Finite Group Databasebeta

← #13356917

Subgroups — #13356917

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
1C7×#2276C211yesmaximal, characteristic, complemented
2C2×#89798C211yesmaximal, characteristic
3#11730860C211yesmaximal, characteristic
4#11729387C211yesmaximal, characteristic
5#11729387C211yesmaximal, characteristic
6C4×#6409C211yesmaximal, characteristic, complemented
7#11729383C211yesmaximal, characteristic, complemented
8#11729382C211yesmaximal, characteristic, complemented
9#11727235C211yesmaximal, characteristic, complemented
10C4×#6383C211yesmaximal, characteristic
11#11727217C211yesmaximal, characteristic
12#11727216C211yesmaximal, characteristic
13#11727215C211yesmaximal, characteristic, complemented
14#11727212C211yesmaximal, characteristic, complemented
15#11727189C211yesmaximal, characteristic, complemented
16C2×C4×C7×Q8C2211yescharacteristic
17C2×C4×C7×Q8C2211yescharacteristic
18C2×C4×C7×Q8C2211yescharacteristic
19C22×#1143C2211yescharacteristic
20C2×C4×D28C2211yescharacteristic
21C4×C7×C4⋊C4—21no—
22C4×C7×C4⋊C4—21no—
23C4×C7×C4⋊C4—21no—
24C4×C7×C4⋊C4C2211yescharacteristic
25C4×C7×C4⋊C4C2211yescharacteristic
26C4×C7×C4⋊C4C2211yescharacteristic
27C7×#376—21no—
28C7×#376C2211yescharacteristic
29C2×#6409C2211yescharacteristic
30C2×#6409C2211yescharacteristic
31C2×#6409C2211yescharacteristic
32#89798C418yescomplemented
33C2×#6383C2211yescharacteristic
34C2×#6383C2211yescharacteristic
35C2×#6383C2211yescharacteristic
36C2×#6382C2211yescharacteristic
37C2×#6381C2211yescharacteristic
38C2×#6381C2211yescharacteristic
39#89711C2211yescharacteristic
40#89711C2211yescharacteristic
41C4×C4⋊Dic7C2211yescharacteristic
42#89700C2211yescharacteristic
43#89700C2211yescharacteristic
44C2×#6377C2211yescharacteristic
45C2×C4×C7⋊C8C2211yescharacteristic
46#89441—21no—
47#89441—21no—
48#89439—21no—
49#89436—21no—
50#89324C2211yescharacteristic
51#89324C2211yescharacteristic
52#89324C2211yescharacteristic
53#89324C2211yescharacteristic
54#89324C2211yescharacteristic
55#89324C2211yescharacteristic
56#89319C2211yescharacteristic
57#89319C2211yescharacteristic
58#89319C2211yescharacteristic
59#89319C2211yescharacteristic
60#21128—71nomaximal, Sylow
61C22×C7×Q8C2311yescharacteristic
62C22×D28C2311yescharacteristic
63C22×C4×D7—21no—
64C4×C7×Q8—22no—
65C4×C7×Q8—22no—
66C4×C7×Q8—22no—
67C4×C7×Q8—22no—
68C4×C7×Q8—22no—
69C4×C7×Q8C2×C414yes—
70C2×C7×C4⋊C4—21no—
71C2×C7×C4⋊C4—21no—
72C2×C7×C4⋊C4—21no—
73C2×C7×C4⋊C4C2311yescharacteristic
74C2×C7×C4⋊C4C2311yescharacteristic
75C2×C7×C4⋊C4C2311yescharacteristic
76C2×C42×C7—21no—
77C2×C42×C7—21no—
78C2×C42×C7—21no—
79C2×C42×C7—21no—
80C2×C42×C7—21no—
81C2×C42×C7—21no—
82C2×C42×C7C2311yescharacteristic
83C2×C42×C7C2311yescharacteristic
84C2×C42×C7C2311yescharacteristic
85C2×#1143—22no—
86C2×#1143—22no—
87C2×#1143C2×C414yes—
88C2×(C2×D7)⋊C4—21no—
89C2×(C2×D7)⋊C4—21no—
90C2×(C2×D7)⋊C4—21no—
91C2×(C2×D7)⋊C4—21no—
92C2×(C2×D7)⋊C4—21no—
93C2×C4⋊Dic7C2311yescharacteristic
94C2×C4⋊Dic7C2311yescharacteristic
95C2×C4⋊Dic7C2311yescharacteristic
96C2×Dic7⋊C4—21no—
97C2×Dic7⋊C4—21no—
98C2×C4×Dic7—21no—
99C22×C7⋊C8C2311yescharacteristic
100C22×C7⋊C8C2311yescharacteristic
101C22×C7⋊C8C2311yescharacteristic
102C22×C7⋊C8C2311yescharacteristic
103C4×D28—22no—
104C4×D28C2×C414yes—
105C7×#95—21no—
106C7×#95—21no—
107C7×#95—21no—
108C7×#95D411yescharacteristic
109C7×#95D411yescharacteristic
110C7×#95D411yescharacteristic
111C7×#95D411yescharacteristic
112#6409—22no—
113#6409—22no—
114#6409C2×C414yes—
115C7⋊#95—21no—
116C7⋊#95—21no—
117C7⋊#95—21no—
118#6383—22no—
119#6383—22no—
120#6383C2×C414yes—
121#6382—22no—
122#6381—22no—
123#6381C2×C414yes—
124#6377C2×C414yes—
125C4×C7⋊C8—22no—
126C2×#440—71no—
127#2319—71no—
128#2276D711yescharacteristic, complemented
129#1926—71no—
130#1925—71no—
131#1921—71no—
132#1918—71no—
133#1880—71no—
134#1880—71no—
135#1865—71no—
136#1863—71no—
137#1776—71no—
138C4×#103—71no—
139C4×#102—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×C7C2×D411yescharacteristic
155C22×C4×C7C2×D411yescharacteristic
156C22×C4×C7C2×D411yescharacteristic
157C22×C4×C7C2×D411yescharacteristic
158C22×C4×C7C2411yescharacteristic
159C22×Dic7—21no—
160C22×Dic7—21no—
161C22×Dic7—21no—
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—
171C7×C4⋊C4—24no—
172C7×C4⋊C4—24no—
173C7×C4⋊C4—24no—
174C7×C4⋊C4—21no—
175C7×C4⋊C4—21no—
176C7×C4⋊C4—21no—
177C7×C4⋊C4C22×C412yes—
178C7×C4⋊C4#4112yes—
179C7×C4⋊C4#4112yes—
180C42×C7—24no—
181C42×C7—24no—
182C42×C7—24no—
183C42×C7—21no—
184C42×C7—21no—
185C42×C7—21no—
186C42×C7—21no—
187C42×C7—81no—
188C42×C7—81no—
189C42×C7—81no—
190C42×C7C22×C412yes—
191C42×C7#4112yes—
192#1143—28no—
193(C2×D7)⋊C4—24no—
194(C2×D7)⋊C4—81no—
195(C2×D7)⋊C4—81no—
196(C2×D7)⋊C4—81no—
197(C2×D7)⋊C4—81no—
198C4⋊Dic7—21no—
199C4⋊Dic7—21no—
200C4⋊Dic7—21no—
201C4⋊Dic7—21no—
202C4⋊Dic7—21no—
203C4⋊Dic7C22×C412yes—
204Dic7⋊C4—81no—
205Dic7⋊C4—81no—
206C4×Dic7—81no—
207C2×C7⋊C8—21no—
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⋊C8—21no—
215C2×C7⋊C8—21no—
216C2×C7⋊C8—21no—
217C2×C7⋊C8C22×C412yes—
218C2×C7⋊C8C22×C412yes—
219C22×SD16—71no—
220C2×C4×Q8C2×D711yescharacteristic
221C2×C4×Q8C2×D711yescharacteristic
222C2×C4×Q8C2×D711yescharacteristic
223C2×C4×D4—71no—
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×C4×C8—71no—
236#390—71no—
237#390—71no—
238#389—71no—
239#389—71no—
240#388—141no—
241#388—141no—
242#381—141no—
243#380—141no—
244C4×C4⋊C4—21no—
245C4×C4⋊C4—21no—
246C4×C4⋊C4—21no—
247C4×C4⋊C4—71no—
248C4×C4⋊C4C2×D711yescharacteristic
249C4×C4⋊C4C2×D711yescharacteristic
250C4×C4⋊C4C2×D711yescharacteristic
251#376—21no—
252#376C2×D711yescharacteristic
253#340—71no—
254#340—71no—
255#340—71no—
256#340—71no—
257#340—71no—
258#340—71no—
259#336—71no—
260#336—71no—
261#336—71no—
262#336—71no—
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—21no—
279C2×C4×C7—21no—
280C2×C4×C7—21no—
281C2×C4×C7—21no—
282C2×C4×C7—22no—
283C2×C4×C7—21no—
284C2×C4×C7—21no—
285C2×C4×C7—21no—
286C2×C4×C7—21no—
287C2×C4×C7—22no—
288C2×C4×C7—22no—
289C2×C4×C7—21no—
290C2×C4×C7—21no—
291C2×C4×C7—21no—
292C2×C4×C7—21no—
293C2×C4×C7—21no—
294C2×C4×C7—21no—
295C2×C4×C7—21no—
296C2×C4×C7—21no—
297C2×C4×C7—41no—
298C2×C4×C7—41no—
299C2×C4×C7—41no—
300C2×C4×C7—41no—
301C2×C4×C7—41no—
302C2×C4×C7—41no—
303C2×C4×C7C4×D412yes—
304C2×C4×C7C4×D412yes—
305C2×C4×C7C23×C411yescharacteristic
306C2×C4×C7C2×#4111yescharacteristic
307C2×C4×C7C2×#4111yescharacteristic
308C2×C4×C7C2×#4111yescharacteristic
309C2×C4×C7C2×#4111yescharacteristic
310C2×C4×C7C2×#4111yescharacteristic
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—
320D28—22no—
321D28—22no—
322D28—41no—
323D28—41no—
324C4×D7—84no—
325C7⋊C8—22no—
326C7⋊C8—22no—
327C7⋊C8—41no—
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×C8—71no—
338C22×C8—71no—
339C4×Q8—22no—
340C4×Q8—22no—
341C4×Q8—22no—
342C4×Q8—22no—
343C4×Q8—22no—
344C4×Q8C4×D714yes—
345C4×D4—74no—
346C4×D4—142no—
347C2×C4⋊C4—21no—
348C2×C4⋊C4—21no—
349C2×C4⋊C4—21no—
350C2×C4⋊C4—71no—
351C2×C4⋊C4—71no—
352C2×C4⋊C4—71no—
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—21no—
365C2×C42—21no—
366C2×C42—21no—
367C2×C42—21no—
368C2×C42—21no—
369C2×C42—141no—
370C2×C42C22×D711yescharacteristic
371C2×C42C22×D711yescharacteristic
372C2×C42C22×D711yescharacteristic
373#107—74no—
374#107—142no—
375#106—142no—
376#103—74no—
377#103—142no—
378#103—142no—
379#102—74no—
380#102—142no—
381#102—142no—
382#97—74no—
383C4×C8—142no—
384#95—21no—
385#95—21no—
386#95—21no—
387#95—141no—
388#95—141no—
389#95—141no—
390#95C22⋊D711yescharacteristic
391#95C22⋊D711yescharacteristic
392#95C22⋊D711yescharacteristic
393#95C22⋊D711yescharacteristic
394C22×C7C2×C4×D411yescharacteristic
395C22×C7#52511yescharacteristic
396C22×C7#52511yescharacteristic
397C22×C7#57611yescharacteristic
398C22×C7#57711yescharacteristic
399C22×C7#57711yescharacteristic
400C22×C7#57811yescharacteristic
401C2×D7—42no—
402C2×D7—42no—
403C2×D7—42no—
404C2×D7—81no—
405C2×D7—81no—
406C2×D7—81no—
407C2×D7—81no—
408C4×C7—22no—
409C4×C7—22no—
410C4×C7—24no—
411C4×C7—41no—
412C4×C7—42no—
413C4×C7—41no—
414C4×C7—41no—
415C4×C7—42no—
416C4×C7—41no—
417C4×C7—42no—
418C4×C7C2×#11711yescharacteristic
419C4×C7C4×#4111yescharacteristic
420C4×C7#52911yescharacteristic
421C4×C7#52911yescharacteristic
422Dic7—42no—
423Dic7—81no—
424Dic7—81no—
425C24—141no—
426C2×Q8—21no—
427C2×Q8—21no—
428C2×Q8—21no—
429C2×Q8C2×C4×D712yes—
430C2×Q8#115712yes—
431C2×Q8#115712yes—
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—141no—
443C22×C4—144no—
444C22×C4—141no—
445C22×C4—141no—
446C22×C4—561no—
447C22×C4—561no—
448C22×C4C2×C22⋊D711yescharacteristic
449C22×C4C2×C22⋊D711yescharacteristic
450C22×C4C2×C22⋊D711yescharacteristic
451C22×C4C2×C22⋊D711yescharacteristic
452C22×C4C2×C22⋊D711yescharacteristic
453C22×C4C2×C22⋊D711yescharacteristic
454C22×C4C23×D711yescharacteristic
455SD16—148no—
456C2×C8—72no—
457C2×C8—72no—
458C2×C8—141no—
459C2×C8—141no—
460C2×C8—141no—
461C2×C8—141no—
462C2×C8—141no—
463C2×C8—141no—
464C2×C8—141no—
465C2×C8—141no—
466C2×C8—141no—
467C2×C8—141no—
468C4⋊C4—24no—
469C4⋊C4—24no—
470C4⋊C4—24no—
471C4⋊C4—21no—
472C4⋊C4—21no—
473C4⋊C4—21no—
474C4⋊C4—72no—
475C4⋊C4—141no—
476C4⋊C4—141no—
477C4⋊C4—141no—
478C4⋊C4—141no—
479C4⋊C4—141no—
480C4⋊C4—561no—
481C4⋊C4—561no—
482C4⋊C4C2×C4×D712yes—
483C4⋊C4#115712yes—
484C4⋊C4#115712yes—
485C22⋊C4—144no—
486C22⋊C4—561no—
487C22⋊C4—561no—
488C22⋊C4—561no—
489C22⋊C4—561no—
490C42—24no—
491C42—24no—
492C42—24no—
493C42—21no—
494C42—21no—
495C42—21no—
496C42—21no—
497C42—81no—
498C42—81no—
499C42—81no—
500C42—561no—
501C42C2×C4×D712yes—
502C42#115712yes—
503C2×C7#229011yescharacteristic
504C2×C7#294611yescharacteristic
505C2×C7#294711yescharacteristic
506C2×C7#311911yescharacteristic
507C2×C7#312111yescharacteristic
508C2×C7#312411yescharacteristic
509C2×C7#312611yescharacteristic
510D7—82no—
511C23—142no—
512C23—281no—
513C23—281no—
514C23—281no—
515C23—281no—
516C23—281no—
517C23—281no—
518C23C22×C22⋊D711yescharacteristic
519Q8—22no—
520Q8—22no—
521Q8—22no—
522Q8#643514yes—
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—21no—
538C2×C4—21no—
539C2×C4—22no—
540C2×C4—22no—
541C2×C4—21no—
542C2×C4—21no—
543C2×C4—21no—
544C2×C4—21no—
545C2×C4—21no—
546C2×C4—21no—
547C2×C4—21no—
548C2×C4—21no—
549C2×C4—41no—
550C2×C4—41no—
551C2×C4—41no—
552C2×C4—41no—
553C2×C4—41no—
554C2×C4—41no—
555C2×C4—142no—
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—564no—
565C2×C4C4×C22⋊D712yes—
566C2×C4C4×C22⋊D712yes—
567C2×C4C22×C4×D711yescharacteristic
568C2×C4C2×#115711yescharacteristic
569C2×C4C2×#115711yescharacteristic
570C2×C4C2×#115711yescharacteristic
571C2×C4C2×#115711yescharacteristic
572C2×C4C2×#115711yescharacteristic
573C8—142no—
574C8—142no—
575C8—281no—
576C8—281no—
577C7#2112811yescharacteristic, complemented, Sylow
578C22—282no—
579C22—282no—
580C22—282no—
581C22—561no—
582C22—561no—
583C22—561no—
584C22—561no—
585C22C2×C4×C22⋊D711yescharacteristic
586C22#9048211yescharacteristic
587C22#9048211yescharacteristic
588C22#9052611yescharacteristic
589C22#9052811yescharacteristic
590C22#9052811yescharacteristic
591C22#9052911yescharacteristic
592C4—22no—
593C4—22no—
594C4—24no—
595C4—41no—
596C4—41no—
597C4—42no—
598C4—41no—
599C4—42no—
600C4—41no—
601C4—42no—
602C4—282no—
603C4—561no—
604C4—561no—
605C4C2×#643511yescharacteristic
606C4C4×#115711yescharacteristic
607C4#9017011yescharacteristic
608C4#9017011yescharacteristic
609C2—562no—
610C2#1173951011yescharacteristic
611C2#1173999211yescharacteristic
612C2#1173999711yescharacteristic
613C2#1173999811yescharacteristic
614C2#1174000911yescharacteristic
615C2#1174001311yescharacteristic
616C2#1174001411yescharacteristic
subgroupG/H
centerC23C22×C22⋊D7
commutatorC2×C4×C7C23×C4
FrattiniC22×C4C23×D7
FittingC7×#2276C2
socleC23×C7C22×D4
prime radicalC22×D28C23
cosocleC22×C4×C7C24
hypercenter#2276D7
hypocenterC7#21128
LCSG ▷ C2×C4×C7 ▷ C2×C7 ▷ C7
UCSC1 ◁ C23 ◁ #376 ◁ #2276

Complements

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

NH ≅ G/Ntype
1. C7×#2276C2semidirect
6. C4×#6409C2semidirect
7. #11729383C2semidirect
8. #11729382C2semidirect
9. #11727235C2semidirect
13. #11727215C2semidirect
14. #11727212C2semidirect
15. #11727189C2semidirect
32. #89798C4semidirect
128. #2276D7semidirect
577. C7#21128semidirect

Maximal subgroups

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

subgroupindex
C7×#22762
C2×#897982
#117308602
#117293872
C4×#64092
#117293832
#117293822
#117272352
C4×#63832
#117272172
#117272162
#117272152
#117272122
#117271892
#211287