Finite Group Databasebeta

← #13395217

Subgroups — #13395217

Order 1792.

746 conjugacy classes of subgroups.

The subgroup lattice has 616 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C7×#433C211yesmaximal, characteristic
2#11739709C211yesmaximal, characteristic
3#11739680C211yesmaximal, characteristic
4C2×#89623C211yesmaximal, characteristic, complemented
5#11728240C211yesmaximal, characteristic, complemented
6#11728213C211yesmaximal, characteristic, complemented
7#11728209C211yesmaximal, characteristic, complemented
8#11727694C211yesmaximal, characteristic
9#11727694C211yesmaximal, characteristic
10#11727691C211yesmaximal, characteristic
11#11727690C211yesmaximal, characteristic
12#11727573C211yesmaximal, characteristic, complemented
13#11727571C211yesmaximal, characteristic, complemented
14#11727523C211yesmaximal, characteristic, complemented
15#11727521C211yesmaximal, characteristic, complemented
16C2×C7×#117C2211yescharacteristic
17C2×#6487C2211yescharacteristic
18C2×#6432C2211yescharacteristic
19C2×C4×Dic14C2211yescharacteristic
20C7×#433—24no—
21C2×C7×C4⋊C8C2211yescharacteristic
22C2×C7×C4⋊C8C2211yescharacteristic
23C2×C7×C22⋊C8C2211yescharacteristic
24C2×C7×C22⋊C8C2211yescharacteristic
25C2×C7×#97C2211yescharacteristic
26C2×C4×C7×C8C2211yescharacteristic
27#89984C2211yescharacteristic
28#89984C2211yescharacteristic
29#89984C2211yescharacteristic
30C2×#6392C2211yescharacteristic
31C2×#6391C2211yescharacteristic
32C2×#6391C2211yescharacteristic
33C2×#6391C2211yescharacteristic
34C2×#6390C2211yescharacteristic
35C2×#6390C2211yescharacteristic
36C2×#6390C2211yescharacteristic
37C2×#6390C2211yescharacteristic
38#89758—21no—
39#89751—21no—
40#89750—21no—
41#89744—21no—
42#89721—21no—
43#89719—21no—
44#89717—21no—
45#89716—21no—
46#89708C2211yescharacteristic
47C4×C4⋊Dic7C2211yescharacteristic
48#89701C2211yescharacteristic
49#89700C2211yescharacteristic
50#89700C2211yescharacteristic
51#89700C2211yescharacteristic
52#89623—24no—
53#89346C2211yescharacteristic
54#89346C2211yescharacteristic
55#89346C2211yescharacteristic
56#89346C2211yescharacteristic
57#89346C2211yescharacteristic
58#89346C2211yescharacteristic
59#89346C2211yescharacteristic
60#89346C2211yescharacteristic
61#24718—71nomaximal, Sylow
62C23×C4×C7C2311yescharacteristic
63C22×Dic14—21no—
64C22×Dic14C2311yescharacteristic
65C22×C7×C8C2311yescharacteristic
66C22×C7×C8C2311yescharacteristic
67C22×C7×C8C2311yescharacteristic
68C22×C7×C8C2311yescharacteristic
69C7×#117—22no—
70C7×#117—22no—
71C2×C7×C4⋊C4D411yescharacteristic
72C2×C7×C4⋊C4D411yescharacteristic
73C2×C7×C22⋊C4D411yescharacteristic
74C2×C7×C22⋊C4D411yescharacteristic
75C2×C42×C7C2311yescharacteristic
76C2×C42×C7C2311yescharacteristic
77C2×C22⋊Dic7—21no—
78C2×C22⋊Dic7—21no—
79C2×C22⋊Dic7—21no—
80C2×C22⋊Dic7—21no—
81C2×C4⋊Dic7—21no—
82C2×C4⋊Dic7C2311yescharacteristic
83C2×C4⋊Dic7C2311yescharacteristic
84C2×C4⋊Dic7C2311yescharacteristic
85C2×C4⋊Dic7C2311yescharacteristic
86C2×C4⋊Dic7C2311yescharacteristic
87C2×C4⋊Dic7C2311yescharacteristic
88C2×C4⋊Dic7C2311yescharacteristic
89#6487—22no—
90#6487—22no—
91C2×Dic7⋊C4—21no—
92C2×Dic7⋊C4—21no—
93C2×Dic7⋊C4—21no—
94C2×Dic7⋊C4—21no—
95C2×Dic7⋊C4—21no—
96C2×C4×Dic7—21no—
97C2×C4×Dic7—21no—
98#6432—22no—
99#6432—22no—
100C4×Dic14—22no—
101C4×Dic14—22no—
102C7×C4⋊C8—22no—
103C7×C4⋊C8D414yes—
104C7×C22⋊C8—22no—
105C7×C22⋊C8—22no—
106C7×#97—22no—
107C4×C7×C8—22no—
108C7⋊#95—21no—
109C7⋊#95—21no—
110C7⋊#95—21no—
111C7⋊#95—21no—
112C7⋊#95—21no—
113C7⋊#95—21no—
114C7⋊#95—21no—
115C7⋊#95—21no—
116C7⋊#95—21no—
117C7⋊#95—21no—
118C7⋊#95—21no—
119#6392—22no—
120#6391—22no—
121#6391—22no—
122#6391—22no—
123#6390—22no—
124#6390—22no—
125#6390—22no—
126#6390—22no—
127C2×#475—71no—
128C2×#433D711yescharacteristic
129#2628—71no—
130#2323—71no—
131#2077—71no—
132#2077—71no—
133#2036—71no—
134#2035—71no—
135#1987—71no—
136#1949—71no—
137#1943—71no—
138#1941—71no—
139#1935—71no—
140#1933—71no—
141#1805—71no—
142C24×C7C2×D411yescharacteristic
143C22×C4×C7—21no—
144C22×C4×C7—21no—
145C22×C4×C7—21no—
146C22×C4×C7—21no—
147C22×C4×C7—21no—
148C22×C4×C7—21no—
149C22×C4×C7C2×D411yescharacteristic
150C22×C4×C7C2×D411yescharacteristic
151C22×C4×C7C2×D411yescharacteristic
152C22×C4×C7C2×D411yescharacteristic
153C22×C4×C7C2×D411yescharacteristic
154C22×C4×C7C2411yescharacteristic
155C22×Dic7—21no—
156C22×Dic7—21no—
157C22×Dic7—21no—
158C22×Dic7—21no—
159C22×Dic7—21no—
160C22×Dic7—21no—
161C22×Dic7—21no—
162C22×Dic7—21no—
163C2×Dic14—21no—
164C2×Dic14—21no—
165C2×Dic14—21no—
166C2×Dic14—21no—
167C2×Dic14—21no—
168C2×Dic14—42no—
169C2×Dic14—81no—
170C2×Dic14—81no—
171C2×Dic14#4112yes—
172C2×C7×C8—21no—
173C2×C7×C8—21no—
174C2×C7×C8—21no—
175C2×C7×C8—21no—
176C2×C7×C8—21no—
177C2×C7×C8—21no—
178C2×C7×C8—21no—
179C2×C7×C8—21no—
180C2×C7×C8—21no—
181C2×C7×C8—21no—
182C2×C7×C8C2×D412yes—
183C2×C7×C8C2×D412yes—
184C7×C4⋊C4—22no—
185C7×C4⋊C4—22no—
186C7×C22⋊C4—22no—
187C7×C22⋊C4—22no—
188C42×C7—21no—
189C42×C7—21no—
190C42×C7C2×D412yes—
191C42×C7#4112yes—
192C22⋊Dic7—24no—
193C22⋊Dic7—81no—
194C22⋊Dic7—81no—
195C22⋊Dic7—81no—
196C4⋊Dic7—21no—
197C4⋊Dic7—21no—
198C4⋊Dic7—21no—
199C4⋊Dic7—21no—
200C4⋊Dic7—21no—
201C4⋊Dic7—21no—
202C4⋊Dic7—21no—
203C4⋊Dic7—21no—
204C4⋊Dic7—21no—
205C4⋊Dic7—21no—
206C4⋊Dic7—21no—
207C4⋊Dic7—21no—
208C4⋊Dic7—21no—
209C4⋊Dic7—42no—
210C4⋊Dic7#4112yes—
211Dic7⋊C4—24no—
212Dic7⋊C4—42no—
213Dic7⋊C4—81no—
214Dic7⋊C4—81no—
215Dic7⋊C4—81no—
216C4×Dic7—42no—
217C4×Dic7—81no—
218C2×C4⋊Q8—71no—
219C2×C22⋊Q8—71no—
220C2×C4×Q8—71no—
221C2×#117C2×D711yescharacteristic
222#475—144no—
223#433—24no—
224C2×#107—71no—
225C2×#106—71no—
226C2×#106—71no—
227C2×#106—71no—
228C2×C4⋊C8C2×D711yescharacteristic
229C2×C4⋊C8C2×D711yescharacteristic
230C2×#103—71no—
231C2×#103—71no—
232C2×#103—71no—
233C2×#103—71no—
234C2×C22⋊C8C2×D711yescharacteristic
235C2×C22⋊C8C2×D711yescharacteristic
236C2×#97C2×D711yescharacteristic
237C2×C4×C8C2×D711yescharacteristic
238#400—141no—
239#399—141no—
240#395—141no—
241#393—141no—
242#391—71no—
243#389—71no—
244#389—71no—
245#389—71no—
246#389—141no—
247#388—141no—
248#388—141no—
249#387—141no—
250#382—71no—
251#380—71no—
252#380—71no—
253#380—71no—
254C4×C4⋊C4—71no—
255#340—71no—
256#340—71no—
257#340—71no—
258#340—71no—
259#340—71no—
260#340—71no—
261#340—71no—
262#340—71no—
263C23×C7—21no—
264C23×C7—21no—
265C23×C7—21no—
266C23×C7—21no—
267C23×C7—21no—
268C23×C7—21no—
269C23×C7—21no—
270C23×C7C22×D411yescharacteristic
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—41no—
285C2×C4×C7—41no—
286C2×C4×C7—41no—
287C2×C4×C7—41no—
288C2×C4×C7#12112yes—
289C2×C4×C7#12112yes—
290C2×C4×C7C22×D411yescharacteristic
291C2×C4×C7C2×#4111yescharacteristic
292C2×C4×C7C2×#4111yescharacteristic
293C2×C4×C7C2×#4111yescharacteristic
294C2×C4×C72−1+411yescharacteristic
295C2×C4×C72−1+411yescharacteristic
296C2×Dic7—22no—
297C2×Dic7—22no—
298C2×Dic7—41no—
299C2×Dic7—41no—
300C2×Dic7—41no—
301C2×Dic7—41no—
302C2×Dic7—41no—
303C2×Dic7—41no—
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—
316C2×Dic7—41no—
317C2×Dic7—41no—
318C2×Dic7—41no—
319C2×Dic7—41no—
320Dic14—22no—
321Dic14—22no—
322Dic14—41no—
323Dic14—41no—
324Dic14—84no—
325C7×C8—22no—
326C7×C8—22no—
327C7×C8—41no—
328C7×C8—41no—
329C22×Q8—71no—
330C22×Q8—141no—
331C23×C4C22×D711yescharacteristic
332C22×C8C22×D711yescharacteristic
333C22×C8C22×D711yescharacteristic
334C22×C8C22×D711yescharacteristic
335C22×C8C22×D711yescharacteristic
336C4⋊Q8—142no—
337C4⋊Q8—142no—
338C22⋊Q8—142no—
339C22⋊Q8—142no—
340C4×Q8—142no—
341C4×Q8—142no—
342#117—22no—
343#117—22no—
344C2×C4⋊C4—71no—
345C2×C4⋊C4—71no—
346C2×C4⋊C4—71no—
347C2×C4⋊C4—71no—
348C2×C4⋊C4—71no—
349C2×C4⋊C4—71no—
350C2×C4⋊C4—71no—
351C2×C4⋊C4—141no—
352C2×C4⋊C4—141no—
353C2×C4⋊C4—141no—
354C2×C4⋊C4—141no—
355C2×C4⋊C4—141no—
356C2×C4⋊C4—141no—
357C2×C4⋊C4D2811yescharacteristic
358C2×C4⋊C4D2811yescharacteristic
359C2×C22⋊C4—141no—
360C2×C22⋊C4—141no—
361C2×C22⋊C4—141no—
362C2×C22⋊C4—141no—
363C2×C22⋊C4D2811yescharacteristic
364C2×C22⋊C4D2811yescharacteristic
365C2×C42—141no—
366C2×C42—141no—
367C2×C42C22×D711yescharacteristic
368C2×C42C22×D711yescharacteristic
369#107—142no—
370#106—142no—
371#106—142no—
372#106—142no—
373C4⋊C8—22no—
374C4⋊C8C22⋊D714yes—
375#103—142no—
376#103—142no—
377#103—142no—
378#103—142no—
379C22⋊C8—22no—
380C22⋊C8—22no—
381#97—22no—
382C4×C8—22no—
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#95—141no—
392#95—141no—
393#95—141no—
394C22×C7—41no—
395C22×C7—41no—
396C22×C7—41no—
397C22×C7—41no—
398C22×C7—41no—
399C22×C7—41no—
400C22×C7—41no—
401C22×C7C2×#12111yescharacteristic
402C22×C7#52511yescharacteristic
403C22×C7#53611yescharacteristic
404C22×C7#57711yescharacteristic
405C22×C7#57711yescharacteristic
406C22×C7#57711yescharacteristic
407C22×C7#57811yescharacteristic
408C4×C7—22no—
409C4×C7—22no—
410C4×C7—41no—
411C4×C7—41no—
412C4×C7—41no—
413C4×C7#54711yescharacteristic
414C4×C7#54811yescharacteristic
415C4×C7#55211yescharacteristic
416C4×C7#55611yescharacteristic
417Dic7—42no—
418Dic7—42no—
419Dic7—81no—
420Dic7—81no—
421Dic7—81no—
422Dic7—81no—
423Dic7—81no—
424Dic7—81no—
425C24C2×D2811yescharacteristic
426C2×Q8—72no—
427C2×Q8—141no—
428C2×Q8—141no—
429C2×Q8—141no—
430C2×Q8—141no—
431C2×Q8—141no—
432C2×Q8—282no—
433C2×Q8—561no—
434C2×Q8—561no—
435C22×C4—21no—
436C22×C4—21no—
437C22×C4—21no—
438C22×C4—21no—
439C22×C4—21no—
440C22×C4—21no—
441C22×C4—141no—
442C22×C4—141no—
443C22×C4—141no—
444C22×C4—141no—
445C22×C4—141no—
446C22×C4—141no—
447C22×C4—141no—
448C22×C4—141no—
449C22×C4C2×D2811yescharacteristic
450C22×C4C2×D2811yescharacteristic
451C22×C4C2×D2811yescharacteristic
452C22×C4C2×D2811yescharacteristic
453C22×C4C2×D2811yescharacteristic
454C22×C4C23×D711yescharacteristic
455C2×C8—21no—
456C2×C8—21no—
457C2×C8—21no—
458C2×C8—21no—
459C2×C8—21no—
460C2×C8—21no—
461C2×C8—21no—
462C2×C8—21no—
463C2×C8—21no—
464C2×C8—21no—
465C2×C8C2×C22⋊D712yes—
466C2×C8C2×C22⋊D712yes—
467C4⋊C4—22no—
468C4⋊C4—22no—
469C4⋊C4—72no—
470C4⋊C4—144no—
471C4⋊C4—141no—
472C4⋊C4—141no—
473C4⋊C4—141no—
474C4⋊C4—141no—
475C4⋊C4—141no—
476C4⋊C4—141no—
477C4⋊C4—141no—
478C4⋊C4—141no—
479C4⋊C4—141no—
480C4⋊C4—141no—
481C4⋊C4—141no—
482C4⋊C4—141no—
483C4⋊C4—141no—
484C4⋊C4—282no—
485C4⋊C4—282no—
486C4⋊C4—561no—
487C4⋊C4—561no—
488C4⋊C4—561no—
489C22⋊C4—22no—
490C22⋊C4—22no—
491C22⋊C4—144no—
492C22⋊C4—561no—
493C22⋊C4—561no—
494C22⋊C4—561no—
495C42—21no—
496C42—21no—
497C42—282no—
498C42—561no—
499C42#115712yes—
500C42C2×C22⋊D712yes—
501C2×C7—81no—
502C2×C7#241511yescharacteristic
503C2×C7#305711yescharacteristic
504C2×C7#306311yescharacteristic
505C2×C7#312111yescharacteristic
506C2×C7#312511yescharacteristic
507C2×C7#324211yescharacteristic
508C2×C7#324411yescharacteristic
509C23—21no—
510C23—21no—
511C23—21no—
512C23—21no—
513C23—21no—
514C23—21no—
515C23—21no—
516C23C22×D2811yescharacteristic
517Q8—142no—
518Q8—142no—
519Q8—281no—
520Q8—281no—
521Q8—564no—
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—41no—
536C2×C4—41no—
537C2×C4—41no—
538C2×C4—41no—
539C2×C4—142no—
540C2×C4—142no—
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×C4—281no—
554C2×C4—281no—
555C2×C4—281no—
556C2×C4—281no—
557C2×C4—281no—
558C2×C4—281no—
559C2×C4—281no—
560C2×C4—281no—
561C2×C4—281no—
562C2×C4—281no—
563C2×C4#649312yes—
564C2×C4#649312yes—
565C2×C4C2×#115711yescharacteristic
566C2×C4D7×#4111yescharacteristic
567C2×C4D7×#4111yescharacteristic
568C2×C4#655411yescharacteristic
569C2×C4#655411yescharacteristic
570C2×C4C22×C22⋊D711yescharacteristic
571C8—22no—
572C8—22no—
573C8—41no—
574C8—41no—
575C7#2471811yescharacteristic, complemented, Sylow
576C22—41no—
577C22—41no—
578C22—41no—
579C22—41no—
580C22—41no—
581C22—41no—
582C22—41no—
583C22#9021511yescharacteristic
584C22#9021711yescharacteristic
585C22#9044211yescharacteristic
586C22#9044211yescharacteristic
587C22#9044211yescharacteristic
588C22#9044411yescharacteristic
589C22C2×#649311yescharacteristic
590C4—22no—
591C4—22no—
592C4—41no—
593C4—41no—
594C4—41no—
595C4—282no—
596C4—282no—
597C4—561no—
598C4—561no—
599C4—561no—
600C4—561no—
601C4—561no—
602C4—561no—
603C4#9022011yescharacteristic
604C4#9022411yescharacteristic
605C4#9051511yescharacteristic
606C4#9052211yescharacteristic
607C2—81no—
608C2#1173680811yescharacteristic
609C2#1173681011yescharacteristic
610C2#1173683411yescharacteristic
611C2#1173683911yescharacteristic
612C2#1173972211yescharacteristic
613C2#1174124311yescharacteristic
614C2#1174125311yescharacteristic
subgroupG/H
centerC23C22×D28
commutator, cosocleC22×C4×C7C24
FrattiniC22×C4C23×D7
FittingC2×C7×#433C2
socleC23×C7C22×D4
prime radicalC24×C7C2×D4
hypercenterC2×#433D7
hypocenterC7#24718
LCSG ▷ C22×C4×C7 ▷ C2×C7 ▷ C7
UCSC1 ◁ C23 ◁ C2×#117 ◁ C2×#433

Complements

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

NH ≅ G/Ntype
4. C2×#89623C2semidirect
5. #11728240C2semidirect
6. #11728213C2semidirect
7. #11728209C2semidirect
12. #11727573C2semidirect
13. #11727571C2semidirect
14. #11727523C2semidirect
15. #11727521C2semidirect
575. C7#24718semidirect

Maximal subgroups

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

subgroupindex
C2×C7×#4332
#117397092
#117396802
C2×#896232
#117282402
#117282132
#117282092
#117276942
#117276912
#117276902
#117275732
#117275712
#117275232
#117275212
#247187