Finite Group Databasebeta

← #13358762

Subgroups — #13358762

Order 1792.

1226 conjugacy classes of subgroups.

The subgroup lattice has 632 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#90229C211yesmaximal, characteristic
2C22×C8×Dic7C211yesmaximal, characteristic, complemented
3C2×#89491C211yesmaximal, characteristic, complemented
4C7×#1869C211yesmaximal, characteristic, complemented
5#11729729C211yesmaximal, characteristic, complemented
6#11729364C211yesmaximal, characteristic, complemented
7#11727706C211yesmaximal, characteristic, complemented
8#11727670C212yesmaximal, complemented
9#11727661C212yesmaximal, complemented
10#11726373C212yesmaximal, complemented
11#11726355C212yesmaximal, complemented
12C23×C7×C8C2211yescharacteristic
13C2×C4×C7×D4C2211yescharacteristic
14C2×#6502C411yescharacteristic
15C2×#6498C411yescharacteristic
16C2×C4×C22⋊D7C2211yescharacteristic
17C2×C4×C22⋊D7C2211yescharacteristic
18C2×#6489C2211yescharacteristic
19C22×C4×Dic7C2211yescharacteristic
20C23×C7⋊C8C2211yescharacteristic
21#90229—24no—
22#90229—24no—
23C2×#6461C411yescharacteristic
24C2×#6452C411yescharacteristic
25C2×#6449C411yescharacteristic
26C2×#6448C411yescharacteristic
27C2×#6442C411yescharacteristic
28C2×#6441C411yescharacteristic
29C2×#6435C2211yescharacteristic
30C2×C4×Dic14C2211yescharacteristic
31C2×C7×C22⋊C8C2212yes—
32C2×C7×C22⋊C8C2211yescharacteristic
33C2×C22⋊(C7⋊C8)C2212yes—
34C2×C22⋊(C7⋊C8)C2211yescharacteristic
35C2×(C2×D7)⋊C8C2212yes—
36C2×(C2×D7)⋊C8C2212yes—
37C2×#6389C2212yes—
38C2×Dic7⋊C8C2212yes—
39C2×C8×Dic7—24no—
40C2×C8×Dic7C2212yes—
41C2×C8×Dic7C2212yes—
42#89491—24no—
43C7×#336C2212yes—
44#89345C2212yes—
45#89345C2212yes—
46#89319C2212yes—
47#21375—71nomaximal, Sylow
48C22×C7×D4C2×C411yescharacteristic
49C23×C4×C7C2311yescharacteristic
50C23×C4×C7C2311yescharacteristic
51C22×C22⋊D7C2×C411yescharacteristic
52C22×C22⋊D7C2×C411yescharacteristic
53C23×Dic7C2×C411yescharacteristic
54C23×Dic7C2×C411yescharacteristic
55C22×C4×D7C2311yescharacteristic
56C22×Dic14C2×C411yescharacteristic
57C22×C7×C8—22no—
58C22×C7×C8—24no—
59C22×C7×C8C2312yes—
60C22×C7×C8C2312yes—
61C4×C7×D4—22no—
62C4×C7×D4—22no—
63C2×C7×C4⋊C4C2×C411yescharacteristic
64C2×C7×C22⋊C4C2×C411yescharacteristic
65C2×C7×C22⋊C4C2×C411yescharacteristic
66C2×C42×C7C2311yescharacteristic
67C2×C22⋊Dic7C2×C411yescharacteristic
68C2×C22⋊Dic7C2×C411yescharacteristic
69C2×C22⋊Dic7C2×C411yescharacteristic
70C2×C22⋊Dic7C2×C411yescharacteristic
71#6502—24no—
72#6498—24no—
73C4×C22⋊D7—22no—
74C4×C22⋊D7—22no—
75C4×C22⋊D7—22no—
76C4×C22⋊D7—22no—
77C2×(C2×D7)⋊C4C2×C411yescharacteristic
78C2×(C2×D7)⋊C4C2×C411yescharacteristic
79C2×(C2×D7)⋊C4C2×C411yescharacteristic
80C2×(C2×D7)⋊C4C2×C411yescharacteristic
81#6489—22no—
82#6489—22no—
83C2×C4⋊Dic7C2×C411yescharacteristic
84C2×C4⋊Dic7C2×C411yescharacteristic
85C2×C4⋊Dic7C2×C411yescharacteristic
86C2×Dic7⋊C4C2×C411yescharacteristic
87C2×Dic7⋊C4C2×C411yescharacteristic
88C2×Dic7⋊C4C2×C411yescharacteristic
89C2×Dic7⋊C4C2×C411yescharacteristic
90C2×Dic7⋊C4C2×C411yescharacteristic
91C2×Dic7⋊C4C2×C411yescharacteristic
92C2×C4×Dic7C2×C411yescharacteristic
93C2×C4×Dic7C2×C411yescharacteristic
94C2×C4×Dic7D414yes—
95C2×C4×Dic7D414yes—
96C2×C4×Dic7C2311yescharacteristic
97C2×C4×Dic7C2311yescharacteristic
98C2×C4×Dic7C2311yescharacteristic
99C22×C7⋊C8—22no—
100C22×C7⋊C8—24no—
101C22×C7⋊C8C2312yes—
102C22×C7⋊C8C2312yes—
103#6461—24no—
104#6452—24no—
105#6449—24no—
106#6448—24no—
107#6442—24no—
108#6441—24no—
109#6435—22no—
110#6435—22no—
111C4×Dic14—22no—
112C4×Dic14—22no—
113C7×C22⋊C8—22no—
114C7×C22⋊C8—24no—
115C22⋊(C7⋊C8)—22no—
116C22⋊(C7⋊C8)—24no—
117(C2×D7)⋊C8—24no—
118(C2×D7)⋊C8—24no—
119#6389—24no—
120Dic7⋊C8—24no—
121C8×Dic7—24no—
122C8×Dic7—24no—
123C2×#529—71no—
124C2×#432—71no—
125C22×C4×C8—71no—
126#1984—72no—
127#1954—72no—
128#1869—71no—
129#1869—71no—
130#1869—71no—
131#1869D711yescharacteristic, complemented
132#1750—72no—
133#1750—72no—
134C24×C7C22×C411yescharacteristic
135C24×C7C22×C411yescharacteristic
136C23×D7C22×C411yescharacteristic
137C2×C7×D4—22no—
138C2×C7×D4—22no—
139C2×C7×D4—22no—
140C22×C4×C7—22no—
141C22×C4×C7—22no—
142C22×C4×C7—21no—
143C22×C4×C7—21no—
144C22×C4×C7—22no—
145C22×C4×C7—22no—
146C22×C4×C7C22×C411yescharacteristic
147C22×C4×C7C22×C411yescharacteristic
148C22×C4×C7C22×C411yescharacteristic
149C22×C4×C7C22×C411yescharacteristic
150C22×C4×C7C2×D412yes—
151C22×C4×C7C2×D412yes—
152C22×C4×C7C2411yescharacteristic
153C2×C22⋊D7—22no—
154C2×C22⋊D7—22no—
155C2×C22⋊D7—22no—
156C2×C22⋊D7—22no—
157C2×C22⋊D7—24no—
158C22×Dic7—22no—
159C22×Dic7—22no—
160C22×Dic7—24no—
161C22×Dic7C22⋊C414yes—
162C22×Dic7C22⋊C414yes—
163C22×Dic7C22×C411yescharacteristic
164C22×Dic7C22×C411yescharacteristic
165C22×Dic7C22×C411yescharacteristic
166C22×Dic7C22×C411yescharacteristic
167C22×Dic7C22×C411yescharacteristic
168C22×Dic7C22×C411yescharacteristic
169C22×Dic7C22×C411yescharacteristic
170C2×C4×D7—21no—
171C2×C4×D7—21no—
172C2×C4×D7—22no—
173C2×C4×D7—22no—
174C2×Dic14—22no—
175C2×Dic14—24no—
176C2×C7×C8—28no—
177C2×C7×C8—22no—
178C2×C7×C8—22no—
179C2×C7×C8—22no—
180C2×C7×C8—22no—
181C2×C7×C8—22no—
182C2×C7×C8#4114yes—
183C7×C4⋊C4—22no—
184C7×C22⋊C4—22no—
185C7×C22⋊C4—22no—
186C42×C7—21no—
187C42×C7—21no—
188C22⋊Dic7—22no—
189C22⋊Dic7—22no—
190C22⋊Dic7—22no—
191C22⋊Dic7—22no—
192(C2×D7)⋊C4—22no—
193(C2×D7)⋊C4—22no—
194(C2×D7)⋊C4—22no—
195(C2×D7)⋊C4—22no—
196C4⋊Dic7—22no—
197C4⋊Dic7—22no—
198C4⋊Dic7—22no—
199Dic7⋊C4—22no—
200Dic7⋊C4—22no—
201Dic7⋊C4—22no—
202Dic7⋊C4—22no—
203Dic7⋊C4—22no—
204Dic7⋊C4—22no—
205C4×Dic7—21no—
206C4×Dic7—21no—
207C4×Dic7C22⋊C414yes—
208C4×Dic7C22⋊C414yes—
209C4×Dic7C2×D412yes—
210C4×Dic7C2×D412yes—
211C4×Dic7C2×D412yes—
212C4×Dic7C2×D412yes—
213C2×C7⋊C8—28no—
214C2×C7⋊C8—22no—
215C2×C7⋊C8—22no—
216C2×C7⋊C8—22no—
217C2×C7⋊C8—22no—
218C2×C7⋊C8—22no—
219C2×C7⋊C8#4114yes—
220C23×C8—71no—
221C23×C8C2×D711yescharacteristic
222#529—144no—
223#529—144no—
224C2×#126—71no—
225C2×#126—71no—
226C2×#125—71no—
227C2×#124—71no—
228C2×#123—71no—
229C2×#123—71no—
230C2×C22⋊Q8—71no—
231C2×#121—71no—
232C2×C4×Q8—71no—
233C2×C4×D4—71no—
234C2×C4×D4—71no—
235C2×C4×D4C2×D711yescharacteristic
236C2×#117—71no—
237C2×#117—71no—
238C22×C42—71no—
239#432—144no—
240C2×C4⋊C8—72no—
241C2×C22⋊C8—71no—
242C2×C22⋊C8—72no—
243C2×C22⋊C8—72no—
244C2×C22⋊C8—72no—
245C2×C22⋊C8C2×D711yescharacteristic
246C2×C22⋊C8C2×D712yes—
247C2×#97—72no—
248C2×C4×C8—72no—
249C2×C4×C8—72no—
250C2×C4×C8—144no—
251#336—72no—
252#336—72no—
253#336—72no—
254#336C2×D712yes—
255C23×C7—22no—
256C23×C7—22no—
257C23×C7—21no—
258C23×C7—22no—
259C23×C7—22no—
260C23×C7—21no—
261C23×C7—21no—
262C23×C7C2×C22⋊C412yes—
263C23×C7#13112yes—
264C23×C7#13112yes—
265C23×C7C23×C411yescharacteristic
266C22×D7—21no—
267C22×D7—22no—
268C22×D7—21no—
269C22×D7—21no—
270C22×D7—22no—
271C7×D4—44no—
272C2×C4×C7—22no—
273C2×C4×C7—22no—
274C2×C4×C7—22no—
275C2×C4×C7—24no—
276C2×C4×C7—21no—
277C2×C4×C7—21no—
278C2×C4×C7—21no—
279C2×C4×C7—22no—
280C2×C4×C7—22no—
281C2×C4×C7—21no—
282C2×C4×C7—21no—
283C2×C4×C7—41no—
284C2×C4×C7—41no—
285C2×C4×C7—42no—
286C2×C4×C7C2×C22⋊C412yes—
287C2×C4×C7C22×D411yescharacteristic
288C2×C4×C7C22×D411yescharacteristic
289C2×C4×C7C2×#4112yes—
290C2×C4×C7C2×#4112yes—
291C22⋊D7—44no—
292C22⋊D7—44no—
293C2×Dic7—21no—
294C2×Dic7—21no—
295C2×Dic7—21no—
296C2×Dic7—21no—
297C2×Dic7—22no—
298C2×Dic7—28no—
299C2×Dic7—28no—
300C2×Dic7—21no—
301C2×Dic7—21no—
302C2×Dic7—21no—
303C2×Dic7—22no—
304C2×Dic7—22no—
305C2×Dic7—21no—
306C2×Dic7—21no—
307C2×Dic7C2×C22⋊C412yes—
308C2×Dic7C2×C22⋊C412yes—
309C2×Dic7C2×C22⋊C412yes—
310C2×Dic7C2×C22⋊C412yes—
311C2×Dic7#13114yes—
312C4×D7—41no—
313C4×D7—41no—
314C4×D7—42no—
315Dic14—44no—
316C7×C8—24no—
317C7×C8—42no—
318C7⋊C8—24no—
319C7⋊C8—42no—
320C22×Q8—71no—
321C22×D4—71no—
322C22×D4—71no—
323C22×D4C4×D711yescharacteristic
324C23×C4—71no—
325C23×C4—71no—
326C23×C4—71no—
327C23×C4C22×D711yescharacteristic
328C23×C4C22×D711yescharacteristic
329C22×C8—22no—
330C22×C8—24no—
331C22×C8—72no—
332C22×C8—72no—
333C22×C8—144no—
334C22×C8—142no—
335C22×C8C22×D712yes—
336C22×C8C22×D712yes—
337#126—144no—
338#126—144no—
339#125—144no—
340#124—144no—
341#123—144no—
342#123—144no—
343C22⋊Q8—144no—
344#121—144no—
345C4×Q8—142no—
346C4×Q8—142no—
347C4×D4—22no—
348C4×D4—22no—
349C4×D4—142no—
350C4×D4—142no—
351C4×D4—142no—
352C4×D4—142no—
353#117—142no—
354#117—142no—
355#117—142no—
356#117—142no—
357C2×C4⋊C4—71no—
358C2×C4⋊C4—71no—
359C2×C4⋊C4—71no—
360C2×C4⋊C4—71no—
361C2×C4⋊C4—71no—
362C2×C4⋊C4—71no—
363C2×C4⋊C4—71no—
364C2×C4⋊C4—71no—
365C2×C4⋊C4—71no—
366C2×C4⋊C4C4×D711yescharacteristic
367C2×C22⋊C4—71no—
368C2×C22⋊C4—71no—
369C2×C22⋊C4—71no—
370C2×C22⋊C4—71no—
371C2×C22⋊C4—71no—
372C2×C22⋊C4—71no—
373C2×C22⋊C4—71no—
374C2×C22⋊C4—71no—
375C2×C22⋊C4C4×D711yescharacteristic
376C2×C22⋊C4C4×D711yescharacteristic
377C2×C42—71no—
378C2×C42—71no—
379C2×C42—74no—
380C2×C42—74no—
381C2×C42—71no—
382C2×C42—71no—
383C2×C42—71no—
384C2×C42C22×D711yescharacteristic
385C4⋊C8—144no—
386C22⋊C8—22no—
387C22⋊C8—24no—
388C22⋊C8—144no—
389C22⋊C8—144no—
390C22⋊C8—142no—
391C22⋊C8—144no—
392#97—144no—
393C4×C8—144no—
394C4×C8—144no—
395C22×C7—22no—
396C22×C7—24no—
397C22×C7—24no—
398C22×C7—22no—
399C22×C7—41no—
400C22×C7—41no—
401C22×C7—42no—
402C22×C7—42no—
403C22×C7—41no—
404C22×C7#40814yes—
405C22×C7C22×C22⋊C411yescharacteristic
406C22×C7C4×#4112yes—
407C22×C7C2×#13111yescharacteristic
408C22×C7C2×#13111yescharacteristic
409C22×C7C2×#13112yes—
410C2×D7—41no—
411C2×D7—41no—
412C2×D7—42no—
413C2×D7—42no—
414C2×D7—41no—
415C4×C7—22no—
416C4×C7—41no—
417C4×C7—41no—
418C4×C7—41no—
419C4×C7#52511yescharacteristic
420C4×C7#52511yescharacteristic
421C4×C7#53212yes—
422Dic7—22no—
423Dic7—22no—
424Dic7—22no—
425Dic7—41no—
426Dic7—41no—
427Dic7—41no—
428Dic7#40814yes—
429C24—71no—
430C24C2×C4×D711yescharacteristic
431C24C2×C4×D711yescharacteristic
432C2×Q8—142no—
433C2×Q8—144no—
434C2×D4—22no—
435C2×D4—22no—
436C2×D4—22no—
437C2×D4—142no—
438C2×D4—144no—
439C2×D4—142no—
440C2×D4—142no—
441C2×D4—142no—
442C22×C4—22no—
443C22×C4—22no—
444C22×C4—21no—
445C22×C4—21no—
446C22×C4—22no—
447C22×C4—22no—
448C22×C4—71no—
449C22×C4—74no—
450C22×C4—74no—
451C22×C4—71no—
452C22×C4—71no—
453C22×C4—71no—
454C22×C4—71no—
455C22×C4—71no—
456C22×C4—71no—
457C22×C4—144no—
458C22×C4—142no—
459C22×C4—142no—
460C22×C4—141no—
461C22×C4—141no—
462C22×C4—142no—
463C22×C4—142no—
464C22×C4C2×C4×D711yescharacteristic
465C22×C4C2×C4×D711yescharacteristic
466C22×C4C2×C4×D711yescharacteristic
467C22×C4C2×C4×D711yescharacteristic
468C22×C4D4×D712yes—
469C22×C4D4×D712yes—
470C22×C4C23×D711yescharacteristic
471C2×C8—28no—
472C2×C8—22no—
473C2×C8—22no—
474C2×C8—22no—
475C2×C8—22no—
476C2×C8—22no—
477C2×C8—74no—
478C2×C8—148no—
479C2×C8—142no—
480C2×C8—142no—
481C2×C8—142no—
482C2×C8—142no—
483C2×C8—142no—
484C2×C8#115914yes—
485C4⋊C4—22no—
486C4⋊C4—142no—
487C4⋊C4—142no—
488C4⋊C4—142no—
489C4⋊C4—142no—
490C4⋊C4—142no—
491C4⋊C4—142no—
492C4⋊C4—142no—
493C4⋊C4—142no—
494C4⋊C4—142no—
495C22⋊C4—22no—
496C22⋊C4—22no—
497C22⋊C4—142no—
498C22⋊C4—142no—
499C22⋊C4—142no—
500C22⋊C4—142no—
501C22⋊C4—142no—
502C22⋊C4—142no—
503C22⋊C4—142no—
504C22⋊C4—142no—
505C42—21no—
506C42—21no—
507C42—74no—
508C42—74no—
509C42—72no—
510C42—72no—
511C42—72no—
512C42—72no—
513C42—141no—
514C42—141no—
515C2×C7—24no—
516C2×C7—81no—
517C2×C7#229711yescharacteristic
518C2×C7C2×#40811yescharacteristic
519C2×C7C2×#40811yescharacteristic
520C2×C7#296612yes—
521C2×C7#296612yes—
522D7—81no—
523C23—22no—
524C23—22no—
525C23—21no—
526C23—21no—
527C23—21no—
528C23—22no—
529C23—22no—
530C23—141no—
531C23—141no—
532C23—141no—
533C23—142no—
534C23—142no—
535C23D7×C22⋊C412yes—
536C23#646412yes—
537C23#647012yes—
538C23C22×C4×D711yescharacteristic
539Q8—284no—
540D4—44no—
541D4—284no—
542D4—284no—
543C2×C4—22no—
544C2×C4—22no—
545C2×C4—24no—
546C2×C4—22no—
547C2×C4—21no—
548C2×C4—21no—
549C2×C4—21no—
550C2×C4—21no—
551C2×C4—21no—
552C2×C4—22no—
553C2×C4—22no—
554C2×C4—41no—
555C2×C4—42no—
556C2×C4—41no—
557C2×C4—72no—
558C2×C4—74no—
559C2×C4—72no—
560C2×C4—72no—
561C2×C4—72no—
562C2×C4—148no—
563C2×C4—141no—
564C2×C4—141no—
565C2×C4—141no—
566C2×C4—141no—
567C2×C4—142no—
568C2×C4—148no—
569C2×C4—141no—
570C2×C4—141no—
571C2×C4—141no—
572C2×C4—141no—
573C2×C4—141no—
574C2×C4—142no—
575C2×C4—142no—
576C2×C4—281no—
577C2×C4—282no—
578C2×C4—281no—
579C2×C4D7×C22⋊C412yes—
580C2×C4C2×D4×D711yescharacteristic
581C2×C4C2×D4×D711yescharacteristic
582C2×C4C2×#115912yes—
583C2×C4D7×#4112yes—
584C8—24no—
585C8—42no—
586C8—144no—
587C8—282no—
588C7#2137511yescharacteristic, complemented, Sylow
589C22—24no—
590C22—22no—
591C22—24no—
592C22—22no—
593C22—42no—
594C22—41no—
595C22—42no—
596C22—41no—
597C22—41no—
598C22—282no—
599C22—281no—
600C22—282no—
601C22—281no—
602C22—281no—
603C22#8949914yes—
604C22C2×D7×C22⋊C411yescharacteristic
605C22C4×#115912yes—
606C22C2×#646411yescharacteristic
607C22C2×#647011yescharacteristic
608C22D7×#13112yes—
609C4—22no—
610C4—41no—
611C4—41no—
612C4—41no—
613C4—74no—
614C4—142no—
615C4—142no—
616C4—142no—
617C4—281no—
618C4—281no—
619C4—281no—
620C4#9027711yescharacteristic
621C4#9028712yes—
622C4#9034711yescharacteristic
623C2—24no—
624C2—81no—
625C2—561no—
626C2#1173210311yescharacteristic
627C2C2×#8949911yescharacteristic
628C2D7×#40811yescharacteristic
629C2#1173684512yes—
630C2#1173689912yes—
subgroupG/H
center, FrattiniC22×C4C23×D7
commutator, socleC23×C7C23×C4
FittingC7×#1869C2
prime radicalC2×#6502C4
cosocleC22×C4×C7C24
hypercenter#1869D7
hypocenterC7#21375
LCSG ▷ C23×C7 ▷ C7
UCSC1 ◁ C22×C4 ◁ #1869

Complements

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

NH ≅ G/Ntype
2. C22×C8×Dic7C2semidirect
3. C2×#89491C2semidirect
4. C7×#1869C2semidirect
5. #11729729C2semidirect
6. #11729364C2semidirect
7. #11727706C2semidirect
8. #11727670C2semidirect
9. #11727661C2semidirect
10. #11726373C2semidirect
11. #11726355C2semidirect
131. #1869D7semidirect
588. C7#21375semidirect

Maximal subgroups

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

subgroupindex
C2×#902292
C22×C8×Dic72
C2×#894912
C7×#18692
#117297292
#117293642
#117277062
#117276702
#117276612
#117263732
#117263552
#213757