Finite Group Databasebeta

← #13275550

Subgroups — #13275550

Order 1792.

1790 conjugacy classes of subgroups.

The subgroup lattice has 612 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C4×Dic14C211yesmaximal, characteristic
2C2×C4×Dic7⋊C4C211yesmaximal, characteristic
3C2×#89704C211yesmaximal, characteristic
4C4×C7×#95C211yesmaximal, characteristic
5C4×C7⋊#95C211yesmaximal, characteristic
6C4×C7⋊#95C211yesmaximal, characteristic
7C4×C7⋊#95C211yesmaximal, characteristic
8#11727178C212yesmaximal
9#11727175C212yesmaximal
10#11727165C212yesmaximal
11#11727163C212yesmaximal
12C23×Dic14C2211yescharacteristic
13C22×C42×C7C2211yescharacteristic
14C22×C42×C7C2211yescharacteristic
15C22×C42×C7C2211yescharacteristic
16C22×C4⋊Dic7C2211yescharacteristic
17C22×Dic7⋊C4C2212yes—
18C22×Dic7⋊C4C2211yescharacteristic
19C22×Dic7⋊C4C2211yescharacteristic
20C22×C4×Dic7C2211yescharacteristic
21C22×C4×Dic7C2211yescharacteristic
22C22×C4×Dic7C2211yescharacteristic
23C22×C4×Dic7C2211yescharacteristic
24C2×C4×Dic14—24no—
25C2×C4×Dic14—24no—
26C2×C4×Dic14C418yescomplemented
27C2×C7×#95C2212yes—
28C2×C7×#95C2212yes—
29C2×C7⋊#95C2212yes—
30C2×C7⋊#95C2212yes—
31C2×C7⋊#95C2212yes—
32C2×C7⋊#95C2212yes—
33C2×C7⋊#95C2212yes—
34C2×C7⋊#95C2212yes—
35C2×C7⋊#95C2212yes—
36C2×C7⋊#95C2212yes—
37C2×C7⋊#95C2212yes—
38#89704—24no—
39C4×Dic7⋊C4—24no—
40#13850—71nomaximal, Sylow
41C23×C4×C7C2311yescharacteristic
42C23×C4×C7C2312yes—
43C23×C4×C7C2312yes—
44C23×C4×C7C2311yescharacteristic
45C23×C4×C7C2311yescharacteristic
46C23×Dic7C2311yescharacteristic
47C23×Dic7C2312yes—
48C23×Dic7C2312yes—
49C23×Dic7C2311yescharacteristic
50C23×Dic7C2311yescharacteristic
51C23×Dic7C2311yescharacteristic
52C22×Dic14—24no—
53C22×Dic14—22no—
54C22×Dic14—22no—
55C22×Dic14—24no—
56C22×Dic14C2×C414yes—
57C2×C42×C7—22no—
58C2×C42×C7—22no—
59C2×C42×C7—22no—
60C2×C42×C7—22no—
61C2×C42×C7—22no—
62C2×C42×C7—22no—
63C2×C42×C7—22no—
64C2×C42×C7C2×C414yes—
65C2×C42×C7Q814yescomplemented
66C2×C4⋊Dic7—22no—
67C2×C4⋊Dic7—22no—
68C2×C4⋊Dic7C2×C414yes—
69C2×Dic7⋊C4—24no—
70C2×Dic7⋊C4—22no—
71C2×Dic7⋊C4—22no—
72C2×Dic7⋊C4—22no—
73C2×Dic7⋊C4—22no—
74C2×Dic7⋊C4—24no—
75C2×Dic7⋊C4—24no—
76C2×Dic7⋊C4C2×C414yes—
77C2×Dic7⋊C4C2×C414yes—
78C2×C4×Dic7—22no—
79C2×C4×Dic7—22no—
80C2×C4×Dic7—22no—
81C2×C4×Dic7—22no—
82C2×C4×Dic7—22no—
83C2×C4×Dic7—22no—
84C2×C4×Dic7—22no—
85C2×C4×Dic7C2×C414yes—
86C2×C4×Dic7C2×C414yes—
87C2×C4×Dic7D414yes—
88C2×C4×Dic7D414yes—
89C2×C4×Dic7Q814yescomplemented
90C4×Dic14—232no—
91C7×#95—24no—
92C7×#95—24no—
93C7⋊#95—24no—
94C7⋊#95—24no—
95C7⋊#95—24no—
96C7⋊#95—24no—
97C7⋊#95—24no—
98C7⋊#95—24no—
99C7⋊#95—24no—
100C7⋊#95—24no—
101C7⋊#95—24no—
102C22×C4×Q8—71no—
103C2×C4×C4⋊C4—71no—
104C2×#376—71no—
105#1446—72no—
106#1445—72no—
107#1441—72no—
108#1441—72no—
109C4×#95—71no—
110C4×#95—71no—
111C4×#95—71no—
112C4×#95D711yescharacteristic
113C24×C7C2411yescharacteristic
114C22×C4×C7—21no—
115C22×C4×C7—21no—
116C22×C4×C7—22no—
117C22×C4×C7—22no—
118C22×C4×C7—22no—
119C22×C4×C7—21no—
120C22×C4×C7—21no—
121C22×C4×C7—22no—
122C22×C4×C7—22no—
123C22×C4×C7—22no—
124C22×C4×C7—22no—
125C22×C4×C7—22no—
126C22×C4×C7—22no—
127C22×C4×C7—22no—
128C22×C4×C7—22no—
129C22×C4×C7—22no—
130C22×C4×C7—22no—
131C22×C4×C7—22no—
132C22×C4×C7—22no—
133C22×C4×C7C22×C412yes—
134C22×C4×C7C22×C412yes—
135C22×C4×C7C22×C412yes—
136C22×C4×C7C2×D412yes—
137C22×C4×C7C2×D412yes—
138C22×C4×C7C2×Q814yes—
139C22×C4×C7C2×Q812yes—
140C22×C4×C7C2×Q812yes—
141C22×C4×C7#4114yes—
142C22×C4×C7#4114yes—
143C22×C4×C7#4112yes—
144C22×C4×C7#4112yes—
145C22×Dic7—21no—
146C22×Dic7—21no—
147C22×Dic7—22no—
148C22×Dic7—22no—
149C22×Dic7—22no—
150C22×Dic7—22no—
151C22×Dic7—22no—
152C22×Dic7—22no—
153C22×Dic7—22no—
154C22×Dic7—21no—
155C22×Dic7—21no—
156C22×Dic7—22no—
157C22×Dic7—22no—
158C22×Dic7—22no—
159C22×Dic7—22no—
160C22×Dic7—22no—
161C22×Dic7—22no—
162C22×Dic7—22no—
163C22×Dic7—22no—
164C22×Dic7—22no—
165C22×Dic7—22no—
166C22×Dic7—22no—
167C22×Dic7—22no—
168C22×Dic7C22×C412yes—
169C22×Dic7C22×C412yes—
170C22×Dic7C22×C412yes—
171C22×Dic7C22×C412yes—
172C22×Dic7C2×D412yes—
173C22×Dic7C2×D412yes—
174C22×Dic7C2×D412yes—
175C22×Dic7C2×D412yes—
176C22×Dic7C2×Q814yes—
177C22×Dic7#4114yes—
178C22×Dic7#4114yes—
179C2×Dic14—216no—
180C2×Dic14—216no—
181C2×Dic14—28no—
182C2×Dic14—28no—
183C2×Dic14—28no—
184C42×C7—28no—
185C42×C7—28no—
186C42×C7—44no—
187C4⋊Dic7—28no—
188Dic7⋊C4—216no—
189Dic7⋊C4—28no—
190Dic7⋊C4—28no—
191C4×Dic7—28no—
192C4×Dic7—28no—
193C4×Dic7—44no—
194C4×Dic7C22⋊C4116yes—
195C23×Q8—71no—
196C2×C4×Q8—78no—
197C2×C4×Q8—144no—
198C2×C4×Q8—144no—
199C22×C4⋊C4—71no—
200C22×C4⋊C4—71no—
201C22×C4⋊C4—71no—
202C22×C4⋊C4—72no—
203C22×C42—71no—
204C22×C42—71no—
205C22×C42—71no—
206C22×C42—71no—
207C22×C42C2×D711yescharacteristic
208C22×C42C2×D711yescharacteristic
209C22×C42C2×D711yescharacteristic
210C4×C4⋊C4—144no—
211#376—144no—
212C2×#95—72no—
213C2×#95—72no—
214C2×#95—72no—
215C2×#95—72no—
216C2×#95—72no—
217C2×#95—72no—
218C2×#95—72no—
219C2×#95—72no—
220C2×#95—72no—
221C2×#95C2×D712yes—
222C2×#95C2×D712yes—
223C23×C7C23×C411yescharacteristic
224C23×C7C22×D411yescharacteristic
225C23×C7C22×D411yescharacteristic
226C23×C7C22×Q811yescharacteristic
227C23×C7C22×Q811yescharacteristic
228C23×C7C2×#4112yes—
229C23×C7C2×#4111yescharacteristic
230C23×C7C2×#4112yes—
231C23×C7C2×#4111yescharacteristic
232C23×C7C2×#4112yes—
233C23×C7C2×#4112yes—
234C2×C4×C7—22no—
235C2×C4×C7—22no—
236C2×C4×C7—24no—
237C2×C4×C7—24no—
238C2×C4×C7—22no—
239C2×C4×C7—22no—
240C2×C4×C7—22no—
241C2×C4×C7—24no—
242C2×C4×C7—24no—
243C2×C4×C7—24no—
244C2×C4×C7—24no—
245C2×C4×C7—24no—
246C2×C4×C7—24no—
247C2×C4×C7—42no—
248C2×C4×C7—42no—
249C2×C4×C7—42no—
250C2×C4×C7—42no—
251C2×C4×C7—42no—
252C2×C4×C7—42no—
253C2×C4×C7—42no—
254C2×C4×C7—42no—
255C2×C4×C7—42no—
256C2×C4×C7—42no—
257C2×C4×C7C2×C22⋊C414yes—
258C2×C4×C7#11714yes—
259C2×C4×C7C4×Q814yes—
260C2×C4×C7C4×Q814yes—
261C2×C4×C7C22⋊Q814yes—
262C2×C4×C7C22⋊Q814yes—
263C2×C4×C7#12414yes—
264C2×C4×C7C4⋊Q814yes—
265C2×Dic7—22no—
266C2×Dic7—22no—
267C2×Dic7—22no—
268C2×Dic7—22no—
269C2×Dic7—22no—
270C2×Dic7—22no—
271C2×Dic7—24no—
272C2×Dic7—24no—
273C2×Dic7—24no—
274C2×Dic7—24no—
275C2×Dic7—24no—
276C2×Dic7—24no—
277C2×Dic7—22no—
278C2×Dic7—22no—
279C2×Dic7—22no—
280C2×Dic7—24no—
281C2×Dic7—24no—
282C2×Dic7—24no—
283C2×Dic7—24no—
284C2×Dic7—24no—
285C2×Dic7—24no—
286C2×Dic7—42no—
287C2×Dic7—42no—
288C2×Dic7—42no—
289C2×Dic7—42no—
290C2×Dic7—42no—
291C2×Dic7—42no—
292C2×Dic7—42no—
293C2×Dic7—42no—
294C2×Dic7—42no—
295C2×Dic7—42no—
296C2×Dic7C2×C22⋊C414yes—
297C2×Dic7C2×C22⋊C414yes—
298C2×Dic7#11714yes—
299Dic14—232no—
300C22×Q8—74no—
301C22×Q8—142no—
302C22×Q8—142no—
303C22×Q8—144no—
304C22×Q8—144no—
305C23×C4—71no—
306C23×C4—71no—
307C23×C4—71no—
308C23×C4—71no—
309C23×C4—72no—
310C23×C4—72no—
311C23×C4C22×D712yes—
312C23×C4C22×D711yescharacteristic
313C23×C4C22×D712yes—
314C23×C4C22×D711yescharacteristic
315C23×C4C22×D711yescharacteristic
316C4×Q8—1432no—
317C2×C4⋊C4—74no—
318C2×C4⋊C4—74no—
319C2×C4⋊C4—74no—
320C2×C4⋊C4—142no—
321C2×C4⋊C4—142no—
322C2×C4⋊C4—142no—
323C2×C4⋊C4—142no—
324C2×C4⋊C4—142no—
325C2×C4⋊C4—142no—
326C2×C4⋊C4—144no—
327C2×C4⋊C4—144no—
328C2×C4⋊C4—144no—
329C2×C42—22no—
330C2×C42—22no—
331C2×C42—22no—
332C2×C42—22no—
333C2×C42—22no—
334C2×C42—22no—
335C2×C42—22no—
336C2×C42—74no—
337C2×C42—74no—
338C2×C42—74no—
339C2×C42—74no—
340C2×C42—74no—
341C2×C42—142no—
342C2×C42—142no—
343C2×C42—142no—
344C2×C42—142no—
345C2×C42—142no—
346C2×C42—142no—
347C2×C42—142no—
348C2×C42Dic1414yescomplemented
349C2×C42C4×D714yes—
350#95—24no—
351#95—24no—
352#95—144no—
353#95—144no—
354#95—144no—
355#95—144no—
356#95—144no—
357#95—144no—
358#95—144no—
359#95—144no—
360#95—144no—
361C22×C7C22×C22⋊C411yescharacteristic
362C22×C7C2×#11711yescharacteristic
363C22×C7C2×#11711yescharacteristic
364C22×C7C2×C4×Q811yescharacteristic
365C22×C7C2×C4×Q811yescharacteristic
366C22×C7C4×#4111yescharacteristic
367C22×C7C4×#4111yescharacteristic
368C22×C7C2×C22⋊Q811yescharacteristic
369C22×C7C2×C22⋊Q811yescharacteristic
370C22×C7#52512yes—
371C22×C7#52512yes—
372C22×C7#52512yes—
373C22×C7C2×#12411yescharacteristic
374C22×C7#52912yes—
375C22×C7#52912yes—
376C22×C7#52912yes—
377C22×C7#52912yes—
378C22×C7C2×C4⋊Q811yescharacteristic
379C22×C7#53212yes—
380C22×C7#53312yes—
381C22×C7#53312yes—
382C22×C7#53312yes—
383C22×C7#53312yes—
384C4×C7—24no—
385C4×C7—44no—
386C4×C7—44no—
387C4×C7—42no—
388C4×C7#39118yes—
389Dic7—24no—
390Dic7—24no—
391Dic7—24no—
392Dic7—44no—
393Dic7—44no—
394Dic7—42no—
395C24C23×D711yescharacteristic
396C2×Q8—148no—
397C2×Q8—148no—
398C2×Q8—1416no—
399C2×Q8—1416no—
400C2×Q8—148no—
401C22×C4—21no—
402C22×C4—21no—
403C22×C4—22no—
404C22×C4—22no—
405C22×C4—22no—
406C22×C4—22no—
407C22×C4—22no—
408C22×C4—22no—
409C22×C4—22no—
410C22×C4—22no—
411C22×C4—21no—
412C22×C4—21no—
413C22×C4—22no—
414C22×C4—22no—
415C22×C4—22no—
416C22×C4—22no—
417C22×C4—22no—
418C22×C4—22no—
419C22×C4—22no—
420C22×C4—72no—
421C22×C4—72no—
422C22×C4—72no—
423C22×C4—72no—
424C22×C4—72no—
425C22×C4—72no—
426C22×C4—72no—
427C22×C4—74no—
428C22×C4—72no—
429C22×C4—74no—
430C22×C4—74no—
431C22×C4—142no—
432C22×C4—142no—
433C22×C4—142no—
434C22×C4—141no—
435C22×C4—141no—
436C22×C4—142no—
437C22×C4—142no—
438C22×C4—142no—
439C22×C4—142no—
440C22×C4—142no—
441C22×C4—142no—
442C22×C4—142no—
443C22×C4—142no—
444C22×C4—142no—
445C22×C4—142no—
446C22×C4—142no—
447C22×C4—141no—
448C22×C4—141no—
449C22×C4—142no—
450C22×C4—142no—
451C22×C4—142no—
452C22×C4—142no—
453C22×C4—142no—
454C22×C4C2×Dic1414yes—
455C22×C4C2×Dic1412yes—
456C22×C4C2×C4×D712yes—
457C22×C4C2×C4×D712yes—
458C22×C4C2×C4×D712yes—
459C22×C4#115714yes—
460C22×C4#115714yes—
461C22×C4#115712yes—
462C22×C4D4×D712yes—
463C22×C4D4×D712yes—
464C22×C4#115912yes—
465C22×C4Q8×D712yes—
466C4⋊C4—148no—
467C4⋊C4—148no—
468C4⋊C4—148no—
469C4⋊C4—1416no—
470C42—28no—
471C42—28no—
472C42—44no—
473C42—716no—
474C42—148no—
475C42—148no—
476C42—284no—
477C2×C7#228011yescharacteristic
478C2×C7C2×#39111yescharacteristic
479C2×C7#229511yescharacteristic
480C2×C7#229511yescharacteristic
481C2×C7#229511yescharacteristic
482C2×C7#229511yescharacteristic
483C2×C7#229711yescharacteristic
484C2×C7#239612yes—
485C2×C7#239612yes—
486C2×C7#239812yes—
487C2×C7#239912yes—
488C23C22×Dic1411yescharacteristic
489C23C22×C4×D711yescharacteristic
490C23C2×#115711yescharacteristic
491C23C2×#115712yes—
492C23C2×#115712yes—
493C23C2×D4×D711yescharacteristic
494C23C2×D4×D711yescharacteristic
495C23C2×#115911yescharacteristic
496C23C2×Q8×D711yescharacteristic
497C23D7×#4112yes—
498C23D7×#4112yes—
499Q8—1432no—
500C2×C4—22no—
501C2×C4—22no—
502C2×C4—24no—
503C2×C4—24no—
504C2×C4—24no—
505C2×C4—22no—
506C2×C4—24no—
507C2×C4—24no—
508C2×C4—22no—
509C2×C4—24no—
510C2×C4—22no—
511C2×C4—24no—
512C2×C4—24no—
513C2×C4—42no—
514C2×C4—42no—
515C2×C4—42no—
516C2×C4—42no—
517C2×C4—42no—
518C2×C4—42no—
519C2×C4—42no—
520C2×C4—42no—
521C2×C4—42no—
522C2×C4—42no—
523C2×C4—74no—
524C2×C4—74no—
525C2×C4—74no—
526C2×C4—142no—
527C2×C4—142no—
528C2×C4—142no—
529C2×C4—142no—
530C2×C4—142no—
531C2×C4—142no—
532C2×C4—144no—
533C2×C4—144no—
534C2×C4—144no—
535C2×C4—144no—
536C2×C4—144no—
537C2×C4—144no—
538C2×C4—142no—
539C2×C4—142no—
540C2×C4—144no—
541C2×C4—142no—
542C2×C4—144no—
543C2×C4—144no—
544C2×C4—144no—
545C2×C4—144no—
546C2×C4—144no—
547C2×C4—282no—
548C2×C4—282no—
549C2×C4—282no—
550C2×C4—282no—
551C2×C4—282no—
552C2×C4—282no—
553C2×C4—282no—
554C2×C4—282no—
555C2×C4—282no—
556C2×C4—282no—
557C2×C4C4×Dic1414yes—
558C2×C4#643514yes—
559C2×C4#644114yes—
560C2×C4D7×C22⋊C414yes—
561C2×C4#644814yes—
562C2×C4#645014yes—
563C2×C4#645114yes—
564C2×C4#645914yes—
565C7#1385011yescharacteristic, complemented, Sylow
566C22C2×C4×Dic1411yescharacteristic
567C22#9016112yes—
568C22C2×#643511yescharacteristic
569C22C4×#115711yescharacteristic
570C22#9017012yes—
571C22C2×#644111yescharacteristic
572C22C2×D7×C22⋊C411yescharacteristic
573C22C2×#644811yescharacteristic
574C22C2×#645011yescharacteristic
575C22C2×#645111yescharacteristic
576C22C2×#645911yescharacteristic
577C22#9020812yes—
578C22D7×#11711yescharacteristic
579C22#9021311yescharacteristic
580C22#9021912yes—
581C22#9022912yes—
582C22#9023812yes—
583C22#9023812yes—
584C22#9023812yes—
585C22#9023912yes—
586C22#9024812yes—
587C22#9026912yes—
588C22#9026912yes—
589C4—24no—
590C4—42no—
591C4—44no—
592C4—44no—
593C4—144no—
594C4—144no—
595C4—144no—
596C4—284no—
597C4—282no—
598C4—284no—
599C4#8941818yes—
600C2#1173074511yescharacteristic
601C2C2×#8941811yescharacteristic
602C2#1173082911yescharacteristic
603C2#1173092512yes—
604C2#1173092612yes—
605C2#1173100611yescharacteristic
606C2#1173100811yescharacteristic
607C2#1173106311yescharacteristic
608C2#1173106411yescharacteristic
609C2#1173111412yes—
610C2#1173122312yes—
subgroupG/H
centerC23×C4C22×D7
commutatorC23×C7C23×C4
FrattiniC24C23×D7
FittingC4×C7×#95C2
socle, prime radical, cosocleC24×C7C24
hypercenterC4×#95D7
hypocenterC7#13850
LCSG ▷ C23×C7 ▷ C7
UCSC1 ◁ C23×C4 ◁ C4×#95

Complements

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

NH ≅ G/Ntype
26. C2×C4×Dic14C4semidirect
65. C2×C42×C7Q8semidirect
89. C2×C4×Dic7Q8semidirect
348. C2×C42Dic14semidirect
565. C7#13850semidirect

Maximal subgroups

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

subgroupindex
C22×C4×Dic142
C2×C4×Dic7⋊C42
C2×#897042
C4×C7×#952
C4×C7⋊#952
#117271782
#117271752
#117271652
#117271632
#138507