Finite Group Databasebeta

← #13358129

Subgroups — #13358129

Order 1792.

874 conjugacy classes of subgroups.

The subgroup lattice has 620 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C7×#2293C211yesmaximal, characteristic
2C2×#89790C211yesmaximal, characteristic
3#11730745C211yesmaximal, characteristic, complemented
4#11729363C211yesmaximal, characteristic
5#11727403C211yesmaximal, characteristic
6#11727400C211yesmaximal, characteristic
7#11727399C211yesmaximal, characteristic
8#11727398C211yesmaximal, characteristic
9#11727374C211yesmaximal, characteristic, complemented
10#11727373C211yesmaximal, characteristic, complemented
11#11727370C211yesmaximal, characteristic, complemented
12#11727368C211yesmaximal, characteristic, complemented
13#11727235C211yesmaximal, characteristic, complemented
14#11727229C211yesmaximal, characteristic, complemented
15C4×#6377C211yesmaximal, characteristic, complemented
16C2×C4×C7×D4C2211yescharacteristic
17C2×C7×#117—21no—
18C22×#1142C2211yescharacteristic
19C2×C4×Dic14C2211yescharacteristic
20C7×#390C2211yescharacteristic
21C7×#390C2211yescharacteristic
22C7×#389C2211yescharacteristic
23C7×#389C2211yescharacteristic
24C7×#388—21no—
25C7×#388—21no—
26C4×C7×C4⋊C4C2211yescharacteristic
27C4×C7×C22⋊C4—21no—
28C43×C7C2211yescharacteristic
29C2×#6406C2211yescharacteristic
30C2×#6406C2211yescharacteristic
31C2×#6406C2211yescharacteristic
32#89790C418yescomplemented
33C2×#6384C2211yescharacteristic
34C2×#6384C2211yescharacteristic
35C2×#6384C2211yescharacteristic
36C2×#6382C2211yescharacteristic
37C2×#6381C2211yescharacteristic
38C2×#6381C2211yescharacteristic
39C4×C4⋊Dic7C2211yescharacteristic
40#89705—21no—
41#89705—21no—
42#89704—21no—
43C4×Dic7⋊C4—21no—
44#89701C2211yescharacteristic
45#89701C2211yescharacteristic
46#89700C2211yescharacteristic
47#89700C2211yescharacteristic
48C2×#6377C2211yescharacteristic
49C2×#6377C2211yescharacteristic
50C2×#6377C2211yescharacteristic
51C2×#6377C2211yescharacteristic
52C2×C4×C7⋊C8C2211yescharacteristic
53C2×C4×C7⋊C8C2211yescharacteristic
54#89324C2211yescharacteristic
55#89324C2211yescharacteristic
56#89324C2211yescharacteristic
57#89324C2211yescharacteristic
58#89324C2211yescharacteristic
59#89324C2211yescharacteristic
60#21288—71nomaximal, Sylow
61C22×C7×D4C2311yescharacteristic
62C23×C4×C7—21no—
63C22×Dic14C2311yescharacteristic
64C4×C7×D4—22no—
65C4×C7×D4C2×C414yes—
66C7×#117—44no—
67C2×C7×C4⋊C4—21no—
68C2×C7×C4⋊C4—21no—
69C2×C7×C4⋊C4C2311yescharacteristic
70C2×C7×C4⋊C4C2311yescharacteristic
71C2×C7×C4⋊C4C2311yescharacteristic
72C2×C7×C22⋊C4—21no—
73C2×C7×C22⋊C4—21no—
74C2×C7×C22⋊C4—21no—
75C2×C7×C22⋊C4—21no—
76C2×C7×C22⋊C4—21no—
77C2×C42×C7—21no—
78C2×C42×C7D411yescharacteristic
79C2×C42×C7D411yescharacteristic
80C2×C42×C7D411yescharacteristic
81C2×C42×C7D411yescharacteristic
82C2×C42×C7C2311yescharacteristic
83C2×C42×C7C2311yescharacteristic
84C2×C42×C7C2311yescharacteristic
85C2×#1142—22no—
86C2×#1142—22no—
87C2×#1142C2×C414yes—
88C2×C4⋊Dic7C2311yescharacteristic
89C2×C4⋊Dic7C2311yescharacteristic
90C2×C4⋊Dic7C2311yescharacteristic
91C2×Dic7⋊C4—21no—
92C2×Dic7⋊C4—21no—
93C2×Dic7⋊C4—21no—
94C2×C4×Dic7—21no—
95C2×C4×Dic7—21no—
96C22×C7⋊C8C2311yescharacteristic
97C22×C7⋊C8C2311yescharacteristic
98C22×C7⋊C8C2311yescharacteristic
99C22×C7⋊C8C2311yescharacteristic
100C4×Dic14—22no—
101C4×Dic14C2×C414yes—
102C7×#95—21no—
103C7×#95—21no—
104C7×#95—21no—
105#6406—22no—
106#6406—22no—
107#6406C2×C414yes—
108C7⋊#95—21no—
109C7⋊#95—21no—
110C7⋊#95—21no—
111C7⋊#95—21no—
112C7⋊#95—21no—
113C7⋊#95—21no—
114C7⋊#95—21no—
115#6384—22no—
116#6384—22no—
117#6384C2×C414yes—
118#6382—22no—
119#6381—22no—
120#6381C2×C414yes—
121#6377—22no—
122#6377—22no—
123#6377—22no—
124#6377C2×C414yes—
125C4×C7⋊C8—22no—
126C4×C7⋊C8—22no—
127C2×#440—71no—
128#2295—71no—
129#2293D711yescharacteristic
130#1973—71no—
131#1968—71no—
132#1943—71no—
133#1942—71no—
134#1936—71no—
135#1935—71no—
136#1934—71no—
137#1933—71no—
138#1776—71no—
139#1763—71no—
140#1762—71no—
141C4×#97—71no—
142C24×C7—21no—
143C2×C7×D4—21no—
144C2×C7×D4—21no—
145C2×C7×D4—21no—
146C2×C7×D4—21no—
147C2×C7×D4—21no—
148C2×C7×D4C22×C412yes—
149C22×C4×C7—21no—
150C22×C4×C7—24no—
151C22×C4×C7—21no—
152C22×C4×C7—21no—
153C22×C4×C7—42no—
154C22×C4×C7—42no—
155C22×C4×C7C2×D411yescharacteristic
156C22×C4×C7C2×D411yescharacteristic
157C22×C4×C7C2×D411yescharacteristic
158C22×C4×C7C2×D411yescharacteristic
159C22×C4×C7C2×D411yescharacteristic
160C22×C4×C7C2×D411yescharacteristic
161C22×C4×C7C2411yescharacteristic
162C22×Dic7—21no—
163C22×Dic7—21no—
164C22×Dic7—21no—
165C22×Dic7—21no—
166C2×Dic14—21no—
167C2×Dic14—21no—
168C2×Dic14—21no—
169C2×Dic14—21no—
170C2×Dic14—21no—
171C2×Dic14C22×C412yes—
172C7×C4⋊C4—21no—
173C7×C4⋊C4—21no—
174C7×C4⋊C4—21no—
175C7×C4⋊C4—21no—
176C7×C4⋊C4—21no—
177C7×C4⋊C4—42no—
178C7×C4⋊C4—42no—
179C7×C4⋊C4C22×C412yes—
180C7×C22⋊C4—24no—
181C7×C22⋊C4—42no—
182C7×C22⋊C4—42no—
183C7×C22⋊C4—42no—
184C7×C22⋊C4—42no—
185C42×C7—22no—
186C42×C7—22no—
187C42×C7—21no—
188C42×C7—21no—
189C42×C7—21no—
190C42×C7—21no—
191C42×C7—41no—
192C42×C7—41no—
193C42×C7—42no—
194C42×C7C22×C412yes—
195C42×C7#4112yes—
196#1142—28no—
197C4⋊Dic7—21no—
198C4⋊Dic7—21no—
199C4⋊Dic7—21no—
200C4⋊Dic7—21no—
201C4⋊Dic7—21no—
202C4⋊Dic7C22×C412yes—
203Dic7⋊C4—24no—
204Dic7⋊C4—42no—
205Dic7⋊C4—42no—
206C4×Dic7—24no—
207C4×Dic7—42no—
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⋊C8C22×C412yes—
215C2×C7⋊C8C22×C412yes—
216C2×C7⋊C8#4112yes—
217C2×C7⋊C8#4112yes—
218C2×C7⋊C8#4112yes—
219C2×C7⋊C8#4112yes—
220C22×SD16—71no—
221C2×C4×Q8—71no—
222C2×C4×D4C2×D711yescharacteristic
223C2×#117—21no—
224#440—78no—
225C2×#107—71no—
226C2×#107—71no—
227C2×#106—71no—
228C2×#103—71no—
229C2×#103—71no—
230C2×#103—71no—
231C2×#102—71no—
232C2×#102—71no—
233C2×#102—71no—
234C2×#97—71no—
235C2×#97—71no—
236C2×#97—71no—
237C2×#97—71no—
238C2×C4×C8—71no—
239C2×C4×C8—71no—
240#391—71no—
241#391—71no—
242#390C2×D711yescharacteristic
243#390C2×D711yescharacteristic
244#389—71no—
245#389—71no—
246#389C2×D711yescharacteristic
247#389C2×D711yescharacteristic
248#388—21no—
249#388—21no—
250#387—141no—
251#387—141no—
252C4×C4⋊C4—71no—
253C4×C4⋊C4—141no—
254C4×C4⋊C4C2×D711yescharacteristic
255C4×C22⋊C4—21no—
256#376—141no—
257C43C2×D711yescharacteristic
258#340—71no—
259#340—71no—
260#340—71no—
261#340—71no—
262#340—71no—
263#340—71no—
264C23×C7—22no—
265C23×C7—41no—
266C23×C7—41no—
267C23×C7—41no—
268C23×C7—41no—
269C23×C7—41no—
270C23×C7—41no—
271C23×C7C22×D411yescharacteristic
272C7×D4—22no—
273C7×D4—22no—
274C7×D4—41no—
275C7×D4—41no—
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—22no—
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—48no—
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×C7C4×D412yes—
301C2×C4×C7C4×D412yes—
302C2×C4×C7AGL(1,ℤ/8)12yes—
303C2×C4×C7#13712yes—
304C2×C4×C7C23×C411yescharacteristic
305C2×C4×C7C2×#4111yescharacteristic
306C2×C4×C7C2×#4111yescharacteristic
307C2×C4×C7C2×#4111yescharacteristic
308C2×C4×C7C2×#4111yescharacteristic
309C2×C4×C7C2×#4111yescharacteristic
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—
319C2×Dic7—41no—
320C2×Dic7—41no—
321C2×Dic7—41no—
322Dic14—22no—
323Dic14—22no—
324Dic14—41no—
325Dic14—41no—
326C7⋊C8—22no—
327C7⋊C8—22no—
328C7⋊C8—22no—
329C7⋊C8#11714yescomplemented
330C22×Q8—71no—
331C22×D4C22×D711yescharacteristic
332C23×C4—21no—
333C2×SD16—74no—
334C2×SD16—142no—
335C2×SD16—142no—
336C22×C8—71no—
337C22×C8—71no—
338C22×C8—71no—
339C22×C8—71no—
340C4×Q8—74no—
341C4×Q8—142no—
342C4×D4—22no—
343C4×D4C4×D714yes—
344#117—44no—
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⋊C4—141no—
352C2×C4⋊C4—141no—
353C2×C4⋊C4C22×D711yescharacteristic
354C2×C4⋊C4C22×D711yescharacteristic
355C2×C4⋊C4C22×D711yescharacteristic
356C2×C22⋊C4—21no—
357C2×C22⋊C4—21no—
358C2×C22⋊C4—21no—
359C2×C22⋊C4—21no—
360C2×C22⋊C4—21no—
361C2×C42—21no—
362C2×C42—141no—
363C2×C42—141no—
364C2×C42C22⋊D711yescharacteristic
365C2×C42C22⋊D711yescharacteristic
366C2×C42C22⋊D711yescharacteristic
367C2×C42C22⋊D711yescharacteristic
368C2×C42C22×D711yescharacteristic
369C2×C42C22×D711yescharacteristic
370C2×C42C22×D711yescharacteristic
371#107—74no—
372#107—142no—
373#106—142no—
374#103—74no—
375#103—142no—
376#103—142no—
377#102—74no—
378#102—142no—
379#102—142no—
380#97—74no—
381#97—142no—
382#97—142no—
383#97—142no—
384C4×C8—142no—
385C4×C8—142no—
386#95—21no—
387#95—21no—
388#95—21no—
389#95—141no—
390#95—141no—
391#95—141no—
392#95—141no—
393#95—141no—
394#95—141no—
395#95—141no—
396C22×C7—42no—
397C22×C7—42no—
398C22×C7—42no—
399C22×C7—81no—
400C22×C7—81no—
401C22×C7—81no—
402C22×C7—81no—
403C22×C7C2×C4×D411yescharacteristic
404C22×C7#53211yescharacteristic
405C22×C7#53211yescharacteristic
406C22×C7C2×AGL(1,ℤ/8)11yescharacteristic
407C22×C7C2×#13711yescharacteristic
408C22×C7#57511yescharacteristic
409C22×C7#57511yescharacteristic
410C4×C7—22no—
411C4×C7—22no—
412C4×C7—22no—
413C4×C7—22no—
414C4×C7—41no—
415C4×C7—41no—
416C4×C7—42no—
417C4×C7—81no—
418C4×C7—81no—
419C4×C7C2×#11711yescharacteristic
420C4×C7C4×#4111yescharacteristic
421C4×C7#52911yescharacteristic
422C4×C7#52911yescharacteristic
423Dic7—42no—
424Dic7—42no—
425Dic7—81no—
426Dic7—81no—
427C24—21no—
428C2×Q8—72no—
429C2×Q8—141no—
430C2×Q8—141no—
431C2×Q8—141no—
432C2×Q8—141no—
433C2×Q8—141no—
434C2×D4—21no—
435C2×D4—21no—
436C2×D4—21no—
437C2×D4—21no—
438C2×D4—21no—
439C2×D4C2×C4×D712yes—
440C22×C4—21no—
441C22×C4—24no—
442C22×C4—21no—
443C22×C4—21no—
444C22×C4—42no—
445C22×C4—42no—
446C22×C4—141no—
447C22×C4—141no—
448C22×C4—141no—
449C22×C4—141no—
450C22×C4C2×C22⋊D711yescharacteristic
451C22×C4C2×C22⋊D711yescharacteristic
452C22×C4C2×C22⋊D711yescharacteristic
453C22×C4C2×C22⋊D711yescharacteristic
454C22×C4C2×C22⋊D711yescharacteristic
455C22×C4C2×C22⋊D711yescharacteristic
456C22×C4C23×D711yescharacteristic
457SD16—148no—
458C2×C8—72no—
459C2×C8—72no—
460C2×C8—72no—
461C2×C8—72no—
462C2×C8—72no—
463C2×C8—72no—
464C2×C8—141no—
465C2×C8—141no—
466C2×C8—141no—
467C2×C8—141no—
468C2×C8—141no—
469C2×C8—141no—
470C4⋊C4—21no—
471C4⋊C4—21no—
472C4⋊C4—21no—
473C4⋊C4—21no—
474C4⋊C4—21no—
475C4⋊C4—42no—
476C4⋊C4—42no—
477C4⋊C4—72no—
478C4⋊C4—144no—
479C4⋊C4—141no—
480C4⋊C4—141no—
481C4⋊C4—141no—
482C4⋊C4—141no—
483C4⋊C4—141no—
484C4⋊C4—282no—
485C4⋊C4—282no—
486C4⋊C4C2×C4×D712yes—
487C22⋊C4—24no—
488C22⋊C4—42no—
489C22⋊C4—42no—
490C22⋊C4—42no—
491C22⋊C4—42no—
492C42—22no—
493C42—22no—
494C42—21no—
495C42—21no—
496C42—21no—
497C42—21no—
498C42—41no—
499C42—41no—
500C42—42no—
501C42—144no—
502C42—282no—
503C42C2×C4×D712yes—
504C42#115712yes—
505C2×C7—82no—
506C2×C7#229311yescharacteristic
507C2×C7C4×AGL(1,ℤ/8)11yescharacteristic
508C2×C7C4×#13711yescharacteristic
509C2×C7#318011yescharacteristic
510C2×C7#318111yescharacteristic
511C2×C7#318211yescharacteristic
512C2×C7#318311yescharacteristic
513C23—22no—
514C23—41no—
515C23—41no—
516C23—41no—
517C23—41no—
518C23—41no—
519C23—41no—
520C23C22×C22⋊D711yescharacteristic
521Q8—142no—
522Q8—142no—
523Q8—281no—
524Q8—281no—
525D4—22no—
526D4—22no—
527D4—41no—
528D4—41no—
529C2×C4—21no—
530C2×C4—21no—
531C2×C4—21no—
532C2×C4—21no—
533C2×C4—21no—
534C2×C4—21no—
535C2×C4—21no—
536C2×C4—21no—
537C2×C4—22no—
538C2×C4—21no—
539C2×C4—21no—
540C2×C4—21no—
541C2×C4—21no—
542C2×C4—21no—
543C2×C4—21no—
544C2×C4—48no—
545C2×C4—41no—
546C2×C4—41no—
547C2×C4—41no—
548C2×C4—41no—
549C2×C4—41no—
550C2×C4—41no—
551C2×C4—41no—
552C2×C4—41no—
553C2×C4—142no—
554C2×C4—142no—
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—281no—
564C2×C4—281no—
565C2×C4C4×C22⋊D712yes—
566C2×C4C4×C22⋊D712yes—
567C2×C4#649512yes—
568C2×C4#651412yes—
569C2×C4C22×C4×D711yescharacteristic
570C2×C4C2×#115711yescharacteristic
571C2×C4D7×#4111yescharacteristic
572C2×C4D7×#4111yescharacteristic
573C2×C4D7×#4111yescharacteristic
574C2×C4D7×#4111yescharacteristic
575C8—74no—
576C8—142no—
577C8—142no—
578C8—142no—
579C7#2128811yescharacteristic, complemented, Sylow
580C22—42no—
581C22—42no—
582C22—42no—
583C22—81no—
584C22—81no—
585C22—81no—
586C22—81no—
587C22C2×C4×C22⋊D711yescharacteristic
588C22C2×#649511yescharacteristic
589C22#9051311yescharacteristic
590C22#9051311yescharacteristic
591C22C2×#651411yescharacteristic
592C22#9052311yescharacteristic
593C22#9052311yescharacteristic
594C4—22no—
595C4—22no—
596C4—22no—
597C4—22no—
598C4—41no—
599C4—42no—
600C4—41no—
601C4—81no—
602C4—81no—
603C4—282no—
604C4—282no—
605C4—561no—
606C4—561no—
607C4D7×#11711yescharacteristic
608C4#9021311yescharacteristic
609C4#9021911yescharacteristic
610C4#9021911yescharacteristic
611C2—82no—
612C2#1173967011yescharacteristic
613C2C4×#649511yescharacteristic
614C2C4×#651411yescharacteristic
615C2#1174058311yescharacteristic
616C2#1174058411yescharacteristic
617C2#1174073811yescharacteristic
618C2#1174073911yescharacteristic
subgroupG/H
centerC23C22×C22⋊D7
commutatorC2×C4×C7C23×C4
FrattiniC22×C4C23×D7
FittingC7×#2293C2
socleC23×C7C22×D4
prime radicalC22×C7×D4C23
cosocleC22×C4×C7C24
hypercenter#2293D7
hypocenterC7#21288
LCSG ▷ C2×C4×C7 ▷ C2×C7 ▷ C7
UCSC1 ◁ C23 ◁ C43 ◁ #2293

Complements

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

NH ≅ G/Ntype
3. #11730745C2semidirect
9. #11727374C2semidirect
10. #11727373C2semidirect
11. #11727370C2semidirect
12. #11727368C2semidirect
13. #11727235C2semidirect
14. #11727229C2semidirect
15. C4×#6377C2semidirect
32. #89790C4semidirect
329. C7⋊C8#117semidirect
579. C7#21288semidirect

Maximal subgroups

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

subgroupindex
C7×#22932
C2×#897902
#117307452
#117293632
#117274032
#117274002
#117273992
#117273982
#117273742
#117273732
#117273702
#117273682
#117272352
#117272292
C4×#63772
#212887