Finite Group Databasebeta

← C2×#11741137 #14233455

Subgroups — C2×#11741137 #14233455

Order 1792.

1854 conjugacy classes of subgroups.

The subgroup lattice has 516 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C7×#557C211yesmaximal, characteristic, complemented
2C2×#90270C211yesmaximal, characteristic
3#11741137C2116yesmaximal, direct product factor
4C2×#89855C211yesmaximal, characteristic
5C2×#89855C212yesmaximal
6C2×#89854C212yesmaximal, complemented
7C2×#89853C211yesmaximal, characteristic, complemented
8C2×#89798C212yesmaximal
9C2×#89796C211yesmaximal, characteristic, complemented
10C2×#89794C212yesmaximal, complemented
11C2×#89793C211yesmaximal, characteristic, complemented
12C2×C4×#1143C211yesmaximal, characteristic
13C7×#557—24no—
14C7×#557C2218yescomplemented
15C2×C7×C4⋊Q8C2211yescharacteristic
16C2×C7×C4⋊Q8C2212yes—
17C2×C7×#125—21no—
18C2×C7×#125—22no—
19C2×C4×C7×Q8—21no—
20C2×C4×C7×Q8C2211yescharacteristic
21C2×C4×C7×Q8C2212yes—
22C2×C4×C7×Q8C2211yescharacteristic
23C2×#6509—21no—
24C22×#1143C2211yescharacteristic
25C22×#1143C2212yes—
26#90270—24no—
27#90270C2218yes—
28C2×#6459—22no—
29C2×D7×C4⋊C4—21no—
30C2×C4×D28C2211yescharacteristic
31C2×C4×D28C2212yes—
32C2×#6433C2212yes—
33C2×#6432C2211yescharacteristic
34C2×#6409C2211yescharacteristic
35C2×#6409C2212yes—
36C2×#6409C2212yes—
37C2×#6409C2212yes—
38C2×#6409C2212yes—
39#89855C22116yes—
40#89855C2218yes—
41#89854C22116yescomplemented
42#89853C2218yescomplemented
43#89798C22116yes—
44C4×#1143C2218yes—
45#89796C2218yescomplemented
46#89794C22116yescomplemented
47#89793C2218yescomplemented
48C2×#6383C2211yescharacteristic
49C2×#6382C2211yescharacteristic
50C2×#6381C2212yes—
51C2×C4⋊(C7⋊C8)C2211yescharacteristic
52C2×C4⋊(C7⋊C8)C2212yes—
53C2×#6377C2212yes—
54C2×C4×C7⋊C8C2211yescharacteristic
55C2×#3372—71nomaximal, Sylow
56C22×C7×Q8D411yescharacteristic
57C22×C7×Q8C2311yescharacteristic
58C22×C7×Q8C2312yes—
59C22×D28C2311yescharacteristic
60C22×C4×D7—21no—
61C22×C4×D7—22no—
62C22×Dic14—21no—
63C7×C4⋊Q8—22no—
64C7×C4⋊Q8—24no—
65C7×C4⋊Q8C2314yes—
66C7×C4⋊Q8C2318yes—
67C7×#125—28no—
68C7×#125—216no—
69C4×C7×Q8—28no—
70C4×C7×Q8—22no—
71C4×C7×Q8—24no—
72C4×C7×Q8D414yes—
73C4×C7×Q8C2314yes—
74C4×C7×Q8C2318yes—
75C4×C7×Q8C2314yes—
76C2×C7×C4⋊C4—22no—
77C2×C7×C4⋊C4—21no—
78C2×C7×C4⋊C4—22no—
79C2×C7×C4⋊C4—21no—
80C2×C7×C4⋊C4—22no—
81C2×C7×C4⋊C4—21no—
82C2×C7×C4⋊C4D411yescharacteristic
83C2×C7×C4⋊C4D412yes—
84C2×C7×C4⋊C4C2311yescharacteristic
85C2×C42×C7—22no—
86C2×C42×C7—21no—
87C2×C42×C7C2311yescharacteristic
88C2×C42×C7C2312yes—
89#6509—28no—
90C2×#1143—24no—
91C2×#1143—28no—
92C2×#1143C2314yes—
93C2×#1143C2318yes—
94C2×(C2×D7)⋊C4—21no—
95C2×(C2×D7)⋊C4—22no—
96C2×C4⋊Dic7—21no—
97C2×C4⋊Dic7C2312yes—
98C2×C4⋊Dic7C2311yescharacteristic
99C2×Dic7⋊C4—22no—
100C2×Dic7⋊C4—22no—
101C22×C7⋊C8C2311yescharacteristic
102C22×C7⋊C8C2311yescharacteristic
103C22×C7⋊C8C2312yes—
104#6459—216no—
105D7×C4⋊C4—28no—
106C4×D28—24no—
107C4×D28—22no—
108C4×D28C2314yes—
109C4×D28C2318yes—
110#6433—24no—
111#6433C2318yes—
112#6432—22no—
113#6432C2314yes—
114#6409C2318yes—
115#6409C2318yes—
116#6409C2318yes—
117#6409C2314yes—
118#6409C2318yes—
119#6383C2314yes—
120#6382C2314yes—
121#6381C2318yes—
122C4⋊(C7⋊C8)C2314yes—
123C4⋊(C7⋊C8)C2318yes—
124#6377C2318yes—
125C4×C7⋊C8C2314yes—
126C2×#557D711yescharacteristic, complemented
127C2×#554—71no—
128#3372—716no—
129C2×#491—72no—
130C2×#487—71no—
131C2×#479—72no—
132C2×#477—71no—
133C2×#461—71no—
134C2×#461—72no—
135C2×#446—71no—
136C2×#440—72no—
137C2×C4×SD16—71no—
138C23×D7—21no—
139C2×C7×Q8—24no—
140C2×C7×Q8—21no—
141C2×C7×Q8—22no—
142C2×C7×Q8—22no—
143C2×C7×Q8—24no—
144C2×C7×Q8—22no—
145C2×C7×Q8—24no—
146C2×C7×Q8C2×D414yes—
147C2×C7×Q8C2412yes—
148C2×C7×Q8C2414yes—
149C22×C4×C7—21no—
150C22×C4×C7—22no—
151C22×C4×C7—21no—
152C22×C4×C7C2×D412yes—
153C22×C4×C7C2×D412yes—
154C22×C4×C7C2×D411yescharacteristic
155C22×C4×C7C2×D411yescharacteristic
156C22×C4×C7C2411yescharacteristic
157C22×Dic7—21no—
158C22×Dic7—22no—
159C2×D28—21no—
160C2×D28—22no—
161C2×D28#4114yes—
162C2×D28C2412yes—
163C2×C4×D7—24no—
164C2×C4×D7—28no—
165C2×C4×D7—44no—
166C2×C4×D7—84no—
167C2×Dic14—24no—
168C2×Dic14—82no—
169C7×C4⋊C4—28no—
170C7×C4⋊C4—24no—
171C7×C4⋊C4—28no—
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—
179C42×C7—28no—
180C42×C7—24no—
181C42×C7C2×D412yes—
182C42×C7C2×D414yes—
183C42×C7C2412yes—
184C42×C7C2414yes—
185#1143—28no—
186#1143—216no—
187(C2×D7)⋊C4—24no—
188(C2×D7)⋊C4—28no—
189C4⋊Dic7—22no—
190C4⋊Dic7—24no—
191C4⋊Dic7—21no—
192C4⋊Dic7C2414yes—
193C4⋊Dic7C2412yes—
194Dic7⋊C4—28no—
195Dic7⋊C4—28no—
196C2×C7⋊C8—22no—
197C2×C7⋊C8—24no—
198C2×C7⋊C8—22no—
199C2×C7⋊C8C2412yes—
200C2×C7⋊C8C2412yes—
201C2×C7⋊C8C2414yes—
202C22×SD16—71no—
203C22×SD16—72no—
204#557—24no—
205#557C2×D718yescomplemented
206#554—78no—
207#554—144no—
208C2×C4⋊Q8—71no—
209C2×C4⋊Q8C2×D711yescharacteristic
210C2×C4⋊Q8C2×D712yes—
211C2×#125—21no—
212C2×#125—22no—
213C2×#125—72no—
214C2×C22⋊Q8—141no—
215C2×C22⋊Q8—142no—
216C2×C4×Q8—21no—
217C2×C4×Q8C2×D711yescharacteristic
218C2×C4×Q8C2×D712yes—
219C2×C4×Q8C2×D711yescharacteristic
220C2×C4×D4—71no—
221C2×C4×D4—72no—
222C22×C4⋊C4—141no—
223#491—716no—
224#487—78no—
225#479—716no—
226#477—78no—
227#461—716no—
228#461—78no—
229#446—78no—
230#440—716no—
231C4×SD16—78no—
232C2×#107—72no—
233C2×#106—71no—
234C2×C4⋊C8—71no—
235C2×C4⋊C8—72no—
236C2×#103—72no—
237C2×#103—72no—
238C2×#103—72no—
239C2×#103—72no—
240C2×#103—71no—
241C2×#102—71no—
242C2×#97—72no—
243C2×C4×C8—71no—
244C23×C7C22×D411yescharacteristic
245C22×D7—24no—
246C22×D7—22no—
247C22×D7—42no—
248C22×D7—42no—
249C7×Q8—28no—
250C7×Q8—22no—
251C7×Q8—24no—
252C7×Q8—22no—
253C7×Q8—24no—
254C7×Q8—42no—
255C7×Q8—44no—
256C2×C4×C7—24no—
257C2×C4×C7—22no—
258C2×C4×C7—24no—
259C2×C4×C7—22no—
260C2×C4×C7—24no—
261C2×C4×C7—22no—
262C2×C4×C7—44no—
263C2×C4×C7—42no—
264C2×C4×C7—42no—
265C2×C4×C7#13714yes—
266C2×C4×C7C22×D414yes—
267C2×C4×C7C22×D414yes—
268C2×C4×C7C22×D412yes—
269C2×C4×C7C22×D411yescharacteristic
270C2×C4×C7C22×D412yes—
271C2×C4×C7C2×#4112yes—
272C2×C4×C72−1+412yes—
273C2×C4×C7C2511yescharacteristic
274C2×Dic7—22no—
275C2×Dic7—24no—
276C2×Dic7—42no—
277C2×Dic7—44no—
278D28—24no—
279D28—22no—
280D28C2×#4114yes—
281C4×D7—48no—
282C4×D7—88no—
283Dic14—84no—
284C7⋊C8—22no—
285C7⋊C8—24no—
286C7⋊C8—22no—
287C22×Q8—141no—
288C22×Q8C22⋊D711yescharacteristic
289C22×Q8C22×D711yescharacteristic
290C22×Q8C22×D712yes—
291C22×D4—71no—
292C23×C4—141no—
293C23×C4—142no—
294C2×SD16—74no—
295C2×SD16—78no—
296C2×SD16—144no—
297C2×SD16—148no—
298C22×C8—71no—
299C22×C8—72no—
300C22×C8—71no—
301C4⋊Q8—24no—
302C4⋊Q8—22no—
303C4⋊Q8—74no—
304C4⋊Q8—142no—
305C4⋊Q8C22×D714yes—
306C4⋊Q8C22×D718yes—
307#125—28no—
308#125—216no—
309#125—78no—
310#125—144no—
311C22⋊Q8—148no—
312C22⋊Q8—1416no—
313C4×Q8—28no—
314C4×Q8—24no—
315C4×Q8—22no—
316C4×Q8C22⋊D714yes—
317C4×Q8C22×D714yes—
318C4×Q8C22×D718yes—
319C4×Q8C22×D714yes—
320C4×D4—74no—
321C4×D4—78no—
322C4×D4—144no—
323C4×D4—142no—
324C2×C4⋊C4—22no—
325C2×C4⋊C4—21no—
326C2×C4⋊C4—21no—
327C2×C4⋊C4—22no—
328C2×C4⋊C4—21no—
329C2×C4⋊C4—22no—
330C2×C4⋊C4—71no—
331C2×C4⋊C4—72no—
332C2×C4⋊C4—142no—
333C2×C4⋊C4—141no—
334C2×C4⋊C4—142no—
335C2×C4⋊C4—148no—
336C2×C4⋊C4C22⋊D711yescharacteristic
337C2×C4⋊C4C22⋊D712yes—
338C2×C4⋊C4C22×D711yescharacteristic
339C2×C22⋊C4—141no—
340C2×C22⋊C4—142no—
341C2×C42—22no—
342C2×C42—21no—
343C2×C42C22×D712yes—
344C2×C42C22×D711yescharacteristic
345#107—78no—
346#106—74no—
347C4⋊C8—74no—
348C4⋊C8—78no—
349#103—74no—
350#103—78no—
351#103—78no—
352#103—78no—
353#103—78no—
354#102—74no—
355#97—78no—
356C4×C8—74no—
357C22×C7#54812yes—
358C22×C7C2×#13712yes—
359C22×C7#57712yes—
360C22×C7C23×D411yescharacteristic
361C2×D7—24no—
362C2×D7—48no—
363C2×D7—42no—
364C2×D7—42no—
365C4×C7—24no—
366C4×C7—22no—
367C4×C7—24no—
368C4×C7—44no—
369C4×C7—42no—
370C4×C7—42no—
371C4×C7#54812yes—
372C4×C7C2×#13714yes—
373C4×C7C22×#4111yescharacteristic
374C4×C7C2×2−1+411yescharacteristic
375Dic7—42no—
376Dic7—44no—
377C24—141no—
378C2×Q8—24no—
379C2×Q8—22no—
380C2×Q8—21no—
381C2×Q8—22no—
382C2×Q8—24no—
383C2×Q8—22no—
384C2×Q8—24no—
385C2×Q8—144no—
386C2×Q8—562no—
387C2×Q8C2×C22⋊D714yes—
388C2×Q8C23×D712yes—
389C2×Q8C23×D714yes—
390C2×D4—74no—
391C2×D4—72no—
392C2×D4—142no—
393C2×D4—141no—
394C22×C4—21no—
395C22×C4—22no—
396C22×C4—21no—
397C22×C4—141no—
398C22×C4—142no—
399C22×C4—144no—
400C22×C4—148no—
401C22×C4—284no—
402C22×C4—564no—
403C22×C4C2×C22⋊D712yes—
404C22×C4C2×C22⋊D711yescharacteristic
405C22×C4C2×C22⋊D712yes—
406C22×C4C2×C22⋊D711yescharacteristic
407C22×C4C23×D711yescharacteristic
408SD16—148no—
409SD16—1416no—
410C2×C8—72no—
411C2×C8—72no—
412C2×C8—74no—
413C2×C8—142no—
414C2×C8—144no—
415C2×C8—142no—
416C4⋊C4—28no—
417C4⋊C4—24no—
418C4⋊C4—24no—
419C4⋊C4—28no—
420C4⋊C4—24no—
421C4⋊C4—28no—
422C4⋊C4—21no—
423C4⋊C4—72no—
424C4⋊C4—74no—
425C4⋊C4—148no—
426C4⋊C4—148no—
427C4⋊C4—141no—
428C4⋊C4—142no—
429C4⋊C4—144no—
430C4⋊C4C2×C22⋊D714yes—
431C4⋊C4C2×C22⋊D718yes—
432C4⋊C4C23×D712yes—
433C22⋊C4—144no—
434C22⋊C4—148no—
435C42—28no—
436C42—24no—
437C42C2×C22⋊D714yes—
438C42C2×C22⋊D712yes—
439C42C23×D712yes—
440C42C23×D714yes—
441C2×C7#337214yescomplemented
442C2×C7C2×#54811yescharacteristic
443C2×C7C22×#13711yescharacteristic
444C2×C7C2×#57711yescharacteristic
445D7—44no—
446C23—144no—
447C23—142no—
448C23—282no—
449C23—282no—
450C23C22×C22⋊D711yescharacteristic
451Q8—28no—
452Q8—22no—
453Q8—24no—
454Q8—22no—
455Q8—24no—
456Q8—44no—
457Q8—42no—
458Q8—564no—
459D4—74no—
460D4—144no—
461D4—142no—
462C2×C4—24no—
463C2×C4—24no—
464C2×C4—22no—
465C2×C4—22no—
466C2×C4—24no—
467C2×C4—22no—
468C2×C4—44no—
469C2×C4—42no—
470C2×C4—42no—
471C2×C4—142no—
472C2×C4—144no—
473C2×C4—282no—
474C2×C4—284no—
475C2×C4—288no—
476C2×C4—568no—
477C2×C4#650514yes—
478C2×C4D7×#4112yes—
479C2×C4#655412yes—
480C2×C4C22×C22⋊D714yes—
481C2×C4C22×C22⋊D712yes—
482C2×C4C22×C22⋊D714yes—
483C2×C4C22×C22⋊D712yes—
484C2×C4C22×C22⋊D711yescharacteristic
485C2×C4C24×D711yescharacteristic
486C8—142no—
487C8—144no—
488C8—142no—
489C7C2×#337211yescharacteristic, complemented, Sylow
490C22—144no—
491C22—282no—
492C22—282no—
493C22—288no—
494C22C2×#650512yes—
495C22#9052212yes—
496C22#9052812yes—
497C22C23×C22⋊D711yescharacteristic
498C4—24no—
499C4—24no—
500C4—22no—
501C4—44no—
502C4—42no—
503C4—42no—
504C4—282no—
505C4—284no—
506C4C2×#650514yes—
507C4#9052212yes—
508C4C2×D7×#4111yescharacteristic
509C4C2×#655411yescharacteristic
510C2—284no—
511C2#1174113714yesdirect product factor
512C2C22×#650511yescharacteristic
513C2C2×#9052211yescharacteristic
514C2C2×#9052811yescharacteristic
subgroupG/H
centerC23C22×C22⋊D7
commutator, cosocleC2×C4×C7C25
FrattiniC2×C4C24×D7
FittingC2×C7×#557C2
socleC23×C7C22×D4
prime radicalC22×D28C23
hypercenterC2×#557D7
hypocenterC7C2×#3372
LCSG ▷ C2×C4×C7 ▷ C2×C7 ▷ C7
UCSC1 ◁ C23 ◁ C2×C4×Q8 ◁ C2×#557

Complements

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

NH ≅ G/Ntype
1. C2×C7×#557C2semidirect
3. #11741137C2direct (N × H)
6. C2×#89854C2semidirect
7. C2×#89853C2semidirect
9. C2×#89796C2semidirect
10. C2×#89794C2semidirect
11. C2×#89793C2semidirect
14. C7×#557C22semidirect
41. #89854C22semidirect
42. #89853C22semidirect
45. #89796C22semidirect
46. #89794C22semidirect
47. #89793C22semidirect
126. C2×#557D7semidirect
205. #557C2×D7semidirect
441. C2×C7#3372semidirect
489. C7C2×#3372semidirect
511. C2#11741137direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C7×#5572
C2×#902702
#117411372
C2×#898552
C2×#898542
C2×#898532
C2×#897982
C2×#897962
C2×#897942
C2×#897932
C2×C4×#11432
C2×#33727