Finite Group Databasebeta

← #13360228

Subgroups — #13360228

Order 1792.

932 conjugacy classes of subgroups.

The subgroup lattice has 626 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#11740672C211yesmaximal, characteristic
2C2×#89862C211yesmaximal, characteristic
3C2×#89561C211yesmaximal, characteristic
4C2×#89562C211yesmaximal, characteristic
5#11731061C211yesmaximal, characteristic
6C7×#1981C211yesmaximal, characteristic
7#11728240C211yesmaximal, characteristic
8#11728196C211yesmaximal, characteristic
9#11728035C211yesmaximal, characteristic
10#11728035C211yesmaximal, characteristic
11#11727996C211yesmaximal, characteristic
12#11727995C211yesmaximal, characteristic
13#11727974C211yesmaximal, characteristic
14Dic7×#103C211yesmaximal, characteristic
15#11727222C211yesmaximal, characteristic
16C2×C7×C4⋊Q8C2211yescharacteristic
17C2×Q8×Dic7C2211yescharacteristic
18C2×Q8×Dic7C2211yescharacteristic
19C22×#1144C2211yescharacteristic
20C22×#1144C2211yescharacteristic
21C2×#6450C2211yescharacteristic
22C2×#6450C2211yescharacteristic
23C2×C4×Dic14C2211yescharacteristic
24C2×C7×C4⋊C8C2211yescharacteristic
25C2×C7×#103C2211yescharacteristic
26C2×C7×#103C2211yescharacteristic
27C2×C7×#103C2211yescharacteristic
28C2×C7×#103C2211yescharacteristic
29C4×C7×C4⋊C4C2211yescharacteristic
30#90002C2211yescharacteristic
31#90002C2211yescharacteristic
32C2×#6409C2211yescharacteristic
33C2×#6409C2211yescharacteristic
34C2×#6390C2211yescharacteristic
35C2×#6390C2211yescharacteristic
36C2×#6389C2211yescharacteristic
37C2×C8×Dic7C2211yescharacteristic
38#89862C418yescomplemented
39#89753—21no—
40#89753—21no—
41#89753—21no—
42#89753—21no—
43C4⋊C4×Dic7C2211yescharacteristic
44C4⋊C4×Dic7C2211yescharacteristic
45C2×#6382C2211yescharacteristic
46C2×#6381C2211yescharacteristic
47#89708C2211yescharacteristic
48#89704C2211yescharacteristic
49C4×Dic7⋊C4—21no—
50C4×Dic7⋊C4—21no—
51C2×C4⋊(C7⋊C8)C2211yescharacteristic
52#89562—24no—
53#89561—24no—
54#89421—21no—
55#89420—21no—
56#89346C2211yescharacteristic
57#89346C2211yescharacteristic
58#89345C2211yescharacteristic
59#89345C2211yescharacteristic
60#89324C2211yescharacteristic
61#89324C2211yescharacteristic
62#21516—71nomaximal, Sylow
63C22×C7×Q8C2311yescharacteristic
64C22×C7×Q8C2311yescharacteristic
65C22×Dic14C2311yescharacteristic
66C22×C7×C8C2311yescharacteristic
67C22×C7×C8C2311yescharacteristic
68C7×C4⋊Q8—22no—
69C7×C4⋊Q8C2×C414yes—
70C2×C7×C4⋊C4—21no—
71C2×C7×C4⋊C4—21no—
72C2×C7×C4⋊C4C2311yescharacteristic
73C2×C7×C4⋊C4C2311yescharacteristic
74C2×C42×C7—21no—
75C2×C42×C7C2311yescharacteristic
76Q8×Dic7—22no—
77Q8×Dic7—22no—
78Q8×Dic7—22no—
79Q8×Dic7—22no—
80C2×#1144—22no—
81C2×#1144—22no—
82C2×#1144—22no—
83C2×#1144—22no—
84C2×#1144C2×C414yes—
85C2×#1144C2×C414yes—
86C2×C4⋊Dic7—21no—
87C2×C4⋊Dic7—21no—
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—
96C2×C4×Dic7—21no—
97C2×C4×Dic7—21no—
98C2×C4×Dic7—21no—
99C2×C4×Dic7—21no—
100C2×C4×Dic7—21no—
101C2×C4×Dic7C2311yescharacteristic
102C2×C4×Dic7C2311yescharacteristic
103C22×C7⋊C8C2311yescharacteristic
104C22×C7⋊C8C2311yescharacteristic
105#6450—22no—
106#6450—22no—
107#6450—22no—
108#6450D414yes—
109C4×Dic14—22no—
110C4×Dic14C2×C414yes—
111C7×C4⋊C8—22no—
112C7×#103—22no—
113C7×#103—22no—
114C7×#103—22no—
115C7×#103—22no—
116C7×#95—21no—
117#6409C2×C414yes—
118#6409C2×C414yes—
119C7⋊#95—21no—
120C7⋊#95—21no—
121C7⋊#95—21no—
122C7⋊#95—21no—
123C7⋊#95—21no—
124C7⋊#95—21no—
125C7⋊#95—21no—
126C7⋊#95—21no—
127C7⋊#95D411yescharacteristic
128C7⋊#95D411yescharacteristic
129C7⋊#95D411yescharacteristic
130C7⋊#95D411yescharacteristic
131#6390—22no—
132#6390—22no—
133#6389—22no—
134C8×Dic7—22no—
135#6382—22no—
136#6381—22no—
137C4⋊(C7⋊C8)C2×C414yes—
138C2×#462—71no—
139C2×#441—71no—
140C2×C4×Q16—71no—
141#2327—71no—
142#2276—71no—
143#1981D711yescharacteristic
144#1949—71no—
145#1928—71no—
146#1927—71no—
147#1878—71no—
148#1878—71no—
149#1805—71no—
150#1768—71no—
151#1763—71no—
152C4×#103—71no—
153C2×C7×Q8—21no—
154C2×C7×Q8—21no—
155C2×C7×Q8—21no—
156C2×C7×Q8—21no—
157C2×C7×Q8—21no—
158C2×C7×Q8—21no—
159C2×C7×Q8—21no—
160C2×C7×Q8—21no—
161C2×C7×Q8—21no—
162C2×C7×Q8—21no—
163C2×C7×Q8C22×C412yes—
164C2×C7×Q8C22×C412yes—
165C22×C4×C7—21no—
166C22×C4×C7—21no—
167C22×C4×C7—21no—
168C22×C4×C7—21no—
169C22×C4×C7C2×D411yescharacteristic
170C22×C4×C7C2×D411yescharacteristic
171C22×C4×C7C2411yescharacteristic
172C22×Dic7—21no—
173C22×Dic7—21no—
174C22×Dic7—21no—
175C22×Dic7—21no—
176C22×Dic7C2×D411yescharacteristic
177C22×Dic7C2×D411yescharacteristic
178C22×Dic7C2×D411yescharacteristic
179C22×Dic7C2×D411yescharacteristic
180C2×Dic14—21no—
181C2×Dic14—21no—
182C2×Dic14—21no—
183C2×Dic14C22×C412yes—
184C2×Dic14C2×D412yes—
185C2×Dic14#4112yes—
186C2×C7×C8—21no—
187C2×C7×C8—21no—
188C2×C7×C8—21no—
189C2×C7×C8—21no—
190C2×C7×C8—21no—
191C2×C7×C8—21no—
192C7×C4⋊C4—24no—
193C7×C4⋊C4—24no—
194C7×C4⋊C4—21no—
195C7×C4⋊C4—21no—
196C7×C4⋊C4C2×D412yes—
197C7×C4⋊C4#4112yes—
198C42×C7—81no—
199C42×C7C22×C412yes—
200C42×C7#4112yes—
201#1144—28no—
202#1144—28no—
203C4⋊Dic7—21no—
204C4⋊Dic7—21no—
205C4⋊Dic7—21no—
206C4⋊Dic7—21no—
207C4⋊Dic7—21no—
208C4⋊Dic7—42no—
209C4⋊Dic7—42no—
210C4⋊Dic7C22×C412yes—
211Dic7⋊C4—24no—
212Dic7⋊C4—24no—
213Dic7⋊C4—24no—
214C4×Dic7—24no—
215C4×Dic7—24no—
216C4×Dic7—21no—
217C4×Dic7—21no—
218C4×Dic7—24no—
219C4×Dic7—42no—
220C4×Dic7—42no—
221C4×Dic7—81no—
222C4×Dic7—81no—
223C4×Dic7C2×D412yes—
224C4×Dic7#4112yes—
225C2×C7⋊C8—21no—
226C2×C7⋊C8—21no—
227C2×C7⋊C8—21no—
228C2×C7⋊C8—21no—
229C2×C7⋊C8C22×C412yes—
230C2×C7⋊C8C22×C412yes—
231C22×Q16—71no—
232C22×Q16—71no—
233C2×C4⋊Q8C2×D711yescharacteristic
234C2×C4×Q8—71no—
235C2×C4×Q8—71no—
236C2×C4×Q8—71no—
237C2×C4×Q8—71no—
238C2×C4×Q8—71no—
239#462—78no—
240#441—144no—
241C4×Q16—144no—
242C2×#107—71no—
243C2×#106—71no—
244C2×C4⋊C8—71no—
245C2×C4⋊C8C2×D711yescharacteristic
246C2×#103—71no—
247C2×#103—71no—
248C2×#103—71no—
249C2×#103—71no—
250C2×#103C2×D711yescharacteristic
251C2×#103C2×D711yescharacteristic
252C2×#103C2×D711yescharacteristic
253C2×#103C2×D711yescharacteristic
254C2×#97—71no—
255C2×C4×C8—71no—
256#391—71no—
257#391—71no—
258#387—141no—
259#387—141no—
260#387—141no—
261#387—141no—
262#382—71no—
263C4×C4⋊C4—71no—
264C4×C4⋊C4—71no—
265C4×C4⋊C4—141no—
266C4×C4⋊C4—141no—
267C4×C4⋊C4—141no—
268C4×C4⋊C4C2×D711yescharacteristic
269#376—71no—
270#376—141no—
271#340—71no—
272#340—71no—
273#340—71no—
274#340—71no—
275#336—71no—
276#336—71no—
277C23×C7C22×D411yescharacteristic
278C7×Q8—22no—
279C7×Q8—22no—
280C7×Q8—22no—
281C7×Q8—22no—
282C7×Q8—41no—
283C7×Q8—41no—
284C7×Q8—41no—
285C7×Q8—41no—
286C2×C4×C7—21no—
287C2×C4×C7—21no—
288C2×C4×C7—21no—
289C2×C4×C7—21no—
290C2×C4×C7—22no—
291C2×C4×C7—22no—
292C2×C4×C7—22no—
293C2×C4×C7—22no—
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×C7C4×D412yes—
303C2×C4×C7C4×D412yes—
304C2×C4×C7C23×C411yescharacteristic
305C2×C4×C7C22×D411yescharacteristic
306C2×C4×C7C2×#4111yescharacteristic
307C2×C4×C7C2×#4111yescharacteristic
308C2×C4×C7C2×#4111yescharacteristic
309C2×C4×C7C2×#4111yescharacteristic
310C2×Dic7—22no—
311C2×Dic7—22no—
312C2×Dic7—22no—
313C2×Dic7—21no—
314C2×Dic7—21no—
315C2×Dic7—21no—
316C2×Dic7—21no—
317C2×Dic7—22no—
318C2×Dic7—21no—
319C2×Dic7—21no—
320C2×Dic7—21no—
321C2×Dic7—21no—
322C2×Dic7—21no—
323C2×Dic7—21no—
324C2×Dic7—41no—
325C2×Dic7—41no—
326C2×Dic7—41no—
327C2×Dic7—41no—
328C2×Dic7—41no—
329C2×Dic7—41no—
330C2×Dic7—41no—
331C2×Dic7—41no—
332C2×Dic7#12112yes—
333C2×Dic7#12112yes—
334Dic14—22no—
335Dic14—22no—
336Dic14—22no—
337Dic14C4×D414yes—
338C7×C8—41no—
339C7×C8—41no—
340C7⋊C8—22no—
341C7⋊C8—22no—
342C22×Q8—71no—
343C22×Q8C22×D711yescharacteristic
344C22×Q8C22×D711yescharacteristic
345C2×Q16—74no—
346C2×Q16—74no—
347C2×Q16—142no—
348C2×Q16—142no—
349C2×Q16—142no—
350C2×Q16—142no—
351C22×C8—71no—
352C22×C8—71no—
353C22×C8C22×D711yescharacteristic
354C22×C8C22×D711yescharacteristic
355C4⋊Q8—22no—
356C4⋊Q8C4×D714yes—
357C4×Q8—74no—
358C4×Q8—74no—
359C4×Q8—142no—
360C4×Q8—142no—
361C4×Q8—142no—
362C4×Q8—142no—
363C4×Q8—142no—
364C4×Q8—142no—
365C4×Q8—142no—
366C4×Q8—142no—
367C2×C4⋊C4—21no—
368C2×C4⋊C4—21no—
369C2×C4⋊C4—71no—
370C2×C4⋊C4—71no—
371C2×C4⋊C4—71no—
372C2×C4⋊C4—141no—
373C2×C4⋊C4—141no—
374C2×C4⋊C4—141no—
375C2×C4⋊C4—141no—
376C2×C4⋊C4—141no—
377C2×C4⋊C4C22×D711yescharacteristic
378C2×C4⋊C4C22×D711yescharacteristic
379C2×C42—21no—
380C2×C42—71no—
381C2×C42—71no—
382C2×C42—141no—
383C2×C42—141no—
384C2×C42—141no—
385C2×C42—141no—
386C2×C42—141no—
387C2×C42—141no—
388C2×C42—141no—
389C2×C42C22×D711yescharacteristic
390#107—142no—
391#106—142no—
392C4⋊C8—22no—
393C4⋊C8—74no—
394#103—22no—
395#103—22no—
396#103—22no—
397#103—22no—
398#103—74no—
399#103—74no—
400#103—142no—
401#103—142no—
402#97—142no—
403C4×C8—142no—
404#95—21no—
405#95—71no—
406#95—71no—
407#95—71no—
408#95—71no—
409#95—141no—
410#95—141no—
411#95—141no—
412#95—141no—
413#95—141no—
414#95—141no—
415#95—141no—
416#95—141no—
417C22×C7C2×C4×D411yescharacteristic
418C22×C7C2×#12111yescharacteristic
419C22×C7#52511yescharacteristic
420C22×C7#57711yescharacteristic
421C22×C7#57811yescharacteristic
422C22×C7#57811yescharacteristic
423C22×C7#57811yescharacteristic
424C4×C7—22no—
425C4×C7—22no—
426C4×C7—42no—
427C4×C7—42no—
428C4×C7—42no—
429C4×C7—42no—
430C4×C7C2×C4×D411yescharacteristic
431C4×C7C4×#4111yescharacteristic
432C4×C7#52911yescharacteristic
433C4×C7#53211yescharacteristic
434Dic7—22no—
435Dic7—22no—
436Dic7—24no—
437Dic7—41no—
438Dic7—41no—
439Dic7—42no—
440Dic7—81no—
441Dic7—81no—
442C2×Q8—21no—
443C2×Q8—21no—
444C2×Q8—21no—
445C2×Q8—21no—
446C2×Q8—21no—
447C2×Q8—21no—
448C2×Q8—21no—
449C2×Q8—21no—
450C2×Q8—21no—
451C2×Q8—21no—
452C2×Q8—72no—
453C2×Q8—72no—
454C2×Q8—72no—
455C2×Q8—141no—
456C2×Q8—141no—
457C2×Q8—141no—
458C2×Q8C2×C4×D712yes—
459C2×Q8C2×C4×D712yes—
460C22×C4—21no—
461C22×C4—21no—
462C22×C4—21no—
463C22×C4—21no—
464C22×C4—71no—
465C22×C4—71no—
466C22×C4—71no—
467C22×C4—71no—
468C22×C4—141no—
469C22×C4—141no—
470C22×C4—141no—
471C22×C4—141no—
472C22×C4D4×D711yescharacteristic
473C22×C4D4×D711yescharacteristic
474C22×C4C23×D711yescharacteristic
475Q16—148no—
476Q16—148no—
477C2×C8—21no—
478C2×C8—21no—
479C2×C8—21no—
480C2×C8—21no—
481C2×C8—21no—
482C2×C8—21no—
483C2×C8—72no—
484C2×C8—72no—
485C2×C8—141no—
486C2×C8—141no—
487C2×C8—141no—
488C2×C8—141no—
489C4⋊C4—24no—
490C4⋊C4—24no—
491C4⋊C4—21no—
492C4⋊C4—21no—
493C4⋊C4—72no—
494C4⋊C4—144no—
495C4⋊C4—144no—
496C4⋊C4—144no—
497C4⋊C4—141no—
498C4⋊C4—141no—
499C4⋊C4—141no—
500C4⋊C4—141no—
501C4⋊C4—141no—
502C4⋊C4—282no—
503C4⋊C4—282no—
504C4⋊C4D4×D712yes—
505C4⋊C4#115912yes—
506C42—72no—
507C42—72no—
508C42—81no—
509C42—144no—
510C42—144no—
511C42—144no—
512C42—141no—
513C42—141no—
514C42—282no—
515C42—282no—
516C42—561no—
517C42—561no—
518C42C2×C4×D712yes—
519C42#115912yes—
520C2×C7C4×#12111yescharacteristic
521C2×C7#294711yescharacteristic
522C2×C7#295011yescharacteristic
523C2×C7#304411yescharacteristic
524C2×C7#304611yescharacteristic
525C2×C7#312011yescharacteristic
526C2×C7#312711yescharacteristic
527C23C2×D4×D711yescharacteristic
528Q8—22no—
529Q8—22no—
530Q8—22no—
531Q8—22no—
532Q8—41no—
533Q8—41no—
534Q8—41no—
535Q8—41no—
536Q8—74no—
537Q8—142no—
538Q8—142no—
539Q8—142no—
540C2×C4—21no—
541C2×C4—21no—
542C2×C4—21no—
543C2×C4—21no—
544C2×C4—22no—
545C2×C4—22no—
546C2×C4—22no—
547C2×C4—22no—
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—72no—
557C2×C4—72no—
558C2×C4—142no—
559C2×C4—141no—
560C2×C4—141no—
561C2×C4—141no—
562C2×C4—141no—
563C2×C4—142no—
564C2×C4—142no—
565C2×C4—142no—
566C2×C4—141no—
567C2×C4—141no—
568C2×C4—141no—
569C2×C4—141no—
570C2×C4—141no—
571C2×C4—141no—
572C2×C4—281no—
573C2×C4—281no—
574C2×C4—281no—
575C2×C4—281no—
576C2×C4—281no—
577C2×C4—281no—
578C2×C4—281no—
579C2×C4—281no—
580C2×C4(C22⋊D7)⋊C412yes—
581C2×C4(C22⋊D7)⋊C412yes—
582C2×C4C22×C4×D711yescharacteristic
583C2×C4C2×D4×D711yescharacteristic
584C2×C4C2×#115911yescharacteristic
585C2×C4C2×#115911yescharacteristic
586C2×C4D7×#4111yescharacteristic
587C2×C4D7×#4111yescharacteristic
588C8—41no—
589C8—41no—
590C8—142no—
591C8—142no—
592C7#2151611yescharacteristic, complemented, Sylow
593C22C2×(C22⋊D7)⋊C411yescharacteristic
594C22D7×#12111yescharacteristic
595C22#9029711yescharacteristic
596C22#9045311yescharacteristic
597C22#9045711yescharacteristic
598C22#9047011yescharacteristic
599C22#9047011yescharacteristic
600C4—22no—
601C4—22no—
602C4—42no—
603C4—42no—
604C4—42no—
605C4—42no—
606C4—142no—
607C4—142no—
608C4—144no—
609C4—281no—
610C4—281no—
611C4—282no—
612C4—561no—
613C4—561no—
614C4C4×#115911yescharacteristic
615C4C4×D4×D711yescharacteristic
616C4#9037111yescharacteristic
617C4#9040711yescharacteristic
618C2#1173373611yescharacteristic
619C2#1173621911yescharacteristic
620C2#1173639311yescharacteristic
621C2#1173785711yescharacteristic
622C2#1173787611yescharacteristic
623C2#1173790611yescharacteristic
624C2#1173792311yescharacteristic
subgroupG/H
centerC23C2×D4×D7
commutatorC2×C4×C7C23×C4
FrattiniC22×C4C23×D7
FittingC7×#1981C2
socle, prime radicalC23×C7C22×D4
cosocleC22×C4×C7C24
hypercenter#1981D7
hypocenterC7#21516
LCSG ▷ C2×C4×C7 ▷ C2×C7 ▷ C7
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1981

Complements

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

NH ≅ G/Ntype
38. #89862C4semidirect
592. C7#21516semidirect

Maximal subgroups

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

subgroupindex
#117406722
C2×#898622
C2×#895612
C2×#895622
#117310612
C7×#19812
#117282402
#117281962
#117280352
#117279962
#117279952
#117279742
Dic7×#1032
#117272222
#215167