Finite Group Databasebeta

← C2×#11741125 #14234764

Subgroups — C2×#11741125 #14234764

Order 1792.

1906 conjugacy classes of subgroups.

The subgroup lattice has 530 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C7×#556C211yesmaximal, characteristic
2C2×#90261C211yesmaximal, characteristic, complemented
3#11741125C2116yesmaximal, direct product factor
4C2×#89862C211yesmaximal, characteristic, complemented
5C2×#89864C211yesmaximal, characteristic, complemented
6C2×#89826C212yesmaximal
7C2×#89832C212yesmaximal
8C2×#89803C212yesmaximal, complemented
9C2×#89796C211yesmaximal, characteristic, complemented
10C2×#89802C212yesmaximal, complemented
11C2×#89791C211yesmaximal, characteristic
12C2×C4×#1142C211yesmaximal, characteristic
13C7×#556—24no—
14C7×#556C2218yes—
15C2×C7×C4⋊Q8C2211yescharacteristic
16C2×C7×#126—22no—
17C2×C7×#124C2212yes—
18C2×C7×C22⋊Q8—21no—
19C2×C4×C7×Q8C2212yes—
20C2×C4×C7×Q8C2211yescharacteristic
21C2×C4×C7×D4C2211yescharacteristic
22C2×C7×#117—21no—
23C2×Q8×Dic7—21no—
24C22×#1144C2212yes—
25C22×#1144C2212yes—
26C22×#1144C2212yes—
27C22×#1142C2211yescharacteristic
28C22×#1142C2212yes—
29#90261—24no—
30#90261C2218yescomplemented
31C2×#6453—21no—
32C2×#6453—22no—
33C2×#6432C2211yescharacteristic
34C2×#6432C2212yes—
35C2×C4×Dic14C2211yescharacteristic
36C2×C4×Dic14C2212yes—
37C2×#6409C2212yes—
38C2×#6406C2211yescharacteristic
39#89864C2218yescomplemented
40#89862C2218yescomplemented
41#89832C22116yes—
42#89826C22116yes—
43#89803C22116yescomplemented
44#89802C22116yescomplemented
45#89796C2218yescomplemented
46#89791C2218yes—
47C4×#1142C2218yes—
48C2×#6384C2211yescharacteristic
49C2×#6384C2212yes—
50C2×#6382C2211yescharacteristic
51C2×C4⋊(C7⋊C8)C2211yescharacteristic
52C2×C4⋊(C7⋊C8)C2212yes—
53C2×#6377C2212yes—
54C2×C4×C7⋊C8C2211yescharacteristic
55C2×#3398—71nomaximal, Sylow
56C22×C7×Q8D411yescharacteristic
57C22×C7×Q8C2312yes—
58C22×C7×D4C2311yescharacteristic
59C23×C4×C7—21no—
60C22×Dic14C2311yescharacteristic
61C22×Dic14C2312yes—
62C7×C4⋊Q8—22no—
63C7×C4⋊Q8C2314yes—
64C7×#126—216no—
65C7×#124—24no—
66C7×#124C2318yes—
67C7×C22⋊Q8—28no—
68C4×C7×Q8—24no—
69C4×C7×Q8D414yes—
70C4×C7×Q8C2318yes—
71C4×C7×Q8C2314yes—
72C4×C7×D4—22no—
73C4×C7×D4C2314yes—
74C7×#117—28no—
75C2×C7×C4⋊C4—21no—
76C2×C7×C4⋊C4—22no—
77C2×C7×C4⋊C4—21no—
78C2×C7×C4⋊C4D411yescharacteristic
79C2×C7×C4⋊C4D412yes—
80C2×C7×C4⋊C4C2311yescharacteristic
81C2×C7×C22⋊C4—22no—
82C2×C7×C22⋊C4—21no—
83C2×C7×C22⋊C4—22no—
84C2×C42×C7—22no—
85C2×C42×C7C2311yescharacteristic
86C2×C42×C7C2312yes—
87Q8×Dic7—28no—
88C2×#1144—28no—
89C2×#1144—44no—
90C2×#1144—44no—
91C2×#1144C2318yes—
92C2×#1144C2318yes—
93C2×#1144C2318yes—
94C2×#1142—24no—
95C2×#1142—44no—
96C2×#1142C2314yes—
97C2×#1142C2318yes—
98C2×C4⋊Dic7—22no—
99C2×C4⋊Dic7—21no—
100C2×C4⋊Dic7—22no—
101C2×C4⋊Dic7—21no—
102C2×C4⋊Dic7C2311yescharacteristic
103C2×Dic7⋊C4—22no—
104C2×Dic7⋊C4—21no—
105C2×C4×Dic7—22no—
106C2×C4×Dic7—21no—
107C22×C7⋊C8C2311yescharacteristic
108C22×C7⋊C8C2312yes—
109C22×C7⋊C8C2311yescharacteristic
110#6453—28no—
111#6453—216no—
112#6432—22no—
113#6432—24no—
114#6432C2314yes—
115#6432C2318yes—
116C4×Dic14—22no—
117C4×Dic14—24no—
118C4×Dic14C2314yes—
119C4×Dic14C2318yes—
120#6409C2318yes—
121#6406C2314yes—
122#6384C2314yes—
123#6384C2318yes—
124#6382C2314yes—
125C4⋊(C7⋊C8)C2314yes—
126C4⋊(C7⋊C8)C2318yes—
127#6377C2318yes—
128C4×C7⋊C8C2314yes—
129C2×#557—71no—
130C2×#556D711yescharacteristic
131#3398—716no—
132C2×#497—72no—
133C2×#494—71no—
134C2×#464—72no—
135C2×#462—71no—
136C2×#462—72no—
137C2×#461—71no—
138C2×#446—71no—
139C2×#441—72no—
140C2×C4×SD16—71no—
141C24×C7—21no—
142C2×C7×Q8—24no—
143C2×C7×Q8—22no—
144C2×C7×Q8—24no—
145C2×C7×Q8—24no—
146C2×C7×Q8C2×D414yes—
147C2×C7×Q8C2414yes—
148C2×C7×D4—21no—
149C2×C7×D4—22no—
150C2×C7×D4—22no—
151C2×C7×D4C2412yes—
152C22×C4×C7—21no—
153C22×C4×C7—22no—
154C22×C4×C7—24no—
155C22×C4×C7—44no—
156C22×C4×C7C2×D412yes—
157C22×C4×C7C2×D412yes—
158C22×C4×C7C2×D411yescharacteristic
159C22×C4×C7C2×D411yescharacteristic
160C22×C4×C7C2411yescharacteristic
161C22×Dic7—21no—
162C22×Dic7—21no—
163C22×Dic7—22no—
164C2×Dic14—22no—
165C2×Dic14—24no—
166C2×Dic14—24no—
167C2×Dic14—22no—
168C2×Dic14—21no—
169C2×Dic14—22no—
170C2×Dic14C2412yes—
171C2×Dic14C2414yes—
172C7×C4⋊C4—24no—
173C7×C4⋊C4—28no—
174C7×C4⋊C4—24no—
175C7×C4⋊C4—21no—
176C7×C4⋊C4C2×D414yes—
177C7×C4⋊C4C2×D418yes—
178C7×C4⋊C4C2412yes—
179C7×C22⋊C4—28no—
180C7×C22⋊C4—24no—
181C7×C22⋊C4—28no—
182C42×C7—28no—
183C42×C7C2×D412yes—
184C42×C7C2×D414yes—
185C42×C7C2412yes—
186C42×C7C2414yes—
187#1144—216no—
188#1144—48no—
189#1144—48no—
190#1142—28no—
191#1142—48no—
192C4⋊Dic7—21no—
193C4⋊Dic7—28no—
194C4⋊Dic7—24no—
195C4⋊Dic7—28no—
196C4⋊Dic7—24no—
197C4⋊Dic7C2412yes—
198Dic7⋊C4—28no—
199Dic7⋊C4—24no—
200C4×Dic7—28no—
201C4×Dic7—24no—
202C2×C7⋊C8—24no—
203C2×C7⋊C8—22no—
204C2×C7⋊C8#4114yes—
205C2×C7⋊C8C2412yes—
206C2×C7⋊C8C2414yes—
207C2×C7⋊C8C2412yes—
208C22×Q16—72no—
209C22×Q16—72no—
210C22×Q16—72no—
211C22×SD16—71no—
212C22×SD16—72no—
213#557—78no—
214#557—144no—
215#556—24no—
216#556C2×D718yes—
217C2×C4⋊Q8—71no—
218C2×C4⋊Q8—72no—
219C2×C4⋊Q8C2×D711yescharacteristic
220C2×#126—22no—
221C2×#125—141no—
222C2×#125—142no—
223C2×#124C2×D712yes—
224C2×C22⋊Q8—21no—
225C2×C4×Q8—71no—
226C2×C4×Q8—72no—
227C2×C4×Q8—141no—
228C2×C4×Q8C2×D712yes—
229C2×C4×Q8C2×D711yescharacteristic
230C2×C4×D4C2×D711yescharacteristic
231C2×#117—21no—
232#497—716no—
233#494—78no—
234#464—716no—
235#462—78no—
236#462—716no—
237#461—78no—
238#446—78no—
239#441—716no—
240C4×SD16—78no—
241C2×#106—71no—
242C2×C4⋊C8—71no—
243C2×C4⋊C8—72no—
244C2×#103—72no—
245C2×#103—71no—
246C2×#103—72no—
247C2×#102—71no—
248C2×#97—72no—
249C2×C4×C8—71no—
250C23×C7—22no—
251C23×C7—42no—
252C23×C7—42no—
253C23×C7—42no—
254C23×C7C22×D411yescharacteristic
255C7×Q8—28no—
256C7×Q8—24no—
257C7×Q8—24no—
258C7×Q8—44no—
259C7×D4—22no—
260C7×D4—22no—
261C7×D4—42no—
262C2×C4×C7—24no—
263C2×C4×C7—24no—
264C2×C4×C7—22no—
265C2×C4×C7—22no—
266C2×C4×C7—24no—
267C2×C4×C7—44no—
268C2×C4×C7—42no—
269C2×C4×C7—48no—
270C2×C4×C7#13714yes—
271C2×C4×C7C22×D414yes—
272C2×C4×C7C22×D414yes—
273C2×C4×C7C22×D412yes—
274C2×C4×C7C22×D411yescharacteristic
275C2×C4×C7C22×D412yes—
276C2×C4×C7C2×#4112yes—
277C2×C4×C7H(5,𝔽2)12yes—
278C2×C4×C7C2511yescharacteristic
279C2×Dic7—22no—
280C2×Dic7—22no—
281C2×Dic7—24no—
282C2×Dic7—42no—
283C2×Dic7—44no—
284C2×Dic7—42no—
285Dic14—22no—
286Dic14—24no—
287Dic14—24no—
288Dic14—22no—
289Dic14—42no—
290Dic14—44no—
291C7⋊C8—24no—
292C7⋊C8—22no—
293C7⋊C8C2×#4114yes—
294C22×Q8—71no—
295C22×Q8—72no—
296C22×Q8C22⋊D711yescharacteristic
297C22×Q8C22×D712yes—
298C22×D4C22×D711yescharacteristic
299C23×C4—21no—
300C2×Q16—78no—
301C2×Q16—78no—
302C2×Q16—78no—
303C2×Q16—148no—
304C2×Q16—284no—
305C2×Q16—284no—
306C2×SD16—74no—
307C2×SD16—78no—
308C2×SD16—144no—
309C2×SD16—284no—
310C22×C8—71no—
311C22×C8—72no—
312C22×C8—71no—
313C4⋊Q8—22no—
314C4⋊Q8—74no—
315C4⋊Q8—78no—
316C4⋊Q8—142no—
317C4⋊Q8—144no—
318C4⋊Q8C22×D714yes—
319#126—216no—
320#125—148no—
321#125—1416no—
322#124—24no—
323#124C22×D718yes—
324C22⋊Q8—28no—
325C4×Q8—24no—
326C4×Q8—74no—
327C4×Q8—78no—
328C4×Q8—148no—
329C4×Q8—142no—
330C4×Q8—144no—
331C4×Q8C22⋊D714yes—
332C4×Q8C22×D718yes—
333C4×Q8C22×D714yes—
334C4×D4—22no—
335C4×D4C22×D714yes—
336#117—28no—
337C2×C4⋊C4—21no—
338C2×C4⋊C4—22no—
339C2×C4⋊C4—21no—
340C2×C4⋊C4—71no—
341C2×C4⋊C4—142no—
342C2×C4⋊C4—141no—
343C2×C4⋊C4—142no—
344C2×C4⋊C4—141no—
345C2×C4⋊C4—142no—
346C2×C4⋊C4—141no—
347C2×C4⋊C4C22⋊D711yescharacteristic
348C2×C4⋊C4C22⋊D712yes—
349C2×C4⋊C4C22×D711yescharacteristic
350C2×C22⋊C4—22no—
351C2×C22⋊C4—21no—
352C2×C22⋊C4—22no—
353C2×C42—22no—
354C2×C42—142no—
355C2×C42—141no—
356C2×C42C22×D711yescharacteristic
357C2×C42C22×D712yes—
358#106—74no—
359C4⋊C8—74no—
360C4⋊C8—78no—
361#103—78no—
362#103—74no—
363#103—78no—
364#102—74no—
365#97—78no—
366C4×C8—74no—
367C22×C7—42no—
368C22×C7—42no—
369C22×C7—42no—
370C22×C7—84no—
371C22×C7#55012yes—
372C22×C7C2×#13712yes—
373C22×C7#57812yes—
374C22×C7C23×D411yescharacteristic
375C4×C7—24no—
376C4×C7—24no—
377C4×C7—22no—
378C4×C7—44no—
379C4×C7—42no—
380C4×C7#55012yes—
381C4×C7C2×#13714yes—
382C4×C7C22×#4111yescharacteristic
383C4×C7C2×H(5,𝔽2)11yescharacteristic
384Dic7—42no—
385Dic7—44no—
386Dic7—42no—
387C24—21no—
388C2×Q8—24no—
389C2×Q8—22no—
390C2×Q8—24no—
391C2×Q8—24no—
392C2×Q8—72no—
393C2×Q8—74no—
394C2×Q8—141no—
395C2×Q8—142no—
396C2×Q8—142no—
397C2×Q8—144no—
398C2×Q8—144no—
399C2×Q8—142no—
400C2×Q8C2×C22⋊D714yes—
401C2×Q8C23×D714yes—
402C2×D4—22no—
403C2×D4—22no—
404C2×D4—21no—
405C2×D4C23×D712yes—
406C22×C4—21no—
407C22×C4—22no—
408C22×C4—24no—
409C22×C4—44no—
410C22×C4—141no—
411C22×C4—141no—
412C22×C4—142no—
413C22×C4C2×C22⋊D712yes—
414C22×C4C2×C22⋊D712yes—
415C22×C4C2×C22⋊D711yescharacteristic
416C22×C4C2×C22⋊D711yescharacteristic
417C22×C4C23×D711yescharacteristic
418Q16—1416no—
419Q16—288no—
420Q16—288no—
421SD16—148no—
422SD16—288no—
423C2×C8—74no—
424C2×C8—72no—
425C2×C8—72no—
426C2×C8—74no—
427C2×C8—144no—
428C2×C8—142no—
429C4⋊C4—24no—
430C4⋊C4—28no—
431C4⋊C4—24no—
432C4⋊C4—21no—
433C4⋊C4—72no—
434C4⋊C4—148no—
435C4⋊C4—144no—
436C4⋊C4—141no—
437C4⋊C4—148no—
438C4⋊C4—144no—
439C4⋊C4—148no—
440C4⋊C4—144no—
441C4⋊C4C2×C22⋊D714yes—
442C4⋊C4C2×C22⋊D718yes—
443C4⋊C4C23×D712yes—
444C22⋊C4—28no—
445C22⋊C4—24no—
446C22⋊C4—28no—
447C42—28no—
448C42—148no—
449C42—144no—
450C42C2×C22⋊D712yes—
451C42C2×C22⋊D714yes—
452C42C23×D712yes—
453C42C23×D714yes—
454C2×C7—82no—
455C2×C7#339814yescomplemented
456C2×C7C2×#55011yescharacteristic
457C2×C7C22×#13711yescharacteristic
458C2×C7C2×#57811yescharacteristic
459C23—22no—
460C23—42no—
461C23—42no—
462C23—42no—
463C23C22×C22⋊D711yescharacteristic
464Q8—28no—
465Q8—24no—
466Q8—24no—
467Q8—44no—
468Q8—142no—
469Q8—144no—
470Q8—144no—
471Q8—142no—
472Q8—282no—
473Q8—284no—
474D4—22no—
475D4—22no—
476D4—42no—
477C2×C4—24no—
478C2×C4—24no—
479C2×C4—22no—
480C2×C4—22no—
481C2×C4—24no—
482C2×C4—42no—
483C2×C4—44no—
484C2×C4—48no—
485C2×C4—142no—
486C2×C4—142no—
487C2×C4—144no—
488C2×C4—282no—
489C2×C4—284no—
490C2×C4—282no—
491C2×C4#651414yes—
492C2×C4D7×#4112yes—
493C2×C4#655312yes—
494C2×C4C22×C22⋊D714yes—
495C2×C4C22×C22⋊D714yes—
496C2×C4C22×C22⋊D712yes—
497C2×C4C22×C22⋊D712yes—
498C2×C4C22×C22⋊D711yescharacteristic
499C2×C4C24×D711yescharacteristic
500C8—74no—
501C8—144no—
502C8—142no—
503C7C2×#339811yescharacteristic, complemented, Sylow
504C22—42no—
505C22—42no—
506C22—42no—
507C22—84no—
508C22C2×#651412yes—
509C22#9052512yes—
510C22#9052912yes—
511C22C23×C22⋊D711yescharacteristic
512C4—24no—
513C4—24no—
514C4—22no—
515C4—42no—
516C4—44no—
517C4—282no—
518C4—284no—
519C4—282no—
520C4C2×#651414yes—
521C4#9052512yes—
522C4C2×D7×#4111yescharacteristic
523C4C2×#655311yescharacteristic
524C2—82no—
525C2#1174112514yesdirect product factor
526C2C22×#651411yescharacteristic
527C2C2×#9052511yescharacteristic
528C2C2×#9052911yescharacteristic
subgroupG/H
centerC23C22×C22⋊D7
commutator, cosocleC2×C4×C7C25
FrattiniC2×C4C24×D7
FittingC2×C7×#556C2
socleC23×C7C22×D4
prime radicalC22×C7×D4C23
hypercenterC2×#556D7
hypocenterC7C2×#3398
LCSG ▷ C2×C4×C7 ▷ C2×C7 ▷ C7
UCSC1 ◁ C23 ◁ C2×C4×Q8 ◁ C2×#556

Complements

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

NH ≅ G/Ntype
2. C2×#90261C2semidirect
3. #11741125C2direct (N × H)
4. C2×#89862C2semidirect
5. C2×#89864C2semidirect
8. C2×#89803C2semidirect
9. C2×#89796C2semidirect
10. C2×#89802C2semidirect
30. #90261C22semidirect
39. #89864C22semidirect
40. #89862C22semidirect
43. #89803C22semidirect
44. #89802C22semidirect
45. #89796C22semidirect
455. C2×C7#3398semidirect
503. C7C2×#3398semidirect
525. C2#11741125direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C7×#5562
C2×#902612
#117411252
C2×#898622
C2×#898642
C2×#898262
C2×#898322
C2×#898032
C2×#897962
C2×#898022
C2×#897912
C2×C4×#11422
C2×#33987