Finite Group Databasebeta

← #13358669

Subgroups — #13358669

Order 1792.

938 conjugacy classes of subgroups.

The subgroup lattice has 612 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#89477C211yesmaximal, characteristic
2#11731197C211yesmaximal, characteristic
3C4×D7×C4⋊C4C211yesmaximal, characteristic
4C7×#1776C211yesmaximal, characteristic, complemented
5#11728386C211yesmaximal, characteristic
6#11728370C211yesmaximal, characteristic, complemented
7#11728333C211yesmaximal, characteristic
8#11728318C211yesmaximal, characteristic, complemented
9#11727568C211yesmaximal, characteristic, complemented
10#11727235C211yesmaximal, characteristic, complemented
11#11727235C211yesmaximal, characteristic, complemented
12#11726629C211yesmaximal, characteristic
13#11726628C211yesmaximal, characteristic
14#11726552C211yesmaximal, characteristic, complemented
15#11726551C211yesmaximal, characteristic, complemented
16C2×D7×C4⋊C4C2211yescharacteristic
17C2×D7×C4⋊C4C2211yescharacteristic
18C2×C42×D7—21no—
19C2×C42×D7C2211yescharacteristic
20C2×C7×#107C2211yescharacteristic
21C2×C7×#106C2211yescharacteristic
22C2×C7×#97C2211yescharacteristic
23C4×C7×C4⋊C4C2211yescharacteristic
24C4×C7×C4⋊C4C2211yescharacteristic
25C2×(C2×D7)⋊C8C2211yescharacteristic
26C2×(C2×D7)⋊C8C2211yescharacteristic
27C2×#6392C2211yescharacteristic
28C2×#6391C2211yescharacteristic
29C2×Dic7⋊C8C2211yescharacteristic
30C2×Dic7⋊C8C2211yescharacteristic
31#89759C2211yescharacteristic
32#89759C2211yescharacteristic
33#89749C2211yescharacteristic
34#89749C2211yescharacteristic
35C4⋊C4×Dic7C2211yescharacteristic
36C4⋊C4×Dic7C2211yescharacteristic
37C2×#6382C2211yescharacteristic
38C2×#6382C2211yescharacteristic
39C2×#6381C2211yescharacteristic
40C2×#6381C2211yescharacteristic
41C4×(C2×D7)⋊C4—21no—
42C4×C4⋊Dic7C2211yescharacteristic
43C4×C4⋊Dic7C2211yescharacteristic
44#89704—21no—
45C4×Dic7⋊C4—21no—
46C2×#6377C2211yescharacteristic
47#89477C418yescomplemented
48#89436—21no—
49D7×#95—21no—
50#89423—21no—
51#89421—21no—
52C7×#340C2211yescharacteristic
53C7×#340C2211yescharacteristic
54#89346C2211yescharacteristic
55#89346C2211yescharacteristic
56#89324C2211yescharacteristic
57#89324C2211yescharacteristic
58#89324C2211yescharacteristic
59#89324C2211yescharacteristic
60#21363—71nomaximal, Sylow
61C22×C4×D7—21no—
62C22×C4×D7—21no—
63C22×C4×D7D411yescharacteristic
64C22×C4×D7D411yescharacteristic
65C22×C4×D7C2311yescharacteristic
66C22×C7×C8C2311yescharacteristic
67C22×C7×C8C2311yescharacteristic
68C2×C7×C4⋊C4C2311yescharacteristic
69C2×C7×C4⋊C4C2311yescharacteristic
70C2×C7×C4⋊C4C2311yescharacteristic
71C2×C7×C4⋊C4C2311yescharacteristic
72C2×C42×C7—21no—
73C2×C42×C7—21no—
74C2×C42×C7C2311yescharacteristic
75C2×(C2×D7)⋊C4—21no—
76C2×(C2×D7)⋊C4—21no—
77C2×C4⋊Dic7C2311yescharacteristic
78C2×C4⋊Dic7C2311yescharacteristic
79C2×C4⋊Dic7C2311yescharacteristic
80C2×C4⋊Dic7C2311yescharacteristic
81C2×Dic7⋊C4—21no—
82C2×Dic7⋊C4—21no—
83C2×C4×Dic7—21no—
84C2×C4×Dic7—21no—
85C2×C4×Dic7—21no—
86C2×C4×Dic7—21no—
87C2×C4×Dic7D411yescharacteristic
88C2×C4×Dic7D411yescharacteristic
89C2×C4×Dic7C2311yescharacteristic
90C22×C7⋊C8C2311yescharacteristic
91C22×C7⋊C8C2311yescharacteristic
92D7×C4⋊C4—22no—
93D7×C4⋊C4—22no—
94D7×C4⋊C4—22no—
95D7×C4⋊C4—22no—
96C42×D7—44no—
97C42×D7C2×C414yes—
98C42×D7Q814yes—
99C7×#107—22no—
100C7×#106—22no—
101C7×#97C2×C414yescomplemented
102C7×#95—21no—
103C7×#95—21no—
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—
113C7⋊#95—21no—
114(C2×D7)⋊C8C2×C414yes—
115(C2×D7)⋊C8C2×C414yes—
116#6392—22no—
117#6391—22no—
118Dic7⋊C8C2×C414yescomplemented
119Dic7⋊C8C2×C414yescomplemented
120#6382—22no—
121#6382—22no—
122#6381—22no—
123#6381—22no—
124#6377C2×C414yescomplemented
125C2×#432—71no—
126#2283—71no—
127C2×C4×C4⋊C4—71no—
128#1949—71no—
129#1949—71no—
130#1949—71no—
131#1949—71no—
132#1853—71no—
133#1853—71no—
134#1852—71no—
135#1852—71no—
136#1776—71no—
137#1776—71no—
138#1776—71no—
139#1776D711yescharacteristic, complemented
140C23×D7C2×D411yescharacteristic
141C22×C4×C7—21no—
142C22×C4×C7—21no—
143C22×C4×C7—21no—
144C22×C4×C7—21no—
145C22×C4×C7C2×D411yescharacteristic
146C22×C4×C7C2×D411yescharacteristic
147C22×C4×C7C2411yescharacteristic
148C22×Dic7—21no—
149C22×Dic7—21no—
150C22×Dic7—21no—
151C22×Dic7—21no—
152C22×Dic7C2×D411yescharacteristic
153C22×Dic7C2×D411yescharacteristic
154C22×Dic7C2×D411yescharacteristic
155C2×C4×D7—22no—
156C2×C4×D7—22no—
157C2×C4×D7—21no—
158C2×C4×D7—21no—
159C2×C4×D7—21no—
160C2×C4×D7—21no—
161C2×C4×D7—24no—
162C2×C4×D7—24no—
163C2×C4×D7—41no—
164C2×C4×D7—41no—
165C2×C4×D7—42no—
166C2×C4×D7—42no—
167C2×C4×D7—42no—
168C2×C4×D7—42no—
169C2×C4×D7C4⋊C414yes—
170C2×C4×D7C4⋊C414yes—
171C2×C4×D7C22×C412yes—
172C2×C4×D7C2×Q812yes—
173C2×C7×C8—21no—
174C2×C7×C8—21no—
175C2×C7×C8—21no—
176C2×C7×C8—21no—
177C2×C7×C8C22×C412yes—
178C2×C7×C8C22×C412yes—
179C7×C4⋊C4—21no—
180C7×C4⋊C4—21no—
181C7×C4⋊C4—21no—
182C7×C4⋊C4—21no—
183C7×C4⋊C4—21no—
184C7×C4⋊C4—21no—
185C7×C4⋊C4#4112yes—
186C7×C4⋊C4#4112yes—
187C42×C7—42no—
188C42×C7—42no—
189C42×C7C22×C412yes—
190C42×C7C2×Q812yes—
191(C2×D7)⋊C4—42no—
192(C2×D7)⋊C4—42no—
193C4⋊Dic7—21no—
194C4⋊Dic7—21no—
195C4⋊Dic7—21no—
196C4⋊Dic7—21no—
197C4⋊Dic7—21no—
198C4⋊Dic7—21no—
199C4⋊Dic7#4112yes—
200C4⋊Dic7#4112yes—
201Dic7⋊C4—24no—
202Dic7⋊C4—24no—
203C4×Dic7—42no—
204C4×Dic7—42no—
205C4×Dic7—42no—
206C4×Dic7—42no—
207C4×Dic7C4⋊C414yes—
208C4×Dic7C4⋊C414yes—
209C4×Dic7C22×C412yes—
210C4×Dic7C2×Q812yes—
211C2×C7⋊C8—21no—
212C2×C7⋊C8—21no—
213C2×C7⋊C8—21no—
214C2×C7⋊C8—21no—
215C2×C7⋊C8C22×C412yes—
216C2×C7⋊C8C22×C412yes—
217C22×C4⋊C4—71no—
218C22×C4⋊C4—71no—
219C22×C42—71no—
220C22×C42—141no—
221#432—78no—
222C2×#107—71no—
223C2×#107—71no—
224C2×#107—71no—
225C2×#107C2×D711yescharacteristic
226C2×#106—71no—
227C2×#106—71no—
228C2×#106—71no—
229C2×#106C2×D711yescharacteristic
230C2×C4⋊C8—71no—
231C2×C4⋊C8—71no—
232C2×C22⋊C8—71no—
233C2×C22⋊C8—71no—
234C2×#97—71no—
235C2×#97C2×D711yescharacteristic
236#383—141no—
237#382—71no—
238#382—71no—
239#381—141no—
240#380—71no—
241#380—71no—
242C4×C4⋊C4—71no—
243C4×C4⋊C4—71no—
244C4×C4⋊C4—71no—
245C4×C4⋊C4—71no—
246C4×C4⋊C4—141no—
247C4×C4⋊C4—141no—
248C4×C4⋊C4C2×D711yescharacteristic
249C4×C4⋊C4C2×D711yescharacteristic
250C4×C22⋊C4—141no—
251#376—141no—
252C2×#95—141no—
253#340—71no—
254#340—71no—
255#340—71no—
256#340—71no—
257#340—71no—
258#340—71no—
259#340C2×D711yescharacteristic
260#340C2×D711yescharacteristic
261C23×C7C22×D411yescharacteristic
262C22×D7—21no—
263C22×D7—21no—
264C22×D7—21no—
265C22×D7—21no—
266C22×D7C2×C4⋊C412yes—
267C22×D7AGL(1,ℤ/8)12yes—
268C22×D7#13712yes—
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—41no—
276C2×C4×C7—41no—
277C2×C4×C7—41no—
278C2×C4×C7—41no—
279C2×C4×C7—41no—
280C2×C4×C7—41no—
281C2×C4×C7—41no—
282C2×C4×C7—41no—
283C2×C4×C7—41no—
284C2×C4×C7—41no—
285C2×C4×C7C2×C4⋊C412yes—
286C2×C4×C7C2×C4⋊C412yes—
287C2×C4×C7C23×C411yescharacteristic
288C2×C4×C7C22×Q811yescharacteristic
289C2×C4×C7C2×#4111yescharacteristic
290C2×C4×C7C2×#4111yescharacteristic
291C2×C4×C7C2×#4111yescharacteristic
292C2×C4×C7C2×#4111yescharacteristic
293C2×Dic7—21no—
294C2×Dic7—21no—
295C2×Dic7—21no—
296C2×Dic7—21no—
297C2×Dic7—21no—
298C2×Dic7—21no—
299C2×Dic7—22no—
300C2×Dic7—22no—
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×Dic7C2×C4⋊C412yes—
312C2×Dic7C2×C4⋊C412yes—
313C2×Dic7C2×C4⋊C412yes—
314C4×D7—28no—
315C4×D7—22no—
316C4×D7—22no—
317C4×D7—22no—
318C4×D7—22no—
319C4×D7—44no—
320C4×D7—48no—
321C4×D7—48no—
322C7×C8—22no—
323C7×C8—22no—
324C7⋊C8—22no—
325C7⋊C8—22no—
326C23×C4—71no—
327C23×C4—71no—
328C23×C4—71no—
329C23×C4—141no—
330C23×C4—141no—
331C22×C8—71no—
332C22×C8—71no—
333C22×C8C22×D711yescharacteristic
334C22×C8C22×D711yescharacteristic
335C2×C4⋊C4—71no—
336C2×C4⋊C4—71no—
337C2×C4⋊C4—71no—
338C2×C4⋊C4—71no—
339C2×C4⋊C4—142no—
340C2×C4⋊C4—142no—
341C2×C4⋊C4—141no—
342C2×C4⋊C4—141no—
343C2×C4⋊C4—142no—
344C2×C4⋊C4—142no—
345C2×C4⋊C4C22×D711yescharacteristic
346C2×C4⋊C4C22×D711yescharacteristic
347C2×C4⋊C4C22×D711yescharacteristic
348C2×C4⋊C4C22×D711yescharacteristic
349C2×C22⋊C4—141no—
350C2×C22⋊C4—141no—
351C2×C42—21no—
352C2×C42—21no—
353C2×C42—71no—
354C2×C42—71no—
355C2×C42—71no—
356C2×C42—74no—
357C2×C42—74no—
358C2×C42—141no—
359C2×C42—141no—
360C2×C42—141no—
361C2×C42—141no—
362C2×C42—284no—
363C2×C42C22×D711yescharacteristic
364#107—22no—
365#107—142no—
366#107—142no—
367#107—142no—
368#106—22no—
369#106—142no—
370#106—142no—
371#106—142no—
372C4⋊C8—74no—
373C4⋊C8—74no—
374C22⋊C8—74no—
375C22⋊C8—74no—
376#97—74no—
377#97C4×D714yescomplemented
378#95—21no—
379#95—21no—
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#95—141no—
390C22×C7C22×C4⋊C411yescharacteristic
391C22×C7#52511yescharacteristic
392C22×C7#52511yescharacteristic
393C22×C7C2×AGL(1,ℤ/8)11yescharacteristic
394C22×C7C2×#13711yescharacteristic
395C22×C7#57511yescharacteristic
396C22×C7#57511yescharacteristic
397C2×D7—22no—
398C2×D7—22no—
399C2×D7—22no—
400C2×D7—22no—
401C2×D7—22no—
402C2×D7—22no—
403C2×D7#42814yes—
404C4×C7—22no—
405C4×C7—22no—
406C4×C7—42no—
407C4×C7—42no—
408C4×C7—81no—
409C4×C7—81no—
410C4×C7C4×#4111yescharacteristic
411C4×C7C4×#4111yescharacteristic
412C4×C7#53311yescharacteristic
413C4×C7#53311yescharacteristic
414Dic7—22no—
415Dic7—22no—
416Dic7—22no—
417Dic7—42no—
418Dic7—42no—
419Dic7—81no—
420Dic7—81no—
421C24—71no—
422C22×C4—21no—
423C22×C4—21no—
424C22×C4—21no—
425C22×C4—21no—
426C22×C4—71no—
427C22×C4—71no—
428C22×C4—71no—
429C22×C4—74no—
430C22×C4—72no—
431C22×C4—72no—
432C22×C4—74no—
433C22×C4—142no—
434C22×C4—142no—
435C22×C4—144no—
436C22×C4—144no—
437C22×C4—141no—
438C22×C4—141no—
439C22×C4—141no—
440C22×C4—141no—
441C22×C4—141no—
442C22×C4—141no—
443C22×C4—141no—
444C22×C4—141no—
445C22×C4—281no—
446C22×C4—281no—
447C22×C4—282no—
448C22×C4—282no—
449C22×C4—282no—
450C22×C4—282no—
451C22×C4D4×D711yescharacteristic
452C22×C4D4×D711yescharacteristic
453C22×C4C23×D711yescharacteristic
454C2×C8—21no—
455C2×C8—21no—
456C2×C8—21no—
457C2×C8—21no—
458C2×C8—72no—
459C2×C8—72no—
460C2×C8—141no—
461C2×C8—141no—
462C2×C8—141no—
463C2×C8—141no—
464C2×C8C2×C4×D712yes—
465C2×C8C2×C4×D712yes—
466C4⋊C4—21no—
467C4⋊C4—21no—
468C4⋊C4—21no—
469C4⋊C4—21no—
470C4⋊C4—21no—
471C4⋊C4—21no—
472C4⋊C4—72no—
473C4⋊C4—72no—
474C4⋊C4—144no—
475C4⋊C4—144no—
476C4⋊C4—141no—
477C4⋊C4—141no—
478C4⋊C4—141no—
479C4⋊C4—141no—
480C4⋊C4—141no—
481C4⋊C4—141no—
482C4⋊C4#115712yes—
483C4⋊C4#115712yes—
484C22⋊C4—282no—
485C22⋊C4—282no—
486C42—42no—
487C42—42no—
488C42—74no—
489C42—74no—
490C42—72no—
491C42—72no—
492C42—282no—
493C42—282no—
494C42—282no—
495C42—282no—
496C42C2×C4×D712yes—
497C42Q8×D712yes—
498C2×C7#229611yescharacteristic
499C2×C7C2×#42811yescharacteristic
500C2×C7#291111yescharacteristic
501C2×C7#311411yescharacteristic
502C2×C7#311411yescharacteristic
503C2×C7#311711yescharacteristic
504C2×C7#311711yescharacteristic
505D7—24no—
506C23—72no—
507C23—72no—
508C23—72no—
509C23—141no—
510C23—141no—
511C23—141no—
512C23—141no—
513C23C2×D4×D711yescharacteristic
514C2×C4—21no—
515C2×C4—21no—
516C2×C4—21no—
517C2×C4—21no—
518C2×C4—22no—
519C2×C4—22no—
520C2×C4—41no—
521C2×C4—41no—
522C2×C4—41no—
523C2×C4—41no—
524C2×C4—41no—
525C2×C4—41no—
526C2×C4—41no—
527C2×C4—41no—
528C2×C4—41no—
529C2×C4—41no—
530C2×C4—72no—
531C2×C4—72no—
532C2×C4—72no—
533C2×C4—148no—
534C2×C4—141no—
535C2×C4—141no—
536C2×C4—141no—
537C2×C4—141no—
538C2×C4—141no—
539C2×C4—141no—
540C2×C4—142no—
541C2×C4—142no—
542C2×C4—142no—
543C2×C4—142no—
544C2×C4—142no—
545C2×C4—142no—
546C2×C4—284no—
547C2×C4—288no—
548C2×C4—288no—
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×C4D7×C4⋊C412yes—
560C2×C4D7×C4⋊C412yes—
561C2×C4C22×C4×D711yescharacteristic
562C2×C4C2×#115711yescharacteristic
563C2×C4C2×#115711yescharacteristic
564C2×C4C2×Q8×D711yescharacteristic
565C2×C4D7×#4111yescharacteristic
566C2×C4D7×#4111yescharacteristic
567C8—22no—
568C8—22no—
569C8—142no—
570C8—142no—
571C7#2136311yescharacteristic, complemented, Sylow
572C22—74no—
573C22—142no—
574C22—142no—
575C22—142no—
576C22—142no—
577C22—142no—
578C22—142no—
579C22C2×D7×C4⋊C411yescharacteristic
580C22#9023811yescharacteristic
581C22#9023811yescharacteristic
582C22D7×AGL(1,ℤ/8)11yescharacteristic
583C22#9046411yescharacteristic
584C22D7×#13711yescharacteristic
585C22#9046811yescharacteristic
586C4—22no—
587C4—22no—
588C4—42no—
589C4—42no—
590C4—81no—
591C4—81no—
592C4—142no—
593C4—142no—
594C4—142no—
595C4—282no—
596C4—282no—
597C4—561no—
598C4—561no—
599C4C4×#115711yescharacteristic
600C4#9021311yescharacteristic
601C4#9026911yescharacteristic
602C4#9026911yescharacteristic
603C2—144no—
604C2#1173120011yescharacteristic
605C2D7×#42811yescharacteristic
606C2#1173665311yescharacteristic
607C2#1173722711yescharacteristic
608C2#1173722911yescharacteristic
609C2#1173727911yescharacteristic
610C2#1173731611yescharacteristic
subgroupG/H
centerC23C2×D4×D7
commutatorC2×C4×C7C23×C4
FrattiniC22×C4C23×D7
FittingC7×#1776C2
socleC23×C7C22×D4
prime radicalC23×D7C2×D4
cosocleC22×C4×C7C24
hypercenter#1776D7
hypocenterC7#21363
LCSG ▷ C2×C4×C7 ▷ C2×C7 ▷ C7
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1776

Complements

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

NH ≅ G/Ntype
4. C7×#1776C2semidirect
6. #11728370C2semidirect
8. #11728318C2semidirect
9. #11727568C2semidirect
10. #11727235C2semidirect
11. #11727235C2semidirect
14. #11726552C2semidirect
15. #11726551C2semidirect
47. #89477C4semidirect
101. C7×#97C2×C4semidirect
118. Dic7⋊C8C2×C4semidirect
119. Dic7⋊C8C2×C4semidirect
124. #6377C2×C4semidirect
139. #1776D7semidirect
377. #97C4×D7semidirect
571. C7#21363semidirect

Maximal subgroups

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

subgroupindex
C2×#894772
#117311972
C4×D7×C4⋊C42
C7×#17762
#117283862
#117283702
#117283332
#117283182
#117275682
#117272352
#117266292
#117266282
#117265522
#117265512
#213637