Finite Group Databasebeta

← #13276261

Subgroups — #13276261

Order 1792.

1650 conjugacy classes of subgroups.

The subgroup lattice has 690 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#6450C211yesmaximal, characteristic
2C2×#89746C211yesmaximal, characteristic
3C2×#89701C211yesmaximal, characteristic
4C7×C4⋊#95C211yesmaximal, characteristic
5#11729317C211yesmaximal, characteristic
6#11729317C211yesmaximal, characteristic
7C4×C7⋊#95C211yesmaximal, characteristic
8#11727175C212yesmaximal
9#11727175C212yesmaximal
10#11727157C212yesmaximal
11#11727155C212yesmaximal
12C23×Dic14C2211yescharacteristic
13C22×C7×C4⋊C4C2211yescharacteristic
14C22×C7×C4⋊C4C2211yescharacteristic
15C22×C42×C7C2211yescharacteristic
16C22×C4⋊Dic7C2211yescharacteristic
17C22×Dic7⋊C4C2212yes—
18C22×C4×Dic7C2211yescharacteristic
19C22×C4×Dic7C2212yes—
20C22×C4×Dic7C2211yescharacteristic
21C2×#6450—24no—
22C2×#6450—24no—
23C2×#6450C418yescomplemented
24C2×C7×#95C2212yes—
25C2×C7×#95C2212yes—
26C2×C7⋊#95C2211yescharacteristic
27C2×C7⋊#95C2212yes—
28C2×C7⋊#95C2212yes—
29C2×C7⋊#95C2212yes—
30C2×C7⋊#95C2212yes—
31C2×C7⋊#95C2212yes—
32C2×C7⋊#95C2212yes—
33C2×C7⋊#95C2211yescharacteristic
34C2×C7⋊#95C2211yescharacteristic
35C2×C7⋊#95C2212yes—
36C2×C7⋊#95C2212yes—
37C2×C7⋊#95C2211yescharacteristic
38#89746—24no—
39#89701—24no—
40#13931—71nomaximal, Sylow
41C23×C4×C7C2312yes—
42C23×C4×C7C2312yes—
43C23×C4×C7C2311yescharacteristic
44C23×C4×C7C2311yescharacteristic
45C23×C4×C7C2311yescharacteristic
46C23×Dic7C2312yes—
47C23×Dic7C2311yescharacteristic
48C23×Dic7C2311yescharacteristic
49C23×Dic7C2311yescharacteristic
50C23×Dic7C2312yes—
51C23×Dic7C2311yescharacteristic
52C22×Dic14—22no—
53C22×Dic14—22no—
54C22×Dic14—22no—
55C22×Dic14—22no—
56C22×Dic14C2×C414yes—
57C22×Dic14D414yes—
58C22×Dic14D414yes—
59C2×C7×C4⋊C4—22no—
60C2×C7×C4⋊C4—22no—
61C2×C7×C4⋊C4—22no—
62C2×C7×C4⋊C4—22no—
63C2×C7×C4⋊C4—22no—
64C2×C7×C4⋊C4C2×C414yes—
65C2×C42×C7—22no—
66C2×C42×C7—22no—
67C2×C42×C7—22no—
68C2×C4⋊Dic7—22no—
69C2×C4⋊Dic7—22no—
70C2×C4⋊Dic7—22no—
71C2×Dic7⋊C4—24no—
72C2×Dic7⋊C4—24no—
73C2×Dic7⋊C4C2×C418yes—
74C2×C4×Dic7—22no—
75C2×C4×Dic7—22no—
76C2×C4×Dic7—24no—
77C2×C4×Dic7—24no—
78C2×C4×Dic7—22no—
79C2×C4×Dic7—22no—
80C2×C4×Dic7—22no—
81C2×C4×Dic7C2×C414yes—
82C2×C4×Dic7C2×C418yes—
83#6450—232no—
84C7×#95—24no—
85C7×#95—42no—
86C7⋊#95—22no—
87C7⋊#95—24no—
88C7⋊#95—24no—
89C7⋊#95—24no—
90C7⋊#95—24no—
91C7⋊#95—22no—
92C7⋊#95—22no—
93C7⋊#95—24no—
94C7⋊#95—24no—
95C7⋊#95—42no—
96C7⋊#95—42no—
97C7⋊#95Q814yescomplemented
98C22×C4×Q8—71no—
99C2×#391—71no—
100C2×#391—71no—
101#1445—72no—
102#1445—72no—
103C4⋊#95—71no—
104C4⋊#95—71no—
105C4⋊#95D711yescharacteristic
106#1434—72no—
107#1434—72no—
108C4×#95—71no—
109C24×C7C2411yescharacteristic
110C22×C4×C7—21no—
111C22×C4×C7—21no—
112C22×C4×C7—22no—
113C22×C4×C7—22no—
114C22×C4×C7—22no—
115C22×C4×C7—21no—
116C22×C4×C7—21no—
117C22×C4×C7—22no—
118C22×C4×C7—21no—
119C22×C4×C7—21no—
120C22×C4×C7—21no—
121C22×C4×C7—21no—
122C22×C4×C7—22no—
123C22×C4×C7—21no—
124C22×C4×C7—22no—
125C22×C4×C7—21no—
126C22×C4×C7—21no—
127C22×C4×C7—21no—
128C22×C4×C7—22no—
129C22×C4×C7—22no—
130C22×C4×C7—22no—
131C22×C4×C7—22no—
132C22×C4×C7—22no—
133C22×C4×C7—22no—
134C22×C4×C7—22no—
135C22×C4×C7C22×C414yes—
136C22×C4×C7C22×C412yes—
137C22×C4×C7C2×D412yes—
138C22×C4×C7C2×D412yes—
139C22×C4×C7C2×Q812yes—
140C22×C4×C7#4112yes—
141C22×C4×C7#4112yes—
142C22×C4×C7#4112yes—
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—21no—
152C22×Dic7—21no—
153C22×Dic7—21no—
154C22×Dic7—21no—
155C22×Dic7—21no—
156C22×Dic7—21no—
157C22×Dic7—21no—
158C22×Dic7—21no—
159C22×Dic7—21no—
160C22×Dic7—21no—
161C22×Dic7—21no—
162C22×Dic7—21no—
163C22×Dic7—21no—
164C22×Dic7—21no—
165C22×Dic7—21no—
166C22×Dic7—21no—
167C22×Dic7—21no—
168C22×Dic7—21no—
169C22×Dic7—21no—
170C22×Dic7—21no—
171C22×Dic7—22no—
172C22×Dic7—22no—
173C22×Dic7—22no—
174C22×Dic7—22no—
175C22×Dic7—22no—
176C22×Dic7—22no—
177C22×Dic7—22no—
178C22×Dic7C22×C412yes—
179C22×Dic7C22×C414yes—
180C22×Dic7C22×C412yes—
181C22×Dic7C2×D414yes—
182C22×Dic7C2×D414yes—
183C22×Dic7C2×Q812yes—
184C22×Dic7C2×Q812yes—
185C22×Dic7#4112yes—
186C22×Dic7#4112yes—
187C2×Dic14—28no—
188C2×Dic14—28no—
189C2×Dic14—28no—
190C2×Dic14—28no—
191C2×Dic14—28no—
192C2×Dic14—28no—
193C2×Dic14C22⋊C4116yes—
194C7×C4⋊C4—28no—
195C7×C4⋊C4—44no—
196C42×C7—44no—
197C4⋊Dic7—44no—
198Dic7⋊C4—216no—
199C4×Dic7—28no—
200C4×Dic7—216no—
201C4×Dic7—44no—
202C23×Q8—71no—
203C2×C4×Q8—78no—
204C2×C4×Q8—144no—
205C2×C4×Q8—144no—
206C22×C4⋊C4—72no—
207C22×C4⋊C4—71no—
208C22×C4⋊C4C2×D711yescharacteristic
209C22×C4⋊C4C2×D711yescharacteristic
210C22×C42—71no—
211C22×C42—72no—
212C22×C42—71no—
213C22×C42C2×D711yescharacteristic
214#391—144no—
215#391—144no—
216C2×#95—71no—
217C2×#95—71no—
218C2×#95—71no—
219C2×#95—71no—
220C2×#95—72no—
221C2×#95—72no—
222C2×#95—72no—
223C2×#95—72no—
224C2×#95—72no—
225C2×#95—72no—
226C2×#95—72no—
227C2×#95—72no—
228C2×#95C2×D712yes—
229C2×#95C2×D712yes—
230C23×C7C23×C411yescharacteristic
231C23×C7C22×D411yescharacteristic
232C23×C7C22×D411yescharacteristic
233C23×C7C22×Q811yescharacteristic
234C23×C7C2×#4111yescharacteristic
235C23×C7C2×#4111yescharacteristic
236C23×C7C2×#4111yescharacteristic
237C23×C7C2×#4111yescharacteristic
238C23×C7C2×#4111yescharacteristic
239C23×C7C2×#4111yescharacteristic
240C23×C7C2×#4111yescharacteristic
241C23×C7H(5,𝔽2)11yescharacteristic
242C23×C72−1+411yescharacteristic
243C23×C72−1+411yescharacteristic
244C23×C72−1+411yescharacteristic
245C2×C4×C7—24no—
246C2×C4×C7—24no—
247C2×C4×C7—24no—
248C2×C4×C7—22no—
249C2×C4×C7—22no—
250C2×C4×C7—22no—
251C2×C4×C7—22no—
252C2×C4×C7—22no—
253C2×C4×C7—22no—
254C2×C4×C7—41no—
255C2×C4×C7—41no—
256C2×C4×C7—41no—
257C2×C4×C7—41no—
258C2×C4×C7—42no—
259C2×C4×C7—42no—
260C2×C4×C7—41no—
261C2×C4×C7—42no—
262C2×C4×C7—42no—
263C2×C4×C7—41no—
264C2×C4×C7—41no—
265C2×C4×C7—41no—
266C2×C4×C7—42no—
267C2×C4×C7—42no—
268C2×C4×C7—42no—
269C2×C4×C7—42no—
270C2×C4×C7—42no—
271C2×C4×C7—42no—
272C2×C4×C7—42no—
273C2×C4×C7C2×C22⋊C414yes—
274C2×C4×C7#11714yes—
275C2×C4×C7#11714yes—
276C2×C4×C7#12314yes—
277C2×C4×C7#12314yes—
278C2×C4×C7#12314yes—
279C2×C4×C7#12314yes—
280C2×Dic7—22no—
281C2×Dic7—24no—
282C2×Dic7—24no—
283C2×Dic7—22no—
284C2×Dic7—24no—
285C2×Dic7—24no—
286C2×Dic7—24no—
287C2×Dic7—24no—
288C2×Dic7—22no—
289C2×Dic7—22no—
290C2×Dic7—22no—
291C2×Dic7—22no—
292C2×Dic7—22no—
293C2×Dic7—22no—
294C2×Dic7—22no—
295C2×Dic7—22no—
296C2×Dic7—22no—
297C2×Dic7—22no—
298C2×Dic7—22no—
299C2×Dic7—22no—
300C2×Dic7—22no—
301C2×Dic7—41no—
302C2×Dic7—41no—
303C2×Dic7—41no—
304C2×Dic7—41no—
305C2×Dic7—41no—
306C2×Dic7—41no—
307C2×Dic7—41no—
308C2×Dic7—41no—
309C2×Dic7—41no—
310C2×Dic7—41no—
311C2×Dic7—41no—
312C2×Dic7—41no—
313C2×Dic7—42no—
314C2×Dic7—42no—
315C2×Dic7—42no—
316C2×Dic7—42no—
317C2×Dic7—42no—
318C2×Dic7—42no—
319C2×Dic7—42no—
320C2×Dic7C2×C22⋊C418yes—
321C2×Dic7C4×Q814yes—
322Dic14—232no—
323C22×Q8—74no—
324C22×Q8—74no—
325C22×Q8—74no—
326C22×Q8—142no—
327C22×Q8—142no—
328C22×Q8—142no—
329C22×Q8—142no—
330C23×C4—72no—
331C23×C4—71no—
332C23×C4—71no—
333C23×C4—71no—
334C23×C4—71no—
335C23×C4—72no—
336C23×C4C22×D712yes—
337C23×C4C22×D712yes—
338C23×C4C22×D711yescharacteristic
339C23×C4C22×D711yescharacteristic
340C23×C4C22×D711yescharacteristic
341C4×Q8—1432no—
342C2×C4⋊C4—22no—
343C2×C4⋊C4—22no—
344C2×C4⋊C4—22no—
345C2×C4⋊C4—22no—
346C2×C4⋊C4—22no—
347C2×C4⋊C4—78no—
348C2×C4⋊C4—144no—
349C2×C4⋊C4—144no—
350C2×C4⋊C4—142no—
351C2×C4⋊C4—142no—
352C2×C4⋊C4—142no—
353C2×C4⋊C4C4×D714yes—
354C2×C42—22no—
355C2×C42—22no—
356C2×C42—22no—
357C2×C42—78no—
358C2×C42—74no—
359C2×C42—144no—
360C2×C42—144no—
361C2×C42—142no—
362C2×C42—142no—
363C2×C42—142no—
364C2×C42—142no—
365C2×C42—142no—
366#95—24no—
367#95—42no—
368#95—74no—
369#95—142no—
370#95—142no—
371#95—144no—
372#95—144no—
373#95—144no—
374#95—144no—
375#95—144no—
376#95—144no—
377#95—142no—
378#95—282no—
379#95—282no—
380C22×C7C22×C22⋊C411yescharacteristic
381C22×C7C2×#11711yescharacteristic
382C22×C7C2×#11711yescharacteristic
383C22×C7C2×C4×Q811yescharacteristic
384C22×C7C4×#4111yescharacteristic
385C22×C7#51911yescharacteristic
386C22×C7#52011yescharacteristic
387C22×C7C2×#12311yescharacteristic
388C22×C7C2×#12311yescharacteristic
389C22×C7C2×#12311yescharacteristic
390C22×C7C2×#12311yescharacteristic
391C22×C7#52911yescharacteristic
392C22×C7#52911yescharacteristic
393C22×C7#53311yescharacteristic
394C22×C7#53311yescharacteristic
395C22×C7#54111yescharacteristic
396C22×C7#54111yescharacteristic
397C22×C7#54211yescharacteristic
398C22×C7#54211yescharacteristic
399C22×C7#54811yescharacteristic
400C22×C7#54811yescharacteristic
401C22×C7#54811yescharacteristic
402C22×C7#54811yescharacteristic
403C22×C7D4×Q811yescharacteristic
404C22×C7D4×Q811yescharacteristic
405C22×C7#55011yescharacteristic
406C22×C7#55011yescharacteristic
407C22×C7#55211yescharacteristic
408C22×C7#55211yescharacteristic
409C22×C7#55411yescharacteristic
410C22×C7#55611yescharacteristic
411C22×C7#55611yescharacteristic
412C22×C7#55611yescharacteristic
413C22×C7#55711yescharacteristic
414C22×C7#55911yescharacteristic
415C4×C7—44no—
416C4×C7—42no—
417C4×C7—42no—
418C4×C7—82no—
419C4×C7#38118yes—
420Dic7—24no—
421Dic7—28no—
422Dic7—42no—
423Dic7—42no—
424Dic7—42no—
425Dic7—82no—
426C24C23×D711yescharacteristic
427C2×Q8—716no—
428C2×Q8—148no—
429C2×Q8—148no—
430C2×Q8—148no—
431C2×Q8—148no—
432C2×Q8—148no—
433C2×Q8—148no—
434C22×C4—21no—
435C22×C4—21no—
436C22×C4—21no—
437C22×C4—21no—
438C22×C4—22no—
439C22×C4—22no—
440C22×C4—22no—
441C22×C4—21no—
442C22×C4—21no—
443C22×C4—21no—
444C22×C4—22no—
445C22×C4—21no—
446C22×C4—22no—
447C22×C4—21no—
448C22×C4—21no—
449C22×C4—22no—
450C22×C4—21no—
451C22×C4—21no—
452C22×C4—22no—
453C22×C4—22no—
454C22×C4—22no—
455C22×C4—22no—
456C22×C4—22no—
457C22×C4—22no—
458C22×C4—22no—
459C22×C4—72no—
460C22×C4—74no—
461C22×C4—74no—
462C22×C4—74no—
463C22×C4—72no—
464C22×C4—72no—
465C22×C4—72no—
466C22×C4—72no—
467C22×C4—72no—
468C22×C4—142no—
469C22×C4—142no—
470C22×C4—141no—
471C22×C4—141no—
472C22×C4—142no—
473C22×C4—142no—
474C22×C4—141no—
475C22×C4—141no—
476C22×C4—141no—
477C22×C4—141no—
478C22×C4—141no—
479C22×C4—141no—
480C22×C4—141no—
481C22×C4—141no—
482C22×C4—141no—
483C22×C4—141no—
484C22×C4—141no—
485C22×C4—141no—
486C22×C4—141no—
487C22×C4—141no—
488C22×C4—141no—
489C22×C4—141no—
490C22×C4—141no—
491C22×C4—141no—
492C22×C4—141no—
493C22×C4—141no—
494C22×C4—142no—
495C22×C4—142no—
496C22×C4—142no—
497C22×C4—142no—
498C22×C4—142no—
499C22×C4—142no—
500C22×C4—142no—
501C22×C4C2×C4×D714yes—
502C22×C4C2×C4×D712yes—
503C22×C4#115712yes—
504C22×C4#115712yes—
505C22×C4D4×D712yes—
506C22×C4D4×D712yes—
507C22×C4#115912yes—
508C22×C4#115912yes—
509C22×C4Q8×D712yes—
510C22×C4#116112yes—
511C4⋊C4—28no—
512C4⋊C4—44no—
513C4⋊C4—1416no—
514C4⋊C4—284no—
515C42—44no—
516C42—1416no—
517C42—148no—
518C42—284no—
519C2×C7C2×#38111yescharacteristic
520C2×C7#229511yescharacteristic
521C2×C7#232011yescharacteristic
522C2×C7Q8×C22⋊C411yescharacteristic
523C2×C7#234111yescharacteristic
524C2×C7#235511yescharacteristic
525C2×C7#235611yescharacteristic
526C2×C7#242111yescharacteristic
527C2×C7#242111yescharacteristic
528C2×C7#242311yescharacteristic
529C2×C7#242311yescharacteristic
530C2×C7#244611yescharacteristic
531C2×C7#244611yescharacteristic
532C2×C7#244811yescharacteristic
533C2×C7#244811yescharacteristic
534C23C22×C4×D711yescharacteristic
535C23C2×#115711yescharacteristic
536C23C2×#115711yescharacteristic
537C23C2×D4×D711yescharacteristic
538C23C2×D4×D711yescharacteristic
539C23C2×#115911yescharacteristic
540C23C2×#115911yescharacteristic
541C23#654811yescharacteristic
542C23C2×Q8×D711yescharacteristic
543C23C2×#116111yescharacteristic
544C23#655111yescharacteristic
545C23D7×#4111yescharacteristic
546C23D7×#4111yescharacteristic
547C23#655411yescharacteristic
548C23#655411yescharacteristic
549Q8—1432no—
550C2×C4—24no—
551C2×C4—22no—
552C2×C4—22no—
553C2×C4—24no—
554C2×C4—24no—
555C2×C4—22no—
556C2×C4—22no—
557C2×C4—22no—
558C2×C4—22no—
559C2×C4—42no—
560C2×C4—42no—
561C2×C4—41no—
562C2×C4—41no—
563C2×C4—41no—
564C2×C4—41no—
565C2×C4—42no—
566C2×C4—41no—
567C2×C4—42no—
568C2×C4—41no—
569C2×C4—41no—
570C2×C4—41no—
571C2×C4—42no—
572C2×C4—42no—
573C2×C4—42no—
574C2×C4—42no—
575C2×C4—42no—
576C2×C4—42no—
577C2×C4—42no—
578C2×C4—78no—
579C2×C4—74no—
580C2×C4—142no—
581C2×C4—142no—
582C2×C4—144no—
583C2×C4—142no—
584C2×C4—144no—
585C2×C4—144no—
586C2×C4—144no—
587C2×C4—144no—
588C2×C4—144no—
589C2×C4—142no—
590C2×C4—142no—
591C2×C4—142no—
592C2×C4—142no—
593C2×C4—142no—
594C2×C4—142no—
595C2×C4—142no—
596C2×C4—142no—
597C2×C4—142no—
598C2×C4—142no—
599C2×C4—142no—
600C2×C4—142no—
601C2×C4—281no—
602C2×C4—281no—
603C2×C4—281no—
604C2×C4—281no—
605C2×C4—281no—
606C2×C4—281no—
607C2×C4—281no—
608C2×C4—281no—
609C2×C4—281no—
610C2×C4—281no—
611C2×C4—281no—
612C2×C4—281no—
613C2×C4—282no—
614C2×C4—282no—
615C2×C4—282no—
616C2×C4—282no—
617C2×C4—282no—
618C2×C4—282no—
619C2×C4—282no—
620C2×C4#643514yes—
621C2×C4D7×C22⋊C414yes—
622C2×C4#644614yes—
623C2×C4#644614yes—
624C2×C4#645514yes—
625C2×C4#645714yes—
626C2×C4#645714yes—
627C7#1393111yescharacteristic, complemented, Sylow
628C22C2×#643511yescharacteristic
629C22C2×D7×C22⋊C411yescharacteristic
630C22C2×#644611yescharacteristic
631C22C2×#644611yescharacteristic
632C22C2×#645511yescharacteristic
633C22C2×#645711yescharacteristic
634C22C2×#645711yescharacteristic
635C22#9020211yescharacteristic
636C22#9020411yescharacteristic
637C22#9022011yescharacteristic
638C22#9022411yescharacteristic
639C22C4×#115911yescharacteristic
640C22#9023311yescharacteristic
641C22#9023711yescharacteristic
642C22#9025011yescharacteristic
643C22#9025811yescharacteristic
644C22#9025911yescharacteristic
645C22C4×Q8×D711yescharacteristic
646C22#9026311yescharacteristic
647C22#9028911yescharacteristic
648C22#9029011yescharacteristic
649C22#9029111yescharacteristic
650C22#9029411yescharacteristic
651C22#9031311yescharacteristic
652C22#9031611yescharacteristic
653C22#9032311yescharacteristic
654C22#9032411yescharacteristic
655C22#9036811yescharacteristic
656C22#9036811yescharacteristic
657C22#9038211yescharacteristic
658C22#9038811yescharacteristic
659C22#9040911yescharacteristic
660C22#9041811yescharacteristic
661C22#9041911yescharacteristic
662C22#9042411yescharacteristic
663C4—42no—
664C4—42no—
665C4—44no—
666C4—82no—
667C4—144no—
668C4—148no—
669C4—282no—
670C4—282no—
671C4—282no—
672C4—562no—
673C4#8943618yes—
674C2C2×#8943611yescharacteristic
675C2#1173108611yescharacteristic
676C2#1173108911yescharacteristic
677C2#1173133711yescharacteristic
678C2#1173133911yescharacteristic
679C2#1173167711yescharacteristic
680C2#1173180811yescharacteristic
681C2#1173340711yescharacteristic
682C2#1173341511yescharacteristic
683C2#1173345011yescharacteristic
684C2#1173345211yescharacteristic
685C2#1173374611yescharacteristic
686C2#1173376611yescharacteristic
687C2#1173394911yescharacteristic
688C2#1173405911yescharacteristic
subgroupG/H
center, FrattiniC24C23×D7
commutatorC23×C7C23×C4
FittingC7×C4⋊#95C2
socle, prime radical, cosocleC24×C7C24
hypercenterC4⋊#95D7
hypocenterC7#13931
LCSG ▷ C23×C7 ▷ C7
UCSC1 ◁ C24 ◁ C4⋊#95

Complements

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

NH ≅ G/Ntype
23. C2×#6450C4semidirect
97. C7⋊#95Q8semidirect
627. C7#13931semidirect

Maximal subgroups

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

subgroupindex
C22×#64502
C2×#897462
C2×#897012
C7×C4⋊#952
#117293172
C4×C7⋊#952
#117271752
#117271572
#117271552
#139317