Finite Group Databasebeta

← C2×#11738460 #14225816

Subgroups — C2×#11738460 #14225816

Order 1792.

2006 conjugacy classes of subgroups.

The subgroup lattice has 570 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×D7×C4⋊Q8C211yesmaximal, characteristic
2C2×#90269C211yesmaximal, characteristic
3C2×C7×#475C211yesmaximal, characteristic, complemented
4C2×#89866C211yesmaximal, characteristic, complemented
5C2×#89792C211yesmaximal, characteristic, complemented
6#11738460C2116yesmaximal, direct product factor
7C2×#89634C212yesmaximal
8C2×#89627C212yesmaximal, complemented
9C2×#89623C211yesmaximal, characteristic, complemented
10C2×#89605C211yesmaximal, characteristic
11C2×#89577C212yesmaximal
12C2×#89564C212yesmaximal, complemented
13C22×Q8×D7—21no—
14C2×C7×C4⋊Q8C2211yescharacteristic
15C2×C4×C7×Q8C2211yescharacteristic
16C2×#6509C2211yescharacteristic
17C2×#6507—21no—
18C2×#6507C2211yescharacteristic
19D7×C4⋊Q8—24no—
20D7×C4⋊Q8C2218yes—
21#90269—24no—
22#90269C2218yes—
23C2×#6460C2211yescharacteristic
24C2×#6459—21no—
25C2×D7×C4⋊C4—21no—
26C2×D7×C4⋊C4C2212yes—
27C2×#6452—21no—
28C2×#6451—21no—
29C2×#6451C2212yes—
30C2×#6451C2211yescharacteristic
31C2×#6435—21no—
32C2×C42×D7C2211yescharacteristic
33C2×#6432C2211yescharacteristic
34C2×C4×Dic14—21no—
35C2×C4×Dic14C2211yescharacteristic
36C7×#475C2218yescomplemented
37C2×C7×#106C2212yes—
38C2×C7×C4⋊C8C2211yescharacteristic
39C2×C7×#103C2212yes—
40C2×#6409C2212yes—
41C2×(C2×D7)⋊C8C2212yes—
42C2×#6391C2212yes—
43C2×#6390C2212yes—
44C2×C8×Dic7C2212yes—
45#89866C2218yescomplemented
46#89792C2218yescomplemented
47C2×#6384C2212yes—
48C2×#6382C2212yes—
49C2×#6382C2212yes—
50C2×C4⋊(C7⋊C8)C2211yescharacteristic
51#89634C22116yes—
52#89627C22116yescomplemented
53#89623C2218yescomplemented
54#89605C2218yes—
55#89577C22116yes—
56#89564C22116yescomplemented
57C2×#3229—71nomaximal, Sylow
58C22×C7×Q8—21no—
59C22×C7×Q8C2311yescharacteristic
60C2×Q8×D7—28no—
61C2×Q8×D7—48no—
62C22×C4×D7—22no—
63C22×C4×D7D411yescharacteristic
64C22×C4×D7D411yescharacteristic
65C22×C4×D7C2311yescharacteristic
66C22×Dic14—21no—
67C22×Dic14—21no—
68C22×Dic14—22no—
69C22×Dic14C2311yescharacteristic
70C22×C7×C8C2312yes—
71C7×C4⋊Q8—22no—
72C7×C4⋊Q8C2314yes—
73C4×C7×Q8—22no—
74C4×C7×Q8C2314yes—
75C2×C7×C4⋊C4—21no—
76C2×C7×C4⋊C4—21no—
77C2×C7×C4⋊C4C2312yes—
78C2×C7×C4⋊C4C2311yescharacteristic
79C2×C42×C7—21no—
80C2×C42×C7C2311yescharacteristic
81#6509—22no—
82#6509C2314yes—
83#6507—28no—
84#6507—22no—
85#6507C2314yes—
86C2×(C2×D7)⋊C4—21no—
87C2×(C2×D7)⋊C4—21no—
88C2×C4⋊Dic7—21no—
89C2×C4⋊Dic7—21no—
90C2×C4⋊Dic7C2312yes—
91C2×C4⋊Dic7C2311yescharacteristic
92C2×Dic7⋊C4—21no—
93C2×Dic7⋊C4—21no—
94C2×Dic7⋊C4—21no—
95C2×Dic7⋊C4—21no—
96C2×Dic7⋊C4—21no—
97C2×Dic7⋊C4—22no—
98C2×Dic7⋊C4—22no—
99C2×C4×Dic7—21no—
100C2×C4×Dic7D411yescharacteristic
101C2×C4×Dic7D411yescharacteristic
102C2×C4×Dic7C2311yescharacteristic
103C22×C7⋊C8C2312yes—
104#6460—22no—
105#6460C2314yes—
106#6459—28no—
107D7×C4⋊C4—24no—
108D7×C4⋊C4—28no—
109D7×C4⋊C4C2318yes—
110#6452—28no—
111#6451—24no—
112#6451—28no—
113#6451—22no—
114#6451C2314yes—
115#6451C2318yes—
116#6435—28no—
117C42×D7D414yes—
118C42×D7C2314yes—
119#6432—22no—
120#6432C2314yes—
121C4×Dic14—22no—
122C4×Dic14—28no—
123C4×Dic14C2314yes—
124C7×#106C2318yes—
125C7×C4⋊C8C2314yes—
126C7×#103C2318yes—
127#6409C2318yes—
128(C2×D7)⋊C8C2318yes—
129#6391C2318yes—
130#6390C2318yes—
131C8×Dic7C2318yes—
132#6384C2318yes—
133#6382C2318yes—
134#6382C2318yes—
135C4⋊(C7⋊C8)C2314yes—
136C2×#533—71no—
137C22×C4⋊Q8—71no—
138#3229—716no—
139C2×#498—72no—
140C2×#487—72no—
141C2×#483—72no—
142C2×#483—72no—
143C2×#475—71no—
144C2×#475—71no—
145C2×#475—71no—
146C2×#475D711yescharacteristic, complemented
147C2×#431—71no—
148C23×D7C2×D411yescharacteristic
149C2×C7×Q8—21no—
150C2×C7×Q8—24no—
151C2×C7×Q8—22no—
152C2×C7×Q8—22no—
153C2×C7×Q8—44no—
154C2×C7×Q8C2412yes—
155C22×C4×C7—21no—
156C22×C4×C7—22no—
157C22×C4×C7—21no—
158C22×C4×C7C2×D411yescharacteristic
159C22×C4×C7C2×D411yescharacteristic
160C22×C4×C7C2411yescharacteristic
161C22×Dic7—21no—
162C22×Dic7—21no—
163C22×Dic7—22no—
164C22×Dic7C2×D411yescharacteristic
165C22×Dic7C2×D411yescharacteristic
166C22×Dic7C2×D411yescharacteristic
167Q8×D7—432no—
168C2×C4×D7—22no—
169C2×C4×D7—22no—
170C2×C4×D7—24no—
171C2×C4×D7—28no—
172C2×C4×D7—48no—
173C2×C4×D7SD1618yes—
174C2×C4×D7C2×D412yes—
175C2×C4×D7C2×D414yes—
176C2×C4×D7C2×D414yes—
177C2×C4×D7C2412yes—
178C2×Dic14—22no—
179C2×Dic14—22no—
180C2×Dic14—21no—
181C2×Dic14—24no—
182C2×Dic14—24no—
183C2×Dic14—28no—
184C2×Dic14—44no—
185C2×Dic14—48no—
186C2×Dic14—44no—
187C2×Dic14C2412yes—
188C2×C7×C8—24no—
189C2×C7×C8C2414yes—
190C7×C4⋊C4—24no—
191C7×C4⋊C4—22no—
192C7×C4⋊C4—21no—
193C7×C4⋊C4—24no—
194C7×C4⋊C4C2414yes—
195C7×C4⋊C4C2412yes—
196C42×C7—24no—
197C42×C7C2×D412yes—
198C42×C7C2412yes—
199(C2×D7)⋊C4—24no—
200(C2×D7)⋊C4—24no—
201C4⋊Dic7—21no—
202C4⋊Dic7—22no—
203C4⋊Dic7—24no—
204C4⋊Dic7—24no—
205C4⋊Dic7C2414yes—
206C4⋊Dic7C2412yes—
207Dic7⋊C4—24no—
208Dic7⋊C4—24no—
209Dic7⋊C4—24no—
210Dic7⋊C4—24no—
211Dic7⋊C4—24no—
212Dic7⋊C4—28no—
213Dic7⋊C4—28no—
214C4×Dic7—24no—
215C4×Dic7C2×D414yes—
216C4×Dic7C2×D412yes—
217C4×Dic7C2×D414yes—
218C4×Dic7C2412yes—
219C2×C7⋊C8—24no—
220C2×C7⋊C8C2414yes—
221C23×Q8—141no—
222#533—78no—
223#533—144no—
224C2×C4⋊Q8—78no—
225C2×C4⋊Q8—72no—
226C2×C4⋊Q8—71no—
227C2×C4⋊Q8—71no—
228C2×C4⋊Q8—71no—
229C2×C4⋊Q8—141no—
230C2×C4⋊Q8—144no—
231C2×C4⋊Q8—141no—
232C2×C4⋊Q8C2×D711yescharacteristic
233C2×#125—141no—
234C2×C22⋊Q8—71no—
235C2×C22⋊Q8—71no—
236C2×C22⋊Q8—141no—
237C2×C4×Q8—71no—
238C2×C4×Q8—141no—
239C2×C4×Q8C2×D711yescharacteristic
240C2×#117—141no—
241C22×C4⋊C4—72no—
242C22×C4⋊C4—141no—
243C22×C42—71no—
244#498—716no—
245#487—716no—
246#483—716no—
247#483—716no—
248#475—78no—
249#475—78no—
250#475—78no—
251#475C2×D718yescomplemented
252#431—78no—
253C2×#106—72no—
254C2×#106—72no—
255C2×#106—72no—
256C2×#106C2×D712yes—
257C2×C4⋊C8—71no—
258C2×C4⋊C8C2×D711yescharacteristic
259C2×#103—72no—
260C2×#103—72no—
261C2×#103—72no—
262C2×#103C2×D712yes—
263C2×C22⋊C8—72no—
264C2×C4×C8—72no—
265C23×C7C22×D411yescharacteristic
266C22×D7—22no—
267C22×D7—22no—
268C22×D7C2×SD1614yes—
269C22×D7C22×D412yes—
270C7×Q8—22no—
271C7×Q8—22no—
272C7×Q8—42no—
273C7×Q8—48no—
274C2×C4×C7—22no—
275C2×C4×C7—22no—
276C2×C4×C7—24no—
277C2×C4×C7—22no—
278C2×C4×C7—42no—
279C2×C4×C7—44no—
280C2×C4×C7—42no—
281C2×C4×C7C2×SD1614yes—
282C2×C4×C7C22×D412yes—
283C2×C4×C7C22×D411yescharacteristic
284C2×C4×C7C22×D412yes—
285C2×C4×C72−1+412yes—
286C2×C4×C72−1+412yes—
287C2×C4×C7C2511yescharacteristic
288C2×Dic7—22no—
289C2×Dic7—22no—
290C2×Dic7—22no—
291C2×Dic7—24no—
292C2×Dic7—42no—
293C2×Dic7—44no—
294C2×Dic7—42no—
295C2×Dic7C2×SD1614yes—
296C2×Dic7#13714yes—
297C2×Dic7C22×D412yes—
298C2×Dic7C22×D412yes—
299C2×Dic7C22×D412yes—
300C4×D7—24no—
301C4×D7—22no—
302C4×D7—22no—
303C4×D7—28no—
304C4×D7—416no—
305C4×D7C2×SD16116yes—
306Dic14—22no—
307Dic14—22no—
308Dic14—42no—
309Dic14—48no—
310Dic14—416no—
311Dic14—48no—
312C7×C8—24no—
313C7⋊C8—24no—
314C22×Q8—21no—
315C22×Q8—71no—
316C22×Q8—141no—
317C22×Q8—142no—
318C22×Q8—148no—
319C22×Q8—141no—
320C22×Q8—288no—
321C22×Q8C22×D711yescharacteristic
322C23×C4—71no—
323C23×C4—71no—
324C23×C4—71no—
325C23×C4—142no—
326C22×C8—72no—
327C22×C8C22×D712yes—
328C4⋊Q8—22no—
329C4⋊Q8—78no—
330C4⋊Q8—74no—
331C4⋊Q8—74no—
332C4⋊Q8—74no—
333C4⋊Q8—148no—
334C4⋊Q8—144no—
335C4⋊Q8—142no—
336C4⋊Q8—148no—
337C4⋊Q8—142no—
338C4⋊Q8—142no—
339C4⋊Q8C22×D714yes—
340#125—148no—
341C22⋊Q8—74no—
342C22⋊Q8—74no—
343C22⋊Q8—142no—
344C22⋊Q8—148no—
345C22⋊Q8—142no—
346C4×Q8—22no—
347C4×Q8—74no—
348C4×Q8—148no—
349C4×Q8—142no—
350C4×Q8C22×D714yes—
351#117—148no—
352C2×C4⋊C4—21no—
353C2×C4⋊C4—21no—
354C2×C4⋊C4—72no—
355C2×C4⋊C4—71no—
356C2×C4⋊C4—78no—
357C2×C4⋊C4—144no—
358C2×C4⋊C4—148no—
359C2×C4⋊C4—142no—
360C2×C4⋊C4—142no—
361C2×C4⋊C4—141no—
362C2×C4⋊C4—141no—
363C2×C4⋊C4—141no—
364C2×C4⋊C4—141no—
365C2×C4⋊C4—141no—
366C2×C4⋊C4—141no—
367C2×C4⋊C4—141no—
368C2×C4⋊C4C22×D712yes—
369C2×C4⋊C4C22×D711yescharacteristic
370C2×C22⋊C4—141no—
371C2×C22⋊C4—141no—
372C2×C42—21no—
373C2×C42—71no—
374C2×C42—71no—
375C2×C42—71no—
376C2×C42—74no—
377C2×C42—74no—
378C2×C42—141no—
379C2×C42C22×D711yescharacteristic
380#106—78no—
381#106—78no—
382#106—78no—
383#106C22×D718yes—
384C4⋊C8—74no—
385C4⋊C8C22×D714yes—
386#103—78no—
387#103—78no—
388#103—78no—
389#103C22×D718yes—
390C22⋊C8—78no—
391C4×C8—78no—
392C22×C7#53612yes—
393C22×C7C22×SD1612yes—
394C22×C7C2×#13712yes—
395C22×C7C23×D411yescharacteristic
396C2×D7—22no—
397C2×D7—28no—
398C2×D7—22no—
399C2×D7C22×SD1614yes—
400C4×C7—22no—
401C4×C7—42no—
402C4×C7—44no—
403C4×C7—42no—
404C4×C7#53612yes—
405C4×C7C22×SD1614yes—
406C4×C7C2×2−1+411yescharacteristic
407C4×C7C2×2−1+411yescharacteristic
408Dic7—22no—
409Dic7—42no—
410Dic7—44no—
411Dic7—42no—
412Dic7C22×SD1614yes—
413Dic7C2×#13714yes—
414C24—71no—
415C2×Q8—21no—
416C2×Q8—24no—
417C2×Q8—22no—
418C2×Q8—22no—
419C2×Q8—44no—
420C2×Q8—72no—
421C2×Q8—144no—
422C2×Q8—148no—
423C2×Q8—141no—
424C2×Q8—144no—
425C2×Q8—142no—
426C2×Q8—142no—
427C2×Q8—284no—
428C2×Q8—288no—
429C2×Q8—2832no—
430C2×Q8—284no—
431C2×Q8C23×D712yes—
432C22×C4—21no—
433C22×C4—21no—
434C22×C4—22no—
435C22×C4—71no—
436C22×C4—71no—
437C22×C4—78no—
438C22×C4—74no—
439C22×C4—71no—
440C22×C4—74no—
441C22×C4—72no—
442C22×C4—72no—
443C22×C4—144no—
444C22×C4—148no—
445C22×C4—142no—
446C22×C4—142no—
447C22×C4—141no—
448C22×C4—141no—
449C22×C4—142no—
450C22×C4—288no—
451C22×C4D4×D711yescharacteristic
452C22×C4D4×D711yescharacteristic
453C22×C4C23×D711yescharacteristic
454C2×C8—24no—
455C2×C8—74no—
456C2×C8—144no—
457C2×C8C23×D714yes—
458C4⋊C4—24no—
459C4⋊C4—24no—
460C4⋊C4—22no—
461C4⋊C4—21no—
462C4⋊C4—74no—
463C4⋊C4—72no—
464C4⋊C4—148no—
465C4⋊C4—148no—
466C4⋊C4—144no—
467C4⋊C4—144no—
468C4⋊C4—144no—
469C4⋊C4—144no—
470C4⋊C4—144no—
471C4⋊C4—144no—
472C4⋊C4—142no—
473C4⋊C4—141no—
474C4⋊C4—144no—
475C4⋊C4C23×D714yes—
476C4⋊C4C23×D712yes—
477C22⋊C4—144no—
478C22⋊C4—144no—
479C42—24no—
480C42—74no—
481C42—74no—
482C42—72no—
483C42—72no—
484C42—144no—
485C42D4×D712yes—
486C42C23×D712yes—
487C2×C7#322914yescomplemented
488C2×C7C2×#53611yescharacteristic
489C2×C7C23×SD1611yescharacteristic
490C2×C7C22×#13711yescharacteristic
491D7—24no—
492C23—74no—
493C23—72no—
494C23—142no—
495C23—142no—
496C23C2×D4×D711yescharacteristic
497Q8—22no—
498Q8—22no—
499Q8—48no—
500Q8—42no—
501Q8—142no—
502Q8—142no—
503Q8—288no—
504Q8—2816no—
505Q8—288no—
506Q8—282no—
507C2×C4—22no—
508C2×C4—22no—
509C2×C4—22no—
510C2×C4—24no—
511C2×C4—44no—
512C2×C4—42no—
513C2×C4—42no—
514C2×C4—74no—
515C2×C4—74no—
516C2×C4—72no—
517C2×C4—72no—
518C2×C4—716no—
519C2×C4—72no—
520C2×C4—148no—
521C2×C4—142no—
522C2×C4—144no—
523C2×C4—142no—
524C2×C4—142no—
525C2×C4—142no—
526C2×C4—142no—
527C2×C4—144no—
528C2×C4—2816no—
529C2×C4—284no—
530C2×C4—282no—
531C2×C4—282no—
532C2×C4D7×SD1614yes—
533C2×C4C2×D4×D712yes—
534C2×C4C2×D4×D712yes—
535C2×C4C2×D4×D711yescharacteristic
536C2×C4#655112yes—
537C2×C4#655412yes—
538C2×C4C24×D711yescharacteristic
539C8—24no—
540C8—144no—
541C7C2×#322911yescharacteristic, complemented, Sylow
542C22—74no—
543C22—142no—
544C22—142no—
545C22—148no—
546C22#9031912yes—
547C22C2×D7×SD1612yes—
548C22D7×#13712yes—
549C22C22×D4×D711yescharacteristic
550C4—22no—
551C4—42no—
552C4—42no—
553C4—44no—
554C4—74no—
555C4—74no—
556C4—142no—
557C4—282no—
558C4—282no—
559C4—284no—
560C4#9031912yes—
561C4C2×D7×SD1614yes—
562C4C2×#655111yescharacteristic
563C4C2×#655411yescharacteristic
564C2—144no—
565C2#1173846014yesdirect product factor
566C2C2×#9031911yescharacteristic
567C2C22×D7×SD1611yescharacteristic
568C2C2×D7×#13711yescharacteristic
subgroupG/H
centerC23C2×D4×D7
commutator, cosocleC2×C4×C7C25
FrattiniC2×C4C24×D7
FittingC2×C7×#475C2
socleC23×C7C22×D4
prime radicalC23×D7C2×D4
hypercenterC2×#475D7
hypocenterC7C2×#3229
LCSG ▷ C2×C4×C7 ▷ C2×C7 ▷ C7
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#475

Complements

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

NH ≅ G/Ntype
3. C2×C7×#475C2semidirect
4. C2×#89866C2semidirect
5. C2×#89792C2semidirect
6. #11738460C2direct (N × H)
8. C2×#89627C2semidirect
9. C2×#89623C2semidirect
12. C2×#89564C2semidirect
36. C7×#475C22semidirect
45. #89866C22semidirect
46. #89792C22semidirect
52. #89627C22semidirect
53. #89623C22semidirect
56. #89564C22semidirect
146. C2×#475D7semidirect
251. #475C2×D7semidirect
487. C2×C7#3229semidirect
541. C7C2×#3229semidirect
565. C2#11738460direct (N × H)

Maximal subgroups

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

subgroupindex
C2×D7×C4⋊Q82
C2×#902692
C2×C7×#4752
C2×#898662
C2×#897922
#117384602
C2×#896342
C2×#896272
C2×#896232
C2×#896052
C2×#895772
C2×#895642
C2×#32297