Finite Group Databasebeta

← #13426987

Subgroups — #13426987

Order 1792.

762 conjugacy classes of subgroups.

The subgroup lattice has 636 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C7×#2365C211yesmaximal, characteristic, complemented
2#11731137C211yesmaximal, characteristic
3#11729545C211yesmaximal, characteristic
4#11729535C211yesmaximal, characteristic, complemented
5#11729387C211yesmaximal, characteristic
6#11729387C211yesmaximal, characteristic
7C4×#6409C211yesmaximal, characteristic, complemented
8#11729380C211yesmaximal, characteristic, complemented
9#11727439C211yesmaximal, characteristic, complemented
10#11727434C211yesmaximal, characteristic
11#11727430C211yesmaximal, characteristic
12#11727420C211yesmaximal, characteristic, complemented
13#11727236C211yesmaximal, characteristic, complemented
14#11727217C211yesmaximal, characteristic
15#11727213C211yesmaximal, characteristic, complemented
16C2×C7×C4⋊Q8C2211yescharacteristic
17C2×C4×C7×Q8C2211yescharacteristic
18C2×C4×C7×Q8C2211yescharacteristic
19C22×#1143C2211yescharacteristic
20C22×#1143C2211yescharacteristic
21C2×#6461—21no—
22C7×#391C2211yescharacteristic
23C7×#391C2211yescharacteristic
24C7×#389—21no—
25C7×#387—21no—
26C7×#387—21no—
27C4×C7×C4⋊C4—21no—
28C4×C7×C4⋊C4C2211yescharacteristic
29C4×C7×C4⋊C4C2211yescharacteristic
30C2×#6409C2211yescharacteristic
31C2×#6409C2211yescharacteristic
32C2×#6409C2211yescharacteristic
33C2×#6409C2211yescharacteristic
34C2×#6409C2211yescharacteristic
35C2×#6409C2211yescharacteristic
36#89766—21no—
37C2×#6383C2211yescharacteristic
38C2×#6383C2211yescharacteristic
39C2×#6382C2211yescharacteristic
40C2×#6382C2211yescharacteristic
41#89711C2211yescharacteristic
42#89711C2211yescharacteristic
43#89711C2211yescharacteristic
44#89707C2211yescharacteristic
45C4×C4⋊Dic7C2211yescharacteristic
46#89700C2211yescharacteristic
47C2×C4⋊(C7⋊C8)C2211yescharacteristic
48C2×C4×C7⋊C8C2211yescharacteristic
49#89446—21no—
50#89442—21no—
51#89324C2211yescharacteristic
52#89324C2211yescharacteristic
53#89324C2211yescharacteristic
54#89324C2211yescharacteristic
55#89319C2211yescharacteristic
56#89319C2211yescharacteristic
57#89319C2211yescharacteristic
58#89319C2211yescharacteristic
59#27066—71nomaximal, Sylow
60C22×C7×Q8C2311yescharacteristic
61C22×C7×Q8C2311yescharacteristic
62C22×D28C2311yescharacteristic
63C7×C4⋊Q8—22no—
64C7×C4⋊Q8—22no—
65C4×C7×Q8—22no—
66C4×C7×Q8—22no—
67C4×C7×Q8—41no—
68C4×C7×Q8—41no—
69C2×C7×C4⋊C4—21no—
70C2×C7×C4⋊C4—21no—
71C2×C7×C4⋊C4—21no—
72C2×C7×C4⋊C4—21no—
73C2×C7×C4⋊C4D411yescharacteristic
74C2×C7×C4⋊C4D411yescharacteristic
75C2×C7×C4⋊C4C2311yescharacteristic
76C2×C7×C4⋊C4C2311yescharacteristic
77C2×C42×C7—21no—
78C2×C42×C7—21no—
79C2×C42×C7—21no—
80C2×C42×C7C2311yescharacteristic
81C2×C42×C7C2311yescharacteristic
82C2×C42×C7C2311yescharacteristic
83C2×#1143—22no—
84C2×#1143—22no—
85C2×#1143—22no—
86C2×#1143—41no—
87C2×#1143—41no—
88C2×#1143—41no—
89C2×(C2×D7)⋊C4—21no—
90C2×(C2×D7)⋊C4—21no—
91C2×(C2×D7)⋊C4—21no—
92C2×(C2×D7)⋊C4—21no—
93C2×(C2×D7)⋊C4—21no—
94C2×(C2×D7)⋊C4—21no—
95C2×C4⋊Dic7—21no—
96C2×C4⋊Dic7—21no—
97C2×C4⋊Dic7C2311yescharacteristic
98C2×C4⋊Dic7C2311yescharacteristic
99C2×C4⋊Dic7C2311yescharacteristic
100C2×Dic7⋊C4—21no—
101C2×C4×Dic7—21no—
102C22×C7⋊C8C2311yescharacteristic
103C22×C7⋊C8C2311yescharacteristic
104C22×C7⋊C8C2311yescharacteristic
105C22×C7⋊C8C2311yescharacteristic
106#6461—44no—
107C7×#95—21no—
108C7×#95—21no—
109C7×#95—21no—
110C7×#95—21no—
111C7×#95—21no—
112C7×#95D411yescharacteristic
113C7×#95D411yescharacteristic
114#6409—22no—
115#6409—22no—
116#6409—22no—
117#6409—41no—
118#6409—41no—
119#6409—41no—
120C7⋊#95—21no—
121C7⋊#95—21no—
122#6383—22no—
123#6383—41no—
124#6382—22no—
125#6382—41no—
126C4⋊(C7⋊C8)—41no—
127C4×C7⋊C8—41no—
128#2512—71no—
129#2365D711yescharacteristic, complemented
130#2096—71no—
131#2055—71no—
132#2043—71no—
133#2013—71no—
134#1968—71no—
135#1927—71no—
136#1926—71no—
137#1919—71no—
138#1916—71no—
139#1880—71no—
140#1880—71no—
141#1803—71no—
142C4×#103—71no—
143C23×D7—21no—
144C2×C7×Q8—21no—
145C2×C7×Q8—21no—
146C2×C7×Q8—21no—
147C2×C7×Q8—21no—
148C2×C7×Q8—21no—
149C2×C7×Q8—21no—
150C2×C7×Q8—21no—
151C2×C7×Q8—21no—
152C2×C7×Q8—21no—
153C2×C7×Q8—21no—
154C2×C7×Q8#4112yes—
155C2×C7×Q8#4112yes—
156C22×C4×C7—21no—
157C22×C4×C7—21no—
158C22×C4×C7—21no—
159C22×C4×C7—21no—
160C22×C4×C7C2×D411yescharacteristic
161C22×C4×C7C2×D411yescharacteristic
162C22×C4×C7C2×D411yescharacteristic
163C22×C4×C7C2×D411yescharacteristic
164C22×C4×C7C2×D411yescharacteristic
165C22×C4×C7C2×D411yescharacteristic
166C22×C4×C7C2411yescharacteristic
167C22×Dic7—21no—
168C22×Dic7—21no—
169C22×Dic7—21no—
170C2×D28—21no—
171C2×D28—21no—
172C2×D28—21no—
173C2×D28—21no—
174C2×D28—21no—
175C2×D28—21no—
176C7×C4⋊C4—24no—
177C7×C4⋊C4—24no—
178C7×C4⋊C4—21no—
179C7×C4⋊C4—21no—
180C7×C4⋊C4—21no—
181C7×C4⋊C4—41no—
182C7×C4⋊C4—42no—
183C7×C4⋊C4—42no—
184C7×C4⋊C4SD1614yescomplemented
185C7×C4⋊C4#4112yes—
186C42×C7—21no—
187C42×C7—21no—
188C42×C7—21no—
189C42×C7—21no—
190C42×C7—21no—
191C42×C7—21no—
192C42×C7—42no—
193C42×C7—42no—
194C42×C7—42no—
195#1143—44no—
196#1143—44no—
197(C2×D7)⋊C4—42no—
198(C2×D7)⋊C4—42no—
199(C2×D7)⋊C4—42no—
200(C2×D7)⋊C4—42no—
201(C2×D7)⋊C4—81no—
202(C2×D7)⋊C4—81no—
203C4⋊Dic7—21no—
204C4⋊Dic7—21no—
205C4⋊Dic7—21no—
206C4⋊Dic7—21no—
207C4⋊Dic7—21no—
208C4⋊Dic7—21no—
209C4⋊Dic7—42no—
210C4⋊Dic7—81no—
211Dic7⋊C4—42no—
212C4×Dic7—42no—
213C2×C7⋊C8—21no—
214C2×C7⋊C8—21no—
215C2×C7⋊C8—21no—
216C2×C7⋊C8—21no—
217C2×C7⋊C8—21no—
218C2×C7⋊C8—21no—
219C2×C7⋊C8—21no—
220C2×C7⋊C8—21no—
221C2×C7⋊C8—21no—
222C2×C7⋊C8—21no—
223C2×C7⋊C8—21no—
224C2×C7⋊C8#4112yes—
225C22×SD16—71no—
226C22×SD16—71no—
227C2×C4⋊Q8C2×D711yescharacteristic
228C2×#126—141no—
229C2×C4×Q8C2×D711yescharacteristic
230C2×C4×Q8C2×D711yescharacteristic
231C2×#106—71no—
232C2×#106—71no—
233C2×C4⋊C8—71no—
234C2×#103—71no—
235C2×#103—71no—
236C2×#103—71no—
237C2×#103—71no—
238C2×#103—71no—
239C2×#103—71no—
240C2×#102—71no—
241C2×#102—71no—
242C2×C4×C8—71no—
243#397—141no—
244#396—141no—
245#391C2×D711yescharacteristic
246#391C2×D711yescharacteristic
247#390—71no—
248#390—71no—
249#390—71no—
250#389—21no—
251#389—71no—
252#388—141no—
253#387—21no—
254#387—21no—
255#384—71no—
256C4×C4⋊C4—21no—
257C4×C4⋊C4—71no—
258C4×C4⋊C4C2×D711yescharacteristic
259C4×C4⋊C4C2×D711yescharacteristic
260#340—71no—
261#340—71no—
262#340—71no—
263#340—71no—
264#336—71no—
265#336—71no—
266#336—71no—
267#336—71no—
268C23×C7C22×D411yescharacteristic
269C22×D7—41no—
270C22×D7—41no—
271C22×D7—41no—
272C22×D7—41no—
273C22×D7—41no—
274C22×D7—41no—
275C22×D7—41no—
276C7×Q8—22no—
277C7×Q8—22no—
278C7×Q8—22no—
279C7×Q8—22no—
280C7×Q8—41no—
281C7×Q8—41no—
282C7×Q8—41no—
283C7×Q8—41no—
284C2×C4×C7—21no—
285C2×C4×C7—21no—
286C2×C4×C7—21no—
287C2×C4×C7—21no—
288C2×C4×C7—21no—
289C2×C4×C7—21no—
290C2×C4×C7—21no—
291C2×C4×C7—22no—
292C2×C4×C7—22no—
293C2×C4×C7—21no—
294C2×C4×C7—21no—
295C2×C4×C7—22no—
296C2×C4×C7—21no—
297C2×C4×C7—21no—
298C2×C4×C7—21no—
299C2×C4×C7—21no—
300C2×C4×C7—21no—
301C2×C4×C7—21no—
302C2×C4×C7—41no—
303C2×C4×C7—41no—
304C2×C4×C7—41no—
305C2×C4×C7—41no—
306C2×C4×C7—41no—
307C2×C4×C7—41no—
308C2×C4×C7—41no—
309C2×C4×C7—41no—
310C2×C4×C7—41no—
311C2×C4×C7C2×SD1612yes—
312C2×C4×C7C2×SD1612yes—
313C2×C4×C7C2×SD1612yes—
314C2×C4×C7C2×#4111yescharacteristic
315C2×C4×C7C2×#4111yescharacteristic
316C2×C4×C7C2×#4111yescharacteristic
317C2×C4×C7C2×#4111yescharacteristic
318C2×C4×C7H(5,𝔽2)11yescharacteristic
319C2×C4×C7H(5,𝔽2)11yescharacteristic
320C2×Dic7—41no—
321C2×Dic7—41no—
322C2×Dic7—41no—
323C2×Dic7—41no—
324C2×Dic7—41no—
325C2×Dic7—41no—
326C2×Dic7—41no—
327C2×Dic7—41no—
328C2×Dic7—41no—
329D28—41no—
330D28—41no—
331D28—41no—
332D28—41no—
333C7⋊C8—22no—
334C7⋊C8—41no—
335C7⋊C8—41no—
336C7⋊C8—41no—
337C22×Q8C22×D711yescharacteristic
338C22×Q8C22×D711yescharacteristic
339C22×D4—71no—
340C2×SD16—142no—
341C2×SD16—142no—
342C2×SD16—142no—
343C2×SD16—281no—
344C2×SD16—281no—
345C2×SD16—281no—
346C22×C8—71no—
347C22×C8—71no—
348C22×C8—71no—
349C22×C8—71no—
350C4⋊Q8—22no—
351C4⋊Q8—22no—
352#126—284no—
353C4×Q8—22no—
354C4×Q8—22no—
355C4×Q8—41no—
356C4×Q8—41no—
357C2×C4⋊C4—21no—
358C2×C4⋊C4—21no—
359C2×C4⋊C4—21no—
360C2×C4⋊C4—21no—
361C2×C4⋊C4—71no—
362C2×C4⋊C4—71no—
363C2×C4⋊C4—71no—
364C2×C4⋊C4—141no—
365C2×C4⋊C4—141no—
366C2×C4⋊C4—141no—
367C2×C4⋊C4C22⋊D711yescharacteristic
368C2×C4⋊C4C22⋊D711yescharacteristic
369C2×C4⋊C4C22×D711yescharacteristic
370C2×C4⋊C4C22×D711yescharacteristic
371C2×C22⋊C4—141no—
372C2×C22⋊C4—141no—
373C2×C22⋊C4—141no—
374C2×C22⋊C4—141no—
375C2×C22⋊C4—141no—
376C2×C22⋊C4—141no—
377C2×C42—21no—
378C2×C42—21no—
379C2×C42—21no—
380C2×C42—141no—
381C2×C42C22×D711yescharacteristic
382C2×C42C22×D711yescharacteristic
383C2×C42C22×D711yescharacteristic
384#106—142no—
385#106—281no—
386C4⋊C8—281no—
387#103—142no—
388#103—142no—
389#103—142no—
390#103—281no—
391#103—281no—
392#103—281no—
393#102—142no—
394#102—281no—
395C4×C8—281no—
396#95—21no—
397#95—21no—
398#95—21no—
399#95—21no—
400#95—21no—
401#95—141no—
402#95—141no—
403#95C22⋊D711yescharacteristic
404#95C22⋊D711yescharacteristic
405C22×C7#52511yescharacteristic
406C22×C7#54611yescharacteristic
407C22×C7#55011yescharacteristic
408C22×C7C22×SD1611yescharacteristic
409C22×C7#57511yescharacteristic
410C22×C7#57711yescharacteristic
411C22×C7#57811yescharacteristic
412C2×D7—81no—
413C2×D7—81no—
414C2×D7—81no—
415C2×D7—81no—
416C2×D7—81no—
417C2×D7—81no—
418C2×D7—81no—
419C4×C7—22no—
420C4×C7—22no—
421C4×C7—22no—
422C4×C7—41no—
423C4×C7—42no—
424C4×C7—42no—
425C4×C7—41no—
426C4×C7—41no—
427C4×C7—42no—
428C4×C7—81no—
429C4×C7#52911yescharacteristic
430C4×C7#53811yescharacteristic
431C4×C7#55111yescharacteristic
432C4×C7#55311yescharacteristic
433Dic7—81no—
434Dic7—81no—
435Dic7—81no—
436C24—141no—
437C2×Q8—21no—
438C2×Q8—21no—
439C2×Q8—21no—
440C2×Q8—21no—
441C2×Q8—21no—
442C2×Q8—21no—
443C2×Q8—21no—
444C2×Q8—21no—
445C2×Q8—21no—
446C2×Q8—21no—
447C2×Q8#115712yes—
448C2×Q8#115712yes—
449C2×D4—141no—
450C2×D4—141no—
451C2×D4—141no—
452C2×D4—141no—
453C2×D4—141no—
454C2×D4—141no—
455C22×C4—21no—
456C22×C4—21no—
457C22×C4—21no—
458C22×C4—21no—
459C22×C4—141no—
460C22×C4—141no—
461C22×C4—141no—
462C22×C4C2×C22⋊D711yescharacteristic
463C22×C4C2×C22⋊D711yescharacteristic
464C22×C4C2×C22⋊D711yescharacteristic
465C22×C4C2×C22⋊D711yescharacteristic
466C22×C4C2×C22⋊D711yescharacteristic
467C22×C4C2×C22⋊D711yescharacteristic
468C22×C4C23×D711yescharacteristic
469SD16—284no—
470SD16—284no—
471C2×C8—72no—
472C2×C8—141no—
473C2×C8—141no—
474C2×C8—141no—
475C2×C8—141no—
476C2×C8—141no—
477C2×C8—141no—
478C2×C8—141no—
479C2×C8—141no—
480C2×C8—141no—
481C2×C8—141no—
482C2×C8—141no—
483C4⋊C4—24no—
484C4⋊C4—24no—
485C4⋊C4—21no—
486C4⋊C4—21no—
487C4⋊C4—21no—
488C4⋊C4—41no—
489C4⋊C4—42no—
490C4⋊C4—42no—
491C4⋊C4—141no—
492C4⋊C4—141no—
493C4⋊C4—141no—
494C4⋊C4—141no—
495C4⋊C4—141no—
496C4⋊C4—141no—
497C4⋊C4—282no—
498C4⋊C4—282no—
499C4⋊C4—561no—
500C4⋊C4#114314yescomplemented
501C4⋊C4#115912yes—
502C22⋊C4—282no—
503C22⋊C4—282no—
504C22⋊C4—282no—
505C22⋊C4—282no—
506C22⋊C4—561no—
507C22⋊C4—561no—
508C42—21no—
509C42—21no—
510C42—21no—
511C42—21no—
512C42—21no—
513C42—21no—
514C42—42no—
515C42—42no—
516C42—42no—
517C42—282no—
518C2×C7#246711yescharacteristic
519C2×C7#310311yescharacteristic
520C2×C7#312111yescharacteristic
521C2×C7#329811yescharacteristic
522C2×C7#330711yescharacteristic
523C2×C7#339211yescharacteristic
524C2×C7#340211yescharacteristic
525D7—161no—
526C23—281no—
527C23—281no—
528C23—281no—
529C23—281no—
530C23—281no—
531C23—281no—
532C23—281no—
533C23C22×C22⋊D711yescharacteristic
534Q8—22no—
535Q8—22no—
536Q8—22no—
537Q8—22no—
538Q8—41no—
539Q8—41no—
540Q8—41no—
541Q8—41no—
542D4—281no—
543D4—281no—
544D4—281no—
545D4—281no—
546C2×C4—21no—
547C2×C4—21no—
548C2×C4—21no—
549C2×C4—21no—
550C2×C4—21no—
551C2×C4—21no—
552C2×C4—21no—
553C2×C4—22no—
554C2×C4—22no—
555C2×C4—21no—
556C2×C4—21no—
557C2×C4—22no—
558C2×C4—21no—
559C2×C4—21no—
560C2×C4—21no—
561C2×C4—21no—
562C2×C4—21no—
563C2×C4—21no—
564C2×C4—41no—
565C2×C4—41no—
566C2×C4—41no—
567C2×C4—41no—
568C2×C4—41no—
569C2×C4—41no—
570C2×C4—41no—
571C2×C4—41no—
572C2×C4—41no—
573C2×C4—281no—
574C2×C4—281no—
575C2×C4—281no—
576C2×C4—281no—
577C2×C4—281no—
578C2×C4—281no—
579C2×C4—281no—
580C2×C4—281no—
581C2×C4—281no—
582C2×C4C2×#114312yes—
583C2×C4C2×#114312yes—
584C2×C4C2×#114312yes—
585C2×C4C2×#115711yescharacteristic
586C2×C4C2×#115711yescharacteristic
587C2×C4C2×#115911yescharacteristic
588C2×C4#654811yescharacteristic
589C2×C4D7×#4111yescharacteristic
590C2×C4#655311yescharacteristic
591C8—142no—
592C8—281no—
593C8—281no—
594C8—281no—
595C7#2706611yescharacteristic, complemented, Sylow
596C22—561no—
597C22—561no—
598C22—561no—
599C22—561no—
600C22—561no—
601C22—561no—
602C22—561no—
603C22#9048211yescharacteristic
604C22#9049711yescharacteristic
605C22C22×#114311yescharacteristic
606C22#9051311yescharacteristic
607C22#9052511yescharacteristic
608C22#9052811yescharacteristic
609C22#9052911yescharacteristic
610C4—22no—
611C4—22no—
612C4—22no—
613C4—41no—
614C4—41no—
615C4—42no—
616C4—41no—
617C4—42no—
618C4—42no—
619C4—81no—
620C4—561no—
621C4—561no—
622C4—561no—
623C4#9022911yescharacteristic
624C4#9024711yescharacteristic
625C4#9025111yescharacteristic
626C4#9025611yescharacteristic
627C2—1121no—
628C2#1173981511yescharacteristic
629C2#1173988711yescharacteristic
630C2#1173999711yescharacteristic
631C2#1174095711yescharacteristic
632C2#1174099511yescharacteristic
633C2#1174112611yescharacteristic
634C2#1174113011yescharacteristic
subgroupG/H
centerC23C22×C22⋊D7
commutator, cosocleC22×C4×C7C24
FrattiniC22×C4C23×D7
FittingC7×#2365C2
socleC23×C7C22×D4
prime radicalC22×D28C23
hypercenter#2365D7
hypocenterC7#27066
LCSG ▷ C22×C4×C7 ▷ C2×C7 ▷ C7
UCSC1 ◁ C23 ◁ C4×C4⋊C4 ◁ #2365

Complements

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

NH ≅ G/Ntype
1. C7×#2365C2semidirect
4. #11729535C2semidirect
7. C4×#6409C2semidirect
8. #11729380C2semidirect
9. #11727439C2semidirect
12. #11727420C2semidirect
13. #11727236C2semidirect
15. #11727213C2semidirect
129. #2365D7semidirect
184. C7×C4⋊C4SD16semidirect
500. C4⋊C4#1143semidirect
595. C7#27066semidirect

Maximal subgroups

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

subgroupindex
C7×#23652
#117311372
#117295452
#117295352
#117293872
C4×#64092
#117293802
#117274392
#117274342
#117274302
#117274202
#117272362
#117272172
#117272132
#270667