Finite Group Databasebeta

← C2×#11737073 #14233457

Subgroups — C2×#11737073 #14233457

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×#90258C211yesmaximal, characteristic, complemented
2C2×#90234C211yesmaximal, characteristic
3C2×C4×C7×SD16C211yesmaximal, characteristic
4C2×#89934C212yesmaximal
5C2×#89793C211yesmaximal, characteristic, complemented
6C2×#89791C211yesmaximal, characteristic
7#11737073C2116yesmaximal, direct product factor
8C2×#89629C212yesmaximal, complemented
9C2×#89569C212yesmaximal, complemented
10C2×#89529C212yesmaximal
11C2×#89453C211yesmaximal, characteristic, complemented
12C2×#89451C211yesmaximal, characteristic, complemented
13C22×C7×SD16C2211yescharacteristic
14C2×C4×C7×Q8C2211yescharacteristic
15C2×C4×C7×D4C2211yescharacteristic
16C2×#6507C2212yes—
17C2×D4×Dic7C2212yes—
18C22×#1142C2212yes—
19C22×C4⋊Dic7—21no—
20C2×#6487—21no—
21#90258—24no—
22#90258C2218yescomplemented
23#90234—24no—
24#90234C2218yes—
25C2×#6453C2212yes—
26C2×#6452—22no—
27C2×#6450C2212yes—
28C2×#6441—22no—
29C2×#6433—21no—
30C2×#6432C2211yescharacteristic
31C2×#6432C2211yescharacteristic
32C2×C4×Dic14—21no—
33C2×C4×Dic14C2211yescharacteristic
34C4×C7×SD16C2218yes—
35C2×C7×#106C2211yescharacteristic
36C2×C7×#103C2211yescharacteristic
37C2×C7×#102C2211yescharacteristic
38C2×C4×C7×C8C2211yescharacteristic
39C2×#6409C2212yes—
40#89934C22116yes—
41C2×#6390C2212yes—
42C2×#6390C2212yes—
43C2×#6389C2212yes—
44C2×Dic7⋊C8C2212yes—
45#89793C2218yescomplemented
46#89791C2218yes—
47C2×#6384C2212yes—
48C2×#6381C2212yes—
49C2×C4⋊(C7⋊C8)C2211yescharacteristic
50#89629C22116yescomplemented
51#89569C22116yescomplemented
52#89529C22116yes—
53#89453C2218yescomplemented
54#89451C2218yescomplemented
55C2×#3372—71nomaximal, Sylow
56C22×C7×Q8C2311yescharacteristic
57C22×C7×D4C2311yescharacteristic
58C23×C4×C7—21no—
59C23×Dic7—22no—
60C22×Dic14—21no—
61C22×Dic14D411yescharacteristic
62C22×Dic14C2312yes—
63C2×C7×SD16—24no—
64C2×C7×SD16C2314yes—
65C22×C7×C8C2311yescharacteristic
66C22×C7×C8C2311yescharacteristic
67C4×C7×Q8—22no—
68C4×C7×Q8C2314yes—
69C4×C7×D4—22no—
70C4×C7×D4C2314yes—
71C2×C7×C4⋊C4—21no—
72C2×C7×C4⋊C4C2311yescharacteristic
73C2×C7×C4⋊C4C2311yescharacteristic
74C2×C7×C22⋊C4—21no—
75C2×C42×C7—21no—
76C2×C42×C7C2311yescharacteristic
77C2×C22⋊Dic7—22no—
78#6507—24no—
79#6507C2318yes—
80D4×Dic7—24no—
81D4×Dic7C2318yes—
82C2×#1142—28no—
83C2×#1142C2318yes—
84C2×C4⋊Dic7—21no—
85C2×C4⋊Dic7—21no—
86C2×C4⋊Dic7—21no—
87C2×C4⋊Dic7—22no—
88C2×C4⋊Dic7—28no—
89C2×C4⋊Dic7D411yescharacteristic
90C2×C4⋊Dic7C2312yes—
91#6487—28no—
92C2×Dic7⋊C4—22no—
93C2×Dic7⋊C4—22no—
94C2×Dic7⋊C4—22no—
95C2×Dic7⋊C4—22no—
96C2×Dic7⋊C4D412yes—
97C2×C4×Dic7—22no—
98C2×C4×Dic7C2312yes—
99C22×C7⋊C8C2312yes—
100#6453—24no—
101#6453C2318yes—
102#6452—216no—
103#6450—24no—
104#6450C2318yes—
105#6441—216no—
106#6433—28no—
107#6432—22no—
108#6432—22no—
109#6432C2314yes—
110#6432C2314yes—
111C4×Dic14—28no—
112C4×Dic14D414yes—
113C4×Dic14C2314yes—
114C7×#106C2314yes—
115C7×#103C2314yes—
116C7×#102C2314yes—
117C4×C7×C8C2314yes—
118#6409C2318yes—
119#6390C2318yes—
120#6390C2318yes—
121#6389C2318yes—
122Dic7⋊C8C2318yes—
123#6384C2318yes—
124#6381C2318yes—
125C4⋊(C7⋊C8)C2314yes—
126C2×#557—71no—
127C2×#554—71no—
128#3372—716no—
129C2×#491—72no—
130C2×#487—71no—
131C2×#479—72no—
132C2×#477—71no—
133C2×#461—72no—
134C2×#461—71no—
135C2×#446—71no—
136C2×#440—72no—
137C2×C4×SD16D711yescharacteristic
138C24×C7—21no—
139C2×C7×Q8—21no—
140C2×C7×Q8—22no—
141C2×C7×Q8—22no—
142C2×C7×Q8C2412yes—
143C2×C7×D4—21no—
144C2×C7×D4—22no—
145C2×C7×D4#4114yes—
146C2×C7×D4C2412yes—
147C22×C4×C7—21no—
148C22×C4×C7—21no—
149C22×C4×C7—21no—
150C22×C4×C7—24no—
151C22×C4×C7—44no—
152C22×C4×C7C2×D411yescharacteristic
153C22×C4×C7C2×D411yescharacteristic
154C22×C4×C7C2411yescharacteristic
155C22×Dic7—22no—
156C22×Dic7—22no—
157C22×Dic7—28no—
158C22×Dic7—84no—
159C22×Dic7C2×D412yes—
160C22×Dic7C2×D412yes—
161C2×Dic14—24no—
162C2×Dic14—24no—
163C2×Dic14—24no—
164C2×Dic14—22no—
165C2×Dic14—24no—
166C2×Dic14—82no—
167C2×Dic14C2×D414yes—
168C2×Dic14C2414yes—
169C7×SD16—28no—
170C2×C7×C8—22no—
171C2×C7×C8—22no—
172C2×C7×C8C2412yes—
173C2×C7×C8C2412yes—
174C7×C4⋊C4—21no—
175C7×C4⋊C4—24no—
176C7×C4⋊C4—21no—
177C7×C4⋊C4C2412yes—
178C7×C4⋊C4C2412yes—
179C7×C22⋊C4—24no—
180C42×C7—24no—
181C42×C7C2×D412yes—
182C42×C7C2412yes—
183C22⋊Dic7—28no—
184#1142—216no—
185C4⋊Dic7—24no—
186C4⋊Dic7—22no—
187C4⋊Dic7—24no—
188C4⋊Dic7—24no—
189C4⋊Dic7—28no—
190C4⋊Dic7C2×D414yes—
191C4⋊Dic7C2414yes—
192Dic7⋊C4—28no—
193Dic7⋊C4—28no—
194Dic7⋊C4—28no—
195Dic7⋊C4—28no—
196Dic7⋊C4C2×D418yes—
197C4×Dic7—28no—
198C4×Dic7C2×D414yes—
199C4×Dic7C2414yes—
200C2×C7⋊C8—24no—
201C2×C7⋊C8C2414yes—
202C22×SD16—72no—
203C22×SD16C2×D711yescharacteristic
204#557—78no—
205#557—144no—
206#554—78no—
207#554—144no—
208C2×C4⋊Q8—72no—
209C2×C4⋊Q8—71no—
210C2×C4⋊Q8—71no—
211C2×#125—72no—
212C2×#125—141no—
213C2×#125—142no—
214C2×C22⋊Q8—142no—
215C2×C22⋊Q8—141no—
216C2×C4×Q8—71no—
217C2×C4×Q8—72no—
218C2×C4×Q8—141no—
219C2×C4×Q8C2×D711yescharacteristic
220C2×C4×D4—72no—
221C2×C4×D4C2×D711yescharacteristic
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×SD16C2×D718yes—
232C2×#107—72no—
233C2×#106C2×D711yescharacteristic
234C2×C4⋊C8—72no—
235C2×C4⋊C8—71no—
236C2×#103—72no—
237C2×#103—72no—
238C2×#103—72no—
239C2×#103—72no—
240C2×#103C2×D711yescharacteristic
241C2×#102C2×D711yescharacteristic
242C2×#97—72no—
243C2×C4×C8C2×D711yescharacteristic
244C23×C7—24no—
245C23×C7—22no—
246C23×C7—42no—
247C23×C7—42no—
248C23×C7C22×D411yescharacteristic
249C7×Q8—22no—
250C7×Q8—22no—
251C7×Q8—42no—
252C7×D4—24no—
253C7×D4—22no—
254C7×D4C2×#4114yes—
255C2×C4×C7—22no—
256C2×C4×C7—22no—
257C2×C4×C7—22no—
258C2×C4×C7—22no—
259C2×C4×C7—42no—
260C2×C4×C7—42no—
261C2×C4×C7—42no—
262C2×C4×C7—48no—
263C2×C4×C7#13714yes—
264C2×C4×C7C22×D412yes—
265C2×C4×C7C22×D411yescharacteristic
266C2×C4×C7C22×D412yes—
267C2×C4×C7C2×#4112yes—
268C2×C4×C72−1+412yes—
269C2×C4×C7C2511yescharacteristic
270C2×Dic7—24no—
271C2×Dic7—24no—
272C2×Dic7—24no—
273C2×Dic7—24no—
274C2×Dic7—44no—
275C2×Dic7—44no—
276C2×Dic7—88no—
277C2×Dic7C22×D414yes—
278C2×Dic7C22×D414yes—
279Dic14—28no—
280Dic14—24no—
281Dic14—24no—
282Dic14—44no—
283Dic14—84no—
284C7×C8—22no—
285C7×C8—22no—
286C7⋊C8—24no—
287C22×Q8—71no—
288C22×Q8—72no—
289C22×Q8—141no—
290C22×Q8C22×D711yescharacteristic
291C22×D4C22×D711yescharacteristic
292C23×C4—21no—
293C23×C4—142no—
294C2×SD16—24no—
295C2×SD16—78no—
296C2×SD16—148no—
297C2×SD16C22×D714yes—
298C22×C8—72no—
299C22×C8C22×D711yescharacteristic
300C22×C8C22×D711yescharacteristic
301C4⋊Q8—78no—
302C4⋊Q8—74no—
303C4⋊Q8—74no—
304C4⋊Q8—144no—
305C4⋊Q8—142no—
306C4⋊Q8—142no—
307#125—78no—
308#125—148no—
309#125—144no—
310#125—1416no—
311C22⋊Q8—1416no—
312C22⋊Q8—148no—
313C4×Q8—22no—
314C4×Q8—74no—
315C4×Q8—74no—
316C4×Q8—78no—
317C4×Q8—148no—
318C4×Q8—144no—
319C4×Q8C22×D714yes—
320C4×D4—22no—
321C4×D4—78no—
322C4×D4—144no—
323C4×D4C22×D714yes—
324C2×C4⋊C4—21no—
325C2×C4⋊C4—71no—
326C2×C4⋊C4—72no—
327C2×C4⋊C4—72no—
328C2×C4⋊C4—148no—
329C2×C4⋊C4—142no—
330C2×C4⋊C4—142no—
331C2×C4⋊C4—142no—
332C2×C4⋊C4—142no—
333C2×C4⋊C4—142no—
334C2×C4⋊C4—141no—
335C2×C4⋊C4—141no—
336C2×C4⋊C4—141no—
337C2×C4⋊C4C22×D711yescharacteristic
338C2×C4⋊C4C22×D711yescharacteristic
339C2×C22⋊C4—21no—
340C2×C22⋊C4—142no—
341C2×C42—21no—
342C2×C42—72no—
343C2×C42—142no—
344C2×C42C22×D711yescharacteristic
345#107—78no—
346#106C22×D714yes—
347C4⋊C8—78no—
348C4⋊C8—74no—
349#103—78no—
350#103—78no—
351#103—78no—
352#103—78no—
353#103C22×D714yes—
354#102C22×D714yes—
355#97—78no—
356C4×C8C22×D714yes—
357C22×C7—24no—
358C22×C7—48no—
359C22×C7—42no—
360C22×C7—42no—
361C22×C7#54812yes—
362C22×C7C2×#13712yes—
363C22×C7#57712yes—
364C22×C7C23×D411yescharacteristic
365C4×C7—22no—
366C4×C7—42no—
367C4×C7—42no—
368C4×C7—42no—
369C4×C7#54812yes—
370C4×C7C2×#13714yes—
371C4×C7C22×#4111yescharacteristic
372C4×C7C2×2−1+411yescharacteristic
373Dic7—24no—
374Dic7—24no—
375Dic7—44no—
376Dic7—44no—
377C24—21no—
378C2×Q8—21no—
379C2×Q8—22no—
380C2×Q8—22no—
381C2×Q8—74no—
382C2×Q8—74no—
383C2×Q8—144no—
384C2×Q8—142no—
385C2×Q8—144no—
386C2×Q8—144no—
387C2×Q8—144no—
388C2×Q8—562no—
389C2×Q8C23×D712yes—
390C2×D4—21no—
391C2×D4—22no—
392C2×D4#115714yes—
393C2×D4C23×D712yes—
394C22×C4—21no—
395C22×C4—21no—
396C22×C4—21no—
397C22×C4—24no—
398C22×C4—44no—
399C22×C4—72no—
400C22×C4—72no—
401C22×C4—148no—
402C22×C4—142no—
403C22×C4—142no—
404C22×C4—564no—
405C22×C4D4×D711yescharacteristic
406C22×C4D4×D711yescharacteristic
407C22×C4C23×D711yescharacteristic
408SD16—28no—
409SD16—1416no—
410C2×C8—22no—
411C2×C8—22no—
412C2×C8—74no—
413C2×C8—144no—
414C2×C8C23×D712yes—
415C2×C8C23×D712yes—
416C4⋊C4—24no—
417C4⋊C4—21no—
418C4⋊C4—21no—
419C4⋊C4—78no—
420C4⋊C4—74no—
421C4⋊C4—74no—
422C4⋊C4—148no—
423C4⋊C4—148no—
424C4⋊C4—148no—
425C4⋊C4—148no—
426C4⋊C4—148no—
427C4⋊C4—142no—
428C4⋊C4—144no—
429C4⋊C4—144no—
430C4⋊C4—144no—
431C4⋊C4C23×D712yes—
432C4⋊C4C23×D712yes—
433C22⋊C4—24no—
434C22⋊C4—148no—
435C42—24no—
436C42—74no—
437C42—74no—
438C42—148no—
439C42D4×D712yes—
440C42C23×D712yes—
441C2×C7—44no—
442C2×C7#337214yescomplemented
443C2×C7C2×#54811yescharacteristic
444C2×C7C22×#13711yescharacteristic
445C2×C7C2×#57711yescharacteristic
446C23—24no—
447C23—22no—
448C23—42no—
449C23—42no—
450C23C2×D4×D711yescharacteristic
451Q8—22no—
452Q8—22no—
453Q8—42no—
454Q8—148no—
455Q8—144no—
456Q8—144no—
457Q8—284no—
458Q8—564no—
459D4—24no—
460D4—22no—
461D4C2×#115714yes—
462C2×C4—22no—
463C2×C4—22no—
464C2×C4—22no—
465C2×C4—22no—
466C2×C4—42no—
467C2×C4—42no—
468C2×C4—42no—
469C2×C4—48no—
470C2×C4—74no—
471C2×C4—74no—
472C2×C4—144no—
473C2×C4—144no—
474C2×C4—144no—
475C2×C4—144no—
476C2×C4—284no—
477C2×C4—284no—
478C2×C4—568no—
479C2×C4#647814yes—
480C2×C4C2×#115712yes—
481C2×C4C2×D4×D712yes—
482C2×C4C2×D4×D712yes—
483C2×C4C2×D4×D711yescharacteristic
484C2×C4#655412yes—
485C2×C4C24×D711yescharacteristic
486C8—22no—
487C8—22no—
488C8—144no—
489C7C2×#337211yescharacteristic, complemented, Sylow
490C22—24no—
491C22—48no—
492C22—42no—
493C22—42no—
494C22#9024312yes—
495C22C2×#647812yes—
496C22#9046112yes—
497C22C22×D4×D711yescharacteristic
498C4—22no—
499C4—42no—
500C4—42no—
501C4—42no—
502C4—144no—
503C4—144no—
504C4—284no—
505C4—284no—
506C4#9024312yes—
507C4C2×#647814yes—
508C4C22×#115711yescharacteristic
509C4C2×#655411yescharacteristic
510C2—44no—
511C2#1173707314yesdirect product factor
512C2C2×#9024311yescharacteristic
513C2C22×#647811yescharacteristic
514C2C2×#9046111yescharacteristic
subgroupG/H
centerC23C2×D4×D7
commutator, cosocleC2×C4×C7C25
FrattiniC2×C4C24×D7
FittingC2×C4×C7×SD16C2
socleC23×C7C22×D4
prime radicalC22×C7×D4C23
hypercenterC2×C4×SD16D7
hypocenterC7C2×#3372
LCSG ▷ C2×C4×C7 ▷ C2×C7 ▷ C7
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×C4×SD16

Complements

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

NH ≅ G/Ntype
1. C2×#90258C2semidirect
5. C2×#89793C2semidirect
7. #11737073C2direct (N × H)
8. C2×#89629C2semidirect
9. C2×#89569C2semidirect
11. C2×#89453C2semidirect
12. C2×#89451C2semidirect
22. #90258C22semidirect
45. #89793C22semidirect
50. #89629C22semidirect
51. #89569C22semidirect
53. #89453C22semidirect
54. #89451C22semidirect
442. C2×C7#3372semidirect
489. C7C2×#3372semidirect
511. C2#11737073direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#902582
C2×#902342
C2×C4×C7×SD162
C2×#899342
C2×#897932
C2×#897912
#117370732
C2×#896292
C2×#895692
C2×#895292
C2×#894532
C2×#894512
C2×#33727