Finite Group Databasebeta

← #13384660

Subgroups — #13384660

Order 1792.

730 conjugacy classes of subgroups.

The subgroup lattice has 606 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C7×#2330C211yesmaximal, characteristic, complemented
2#11730832C211yesmaximal, characteristic
3#11729498C211yesmaximal, characteristic, complemented
4#11729497C211yesmaximal, characteristic
5#11727382C211yesmaximal, characteristic
6#11727382C211yesmaximal, characteristic
7#11727366C211yesmaximal, characteristic, complemented
8#11727365C211yesmaximal, characteristic, complemented
9#11727343C211yesmaximal, characteristic, complemented
10#11727339C211yesmaximal, characteristic
11#11727229C211yesmaximal, characteristic, complemented
12#11727228C211yesmaximal, characteristic
13C4×#6384C211yesmaximal, characteristic, complemented
14C4×#6383C211yesmaximal, characteristic
15#11727189C211yesmaximal, characteristic, complemented
16C2×C7×#125C2211yescharacteristic
17C2×#6438C2211yescharacteristic
18C2×C4×D28C2211yescharacteristic
19C2×C4×Dic14C2211yescharacteristic
20C7×#389—21no—
21C7×#389—21no—
22C7×#389C2211yescharacteristic
23C7×#389C2211yescharacteristic
24C7×#387—21no—
25C7×#387—21no—
26C7×#384C2211yescharacteristic
27C4×C7×C4⋊C4C2211yescharacteristic
28C4×C7×C4⋊C4C2211yescharacteristic
29C7×#376C2211yescharacteristic
30C2×#6384C2211yescharacteristic
31C2×#6384C2211yescharacteristic
32C2×#6384C2211yescharacteristic
33C2×#6384C2211yescharacteristic
34C2×#6383C2211yescharacteristic
35C2×#6383C2211yescharacteristic
36C2×#6383C2211yescharacteristic
37C2×#6383C2211yescharacteristic
38#89711C2211yescharacteristic
39#89707C2211yescharacteristic
40#89701C2211yescharacteristic
41C2×#6377C2211yescharacteristic
42C2×C4×C7⋊C8C2211yescharacteristic
43#89442—21no—
44#89442—21no—
45#89440—21no—
46#89440—21no—
47#89324C2211yescharacteristic
48#89324C2211yescharacteristic
49#89324C2211yescharacteristic
50#89324C2211yescharacteristic
51#89324C2211yescharacteristic
52#89324C2211yescharacteristic
53#89324C2211yescharacteristic
54#89324C2211yescharacteristic
55#89319C2211yescharacteristic
56#89319C2211yescharacteristic
57#89319C2211yescharacteristic
58#89319C2211yescharacteristic
59#23832—71nomaximal, Sylow
60C22×D28C2311yescharacteristic
61C22×C4×D7—21no—
62C22×Dic14C2311yescharacteristic
63C7×#125—22no—
64C7×#125—22no—
65C2×C7×C4⋊C4—21no—
66C2×C7×C4⋊C4—21no—
67C2×C7×C4⋊C4—21no—
68C2×C7×C4⋊C4—21no—
69C2×C7×C4⋊C4—21no—
70C2×C7×C4⋊C4—21no—
71C2×C7×C4⋊C4C2311yescharacteristic
72C2×C7×C4⋊C4C2311yescharacteristic
73C2×C7×C4⋊C4C2311yescharacteristic
74C2×C7×C4⋊C4C2311yescharacteristic
75C2×C42×C7—21no—
76C2×C42×C7—21no—
77C2×C42×C7C2311yescharacteristic
78C2×C42×C7C2311yescharacteristic
79C2×C42×C7C2311yescharacteristic
80C2×(C2×D7)⋊C4—21no—
81C2×(C2×D7)⋊C4—21no—
82C2×(C2×D7)⋊C4—21no—
83C2×(C2×D7)⋊C4—21no—
84C2×(C2×D7)⋊C4—21no—
85C2×C4⋊Dic7—21no—
86C2×C4⋊Dic7—21no—
87C2×C4⋊Dic7C2311yescharacteristic
88C2×C4⋊Dic7C2311yescharacteristic
89C2×Dic7⋊C4—21no—
90C2×C4×Dic7—21no—
91C22×C7⋊C8C2311yescharacteristic
92C22×C7⋊C8C2311yescharacteristic
93C22×C7⋊C8C2311yescharacteristic
94C22×C7⋊C8C2311yescharacteristic
95#6438—22no—
96#6438—22no—
97C4×D28—22no—
98C4×D28—22no—
99C4×Dic14—22no—
100C4×Dic14—22no—
101C7×#95—21no—
102C7×#95—21no—
103C7×#95—21no—
104C7×#95—21no—
105C7×#95D411yescharacteristic
106C7×#95D411yescharacteristic
107C7×#95D411yescharacteristic
108C7×#95D411yescharacteristic
109C7⋊#95—21no—
110C7⋊#95—21no—
111#6384—22no—
112#6384—22no—
113#6384—22no—
114#6384—22no—
115#6383—22no—
116#6383—22no—
117#6383—22no—
118#6383—22no—
119#6377—22no—
120C4×C7⋊C8—22no—
121#2330D711yescharacteristic, complemented
122#2326—71no—
123#2100—71no—
124#2099—71no—
125#2072—71no—
126#2071—71no—
127#2042—71no—
128#2042—71no—
129#2026—71no—
130#2025—71no—
131#1763—71no—
132#1762—71no—
133C4×#103—71no—
134C4×#102—71no—
135#1746—71no—
136C23×D7—21no—
137C22×C4×C7—21no—
138C22×C4×C7—21no—
139C22×C4×C7—21no—
140C22×C4×C7—21no—
141C22×C4×C7C2×D411yescharacteristic
142C22×C4×C7C2×D411yescharacteristic
143C22×C4×C7C2×D411yescharacteristic
144C22×C4×C7C2×D411yescharacteristic
145C22×C4×C7C2×D411yescharacteristic
146C22×C4×C7C2×D411yescharacteristic
147C22×C4×C7C2411yescharacteristic
148C22×Dic7—21no—
149C22×Dic7—21no—
150C22×Dic7—21no—
151C2×D28—21no—
152C2×D28—21no—
153C2×D28—21no—
154C2×D28—21no—
155C2×D28—21no—
156C2×D28#4112yes—
157C2×C4×D7—42no—
158C2×C4×D7—81no—
159C2×C4×D7—81no—
160C2×Dic14—21no—
161C2×Dic14—21no—
162C2×Dic14—21no—
163C2×Dic14—21no—
164C2×Dic14—21no—
165C2×Dic14#4112yes—
166C7×C4⋊C4—24no—
167C7×C4⋊C4—24no—
168C7×C4⋊C4—21no—
169C7×C4⋊C4—21no—
170C7×C4⋊C4—21no—
171C7×C4⋊C4—21no—
172C7×C4⋊C4—21no—
173C7×C4⋊C4—21no—
174C7×C4⋊C4—81no—
175C7×C4⋊C4—81no—
176C7×C4⋊C4—81no—
177C7×C4⋊C4—81no—
178C7×C4⋊C4#4112yes—
179C7×C4⋊C4#4112yes—
180C42×C7—21no—
181C42×C7—21no—
182C42×C7—21no—
183C42×C7—21no—
184C42×C7—81no—
185C42×C7—81no—
186C42×C7#4112yes—
187C42×C7#4112yes—
188(C2×D7)⋊C4—24no—
189(C2×D7)⋊C4—24no—
190(C2×D7)⋊C4—42no—
191(C2×D7)⋊C4—81no—
192(C2×D7)⋊C4—81no—
193C4⋊Dic7—21no—
194C4⋊Dic7—21no—
195C4⋊Dic7—21no—
196C4⋊Dic7—21no—
197C4⋊Dic7—81no—
198C4⋊Dic7—81no—
199Dic7⋊C4—42no—
200C4×Dic7—42no—
201C2×C7⋊C8—21no—
202C2×C7⋊C8—21no—
203C2×C7⋊C8—21no—
204C2×C7⋊C8—21no—
205C2×C7⋊C8—21no—
206C2×C7⋊C8—21no—
207C2×C7⋊C8—21no—
208C2×C7⋊C8—21no—
209C2×C7⋊C8—21no—
210C2×C7⋊C8—21no—
211C2×C7⋊C8—21no—
212C2×C7⋊C8—21no—
213C2×#125C2×D711yescharacteristic
214C2×#124—71no—
215C2×C4×Q8—71no—
216C2×C4×D4—71no—
217C2×#103—71no—
218C2×#103—71no—
219C2×#103—71no—
220C2×#103—71no—
221C2×#102—71no—
222C2×#102—71no—
223C2×#102—71no—
224C2×#102—71no—
225C2×#97—71no—
226C2×C4×C8—71no—
227#391—71no—
228#390—71no—
229#389—21no—
230#389—21no—
231#389C2×D711yescharacteristic
232#389C2×D711yescharacteristic
233#388—141no—
234#388—141no—
235#387—21no—
236#387—21no—
237#385—141no—
238#385—141no—
239#384—71no—
240#384C2×D711yescharacteristic
241C4×C4⋊C4C2×D711yescharacteristic
242C4×C4⋊C4C2×D711yescharacteristic
243#376C2×D711yescharacteristic
244#340—71no—
245#340—71no—
246#340—71no—
247#340—71no—
248#340—71no—
249#340—71no—
250#340—71no—
251#340—71no—
252#336—71no—
253#336—71no—
254#336—71no—
255#336—71no—
256C23×C7C22×D411yescharacteristic
257C22×D7—22no—
258C22×D7—41no—
259C22×D7—41no—
260C22×D7—41no—
261C22×D7—41no—
262C22×D7—41no—
263C22×D7—41no—
264C2×C4×C7—21no—
265C2×C4×C7—21no—
266C2×C4×C7—21no—
267C2×C4×C7—21no—
268C2×C4×C7—21no—
269C2×C4×C7—21no—
270C2×C4×C7—21no—
271C2×C4×C7—21no—
272C2×C4×C7—22no—
273C2×C4×C7—22no—
274C2×C4×C7—21no—
275C2×C4×C7—21no—
276C2×C4×C7—21no—
277C2×C4×C7—21no—
278C2×C4×C7—21no—
279C2×C4×C7—21no—
280C2×C4×C7—21no—
281C2×C4×C7—21no—
282C2×C4×C7—41no—
283C2×C4×C7—41no—
284C2×C4×C7—41no—
285C2×C4×C7—41no—
286C2×C4×C7—41no—
287C2×C4×C7—41no—
288C2×C4×C7—41no—
289C2×C4×C7—41no—
290C2×C4×C7—41no—
291C2×C4×C7—41no—
292C2×C4×C7#12412yes—
293C2×C4×C7#12412yes—
294C2×C4×C7C2×#4111yescharacteristic
295C2×C4×C7C2×#4111yescharacteristic
296C2×C4×C7C2×#4111yescharacteristic
297C2×C4×C7C2×#4111yescharacteristic
298C2×C4×C7C2×#4111yescharacteristic
299C2×C4×C7C2×#4111yescharacteristic
300C2×Dic7—22no—
301C2×Dic7—41no—
302C2×Dic7—41no—
303C2×Dic7—41no—
304C2×Dic7—41no—
305C2×Dic7—41no—
306C2×Dic7—41no—
307C2×Dic7—41no—
308C2×Dic7—41no—
309D28—22no—
310D28—22no—
311D28—41no—
312D28—41no—
313C4×D7—84no—
314Dic14—22no—
315Dic14—22no—
316Dic14—41no—
317Dic14—41no—
318C7⋊C8—41no—
319C7⋊C8—41no—
320C7⋊C8—41no—
321C7⋊C8—41no—
322C22×Q8—71no—
323C22×D4—71no—
324C23×C4—141no—
325C22×C8—71no—
326C22×C8—71no—
327C22×C8—71no—
328C22×C8—71no—
329#125—22no—
330#125—22no—
331#124—142no—
332#124—142no—
333C4×Q8—142no—
334C4×Q8—142no—
335C4×D4—142no—
336C4×D4—142no—
337C2×C4⋊C4—21no—
338C2×C4⋊C4—21no—
339C2×C4⋊C4—21no—
340C2×C4⋊C4—21no—
341C2×C4⋊C4—21no—
342C2×C4⋊C4—21no—
343C2×C4⋊C4—71no—
344C2×C4⋊C4—71no—
345C2×C4⋊C4—141no—
346C2×C4⋊C4—141no—
347C2×C4⋊C4—141no—
348C2×C4⋊C4C22×D711yescharacteristic
349C2×C4⋊C4C22×D711yescharacteristic
350C2×C4⋊C4C22×D711yescharacteristic
351C2×C4⋊C4C22×D711yescharacteristic
352C2×C22⋊C4—141no—
353C2×C22⋊C4—141no—
354C2×C22⋊C4—141no—
355C2×C22⋊C4—141no—
356C2×C22⋊C4—141no—
357C2×C42—21no—
358C2×C42—21no—
359C2×C42—141no—
360C2×C42C22×D711yescharacteristic
361C2×C42C22×D711yescharacteristic
362C2×C42C22×D711yescharacteristic
363#103—142no—
364#103—142no—
365#103—142no—
366#103—142no—
367#102—142no—
368#102—142no—
369#102—142no—
370#102—142no—
371#97—142no—
372C4×C8—142no—
373#95—21no—
374#95—21no—
375#95—21no—
376#95—21no—
377#95—141no—
378#95—141no—
379#95C22⋊D711yescharacteristic
380#95C22⋊D711yescharacteristic
381#95C22⋊D711yescharacteristic
382#95C22⋊D711yescharacteristic
383C22×C7#52511yescharacteristic
384C22×C7#52511yescharacteristic
385C22×C7C2×#12411yescharacteristic
386C22×C7#57611yescharacteristic
387C22×C7#57711yescharacteristic
388C22×C7#57711yescharacteristic
389C22×C7#57811yescharacteristic
390C2×D7—42no—
391C2×D7—42no—
392C2×D7—42no—
393C2×D7—81no—
394C2×D7—81no—
395C2×D7—81no—
396C2×D7—81no—
397C4×C7—22no—
398C4×C7—22no—
399C4×C7—41no—
400C4×C7—41no—
401C4×C7—41no—
402C4×C7—42no—
403C4×C7—41no—
404C4×C7—42no—
405C4×C7—81no—
406C4×C7—81no—
407C4×C7#52911yescharacteristic
408C4×C7#52911yescharacteristic
409C4×C7#52911yescharacteristic
410C4×C7#52911yescharacteristic
411Dic7—42no—
412Dic7—81no—
413Dic7—81no—
414C24—141no—
415C2×Q8—72no—
416C2×Q8—141no—
417C2×Q8—141no—
418C2×Q8—141no—
419C2×Q8—141no—
420C2×Q8—141no—
421C2×D4—72no—
422C2×D4—141no—
423C2×D4—141no—
424C2×D4—141no—
425C2×D4—141no—
426C2×D4—141no—
427C22×C4—21no—
428C22×C4—21no—
429C22×C4—21no—
430C22×C4—21no—
431C22×C4—141no—
432C22×C4—141no—
433C22×C4—141no—
434C22×C4—282no—
435C22×C4—561no—
436C22×C4—561no—
437C22×C4C2×C22⋊D711yescharacteristic
438C22×C4C2×C22⋊D711yescharacteristic
439C22×C4C2×C22⋊D711yescharacteristic
440C22×C4C2×C22⋊D711yescharacteristic
441C22×C4C2×C22⋊D711yescharacteristic
442C22×C4C2×C22⋊D711yescharacteristic
443C22×C4C23×D711yescharacteristic
444C2×C8—141no—
445C2×C8—141no—
446C2×C8—141no—
447C2×C8—141no—
448C2×C8—141no—
449C2×C8—141no—
450C2×C8—141no—
451C2×C8—141no—
452C2×C8—141no—
453C2×C8—141no—
454C2×C8—141no—
455C2×C8—141no—
456C4⋊C4—24no—
457C4⋊C4—24no—
458C4⋊C4—21no—
459C4⋊C4—21no—
460C4⋊C4—21no—
461C4⋊C4—21no—
462C4⋊C4—21no—
463C4⋊C4—21no—
464C4⋊C4—81no—
465C4⋊C4—81no—
466C4⋊C4—81no—
467C4⋊C4—81no—
468C4⋊C4—141no—
469C4⋊C4—141no—
470C4⋊C4—141no—
471C4⋊C4—141no—
472C4⋊C4—282no—
473C4⋊C4—561no—
474C4⋊C4—561no—
475C4⋊C4#115712yes—
476C4⋊C4#115712yes—
477C22⋊C4—144no—
478C22⋊C4—144no—
479C22⋊C4—282no—
480C22⋊C4—561no—
481C22⋊C4—561no—
482C42—21no—
483C42—21no—
484C42—21no—
485C42—21no—
486C42—81no—
487C42—81no—
488C42—282no—
489C42#116112yes—
490C42#116112yes—
491C2×C7#239811yescharacteristic
492C2×C7#311911yescharacteristic
493C2×C7#312011yescharacteristic
494C2×C7#312411yescharacteristic
495C2×C7#312511yescharacteristic
496C2×C7#313611yescharacteristic
497C2×C7#313711yescharacteristic
498D7—82no—
499C23—142no—
500C23—281no—
501C23—281no—
502C23—281no—
503C23—281no—
504C23—281no—
505C23—281no—
506C23C22×C22⋊D711yescharacteristic
507Q8—142no—
508Q8—142no—
509Q8—281no—
510Q8—281no—
511D4—142no—
512D4—142no—
513D4—281no—
514D4—281no—
515C2×C4—21no—
516C2×C4—21no—
517C2×C4—21no—
518C2×C4—21no—
519C2×C4—21no—
520C2×C4—21no—
521C2×C4—22no—
522C2×C4—22no—
523C2×C4—21no—
524C2×C4—21no—
525C2×C4—21no—
526C2×C4—21no—
527C2×C4—21no—
528C2×C4—21no—
529C2×C4—21no—
530C2×C4—21no—
531C2×C4—21no—
532C2×C4—21no—
533C2×C4—41no—
534C2×C4—41no—
535C2×C4—41no—
536C2×C4—41no—
537C2×C4—41no—
538C2×C4—41no—
539C2×C4—41no—
540C2×C4—41no—
541C2×C4—41no—
542C2×C4—41no—
543C2×C4—142no—
544C2×C4—281no—
545C2×C4—281no—
546C2×C4—281no—
547C2×C4—281no—
548C2×C4—281no—
549C2×C4—281no—
550C2×C4—281no—
551C2×C4—281no—
552C2×C4—564no—
553C2×C4#651012yes—
554C2×C4#651012yes—
555C2×C4C2×#115711yescharacteristic
556C2×C4C2×#115711yescharacteristic
557C2×C4C2×#116111yescharacteristic
558C2×C4C2×#116111yescharacteristic
559C2×C4D7×#4111yescharacteristic
560C2×C4D7×#4111yescharacteristic
561C8—281no—
562C8—281no—
563C8—281no—
564C8—281no—
565C7#2383211yescharacteristic, complemented, Sylow
566C22—282no—
567C22—282no—
568C22—282no—
569C22—561no—
570C22—561no—
571C22—561no—
572C22—561no—
573C22#9048211yescharacteristic
574C22C2×#651011yescharacteristic
575C22#9051911yescharacteristic
576C22#9052611yescharacteristic
577C22#9052711yescharacteristic
578C22#9052811yescharacteristic
579C22#9052911yescharacteristic
580C4—22no—
581C4—22no—
582C4—41no—
583C4—42no—
584C4—41no—
585C4—42no—
586C4—41no—
587C4—41no—
588C4—81no—
589C4—81no—
590C4—282no—
591C4—561no—
592C4—561no—
593C4#9027111yescharacteristic
594C4#9027111yescharacteristic
595C4#9027111yescharacteristic
596C4#9027111yescharacteristic
597C2—562no—
598C2#1173993711yescharacteristic
599C2#1174001411yescharacteristic
600C2#1174002111yescharacteristic
601C2#1174087911yescharacteristic
602C2#1174089111yescharacteristic
603C2#1174091511yescharacteristic
604C2#1174091611yescharacteristic
subgroupG/H
centerC23C22×C22⋊D7
commutator, cosocleC22×C4×C7C24
FrattiniC22×C4C23×D7
FittingC7×#2330C2
socleC23×C7C22×D4
prime radicalC22×D28C23
hypercenter#2330D7
hypocenterC7#23832
LCSG ▷ C22×C4×C7 ▷ C2×C7 ▷ C7
UCSC1 ◁ C23 ◁ #376 ◁ #2330

Complements

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

NH ≅ G/Ntype
1. C7×#2330C2semidirect
3. #11729498C2semidirect
7. #11727366C2semidirect
8. #11727365C2semidirect
9. #11727343C2semidirect
11. #11727229C2semidirect
13. C4×#6384C2semidirect
15. #11727189C2semidirect
121. #2330D7semidirect
565. C7#23832semidirect

Maximal subgroups

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

subgroupindex
C7×#23302
#117308322
#117294982
#117294972
#117273822
#117273662
#117273652
#117273432
#117273392
#117272292
#117272282
C4×#63842
C4×#63832
#117271892
#238327