Finite Group Databasebeta

← #13395135

Subgroups — #13395135

Order 1792.

802 conjugacy classes of subgroups.

The subgroup lattice has 654 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C7×#2628C211yesmaximal, characteristic, complemented
2C2×#89859C211yesmaximal, characteristic, complemented
3#11739681C211yesmaximal, characteristic
4C2×#89772C211yesmaximal, characteristic, complemented
5#11729533C211yesmaximal, characteristic, complemented
6#11727375C211yesmaximal, characteristic, complemented
7#11727373C211yesmaximal, characteristic, complemented
8#11727371C211yesmaximal, characteristic, complemented
9#11727369C211yesmaximal, characteristic, complemented
10#11727310C211yesmaximal, characteristic, complemented
11#11727294C211yesmaximal, characteristic, complemented
12#11727278C211yesmaximal, characteristic
13#11727277C211yesmaximal, characteristic
14#11727273C211yesmaximal, characteristic, complemented
15#11727272C211yesmaximal, characteristic, complemented
16C2×C7×C4⋊Q8C2211yescharacteristic
17C2×C7×#117C2211yescharacteristic
18C2×#6493C2211yescharacteristic
19C2×C4×D28C2211yescharacteristic
20C7×#400—21no—
21C7×#399—21no—
22C7×#395—21no—
23C7×#393—21no—
24C7×#389C2211yescharacteristic
25C7×#389C2211yescharacteristic
26C7×#382C2211yescharacteristic
27C7×#380C2211yescharacteristic
28C7×#380C2211yescharacteristic
29#89984C2211yescharacteristic
30C2×C22⋊(C7⋊C8)C2211yescharacteristic
31C2×C22⋊(C7⋊C8)C2211yescharacteristic
32#89859—24no—
33#89772—24no—
34#89762—21no—
35#89761—21no—
36C2×#6383C2211yescharacteristic
37C2×#6383C2211yescharacteristic
38C2×#6383C2211yescharacteristic
39C2×#6383C2211yescharacteristic
40C2×#6382C2211yescharacteristic
41C2×#6381C2211yescharacteristic
42C2×#6381C2211yescharacteristic
43C2×#6381C2211yescharacteristic
44#89729—21no—
45#89728—21no—
46#89711C2211yescharacteristic
47C4×C4⋊Dic7C2211yescharacteristic
48#89700C2211yescharacteristic
49C2×C4⋊(C7⋊C8)C2211yescharacteristic
50C2×C4⋊(C7⋊C8)C2211yescharacteristic
51C2×#6377C2211yescharacteristic
52C2×C4×C7⋊C8C2211yescharacteristic
53#89324C2211yescharacteristic
54#89324C2211yescharacteristic
55#89324C2211yescharacteristic
56#89324C2211yescharacteristic
57#89324C2211yescharacteristic
58#89324C2211yescharacteristic
59#89324C2211yescharacteristic
60#89324C2211yescharacteristic
61#24712—71nomaximal, Sylow
62C22×C7×Q8—21no—
63C23×C4×C7C2311yescharacteristic
64C22×C22⋊D7—21no—
65C22×D28C2311yescharacteristic
66C22×C4×D7—21no—
67C7×C4⋊Q8—22no—
68C7×C4⋊Q8—22no—
69C7×#117—22no—
70C7×#117—22no—
71C2×C7×C4⋊C4—21no—
72C2×C7×C4⋊C4—21no—
73C2×C7×C4⋊C4—21no—
74C2×C7×C4⋊C4D411yescharacteristic
75C2×C7×C4⋊C4D411yescharacteristic
76C2×C7×C4⋊C4C2311yescharacteristic
77C2×C7×C4⋊C4C2311yescharacteristic
78C2×C7×C4⋊C4C2311yescharacteristic
79C2×C7×C4⋊C4C2311yescharacteristic
80C2×C7×C22⋊C4—21no—
81C2×C7×C22⋊C4—21no—
82C2×C7×C22⋊C4D411yescharacteristic
83C2×C7×C22⋊C4D411yescharacteristic
84C2×C42×C7C2311yescharacteristic
85C2×C42×C7C2311yescharacteristic
86C2×C22⋊Dic7—21no—
87#6493—22no—
88#6493—22no—
89C2×(C2×D7)⋊C4—21no—
90C2×(C2×D7)⋊C4—21no—
91C2×(C2×D7)⋊C4—21no—
92C2×(C2×D7)⋊C4—21no—
93C2×C4⋊Dic7C2311yescharacteristic
94C2×C4⋊Dic7C2311yescharacteristic
95C2×C4⋊Dic7C2311yescharacteristic
96C2×Dic7⋊C4—21no—
97C2×C4×Dic7—21no—
98C22×C7⋊C8C2311yescharacteristic
99C22×C7⋊C8C2311yescharacteristic
100C22×C7⋊C8C2311yescharacteristic
101C22×C7⋊C8C2311yescharacteristic
102C4×D28—22no—
103C4×D28—22no—
104C7×#95—21no—
105C7×#95—21no—
106C7×#95—21no—
107C7×#95—21no—
108C7×#95—21no—
109C7×#95—21no—
110C7⋊#95—21no—
111C7⋊#95—21no—
112C7⋊#95—21no—
113C22⋊(C7⋊C8)—22no—
114C22⋊(C7⋊C8)—22no—
115#6383—22no—
116#6383—22no—
117#6383—22no—
118#6383—22no—
119#6382—22no—
120#6381—22no—
121#6381—22no—
122#6381—22no—
123C4⋊(C7⋊C8)—22no—
124C4⋊(C7⋊C8)D414yescomplemented
125#6377—22no—
126C4×C7⋊C8—22no—
127C2×#474—71no—
128C2×#433—71no—
129#2628D711yescharacteristic, complemented
130#2324—71no—
131#2076—71no—
132#2075—71no—
133#2034—71no—
134#2033—71no—
135#1987—71no—
136#1949—71no—
137#1944—71no—
138#1942—71no—
139#1936—71no—
140#1934—71no—
141#1804—71no—
142C24×C7C2×D411yescharacteristic
143C23×D7—21no—
144C2×C7×Q8—42no—
145C2×C7×Q8—81no—
146C2×C7×Q8—81no—
147C22×C4×C7—21no—
148C22×C4×C7—21no—
149C22×C4×C7—21no—
150C22×C4×C7—21no—
151C22×C4×C7—21no—
152C22×C4×C7—21no—
153C22×C4×C7—21no—
154C22×C4×C7—21no—
155C22×C4×C7—21no—
156C22×C4×C7—21no—
157C22×C4×C7C2×D411yescharacteristic
158C22×C4×C7C2×D411yescharacteristic
159C22×C4×C7C2×D411yescharacteristic
160C22×C4×C7C2×D411yescharacteristic
161C22×C4×C7C2×D411yescharacteristic
162C22×C4×C7C2411yescharacteristic
163C2×C22⋊D7—24no—
164C2×C22⋊D7—81no—
165C2×C22⋊D7—81no—
166C22×Dic7—21no—
167C22×Dic7—21no—
168C22×Dic7—21no—
169C2×D28—21no—
170C2×D28—21no—
171C2×D28—21no—
172C2×D28—21no—
173C2×D28—21no—
174C2×D28#4112yes—
175C2×C4×D7—42no—
176C2×C4×D7—81no—
177C2×C4×D7—81no—
178C7×C4⋊C4—22no—
179C7×C4⋊C4—22no—
180C7×C4⋊C4—21no—
181C7×C4⋊C4—21no—
182C7×C4⋊C4—21no—
183C7×C4⋊C4—21no—
184C7×C4⋊C4—21no—
185C7×C4⋊C4—21no—
186C7×C4⋊C4—21no—
187C7×C4⋊C4—21no—
188C7×C4⋊C4—42no—
189C7×C4⋊C4—81no—
190C7×C4⋊C4—81no—
191C7×C22⋊C4—22no—
192C7×C22⋊C4—22no—
193C7×C22⋊C4—81no—
194C7×C22⋊C4—81no—
195C42×C7—21no—
196C42×C7—21no—
197C42×C7C2×D412yes—
198C42×C7#4112yes—
199C22⋊Dic7—81no—
200(C2×D7)⋊C4—24no—
201(C2×D7)⋊C4—42no—
202(C2×D7)⋊C4—81no—
203(C2×D7)⋊C4—81no—
204C4⋊Dic7—21no—
205C4⋊Dic7—21no—
206C4⋊Dic7—21no—
207C4⋊Dic7—21no—
208C4⋊Dic7—21no—
209C4⋊Dic7#4112yes—
210Dic7⋊C4—81no—
211C4×Dic7—81no—
212C2×C7⋊C8—21no—
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⋊C8C2×D412yes—
223C2×C7⋊C8C2×D412yes—
224C2×C4⋊Q8C2×D711yescharacteristic
225C2×#121—71no—
226C2×C4×D4—71no—
227C2×#117C2×D711yescharacteristic
228#474—144no—
229#433—144no—
230C2×#107—71no—
231C2×#107—71no—
232C2×#107—71no—
233C2×#106—71no—
234C2×C4⋊C8—71no—
235C2×C4⋊C8—71no—
236C2×#102—71no—
237C2×#102—71no—
238C2×#102—71no—
239C2×#102—71no—
240C2×C22⋊C8—71no—
241C2×C22⋊C8—71no—
242C2×#97—71no—
243C2×C4×C8—71no—
244#400—21no—
245#399—21no—
246#395—21no—
247#393—21no—
248#390—71no—
249#390—141no—
250#389—71no—
251#389C2×D711yescharacteristic
252#389C2×D711yescharacteristic
253#388—141no—
254#386—141no—
255#385—141no—
256#382C2×D711yescharacteristic
257#380—71no—
258#380C2×D711yescharacteristic
259#380C2×D711yescharacteristic
260C4×C4⋊C4—71no—
261#340—71no—
262#340—71no—
263#340—71no—
264#340—71no—
265#340—71no—
266#340—71no—
267#340—71no—
268#340—71no—
269C23×C7—21no—
270C23×C7—21no—
271C23×C7—21no—
272C23×C7—21no—
273C23×C7—21no—
274C23×C7—21no—
275C23×C7—21no—
276C23×C7C22×D411yescharacteristic
277C22×D7—22no—
278C22×D7—41no—
279C22×D7—41no—
280C22×D7—41no—
281C22×D7—41no—
282C22×D7—41no—
283C22×D7—41no—
284C7×Q8—84no—
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—21no—
292C2×C4×C7—21no—
293C2×C4×C7—21no—
294C2×C4×C7—21no—
295C2×C4×C7—21no—
296C2×C4×C7—21no—
297C2×C4×C7—21no—
298C2×C4×C7—41no—
299C2×C4×C7—41no—
300C2×C4×C7—41no—
301C2×C4×C7—41no—
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×C7—41no—
312C2×C4×C7—41no—
313C2×C4×C7—41no—
314C2×C4×C7#12112yes—
315C2×C4×C7#12112yes—
316C2×C4×C7C22×D411yescharacteristic
317C2×C4×C7C2×#4111yescharacteristic
318C2×C4×C7C2×#4111yescharacteristic
319C2×C4×C7C2×#4111yescharacteristic
320C2×C4×C72−1+411yescharacteristic
321C2×C4×C72−1+411yescharacteristic
322C22⋊D7—84no—
323C2×Dic7—22no—
324C2×Dic7—41no—
325C2×Dic7—41no—
326C2×Dic7—41no—
327C2×Dic7—41no—
328C2×Dic7—41no—
329C2×Dic7—41no—
330C2×Dic7—41no—
331C2×Dic7—41no—
332D28—22no—
333D28—22no—
334D28—41no—
335D28—41no—
336C4×D7—84no—
337C7⋊C8—22no—
338C7⋊C8—22no—
339C7⋊C8—41no—
340C7⋊C8—41no—
341C22×Q8—21no—
342C22×D4—71no—
343C22×D4—141no—
344C23×C4—141no—
345C23×C4C22×D711yescharacteristic
346C22×C8—71no—
347C22×C8—71no—
348C22×C8—71no—
349C22×C8—71no—
350C4⋊Q8—22no—
351C4⋊Q8—22no—
352#121—142no—
353#121—142no—
354C4×D4—142no—
355C4×D4—142no—
356#117—22no—
357#117—22no—
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⋊C4C22⋊D711yescharacteristic
366C2×C4⋊C4C22⋊D711yescharacteristic
367C2×C4⋊C4C22×D711yescharacteristic
368C2×C4⋊C4C22×D711yescharacteristic
369C2×C4⋊C4C22×D711yescharacteristic
370C2×C4⋊C4C22×D711yescharacteristic
371C2×C22⋊C4—21no—
372C2×C22⋊C4—21no—
373C2×C22⋊C4—141no—
374C2×C22⋊C4—141no—
375C2×C22⋊C4—141no—
376C2×C22⋊C4—141no—
377C2×C22⋊C4—141no—
378C2×C22⋊C4C22⋊D711yescharacteristic
379C2×C22⋊C4C22⋊D711yescharacteristic
380C2×C42—141no—
381C2×C42C22×D711yescharacteristic
382C2×C42C22×D711yescharacteristic
383#107—142no—
384#107—142no—
385#107—142no—
386#106—142no—
387C4⋊C8—74no—
388C4⋊C8—142no—
389#102—142no—
390#102—142no—
391#102—142no—
392#102—142no—
393C22⋊C8—142no—
394C22⋊C8—142no—
395#97—142no—
396C4×C8—142no—
397#95—21no—
398#95—21no—
399#95—21no—
400#95—21no—
401#95—21no—
402#95—21no—
403#95—141no—
404#95—141no—
405#95—141no—
406C22×C7—41no—
407C22×C7—41no—
408C22×C7—41no—
409C22×C7—41no—
410C22×C7—41no—
411C22×C7—41no—
412C22×C7—41no—
413C22×C7C2×#12111yescharacteristic
414C22×C7#52511yescharacteristic
415C22×C7#53611yescharacteristic
416C22×C7#57611yescharacteristic
417C22×C7#57611yescharacteristic
418C22×C7#57711yescharacteristic
419C22×C7#57811yescharacteristic
420C2×D7—42no—
421C2×D7—42no—
422C2×D7—42no—
423C2×D7—81no—
424C2×D7—81no—
425C2×D7—81no—
426C2×D7—81no—
427C4×C7—22no—
428C4×C7—22no—
429C4×C7—41no—
430C4×C7—41no—
431C4×C7—41no—
432C4×C7—81no—
433C4×C7—81no—
434C4×C7—81no—
435C4×C7—81no—
436C4×C7#54711yescharacteristic
437C4×C7#54811yescharacteristic
438C4×C7#55211yescharacteristic
439C4×C7#55611yescharacteristic
440Dic7—42no—
441Dic7—81no—
442Dic7—81no—
443C24—141no—
444C24C2×C22⋊D711yescharacteristic
445C2×Q8—42no—
446C2×Q8—81no—
447C2×Q8—81no—
448C2×D4—72no—
449C2×D4—144no—
450C2×D4—141no—
451C2×D4—141no—
452C2×D4—141no—
453C2×D4—141no—
454C2×D4—141no—
455C2×D4—561no—
456C2×D4—561no—
457C22×C4—21no—
458C22×C4—21no—
459C22×C4—21no—
460C22×C4—21no—
461C22×C4—21no—
462C22×C4—21no—
463C22×C4—21no—
464C22×C4—21no—
465C22×C4—21no—
466C22×C4—21no—
467C22×C4—141no—
468C22×C4—141no—
469C22×C4—141no—
470C22×C4—282no—
471C22×C4—561no—
472C22×C4—561no—
473C22×C4C2×C22⋊D711yescharacteristic
474C22×C4C2×C22⋊D711yescharacteristic
475C22×C4C2×C22⋊D711yescharacteristic
476C22×C4C2×C22⋊D711yescharacteristic
477C22×C4C2×C22⋊D711yescharacteristic
478C22×C4C23×D711yescharacteristic
479C2×C8—72no—
480C2×C8—72no—
481C2×C8—141no—
482C2×C8—141no—
483C2×C8—141no—
484C2×C8—141no—
485C2×C8—141no—
486C2×C8—141no—
487C2×C8—141no—
488C2×C8—141no—
489C2×C8—141no—
490C2×C8—141no—
491C4⋊C4—22no—
492C4⋊C4—22no—
493C4⋊C4—21no—
494C4⋊C4—21no—
495C4⋊C4—21no—
496C4⋊C4—21no—
497C4⋊C4—21no—
498C4⋊C4—21no—
499C4⋊C4—21no—
500C4⋊C4—21no—
501C4⋊C4—42no—
502C4⋊C4—72no—
503C4⋊C4—81no—
504C4⋊C4—81no—
505C4⋊C4—141no—
506C4⋊C4—141no—
507C4⋊C4—141no—
508C4⋊C4—141no—
509C4⋊C4—141no—
510C4⋊C4—561no—
511C22⋊C4—22no—
512C22⋊C4—22no—
513C22⋊C4—81no—
514C22⋊C4—81no—
515C22⋊C4—144no—
516C22⋊C4—282no—
517C22⋊C4—561no—
518C22⋊C4—561no—
519C22⋊C4—561no—
520C42—21no—
521C42—21no—
522C42—561no—
523C42D4×D712yes—
524C42#115912yes—
525C2×C7—81no—
526C2×C7#241511yescharacteristic
527C2×C7#305811yescharacteristic
528C2×C7#306311yescharacteristic
529C2×C7#311811yescharacteristic
530C2×C7#312411yescharacteristic
531C2×C7#324111yescharacteristic
532C2×C7#324311yescharacteristic
533D7—82no—
534C23—21no—
535C23—21no—
536C23—21no—
537C23—21no—
538C23—21no—
539C23—21no—
540C23—21no—
541C23—142no—
542C23—281no—
543C23—281no—
544C23—281no—
545C23—281no—
546C23—281no—
547C23—281no—
548C23C22×C22⋊D711yescharacteristic
549Q8—84no—
550D4—142no—
551D4—142no—
552D4—281no—
553D4—281no—
554D4—564no—
555C2×C4—21no—
556C2×C4—21no—
557C2×C4—21no—
558C2×C4—21no—
559C2×C4—21no—
560C2×C4—21no—
561C2×C4—21no—
562C2×C4—21no—
563C2×C4—21no—
564C2×C4—21no—
565C2×C4—21no—
566C2×C4—21no—
567C2×C4—21no—
568C2×C4—41no—
569C2×C4—41no—
570C2×C4—41no—
571C2×C4—41no—
572C2×C4—41no—
573C2×C4—41no—
574C2×C4—41no—
575C2×C4—41no—
576C2×C4—41no—
577C2×C4—41no—
578C2×C4—41no—
579C2×C4—41no—
580C2×C4—41no—
581C2×C4—41no—
582C2×C4—41no—
583C2×C4—41no—
584C2×C4—142no—
585C2×C4—281no—
586C2×C4—281no—
587C2×C4—281no—
588C2×C4—281no—
589C2×C4—281no—
590C2×C4—281no—
591C2×C4—281no—
592C2×C4—281no—
593C2×C4—564no—
594C2×C4#650212yes—
595C2×C4#650212yes—
596C2×C4C2×D4×D711yescharacteristic
597C2×C4C2×#115911yescharacteristic
598C2×C4#655111yescharacteristic
599C2×C4#655111yescharacteristic
600C2×C4D7×#4111yescharacteristic
601C2×C4D7×#4111yescharacteristic
602C8—142no—
603C8—142no—
604C8—281no—
605C8—281no—
606C7#2471211yescharacteristic, complemented, Sylow
607C22—41no—
608C22—41no—
609C22—41no—
610C22—41no—
611C22—41no—
612C22—41no—
613C22—41no—
614C22—282no—
615C22—282no—
616C22—282no—
617C22—561no—
618C22—561no—
619C22—561no—
620C22—561no—
621C22C2×#650211yescharacteristic
622C22#9050711yescharacteristic
623C22#9051911yescharacteristic
624C22#9052611yescharacteristic
625C22#9052611yescharacteristic
626C22#9052811yescharacteristic
627C22#9052911yescharacteristic
628C4—22no—
629C4—22no—
630C4—41no—
631C4—41no—
632C4—41no—
633C4—81no—
634C4—81no—
635C4—81no—
636C4—81no—
637C4—282no—
638C4—561no—
639C4—561no—
640C4#9032211yescharacteristic
641C4#9032411yescharacteristic
642C4#9033011yescharacteristic
643C4#9033211yescharacteristic
644C2—81no—
645C2—562no—
646C2#1174025911yescharacteristic
647C2#1174082311yescharacteristic
648C2#1174084511yescharacteristic
649C2#1174090511yescharacteristic
650C2#1174090611yescharacteristic
651C2#1174092211yescharacteristic
652C2#1174092311yescharacteristic
subgroupG/H
centerC23C22×C22⋊D7
commutator, cosocleC22×C4×C7C24
FrattiniC22×C4C23×D7
FittingC7×#2628C2
socleC23×C7C22×D4
prime radicalC2×#6493C22
hypercenter#2628D7
hypocenterC7#24712
LCSG ▷ C22×C4×C7 ▷ C2×C7 ▷ C7
UCSC1 ◁ C23 ◁ C2×#117 ◁ #2628

Complements

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

NH ≅ G/Ntype
1. C7×#2628C2semidirect
2. C2×#89859C2semidirect
4. C2×#89772C2semidirect
5. #11729533C2semidirect
6. #11727375C2semidirect
7. #11727373C2semidirect
8. #11727371C2semidirect
9. #11727369C2semidirect
10. #11727310C2semidirect
11. #11727294C2semidirect
14. #11727273C2semidirect
15. #11727272C2semidirect
124. C4⋊(C7⋊C8)D4semidirect
129. #2628D7semidirect
606. C7#24712semidirect

Maximal subgroups

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

subgroupindex
C7×#26282
C2×#898592
#117396812
C2×#897722
#117295332
#117273752
#117273732
#117273712
#117273692
#117273102
#117272942
#117272782
#117272772
#117272732
#117272722
#247127