Finite Group Databasebeta

← #13373188

Subgroups — #13373188

Order 1792.

894 conjugacy classes of subgroups.

The subgroup lattice has 628 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C7×#2356C211yesmaximal, characteristic, complemented
2C2×#89798C211yesmaximal, characteristic
3C4⋊C4×D28C211yesmaximal, characteristic
4#11729380C211yesmaximal, characteristic, complemented
5#11727441C211yesmaximal, characteristic
6#11727441C211yesmaximal, characteristic
7#11727429C211yesmaximal, characteristic, complemented
8#11727428C211yesmaximal, characteristic, complemented
9#11727310C211yesmaximal, characteristic
10#11727302C211yesmaximal, characteristic, complemented
11#11727232C211yesmaximal, characteristic, complemented
12#11727228C211yesmaximal, characteristic
13C4×#6383C211yesmaximal, characteristic
14#11727215C211yesmaximal, characteristic, complemented
15#11727212C211yesmaximal, characteristic, complemented
16C2×C4×C7×Q8C2211yescharacteristic
17C22×#1143C2211yescharacteristic
18C2×D7×C4⋊C4—21no—
19C2×C4×D28C2211yescharacteristic
20C2×C4×D28C2211yescharacteristic
21C2×C4×D28C2211yescharacteristic
22C7×#391C2211yescharacteristic
23C7×#391C2211yescharacteristic
24C7×#387—21no—
25C7×#387—21no—
26C7×#383—21no—
27C7×#382C2211yescharacteristic
28C4×C7×C4⋊C4C2211yescharacteristic
29C4×C7×C4⋊C4C2211yescharacteristic
30C4×C7×C4⋊C4C2211yescharacteristic
31C7×#376—21no—
32C2×#6409C2211yescharacteristic
33C2×#6409C2211yescharacteristic
34C2×#6409C2211yescharacteristic
35#89798C418yescomplemented
36#89759—21no—
37C2×#6383C2211yescharacteristic
38C2×#6383C2211yescharacteristic
39C2×#6383C2211yescharacteristic
40C2×#6381C2211yescharacteristic
41#89707C2211yescharacteristic
42#89700C2211yescharacteristic
43#89700C2211yescharacteristic
44C2×C4⋊(C7⋊C8)C2211yescharacteristic
45C2×#6377C2211yescharacteristic
46C2×#6377C2211yescharacteristic
47C2×C4×C7⋊C8C2211yescharacteristic
48#89440—21no—
49#89440—21no—
50#89324C2211yescharacteristic
51#89324C2211yescharacteristic
52#89324C2211yescharacteristic
53#89324C2211yescharacteristic
54#89324C2211yescharacteristic
55#89324C2211yescharacteristic
56#89324C2211yescharacteristic
57#89324C2211yescharacteristic
58#89319C2211yescharacteristic
59#89319C2211yescharacteristic
60#22778—71nomaximal, Sylow
61C22×C7×Q8C2311yescharacteristic
62C22×D28C2311yescharacteristic
63C22×C4×D7—21no—
64C22×C4×D7—21no—
65C22×C4×D7—21no—
66C4×C7×Q8—22no—
67C4×C7×Q8C2×C414yescomplemented
68C2×C7×C4⋊C4—21no—
69C2×C7×C4⋊C4D411yescharacteristic
70C2×C7×C4⋊C4D411yescharacteristic
71C2×C7×C4⋊C4C2311yescharacteristic
72C2×C7×C4⋊C4C2311yescharacteristic
73C2×C7×C4⋊C4C2311yescharacteristic
74C2×C42×C7—21no—
75C2×C42×C7—21no—
76C2×C42×C7—21no—
77C2×C42×C7C2311yescharacteristic
78C2×C42×C7C2311yescharacteristic
79C2×C42×C7C2311yescharacteristic
80C2×#1143—22no—
81C2×#1143—22no—
82C2×#1143C2×C414yes—
83C2×(C2×D7)⋊C4—21no—
84C2×(C2×D7)⋊C4—21no—
85C2×(C2×D7)⋊C4—21no—
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—
93C22×C7⋊C8C2311yescharacteristic
94C22×C7⋊C8C2311yescharacteristic
95C22×C7⋊C8C2311yescharacteristic
96C22×C7⋊C8C2311yescharacteristic
97D7×C4⋊C4—44no—
98C4×D28—22no—
99C4×D28—22no—
100C4×D28—22no—
101C4×D28—41no—
102C4×D28—41no—
103C4×D28C2×C414yes—
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×#95D411yescharacteristic
113C7×#95D411yescharacteristic
114#6409—41no—
115#6409—41no—
116#6409C2×C414yescomplemented
117C7⋊#95—21no—
118C7⋊#95—21no—
119#6383—22no—
120#6383—22no—
121#6383C2×C414yes—
122#6381C2×C414yescomplemented
123C4⋊(C7⋊C8)—22no—
124#6377—41no—
125#6377C2×C414yescomplemented
126C4×C7⋊C8—41no—
127C2×#440—71no—
128#2356D711yescharacteristic, complemented
129D4×C4⋊C4—71no—
130#1935—71no—
131#1933—71no—
132#1921—71no—
133#1918—71no—
134#1877—71no—
135#1877—71no—
136#1836—71no—
137#1804—71no—
138#1803—71no—
139#1771—71no—
140#1762—71no—
141C4×#102—71no—
142C23×D7—21no—
143C2×C7×Q8—21no—
144C2×C7×Q8—21no—
145C2×C7×Q8—21no—
146C2×C7×Q8—21no—
147C2×C7×Q8—21no—
148C2×C7×Q8C22×C412yes—
149C22×C4×C7—21no—
150C22×C4×C7—21no—
151C22×C4×C7—21no—
152C22×C4×C7—21no—
153C22×C4×C7C2×D411yescharacteristic
154C22×C4×C7C2×D411yescharacteristic
155C22×C4×C7C2×D411yescharacteristic
156C22×C4×C7C2×D411yescharacteristic
157C22×C4×C7C2×D411yescharacteristic
158C22×C4×C7C2×D411yescharacteristic
159C22×C4×C7C2411yescharacteristic
160C22×Dic7—21no—
161C22×Dic7—21no—
162C22×Dic7—21no—
163C2×D28—21no—
164C2×D28—21no—
165C2×D28—21no—
166C2×D28C22×C412yes—
167C2×D28#4112yes—
168C2×D28#4112yes—
169C2×C4×D7—24no—
170C2×C4×D7—42no—
171C2×C4×D7—42no—
172C2×C4×D7—42no—
173C2×C4×D7—42no—
174C2×C4×D7—42no—
175C2×C4×D7—42no—
176C2×C4×D7—81no—
177C2×C4×D7—81no—
178C7×C4⋊C4—24no—
179C7×C4⋊C4—22no—
180C7×C4⋊C4—21no—
181C7×C4⋊C4—21no—
182C7×C4⋊C4—21no—
183C7×C4⋊C4—21no—
184C7×C4⋊C4—21no—
185C7×C4⋊C4—41no—
186C7×C4⋊C4C22×C412yes—
187C42×C7—24no—
188C42×C7—21no—
189C42×C7—21no—
190C42×C7—21no—
191C42×C7—21no—
192C42×C7—42no—
193C42×C7—42no—
194C42×C7C22×C412yes—
195C42×C7#4112yes—
196#1143—28no—
197(C2×D7)⋊C4—24no—
198(C2×D7)⋊C4—42no—
199(C2×D7)⋊C4—42no—
200C4⋊Dic7—21no—
201C4⋊Dic7—21no—
202C4⋊Dic7—21no—
203C4⋊Dic7—21no—
204C4⋊Dic7—21no—
205C4⋊Dic7—42no—
206C4⋊Dic7—81no—
207C4⋊Dic7C22×C412yes—
208Dic7⋊C4—42no—
209Dic7⋊C4—42no—
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⋊C8—21no—
218C2×C7⋊C8—21no—
219C2×C7⋊C8—21no—
220C2×C7⋊C8C22×C412yes—
221C2×C7⋊C8C22×C412yes—
222C22×SD16—71no—
223C2×C4×Q8C2×D711yescharacteristic
224C2×C4×D4—71no—
225C2×C4×D4—71no—
226C2×C4×D4—71no—
227C22×C4⋊C4—141no—
228#440—78no—
229C2×#107—71no—
230C2×C4⋊C8—71no—
231C2×#103—71no—
232C2×#103—71no—
233C2×#103—71no—
234C2×#102—71no—
235C2×#102—71no—
236C2×#102—71no—
237C2×#97—71no—
238C2×#97—71no—
239C2×C4×C8—71no—
240#391C2×D711yescharacteristic
241#391C2×D711yescharacteristic
242#389—71no—
243#389—71no—
244#387—21no—
245#387—21no—
246#385—141no—
247#385—141no—
248#384—71no—
249#383—21no—
250#382C2×D711yescharacteristic
251#380—141no—
252C4×C4⋊C4C2×D711yescharacteristic
253C4×C4⋊C4C2×D711yescharacteristic
254C4×C4⋊C4C2×D711yescharacteristic
255#376—21no—
256#340—71no—
257#340—71no—
258#340—71no—
259#340—71no—
260#340—71no—
261#340—71no—
262#340—71no—
263#340—71no—
264#336—71no—
265#336—71no—
266C23×C7C22×D411yescharacteristic
267C22×D7—22no—
268C22×D7—22no—
269C22×D7—22no—
270C22×D7—41no—
271C22×D7—41no—
272C22×D7—41no—
273C22×D7—41no—
274C7×Q8—22no—
275C7×Q8—22no—
276C7×Q8—41no—
277C7×Q8—41no—
278C2×C4×C7—21no—
279C2×C4×C7—21no—
280C2×C4×C7—21no—
281C2×C4×C7—21no—
282C2×C4×C7—21no—
283C2×C4×C7—21no—
284C2×C4×C7—22no—
285C2×C4×C7—22no—
286C2×C4×C7—21no—
287C2×C4×C7—21no—
288C2×C4×C7—21no—
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—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×C7—41no—
303C2×C4×C7—41no—
304C2×C4×C7—41no—
305C2×C4×C7C4×D412yes—
306C2×C4×C7C4×D412yes—
307C2×C4×C7AGL(1,ℤ/8)12yes—
308C2×C4×C7C23×C411yescharacteristic
309C2×C4×C7C2×#4111yescharacteristic
310C2×C4×C7C2×#4111yescharacteristic
311C2×C4×C7C2×#4111yescharacteristic
312C2×C4×C7H(5,𝔽2)11yescharacteristic
313C2×C4×C72−1+411yescharacteristic
314C2×Dic7—22no—
315C2×Dic7—41no—
316C2×Dic7—41no—
317C2×Dic7—41no—
318C2×Dic7—41no—
319C2×Dic7—41no—
320C2×Dic7—41no—
321C2×Dic7—41no—
322C2×Dic7—41no—
323D28—22no—
324D28—22no—
325D28—22no—
326D28#11714yes—
327C4×D7—48no—
328C4×D7—84no—
329C4×D7—84no—
330C7⋊C8—22no—
331C7⋊C8—22no—
332C7⋊C8—41no—
333C7⋊C8—41no—
334C22×Q8C22×D711yescharacteristic
335C22×D4—71no—
336C23×C4—141no—
337C23×C4—141no—
338C23×C4—141no—
339C2×SD16—74no—
340C2×SD16—142no—
341C2×SD16—142no—
342C22×C8—71no—
343C22×C8—71no—
344C22×C8—71no—
345C22×C8—71no—
346C4×Q8—22no—
347C4×Q8C4×D714yescomplemented
348C4×D4—74no—
349C4×D4—142no—
350C4×D4—142no—
351C4×D4—142no—
352C4×D4—281no—
353C4×D4—281no—
354C2×C4⋊C4—21no—
355C2×C4⋊C4—71no—
356C2×C4⋊C4—71no—
357C2×C4⋊C4—71no—
358C2×C4⋊C4—141no—
359C2×C4⋊C4—141no—
360C2×C4⋊C4—141no—
361C2×C4⋊C4—141no—
362C2×C4⋊C4—284no—
363C2×C4⋊C4C22⋊D711yescharacteristic
364C2×C4⋊C4C22⋊D711yescharacteristic
365C2×C4⋊C4C22×D711yescharacteristic
366C2×C4⋊C4C22×D711yescharacteristic
367C2×C4⋊C4C22×D711yescharacteristic
368C2×C22⋊C4—141no—
369C2×C22⋊C4—141no—
370C2×C22⋊C4—141no—
371C2×C42—21no—
372C2×C42—21no—
373C2×C42—21no—
374C2×C42C22×D711yescharacteristic
375C2×C42C22×D711yescharacteristic
376C2×C42C22×D711yescharacteristic
377#107—74no—
378C4⋊C8—142no—
379#103—74no—
380#103—281no—
381#103—281no—
382#102—74no—
383#102—142no—
384#102—142no—
385#97—74no—
386#97—281no—
387C4×C8—281no—
388#95—21no—
389#95—21no—
390#95—21no—
391#95—21no—
392#95—21no—
393#95—21no—
394#95—21no—
395#95—21no—
396#95—141no—
397#95—141no—
398#95C22⋊D711yescharacteristic
399#95C22⋊D711yescharacteristic
400C22×C7C2×C4×D411yescharacteristic
401C22×C7#54611yescharacteristic
402C22×C7#54811yescharacteristic
403C22×C7C2×AGL(1,ℤ/8)11yescharacteristic
404C22×C7#57511yescharacteristic
405C22×C7#57711yescharacteristic
406C22×C7#57811yescharacteristic
407C2×D7—24no—
408C2×D7—42no—
409C2×D7—42no—
410C2×D7—42no—
411C2×D7—42no—
412C2×D7—42no—
413C2×D7—42no—
414C4×C7—22no—
415C4×C7—22no—
416C4×C7—22no—
417C4×C7—42no—
418C4×C7—42no—
419C4×C7—41no—
420C4×C7—41no—
421C4×C7—41no—
422C4×C7—81no—
423C4×C7—81no—
424C4×C7C2×#11711yescharacteristic
425C4×C7#52011yescharacteristic
426C4×C7#55211yescharacteristic
427C4×C7#55311yescharacteristic
428Dic7—42no—
429Dic7—81no—
430Dic7—81no—
431C24—141no—
432C2×Q8—21no—
433C2×Q8—21no—
434C2×Q8—21no—
435C2×Q8—21no—
436C2×Q8—21no—
437C2×Q8C2×C4×D712yes—
438C2×D4—72no—
439C2×D4—72no—
440C2×D4—72no—
441C2×D4—141no—
442C2×D4—141no—
443C2×D4—141no—
444C22×C4—21no—
445C22×C4—21no—
446C22×C4—21no—
447C22×C4—21no—
448C22×C4—141no—
449C22×C4—144no—
450C22×C4—141no—
451C22×C4—141no—
452C22×C4—282no—
453C22×C4—282no—
454C22×C4—282no—
455C22×C4—282no—
456C22×C4—282no—
457C22×C4—282no—
458C22×C4—561no—
459C22×C4—561no—
460C22×C4C2×C22⋊D711yescharacteristic
461C22×C4C2×C22⋊D711yescharacteristic
462C22×C4C2×C22⋊D711yescharacteristic
463C22×C4C2×C22⋊D711yescharacteristic
464C22×C4C2×C22⋊D711yescharacteristic
465C22×C4C2×C22⋊D711yescharacteristic
466C22×C4C23×D711yescharacteristic
467SD16—148no—
468C2×C8—72no—
469C2×C8—72no—
470C2×C8—141no—
471C2×C8—141no—
472C2×C8—141no—
473C2×C8—141no—
474C2×C8—141no—
475C2×C8—141no—
476C2×C8—141no—
477C2×C8—141no—
478C2×C8—141no—
479C2×C8—141no—
480C4⋊C4—24no—
481C4⋊C4—22no—
482C4⋊C4—21no—
483C4⋊C4—21no—
484C4⋊C4—21no—
485C4⋊C4—21no—
486C4⋊C4—21no—
487C4⋊C4—41no—
488C4⋊C4—72no—
489C4⋊C4—141no—
490C4⋊C4—141no—
491C4⋊C4—141no—
492C4⋊C4—141no—
493C4⋊C4—141no—
494C4⋊C4—282no—
495C4⋊C4—282no—
496C4⋊C4—282no—
497C4⋊C4—561no—
498C4⋊C4C2×C4×D712yes—
499C22⋊C4—144no—
500C22⋊C4—282no—
501C22⋊C4—282no—
502C42—24no—
503C42—21no—
504C42—21no—
505C42—21no—
506C42—21no—
507C42—42no—
508C42—42no—
509C42C2×C4×D712yes—
510C42#115712yes—
511C2×C7#235211yescharacteristic
512C2×C7C4×AGL(1,ℤ/8)11yescharacteristic
513C2×C7#294711yescharacteristic
514C2×C7#331011yescharacteristic
515C2×C7#331511yescharacteristic
516C2×C7#336711yescharacteristic
517C2×C7#337611yescharacteristic
518D7—44no—
519C23—142no—
520C23—142no—
521C23—142no—
522C23—281no—
523C23—281no—
524C23—281no—
525C23—281no—
526C23C22×C22⋊D711yescharacteristic
527Q8—22no—
528Q8—22no—
529Q8—41no—
530Q8—41no—
531D4—74no—
532D4—142no—
533D4—142no—
534D4—142no—
535C2×C4—21no—
536C2×C4—21no—
537C2×C4—21no—
538C2×C4—21no—
539C2×C4—21no—
540C2×C4—21no—
541C2×C4—22no—
542C2×C4—22no—
543C2×C4—21no—
544C2×C4—21no—
545C2×C4—21no—
546C2×C4—21no—
547C2×C4—21no—
548C2×C4—21no—
549C2×C4—21no—
550C2×C4—21no—
551C2×C4—21no—
552C2×C4—41no—
553C2×C4—41no—
554C2×C4—41no—
555C2×C4—41no—
556C2×C4—41no—
557C2×C4—41no—
558C2×C4—41no—
559C2×C4—41no—
560C2×C4—41no—
561C2×C4—41no—
562C2×C4—142no—
563C2×C4—288no—
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—564no—
573C2×C4—564no—
574C2×C4C4×C22⋊D712yes—
575C2×C4C4×C22⋊D712yes—
576C2×C4#651212yes—
577C2×C4C22×C4×D711yescharacteristic
578C2×C4C2×#115711yescharacteristic
579C2×C4D7×#4111yescharacteristic
580C2×C4D7×#4111yescharacteristic
581C2×C4#655311yescharacteristic
582C2×C4#655411yescharacteristic
583C8—142no—
584C8—142no—
585C8—281no—
586C8—281no—
587C7#2277811yescharacteristic, complemented, Sylow
588C22—144no—
589C22—282no—
590C22—282no—
591C22—282no—
592C22—282no—
593C22—282no—
594C22—282no—
595C22C2×C4×C22⋊D711yescharacteristic
596C22C2×#651211yescharacteristic
597C22#9051311yescharacteristic
598C22#9052011yescharacteristic
599C22#9052211yescharacteristic
600C22#9052811yescharacteristic
601C22#9052911yescharacteristic
602C4—22no—
603C4—22no—
604C4—22no—
605C4—42no—
606C4—42no—
607C4—41no—
608C4—41no—
609C4—41no—
610C4—81no—
611C4—81no—
612C4—282no—
613C4—561no—
614C4—561no—
615C4D7×#11711yescharacteristic
616C4#9021411yescharacteristic
617C4#9022011yescharacteristic
618C4#9022111yescharacteristic
619C2—284no—
620C2#1173971711yescharacteristic
621C2C4×#651211yescharacteristic
622C2#1173999211yescharacteristic
623C2#1174104411yescharacteristic
624C2#1174104511yescharacteristic
625C2#1174111311yescharacteristic
626C2#1174111411yescharacteristic
subgroupG/H
centerC23C22×C22⋊D7
commutatorC2×C4×C7C23×C4
FrattiniC22×C4C23×D7
FittingC7×#2356C2
socleC23×C7C22×D4
prime radicalC22×D28C23
cosocleC22×C4×C7C24
hypercenter#2356D7
hypocenterC7#22778
LCSG ▷ C2×C4×C7 ▷ C2×C7 ▷ C7
UCSC1 ◁ C23 ◁ C4×C4⋊C4 ◁ #2356

Complements

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

NH ≅ G/Ntype
1. C7×#2356C2semidirect
4. #11729380C2semidirect
7. #11727429C2semidirect
8. #11727428C2semidirect
10. #11727302C2semidirect
11. #11727232C2semidirect
14. #11727215C2semidirect
15. #11727212C2semidirect
35. #89798C4semidirect
67. C4×C7×Q8C2×C4semidirect
116. #6409C2×C4semidirect
122. #6381C2×C4semidirect
125. #6377C2×C4semidirect
128. #2356D7semidirect
347. C4×Q8C4×D7semidirect
587. C7#22778semidirect

Maximal subgroups

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

subgroupindex
C7×#23562
C2×#897982
C4⋊C4×D282
#117293802
#117274412
#117274292
#117274282
#117273102
#117273022
#117272322
#117272282
C4×#63832
#117272152
#117272122
#227787