Finite Group Databasebeta

← #13367742

Subgroups — #13367742

Order 1792.

722 conjugacy classes of subgroups.

The subgroup lattice has 618 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#11731113C211yesmaximal, characteristic
2C7×#1916C211yesmaximal, characteristic, complemented
3#11728232C211yesmaximal, characteristic
4#11728222C211yesmaximal, characteristic, complemented
5#11727540C211yesmaximal, characteristic, complemented
6C8×(C2×D7)⋊C4C211yesmaximal, characteristic
7#11727236C211yesmaximal, characteristic, complemented
8#11726421C211yesmaximal, characteristic
9#11726417C211yesmaximal, characteristic
10#11726415C211yesmaximal, characteristic
11#11726401C211yesmaximal, characteristic
12#11726373C211yesmaximal, characteristic, complemented
13#11726373C211yesmaximal, characteristic, complemented
14#11726364C211yesmaximal, characteristic, complemented
15#11726363C211yesmaximal, characteristic, complemented
16C22×#1131C2211yescharacteristic
17C22×C8×D7C2211yescharacteristic
18C2×#6435C2211yescharacteristic
19C2×C4×Dic14C2211yescharacteristic
20C2×C7×C4⋊C8C2211yescharacteristic
21C2×C4×C7×C8C2211yescharacteristic
22C4×C7×C4⋊C4C2211yescharacteristic
23C2×(C2×D7)⋊C8C2211yescharacteristic
24C2×(C2×D7)⋊C8C2211yescharacteristic
25C2×Dic7⋊C8C2211yescharacteristic
26C2×Dic7⋊C8C2211yescharacteristic
27C2×Dic7⋊C8C2211yescharacteristic
28C2×Dic7⋊C8C2211yescharacteristic
29C2×C8×Dic7C2211yescharacteristic
30C2×C8×Dic7C2211yescharacteristic
31#89766C411yescharacteristic
32#89766C411yescharacteristic
33#89755C411yescharacteristic
34#89755C411yescharacteristic
35C4×(C2×D7)⋊C4C2211yescharacteristic
36C4×(C2×D7)⋊C4C2211yescharacteristic
37C4×C4⋊Dic7C2211yescharacteristic
38C4×C4⋊Dic7C2211yescharacteristic
39C2×C4⋊(C7⋊C8)C2211yescharacteristic
40C2×C4×C7⋊C8C2211yescharacteristic
41#89449C411yescharacteristic
42#89445C411yescharacteristic
43#89431C411yescharacteristic
44#89428C411yescharacteristic
45C7×#336C2211yescharacteristic
46C7×#336C2211yescharacteristic
47C7×#336C2211yescharacteristic
48C7×#336C2211yescharacteristic
49#89345C2211yescharacteristic
50#89345C2211yescharacteristic
51#89345C2211yescharacteristic
52#89345C2211yescharacteristic
53#89345C2211yescharacteristic
54#89345C2211yescharacteristic
55#89319C2211yescharacteristic
56#89319C2211yescharacteristic
57#89319C2211yescharacteristic
58#89319C2211yescharacteristic
59#22288—71nomaximal, Sylow
60C22×C4×D7C2311yescharacteristic
61C22×Dic14C2×C411yescharacteristic
62C22×C7×C8C2311yescharacteristic
63C22×C7×C8C2311yescharacteristic
64C22×C7×C8C2311yescharacteristic
65C22×C7×C8C2311yescharacteristic
66C2×C7×C4⋊C4C2×C411yescharacteristic
67C2×C7×C4⋊C4C2×C411yescharacteristic
68C2×C42×C7C2311yescharacteristic
69C2×C42×C7C2311yescharacteristic
70C2×C42×C7C2311yescharacteristic
71C2×(C2×D7)⋊C4C2×C411yescharacteristic
72C2×(C2×D7)⋊C4C2×C411yescharacteristic
73C2×(C2×D7)⋊C4C2×C411yescharacteristic
74C2×(C2×D7)⋊C4C2×C411yescharacteristic
75C2×(C2×D7)⋊C4C2×C411yescharacteristic
76C2×(C2×D7)⋊C4C2×C411yescharacteristic
77C2×C4⋊Dic7C2×C411yescharacteristic
78C2×C4⋊Dic7C2×C411yescharacteristic
79C2×C4⋊Dic7C2×C411yescharacteristic
80C2×C4⋊Dic7C2×C411yescharacteristic
81C2×C4⋊Dic7C2×C411yescharacteristic
82C2×Dic7⋊C4C2×C411yescharacteristic
83C2×Dic7⋊C4C2×C411yescharacteristic
84C2×Dic7⋊C4C2×C411yescharacteristic
85C2×Dic7⋊C4C2×C411yescharacteristic
86C2×C4×Dic7C2311yescharacteristic
87C2×C4×Dic7C2311yescharacteristic
88C2×C4×Dic7C2311yescharacteristic
89C22×C7⋊C8C2311yescharacteristic
90C22×C7⋊C8C2311yescharacteristic
91C22×C7⋊C8C2311yescharacteristic
92C22×C7⋊C8C2311yescharacteristic
93C2×#1131—22no—
94C2×#1131—41no—
95C2×#1131—41no—
96C2×C8×D7—41no—
97C2×C8×D7—41no—
98C2×C8×D7Q814yescomplemented
99#6435—41no—
100#6435—41no—
101C4×Dic14—41no—
102C4×Dic14—41no—
103C7×C4⋊C8—41no—
104C4×C7×C8—41no—
105C7×#95C2×C411yescharacteristic
106C7×#95C2×C411yescharacteristic
107C7⋊#95C2×C411yescharacteristic
108C7⋊#95C2×C411yescharacteristic
109C7⋊#95C2×C411yescharacteristic
110C7⋊#95C2×C411yescharacteristic
111C7⋊#95C2×C411yescharacteristic
112C7⋊#95C2×C411yescharacteristic
113C7⋊#95C2×C411yescharacteristic
114C7⋊#95C2×C411yescharacteristic
115(C2×D7)⋊C8—22no—
116(C2×D7)⋊C8—22no—
117Dic7⋊C8—41no—
118Dic7⋊C8—41no—
119Dic7⋊C8—41no—
120Dic7⋊C8—41no—
121C8×Dic7—41no—
122C8×Dic7—41no—
123C4⋊(C7⋊C8)—41no—
124C4×C7⋊C8—41no—
125#2396—71no—
126#1984—71no—
127#1984—71no—
128#1939—71no—
129#1939—71no—
130#1916—71no—
131#1916—71no—
132#1916—71no—
133#1916D711yescharacteristic, complemented
134#1851—71no—
135#1851—71no—
136#1798—71no—
137C8×C22⋊C4—71no—
138C8×C22⋊C4—71no—
139#1729—71no—
140C23×D7C22×C411yescharacteristic
141C22×C4×C7C22×C411yescharacteristic
142C22×C4×C7C22×C411yescharacteristic
143C22×C4×C7C22×C411yescharacteristic
144C22×C4×C7C22×C411yescharacteristic
145C22×C4×C7C22×C411yescharacteristic
146C22×C4×C7C22×C411yescharacteristic
147C22×C4×C7C2411yescharacteristic
148C22×Dic7C22×C411yescharacteristic
149C22×Dic7C22×C411yescharacteristic
150C22×Dic7C22×C411yescharacteristic
151C22×Dic7C22×C411yescharacteristic
152C22×Dic7C22×C411yescharacteristic
153C22×Dic7C22×C411yescharacteristic
154C22×Dic7C22×C411yescharacteristic
155C2×C4×D7—21no—
156C2×C4×D7—21no—
157C2×C4×D7—21no—
158C2×C4×D7—21no—
159C2×C4×D7C2×Q812yes—
160C2×C4×D7#4112yes—
161C2×Dic14—22no—
162C2×Dic14—22no—
163C2×Dic14—41no—
164C2×C7×C8—21no—
165C2×C7×C8—21no—
166C2×C7×C8—21no—
167C2×C7×C8—21no—
168C2×C7×C8—21no—
169C2×C7×C8—21no—
170C2×C7×C8—21no—
171C2×C7×C8—21no—
172C2×C7×C8—21no—
173C2×C7×C8—21no—
174C2×C7×C8—21no—
175C2×C7×C8C2×Q812yes—
176C7×C4⋊C4—22no—
177C7×C4⋊C4—22no—
178C42×C7—21no—
179C42×C7—21no—
180C42×C7—21no—
181C42×C7—21no—
182C42×C7—21no—
183C42×C7—21no—
184(C2×D7)⋊C4—22no—
185(C2×D7)⋊C4—22no—
186(C2×D7)⋊C4—22no—
187(C2×D7)⋊C4—22no—
188(C2×D7)⋊C4—41no—
189(C2×D7)⋊C4—41no—
190C4⋊Dic7—22no—
191C4⋊Dic7—22no—
192C4⋊Dic7—22no—
193C4⋊Dic7—22no—
194C4⋊Dic7—41no—
195Dic7⋊C4—41no—
196Dic7⋊C4—41no—
197Dic7⋊C4—41no—
198Dic7⋊C4—41no—
199C4×Dic7—21no—
200C4×Dic7—21no—
201C4×Dic7—21no—
202C4×Dic7—21no—
203C4×Dic7—21no—
204C4×Dic7—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×C7⋊C8—21no—
214C2×C7⋊C8—21no—
215C2×C7⋊C8—21no—
216C2×C7⋊C8C2×Q812yes—
217#1131—44no—
218C8×D7—44no—
219C22×M16—71no—
220C23×C8—71no—
221C2×C4×Q8—71no—
222C2×#117—71no—
223C2×C4⋊C8—71no—
224C2×C4⋊C8—71no—
225C2×C4⋊C8—71no—
226C2×C4⋊C8—71no—
227C2×C4⋊C8—71no—
228C2×C4⋊C8C2×D711yescharacteristic
229C2×C22⋊C8—71no—
230C2×C22⋊C8—71no—
231C2×C4×C8—71no—
232C2×C4×C8—71no—
233C2×C4×C8—71no—
234C2×C4×C8C2×D711yescharacteristic
235#400—71no—
236#399—71no—
237#398—71no—
238#398—71no—
239#396—71no—
240#396—71no—
241#395—71no—
242#393—71no—
243C4×C4⋊C4—71no—
244C4×C4⋊C4—71no—
245C4×C4⋊C4C2×D711yescharacteristic
246C4×C22⋊C4—71no—
247C4×C22⋊C4—71no—
248#336—71no—
249#336—71no—
250#336—71no—
251#336—71no—
252#336—71no—
253#336—71no—
254#336—71no—
255#336—71no—
256#336—71no—
257#336—71no—
258#336C2×D711yescharacteristic
259#336C2×D711yescharacteristic
260#336C2×D711yescharacteristic
261#336C2×D711yescharacteristic
262C23×C7C23×C411yescharacteristic
263C22×D7—21no—
264C22×D7—21no—
265C22×D7—21no—
266C22×D7—21no—
267C22×D7—21no—
268C22×D7—21no—
269C22×D7C4×Q812yes—
270C2×C4×C7—21no—
271C2×C4×C7—21no—
272C2×C4×C7—21no—
273C2×C4×C7—21no—
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—21no—
283C2×C4×C7—21no—
284C2×C4×C7—21no—
285C2×C4×C7—21no—
286C2×C4×C7#13112yes—
287C2×C4×C7#13112yes—
288C2×C4×C7C22×Q811yescharacteristic
289C2×C4×C7C2×#4111yescharacteristic
290C2×C4×C7H(5,𝔽2)11yescharacteristic
291C2×C4×C7H(5,𝔽2)11yescharacteristic
292C2×C4×C7H(5,𝔽2)11yescharacteristic
293C2×C4×C72−1+411yescharacteristic
294C2×Dic7—21no—
295C2×Dic7—21no—
296C2×Dic7—21no—
297C2×Dic7—21no—
298C2×Dic7—21no—
299C2×Dic7—21no—
300C2×Dic7—21no—
301C2×Dic7—21no—
302C2×Dic7—21no—
303C2×Dic7—21no—
304C2×Dic7—21no—
305C2×Dic7—21no—
306C2×Dic7—21no—
307C2×Dic7—21no—
308C2×Dic7—21no—
309C2×Dic7—21no—
310C2×Dic7—21no—
311C2×Dic7—21no—
312C2×Dic7C4×Q812yes—
313C2×Dic7#13112yes—
314C2×Dic7#13112yes—
315C4×D7—22no—
316C4×D7—22no—
317C4×D7—22no—
318C4×D7—22no—
319Dic14—44no—
320C7×C8—22no—
321C7×C8—41no—
322C7×C8—41no—
323C7×C8—41no—
324C7⋊C8—22no—
325C7⋊C8—41no—
326C7⋊C8—41no—
327C7⋊C8—41no—
328C22×Q8—71no—
329C23×C4—71no—
330C2×M16—142no—
331C2×M16—281no—
332C2×M16—281no—
333C22×C8—71no—
334C22×C8—74no—
335C22×C8—71no—
336C22×C8—71no—
337C22×C8—71no—
338C22×C8—281no—
339C22×C8—281no—
340C22×C8C22×D711yescharacteristic
341C22×C8C22×D711yescharacteristic
342C22×C8C22×D711yescharacteristic
343C22×C8C22×D711yescharacteristic
344C4×Q8—281no—
345C4×Q8—281no—
346#117—281no—
347#117—281no—
348C2×C4⋊C4—71no—
349C2×C4⋊C4—71no—
350C2×C4⋊C4—71no—
351C2×C4⋊C4—71no—
352C2×C4⋊C4—71no—
353C2×C4⋊C4—71no—
354C2×C4⋊C4—71no—
355C2×C4⋊C4—71no—
356C2×C4⋊C4—71no—
357C2×C4⋊C4C4×D711yescharacteristic
358C2×C4⋊C4C4×D711yescharacteristic
359C2×C22⋊C4—71no—
360C2×C22⋊C4—71no—
361C2×C22⋊C4—71no—
362C2×C22⋊C4—71no—
363C2×C22⋊C4—71no—
364C2×C22⋊C4—71no—
365C2×C42—71no—
366C2×C42—71no—
367C2×C42—71no—
368C2×C42C22×D711yescharacteristic
369C2×C42C22×D711yescharacteristic
370C2×C42C22×D711yescharacteristic
371C4⋊C8—41no—
372C4⋊C8—281no—
373C4⋊C8—281no—
374C4⋊C8—281no—
375C4⋊C8—281no—
376C4⋊C8—281no—
377C22⋊C8—142no—
378C22⋊C8—142no—
379C4×C8—41no—
380C4×C8—281no—
381C4×C8—281no—
382C4×C8—281no—
383#95—71no—
384#95—71no—
385#95—71no—
386#95—71no—
387#95—71no—
388#95—71no—
389#95—71no—
390#95—71no—
391#95C4×D711yescharacteristic
392#95C4×D711yescharacteristic
393C22×C7C2×C4×Q811yescharacteristic
394C22×C7#51811yescharacteristic
395C22×C7#52011yescharacteristic
396C22×C7C2×#13111yescharacteristic
397C22×C7C2×#13111yescharacteristic
398C22×C7C2×#13111yescharacteristic
399C22×C7C2×#13111yescharacteristic
400C2×D7—22no—
401C2×D7—22no—
402C2×D7—22no—
403C2×D7—41no—
404C2×D7—41no—
405C2×D7—41no—
406C2×D7—41no—
407C4×C7—22no—
408C4×C7—22no—
409C4×C7—41no—
410C4×C7—41no—
411C4×C7—41no—
412C4×C7—41no—
413C4×C7#53811yescharacteristic
414C4×C7#53911yescharacteristic
415C4×C7#54311yescharacteristic
416C4×C7#54411yescharacteristic
417Dic7—22no—
418Dic7—22no—
419Dic7—22no—
420Dic7—41no—
421Dic7—41no—
422Dic7—41no—
423Dic7—41no—
424C24—71no—
425C2×Q8—142no—
426C2×Q8—142no—
427C2×Q8—281no—
428C22×C4—71no—
429C22×C4—71no—
430C22×C4—71no—
431C22×C4—72no—
432C22×C4—72no—
433C22×C4—71no—
434C22×C4—71no—
435C22×C4—71no—
436C22×C4—71no—
437C22×C4—141no—
438C22×C4—141no—
439C22×C4—141no—
440C22×C4—141no—
441C22×C4C2×C4×D711yescharacteristic
442C22×C4C2×C4×D711yescharacteristic
443C22×C4C2×C4×D711yescharacteristic
444C22×C4C2×C4×D711yescharacteristic
445C22×C4C2×C4×D711yescharacteristic
446C22×C4C2×C4×D711yescharacteristic
447C22×C4C23×D711yescharacteristic
448M16—284no—
449C2×C8—21no—
450C2×C8—21no—
451C2×C8—21no—
452C2×C8—21no—
453C2×C8—21no—
454C2×C8—21no—
455C2×C8—21no—
456C2×C8—21no—
457C2×C8—21no—
458C2×C8—21no—
459C2×C8—21no—
460C2×C8—72no—
461C2×C8—141no—
462C2×C8—141no—
463C2×C8—141no—
464C2×C8—141no—
465C2×C8—141no—
466C2×C8—141no—
467C2×C8—141no—
468C2×C8—141no—
469C2×C8—141no—
470C2×C8—141no—
471C2×C8—141no—
472C2×C8—284no—
473C2×C8Q8×D712yes—
474C4⋊C4—22no—
475C4⋊C4—22no—
476C4⋊C4—142no—
477C4⋊C4—142no—
478C4⋊C4—142no—
479C4⋊C4—142no—
480C4⋊C4—281no—
481C4⋊C4—281no—
482C4⋊C4—281no—
483C4⋊C4—281no—
484C4⋊C4—281no—
485C22⋊C4—142no—
486C22⋊C4—142no—
487C22⋊C4—142no—
488C22⋊C4—142no—
489C22⋊C4—281no—
490C22⋊C4—281no—
491C42—21no—
492C42—21no—
493C42—21no—
494C42—21no—
495C42—21no—
496C42—21no—
497C42—141no—
498C42—141no—
499C42—141no—
500C42—141no—
501C42—141no—
502C42—141no—
503C2×C7#232911yescharacteristic
504C2×C7#296011yescharacteristic
505C2×C7#296011yescharacteristic
506C2×C7#297711yescharacteristic
507C2×C7#297911yescharacteristic
508C2×C7#299411yescharacteristic
509C2×C7#299411yescharacteristic
510D7—42no—
511C23—72no—
512C23—141no—
513C23—141no—
514C23—141no—
515C23—141no—
516C23—141no—
517C23—141no—
518C23C22×C4×D711yescharacteristic
519Q8—284no—
520C2×C4—21no—
521C2×C4—21no—
522C2×C4—21no—
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—21no—
534C2×C4—21no—
535C2×C4—21no—
536C2×C4—72no—
537C2×C4—72no—
538C2×C4—72no—
539C2×C4—141no—
540C2×C4—141no—
541C2×C4—141no—
542C2×C4—141no—
543C2×C4—141no—
544C2×C4—141no—
545C2×C4—142no—
546C2×C4—142no—
547C2×C4—142no—
548C2×C4—142no—
549C2×C4—141no—
550C2×C4—141no—
551C2×C4—141no—
552C2×C4—141no—
553C2×C4—141no—
554C2×C4—141no—
555C2×C4—141no—
556C2×C4—141no—
557C2×C4—141no—
558C2×C4—141no—
559C2×C4—141no—
560C2×C4—141no—
561C2×C4#646412yes—
562C2×C4#647012yes—
563C2×C4#654811yescharacteristic
564C2×C4C2×Q8×D711yescharacteristic
565C2×C4D7×#4111yescharacteristic
566C2×C4#655311yescharacteristic
567C2×C4#655311yescharacteristic
568C2×C4#655411yescharacteristic
569C8—22no—
570C8—41no—
571C8—41no—
572C8—41no—
573C8—142no—
574C8—281no—
575C8—281no—
576C8—281no—
577C7#2228811yescharacteristic, complemented, Sylow
578C22—142no—
579C22—142no—
580C22—142no—
581C22—281no—
582C22—281no—
583C22—281no—
584C22—281no—
585C22#9021211yescharacteristic
586C22#9023711yescharacteristic
587C22C4×Q8×D711yescharacteristic
588C22C2×#646411yescharacteristic
589C22C2×#647011yescharacteristic
590C22D7×#13111yescharacteristic
591C22D7×#13111yescharacteristic
592C4—22no—
593C4—22no—
594C4—41no—
595C4—41no—
596C4—41no—
597C4—41no—
598C4—142no—
599C4—142no—
600C4—142no—
601C4—281no—
602C4—281no—
603C4—281no—
604C4—281no—
605C4#9032511yescharacteristic
606C4#9034811yescharacteristic
607C4#9038011yescharacteristic
608C4#9039811yescharacteristic
609C2—282no—
610C2#1173274511yescharacteristic
611C2#1173673411yescharacteristic
612C2#1173682211yescharacteristic
613C2#1173685411yescharacteristic
614C2#1173691111yescharacteristic
615C2#1173736211yescharacteristic
616C2#1173740311yescharacteristic
subgroupG/H
center, FrattiniC22×C4C23×D7
commutator, socleC23×C7C23×C4
FittingC7×#1916C2
prime radicalC23×D7C22×C4
cosocleC22×C4×C7C24
hypercenter#1916D7
hypocenterC7#22288
LCSG ▷ C23×C7 ▷ C7
UCSC1 ◁ C22×C4 ◁ #1916

Complements

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

NH ≅ G/Ntype
2. C7×#1916C2semidirect
4. #11728222C2semidirect
5. #11727540C2semidirect
7. #11727236C2semidirect
12. #11726373C2semidirect
13. #11726373C2semidirect
14. #11726364C2semidirect
15. #11726363C2semidirect
98. C2×C8×D7Q8semidirect
133. #1916D7semidirect
577. C7#22288semidirect

Maximal subgroups

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

subgroupindex
#117311132
C7×#19162
#117282322
#117282222
#117275402
C8×(C2×D7)⋊C42
#117272362
#117264212
#117264172
#117264152
#117264012
#117263732
#117263642
#117263632
#222887