Finite Group Databasebeta

← #13427017

Subgroups — #13427017

Order 1792.

708 conjugacy classes of subgroups.

The subgroup lattice has 600 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C7×#2365C211yesmaximal, characteristic
2#11731135C211yesmaximal, characteristic
3#11729547C211yesmaximal, characteristic
4#11729535C211yesmaximal, characteristic
5#11729386C211yesmaximal, characteristic
6#11729386C211yesmaximal, characteristic
7C4×#6409C211yesmaximal, characteristic
8#11729380C211yesmaximal, characteristic
9#11727438C211yesmaximal, characteristic
10#11727435C211yesmaximal, characteristic
11#11727431C211yesmaximal, characteristic
12#11727421C211yesmaximal, characteristic
13#11727236C211yesmaximal, characteristic
14#11727219C211yesmaximal, characteristic
15#11727215C211yesmaximal, characteristic
16C2×C7×C4⋊Q8C2211yescharacteristic
17C2×C4×C7×Q8C2211yescharacteristic
18C2×C4×C7×Q8C2211yescharacteristic
19C22×#1144C2211yescharacteristic
20C22×#1144C2211yescharacteristic
21C7×#391C2211yescharacteristic
22C7×#391C2211yescharacteristic
23C7×#389—21no—
24C7×#387—21no—
25C7×#387—21no—
26C4×C7×C4⋊C4—21no—
27C4×C7×C4⋊C4C2211yescharacteristic
28C4×C7×C4⋊C4C2211yescharacteristic
29C2×#6409C2211yescharacteristic
30C2×#6409C2211yescharacteristic
31C2×#6409C2211yescharacteristic
32C2×#6409C2211yescharacteristic
33C2×#6409C2211yescharacteristic
34C2×#6409C2211yescharacteristic
35#89758—21no—
36#89753—21no—
37C2×#6384C2211yescharacteristic
38C2×#6384C2211yescharacteristic
39C2×#6381C2211yescharacteristic
40C2×#6381C2211yescharacteristic
41#89707C2211yescharacteristic
42C4×C4⋊Dic7C2211yescharacteristic
43#89701C2211yescharacteristic
44#89701C2211yescharacteristic
45#89701C2211yescharacteristic
46#89700C2211yescharacteristic
47C2×C4⋊(C7⋊C8)C2211yescharacteristic
48C2×C4×C7⋊C8C2211yescharacteristic
49#89432—21no—
50#89426—21no—
51#89324C2211yescharacteristic
52#89324C2211yescharacteristic
53#89324C2211yescharacteristic
54#89324C2211yescharacteristic
55#89319C2211yescharacteristic
56#89319C2211yescharacteristic
57#89319C2211yescharacteristic
58#89319C2211yescharacteristic
59#27068—71nomaximal, Sylow
60C22×C7×Q8C2311yescharacteristic
61C22×C7×Q8C2311yescharacteristic
62C22×Dic14C2311yescharacteristic
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×#1144—22no—
84C2×#1144—22no—
85C2×#1144—22no—
86C2×#1144—41no—
87C2×#1144—41no—
88C2×#1144—41no—
89C2×C4⋊Dic7—21no—
90C2×C4⋊Dic7—21no—
91C2×C4⋊Dic7C2311yescharacteristic
92C2×C4⋊Dic7C2311yescharacteristic
93C2×C4⋊Dic7C2311yescharacteristic
94C2×Dic7⋊C4—21no—
95C2×C4×Dic7—21no—
96C22×C7⋊C8C2311yescharacteristic
97C22×C7⋊C8C2311yescharacteristic
98C22×C7⋊C8C2311yescharacteristic
99C22×C7⋊C8C2311yescharacteristic
100C7×#95—21no—
101C7×#95—21no—
102C7×#95—21no—
103C7×#95—21no—
104C7×#95—21no—
105C7×#95D411yescharacteristic
106C7×#95D411yescharacteristic
107#6409—22no—
108#6409—22no—
109#6409—22no—
110#6409—41no—
111#6409—41no—
112#6409—41no—
113C7⋊#95—21no—
114C7⋊#95—21no—
115C7⋊#95—21no—
116C7⋊#95—21no—
117C7⋊#95—21no—
118C7⋊#95—21no—
119C7⋊#95—21no—
120C7⋊#95—21no—
121#6384—22no—
122#6384—41no—
123#6381—22no—
124#6381—41no—
125C4⋊(C7⋊C8)—41no—
126C4×C7⋊C8—41no—
127#2511—71no—
128#2365D711yescharacteristic
129#2095—71no—
130#2056—71no—
131#2043—71no—
132#2016—71no—
133#1969—71no—
134#1928—71no—
135#1928—71no—
136#1921—71no—
137#1916—71no—
138#1878—71no—
139#1878—71no—
140#1803—71no—
141C4×#103—71no—
142C2×C7×Q8—21no—
143C2×C7×Q8—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#4112yes—
153C2×C7×Q8#4112yes—
154C22×C4×C7—21no—
155C22×C4×C7—21no—
156C22×C4×C7—21no—
157C22×C4×C7—21no—
158C22×C4×C7C2×D411yescharacteristic
159C22×C4×C7C2×D411yescharacteristic
160C22×C4×C7C2×D411yescharacteristic
161C22×C4×C7C2×D411yescharacteristic
162C22×C4×C7C2×D411yescharacteristic
163C22×C4×C7C2×D411yescharacteristic
164C22×C4×C7C2411yescharacteristic
165C22×Dic7—21no—
166C22×Dic7—21no—
167C22×Dic7—21no—
168C22×Dic7—21no—
169C2×Dic14—21no—
170C2×Dic14—21no—
171C2×Dic14—21no—
172C2×Dic14—21no—
173C2×Dic14—21no—
174C2×Dic14—21no—
175C7×C4⋊C4—24no—
176C7×C4⋊C4—24no—
177C7×C4⋊C4—21no—
178C7×C4⋊C4—21no—
179C7×C4⋊C4—21no—
180C7×C4⋊C4—41no—
181C7×C4⋊C4—42no—
182C7×C4⋊C4—42no—
183C7×C4⋊C4Q1614yescomplemented
184C7×C4⋊C4#4112yes—
185C42×C7—21no—
186C42×C7—21no—
187C42×C7—21no—
188C42×C7—21no—
189C42×C7—21no—
190C42×C7—21no—
191C42×C7—42no—
192C42×C7—42no—
193C42×C7—42no—
194#1144—44no—
195#1144—44no—
196C4⋊Dic7—21no—
197C4⋊Dic7—21no—
198C4⋊Dic7—21no—
199C4⋊Dic7—21no—
200C4⋊Dic7—21no—
201C4⋊Dic7—21no—
202C4⋊Dic7—42no—
203C4⋊Dic7—81no—
204Dic7⋊C4—81no—
205C4×Dic7—81no—
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⋊C8—21no—
217C2×C7⋊C8#4112yes—
218C22×Q16—71no—
219C22×Q16—71no—
220C2×C4⋊Q8C2×D711yescharacteristic
221C2×C4×Q8C2×D711yescharacteristic
222C2×C4×Q8C2×D711yescharacteristic
223C2×#107—71no—
224C2×#107—71no—
225C2×C4⋊C8—71no—
226C2×#103—71no—
227C2×#103—71no—
228C2×#103—71no—
229C2×#103—71no—
230C2×#103—71no—
231C2×#103—71no—
232C2×#103—71no—
233C2×#103—71no—
234C2×C4×C8—71no—
235#400—141no—
236#400—141no—
237#391—71no—
238#391—71no—
239#391—71no—
240#391C2×D711yescharacteristic
241#391C2×D711yescharacteristic
242#389—21no—
243#389—71no—
244#387—21no—
245#387—21no—
246#387—141no—
247#387—141no—
248#384—71no—
249C4×C4⋊C4—21no—
250C4×C4⋊C4—71no—
251C4×C4⋊C4C2×D711yescharacteristic
252C4×C4⋊C4C2×D711yescharacteristic
253#340—71no—
254#340—71no—
255#340—71no—
256#340—71no—
257#336—71no—
258#336—71no—
259#336—71no—
260#336—71no—
261C23×C7C22×D411yescharacteristic
262C7×Q8—22no—
263C7×Q8—22no—
264C7×Q8—22no—
265C7×Q8—22no—
266C7×Q8—41no—
267C7×Q8—41no—
268C7×Q8—41no—
269C7×Q8—41no—
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—22no—
278C2×C4×C7—22no—
279C2×C4×C7—21no—
280C2×C4×C7—21no—
281C2×C4×C7—22no—
282C2×C4×C7—21no—
283C2×C4×C7—21no—
284C2×C4×C7—21no—
285C2×C4×C7—21no—
286C2×C4×C7—21no—
287C2×C4×C7—21no—
288C2×C4×C7—41no—
289C2×C4×C7—41no—
290C2×C4×C7—41no—
291C2×C4×C7—41no—
292C2×C4×C7—41no—
293C2×C4×C7—41no—
294C2×C4×C7—41no—
295C2×C4×C7—41no—
296C2×C4×C7—41no—
297C2×C4×C7C2×Q1612yes—
298C2×C4×C7C2×Q1612yes—
299C2×C4×C7C2×Q1612yes—
300C2×C4×C7C2×#4111yescharacteristic
301C2×C4×C7C2×#4111yescharacteristic
302C2×C4×C7C2×#4111yescharacteristic
303C2×C4×C7C2×#4111yescharacteristic
304C2×C4×C7H(5,𝔽2)11yescharacteristic
305C2×C4×C7H(5,𝔽2)11yescharacteristic
306C2×Dic7—41no—
307C2×Dic7—41no—
308C2×Dic7—41no—
309C2×Dic7—41no—
310C2×Dic7—41no—
311C2×Dic7—41no—
312C2×Dic7—41no—
313C2×Dic7—41no—
314C2×Dic7—41no—
315C2×Dic7—41no—
316C2×Dic7—41no—
317C2×Dic7—41no—
318Dic14—41no—
319Dic14—41no—
320Dic14—41no—
321Dic14—41no—
322C7⋊C8—22no—
323C7⋊C8—41no—
324C7⋊C8—41no—
325C7⋊C8—41no—
326C22×Q8—71no—
327C22×Q8C22×D711yescharacteristic
328C22×Q8C22×D711yescharacteristic
329C2×Q16—142no—
330C2×Q16—142no—
331C2×Q16—142no—
332C2×Q16—281no—
333C2×Q16—281no—
334C2×Q16—281no—
335C22×C8—71no—
336C22×C8—71no—
337C22×C8—71no—
338C22×C8—71no—
339C4⋊Q8—22no—
340C4⋊Q8—22no—
341C4×Q8—22no—
342C4×Q8—22no—
343C4×Q8—41no—
344C4×Q8—41no—
345C2×C4⋊C4—21no—
346C2×C4⋊C4—21no—
347C2×C4⋊C4—21no—
348C2×C4⋊C4—21no—
349C2×C4⋊C4—71no—
350C2×C4⋊C4—71no—
351C2×C4⋊C4—71no—
352C2×C4⋊C4—141no—
353C2×C4⋊C4—141no—
354C2×C4⋊C4—141no—
355C2×C4⋊C4C22⋊D711yescharacteristic
356C2×C4⋊C4C22⋊D711yescharacteristic
357C2×C4⋊C4C22×D711yescharacteristic
358C2×C4⋊C4C22×D711yescharacteristic
359C2×C42—21no—
360C2×C42—21no—
361C2×C42—21no—
362C2×C42—141no—
363C2×C42C22×D711yescharacteristic
364C2×C42C22×D711yescharacteristic
365C2×C42C22×D711yescharacteristic
366#107—142no—
367#107—281no—
368C4⋊C8—281no—
369#103—142no—
370#103—142no—
371#103—142no—
372#103—142no—
373#103—281no—
374#103—281no—
375#103—281no—
376#103—281no—
377C4×C8—281no—
378#95—21no—
379#95—21no—
380#95—21no—
381#95—21no—
382#95—21no—
383#95—141no—
384#95—141no—
385#95—141no—
386#95—141no—
387#95—141no—
388#95—141no—
389#95—141no—
390#95—141no—
391#95C22⋊D711yescharacteristic
392#95C22⋊D711yescharacteristic
393C22×C7#52511yescharacteristic
394C22×C7#54611yescharacteristic
395C22×C7#55011yescharacteristic
396C22×C7C22×Q1611yescharacteristic
397C22×C7#57511yescharacteristic
398C22×C7#57711yescharacteristic
399C22×C7#57811yescharacteristic
400C4×C7—22no—
401C4×C7—22no—
402C4×C7—22no—
403C4×C7—41no—
404C4×C7—42no—
405C4×C7—42no—
406C4×C7—41no—
407C4×C7—41no—
408C4×C7—42no—
409C4×C7—81no—
410C4×C7#52911yescharacteristic
411C4×C7#53811yescharacteristic
412C4×C7#55111yescharacteristic
413C4×C7#55311yescharacteristic
414Dic7—81no—
415Dic7—81no—
416Dic7—81no—
417Dic7—81no—
418C2×Q8—21no—
419C2×Q8—21no—
420C2×Q8—21no—
421C2×Q8—21no—
422C2×Q8—21no—
423C2×Q8—21no—
424C2×Q8—21no—
425C2×Q8—21no—
426C2×Q8—21no—
427C2×Q8—21no—
428C2×Q8—141no—
429C2×Q8—141no—
430C2×Q8—141no—
431C2×Q8—141no—
432C2×Q8—141no—
433C2×Q8—141no—
434C2×Q8#115712yes—
435C2×Q8#115712yes—
436C22×C4—21no—
437C22×C4—21no—
438C22×C4—21no—
439C22×C4—21no—
440C22×C4—141no—
441C22×C4—141no—
442C22×C4—141no—
443C22×C4—141no—
444C22×C4C2×C22⋊D711yescharacteristic
445C22×C4C2×C22⋊D711yescharacteristic
446C22×C4C2×C22⋊D711yescharacteristic
447C22×C4C2×C22⋊D711yescharacteristic
448C22×C4C2×C22⋊D711yescharacteristic
449C22×C4C2×C22⋊D711yescharacteristic
450C22×C4C23×D711yescharacteristic
451Q16—284no—
452Q16—284no—
453C2×C8—72no—
454C2×C8—141no—
455C2×C8—141no—
456C2×C8—141no—
457C2×C8—141no—
458C2×C8—141no—
459C2×C8—141no—
460C2×C8—141no—
461C2×C8—141no—
462C2×C8—141no—
463C2×C8—141no—
464C2×C8—141no—
465C4⋊C4—24no—
466C4⋊C4—24no—
467C4⋊C4—21no—
468C4⋊C4—21no—
469C4⋊C4—21no—
470C4⋊C4—41no—
471C4⋊C4—42no—
472C4⋊C4—42no—
473C4⋊C4—141no—
474C4⋊C4—141no—
475C4⋊C4—141no—
476C4⋊C4—141no—
477C4⋊C4—141no—
478C4⋊C4—141no—
479C4⋊C4—282no—
480C4⋊C4—561no—
481C4⋊C4—561no—
482C4⋊C4#114414yescomplemented
483C4⋊C4#115912yes—
484C42—21no—
485C42—21no—
486C42—21no—
487C42—21no—
488C42—21no—
489C42—21no—
490C42—42no—
491C42—42no—
492C42—42no—
493C42—561no—
494C2×C7#246711yescharacteristic
495C2×C7#310411yescharacteristic
496C2×C7#312111yescharacteristic
497C2×C7#329911yescharacteristic
498C2×C7#331511yescharacteristic
499C2×C7#339511yescharacteristic
500C2×C7#340111yescharacteristic
501C23C22×C22⋊D711yescharacteristic
502Q8—22no—
503Q8—22no—
504Q8—22no—
505Q8—22no—
506Q8—41no—
507Q8—41no—
508Q8—41no—
509Q8—41no—
510Q8—281no—
511Q8—281no—
512Q8—281no—
513Q8—281no—
514C2×C4—21no—
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—22no—
526C2×C4—21no—
527C2×C4—21no—
528C2×C4—21no—
529C2×C4—21no—
530C2×C4—21no—
531C2×C4—21no—
532C2×C4—41no—
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—281no—
542C2×C4—281no—
543C2×C4—281no—
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—281no—
553C2×C4C2×#114412yes—
554C2×C4C2×#114412yes—
555C2×C4C2×#114412yes—
556C2×C4C2×#115711yescharacteristic
557C2×C4C2×#115711yescharacteristic
558C2×C4C2×#115911yescharacteristic
559C2×C4#654811yescharacteristic
560C2×C4D7×#4111yescharacteristic
561C2×C4#655311yescharacteristic
562C8—142no—
563C8—281no—
564C8—281no—
565C8—281no—
566C7#2706811yescharacteristic, complemented, Sylow
567C22#9048211yescharacteristic
568C22#9049711yescharacteristic
569C22C22×#114411yescharacteristic
570C22#9051311yescharacteristic
571C22#9052511yescharacteristic
572C22#9052811yescharacteristic
573C22#9052911yescharacteristic
574C4—22no—
575C4—22no—
576C4—22no—
577C4—41no—
578C4—41no—
579C4—42no—
580C4—41no—
581C4—42no—
582C4—42no—
583C4—81no—
584C4—561no—
585C4—561no—
586C4—561no—
587C4—561no—
588C4#9022911yescharacteristic
589C4#9024711yescharacteristic
590C4#9025111yescharacteristic
591C4#9025611yescharacteristic
592C2#1173981511yescharacteristic
593C2#1173989211yescharacteristic
594C2#1173999711yescharacteristic
595C2#1174095811yescharacteristic
596C2#1174099611yescharacteristic
597C2#1174111711yescharacteristic
598C2#1174114611yescharacteristic
subgroupG/H
centerC23C22×C22⋊D7
commutator, cosocleC22×C4×C7C24
FrattiniC22×C4C23×D7
FittingC7×#2365C2
socle, prime radicalC23×C7C22×D4
hypercenter#2365D7
hypocenterC7#27068
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
183. C7×C4⋊C4Q16semidirect
482. C4⋊C4#1144semidirect
566. C7#27068semidirect

Maximal subgroups

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

subgroupindex
C7×#23652
#117311352
#117295472
#117295352
#117293862
C4×#64092
#117293802
#117274382
#117274352
#117274312
#117274212
#117272362
#117272192
#117272152
#270687