Finite Group Databasebeta

← #13356947

Subgroups — #13356947

Order 1792.

862 conjugacy classes of subgroups.

The subgroup lattice has 618 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#11739895C211yesmaximal, characteristic, complemented
2C2×#89560C211yesmaximal, characteristic
3#11733414C211yesmaximal, characteristic
4C7×#1865C211yesmaximal, characteristic, complemented
5#11729387C211yesmaximal, characteristic
6#11728323C211yesmaximal, characteristic
7Dic7×#106C211yesmaximal, characteristic, complemented
8#11727994C211yesmaximal, characteristic
9#11727992C211yesmaximal, characteristic, complemented
10#11727974C211yesmaximal, characteristic, complemented
11#11727356C211yesmaximal, characteristic, complemented
12#11726573C211yesmaximal, characteristic, complemented
13#11726536C211yesmaximal, characteristic
14#11726380C211yesmaximal, characteristic
15#11726352C211yesmaximal, characteristic, complemented
16C2×C4×C7×Q8C2211yescharacteristic
17C2×Q8×Dic7C2211yescharacteristic
18C2×Q8×Dic7C2211yescharacteristic
19C22×#1143C2211yescharacteristic
20C2×#6456C2211yescharacteristic
21C2×C7×#106C2211yescharacteristic
22C2×C7×#103C2211yescharacteristic
23C2×C7×#103C2211yescharacteristic
24C7×#389C2211yescharacteristic
25C2×#6409C2211yescharacteristic
26C2×#6395C2211yescharacteristic
27C2×#6395C2211yescharacteristic
28C2×#6391C2211yescharacteristic
29C2×#6389C2211yescharacteristic
30C2×C8×Dic7C2211yescharacteristic
31#89762—21no—
32#89760C2211yescharacteristic
33#89759—21no—
34#89757C2211yescharacteristic
35C4⋊C4×Dic7—21no—
36C4⋊C4×Dic7—21no—
37C4⋊C4×Dic7C2211yescharacteristic
38C4⋊C4×Dic7C2211yescharacteristic
39C4⋊C4×Dic7C2211yescharacteristic
40C2×#6383C2211yescharacteristic
41C2×#6382C2211yescharacteristic
42#89711C2211yescharacteristic
43C4×C4⋊Dic7—21no—
44C4×C4⋊Dic7C2211yescharacteristic
45#89704—21no—
46#89704C2211yescharacteristic
47#89560C418yescomplemented
48#89442—21no—
49#89436—21no—
50C7×#340C2211yescharacteristic
51C7×#336C2211yescharacteristic
52#89346C2211yescharacteristic
53#89345C2211yescharacteristic
54#89345C2211yescharacteristic
55#89324C2211yescharacteristic
56#89324C2211yescharacteristic
57#89324C2211yescharacteristic
58#89324C2211yescharacteristic
59#89319C2211yescharacteristic
60#21131—71nomaximal, Sylow
61C22×C7×Q8C2311yescharacteristic
62C22×D28C2311yescharacteristic
63C22×C4×D7—21no—
64C22×C7×C8C2311yescharacteristic
65C22×C7×C8C2311yescharacteristic
66C4×C7×Q8—22no—
67C4×C7×Q8—22no—
68C2×C7×C4⋊C4—21no—
69C2×C7×C4⋊C4—21no—
70C2×C7×C4⋊C4C2311yescharacteristic
71C2×C7×C4⋊C4C2311yescharacteristic
72C2×C7×C4⋊C4C2311yescharacteristic
73C2×C42×C7—21no—
74C2×C42×C7C2311yescharacteristic
75Q8×Dic7—22no—
76Q8×Dic7—22no—
77Q8×Dic7—22no—
78Q8×Dic7C2×C414yes—
79C2×#1143—22no—
80C2×#1143—22no—
81C2×#1143C2×C414yes—
82C2×(C2×D7)⋊C4—21no—
83C2×(C2×D7)⋊C4—21no—
84C2×(C2×D7)⋊C4—21no—
85C2×(C2×D7)⋊C4—21no—
86C2×(C2×D7)⋊C4—21no—
87C2×C4⋊Dic7—21no—
88C2×C4⋊Dic7—21no—
89C2×C4⋊Dic7—21no—
90C2×C4⋊Dic7C2311yescharacteristic
91C2×C4⋊Dic7C2311yescharacteristic
92C2×C4⋊Dic7C2311yescharacteristic
93C2×C4×Dic7—21no—
94C2×C4×Dic7—21no—
95C2×C4×Dic7—21no—
96C2×C4×Dic7—21no—
97C2×C4×Dic7—21no—
98C2×C4×Dic7—21no—
99C2×C4×Dic7C2311yescharacteristic
100C2×C4×Dic7C2311yescharacteristic
101C22×C7⋊C8C2311yescharacteristic
102C22×C7⋊C8C2311yescharacteristic
103#6456—22no—
104#6456C2×C414yes—
105C7×#106—22no—
106C7×#103—22no—
107C7×#103C2×C414yes—
108C7×#95—21no—
109#6409—22no—
110C7⋊#95—21no—
111C7⋊#95—21no—
112C7⋊#95—21no—
113C7⋊#95—21no—
114C7⋊#95—21no—
115C7⋊#95D411yescharacteristic
116C7⋊#95D411yescharacteristic
117C7⋊#95D411yescharacteristic
118C7⋊#95D411yescharacteristic
119#6395—22no—
120#6395C2×C414yes—
121#6391—22no—
122#6389—22no—
123C8×Dic7C2×C414yes—
124#6383—22no—
125#6382C2×C414yes—
126C2×C4×SD16—71no—
127#2319—71no—
128#2276—71no—
129#1926—71no—
130#1926—71no—
131#1920—71no—
132#1920—71no—
133#1880—71no—
134#1880—71no—
135#1865—71no—
136#1865D711yescharacteristic, complemented
137C4×#106—71no—
138#1763—71no—
139#1762—71no—
140#1746—71no—
141C23×D7—21no—
142C2×C7×Q8—21no—
143C2×C7×Q8—21no—
144C2×C7×Q8—21no—
145C2×C7×Q8C22×C412yes—
146C2×C7×Q8#4112yes—
147C2×C7×Q8#4112yes—
148C22×C4×C7—21no—
149C22×C4×C7—21no—
150C22×C4×C7—21no—
151C22×C4×C7—21no—
152C22×C4×C7C2×D411yescharacteristic
153C22×C4×C7C2×D411yescharacteristic
154C22×C4×C7C2411yescharacteristic
155C22×Dic7—21no—
156C22×Dic7—21no—
157C22×Dic7—21no—
158C22×Dic7C2×D411yescharacteristic
159C22×Dic7C2×D411yescharacteristic
160C22×Dic7C2×D411yescharacteristic
161C22×Dic7C2×D411yescharacteristic
162C2×D28—21no—
163C2×D28—21no—
164C2×D28—21no—
165C2×D28—21no—
166C2×D28—21no—
167C2×D28C22×C412yes—
168C2×C4×D7—24no—
169C2×C4×D7—81no—
170C2×C4×D7—81no—
171C2×C7×C8—21no—
172C2×C7×C8—21no—
173C2×C7×C8—21no—
174C2×C7×C8—21no—
175C2×C7×C8—21no—
176C2×C7×C8C22×C412yes—
177C7×C4⋊C4—24no—
178C7×C4⋊C4—21no—
179C7×C4⋊C4—21no—
180C7×C4⋊C4—21no—
181C7×C4⋊C4—21no—
182C7×C4⋊C4—81no—
183C7×C4⋊C4C22×C412yes—
184C7×C4⋊C4#4112yes—
185C42×C7—24no—
186C42×C7—21no—
187C42×C7—21no—
188#1143—28no—
189(C2×D7)⋊C4—24no—
190(C2×D7)⋊C4—81no—
191(C2×D7)⋊C4—81no—
192(C2×D7)⋊C4—81no—
193(C2×D7)⋊C4—81no—
194C4⋊Dic7—24no—
195C4⋊Dic7—21no—
196C4⋊Dic7—21no—
197C4⋊Dic7—24no—
198C4⋊Dic7—21no—
199C4⋊Dic7—21no—
200C4⋊Dic7—81no—
201C4⋊Dic7C22×C412yes—
202C4⋊Dic7#4112yes—
203C4×Dic7—24no—
204C4×Dic7—21no—
205C4×Dic7—21no—
206C4×Dic7—24no—
207C4×Dic7—81no—
208C4×Dic7—81no—
209C4×Dic7—81no—
210C4×Dic7—81no—
211C4×Dic7C22×C412yes—
212C4×Dic7#4112yes—
213C2×C7⋊C8—21no—
214C2×C7⋊C8—21no—
215C2×C7⋊C8—21no—
216C2×C7⋊C8—21no—
217C2×C7⋊C8—21no—
218C2×C7⋊C8C22×C412yes—
219C22×SD16—71no—
220C2×C4×Q8—71no—
221C2×C4×Q8—71no—
222C2×C4×Q8C2×D711yescharacteristic
223C2×C4×D4—71no—
224C4×SD16—78no—
225C2×#106—71no—
226C2×#106—71no—
227C2×#106C2×D711yescharacteristic
228C2×#103—71no—
229C2×#103C2×D711yescharacteristic
230C2×#103C2×D711yescharacteristic
231C2×#102—71no—
232C2×#102—71no—
233C2×#102—71no—
234C2×#97—71no—
235C2×C4×C8—71no—
236#390—71no—
237#390—71no—
238#389—71no—
239#389C2×D711yescharacteristic
240#388—141no—
241#388—141no—
242#381—141no—
243#380—141no—
244C4×C4⋊C4—71no—
245C4×C4⋊C4—71no—
246C4×C4⋊C4—71no—
247C4×C4⋊C4—71no—
248C4×C4⋊C4—141no—
249C4×C4⋊C4—141no—
250C4×C4⋊C4—141no—
251#376—71no—
252#376—141no—
253#340—71no—
254#340—71no—
255#340—71no—
256#340—71no—
257#340—71no—
258#340C2×D711yescharacteristic
259#336—71no—
260#336—71no—
261#336—71no—
262#336C2×D711yescharacteristic
263C23×C7C22×D411yescharacteristic
264C22×D7—22no—
265C22×D7—41no—
266C22×D7—41no—
267C22×D7—41no—
268C22×D7—41no—
269C22×D7—41no—
270C22×D7—41no—
271C7×Q8—22no—
272C7×Q8—22no—
273C7×Q8—22no—
274C7×Q8#11714yes—
275C2×C4×C7—22no—
276C2×C4×C7—22no—
277C2×C4×C7—22no—
278C2×C4×C7—22no—
279C2×C4×C7—21no—
280C2×C4×C7—21no—
281C2×C4×C7—22no—
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×C7C23×C411yescharacteristic
294C2×C4×C7C2×#4111yescharacteristic
295C2×C4×C7C2×#4111yescharacteristic
296C2×C4×C7C2×#4111yescharacteristic
297C2×C4×C7C2×#4111yescharacteristic
298C2×C4×C7C2×#4111yescharacteristic
299C2×Dic7—21no—
300C2×Dic7—21no—
301C2×Dic7—21no—
302C2×Dic7—21no—
303C2×Dic7—22no—
304C2×Dic7—21no—
305C2×Dic7—21no—
306C2×Dic7—22no—
307C2×Dic7—21no—
308C2×Dic7—21no—
309C2×Dic7—21no—
310C2×Dic7—21no—
311C2×Dic7—41no—
312C2×Dic7—41no—
313C2×Dic7—41no—
314C2×Dic7—41no—
315C2×Dic7—41no—
316C2×Dic7—41no—
317C2×Dic7—41no—
318C2×Dic7C4×D412yes—
319C2×Dic7C4×D412yes—
320D28—22no—
321D28—22no—
322D28—41no—
323D28—41no—
324C4×D7—84no—
325C7×C8—22no—
326C7×C8—41no—
327C7⋊C8—22no—
328C7⋊C8—41no—
329C22×Q8C22×D711yescharacteristic
330C22×D4—71no—
331C23×C4—141no—
332C2×SD16—74no—
333C2×SD16—142no—
334C2×SD16—142no—
335C22×C8—71no—
336C22×C8—71no—
337C22×C8C22×D711yescharacteristic
338C22×C8C22×D711yescharacteristic
339C4×Q8—22no—
340C4×Q8—22no—
341C4×Q8—74no—
342C4×Q8—142no—
343C4×Q8—142no—
344C4×Q8—142no—
345C4×D4—74no—
346C4×D4—142no—
347C2×C4⋊C4—21no—
348C2×C4⋊C4—21no—
349C2×C4⋊C4—71no—
350C2×C4⋊C4—71no—
351C2×C4⋊C4—71no—
352C2×C4⋊C4—141no—
353C2×C4⋊C4—141no—
354C2×C4⋊C4—141no—
355C2×C4⋊C4C22×D711yescharacteristic
356C2×C4⋊C4C22×D711yescharacteristic
357C2×C4⋊C4C22×D711yescharacteristic
358C2×C22⋊C4—141no—
359C2×C22⋊C4—141no—
360C2×C22⋊C4—141no—
361C2×C22⋊C4—141no—
362C2×C22⋊C4—141no—
363C2×C42—21no—
364C2×C42—71no—
365C2×C42—71no—
366C2×C42—141no—
367C2×C42—141no—
368C2×C42—141no—
369C2×C42—141no—
370C2×C42—141no—
371C2×C42—141no—
372C2×C42C22×D711yescharacteristic
373#106—22no—
374#106—74no—
375#106—142no—
376#103—22no—
377#103—142no—
378#103C4×D714yes—
379#102—74no—
380#102—142no—
381#102—142no—
382#97—142no—
383C4×C8—74no—
384#95—21no—
385#95—71no—
386#95—71no—
387#95—71no—
388#95—71no—
389#95—141no—
390#95—141no—
391#95—141no—
392#95—141no—
393#95—141no—
394C22×C7C2×C4×D411yescharacteristic
395C22×C7#52511yescharacteristic
396C22×C7#52511yescharacteristic
397C22×C7#57711yescharacteristic
398C22×C7#57711yescharacteristic
399C22×C7#57711yescharacteristic
400C22×C7#57711yescharacteristic
401C2×D7—42no—
402C2×D7—42no—
403C2×D7—42no—
404C2×D7—81no—
405C2×D7—81no—
406C2×D7—81no—
407C2×D7—81no—
408C4×C7—24no—
409C4×C7—41no—
410C4×C7—42no—
411C4×C7—41no—
412C4×C7—42no—
413C4×C7—81no—
414C4×C7C2×#11711yescharacteristic
415C4×C7C4×#4111yescharacteristic
416C4×C7#52911yescharacteristic
417C4×C7#52911yescharacteristic
418Dic7—22no—
419Dic7—22no—
420Dic7—41no—
421Dic7—42no—
422Dic7—41no—
423Dic7—42no—
424Dic7—81no—
425C24—141no—
426C2×Q8—21no—
427C2×Q8—21no—
428C2×Q8—21no—
429C2×Q8C2×C4×D712yes—
430C2×Q8#115912yes—
431C2×Q8#116112yes—
432C2×D4—72no—
433C2×D4—141no—
434C2×D4—141no—
435C2×D4—141no—
436C2×D4—141no—
437C2×D4—141no—
438C22×C4—21no—
439C22×C4—21no—
440C22×C4—21no—
441C22×C4—21no—
442C22×C4—71no—
443C22×C4—71no—
444C22×C4—71no—
445C22×C4—71no—
446C22×C4—144no—
447C22×C4—141no—
448C22×C4—141no—
449C22×C4—141no—
450C22×C4—561no—
451C22×C4—561no—
452C22×C4D4×D711yescharacteristic
453C22×C4D4×D711yescharacteristic
454C22×C4C23×D711yescharacteristic
455SD16—148no—
456C2×C8—21no—
457C2×C8—21no—
458C2×C8—21no—
459C2×C8—21no—
460C2×C8—21no—
461C2×C8—72no—
462C2×C8—141no—
463C2×C8—141no—
464C2×C8—141no—
465C2×C8—141no—
466C2×C8—141no—
467C2×C8C2×C4×D712yes—
468C4⋊C4—24no—
469C4⋊C4—21no—
470C4⋊C4—21no—
471C4⋊C4—21no—
472C4⋊C4—21no—
473C4⋊C4—72no—
474C4⋊C4—72no—
475C4⋊C4—81no—
476C4⋊C4—144no—
477C4⋊C4—144no—
478C4⋊C4—141no—
479C4⋊C4—141no—
480C4⋊C4—141no—
481C4⋊C4—141no—
482C4⋊C4—561no—
483C4⋊C4C2×C4×D712yes—
484C4⋊C4#115912yes—
485C22⋊C4—144no—
486C22⋊C4—561no—
487C22⋊C4—561no—
488C22⋊C4—561no—
489C22⋊C4—561no—
490C42—24no—
491C42—21no—
492C42—21no—
493C42—72no—
494C42—72no—
495C42—144no—
496C42—144no—
497C42—141no—
498C42—141no—
499C42—561no—
500C42—561no—
501C42—561no—
502C42—561no—
503C2×C7#229011yescharacteristic
504C2×C7#294911yescharacteristic
505C2×C7#295211yescharacteristic
506C2×C7#312511yescharacteristic
507C2×C7#312511yescharacteristic
508C2×C7#312611yescharacteristic
509C2×C7#312611yescharacteristic
510D7—82no—
511C23—142no—
512C23—281no—
513C23—281no—
514C23—281no—
515C23—281no—
516C23—281no—
517C23—281no—
518C23C2×D4×D711yescharacteristic
519Q8—22no—
520Q8—22no—
521Q8—22no—
522Q8#645514yes—
523D4—142no—
524D4—142no—
525D4—281no—
526D4—281no—
527C2×C4—22no—
528C2×C4—22no—
529C2×C4—22no—
530C2×C4—21no—
531C2×C4—21no—
532C2×C4—21no—
533C2×C4—21no—
534C2×C4—22no—
535C2×C4—21no—
536C2×C4—21no—
537C2×C4—22no—
538C2×C4—41no—
539C2×C4—41no—
540C2×C4—41no—
541C2×C4—41no—
542C2×C4—41no—
543C2×C4—41no—
544C2×C4—41no—
545C2×C4—72no—
546C2×C4—72no—
547C2×C4—141no—
548C2×C4—141no—
549C2×C4—141no—
550C2×C4—141no—
551C2×C4—141no—
552C2×C4—141no—
553C2×C4—141no—
554C2×C4—141no—
555C2×C4—142no—
556C2×C4—141no—
557C2×C4—142no—
558C2×C4—141no—
559C2×C4—281no—
560C2×C4—281no—
561C2×C4—281no—
562C2×C4—281no—
563C2×C4—281no—
564C2×C4—281no—
565C2×C4—281no—
566C2×C4—564no—
567C2×C4C22×C4×D711yescharacteristic
568C2×C4C2×#115911yescharacteristic
569C2×C4C2×#115911yescharacteristic
570C2×C4C2×#116111yescharacteristic
571C2×C4D7×#4111yescharacteristic
572C2×C4D7×#4111yescharacteristic
573C8—22no—
574C8—41no—
575C8—142no—
576C8—281no—
577C7#2113111yescharacteristic, complemented, Sylow
578C22—282no—
579C22—282no—
580C22—282no—
581C22—561no—
582C22—561no—
583C22—561no—
584C22—561no—
585C22C4×D4×D711yescharacteristic
586C22#9027711yescharacteristic
587C22#9031811yescharacteristic
588C22#9045311yescharacteristic
589C22#9046111yescharacteristic
590C22#9046911yescharacteristic
591C22#9046911yescharacteristic
592C4—24no—
593C4—42no—
594C4—41no—
595C4—42no—
596C4—41no—
597C4—81no—
598C4—142no—
599C4—142no—
600C4—281no—
601C4—281no—
602C4—282no—
603C4—282no—
604C4—561no—
605C4C2×#645511yescharacteristic
606C4C4×#115911yescharacteristic
607C4#9031511yescharacteristic
608C4#9034011yescharacteristic
609C2—562no—
610C2#1173182211yescharacteristic
611C2#1173709411yescharacteristic
612C2#1173727711yescharacteristic
613C2#1173747811yescharacteristic
614C2#1173766411yescharacteristic
615C2#1173844611yescharacteristic
616C2#1173865511yescharacteristic
subgroupG/H
centerC23C2×D4×D7
commutatorC2×C4×C7C23×C4
FrattiniC22×C4C23×D7
FittingC7×#1865C2
socleC23×C7C22×D4
prime radicalC22×D28C23
cosocleC22×C4×C7C24
hypercenter#1865D7
hypocenterC7#21131
LCSG ▷ C2×C4×C7 ▷ C2×C7 ▷ C7
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1865

Complements

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

NH ≅ G/Ntype
1. #11739895C2semidirect
4. C7×#1865C2semidirect
7. Dic7×#106C2semidirect
9. #11727992C2semidirect
10. #11727974C2semidirect
11. #11727356C2semidirect
12. #11726573C2semidirect
15. #11726352C2semidirect
47. #89560C4semidirect
136. #1865D7semidirect
577. C7#21131semidirect

Maximal subgroups

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

subgroupindex
#117398952
C2×#895602
#117334142
C7×#18652
#117293872
#117283232
Dic7×#1062
#117279942
#117279922
#117279742
#117273562
#117265732
#117265362
#117263802
#117263522
#211317