Finite Group Databasebeta

← #13427002

Subgroups — #13427002

Order 1792.

700 conjugacy classes of subgroups.

The subgroup lattice has 596 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C7×#2365C211yesmaximal, characteristic
2#11731141C211yesmaximal, characteristic
3#11729547C211yesmaximal, characteristic
4#11729535C211yesmaximal, characteristic
5#11729386C211yesmaximal, characteristic
6#11729386C211yesmaximal, characteristic
7C4×#6409C211yesmaximal, characteristic
8#11729381C211yesmaximal, characteristic
9#11727440C211yesmaximal, characteristic
10#11727435C211yesmaximal, characteristic
11#11727431C211yesmaximal, characteristic
12#11727420C211yesmaximal, characteristic
13#11727236C211yesmaximal, characteristic
14#11727218C211yesmaximal, characteristic
15#11727212C211yesmaximal, 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#89754—21no—
36#89750—21no—
37C2×#6384C2211yescharacteristic
38C2×#6384C2211yescharacteristic
39C2×#6382C2211yescharacteristic
40C2×#6381C2211yescharacteristic
41#89708C2211yescharacteristic
42C4×C4⋊Dic7C2211yescharacteristic
43#89701C2211yescharacteristic
44#89701C2211yescharacteristic
45#89701C2211yescharacteristic
46#89700C2211yescharacteristic
47C2×C4⋊(C7⋊C8)C2211yescharacteristic
48C2×C4×C7⋊C8C2211yescharacteristic
49C7⋊#401—21no—
50#89423—21no—
51#89324C2211yescharacteristic
52#89324C2211yescharacteristic
53#89324C2211yescharacteristic
54#89324C2211yescharacteristic
55#89319C2211yescharacteristic
56#89319C2211yescharacteristic
57#89319C2211yescharacteristic
58#89319C2211yescharacteristic
59#27067—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⋊Dic7C2311yescharacteristic
90C2×C4⋊Dic7C2311yescharacteristic
91C2×C4⋊Dic7C2311yescharacteristic
92C2×Dic7⋊C4—21no—
93C2×C4×Dic7—21no—
94C22×C7⋊C8C2311yescharacteristic
95C22×C7⋊C8C2311yescharacteristic
96C22×C7⋊C8C2311yescharacteristic
97C22×C7⋊C8C2311yescharacteristic
98C7×#95—21no—
99C7×#95—21no—
100C7×#95—21no—
101C7×#95—21no—
102C7×#95—21no—
103C7×#95D411yescharacteristic
104C7×#95D411yescharacteristic
105#6409—22no—
106#6409—22no—
107#6409—22no—
108#6409—41no—
109#6409—41no—
110#6409—41no—
111C7⋊#95—21no—
112C7⋊#95—21no—
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#6382—41no—
124#6381—22no—
125C4⋊(C7⋊C8)—41no—
126C4×C7⋊C8—41no—
127#2514—71no—
128#2365D711yescharacteristic
129#2097—71no—
130#2056—71no—
131#2043—71no—
132#2016—71no—
133#1969—71no—
134#1927—71no—
135#1927—71no—
136#1918—71no—
137#1916—71no—
138#1878—71no—
139#1878—71no—
140#1805—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—22no—
178C7×C4⋊C4—22no—
179C7×C4⋊C4—21no—
180C7×C4⋊C4—21no—
181C7×C4⋊C4—21no—
182C7×C4⋊C4—42no—
183C7×C4⋊C4—42no—
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—
202Dic7⋊C4—42no—
203C4×Dic7—42no—
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×C7⋊C8—21no—
214C2×C7⋊C8—21no—
215C2×C7⋊C8#4112yes—
216C22×Q16—71no—
217C22×Q16—71no—
218C2×C4⋊Q8C2×D711yescharacteristic
219C2×C4×Q8C2×D711yescharacteristic
220C2×C4×Q8C2×D711yescharacteristic
221C2×#107—71no—
222C2×#106—71no—
223C2×C4⋊C8—71no—
224C2×#103—71no—
225C2×#103—71no—
226C2×#103—71no—
227C2×#103—71no—
228C2×#103—71no—
229C2×#103—71no—
230C2×#103—71no—
231C2×#103—71no—
232C2×C4×C8—71no—
233#401—141no—
234#400—141no—
235#391—71no—
236#391—71no—
237#391—71no—
238#391C2×D711yescharacteristic
239#391C2×D711yescharacteristic
240#389—21no—
241#389—71no—
242#387—21no—
243#387—21no—
244#387—141no—
245#383—141no—
246#382—71no—
247C4×C4⋊C4—21no—
248C4×C4⋊C4—71no—
249C4×C4⋊C4C2×D711yescharacteristic
250C4×C4⋊C4C2×D711yescharacteristic
251#340—71no—
252#340—71no—
253#340—71no—
254#340—71no—
255#336—71no—
256#336—71no—
257#336—71no—
258#336—71no—
259C23×C7C22×D411yescharacteristic
260C7×Q8—22no—
261C7×Q8—22no—
262C7×Q8—22no—
263C7×Q8—22no—
264C7×Q8—41no—
265C7×Q8—41no—
266C7×Q8—41no—
267C7×Q8—41no—
268C2×C4×C7—21no—
269C2×C4×C7—21no—
270C2×C4×C7—21no—
271C2×C4×C7—21no—
272C2×C4×C7—21no—
273C2×C4×C7—22no—
274C2×C4×C7—22no—
275C2×C4×C7—21no—
276C2×C4×C7—21no—
277C2×C4×C7—21no—
278C2×C4×C7—22no—
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—21no—
287C2×C4×C7—41no—
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#13512yes—
297C2×C4×C7#13712yes—
298C2×C4×C7C2×#4111yescharacteristic
299C2×C4×C7C2×#4111yescharacteristic
300C2×C4×C7C2×#4111yescharacteristic
301C2×C4×C7C2×#4111yescharacteristic
302C2×C4×C7H(5,𝔽2)11yescharacteristic
303C2×C4×C7H(5,𝔽2)11yescharacteristic
304C2×Dic7—41no—
305C2×Dic7—41no—
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—
316Dic14—41no—
317Dic14—41no—
318Dic14—41no—
319Dic14—41no—
320C7⋊C8—22no—
321C7⋊C8—41no—
322C7⋊C8—41no—
323C7⋊C8—41no—
324C22×Q8—71no—
325C22×Q8C22×D711yescharacteristic
326C22×Q8C22×D711yescharacteristic
327C2×Q16—142no—
328C2×Q16—142no—
329C2×Q16—142no—
330C2×Q16—281no—
331C2×Q16—281no—
332C2×Q16—281no—
333C22×C8—71no—
334C22×C8—71no—
335C22×C8—71no—
336C22×C8—71no—
337C4⋊Q8—22no—
338C4⋊Q8—22no—
339C4×Q8—22no—
340C4×Q8—22no—
341C4×Q8—41no—
342C4×Q8—41no—
343C2×C4⋊C4—21no—
344C2×C4⋊C4—21no—
345C2×C4⋊C4—21no—
346C2×C4⋊C4—21no—
347C2×C4⋊C4—71no—
348C2×C4⋊C4—71no—
349C2×C4⋊C4—71no—
350C2×C4⋊C4—141no—
351C2×C4⋊C4C22⋊D711yescharacteristic
352C2×C4⋊C4C22⋊D711yescharacteristic
353C2×C4⋊C4C22×D711yescharacteristic
354C2×C4⋊C4C22×D711yescharacteristic
355C2×C42—21no—
356C2×C42—21no—
357C2×C42—21no—
358C2×C42—141no—
359C2×C42C22×D711yescharacteristic
360C2×C42C22×D711yescharacteristic
361C2×C42C22×D711yescharacteristic
362#107—142no—
363#106—281no—
364C4⋊C8—281no—
365#103—142no—
366#103—142no—
367#103—142no—
368#103—142no—
369#103—281no—
370#103—281no—
371#103—281no—
372#103—281no—
373C4×C8—281no—
374#95—21no—
375#95—21no—
376#95—21no—
377#95—21no—
378#95—21no—
379#95—141no—
380#95—141no—
381#95—141no—
382#95—141no—
383#95—141no—
384#95—141no—
385#95—141no—
386#95—141no—
387#95—141no—
388#95—141no—
389#95C22⋊D711yescharacteristic
390#95C22⋊D711yescharacteristic
391C22×C7#52511yescharacteristic
392C22×C7#54611yescharacteristic
393C22×C7#55011yescharacteristic
394C22×C7C2×#13511yescharacteristic
395C22×C7C2×#13711yescharacteristic
396C22×C7#57811yescharacteristic
397C22×C7#57811yescharacteristic
398C4×C7—22no—
399C4×C7—22no—
400C4×C7—41no—
401C4×C7—42no—
402C4×C7—42no—
403C4×C7—41no—
404C4×C7—41no—
405C4×C7—42no—
406C4×C7—41no—
407C4×C7—81no—
408C4×C7#52911yescharacteristic
409C4×C7#53811yescharacteristic
410C4×C7#55111yescharacteristic
411C4×C7#55311yescharacteristic
412Dic7—81no—
413Dic7—81no—
414Dic7—81no—
415Dic7—81no—
416C2×Q8—21no—
417C2×Q8—21no—
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—141no—
427C2×Q8—141no—
428C2×Q8—141no—
429C2×Q8—141no—
430C2×Q8—141no—
431C2×Q8—141no—
432C2×Q8#115712yes—
433C2×Q8#115712yes—
434C22×C4—21no—
435C22×C4—21no—
436C22×C4—21no—
437C22×C4—21no—
438C22×C4—141no—
439C22×C4—141no—
440C22×C4—141no—
441C22×C4—141no—
442C22×C4C2×C22⋊D711yescharacteristic
443C22×C4C2×C22⋊D711yescharacteristic
444C22×C4C2×C22⋊D711yescharacteristic
445C22×C4C2×C22⋊D711yescharacteristic
446C22×C4C2×C22⋊D711yescharacteristic
447C22×C4C2×C22⋊D711yescharacteristic
448C22×C4C23×D711yescharacteristic
449Q16—284no—
450Q16—284no—
451C2×C8—72no—
452C2×C8—141no—
453C2×C8—141no—
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—
463C4⋊C4—24no—
464C4⋊C4—24no—
465C4⋊C4—22no—
466C4⋊C4—22no—
467C4⋊C4—21no—
468C4⋊C4—21no—
469C4⋊C4—21no—
470C4⋊C4—42no—
471C4⋊C4—42no—
472C4⋊C4—141no—
473C4⋊C4—141no—
474C4⋊C4—141no—
475C4⋊C4—141no—
476C4⋊C4—141no—
477C4⋊C4—141no—
478C4⋊C4—282no—
479C4⋊C4#115912yes—
480C42—21no—
481C42—21no—
482C42—21no—
483C42—21no—
484C42—21no—
485C42—21no—
486C42—42no—
487C42—42no—
488C42—42no—
489C42—282no—
490C2×C7#246711yescharacteristic
491C2×C7#310811yescharacteristic
492C2×C7#312711yescharacteristic
493C2×C7#330211yescharacteristic
494C2×C7#331211yescharacteristic
495C2×C7#339311yescharacteristic
496C2×C7#339811yescharacteristic
497C23C22×C22⋊D711yescharacteristic
498Q8—22no—
499Q8—22no—
500Q8—22no—
501Q8—22no—
502Q8—41no—
503Q8—41no—
504Q8—41no—
505Q8—41no—
506Q8—281no—
507Q8—281no—
508Q8—281no—
509Q8—281no—
510C2×C4—21no—
511C2×C4—21no—
512C2×C4—21no—
513C2×C4—21no—
514C2×C4—21no—
515C2×C4—22no—
516C2×C4—22no—
517C2×C4—21no—
518C2×C4—21no—
519C2×C4—21no—
520C2×C4—22no—
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—41no—
530C2×C4—41no—
531C2×C4—41no—
532C2×C4—41no—
533C2×C4—41no—
534C2×C4—41no—
535C2×C4—41no—
536C2×C4—41no—
537C2×C4—41no—
538C2×C4—281no—
539C2×C4—281no—
540C2×C4—281no—
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#650512yes—
551C2×C4#651312yes—
552C2×C4C2×#115711yescharacteristic
553C2×C4C2×#115711yescharacteristic
554C2×C4C2×#115911yescharacteristic
555C2×C4#654811yescharacteristic
556C2×C4D7×#4111yescharacteristic
557C2×C4#655311yescharacteristic
558C8—142no—
559C8—281no—
560C8—281no—
561C8—281no—
562C7#2706711yescharacteristic, complemented, Sylow
563C22#9048211yescharacteristic
564C22#9049711yescharacteristic
565C22C2×#650511yescharacteristic
566C22C2×#651311yescharacteristic
567C22#9052511yescharacteristic
568C22#9052911yescharacteristic
569C22#9052911yescharacteristic
570C4—22no—
571C4—22no—
572C4—41no—
573C4—41no—
574C4—42no—
575C4—41no—
576C4—41no—
577C4—42no—
578C4—42no—
579C4—81no—
580C4—561no—
581C4—561no—
582C4—561no—
583C4—561no—
584C4#9022911yescharacteristic
585C4#9024711yescharacteristic
586C4#9025111yescharacteristic
587C4#9025611yescharacteristic
588C2#1173981511yescharacteristic
589C2#1173988811yescharacteristic
590C2#1174000011yescharacteristic
591C2#1174095511yescharacteristic
592C2#1174099711yescharacteristic
593C2#1174111511yescharacteristic
594C2#1174113111yescharacteristic
subgroupG/H
centerC23C22×C22⋊D7
commutator, cosocleC22×C4×C7C24
FrattiniC22×C4C23×D7
FittingC7×#2365C2
socle, prime radicalC23×C7C22×D4
hypercenter#2365D7
hypocenterC7#27067
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
562. C7#27067semidirect

Maximal subgroups

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

subgroupindex
C7×#23652
#117311412
#117295472
#117295352
#117293862
C4×#64092
#117293812
#117274402
#117274352
#117274312
#117274202
#117272362
#117272182
#117272122
#270677