Finite Group Databasebeta

← #13358443

Subgroups — #13358443

Order 1792.

1338 conjugacy classes of subgroups.

The subgroup lattice has 588 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#90325C211yesmaximal, characteristic
2#11731450C211yesmaximal, characteristic
3#11731005C211yesmaximal, characteristic
4C7×#1996C211yesmaximal, characteristic, complemented
5#11729455C211yesmaximal, characteristic, complemented
6#11727283C211yesmaximal, characteristic, complemented
7#11727211C211yesmaximal, characteristic, complemented
8D7×#342C214yesmaximal
9#11726709C214yesmaximal, complemented
10C2×C7×C22⋊Q8C2211yescharacteristic
11C2×#6509C412yescomplemented
12C22×(C2×D7)⋊C4C2211yescharacteristic
13C2×#6487C2211yescharacteristic
14#90325—22no—
15#90325—22no—
16#90325—22no—
17#90325—22no—
18C2×#6460C412yescomplemented
19C2×#6459C412yescomplemented
20C2×#6459C412yescomplemented
21C2×D7×C22⋊C4C2212yes—
22C2×D7×C22⋊C4C2212yes—
23C2×D7×C22⋊C4C2212yes—
24C2×#6441C2212yes—
25C7×#380C2211yescharacteristic
26C4×C7×C22⋊C4C2211yescharacteristic
27#89984C2211yescharacteristic
28C4×C22⋊Dic7C2211yescharacteristic
29#89761—22no—
30#89714C2212yes—
31C22⋊C4×Dic7C2212yes—
32C4×(C2×D7)⋊C4—22no—
33#89440—22no—
34#89438—22no—
35C7×#342C2214yes—
36#89322C2214yes—
37#89322C2214yes—
38#89321C2214yes—
39#21333—71nomaximal, Sylow
40C24×D7C2311yescharacteristic
41C22×C7×Q8C2×C411yescharacteristic, complemented
42C23×C4×C7C2311yescharacteristic
43C23×Dic7C2311yescharacteristic
44C22×C4×D7—22no—
45C22×C4×D7—22no—
46C22×C4×D7C2×C412yes—
47C22×C4×D7C2×C412yes—
48C22×Dic14C2×C412yescomplemented
49C22×Dic14C2×C411yescharacteristic, complemented
50C7×C22⋊Q8—21no—
51C7×C22⋊Q8—21no—
52C7×C22⋊Q8—21no—
53C7×C22⋊Q8—21no—
54C2×C7×C4⋊C4—21no—
55C2×C7×C4⋊C4C2×C411yescharacteristic, complemented
56C2×C7×C4⋊C4C2×C412yescomplemented
57C2×C7×C22⋊C4C2312yes—
58C2×C7×C22⋊C4C2312yes—
59C2×C7×C22⋊C4C2312yes—
60C2×C42×C7—21no—
61C2×C22⋊Dic7C2312yes—
62C2×C22⋊Dic7C2312yes—
63C2×C22⋊Dic7C2312yes—
64#6509—24no—
65#6509—24no—
66C2×(C2×D7)⋊C4—22no—
67C2×(C2×D7)⋊C4—22no—
68C2×(C2×D7)⋊C4C2×C412yes—
69C2×(C2×D7)⋊C4C2×C412yes—
70C2×(C2×D7)⋊C4C2×C412yes—
71C2×(C2×D7)⋊C4C2×C412yes—
72C2×(C2×D7)⋊C4D412yes—
73C2×(C2×D7)⋊C4D412yes—
74C2×(C2×D7)⋊C4D412yes—
75C2×(C2×D7)⋊C4D412yes—
76C2×C4⋊Dic7—21no—
77C2×C4⋊Dic7C2×C412yescomplemented
78C2×C4⋊Dic7C2×C411yescharacteristic, complemented
79#6487—21no—
80#6487—21no—
81#6487—21no—
82#6487—21no—
83C2×Dic7⋊C4—22no—
84C2×Dic7⋊C4C2×C412yescomplemented
85C2×Dic7⋊C4C2×C412yescomplemented
86C2×Dic7⋊C4C2×C412yescomplemented
87C2×C4×Dic7—21no—
88C2×C4×Dic7—22no—
89#6460—24no—
90#6460—24no—
91#6459—24no—
92#6459—24no—
93#6459—24no—
94#6459—24no—
95D7×C22⋊C4—24no—
96D7×C22⋊C4—24no—
97D7×C22⋊C4—24no—
98D7×C22⋊C4—28no—
99D7×C22⋊C4Q818yescomplemented
100#6441—24no—
101#6441—24no—
102C7×#95—21no—
103C7×#95—21no—
104C7⋊#95—21no—
105C7⋊#95—21no—
106C7⋊#95—22no—
107C7⋊#95—22no—
108C2×#543—71no—
109#2315—71no—
110#2273—71no—
111#1996—71no—
112#1996—71no—
113#1996—74no—
114#1996—71no—
115#1996D711yescharacteristic, complemented
116C2×#342—74no—
117C24×C7C2411yescharacteristic
118C23×D7—81no—
119C23×D7—81no—
120C23×D7C22×C412yes—
121C23×D7C2×D412yes—
122C23×D7C2×D412yes—
123C23×D7C2×Q814yes—
124C23×D7#4114yes—
125C2×C7×Q8—21no—
126C2×C7×Q8—21no—
127C2×C7×Q8—81no—
128C22×C4×C7—22no—
129C22×C4×C7—22no—
130C22×C4×C7—81no—
131C22×C4×C7C22×C412yes—
132C22×C4×C7C22×C412yes—
133C22×C4×C7C22×C411yescharacteristic
134C22×C4×C7C22×C411yescharacteristic
135C22×C4×C7C2×D411yescharacteristic
136C22×C4×C7C2×D411yescharacteristic
137C22×C4×C7C2×D411yescharacteristic
138C22×C4×C7C2×D411yescharacteristic
139C22×Dic7—22no—
140C22×Dic7—22no—
141C22×Dic7—81no—
142C22×Dic7C22×C412yes—
143C22×Dic7C22×C412yes—
144C22×Dic7C22×C412yes—
145C22×Dic7C2×D412yes—
146C22×Dic7C2×D412yes—
147C2×C4×D7—24no—
148C2×C4×D7—24no—
149C2×C4×D7—28no—
150C2×C4×D7—44no—
151C2×C4×D7—82no—
152C2×C4×D7—82no—
153C2×C4×D7—82no—
154C2×C4×D7—82no—
155C2×C4×D7—82no—
156C2×C4×D7—82no—
157C2×Dic14—21no—
158C2×Dic14—21no—
159C2×Dic14—24no—
160C2×Dic14—82no—
161C2×Dic14—81no—
162C7×C4⋊C4—21no—
163C7×C4⋊C4—21no—
164C7×C4⋊C4—22no—
165C7×C4⋊C4—22no—
166C7×C4⋊C4—81no—
167C7×C22⋊C4—22no—
168C7×C22⋊C4—22no—
169C7×C22⋊C4—22no—
170C7×C22⋊C4—24no—
171C7×C22⋊C4C2×Q814yes—
172C42×C7—81no—
173C22⋊Dic7—22no—
174C22⋊Dic7—22no—
175C22⋊Dic7—22no—
176C22⋊Dic7—24no—
177C22⋊Dic7C2×Q814yes—
178(C2×D7)⋊C4—24no—
179(C2×D7)⋊C4—24no—
180(C2×D7)⋊C4—28no—
181(C2×D7)⋊C4—44no—
182(C2×D7)⋊C4C22⋊C414yes—
183(C2×D7)⋊C4C22⋊C414yes—
184(C2×D7)⋊C4C22⋊C414yes—
185(C2×D7)⋊C4C22⋊C414yes—
186C4⋊Dic7—21no—
187C4⋊Dic7—21no—
188C4⋊Dic7—24no—
189C4⋊Dic7—81no—
190Dic7⋊C4—22no—
191Dic7⋊C4—22no—
192Dic7⋊C4—24no—
193Dic7⋊C4—24no—
194Dic7⋊C4—82no—
195C4×Dic7—82no—
196C4×Dic7—81no—
197#543—142no—
198#543—142no—
199#543—142no—
200#543—142no—
201C2×C22⋊Q8—72no—
202C2×C22⋊Q8—71no—
203C2×C22⋊Q8—72no—
204C2×C22⋊Q8—72no—
205C2×C22⋊Q8—72no—
206C2×C22⋊Q8—72no—
207C2×C22⋊Q8C2×D711yescharacteristic
208C22×C22⋊C4—71no—
209C22×C22⋊C4—72no—
210C22×C22⋊C4—72no—
211C22×C22⋊C4—72no—
212#385—142no—
213#385—142no—
214#380—71no—
215#380—72no—
216#380C2×D711yescharacteristic
217C4×C22⋊C4—71no—
218C4×C22⋊C4—72no—
219C4×C22⋊C4—142no—
220C4×C22⋊C4—142no—
221C4×C22⋊C4C2×D711yescharacteristic
222#342—74no—
223#342—74no—
224#342—74no—
225#342C2×D714yes—
226C23×C7—41no—
227C23×C7—41no—
228C23×C7C23×C411yescharacteristic
229C23×C7C22×D411yescharacteristic
230C23×C7C22×D411yescharacteristic
231C23×C7C22×Q812yes—
232C23×C7C2×#4112yes—
233C22×D7—42no—
234C22×D7—42no—
235C22×D7—42no—
236C22×D7—42no—
237C22×D7—42no—
238C22×D7—42no—
239C22×D7—84no—
240C22×D7—84no—
241C22×D7C2×C22⋊C414yes—
242C22×D7C4×Q818yes—
243C22×D7C22⋊Q814yes—
244C22×D7C22⋊Q814yes—
245C22×D7#12414yes—
246C22×D7C4⋊Q814yes—
247C7×Q8—81no—
248C7×Q8—81no—
249C2×C4×C7—22no—
250C2×C4×C7—22no—
251C2×C4×C7—24no—
252C2×C4×C7—41no—
253C2×C4×C7—41no—
254C2×C4×C7—41no—
255C2×C4×C7—41no—
256C2×C4×C7—41no—
257C2×C4×C7—41no—
258C2×C4×C7—42no—
259C2×C4×C7—42no—
260C2×C4×C7—42no—
261C2×C4×C7—42no—
262C2×C4×C7—42no—
263C2×C4×C7—42no—
264C2×C4×C7—42no—
265C2×C4×C7C2×C22⋊C411yescharacteristic
266C2×C4×C7C2×C22⋊C411yescharacteristic
267C2×C4×C7C2×C22⋊C411yescharacteristic
268C2×C4×C7C2×C22⋊C411yescharacteristic
269C2×Dic7—22no—
270C2×Dic7—22no—
271C2×Dic7—24no—
272C2×Dic7—42no—
273C2×Dic7—42no—
274C2×Dic7—42no—
275C2×Dic7—42no—
276C2×Dic7—42no—
277C2×Dic7—42no—
278C2×Dic7—42no—
279C2×Dic7—42no—
280C2×Dic7—42no—
281C2×Dic7—42no—
282C2×Dic7C2×C22⋊C414yes—
283C4×D7—84no—
284C4×D7—84no—
285C4×D7—88no—
286C4×D7—88no—
287Dic14—84no—
288Dic14—81no—
289Dic14—81no—
290C25—71no—
291C22×Q8—72no—
292C22×Q8—71no—
293C22×Q8C4×D711yescharacteristic, complemented
294C23×C4—71no—
295C23×C4—72no—
296C23×C4—72no—
297C23×C4—142no—
298C23×C4—142no—
299C23×C4C22×D711yescharacteristic
300C22⋊Q8—21no—
301C22⋊Q8—21no—
302C22⋊Q8—21no—
303C22⋊Q8—21no—
304C22⋊Q8—144no—
305C22⋊Q8—144no—
306C22⋊Q8—144no—
307C22⋊Q8—144no—
308C22⋊Q8—144no—
309C22⋊Q8—144no—
310C22⋊Q8—144no—
311C22⋊Q8—144no—
312C22⋊Q8—144no—
313C22⋊Q8—144no—
314C22⋊Q8—141no—
315C22⋊Q8—141no—
316C22⋊Q8—141no—
317C22⋊Q8—141no—
318C2×C4⋊C4—21no—
319C2×C4⋊C4—72no—
320C2×C4⋊C4—72no—
321C2×C4⋊C4—72no—
322C2×C4⋊C4—72no—
323C2×C4⋊C4—71no—
324C2×C4⋊C4—142no—
325C2×C4⋊C4—141no—
326C2×C4⋊C4C4×D712yescomplemented
327C2×C4⋊C4C4×D711yescharacteristic, complemented
328C2×C22⋊C4—72no—
329C2×C22⋊C4—72no—
330C2×C22⋊C4—72no—
331C2×C22⋊C4—72no—
332C2×C22⋊C4—72no—
333C2×C22⋊C4—72no—
334C2×C22⋊C4—72no—
335C2×C22⋊C4—78no—
336C2×C22⋊C4—72no—
337C2×C22⋊C4—72no—
338C2×C22⋊C4—72no—
339C2×C22⋊C4—72no—
340C2×C22⋊C4—144no—
341C2×C22⋊C4—144no—
342C2×C22⋊C4—144no—
343C2×C22⋊C4—148no—
344C2×C22⋊C4—142no—
345C2×C22⋊C4—142no—
346C2×C22⋊C4C22×D712yes—
347C2×C22⋊C4C22×D712yes—
348C2×C22⋊C4C22×D712yes—
349C2×C42—21no—
350C2×C42—142no—
351C2×C42—141no—
352#95—21no—
353#95—21no—
354#95—142no—
355#95—142no—
356#95—141no—
357#95—141no—
358C22×C7—21no—
359C22×C7—21no—
360C22×C7—21no—
361C22×C7—21no—
362C22×C7—21no—
363C22×C7—21no—
364C22×C7—42no—
365C22×C7—42no—
366C22×C7C22×C22⋊C411yescharacteristic
367C22×C7C2×C4×Q812yes—
368C22×C7C2×C22⋊Q812yes—
369C22×C7C2×#12411yescharacteristic
370C22×C7C2×C4⋊Q811yescharacteristic
371C2×D7—24no—
372C2×D7—24no—
373C2×D7—44no—
374C2×D7—44no—
375C2×D7—48no—
376C2×D7—44no—
377C2×D7—44no—
378C2×D7#39118yes—
379C4×C7—21no—
380C4×C7—21no—
381C4×C7—21no—
382C4×C7—21no—
383C4×C7—44no—
384C4×C7—42no—
385C4×C7—42no—
386C4×C7—82no—
387Dic7—24no—
388Dic7—44no—
389Dic7—42no—
390Dic7—42no—
391Dic7—82no—
392C24—72no—
393C24—72no—
394C24—72no—
395C24—74no—
396C24—74no—
397C24—561no—
398C24—561no—
399C24C23×D711yescharacteristic
400C2×Q8—21no—
401C2×Q8—21no—
402C2×Q8—81no—
403C2×Q8—144no—
404C2×Q8—141no—
405C2×Q8—141no—
406C2×Q8—561no—
407C2×Q8—562no—
408C22×C4—22no—
409C22×C4—22no—
410C22×C4—72no—
411C22×C4—72no—
412C22×C4—72no—
413C22×C4—72no—
414C22×C4—72no—
415C22×C4—81no—
416C22×C4—148no—
417C22×C4—144no—
418C22×C4—144no—
419C22×C4—142no—
420C22×C4—142no—
421C22×C4—284no—
422C22×C4—562no—
423C22×C4—562no—
424C22×C4—562no—
425C22×C4—562no—
426C22×C4—562no—
427C22×C4—562no—
428C22×C4—561no—
429C22×C4C2×C4×D712yes—
430C22×C4C2×C4×D712yes—
431C22×C4C2×C4×D711yescharacteristic
432C22×C4C2×C4×D711yescharacteristic
433C22×C4D4×D711yescharacteristic
434C22×C4D4×D711yescharacteristic
435C22×C4D4×D711yescharacteristic
436C22×C4D4×D711yescharacteristic
437C4⋊C4—21no—
438C4⋊C4—21no—
439C4⋊C4—22no—
440C4⋊C4—22no—
441C4⋊C4—81no—
442C4⋊C4—144no—
443C4⋊C4—144no—
444C4⋊C4—144no—
445C4⋊C4—142no—
446C4⋊C4—142no—
447C4⋊C4—141no—
448C4⋊C4—141no—
449C4⋊C4—562no—
450C4⋊C4—561no—
451C22⋊C4—22no—
452C22⋊C4—22no—
453C22⋊C4—22no—
454C22⋊C4—24no—
455C22⋊C4—74no—
456C22⋊C4—74no—
457C22⋊C4—74no—
458C22⋊C4—74no—
459C22⋊C4—74no—
460C22⋊C4—148no—
461C22⋊C4—144no—
462C22⋊C4—144no—
463C22⋊C4—142no—
464C22⋊C4—142no—
465C22⋊C4—142no—
466C22⋊C4—144no—
467C22⋊C4—284no—
468C22⋊C4Q8×D714yes—
469C42—81no—
470C42—561no—
471C42—562no—
472C2×C7—22no—
473C2×C7—21no—
474C2×C7—22no—
475C2×C7—21no—
476C2×C7C2×#39111yescharacteristic
477C2×C7#288311yescharacteristic
478C2×C7#288311yescharacteristic
479D7—28no—
480C23—41no—
481C23—41no—
482C23—74no—
483C23—74no—
484C23—78no—
485C23—74no—
486C23—74no—
487C23—74no—
488C23—282no—
489C23—282no—
490C23—282no—
491C23—282no—
492C23—282no—
493C23—282no—
494C23—564no—
495C23—564no—
496C23C22×C4×D711yescharacteristic
497C23C2×D4×D711yescharacteristic
498C23C2×D4×D711yescharacteristic
499C23C2×Q8×D712yes—
500C23D7×#4112yes—
501Q8—81no—
502Q8—81no—
503Q8—561no—
504Q8—561no—
505Q8—564no—
506C2×C4—22no—
507C2×C4—22no—
508C2×C4—24no—
509C2×C4—41no—
510C2×C4—41no—
511C2×C4—41no—
512C2×C4—41no—
513C2×C4—41no—
514C2×C4—41no—
515C2×C4—42no—
516C2×C4—42no—
517C2×C4—42no—
518C2×C4—42no—
519C2×C4—42no—
520C2×C4—42no—
521C2×C4—42no—
522C2×C4—74no—
523C2×C4—142no—
524C2×C4—142no—
525C2×C4—144no—
526C2×C4—282no—
527C2×C4—282no—
528C2×C4—282no—
529C2×C4—282no—
530C2×C4—282no—
531C2×C4—282no—
532C2×C4—282no—
533C2×C4—282no—
534C2×C4—282no—
535C2×C4—282no—
536C2×C4—564no—
537C2×C4—564no—
538C2×C4—568no—
539C2×C4—568no—
540C2×C4D7×C22⋊C411yescharacteristic
541C2×C4D7×C22⋊C411yescharacteristic
542C2×C4D7×C22⋊C411yescharacteristic
543C2×C4D7×C22⋊C411yescharacteristic
544C7#2133311yescharacteristic, complemented, Sylow
545C22—21no—
546C22—21no—
547C22—21no—
548C22—21no—
549C22—21no—
550C22—21no—
551C22—42no—
552C22—42no—
553C22—78no—
554C22—144no—
555C22—144no—
556C22—284no—
557C22—284no—
558C22—284no—
559C22—284no—
560C22—288no—
561C22C2×D7×C22⋊C411yescharacteristic
562C22C4×Q8×D712yes—
563C22D7×C22⋊Q812yes—
564C22D7×#12411yescharacteristic
565C22D7×C4⋊Q811yescharacteristic
566C4—21no—
567C4—21no—
568C4—21no—
569C4—21no—
570C4—44no—
571C4—42no—
572C4—42no—
573C4—82no—
574C4—144no—
575C4—284no—
576C4—282no—
577C4—282no—
578C4—562no—
579C2—22no—
580C2—21no—
581C2—21no—
582C2—22no—
583C2—148no—
584C2D7×#39111yescharacteristic
585C2#1173613311yescharacteristic
586C2#1173613911yescharacteristic
subgroupG/H
centerC22C2×D7×C22⋊C4
commutatorC23×C7C23×C4
FrattiniC24C23×D7
FittingC7×#1996C2
socleC22×C7C22×C22⋊C4
prime radicalC24×D7C23
cosocleC24×C7C24
hypercenter#1996D7
hypocenterC7#21333
LCSG ▷ C23×C7 ▷ C2×C7 ▷ C7
UCSC1 ◁ C22 ◁ C23×C4 ◁ #1996

Complements

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

NH ≅ G/Ntype
4. C7×#1996C2semidirect
5. #11729455C2semidirect
6. #11727283C2semidirect
7. #11727211C2semidirect
9. #11726709C2semidirect
11. C2×#6509C4semidirect
18. C2×#6460C4semidirect
19. C2×#6459C4semidirect
20. C2×#6459C4semidirect
41. C22×C7×Q8C2×C4semidirect
48. C22×Dic14C2×C4semidirect
49. C22×Dic14C2×C4semidirect
55. C2×C7×C4⋊C4C2×C4semidirect
56. C2×C7×C4⋊C4C2×C4semidirect
77. C2×C4⋊Dic7C2×C4semidirect
78. C2×C4⋊Dic7C2×C4semidirect
84. C2×Dic7⋊C4C2×C4semidirect
85. C2×Dic7⋊C4C2×C4semidirect
86. C2×Dic7⋊C4C2×C4semidirect
99. D7×C22⋊C4Q8semidirect
115. #1996D7semidirect
293. C22×Q8C4×D7semidirect
326. C2×C4⋊C4C4×D7semidirect
327. C2×C4⋊C4C4×D7semidirect
544. C7#21333semidirect

Maximal subgroups

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

subgroupindex
C2×#903252
#117314502
#117310052
C7×#19962
#117294552
#117272832
#117272112
D7×#3422
#117267092
#213337