Finite Group Databasebeta

← #13426569

Subgroups — #13426569

Order 1792.

734 conjugacy classes of subgroups.

The subgroup lattice has 632 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C7×#2495C211yesmaximal, characteristic, complemented
2#11730914C211yesmaximal, characteristic
3#11727384C211yesmaximal, characteristic, complemented
4#11727380C211yesmaximal, characteristic, complemented
5#11727373C211yesmaximal, characteristic, complemented
6#11727356C211yesmaximal, characteristic, complemented
7#11727311C211yesmaximal, characteristic, complemented
8#11727294C211yesmaximal, characteristic, complemented
9#11727278C211yesmaximal, characteristic
10#11727277C211yesmaximal, characteristic
11#11727260C211yesmaximal, characteristic, complemented
12#11727257C211yesmaximal, characteristic, complemented
13C4×#6383C211yesmaximal, characteristic, complemented
14#11727214C211yesmaximal, characteristic, complemented
15#11727205C211yesmaximal, characteristic, complemented
16C2×#6493C2211yescharacteristic
17C2×#6489C2211yescharacteristic
18C2×C4×D28C2211yescharacteristic
19C7×#400—21no—
20C7×#397—21no—
21C7×#389C2211yescharacteristic
22C7×#389C2211yescharacteristic
23C7×#388—21no—
24C7×#383—21no—
25C7×#382C2211yescharacteristic
26C7×#380C2211yescharacteristic
27C7×#380C2211yescharacteristic
28C4×C7×C4⋊C4C2211yescharacteristic
29C4×C7×C22⋊C4C2211yescharacteristic
30C2×C22⋊(C7⋊C8)C2211yescharacteristic
31C2×C22⋊(C7⋊C8)C2211yescharacteristic
32C2×#6383C2211yescharacteristic
33C2×#6383C2211yescharacteristic
34C2×#6383C2211yescharacteristic
35C2×#6383C2211yescharacteristic
36C2×#6382C2211yescharacteristic
37C2×#6382C2211yescharacteristic
38C2×#6381C2211yescharacteristic
39C2×#6381C2211yescharacteristic
40#89729—21no—
41#89728—21no—
42#89711C2211yescharacteristic
43C4×C4⋊Dic7C2211yescharacteristic
44#89700C2211yescharacteristic
45C2×C4⋊(C7⋊C8)C2211yescharacteristic
46C2×C4×C7⋊C8C2211yescharacteristic
47#89441—21no—
48#89438—21no—
49#89324C2211yescharacteristic
50#89324C2211yescharacteristic
51#89324C2211yescharacteristic
52#89324C2211yescharacteristic
53#89324C2211yescharacteristic
54#89324C2211yescharacteristic
55#89324C2211yescharacteristic
56#89324C2211yescharacteristic
57#89319C2211yescharacteristic
58#89319C2211yescharacteristic
59#27038—71nomaximal, Sylow
60C23×C4×C7C2311yescharacteristic
61C22×C22⋊D7—21no—
62C22×D28C2311yescharacteristic
63C22×C4×D7—21no—
64C2×C7×C4⋊C4—21no—
65C2×C7×C4⋊C4—21no—
66C2×C7×C4⋊C4C2311yescharacteristic
67C2×C7×C4⋊C4C2311yescharacteristic
68C2×C7×C4⋊C4C2311yescharacteristic
69C2×C7×C4⋊C4C2311yescharacteristic
70C2×C7×C22⋊C4—21no—
71C2×C7×C22⋊C4—21no—
72C2×C7×C22⋊C4D411yescharacteristic
73C2×C7×C22⋊C4D411yescharacteristic
74C2×C42×C7—21no—
75C2×C42×C7C2311yescharacteristic
76C2×C42×C7C2311yescharacteristic
77C2×C22⋊Dic7—21no—
78#6493—22no—
79#6493—22no—
80C2×(C2×D7)⋊C4—21no—
81C2×(C2×D7)⋊C4—21no—
82C2×(C2×D7)⋊C4—21no—
83C2×(C2×D7)⋊C4—21no—
84#6489—22no—
85#6489—41no—
86C2×C4⋊Dic7C2311yescharacteristic
87C2×C4⋊Dic7C2311yescharacteristic
88C2×C4⋊Dic7C2311yescharacteristic
89C2×Dic7⋊C4—21no—
90C2×C4×Dic7—21no—
91C2×C4×Dic7—21no—
92C22×C7⋊C8C2311yescharacteristic
93C22×C7⋊C8C2311yescharacteristic
94C22×C7⋊C8C2311yescharacteristic
95C22×C7⋊C8C2311yescharacteristic
96C4×D28—22no—
97C4×D28—41no—
98C7×#95—21no—
99C7×#95—21no—
100C7×#95—21no—
101C7×#95—21no—
102C7×#95—21no—
103C7×#95—21no—
104C7×#95—21no—
105C7×#95D411yescharacteristic
106C7×#95D411yescharacteristic
107C7⋊#95—21no—
108C7⋊#95—21no—
109C22⋊(C7⋊C8)—22no—
110C22⋊(C7⋊C8)—41no—
111#6383—22no—
112#6383—22no—
113#6383—22no—
114#6383—41no—
115#6382—22no—
116#6382—22no—
117#6381—22no—
118#6381—41no—
119C4⋊(C7⋊C8)—22no—
120C4×C7⋊C8—41no—
121#2495D711yescharacteristic, complemented
122#2363—71no—
123#2073—71no—
124#2067—71no—
125#2034—71no—
126#2033—71no—
127#1949—71no—
128#1942—71no—
129#1923—71no—
130#1920—71no—
131#1920—71no—
132#1864—71no—
133#1854—71no—
134#1825—71no—
135C4×#102—71no—
136C24×C7C2×D411yescharacteristic
137C23×D7—21no—
138C22×C4×C7—21no—
139C22×C4×C7—21no—
140C22×C4×C7—21no—
141C22×C4×C7—21no—
142C22×C4×C7—21no—
143C22×C4×C7—21no—
144C22×C4×C7—21no—
145C22×C4×C7—21no—
146C22×C4×C7—21no—
147C22×C4×C7—21no—
148C22×C4×C7C2×D411yescharacteristic
149C22×C4×C7C2×D411yescharacteristic
150C22×C4×C7C2×D411yescharacteristic
151C22×C4×C7C2×D411yescharacteristic
152C22×C4×C7C2×D411yescharacteristic
153C22×C4×C7C2411yescharacteristic
154C2×C22⋊D7—24no—
155C2×C22⋊D7—81no—
156C2×C22⋊D7—81no—
157C22×Dic7—21no—
158C22×Dic7—21no—
159C22×Dic7—21no—
160C2×D28—21no—
161C2×D28—21no—
162C2×D28—21no—
163C2×D28—21no—
164C2×D28—21no—
165C2×D28#4112yes—
166C2×C4×D7—42no—
167C2×C4×D7—42no—
168C2×C4×D7—81no—
169C7×C4⋊C4—21no—
170C7×C4⋊C4—21no—
171C7×C4⋊C4—21no—
172C7×C4⋊C4—21no—
173C7×C4⋊C4—21no—
174C7×C4⋊C4—21no—
175C7×C4⋊C4—21no—
176C7×C4⋊C4—21no—
177C7×C4⋊C4—81no—
178C7×C4⋊C4—81no—
179C7×C22⋊C4—22no—
180C7×C22⋊C4—41no—
181C7×C22⋊C4—42no—
182C7×C22⋊C4—81no—
183C42×C7—21no—
184C42×C7—21no—
185C42×C7—21no—
186C42×C7—21no—
187C42×C7—42no—
188C22⋊Dic7—42no—
189(C2×D7)⋊C4—24no—
190(C2×D7)⋊C4—42no—
191(C2×D7)⋊C4—42no—
192(C2×D7)⋊C4—81no—
193C4⋊Dic7—21no—
194C4⋊Dic7—21no—
195C4⋊Dic7—21no—
196C4⋊Dic7—21no—
197C4⋊Dic7#4112yes—
198C4⋊Dic7#4112yes—
199Dic7⋊C4—81no—
200C4×Dic7—42no—
201C4×Dic7—81no—
202C2×C7⋊C8—21no—
203C2×C7⋊C8—21no—
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#4112yes—
214C2×#121—71no—
215C2×C4×D4—71no—
216C2×#117—71no—
217C2×#107—71no—
218C2×#107—71no—
219C2×#106—71no—
220C2×#106—71no—
221C2×C4⋊C8—71no—
222C2×#102—71no—
223C2×#102—71no—
224C2×#102—71no—
225C2×#102—71no—
226C2×C22⋊C8—71no—
227C2×C22⋊C8—71no—
228C2×C4×C8—71no—
229#400—21no—
230#397—21no—
231#390—71no—
232#390—141no—
233#389—71no—
234#389C2×D711yescharacteristic
235#389C2×D711yescharacteristic
236#388—21no—
237#388—141no—
238#386—141no—
239#383—21no—
240#382C2×D711yescharacteristic
241#380C2×D711yescharacteristic
242#380C2×D711yescharacteristic
243C4×C4⋊C4—71no—
244C4×C4⋊C4C2×D711yescharacteristic
245C4×C22⋊C4—141no—
246C4×C22⋊C4C2×D711yescharacteristic
247#340—71no—
248#340—71no—
249#340—71no—
250#340—71no—
251#340—71no—
252#340—71no—
253#340—71no—
254#340—71no—
255#336—71no—
256#336—71no—
257C23×C7—21no—
258C23×C7—21no—
259C23×C7—21no—
260C23×C7—21no—
261C23×C7—21no—
262C23×C7—21no—
263C23×C7—21no—
264C23×C7C22×D411yescharacteristic
265C22×D7—22no—
266C22×D7—41no—
267C22×D7—41no—
268C22×D7—41no—
269C22×D7—41no—
270C22×D7—41no—
271C22×D7—41no—
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—21no—
285C2×C4×C7—21no—
286C2×C4×C7—41no—
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—41no—
297C2×C4×C7—41no—
298C2×C4×C7—41no—
299C2×C4×C7—41no—
300C2×C4×C7—41no—
301C2×C4×C7—41no—
302C2×C4×C7#13512yes—
303C2×C4×C7C2×#4111yescharacteristic
304C2×C4×C7C2×#4111yescharacteristic
305C2×C4×C7C2×#4111yescharacteristic
306C2×C4×C7C2×#4111yescharacteristic
307C2×C4×C7H(5,𝔽2)11yescharacteristic
308C2×C4×C72−1+411yescharacteristic
309C22⋊D7—84no—
310C2×Dic7—22no—
311C2×Dic7—22no—
312C2×Dic7—41no—
313C2×Dic7—41no—
314C2×Dic7—41no—
315C2×Dic7—41no—
316C2×Dic7—41no—
317C2×Dic7—41no—
318C2×Dic7—41no—
319D28—22no—
320D28—22no—
321D28—41no—
322D28—41no—
323C4×D7—84no—
324C7⋊C8—22no—
325C7⋊C8—41no—
326C7⋊C8—41no—
327C7⋊C8—41no—
328C22×D4—71no—
329C22×D4—141no—
330C23×C4—141no—
331C23×C4C22×D711yescharacteristic
332C22×C8—71no—
333C22×C8—71no—
334C22×C8—71no—
335C22×C8—71no—
336#121—142no—
337#121—142no—
338C4×D4—142no—
339C4×D4—281no—
340#117—142no—
341#117—281no—
342C2×C4⋊C4—21no—
343C2×C4⋊C4—21no—
344C2×C4⋊C4—71no—
345C2×C4⋊C4—71no—
346C2×C4⋊C4—71no—
347C2×C4⋊C4—141no—
348C2×C4⋊C4C22×D711yescharacteristic
349C2×C4⋊C4C22×D711yescharacteristic
350C2×C4⋊C4C22×D711yescharacteristic
351C2×C4⋊C4C22×D711yescharacteristic
352C2×C22⋊C4—21no—
353C2×C22⋊C4—21no—
354C2×C22⋊C4—141no—
355C2×C22⋊C4—141no—
356C2×C22⋊C4—141no—
357C2×C22⋊C4—141no—
358C2×C22⋊C4—141no—
359C2×C22⋊C4C22⋊D711yescharacteristic
360C2×C22⋊C4C22⋊D711yescharacteristic
361C2×C42—21no—
362C2×C42—141no—
363C2×C42—141no—
364C2×C42C22×D711yescharacteristic
365C2×C42C22×D711yescharacteristic
366#107—142no—
367#107—281no—
368#106—142no—
369#106—142no—
370C4⋊C8—142no—
371#102—142no—
372#102—142no—
373#102—142no—
374#102—281no—
375C22⋊C8—142no—
376C22⋊C8—281no—
377C4×C8—281no—
378#95—21no—
379#95—21no—
380#95—21no—
381#95—21no—
382#95—21no—
383#95—21no—
384#95—21no—
385#95—141no—
386#95—141no—
387#95C22⋊D711yescharacteristic
388#95C22⋊D711yescharacteristic
389C22×C7—41no—
390C22×C7—41no—
391C22×C7—41no—
392C22×C7—41no—
393C22×C7—41no—
394C22×C7—41no—
395C22×C7—41no—
396C22×C7#52511yescharacteristic
397C22×C7#54611yescharacteristic
398C22×C7#54711yescharacteristic
399C22×C7C2×#13511yescharacteristic
400C22×C7#57511yescharacteristic
401C22×C7#57611yescharacteristic
402C22×C7#57711yescharacteristic
403C2×D7—42no—
404C2×D7—42no—
405C2×D7—42no—
406C2×D7—81no—
407C2×D7—81no—
408C2×D7—81no—
409C2×D7—81no—
410C4×C7—22no—
411C4×C7—41no—
412C4×C7—41no—
413C4×C7—41no—
414C4×C7—41no—
415C4×C7—81no—
416C4×C7—81no—
417C4×C7—81no—
418C4×C7—81no—
419C4×C7#52911yescharacteristic
420C4×C7#53911yescharacteristic
421C4×C7#55311yescharacteristic
422C4×C7#55611yescharacteristic
423Dic7—42no—
424Dic7—42no—
425Dic7—81no—
426C24—141no—
427C24C2×C22⋊D711yescharacteristic
428C2×D4—72no—
429C2×D4—144no—
430C2×D4—141no—
431C2×D4—141no—
432C2×D4—141no—
433C2×D4—141no—
434C2×D4—141no—
435C2×D4—561no—
436C2×D4—561no—
437C22×C4—21no—
438C22×C4—21no—
439C22×C4—21no—
440C22×C4—21no—
441C22×C4—21no—
442C22×C4—21no—
443C22×C4—21no—
444C22×C4—21no—
445C22×C4—21no—
446C22×C4—21no—
447C22×C4—141no—
448C22×C4—141no—
449C22×C4—141no—
450C22×C4—282no—
451C22×C4—282no—
452C22×C4—561no—
453C22×C4C2×C22⋊D711yescharacteristic
454C22×C4C2×C22⋊D711yescharacteristic
455C22×C4C2×C22⋊D711yescharacteristic
456C22×C4C2×C22⋊D711yescharacteristic
457C22×C4C2×C22⋊D711yescharacteristic
458C22×C4C23×D711yescharacteristic
459C2×C8—72no—
460C2×C8—141no—
461C2×C8—141no—
462C2×C8—141no—
463C2×C8—141no—
464C2×C8—141no—
465C2×C8—141no—
466C2×C8—141no—
467C2×C8—141no—
468C2×C8—141no—
469C2×C8—141no—
470C2×C8—141no—
471C4⋊C4—21no—
472C4⋊C4—21no—
473C4⋊C4—21no—
474C4⋊C4—21no—
475C4⋊C4—21no—
476C4⋊C4—21no—
477C4⋊C4—21no—
478C4⋊C4—21no—
479C4⋊C4—72no—
480C4⋊C4—72no—
481C4⋊C4—81no—
482C4⋊C4—81no—
483C4⋊C4—141no—
484C4⋊C4—141no—
485C4⋊C4—141no—
486C4⋊C4—141no—
487C4⋊C4—561no—
488C22⋊C4—22no—
489C22⋊C4—41no—
490C22⋊C4—42no—
491C22⋊C4—81no—
492C22⋊C4—144no—
493C22⋊C4—282no—
494C22⋊C4—282no—
495C22⋊C4—282no—
496C22⋊C4—561no—
497C42—21no—
498C42—21no—
499C42—21no—
500C42—21no—
501C42—42no—
502C42—282no—
503C42—561no—
504C2×C7—81no—
505C2×C7#246611yescharacteristic
506C2×C7#310211yescharacteristic
507C2×C7#311811yescharacteristic
508C2×C7#329611yescharacteristic
509C2×C7#330911yescharacteristic
510C2×C7#334111yescharacteristic
511C2×C7#335111yescharacteristic
512D7—82no—
513C23—21no—
514C23—21no—
515C23—21no—
516C23—21no—
517C23—21no—
518C23—21no—
519C23—21no—
520C23—142no—
521C23—281no—
522C23—281no—
523C23—281no—
524C23—281no—
525C23—281no—
526C23—281no—
527C23C22×C22⋊D711yescharacteristic
528D4—142no—
529D4—142no—
530D4—281no—
531D4—281no—
532D4—564no—
533C2×C4—21no—
534C2×C4—21no—
535C2×C4—21no—
536C2×C4—21no—
537C2×C4—21no—
538C2×C4—21no—
539C2×C4—21no—
540C2×C4—21no—
541C2×C4—21no—
542C2×C4—21no—
543C2×C4—21no—
544C2×C4—21no—
545C2×C4—21no—
546C2×C4—21no—
547C2×C4—41no—
548C2×C4—41no—
549C2×C4—41no—
550C2×C4—41no—
551C2×C4—41no—
552C2×C4—41no—
553C2×C4—41no—
554C2×C4—41no—
555C2×C4—41no—
556C2×C4—41no—
557C2×C4—41no—
558C2×C4—41no—
559C2×C4—41no—
560C2×C4—41no—
561C2×C4—41no—
562C2×C4—41no—
563C2×C4—142no—
564C2×C4—142no—
565C2×C4—281no—
566C2×C4—281no—
567C2×C4—281no—
568C2×C4—281no—
569C2×C4—281no—
570C2×C4—281no—
571C2×C4—281no—
572C2×C4—564no—
573C2×C4#651312yes—
574C2×C4D7×#4111yescharacteristic
575C2×C4D7×#4111yescharacteristic
576C2×C4D7×#4111yescharacteristic
577C2×C4D7×#4111yescharacteristic
578C2×C4#655311yescharacteristic
579C2×C4#655411yescharacteristic
580C8—142no—
581C8—281no—
582C8—281no—
583C8—281no—
584C7#2703811yescharacteristic, complemented, Sylow
585C22—41no—
586C22—41no—
587C22—41no—
588C22—41no—
589C22—41no—
590C22—41no—
591C22—41no—
592C22—282no—
593C22—282no—
594C22—282no—
595C22—561no—
596C22—561no—
597C22—561no—
598C22—561no—
599C22C2×#651311yescharacteristic
600C22#9051311yescharacteristic
601C22#9051511yescharacteristic
602C22#9051911yescharacteristic
603C22#9052011yescharacteristic
604C22#9052611yescharacteristic
605C22#9052811yescharacteristic
606C4—22no—
607C4—41no—
608C4—41no—
609C4—41no—
610C4—41no—
611C4—81no—
612C4—81no—
613C4—81no—
614C4—81no—
615C4—282no—
616C4—282no—
617C4—561no—
618C4#9039311yescharacteristic
619C4#9039711yescharacteristic
620C4#9039811yescharacteristic
621C4#9040011yescharacteristic
622C2—81no—
623C2—562no—
624C2#1174055011yescharacteristic
625C2#1174058511yescharacteristic
626C2#1174090511yescharacteristic
627C2#1174104111yescharacteristic
628C2#1174104311yescharacteristic
629C2#1174106411yescharacteristic
630C2#1174109211yescharacteristic
subgroupG/H
centerC23C22×C22⋊D7
commutator, cosocleC22×C4×C7C24
FrattiniC22×C4C23×D7
FittingC7×#2495C2
socleC23×C7C22×D4
prime radicalC2×#6493C22
hypercenter#2495D7
hypocenterC7#27038
LCSG ▷ C22×C4×C7 ▷ C2×C7 ▷ C7
UCSC1 ◁ C23 ◁ C4×C22⋊C4 ◁ #2495

Complements

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

NH ≅ G/Ntype
1. C7×#2495C2semidirect
3. #11727384C2semidirect
4. #11727380C2semidirect
5. #11727373C2semidirect
6. #11727356C2semidirect
7. #11727311C2semidirect
8. #11727294C2semidirect
11. #11727260C2semidirect
12. #11727257C2semidirect
13. C4×#6383C2semidirect
14. #11727214C2semidirect
15. #11727205C2semidirect
121. #2495D7semidirect
584. C7#27038semidirect

Maximal subgroups

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

subgroupindex
C7×#24952
#117309142
#117273842
#117273802
#117273732
#117273562
#117273112
#117272942
#117272782
#117272772
#117272602
#117272572
C4×#63832
#117272142
#117272052
#270387