Finite Group Databasebeta

← #13385954

Subgroups — #13385954

Order 1792.

1494 conjugacy classes of subgroups.

The subgroup lattice has 636 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C7×#547C211yesmaximal, characteristic
2C2×#89812C211yesmaximal, characteristic, complemented
3#11739794C211yesmaximal, characteristic, complemented
4C22×#6384C211yesmaximal, characteristic, complemented
5#11729548C212yesmaximal, complemented
6#11729439C212yesmaximal, complemented
7#11729435C211yesmaximal, characteristic, complemented
8#11729366C212yesmaximal, complemented
9#11729364C211yesmaximal, characteristic, complemented
10#11729313C212yesmaximal, complemented
11#11729307C211yesmaximal, characteristic, complemented
12C22×C7×#41—21no—
13C23×Dic14C2211yescharacteristic
14C7×#547—24no—
15C7×#547—24no—
16C2×C7×C4⋊Q8C2211yescharacteristic
17C2×C7×#123—21no—
18C2×C7×#123—21no—
19C2×C7×C22⋊Q8—21no—
20C2×C7×#121C2211yescharacteristic
21C2×C7×#121C2211yescharacteristic
22C2×C4×C7×D4C2211yescharacteristic
23C2×C4×C7×D4C2211yescharacteristic
24C22×C7×C4⋊C4C2211yescharacteristic
25C22×C7×C4⋊C4C2211yescharacteristic
26C22×#1142C2212yes—
27C2×#6487C2212yes—
28C23×C7⋊C8C2211yescharacteristic
29#89992—21no—
30C2×#6406C2212yes—
31#89984C2211yescharacteristic
32C2×C22⋊(C7⋊C8)C2211yescharacteristic
33C2×C22⋊(C7⋊C8)C2212yes—
34#89812—24no—
35#89751—21no—
36C2×#6384—24no—
37C2×#6384C2212yes—
38C2×#6384C2212yes—
39C2×#6384C2212yes—
40#89719—21no—
41#89718—21no—
42#89701C2212yes—
43#89324C2212yes—
44#89324C2212yes—
45#89324C2212yes—
46#89319C2212yes—
47#23961—71nomaximal, Sylow
48C2×C7×#41—28no—
49C2×C7×#41—44no—
50C2×C7×#41—44no—
51C22×C7×Q8—21no—
52C22×C7×D4—21no—
53C22×C7×D4—21no—
54C22×C7×D4D411yescharacteristic
55C22×C7×D4C2311yescharacteristic
56C23×C4×C7—21no—
57C23×C4×C7—21no—
58C23×C4×C7—21no—
59C23×C4×C7C2311yescharacteristic
60C23×C4×C7C2311yescharacteristic
61C23×Dic7—21no—
62C22×Dic14—22no—
63C22×Dic14—24no—
64C22×Dic14—22no—
65C22×Dic14—21no—
66C22×Dic14—42no—
67C22×Dic14C2312yes—
68C7×C4⋊Q8—22no—
69C7×C4⋊Q8—22no—
70C7×#123—28no—
71C7×#123—28no—
72C7×C22⋊Q8—28no—
73C7×#121—22no—
74C7×#121—22no—
75C7×#121—22no—
76C7×#121D414yes—
77C4×C7×D4—22no—
78C4×C7×D4—22no—
79C4×C7×D4—22no—
80C4×C7×D4—22no—
81C2×C7×C4⋊C4—21no—
82C2×C7×C4⋊C4—21no—
83C2×C7×C4⋊C4—22no—
84C2×C7×C4⋊C4—21no—
85C2×C7×C4⋊C4—22no—
86C2×C7×C4⋊C4—22no—
87C2×C7×C4⋊C4D411yescharacteristic
88C2×C7×C4⋊C4D414yes—
89C2×C7×C4⋊C4C2311yescharacteristic
90C2×C7×C4⋊C4C2311yescharacteristic
91C2×C7×C4⋊C4C2311yescharacteristic
92C2×C7×C22⋊C4—21no—
93C2×C7×C22⋊C4—21no—
94C2×C7×C22⋊C4—21no—
95C2×C7×C22⋊C4D411yescharacteristic
96C2×C7×C22⋊C4D411yescharacteristic
97C2×C42×C7C2311yescharacteristic
98C2×C22⋊Dic7—22no—
99C2×C22⋊Dic7—21no—
100C2×#1142—24no—
101C2×#1142—24no—
102C2×#1142—42no—
103C2×C4⋊Dic7C2312yes—
104#6487—24no—
105#6487—42no—
106C2×Dic7⋊C4—22no—
107C22×C7⋊C8—22no—
108C22×C7⋊C8—42no—
109C22×C7⋊C8C2312yes—
110C22×C7⋊C8C2312yes—
111#6406—42no—
112C7⋊#95—22no—
113C7⋊#95—22no—
114C7⋊#95—21no—
115C22⋊(C7⋊C8)—22no—
116C22⋊(C7⋊C8)—42no—
117#6384—24no—
118#6384—24no—
119#6384—24no—
120C2×#547D711yescharacteristic
121C2×#448—71no—
122C22×#103—71no—
123#2409—71no—
124#2024—72no—
125#2000—72no—
126#1893—71no—
127#1877—72no—
128#1872—72no—
129#1869—71no—
130#1823—71no—
131C24×C7—21no—
132C24×C7C2×D411yescharacteristic
133C24×C7C2×D411yescharacteristic
134C7×#41—432no—
135C2×C7×Q8—24no—
136C2×C7×Q8—42no—
137C2×C7×Q8—42no—
138C2×C7×D4—22no—
139C2×C7×D4—22no—
140C2×C7×D4—24no—
141C2×C7×D4—24no—
142C2×C7×D4—21no—
143C2×C7×D4—22no—
144C2×C7×D4—22no—
145C2×C7×D4—42no—
146C2×C7×D4—42no—
147C2×C7×D4—42no—
148C2×C7×D4—42no—
149C2×C7×D4SD1614yescomplemented
150C2×C7×D4C2×D412yes—
151C22×C4×C7—22no—
152C22×C4×C7—22no—
153C22×C4×C7—24no—
154C22×C4×C7—24no—
155C22×C4×C7—24no—
156C22×C4×C7—21no—
157C22×C4×C7—21no—
158C22×C4×C7—21no—
159C22×C4×C7—21no—
160C22×C4×C7—21no—
161C22×C4×C7—22no—
162C22×C4×C7—22no—
163C22×C4×C7—42no—
164C22×C4×C7—42no—
165C22×C4×C7—42no—
166C22×C4×C7—42no—
167C22×C4×C7—42no—
168C22×C4×C7—42no—
169C22×C4×C7C2×D411yescharacteristic
170C22×C4×C7C2×D411yescharacteristic
171C22×C4×C7C2×D411yescharacteristic
172C22×C4×C7C2×D412yes—
173C22×C4×C7C2×D412yes—
174C22×C4×C7C2×D411yescharacteristic
175C22×C4×C7C2411yescharacteristic
176C22×Dic7—22no—
177C22×Dic7—22no—
178C22×Dic7—44no—
179C22×Dic7—42no—
180C2×Dic14—28no—
181C2×Dic14—22no—
182C2×Dic14—22no—
183C2×Dic14—22no—
184C2×Dic14—22no—
185C2×Dic14—22no—
186C2×Dic14—48no—
187C2×Dic14—44no—
188C2×Dic14—44no—
189C2×Dic14—42no—
190C2×Dic14#4114yescomplemented
191C7×C4⋊C4—24no—
192C7×C4⋊C4—24no—
193C7×C4⋊C4—24no—
194C7×C4⋊C4—22no—
195C7×C4⋊C4—21no—
196C7×C4⋊C4—21no—
197C7×C4⋊C4—21no—
198C7×C4⋊C4C2×D412yes—
199C7×C4⋊C4C2×D412yes—
200C7×C4⋊C4C2×D412yes—
201C7×C22⋊C4—24no—
202C7×C22⋊C4—24no—
203C7×C22⋊C4—22no—
204C7×C22⋊C4—24no—
205C7×C22⋊C4—22no—
206C42×C7—21no—
207C42×C7—21no—
208C22⋊Dic7—44no—
209C22⋊Dic7—42no—
210#1142—48no—
211C4⋊Dic7—22no—
212C4⋊Dic7—22no—
213Dic7⋊C4—44no—
214C2×C7⋊C8—22no—
215C2×C7⋊C8—22no—
216C2×C7⋊C8—22no—
217C2×C7⋊C8—22no—
218C2×C7⋊C8—22no—
219C2×C7⋊C8—22no—
220C2×C7⋊C8—44no—
221C22×#41—21no—
222C23×Q8—71no—
223C22×SD16—72no—
224C23×C8—71no—
225#547—24no—
226#547—24no—
227C2×C4⋊Q8C2×D711yescharacteristic
228C2×#123—21no—
229C2×#123—21no—
230C2×C22⋊Q8—21no—
231C2×C22⋊Q8—72no—
232C2×#121C2×D711yescharacteristic
233C2×#121C2×D711yescharacteristic
234C2×C4×D4C2×D711yescharacteristic
235C2×C4×D4C2×D711yescharacteristic
236C22×C4⋊C4C2×D711yescharacteristic
237C22×C4⋊C4C2×D711yescharacteristic
238#448—144no—
239C2×#103—72no—
240C2×#103—72no—
241C2×#103—72no—
242C2×#103—144no—
243C2×#102—72no—
244C2×C22⋊C8—71no—
245C2×C22⋊C8—72no—
246#395—141no—
247#393—141no—
248#391—72no—
249#386—141no—
250#385—141no—
251#380—71no—
252#340—72no—
253#340—72no—
254#340—72no—
255#336—72no—
256C23×C7—22no—
257C23×C7—22no—
258C23×C7—21no—
259C23×C7—22no—
260C23×C7—21no—
261C23×C7—22no—
262C23×C7—22no—
263C23×C7—42no—
264C23×C7—41no—
265C23×C7—41no—
266C23×C7—42no—
267C23×C7#12012yes—
268C23×C7C2×SD1612yes—
269C23×C7C2×SD1612yes—
270C23×C7AGL(1,ℤ/8)12yes—
271C23×C7C22×D411yescharacteristic
272C7×Q8—48no—
273C7×D4—28no—
274C7×D4—24no—
275C7×D4—48no—
276C7×D4—48no—
277C7×D4—41no—
278C7×D4—41no—
279C2×C4×C7—21no—
280C2×C4×C7—22no—
281C2×C4×C7—21no—
282C2×C4×C7—22no—
283C2×C4×C7—22no—
284C2×C4×C7—24no—
285C2×C4×C7—21no—
286C2×C4×C7—21no—
287C2×C4×C7—22no—
288C2×C4×C7—22no—
289C2×C4×C7—22no—
290C2×C4×C7—22no—
291C2×C4×C7—22no—
292C2×C4×C7—48no—
293C2×C4×C7—48no—
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—48no—
301C2×C4×C7—41no—
302C2×C4×C7—41no—
303C2×C4×C7—42no—
304C2×C4×C7#12012yes—
305C2×C4×C7C2×SD1612yes—
306C2×C4×C7C22×D411yescharacteristic
307C2×C4×C7C22×D411yescharacteristic
308C2×C4×C7C2×#4112yes—
309C2×C4×C7H(5,𝔽2)12yes—
310C2×Dic7—24no—
311C2×Dic7—48no—
312C2×Dic7—42no—
313C2×Dic7—42no—
314C2×Dic7—42no—
315C2×Dic7—42no—
316C2×Dic7—42no—
317Dic14—24no—
318Dic14—24no—
319Dic14—48no—
320Dic14—42no—
321Dic14—42no—
322C7⋊C8—42no—
323C7⋊C8—42no—
324C2×#41—28no—
325C2×#41—44no—
326C2×#41—44no—
327C22×Q8—21no—
328C22×Q8—72no—
329C22×Q8—144no—
330C22×Q8—141no—
331C22×Q8—142no—
332C22×Q8—142no—
333C22×Q8—282no—
334C22×D4—21no—
335C22×D4—21no—
336C22×D4C22⋊D711yescharacteristic
337C22×D4C22×D711yescharacteristic
338C23×C4—21no—
339C23×C4—21no—
340C23×C4—21no—
341C23×C4—141no—
342C23×C4C22×D711yescharacteristic
343C23×C4C22×D711yescharacteristic
344C2×SD16—144no—
345C2×SD16—144no—
346C2×SD16—282no—
347C22×C8—72no—
348C22×C8—72no—
349C22×C8—142no—
350C22×C8—282no—
351C4⋊Q8—22no—
352C4⋊Q8—22no—
353#123—28no—
354#123—28no—
355C22⋊Q8—28no—
356C22⋊Q8—144no—
357C22⋊Q8—282no—
358#121—22no—
359#121—22no—
360#121—22no—
361#121C22⋊D714yes—
362C4×D4—22no—
363C4×D4—22no—
364C4×D4—22no—
365C4×D4—22no—
366C2×C4⋊C4—21no—
367C2×C4⋊C4—21no—
368C2×C4⋊C4—22no—
369C2×C4⋊C4—21no—
370C2×C4⋊C4—22no—
371C2×C4⋊C4—22no—
372C2×C4⋊C4—72no—
373C2×C4⋊C4—142no—
374C2×C4⋊C4C22⋊D711yescharacteristic
375C2×C4⋊C4C22⋊D714yes—
376C2×C4⋊C4C22×D711yescharacteristic
377C2×C4⋊C4C22×D711yescharacteristic
378C2×C4⋊C4C22×D711yescharacteristic
379C2×C22⋊C4—21no—
380C2×C22⋊C4—21no—
381C2×C22⋊C4—21no—
382C2×C22⋊C4—142no—
383C2×C22⋊C4—141no—
384C2×C22⋊C4C22⋊D711yescharacteristic
385C2×C22⋊C4C22⋊D711yescharacteristic
386C2×C42C22×D711yescharacteristic
387#103—144no—
388#103—144no—
389#103—144no—
390#102—282no—
391C22⋊C8—142no—
392C22⋊C8—282no—
393#95—141no—
394#95—142no—
395#95—142no—
396C22×C7—22no—
397C22×C7—22no—
398C22×C7—24no—
399C22×C7—24no—
400C22×C7—22no—
401C22×C7—24no—
402C22×C7—41no—
403C22×C7—41no—
404C22×C7—42no—
405C22×C7—42no—
406C22×C7—42no—
407C22×C7—42no—
408C22×C7—82no—
409C22×C7—82no—
410C22×C7#45014yes—
411C22×C7C2×#12011yescharacteristic
412C22×C7#54612yes—
413C22×C7C22×SD1611yescharacteristic
414C22×C7C2×AGL(1,ℤ/8)11yescharacteristic
415C22×C7#57812yes—
416C4×C7—22no—
417C4×C7—22no—
418C4×C7—41no—
419C4×C7—42no—
420C4×C7—42no—
421C4×C7—42no—
422C4×C7—41no—
423C4×C7#52511yescharacteristic
424C4×C7#53511yescharacteristic
425C4×C7#54612yes—
426Dic7—44no—
427Dic7—82no—
428C24—21no—
429C24C2×C22⋊D711yescharacteristic
430C24C2×C22⋊D711yescharacteristic
431#41—432no—
432C2×Q8—24no—
433C2×Q8—42no—
434C2×Q8—42no—
435C2×Q8—74no—
436C2×Q8—148no—
437C2×Q8—142no—
438C2×Q8—142no—
439C2×Q8—142no—
440C2×Q8—142no—
441C2×Q8—142no—
442C2×Q8—284no—
443C2×Q8—288no—
444C2×Q8—284no—
445C2×Q8—282no—
446C2×D4—22no—
447C2×D4—22no—
448C2×D4—24no—
449C2×D4—24no—
450C2×D4—22no—
451C2×D4—22no—
452C2×D4—21no—
453C2×D4—42no—
454C2×D4—42no—
455C2×D4—42no—
456C2×D4—42no—
457C2×D4#114214yescomplemented
458C2×D4C2×C22⋊D712yes—
459C22×C4—22no—
460C22×C4—22no—
461C22×C4—24no—
462C22×C4—24no—
463C22×C4—24no—
464C22×C4—21no—
465C22×C4—21no—
466C22×C4—21no—
467C22×C4—22no—
468C22×C4—22no—
469C22×C4—21no—
470C22×C4—21no—
471C22×C4—42no—
472C22×C4—42no—
473C22×C4—42no—
474C22×C4—42no—
475C22×C4—42no—
476C22×C4—42no—
477C22×C4—142no—
478C22×C4—142no—
479C22×C4—284no—
480C22×C4—282no—
481C22×C4C2×C22⋊D711yescharacteristic
482C22×C4C2×C22⋊D711yescharacteristic
483C22×C4C2×C22⋊D711yescharacteristic
484C22×C4C2×C22⋊D711yescharacteristic
485C22×C4C2×C22⋊D712yes—
486C22×C4C2×C22⋊D712yes—
487C22×C4C23×D711yescharacteristic
488SD16—288no—
489C2×C8—142no—
490C2×C8—142no—
491C2×C8—142no—
492C2×C8—142no—
493C2×C8—142no—
494C2×C8—142no—
495C2×C8—284no—
496C4⋊C4—24no—
497C4⋊C4—24no—
498C4⋊C4—24no—
499C4⋊C4—22no—
500C4⋊C4—21no—
501C4⋊C4—21no—
502C4⋊C4—21no—
503C4⋊C4—142no—
504C4⋊C4—142no—
505C4⋊C4—284no—
506C4⋊C4C2×C22⋊D712yes—
507C4⋊C4C2×C22⋊D712yes—
508C4⋊C4C2×C22⋊D712yes—
509C22⋊C4—24no—
510C22⋊C4—24no—
511C22⋊C4—22no—
512C22⋊C4—24no—
513C22⋊C4—22no—
514C22⋊C4—284no—
515C22⋊C4—282no—
516C42—21no—
517C42—21no—
518C2×C7—24no—
519C2×C7—42no—
520C2×C7—82no—
521C2×C7#240411yescharacteristic
522C2×C7C2×#45011yescharacteristic
523C2×C7#301111yescharacteristic
524C2×C7#329812yes—
525C2×C7#330812yes—
526C23—22no—
527C23—22no—
528C23—21no—
529C23—22no—
530C23—22no—
531C23—21no—
532C23—22no—
533C23—41no—
534C23—41no—
535C23—42no—
536C23—42no—
537C23#649512yes—
538C23C2×#114212yes—
539C23C2×#114212yes—
540C23#651612yes—
541C23C22×C22⋊D711yescharacteristic
542Q8—48no—
543Q8—144no—
544Q8—144no—
545Q8—288no—
546Q8—282no—
547Q8—282no—
548D4—28no—
549D4—24no—
550D4—48no—
551D4—48no—
552D4—41no—
553D4—41no—
554C2×C4—21no—
555C2×C4—22no—
556C2×C4—21no—
557C2×C4—22no—
558C2×C4—24no—
559C2×C4—22no—
560C2×C4—22no—
561C2×C4—22no—
562C2×C4—21no—
563C2×C4—21no—
564C2×C4—22no—
565C2×C4—22no—
566C2×C4—22no—
567C2×C4—48no—
568C2×C4—48no—
569C2×C4—41no—
570C2×C4—41no—
571C2×C4—41no—
572C2×C4—41no—
573C2×C4—41no—
574C2×C4—41no—
575C2×C4—48no—
576C2×C4—41no—
577C2×C4—42no—
578C2×C4—41no—
579C2×C4—144no—
580C2×C4—288no—
581C2×C4—282no—
582C2×C4—282no—
583C2×C4—282no—
584C2×C4—282no—
585C2×C4—282no—
586C2×C4C2×#114212yes—
587C2×C4#651612yes—
588C2×C4D7×#4112yes—
589C2×C4#655312yes—
590C2×C4C22×C22⋊D711yescharacteristic
591C2×C4C22×C22⋊D711yescharacteristic
592C8—282no—
593C8—282no—
594C7#2396111yescharacteristic, complemented, Sylow
595C22—24no—
596C22—24no—
597C22—22no—
598C22—22no—
599C22—22no—
600C22—24no—
601C22—42no—
602C22—41no—
603C22—41no—
604C22—42no—
605C22—42no—
606C22—42no—
607C22—82no—
608C22—82no—
609C22#8999014yes—
610C22C2×#649511yescharacteristic
611C22C22×#114211yescharacteristic
612C22#9052012yes—
613C22#9052912yes—
614C22C2×#651611yescharacteristic
615C4—22no—
616C4—22no—
617C4—42no—
618C4—42no—
619C4—42no—
620C4—41no—
621C4—41no—
622C4—284no—
623C4—562no—
624C4#9051911yescharacteristic
625C4#9052012yes—
626C4#9052111yescharacteristic
627C2—24no—
628C2—42no—
629C2—82no—
630C2#1174097612yes—
631C2#1174097712yes—
632C2C2×#8999011yescharacteristic
633C2#1174154111yescharacteristic
634C2#1174156211yescharacteristic
subgroupG/H
centerC23C22×C22⋊D7
commutator, cosocleC22×C4×C7C24
FrattiniC22×C4C23×D7
Fitting, prime radicalC2×C7×#547C2
socleC23×C7C22×D4
hypercenterC2×#547D7
hypocenterC7#23961
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
2. C2×#89812C2semidirect
3. #11739794C2semidirect
4. C22×#6384C2semidirect
5. #11729548C2semidirect
6. #11729439C2semidirect
7. #11729435C2semidirect
8. #11729366C2semidirect
9. #11729364C2semidirect
10. #11729313C2semidirect
11. #11729307C2semidirect
149. C2×C7×D4SD16semidirect
190. C2×Dic14#41semidirect
457. C2×D4#1142semidirect
594. C7#23961semidirect

Maximal subgroups

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

subgroupindex
C2×C7×#5472
C2×#898122
#117397942
C22×#63842
#117295482
#117294392
#117294352
#117293662
#117293642
#117293132
#117293072
#239617