Finite Group Databasebeta

← #13387683

Subgroups — #13387683

Order 1792.

1434 conjugacy classes of subgroups.

The subgroup lattice has 622 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C7×#547C211yesmaximal, characteristic, complemented
2C2×#89859C211yesmaximal, characteristic, complemented
3#11739862C211yesmaximal, characteristic, complemented
4C2×C4×#1141C211yesmaximal, characteristic, complemented
5#11729541C211yesmaximal, characteristic, complemented
6#11729438C212yesmaximal, complemented
7#11729433C212yesmaximal, complemented
8#11729368C211yesmaximal, characteristic, complemented
9#11729358C211yesmaximal, characteristic, complemented
10#11729314C212yesmaximal, complemented
11#11729309C212yesmaximal, complemented
12C22×C7×#41—21no—
13C7×#547—24no—
14C7×#547—24no—
15C2×C7×C4⋊Q8C2211yescharacteristic
16C2×C7×#123—22no—
17C2×C7×C22⋊Q8—21no—
18C2×C7×#121C2212yes—
19C2×C4×C7×D4C2211yescharacteristic
20C2×C4×C7×D4C2211yescharacteristic
21C22×C7×C4⋊C4C2212yes—
22C2×#6501—21no—
23C22×#1141C2211yescharacteristic
24C2×#6493C2212yes—
25C2×C4×D28C2211yescharacteristic
26C2×#6406C2211yescharacteristic
27C2×#6406C2212yes—
28#89984C2212yes—
29C2×C22⋊(C7⋊C8)C2212yes—
30C2×C22⋊(C7⋊C8)C2212yes—
31#89859—24no—
32C4×#1141—24no—
33#89759—21no—
34C2×#6383C2212yes—
35C2×#6383C2211yescharacteristic
36C2×#6381C2212yes—
37C2×#6381C2211yescharacteristic
38#89733—22no—
39#89707C2211yescharacteristic
40C2×C4⋊(C7⋊C8)C2211yescharacteristic
41C2×C4×C7⋊C8C2211yescharacteristic
42#89324C2212yes—
43#89324C2212yes—
44#89324C2212yes—
45#24116—71nomaximal, Sylow
46C2×C7×#41—28no—
47C2×C7×#41—44no—
48C2×C7×#41—44no—
49C22×C7×Q8—21no—
50C22×C7×D4—22no—
51C22×C7×D4D411yescharacteristic
52C22×C7×D4C2311yescharacteristic
53C23×C4×C7—22no—
54C23×C4×C7—21no—
55C23×C4×C7C2312yes—
56C22×C22⋊D7—22no—
57C22×D28C2311yescharacteristic
58C22×C4×D7—21no—
59C7×C4⋊Q8—22no—
60C7×C4⋊Q8D414yescomplemented
61C7×#123—216no—
62C7×C22⋊Q8—28no—
63C7×#121—24no—
64C7×#121—24no—
65C4×C7×D4—22no—
66C4×C7×D4—22no—
67C4×C7×D4—22no—
68C4×C7×D4D414yescomplemented
69C2×C7×C4⋊C4—22no—
70C2×C7×C4⋊C4—21no—
71C2×C7×C4⋊C4—24no—
72C2×C7×C4⋊C4—24no—
73C2×C7×C4⋊C4D411yescharacteristic
74C2×C7×C4⋊C4C2311yescharacteristic
75C2×C7×C4⋊C4C2312yes—
76C2×C7×C22⋊C4—21no—
77C2×C7×C22⋊C4—22no—
78C2×C7×C22⋊C4D412yes—
79C2×C42×C7C2311yescharacteristic
80C2×C22⋊Dic7—22no—
81#6501—44no—
82C2×#1141—22no—
83C2×#1141—22no—
84C2×#1141—22no—
85#6493—24no—
86#6493—42no—
87C2×(C2×D7)⋊C4—21no—
88C2×(C2×D7)⋊C4—22no—
89C2×C4⋊Dic7—21no—
90C2×C4⋊Dic7—21no—
91C2×C4⋊Dic7C2311yescharacteristic
92C2×C4⋊Dic7C2312yes—
93C22×C7⋊C8C2311yescharacteristic
94C22×C7⋊C8C2312yes—
95C22×C7⋊C8C2311yescharacteristic
96C4×D28—22no—
97C4×D28—22no—
98#6406—22no—
99#6406—42no—
100C7⋊#95—22no—
101C22⋊(C7⋊C8)—24no—
102C22⋊(C7⋊C8)—42no—
103#6383—24no—
104#6383—22no—
105#6381—24no—
106#6381—22no—
107C4⋊(C7⋊C8)—22no—
108C4×C7⋊C8—22no—
109C2×#547D711yescharacteristic, complemented
110C2×#474—71no—
111C2×C4×D8—71no—
112#2537—71no—
113#2033—72no—
114#1999—72no—
115#1990—71no—
116#1954—71no—
117#1874—72no—
118#1852—72no—
119#1802—71no—
120C24×C7—21no—
121C24×C7C2×D412yes—
122C23×D7—21no—
123C7×#41—432no—
124C2×C7×Q8—24no—
125C2×C7×Q8—42no—
126C2×C7×Q8—42no—
127C2×C7×D4—28no—
128C2×C7×D4—22no—
129C2×C7×D4—22no—
130C2×C7×D4—21no—
131C2×C7×D4—21no—
132C2×C7×D4—21no—
133C2×C7×D4—21no—
134C2×C7×D4—21no—
135C2×C7×D4—44no—
136C2×C7×D4—44no—
137C2×C7×D4D814yescomplemented
138C2×C7×D4C2×D412yes—
139C22×C4×C7—28no—
140C22×C4×C7—21no—
141C22×C4×C7—22no—
142C22×C4×C7—24no—
143C22×C4×C7—22no—
144C22×C4×C7—22no—
145C22×C4×C7—22no—
146C22×C4×C7—22no—
147C22×C4×C7—22no—
148C22×C4×C7—22no—
149C22×C4×C7—44no—
150C22×C4×C7—44no—
151C22×C4×C7—42no—
152C22×C4×C7—42no—
153C22×C4×C7C2×D412yes—
154C22×C4×C7C2×D411yescharacteristic
155C22×C4×C7C2×D411yescharacteristic
156C22×C4×C7C2411yescharacteristic
157C2×C22⋊D7—44no—
158C2×C22⋊D7—44no—
159C2×C22⋊D7—82no—
160C22×Dic7—21no—
161C22×Dic7—22no—
162C2×D28—21no—
163C2×D28—21no—
164C2×D28—21no—
165C2×D28—21no—
166C2×D28—21no—
167C2×D28#4112yescomplemented
168C2×C4×D7—42no—
169C2×C4×D7—42no—
170C2×C4×D7—42no—
171C7×C4⋊C4—28no—
172C7×C4⋊C4—24no—
173C7×C4⋊C4—22no—
174C7×C4⋊C4—21no—
175C7×C4⋊C4—22no—
176C7×C4⋊C4C2×D412yes—
177C7×C4⋊C4C2×D414yes—
178C7×C22⋊C4—28no—
179C7×C22⋊C4—24no—
180C7×C22⋊C4—24no—
181C42×C7C2×D412yes—
182C42×C7C2×D412yes—
183C22⋊Dic7—44no—
184#1141—28no—
185(C2×D7)⋊C4—44no—
186(C2×D7)⋊C4—42no—
187C4⋊Dic7—21no—
188C4⋊Dic7—21no—
189C4⋊Dic7—22no—
190C4⋊Dic7—22no—
191C4⋊Dic7—42no—
192C4⋊Dic7—81no—
193C2×C7⋊C8—21no—
194C2×C7⋊C8—21no—
195C2×C7⋊C8—21no—
196C2×C7⋊C8—22no—
197C2×C7⋊C8—22no—
198C2×C7⋊C8—21no—
199C2×C7⋊C8—22no—
200C2×C7⋊C8—21no—
201C2×C7⋊C8#4112yescomplemented
202C22×#41—21no—
203C22×D8—71no—
204#547—24no—
205#547—24no—
206C2×C4⋊Q8C2×D711yescharacteristic
207C2×#123—22no—
208C2×C22⋊Q8—21no—
209C2×#121—72no—
210C2×#121—141no—
211C2×#121C2×D712yes—
212C2×C4×D4—71no—
213C2×C4×D4C2×D711yescharacteristic
214C2×C4×D4C2×D711yescharacteristic
215C22×C4⋊C4C2×D712yes—
216#474—144no—
217C4×D8—144no—
218C2×#107—71no—
219C2×#107—72no—
220C2×C4⋊C8—71no—
221C2×#102—71no—
222C2×#102—71no—
223C2×#102—72no—
224C2×#102—72no—
225C2×C22⋊C8—72no—
226C2×C22⋊C8—72no—
227C2×C4×C8—71no—
228#394—142no—
229#384—71no—
230#380—72no—
231#380—141no—
232#340—72no—
233#340—72no—
234#340—72no—
235C23×C7—22no—
236C23×C7—22no—
237C23×C7—22no—
238C23×C7—22no—
239C23×C7—22no—
240C23×C7—22no—
241C23×C7—22no—
242C23×C7—41no—
243C23×C7—41no—
244C23×C7—41no—
245C23×C7—41no—
246C23×C7—41no—
247C23×C7—41no—
248C23×C7C2×D814yes—
249C23×C7C22×D411yescharacteristic
250C22×D7—22no—
251C22×D7—41no—
252C22×D7—41no—
253C22×D7—41no—
254C22×D7—41no—
255C22×D7—41no—
256C22×D7—41no—
257C7×Q8—48no—
258C7×D4—22no—
259C7×D4—22no—
260C7×D4—28no—
261C7×D4—416no—
262C7×D4—41no—
263C7×D4—41no—
264C2×C4×C7—21no—
265C2×C4×C7—21no—
266C2×C4×C7—22no—
267C2×C4×C7—22no—
268C2×C4×C7—24no—
269C2×C4×C7—22no—
270C2×C4×C7—22no—
271C2×C4×C7—416no—
272C2×C4×C7—41no—
273C2×C4×C7—42no—
274C2×C4×C7—41no—
275C2×C4×C7—42no—
276C2×C4×C7—42no—
277C2×C4×C7—42no—
278C2×C4×C7—42no—
279C2×C4×C7—42no—
280C2×C4×C7—48no—
281C2×C4×C7#12012yes—
282C2×C4×C7#12012yes—
283C2×C4×C7C2×D812yes—
284C2×C4×C7AGL(1,ℤ/8)12yes—
285C2×C4×C7C22×D411yescharacteristic
286C2×C4×C7C22×D411yescharacteristic
287C2×C4×C7C2×#4111yescharacteristic
288C2×C4×C7C2×#4111yescharacteristic
289C2×C4×C7H(5,𝔽2)11yescharacteristic
290C2×C4×C72−1+411yescharacteristic
291C22⋊D7—88no—
292C2×Dic7—41no—
293C2×Dic7—42no—
294C2×Dic7—42no—
295C2×Dic7—41no—
296C2×Dic7—41no—
297C2×Dic7—42no—
298D28—22no—
299D28—22no—
300D28—41no—
301D28—41no—
302C4×D7—84no—
303C7⋊C8—22no—
304C7⋊C8—41no—
305C7⋊C8—42no—
306C2×#41—28no—
307C2×#41—44no—
308C2×#41—44no—
309C22×Q8—21no—
310C22×D4—22no—
311C22×D4—71no—
312C22×D4—142no—
313C22×D4C22⋊D711yescharacteristic
314C22×D4C22×D711yescharacteristic
315C23×C4—22no—
316C23×C4—21no—
317C23×C4—141no—
318C23×C4C22×D712yes—
319C2×D8—142no—
320C2×D8—142no—
321C2×D8—142no—
322C22×C8—71no—
323C22×C8—71no—
324C22×C8—72no—
325C4⋊Q8—22no—
326C4⋊Q8C22⋊D714yescomplemented
327#123—216no—
328C22⋊Q8—28no—
329#121—24no—
330#121—24no—
331#121—144no—
332#121—282no—
333#121—284no—
334C4×D4—22no—
335C4×D4—22no—
336C4×D4—22no—
337C4×D4—142no—
338C4×D4—142no—
339C4×D4C22⋊D714yescomplemented
340C2×C4⋊C4—22no—
341C2×C4⋊C4—21no—
342C2×C4⋊C4—24no—
343C2×C4⋊C4—24no—
344C2×C4⋊C4—71no—
345C2×C4⋊C4—72no—
346C2×C4⋊C4—141no—
347C2×C4⋊C4—141no—
348C2×C4⋊C4C22⋊D711yescharacteristic
349C2×C4⋊C4C22×D711yescharacteristic
350C2×C4⋊C4C22×D712yes—
351C2×C22⋊C4—21no—
352C2×C22⋊C4—22no—
353C2×C22⋊C4—142no—
354C2×C22⋊C4—141no—
355C2×C22⋊C4—142no—
356C2×C22⋊C4C22⋊D712yes—
357C2×C42C22×D711yescharacteristic
358#107—142no—
359#107—144no—
360C4⋊C8—142no—
361#102—142no—
362#102—142no—
363#102—144no—
364#102—282no—
365C22⋊C8—144no—
366C22⋊C8—282no—
367C4×C8—142no—
368#95—142no—
369C22×C7—24no—
370C22×C7—24no—
371C22×C7—24no—
372C22×C7—42no—
373C22×C7—42no—
374C22×C7—42no—
375C22×C7—42no—
376C22×C7—42no—
377C22×C7—42no—
378C22×C7—42no—
379C22×C7—81no—
380C22×C7—81no—
381C22×C7—81no—
382C22×C7—81no—
383C22×C7C2×#12011yescharacteristic
384C22×C7#54611yescharacteristic
385C22×C7#54711yescharacteristic
386C22×C7C22×D811yescharacteristic
387C22×C7C2×AGL(1,ℤ/8)11yescharacteristic
388C22×C7#57711yescharacteristic
389C22×C7#57811yescharacteristic
390C2×D7—42no—
391C2×D7—42no—
392C2×D7—42no—
393C2×D7—81no—
394C2×D7—81no—
395C2×D7—81no—
396C2×D7—81no—
397C4×C7—22no—
398C4×C7—42no—
399C4×C7—42no—
400C4×C7—44no—
401C4×C7#44714yes—
402C4×C7#52511yescharacteristic
403C4×C7#53711yescharacteristic
404C4×C7#54811yescharacteristic
405C4×C7#55011yescharacteristic
406Dic7—81no—
407Dic7—82no—
408C24—21no—
409C24—141no—
410C24C2×C22⋊D712yes—
411#41—432no—
412C2×Q8—24no—
413C2×Q8—42no—
414C2×Q8—42no—
415C2×D4—28no—
416C2×D4—22no—
417C2×D4—22no—
418C2×D4—21no—
419C2×D4—21no—
420C2×D4—21no—
421C2×D4—21no—
422C2×D4—21no—
423C2×D4—44no—
424C2×D4—44no—
425C2×D4—72no—
426C2×D4—141no—
427C2×D4—141no—
428C2×D4—141no—
429C2×D4—141no—
430C2×D4—141no—
431C2×D4—284no—
432C2×D4—284no—
433C2×D4—562no—
434C2×D4#114114yescomplemented
435C2×D4C2×C22⋊D712yes—
436C22×C4—28no—
437C22×C4—21no—
438C22×C4—22no—
439C22×C4—24no—
440C22×C4—22no—
441C22×C4—22no—
442C22×C4—22no—
443C22×C4—22no—
444C22×C4—22no—
445C22×C4—22no—
446C22×C4—44no—
447C22×C4—44no—
448C22×C4—42no—
449C22×C4—42no—
450C22×C4—141no—
451C22×C4—142no—
452C22×C4—282no—
453C22×C4—282no—
454C22×C4—282no—
455C22×C4C2×C22⋊D712yes—
456C22×C4C2×C22⋊D711yescharacteristic
457C22×C4C2×C22⋊D711yescharacteristic
458C22×C4C23×D711yescharacteristic
459D8—148no—
460C2×C8—72no—
461C2×C8—141no—
462C2×C8—141no—
463C2×C8—142no—
464C2×C8—141no—
465C2×C8—142no—
466C2×C8—141no—
467C2×C8—141no—
468C2×C8—142no—
469C4⋊C4—28no—
470C4⋊C4—24no—
471C4⋊C4—22no—
472C4⋊C4—21no—
473C4⋊C4—22no—
474C4⋊C4—142no—
475C4⋊C4—142no—
476C4⋊C4—141no—
477C4⋊C4—141no—
478C4⋊C4—282no—
479C4⋊C4—561no—
480C4⋊C4C2×C22⋊D712yes—
481C4⋊C4C2×C22⋊D714yes—
482C22⋊C4—28no—
483C22⋊C4—24no—
484C22⋊C4—24no—
485C22⋊C4—284no—
486C22⋊C4—284no—
487C22⋊C4—282no—
488C42C2×C22⋊D712yes—
489C42C2×C22⋊D712yes—
490C2×C7—44no—
491C2×C7—82no—
492C2×C7#240711yescharacteristic
493C2×C7C2×#44711yescharacteristic
494C2×C7#301311yescharacteristic
495C2×C7#329411yescharacteristic
496C2×C7#333011yescharacteristic
497C2×C7#333411yescharacteristic
498C2×C7#335411yescharacteristic
499D7—82no—
500C23—22no—
501C23—22no—
502C23—22no—
503C23—22no—
504C23—22no—
505C23—22no—
506C23—22no—
507C23—41no—
508C23—41no—
509C23—41no—
510C23—41no—
511C23—41no—
512C23—41no—
513C23—142no—
514C23—281no—
515C23—281no—
516C23—281no—
517C23—281no—
518C23—281no—
519C23—281no—
520C23C2×#114114yes—
521C23C22×C22⋊D711yescharacteristic
522Q8—48no—
523D4—28no—
524D4—22no—
525D4—22no—
526D4—416no—
527D4—41no—
528D4—41no—
529D4—142no—
530D4—142no—
531D4—281no—
532D4—281no—
533D4—568no—
534C2×C4—21no—
535C2×C4—21no—
536C2×C4—22no—
537C2×C4—22no—
538C2×C4—22no—
539C2×C4—22no—
540C2×C4—24no—
541C2×C4—416no—
542C2×C4—41no—
543C2×C4—42no—
544C2×C4—41no—
545C2×C4—42no—
546C2×C4—48no—
547C2×C4—42no—
548C2×C4—42no—
549C2×C4—42no—
550C2×C4—42no—
551C2×C4—281no—
552C2×C4—282no—
553C2×C4—281no—
554C2×C4—282no—
555C2×C4—282no—
556C2×C4—281no—
557C2×C4—564no—
558C2×C4C2×#114112yes—
559C2×C4#649512yes—
560C2×C4#651612yes—
561C2×C4#651612yes—
562C2×C4D7×#4111yescharacteristic
563C2×C4D7×#4111yescharacteristic
564C2×C4#655311yescharacteristic
565C2×C4#655411yescharacteristic
566C2×C4C22×C22⋊D711yescharacteristic
567C2×C4C22×C22⋊D711yescharacteristic
568C8—142no—
569C8—281no—
570C8—282no—
571C7#2411611yescharacteristic, complemented, Sylow
572C22—24no—
573C22—24no—
574C22—24no—
575C22—42no—
576C22—42no—
577C22—42no—
578C22—42no—
579C22—42no—
580C22—42no—
581C22—42no—
582C22—81no—
583C22—81no—
584C22—81no—
585C22—81no—
586C22—282no—
587C22—282no—
588C22—282no—
589C22—561no—
590C22—561no—
591C22—561no—
592C22—561no—
593C22C22×#114111yescharacteristic
594C22C2×#649511yescharacteristic
595C22#9051511yescharacteristic
596C22#9052011yescharacteristic
597C22#9052811yescharacteristic
598C22#9052911yescharacteristic
599C22C2×#651611yescharacteristic
600C4—22no—
601C4—42no—
602C4—44no—
603C4—42no—
604C4—562no—
605C4—561no—
606C4#8998914yes—
607C4#9051911yescharacteristic
608C4#9052211yescharacteristic
609C4#9052411yescharacteristic
610C4#9052511yescharacteristic
611C2—44no—
612C2—82no—
613C2—562no—
614C2#1174096111yescharacteristic
615C2#1174096611yescharacteristic
616C2#1174097011yescharacteristic
617C2#1174097211yescharacteristic
618C2C2×#8998911yescharacteristic
619C2#1174154211yescharacteristic
620C2#1174155911yescharacteristic
subgroupG/H
centerC23C22×C22⋊D7
commutator, cosocleC22×C4×C7C24
FrattiniC22×C4C23×D7
FittingC2×C7×#547C2
socleC23×C7C22×D4
hypercenterC2×#547D7
hypocenterC7#24116
LCSG ▷ C22×C4×C7 ▷ C2×C7 ▷ C7
UCSC1 ◁ C23 ◁ C2×C4×D4 ◁ C2×#547

Complements

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

NH ≅ G/Ntype
1. C2×C7×#547C2semidirect
2. C2×#89859C2semidirect
3. #11739862C2semidirect
4. C2×C4×#1141C2semidirect
5. #11729541C2semidirect
6. #11729438C2semidirect
7. #11729433C2semidirect
8. #11729368C2semidirect
9. #11729358C2semidirect
10. #11729314C2semidirect
11. #11729309C2semidirect
60. C7×C4⋊Q8D4semidirect
68. C4×C7×D4D4semidirect
109. C2×#547D7semidirect
137. C2×C7×D4D8semidirect
167. C2×D28#41semidirect
201. C2×C7⋊C8#41semidirect
326. C4⋊Q8C22⋊D7semidirect
339. C4×D4C22⋊D7semidirect
434. C2×D4#1141semidirect
571. C7#24116semidirect

Maximal subgroups

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

subgroupindex
C2×C7×#5472
C2×#898592
#117398622
C2×C4×#11412
#117295412
#117294382
#117294332
#117293682
#117293582
#117293142
#117293092
#241167