Finite Group Databasebeta

← #13361440

Subgroups — #13361440

Order 1792.

988 conjugacy classes of subgroups.

The subgroup lattice has 624 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C4×D4×Dic7C211yesmaximal, characteristic
2C2×#89533C211yesmaximal, characteristic
3#11733412C211yesmaximal, characteristic, complemented
4C7×#1862C211yesmaximal, characteristic
5#11729360C211yesmaximal, characteristic
6#11728369C211yesmaximal, characteristic, complemented
7#11728359C211yesmaximal, characteristic, complemented
8#11727907C211yesmaximal, characteristic
9#11727906C211yesmaximal, characteristic
10#11727906C211yesmaximal, characteristic
11#11727355C211yesmaximal, characteristic, complemented
12#11726553C211yesmaximal, characteristic, complemented
13#11726540C211yesmaximal, characteristic, complemented
14#11726376C211yesmaximal, characteristic, complemented
15#11726357C211yesmaximal, characteristic, complemented
16C2×C4×C7×D4C2211yescharacteristic
17C2×D4×Dic7C2211yescharacteristic
18C2×D4×Dic7C2211yescharacteristic
19C22×C4×Dic7—21no—
20C2×#6451C2211yescharacteristic
21C2×#6450—21no—
22C2×C7×#107C2211yescharacteristic
23C2×C7×#102C2211yescharacteristic
24C2×C7×#102C2211yescharacteristic
25C7×#389C2211yescharacteristic
26C2×#6406C2211yescharacteristic
27C2×#6406C2211yescharacteristic
28C4×C22⋊Dic7—21no—
29C2×#6391C2211yescharacteristic
30C2×#6389C2211yescharacteristic
31C2×#6389C2211yescharacteristic
32C2×Dic7⋊C8C2211yescharacteristic
33C2×Dic7⋊C8C2211yescharacteristic
34#89748C2211yescharacteristic
35C4⋊C4×Dic7C2211yescharacteristic
36C4⋊C4×Dic7C2211yescharacteristic
37C4⋊C4×Dic7C2211yescharacteristic
38C4⋊C4×Dic7C2211yescharacteristic
39#89744—21no—
40C2×#6382C2211yescharacteristic
41C2×#6381C2211yescharacteristic
42C22⋊C4×Dic7—21no—
43C22⋊C4×Dic7—21no—
44C4×C4⋊Dic7C2211yescharacteristic
45C42×Dic7C2211yescharacteristic
46#89700C2211yescharacteristic
47#89533C418yescomplemented
48#89421—21no—
49#89418—21no—
50C7×#340C2211yescharacteristic
51C7×#336C2211yescharacteristic
52#89346C2211yescharacteristic
53#89346C2211yescharacteristic
54#89346C2211yescharacteristic
55#89324C2211yescharacteristic
56#89324C2211yescharacteristic
57#89324C2211yescharacteristic
58#89324C2211yescharacteristic
59#89319C2211yescharacteristic
60#21614—71nomaximal, Sylow
61C22×C7×D4C2311yescharacteristic
62C23×C4×C7—21no—
63C23×Dic7—21no—
64C23×Dic7—21no—
65C22×Dic14—21no—
66C22×C7×C8C2311yescharacteristic
67C22×C7×C8C2311yescharacteristic
68C4×C7×D4—22no—
69C4×C7×D4—22no—
70C2×C7×C4⋊C4—21no—
71C2×C7×C4⋊C4C2311yescharacteristic
72C2×C7×C4⋊C4C2311yescharacteristic
73C2×C7×C4⋊C4C2311yescharacteristic
74C2×C7×C22⋊C4—21no—
75C2×C42×C7C2311yescharacteristic
76C2×C22⋊Dic7—21no—
77C2×C22⋊Dic7—21no—
78D4×Dic7—22no—
79D4×Dic7—22no—
80D4×Dic7C2×C414yes—
81D4×Dic7Q814yescomplemented
82C2×C4⋊Dic7C2311yescharacteristic
83C2×C4⋊Dic7C2311yescharacteristic
84C2×C4⋊Dic7C2311yescharacteristic
85C2×C4⋊Dic7C2311yescharacteristic
86C2×Dic7⋊C4—21no—
87C2×Dic7⋊C4—21no—
88C2×Dic7⋊C4—21no—
89C2×Dic7⋊C4—21no—
90C2×C4×Dic7—21no—
91C2×C4×Dic7—21no—
92C2×C4×Dic7—21no—
93C2×C4×Dic7—21no—
94C2×C4×Dic7—21no—
95C2×C4×Dic7—44no—
96C2×C4×Dic7D411yescharacteristic
97C2×C4×Dic7D411yescharacteristic
98C2×C4×Dic7D411yescharacteristic
99C2×C4×Dic7D411yescharacteristic
100C2×C4×Dic7C2311yescharacteristic
101C2×C4×Dic7C2311yescharacteristic
102C22×C7⋊C8C2311yescharacteristic
103C22×C7⋊C8C2311yescharacteristic
104#6451—22no—
105#6451C2×C414yescomplemented
106#6450—44no—
107C7×#107—22no—
108C7×#102—22no—
109C7×#102C2×C414yes—
110C7×#95—21no—
111#6406—22no—
112#6406C2×C414yes—
113C7⋊#95—21no—
114C7⋊#95—21no—
115C7⋊#95—21no—
116C7⋊#95—21no—
117C7⋊#95—21no—
118C7⋊#95—21no—
119#6391C2×C414yescomplemented
120#6389—22no—
121#6389—22no—
122Dic7⋊C8—22no—
123Dic7⋊C8C2×C414yescomplemented
124#6382C2×C414yescomplemented
125#6381—22no—
126C2×#476—71no—
127C4×C4⋊Q8—71no—
128C42×D4—71no—
129#1987—71no—
130#1947—71no—
131#1919—71no—
132#1919—71no—
133#1862—71no—
134#1862D711yescharacteristic
135#1802—71no—
136#1776—71no—
137#1776—71no—
138#1767—71no—
139#1762—71no—
140#1762—71no—
141C24×C7—21no—
142C2×C7×D4—21no—
143C2×C7×D4—21no—
144C2×C7×D4—21no—
145C2×C7×D4C22×C412yes—
146C2×C7×D4C2×Q812yes—
147C2×C7×D4#4112yes—
148C22×C4×C7—24no—
149C22×C4×C7—21no—
150C22×C4×C7—21no—
151C22×C4×C7—21no—
152C22×C4×C7—42no—
153C22×C4×C7—42no—
154C22×C4×C7C2×D411yescharacteristic
155C22×C4×C7C2×D411yescharacteristic
156C22×C4×C7C2411yescharacteristic
157C22×Dic7—21no—
158C22×Dic7—21no—
159C22×Dic7—21no—
160C22×Dic7—24no—
161C22×Dic7—24no—
162C22×Dic7—21no—
163C22×Dic7—42no—
164C22×Dic7—42no—
165C22×Dic7—42no—
166C22×Dic7—42no—
167C22×Dic7C2×D411yescharacteristic
168C22×Dic7C2×D411yescharacteristic
169C22×Dic7C2×D411yescharacteristic
170C22×Dic7C2×D411yescharacteristic
171C2×Dic14—24no—
172C2×Dic14—42no—
173C2×Dic14—42no—
174C2×C7×C8—21no—
175C2×C7×C8—21no—
176C2×C7×C8—21no—
177C2×C7×C8—21no—
178C2×C7×C8—21no—
179C2×C7×C8C22×C412yes—
180C7×C4⋊C4—21no—
181C7×C4⋊C4—21no—
182C7×C4⋊C4—21no—
183C7×C4⋊C4—21no—
184C7×C4⋊C4—42no—
185C7×C4⋊C4C22×C412yes—
186C7×C4⋊C4#4112yes—
187C7×C22⋊C4—24no—
188C42×C7—21no—
189C42×C7—21no—
190C22⋊Dic7—24no—
191C22⋊Dic7—24no—
192C4⋊Dic7—21no—
193C4⋊Dic7—21no—
194C4⋊Dic7—21no—
195C4⋊Dic7—21no—
196C4⋊Dic7—21no—
197C4⋊Dic7C22×C412yes—
198C4⋊Dic7C22×C412yes—
199C4⋊Dic7C2×Q812yes—
200Dic7⋊C4—24no—
201Dic7⋊C4—42no—
202Dic7⋊C4—42no—
203Dic7⋊C4—42no—
204C4×Dic7—22no—
205C4×Dic7—22no—
206C4×Dic7—22no—
207C4×Dic7—41no—
208C4×Dic7—42no—
209C4×Dic7—42no—
210C4×Dic7—42no—
211C4×Dic7—42no—
212C4×Dic7—42no—
213C4×Dic7C22×C412yes—
214C4×Dic7C2×Q812yes—
215C4×Dic7#4112yes—
216C4×Dic7#4112yes—
217C2×C7⋊C8—21no—
218C2×C7⋊C8—21no—
219C2×C7⋊C8—21no—
220C2×C7⋊C8—21no—
221C2×C7⋊C8—21no—
222C2×C7⋊C8C22×C412yes—
223C2×C4⋊Q8—71no—
224C2×C4×Q8—141no—
225C2×C4×D4—71no—
226C2×C4×D4—71no—
227C2×C4×D4C2×D711yescharacteristic
228C22×C42—141no—
229#476—78no—
230C2×#107—71no—
231C2×#107C2×D711yescharacteristic
232C2×#106—71no—
233C2×#106—71no—
234C2×C4⋊C8—71no—
235C2×C4⋊C8—71no—
236C2×#102—71no—
237C2×#102—71no—
238C2×#102C2×D711yescharacteristic
239C2×#102C2×D711yescharacteristic
240C2×#97—71no—
241C2×#97—71no—
242#391—141no—
243#389—71no—
244#389—141no—
245#389C2×D711yescharacteristic
246#384—71no—
247C4×C4⋊C4—71no—
248C4×C4⋊C4—71no—
249C4×C4⋊C4—71no—
250C4×C4⋊C4—71no—
251C4×C4⋊C4—71no—
252C4×C4⋊C4—141no—
253C4×C22⋊C4—141no—
254C4×C22⋊C4—141no—
255C4×C22⋊C4—141no—
256C43—71no—
257#340—71no—
258#340—71no—
259#340—71no—
260#340—71no—
261#340—71no—
262#340—71no—
263#340—71no—
264#340C2×D711yescharacteristic
265#336—71no—
266#336C2×D711yescharacteristic
267C23×C7—22no—
268C23×C7—22no—
269C23×C7—22no—
270C23×C7—41no—
271C23×C7—41no—
272C23×C7—41no—
273C23×C7—41no—
274C23×C7C22×D411yescharacteristic
275C7×D4—22no—
276C7×D4—22no—
277C7×D4—22no—
278C7×D4C4×Q814yescomplemented
279C2×C4×C7—21no—
280C2×C4×C7—21no—
281C2×C4×C7—22no—
282C2×C4×C7—21no—
283C2×C4×C7—22no—
284C2×C4×C7—21no—
285C2×C4×C7—21no—
286C2×C4×C7—48no—
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×C7AGL(1,ℤ/8)12yes—
295C2×C4×C7C23×C411yescharacteristic
296C2×C4×C7C22×Q811yescharacteristic
297C2×C4×C7C2×#4111yescharacteristic
298C2×C4×C7C2×#4111yescharacteristic
299C2×C4×C7C2×#4111yescharacteristic
300C2×C4×C7C2×#4111yescharacteristic
301C2×Dic7—21no—
302C2×Dic7—21no—
303C2×Dic7—21no—
304C2×Dic7—21no—
305C2×Dic7—21no—
306C2×Dic7—21no—
307C2×Dic7—22no—
308C2×Dic7—22no—
309C2×Dic7—22no—
310C2×Dic7—48no—
311C2×Dic7—41no—
312C2×Dic7—41no—
313C2×Dic7—41no—
314C2×Dic7—41no—
315C2×Dic7—41no—
316C2×Dic7—41no—
317C2×Dic7—48no—
318C2×Dic7—41no—
319C2×Dic7—41no—
320C2×Dic7—41no—
321C2×Dic7C4×D412yes—
322C2×Dic7C4×D412yes—
323C2×Dic7C22⋊Q812yes—
324C2×Dic7C22⋊Q812yes—
325C2×Dic7AGL(1,ℤ/8)12yes—
326C2×Dic7#13712yes—
327Dic14—48no—
328C7×C8—22no—
329C7×C8—41no—
330C7⋊C8—22no—
331C7⋊C8—41no—
332C22×Q8—141no—
333C22×D4C22×D711yescharacteristic
334C23×C4—21no—
335C23×C4—141no—
336C23×C4—141no—
337C22×C8—71no—
338C22×C8—71no—
339C22×C8C22×D711yescharacteristic
340C22×C8C22×D711yescharacteristic
341C4⋊Q8—74no—
342C4⋊Q8—142no—
343C4×Q8—284no—
344C4×D4—22no—
345C4×D4—22no—
346C4×D4—74no—
347C4×D4—74no—
348C4×D4—142no—
349C4×D4—142no—
350C2×C4⋊C4—21no—
351C2×C4⋊C4—71no—
352C2×C4⋊C4—71no—
353C2×C4⋊C4—71no—
354C2×C4⋊C4—71no—
355C2×C4⋊C4—141no—
356C2×C4⋊C4—141no—
357C2×C4⋊C4—141no—
358C2×C4⋊C4—141no—
359C2×C4⋊C4C22×D711yescharacteristic
360C2×C4⋊C4C22×D711yescharacteristic
361C2×C4⋊C4C22×D711yescharacteristic
362C2×C22⋊C4—21no—
363C2×C22⋊C4—141no—
364C2×C22⋊C4—141no—
365C2×C42—71no—
366C2×C42—71no—
367C2×C42—71no—
368C2×C42—71no—
369C2×C42—71no—
370C2×C42—71no—
371C2×C42—141no—
372C2×C42—141no—
373C2×C42—141no—
374C2×C42—141no—
375C2×C42—141no—
376C2×C42—284no—
377C2×C42C22×D711yescharacteristic
378#107—22no—
379#107—142no—
380#106—74no—
381#106—74no—
382C4⋊C8—74no—
383C4⋊C8—142no—
384#102—22no—
385#102—74no—
386#102—142no—
387#102C4×D714yes—
388#97—142no—
389#97—142no—
390#95—21no—
391#95—141no—
392#95—141no—
393#95—141no—
394#95—141no—
395#95—141no—
396#95—141no—
397C22×C7—24no—
398C22×C7—42no—
399C22×C7—42no—
400C22×C7—42no—
401C22×C7—42no—
402C22×C7—42no—
403C22×C7—42no—
404C22×C7C2×C4×D411yescharacteristic
405C22×C7C2×C22⋊Q811yescharacteristic
406C22×C7#52511yescharacteristic
407C22×C7C2×AGL(1,ℤ/8)11yescharacteristic
408C22×C7C2×AGL(1,ℤ/8)11yescharacteristic
409C22×C7C2×#13711yescharacteristic
410C22×C7#57511yescharacteristic
411C4×C7—22no—
412C4×C7—42no—
413C4×C7—41no—
414C4×C7—42no—
415C4×C7—81no—
416C4×C7C2×C4×Q811yescharacteristic
417C4×C7C4×#4111yescharacteristic
418C4×C7#52911yescharacteristic
419C4×C7#53311yescharacteristic
420Dic7—22no—
421Dic7—22no—
422Dic7—22no—
423Dic7—42no—
424Dic7—42no—
425Dic7—42no—
426Dic7—81no—
427Dic7#44014yes—
428C24—21no—
429C2×Q8—144no—
430C2×Q8—282no—
431C2×Q8—282no—
432C2×D4—21no—
433C2×D4—21no—
434C2×D4—21no—
435C2×D4C2×C4×D712yes—
436C2×D4#115912yes—
437C2×D4Q8×D712yes—
438C22×C4—24no—
439C22×C4—21no—
440C22×C4—21no—
441C22×C4—21no—
442C22×C4—42no—
443C22×C4—42no—
444C22×C4—71no—
445C22×C4—71no—
446C22×C4—71no—
447C22×C4—71no—
448C22×C4—144no—
449C22×C4—144no—
450C22×C4—141no—
451C22×C4—141no—
452C22×C4—141no—
453C22×C4—141no—
454C22×C4—282no—
455C22×C4—282no—
456C22×C4—282no—
457C22×C4—282no—
458C22×C4D4×D711yescharacteristic
459C22×C4D4×D711yescharacteristic
460C22×C4C23×D711yescharacteristic
461C2×C8—21no—
462C2×C8—21no—
463C2×C8—21no—
464C2×C8—21no—
465C2×C8—21no—
466C2×C8—72no—
467C2×C8—141no—
468C2×C8—141no—
469C2×C8—141no—
470C2×C8—141no—
471C2×C8—141no—
472C2×C8C2×C4×D712yes—
473C4⋊C4—21no—
474C4⋊C4—21no—
475C4⋊C4—21no—
476C4⋊C4—21no—
477C4⋊C4—42no—
478C4⋊C4—72no—
479C4⋊C4—72no—
480C4⋊C4—72no—
481C4⋊C4—144no—
482C4⋊C4—141no—
483C4⋊C4—141no—
484C4⋊C4—141no—
485C4⋊C4—141no—
486C4⋊C4—141no—
487C4⋊C4—282no—
488C4⋊C4—282no—
489C4⋊C4—282no—
490C4⋊C4C2×C4×D712yes—
491C4⋊C4#115912yes—
492C22⋊C4—24no—
493C22⋊C4—144no—
494C22⋊C4—144no—
495C42—21no—
496C42—21no—
497C42—72no—
498C42—72no—
499C42—72no—
500C42—72no—
501C42—142no—
502C42—142no—
503C42—142no—
504C42—281no—
505C42—282no—
506C42—282no—
507C42—282no—
508C42—282no—
509C42—282no—
510C2×C7—44no—
511C2×C7C4×C22⋊Q811yescharacteristic
512C2×C7C2×#44011yescharacteristic
513C2×C7C4×AGL(1,ℤ/8)11yescharacteristic
514C2×C7#307711yescharacteristic
515C2×C7#307911yescharacteristic
516C2×C7#310911yescharacteristic
517C2×C7#311611yescharacteristic
518C23—22no—
519C23—22no—
520C23—22no—
521C23—41no—
522C23—41no—
523C23—41no—
524C23—41no—
525C23C2×D4×D711yescharacteristic
526Q8—288no—
527D4—22no—
528D4—22no—
529D4—22no—
530D4#645014yescomplemented
531C2×C4—21no—
532C2×C4—21no—
533C2×C4—21no—
534C2×C4—21no—
535C2×C4—22no—
536C2×C4—21no—
537C2×C4—22no—
538C2×C4—48no—
539C2×C4—41no—
540C2×C4—41no—
541C2×C4—41no—
542C2×C4—41no—
543C2×C4—41no—
544C2×C4—41no—
545C2×C4—41no—
546C2×C4—72no—
547C2×C4—72no—
548C2×C4—72no—
549C2×C4—72no—
550C2×C4—72no—
551C2×C4—72no—
552C2×C4—141no—
553C2×C4—141no—
554C2×C4—141no—
555C2×C4—141no—
556C2×C4—141no—
557C2×C4—141no—
558C2×C4—142no—
559C2×C4—142no—
560C2×C4—142no—
561C2×C4—288no—
562C2×C4—288no—
563C2×C4—281no—
564C2×C4—281no—
565C2×C4—281no—
566C2×C4—281no—
567C2×C4—281no—
568C2×C4—281no—
569C2×C4—281no—
570C2×C4—281no—
571C2×C4—281no—
572C2×C4#647412yes—
573C2×C4C22×C4×D711yescharacteristic
574C2×C4C2×#115911yescharacteristic
575C2×C4C2×#115911yescharacteristic
576C2×C4C2×Q8×D711yescharacteristic
577C2×C4D7×#4111yescharacteristic
578C2×C4D7×#4111yescharacteristic
579C8—22no—
580C8—41no—
581C8—142no—
582C8—281no—
583C7#2161411yescharacteristic, complemented, Sylow
584C22—24no—
585C22—42no—
586C22—42no—
587C22—42no—
588C22—42no—
589C22—42no—
590C22—42no—
591C22C4×D4×D711yescharacteristic
592C22#9027711yescharacteristic
593C22D7×C22⋊Q811yescharacteristic
594C22C2×#647411yescharacteristic
595C22#9045911yescharacteristic
596C22D7×AGL(1,ℤ/8)11yescharacteristic
597C22D7×#13711yescharacteristic
598C4—22no—
599C4—41no—
600C4—42no—
601C4—42no—
602C4—74no—
603C4—81no—
604C4—142no—
605C4—142no—
606C4—142no—
607C4—282no—
608C4—282no—
609C4—282no—
610C4—561no—
611C4C2×#645011yescharacteristic
612C4C4×#115911yescharacteristic
613C4#9031311yescharacteristic
614C4#9034011yescharacteristic
615C2—44no—
616C2#1173182611yescharacteristic
617C2C4×#647411yescharacteristic
618C2D7×#44011yescharacteristic
619C2#1173743511yescharacteristic
620C2#1173766011yescharacteristic
621C2#1173841111yescharacteristic
622C2#1173861111yescharacteristic
subgroupG/H
centerC23C2×D4×D7
commutatorC2×C4×C7C23×C4
FrattiniC22×C4C23×D7
FittingC7×#1862C2
socleC23×C7C22×D4
prime radicalC22×C7×D4C23
cosocleC22×C4×C7C24
hypercenter#1862D7
hypocenterC7#21614
LCSG ▷ C2×C4×C7 ▷ C2×C7 ▷ C7
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1862

Complements

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

NH ≅ G/Ntype
3. #11733412C2semidirect
6. #11728369C2semidirect
7. #11728359C2semidirect
11. #11727355C2semidirect
12. #11726553C2semidirect
13. #11726540C2semidirect
14. #11726376C2semidirect
15. #11726357C2semidirect
47. #89533C4semidirect
81. D4×Dic7Q8semidirect
105. #6451C2×C4semidirect
119. #6391C2×C4semidirect
123. Dic7⋊C8C2×C4semidirect
124. #6382C2×C4semidirect
278. C7×D4C4×Q8semidirect
530. D4#6450semidirect
583. C7#21614semidirect

Maximal subgroups

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

subgroupindex
C4×D4×Dic72
C2×#895332
#117334122
C7×#18622
#117293602
#117283692
#117283592
#117279072
#117279062
#117273552
#117265532
#117265402
#117263762
#117263572
#216147