes—
180C7×C4⋊C4—216no—
181C7×C4⋊C4—216no—
182C7×C4⋊C4—22no—
183C7×C4⋊C4C2×D418yes—
184C7×C4⋊C4C2414yes—
185C7×C22⋊C4—24no—
186C7×C22⋊C4—216no—
187C7×C22⋊C4C2×D418yes—
188C42×C7—216no—
189C42×C7—24no—
190C42×C7C2×D414yes—
191C42×C7C2414yes—
192C22×#41C22×C711yescharacteristic
193C23×Q8C22×C711yescharacteristic
194C23×Q8C22×C711yescharacteristic
195C2×#137—28no—
196C2×#137C22×C718yes—
197C22×Q16—28no—
198C22×Q16C22×C712yes—
199C22×Q16C22×C714yes—
200C22×Q16C22×C718yescomplemented
201C22×SD16C22×C712yes—
202C22×M16C22×C711yescharacteristic
203C23×C8C22×C711yescharacteristic
204#536—24no—
205#536C22×C718yes—
206C2×C4⋊Q8C22×C712yes—
207C2×#124C22×C712yes—
208C2×#123—22no—
209C2×C22⋊Q8—22no—
210#519—24no—
211#519C22×C718yescomplemented
212C2×C4×Q8—22no—
213C2×C4×Q8C22×C714yes—
214C2×#117—22no—
215C2×#117C22×C711yescharacteristic
216C2×#117C22×C711yescharacteristic
217#464C22×C7132yescomplemented
218#462C22×C7132yescomplemented
219#424C22×C718yescomplemented
220C2×C4⋊C8C22×C714yes—
221#419C22×C718yescomplemented
222#416C22×C718yes—
223C2×#103C22×C712yes—
224C2×#103C22×C714yes—
225C2×#102C22×C712yes—
226C23×C7—24no—
227C23×C7—22no—
228C23×C7—42no—
229C23×C7—44no—
230C23×C7#12114yes—
231C23×C7C22×D412yes—
232C23×C7C22×D411yescharacteristic
233C7×Q8—216no—
234C7×Q8—28no—
235C7×Q8—24no—
236C7×Q8—24no—
237C7×Q8—22no—
238C7×Q8—24no—
239C7×Q8—22no—
240C7×Q8—48no—
241C7×Q8—44no—
242C7×Q8—42no—
243C7×Q8C22×D418yes—
244C7×D4—22no—
245C7×D4—22no—
246C7×D4—48no—
247C7×D4—42no—
248C2×C4×C7—216no—
249C2×C4×C7—28no—
250C2×C4×C7—28no—
251C2×C4×C7—24no—
252C2×C4×C7—24no—
253C2×C4×C7—24no—
254C2×C4×C7—22no—
255C2×C4×C7—42no—
256C2×C4×C7—48no—
257C2×C4×C7—44no—
258C2×C4×C7—44no—
259C2×C4×C7—48no—
260C2×C4×C7#12114yes—
261C2×C4×C7#12118yes—
262C2×C4×C7C22×D418yes—
263C2×C4×C7C22×D412yes—
264C2×C4×C7C22×D411yescharacteristic
265C2×C4×C7C22×D412yes—
266C2×C4×C7C22×D414yes—
267C2×C4×C7C2×#4112yes—
268C2×C4×C7C2×#4114yes—
269C2×C4×C7C2511yescharacteristic
270C7×C8—24no—
271C7×C8—24no—
272C2×#41—22no—
273C2×#41—24no—
274C2×#41—24no—
275C2×#41C23×C714yes—
276C22×Q8—21no—
277C22×Q8—22no—
278C22×Q8—21no—
279C22×Q8—22no—
280C22×Q8—24no—
281C22×Q8—24no—
282C22×Q8—24no—
283C22×Q8C7×D418yes—
284C22×Q8C23×C712yes—
285C22×Q8C23×C711yescharacteristic
286C22×Q8C23×C714yes—
287C22×Q8C23×C712yes—
288C22×Q8C23×C714yes—
289C22×D4—21no—
290C22×D4C23×C711yescharacteristic
291C23×C4—21no—
292C23×C4—21no—
293C23×C4—21no—
294C23×C4C23×C711yescharacteristic
295#137—232no—
296C2×Q16—216no—
297C2×Q16—232no—
298C2×Q16—28no—
299C2×Q16C23×C7116yes—
300C2×Q16C23×C718yes—
301C2×SD16—28no—
302C2×SD16C23×C718yes—
303C2×M16—24no—
304C2×M16C23×C714yes—
305C22×C8—24no—
306C22×C8C23×C712yes—
307C22×C8C23×C714yes—
308C22×C8C23×C712yes—
309C4⋊Q8—24no—
310C4⋊Q8C23×C718yes—
311#124—24no—
312#124C23×C718yes—
313#123—216no—
314C22⋊Q8—216no—
315C4×Q8—216no—
316C4×Q8—28no—
317C4×Q8C23×C7116yes—
318#117—22no—
319#117—216no—
320#117C7×D414yes—
321#117C23×C714yes—
322#117C23×C714yes—
323C2×C4⋊C4—24no—
324C2×C4⋊C4—24no—
325C2×C4⋊C4C7×D412yes—
326C2×C4⋊C4C23×C712yes—
327C2×C22⋊C4—21no—
328C2×C22⋊C4—24no—
329C2×C22⋊C4C7×D412yes—
330C2×C42—24no—
331C2×C42—21no—
332C2×C42C23×C712yes—
333C4⋊C8C23×C7116yes—
334#103C23×C718yes—
335#103C23×C7116yes—
336#102C23×C718yes—
337C22×C7—28no—
338C22×C7—24no—
339C22×C7—42no—
340C22×C7—44no—
341C22×C7—84no—
342C22×C7C2×#12114yes—
343C22×C7C2×#12112yes—
344C22×C7#57814yes—
345C22×C7C23×D411yescharacteristic
346C4×C7—28no—
347C4×C7—28no—
348C4×C7—42no—
349C4×C7—44no—
350C4×C7—44no—
351C4×C7C2×#12114yes—
352C4×C7C2×#12112yes—
353C4×C7C23×D411yescharacteristic
354C4×C7C22×#4111yescharacteristic
355C24—21no—
356C24C2×C7×D411yescharacteristic
357#41—28no—
358#41—28no—
359#41—48no—
360C2×Q8—28no—
361C2×Q8—216no—
362C2×Q8—24no—
363C2×Q8—22no—
364C2×Q8—24no—
365C2×Q8—22no—
366C2×Q8—21no—
367C2×Q8—24no—
368C2×Q8—28no—
369C2×Q8—24no—
370C2×Q8—28no—
371C2×Q8—22no—
372C2×Q8—24no—
373C2×Q8—28no—
374C2×Q8—22no—
375C2×Q8—44no—
376C2×Q8—48no—
377C2×Q8C2×C7×D418yes—
378C2×Q8C2×C7×D4116yes—
379C2×Q8C24×C714yes—
380C2×Q8C24×C712yes—
381C2×Q8C24×C714yes—
382C2×D4—24no—
383C2×D4—22no—
384C2×D4—21no—
385C2×D4—22no—
386C2×D4—44no—
387C2×D4C24×C712yes—
388C22×C4—28no—
389C22×C4—22no—
390C22×C4—24no—
391C22×C4—22no—
392C22×C4—22no—
393C22×C4—21no—
394C22×C4—24no—
395C22×C4—24no—
396C22×C4—44no—
397C22×C4—44no—
398C22×C4C2×C7×D414yes—
399C22×C4C2×C7×D411yescharacteristic
400C22×C4C2×C7×D412yes—
401C22×C4C2×C7×D414yes—
402C22×C4C7×#4114yes—
403C22×C4C24×C711yescharacteristic
404C22×C4C24×C712yes—
405Q16—232no—
406Q16—216no—
407SD16—216no—
408M16—28no—
409C2×C8—24no—
410C2×C8—28no—
411C2×C8—24no—
412C2×C8C24×C714yes—
413C2×C8C24×C714yes—
414C4⋊C4—216no—
415C4⋊C4—216no—
416C4⋊C4—22no—
417C4⋊C4C2×C7×D418yes—
418C4⋊C4C24×C714yes—
419C22⋊C4—24no—
420C22⋊C4—216no—
421C22⋊C4C2×C7×D418yes—
422C42—216no—
423C42—24no—
424C42C2×C7×D414yes—
425C42C24×C714yes—
426C2×C7—24no—
427C2×C7—82no—
428C2×C7#304414yesdirect product factor
429C2×C7C22×#12111yescharacteristic
430C2×C7C2×#57812yes—
431C23—24no—
432C23—22no—
433C23—42no—
434C23—44no—
435C23C7×#12114yes—
436C23C22×C7×D412yes—
437C23C22×C7×D411yescharacteristic
438Q8—24no—
439Q8—216no—
440Q8—28no—
441Q8—24no—
442Q8—22no—
443Q8—24no—
444Q8—22no—
445Q8—48no—
446Q8—44no—
447Q8—42no—
448Q8C22×C7×D418yes—
449D4—22no—
450D4—22no—
451D4—48no—
452D4—42no—
453C2×C4—24no—
454C2×C4—216no—
455C2×C4—28no—
456C2×C4—28no—
457C2×C4—24no—
458C2×C4—24no—
459C2×C4—22no—
460C2×C4—42no—
461C2×C4—48no—
462C2×C4—44no—
463C2×C4—44no—
464C2×C4—48no—
465C2×C4C7×#12114yes—
466C2×C4C7×#12118yes—
467C2×C4C22×C7×D418yes—
468C2×C4C22×C7×D412yes—
469C2×C4C22×C7×D414yes—
470C2×C4C22×C7×D412yes—
471C2×C4C22×C7×D411yescharacteristic
472C2×C4C2×C7×#4112yes—
473C2×C4C2×C7×#4114yes—
474C2×C4C25×C711yescharacteristic
475C8—24no—
476C8—24no—
477C7C2×#304411yescharacteristic, direct product factor, Sylow
478C22—24no—
479C22—28no—
480C22—44no—
481C22—42no—
482C22—84no—
483C22C2×C7×#12114yes—
484C22C2×C7×#12112yes—
485C22C7×#57814yes—
486C22C23×C7×D411yescharacteristic
487C4—28no—
488C4—28no—
489C4—44no—
490C4—42no—
491C4—44no—
492C4C2×C7×#12114yes—
493C4C2×C7×#12112yes—
494C4C23×C7×D411yescharacteristic
495C4C22×C7×#4111yescharacteristic
496C2—24no—
497C2—82no—
498C2C7×#304414yesdirect product factor
499C2C22×C7×#12111yescharacteristic
500C2C2×C7×#57812yes—
subgroupG/H
center, socleC23×C7C22×D4
commutator, Frattini, cosocleC2×C4C25×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
2. C23×C7×Q16C2semidirect
4. C2×C7×#519C2semidirect
5. C7×#3044C2direct (N × H)
6. C2×C7×#464C2semidirect
7. C2×C7×#462C2semidirect
8. C2×C7×#424C2semidirect
9. C2×C7×#419C2semidirect
19. C22×C7×Q16C22semidirect
30. C7×#519C22semidirect
36. C7×#464C22semidirect
37. C7×#462C22semidirect
38. C7×#424C22semidirect
40. C7×#419C22semidirect
45. C2×#3044C7direct (N × H)
112. C23×Q16C2×C7semidirect
114. C2×#519C2×C7semidirect
115. #3044C2×C7direct (N × H)
116. C2×#464C2×C7semidirect
117. C2×#462C2×C7semidirect
118. C2×#424C2×C7semidirect
119. C2×#419C2×C7semidirect
200. C22×Q16C22×C7semidirect
211. #519C22×C7semidirect
217. #464C22×C7semidirect
218. #462C22×C7semidirect
219. #424C22×C7semidirect
221. #419C22×C7semidirect
428. C2×C7#3044direct (N × H)
477. C7C2×#3044direct (N × H)
498. C2C7×#3044direct (N × H)

Maximal subgroups

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

subgroupindex
C22×C7×#1372
C23×C7×Q162
C2×C7×#5362
C2×C7×#5192
C7×#30442
C2×C7×#4642
C2×C7×#4622
C2×C7×#4242
C2×C7×#4192
C2×C7×#4162
C2×#30447