Finite Group Databasebeta

← #13360226

Subgroups — #13360226

Order 1792.

932 conjugacy classes of subgroups.

The subgroup lattice has 626 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C7×#462C211yesmaximal, characteristic
2C2×#89956C211yesmaximal, characteristic
3C2×Q16×Dic7C211yesmaximal, characteristic
4#11740672C211yesmaximal, characteristic
5#11739895C211yesmaximal, characteristic
6#11729819C211yesmaximal, characteristic
7#11729819C211yesmaximal, characteristic
8#11729532C211yesmaximal, characteristic
9#11729381C211yesmaximal, characteristic
10#11728209C211yesmaximal, characteristic
11#11728196C211yesmaximal, characteristic
12#11727978C211yesmaximal, characteristic
13#11727977C211yesmaximal, characteristic
14#11727974C211yesmaximal, characteristic
15Dic7×#103C211yesmaximal, characteristic
16C22×C7×Q16C2211yescharacteristic
17C22×C7×Q16C2211yescharacteristic
18C2×C7×C4⋊Q8C2211yescharacteristic
19C2×C4×C7×Q8C2211yescharacteristic
20C2×Q8×Dic7C2211yescharacteristic
21C2×Q8×Dic7C2211yescharacteristic
22C2×Q8×Dic7C2211yescharacteristic
23C2×Q8×Dic7C2211yescharacteristic
24C7×#462C418yescomplemented
25C2×C7×C4⋊C8C2211yescharacteristic
26C2×C7×#103C2211yescharacteristic
27C2×C7×#103C2211yescharacteristic
28#90002C2211yescharacteristic
29#90002C2211yescharacteristic
30C2×#6409C2211yescharacteristic
31C2×#6409C2211yescharacteristic
32C2×#6409C2211yescharacteristic
33C2×#6409C2211yescharacteristic
34C2×#6409C2211yescharacteristic
35C2×#6409C2211yescharacteristic
36#89956—24no—
37Q16×Dic7—24no—
38C2×#6392C2211yescharacteristic
39C2×#6391C2211yescharacteristic
40C2×#6389C2211yescharacteristic
41C2×C8×Dic7C2211yescharacteristic
42#89753—21no—
43#89753—21no—
44#89753—21no—
45#89753—21no—
46C4⋊C4×Dic7—21no—
47C4⋊C4×Dic7—21no—
48C4⋊C4×Dic7C2211yescharacteristic
49C4⋊C4×Dic7C2211yescharacteristic
50#89708C2211yescharacteristic
51C4×C4⋊Dic7—21no—
52C4×C4⋊Dic7C2211yescharacteristic
53#89704—21no—
54#89704C2211yescharacteristic
55C2×C4⋊(C7⋊C8)C2211yescharacteristic
56#89346C2211yescharacteristic
57#89346C2211yescharacteristic
58#89345C2211yescharacteristic
59#89345C2211yescharacteristic
60#89324C2211yescharacteristic
61#89324C2211yescharacteristic
62#21516—71nomaximal, Sylow
63C22×C7×Q8C2311yescharacteristic
64C22×C7×Q8C2311yescharacteristic
65C22×C7×Q8C2311yescharacteristic
66C2×C7×Q16—22no—
67C2×C7×Q16—22no—
68C2×C7×Q16—22no—
69C2×C7×Q16—22no—
70C2×C7×Q16C2×C414yes—
71C2×C7×Q16C2×C414yes—
72C22×C7×C8C2311yescharacteristic
73C22×C7×C8C2311yescharacteristic
74C7×C4⋊Q8—22no—
75C7×C4⋊Q8C2×C414yes—
76C4×C7×Q8—22no—
77C4×C7×Q8C2×C414yes—
78C2×C7×C4⋊C4—21no—
79C2×C7×C4⋊C4—21no—
80C2×C7×C4⋊C4—21no—
81C2×C7×C4⋊C4C2311yescharacteristic
82C2×C42×C7—21no—
83C2×C42×C7C2311yescharacteristic
84Q8×Dic7—22no—
85Q8×Dic7—22no—
86Q8×Dic7—22no—
87Q8×Dic7—22no—
88Q8×Dic7—22no—
89Q8×Dic7—22no—
90Q8×Dic7—22no—
91Q8×Dic7D414yes—
92C2×C4⋊Dic7—21no—
93C2×C4⋊Dic7—21no—
94C2×C4⋊Dic7—21no—
95C2×C4⋊Dic7—21no—
96C2×C4⋊Dic7C2311yescharacteristic
97C2×C4⋊Dic7C2311yescharacteristic
98C2×C4⋊Dic7C2311yescharacteristic
99C2×C4⋊Dic7C2311yescharacteristic
100C2×C4×Dic7—21no—
101C2×C4×Dic7—21no—
102C2×C4×Dic7—21no—
103C2×C4×Dic7—21no—
104C2×C4×Dic7—21no—
105C2×C4×Dic7—21no—
106C2×C4×Dic7—21no—
107C2×C4×Dic7C2311yescharacteristic
108C2×C4×Dic7C2311yescharacteristic
109C22×C7⋊C8C2311yescharacteristic
110C22×C7⋊C8C2311yescharacteristic
111C7×C4⋊C8C2×C414yes—
112C7×#103C2×C414yes—
113C7×#103C2×C414yes—
114#6409—22no—
115#6409—22no—
116#6409—22no—
117#6409—22no—
118#6409—22no—
119#6409—22no—
120C7⋊#95—21no—
121C7⋊#95—21no—
122C7⋊#95—21no—
123C7⋊#95—21no—
124C7⋊#95—21no—
125C7⋊#95—21no—
126C7⋊#95—21no—
127C7⋊#95—21no—
128C7⋊#95—21no—
129C7⋊#95D411yescharacteristic
130C7⋊#95D411yescharacteristic
131C7⋊#95D411yescharacteristic
132C7⋊#95D411yescharacteristic
133#6392—22no—
134#6391—22no—
135#6389—22no—
136C8×Dic7—22no—
137C4⋊(C7⋊C8)—22no—
138C2×#462D711yescharacteristic
139C2×#441—71no—
140C2×C4×Q16—71no—
141#2327—71no—
142#2276—71no—
143#1981—71no—
144#1949—71no—
145#1928—71no—
146#1927—71no—
147#1878—71no—
148#1878—71no—
149#1805—71no—
150#1768—71no—
151#1763—71no—
152C4×#103—71no—
153C2×C7×Q8—21no—
154C2×C7×Q8—21no—
155C2×C7×Q8—21no—
156C2×C7×Q8—21no—
157C2×C7×Q8—21no—
158C2×C7×Q8—21no—
159C2×C7×Q8—21no—
160C2×C7×Q8—21no—
161C2×C7×Q8—21no—
162C2×C7×Q8—21no—
163C2×C7×Q8—21no—
164C2×C7×Q8—21no—
165C2×C7×Q8—21no—
166C2×C7×Q8C22×C412yes—
167C2×C7×Q8C22×C412yes—
168C2×C7×Q8C22×C412yes—
169C2×C7×Q8C2×D412yes—
170C2×C7×Q8#4112yes—
171C22×C4×C7—21no—
172C22×C4×C7—21no—
173C22×C4×C7—21no—
174C22×C4×C7—21no—
175C22×C4×C7C2×D411yescharacteristic
176C22×C4×C7C2×D411yescharacteristic
177C22×C4×C7C2411yescharacteristic
178C22×Dic7—21no—
179C22×Dic7—21no—
180C22×Dic7—21no—
181C22×Dic7—21no—
182C22×Dic7C2×D411yescharacteristic
183C22×Dic7C2×D411yescharacteristic
184C22×Dic7C2×D411yescharacteristic
185C22×Dic7C2×D411yescharacteristic
186C7×Q16—28no—
187C7×Q16—28no—
188C2×C7×C8—21no—
189C2×C7×C8—21no—
190C2×C7×C8—21no—
191C2×C7×C8—21no—
192C2×C7×C8C22×C412yes—
193C2×C7×C8C22×C412yes—
194C7×C4⋊C4—24no—
195C7×C4⋊C4—24no—
196C7×C4⋊C4—24no—
197C7×C4⋊C4—21no—
198C7×C4⋊C4C22×C412yes—
199C42×C7—24no—
200C42×C7C22×C412yes—
201C42×C7#4112yes—
202C4⋊Dic7—24no—
203C4⋊Dic7—21no—
204C4⋊Dic7—21no—
205C4⋊Dic7—24no—
206C4⋊Dic7—21no—
207C4⋊Dic7—21no—
208C4⋊Dic7—21no—
209C4⋊Dic7—21no—
210C4⋊Dic7—42no—
211C4⋊Dic7—42no—
212C4⋊Dic7C2×D412yes—
213C4⋊Dic7#4112yes—
214C4×Dic7—24no—
215C4×Dic7—21no—
216C4×Dic7—21no—
217C4×Dic7—24no—
218C4×Dic7—42no—
219C4×Dic7—42no—
220C4×Dic7—81no—
221C4×Dic7—81no—
222C4×Dic7—81no—
223C4×Dic7C2×D412yes—
224C4×Dic7#4112yes—
225C2×C7⋊C8—21no—
226C2×C7⋊C8—21no—
227C2×C7⋊C8—21no—
228C2×C7⋊C8—21no—
229C2×C7⋊C8—21no—
230C2×C7⋊C8—21no—
231C22×Q16C2×D711yescharacteristic
232C22×Q16C2×D711yescharacteristic
233C2×C4⋊Q8C2×D711yescharacteristic
234C2×C4×Q8—71no—
235C2×C4×Q8—71no—
236C2×C4×Q8—71no—
237C2×C4×Q8—71no—
238C2×C4×Q8C2×D711yescharacteristic
239#462Dic718yescomplemented
240#441—144no—
241C4×Q16—144no—
242C2×#107—71no—
243C2×#106—71no—
244C2×C4⋊C8—71no—
245C2×C4⋊C8C2×D711yescharacteristic
246C2×#103—71no—
247C2×#103—71no—
248C2×#103—71no—
249C2×#103—71no—
250C2×#103—71no—
251C2×#103—71no—
252C2×#103C2×D711yescharacteristic
253C2×#103C2×D711yescharacteristic
254C2×#97—71no—
255C2×C4×C8—71no—
256#391—71no—
257#391—71no—
258#387—141no—
259#387—141no—
260#387—141no—
261#387—141no—
262#382—71no—
263C4×C4⋊C4—71no—
264C4×C4⋊C4—71no—
265C4×C4⋊C4—71no—
266C4×C4⋊C4—141no—
267C4×C4⋊C4—141no—
268C4×C4⋊C4—141no—
269#376—71no—
270#376—141no—
271#340—71no—
272#340—71no—
273#340—71no—
274#340—71no—
275#336—71no—
276#336—71no—
277C23×C7C22×D411yescharacteristic
278C7×Q8—22no—
279C7×Q8—22no—
280C7×Q8—22no—
281C7×Q8—22no—
282C7×Q8—22no—
283C7×Q8—22no—
284C7×Q8—22no—
285C7×Q8—41no—
286C7×Q8—41no—
287C7×Q8—41no—
288C7×Q8—41no—
289C7×Q8C4×D414yes—
290C2×C4×C7—22no—
291C2×C4×C7—22no—
292C2×C4×C7—22no—
293C2×C4×C7—21no—
294C2×C4×C7—21no—
295C2×C4×C7—21no—
296C2×C4×C7—21no—
297C2×C4×C7—22no—
298C2×C4×C7—22no—
299C2×C4×C7—22no—
300C2×C4×C7—41no—
301C2×C4×C7—41no—
302C2×C4×C7—41no—
303C2×C4×C7—41no—
304C2×C4×C7—41no—
305C2×C4×C7—41no—
306C2×C4×C7C4×D412yes—
307C2×C4×C7C4×D412yes—
308C2×C4×C7C23×C411yescharacteristic
309C2×C4×C7C22×D411yescharacteristic
310C2×C4×C7C2×#4111yescharacteristic
311C2×C4×C7C2×#4111yescharacteristic
312C2×C4×C7C2×#4111yescharacteristic
313C2×C4×C7C2×#4111yescharacteristic
314C2×Dic7—21no—
315C2×Dic7—21no—
316C2×Dic7—21no—
317C2×Dic7—21no—
318C2×Dic7—22no—
319C2×Dic7—21no—
320C2×Dic7—21no—
321C2×Dic7—22no—
322C2×Dic7—21no—
323C2×Dic7—21no—
324C2×Dic7—21no—
325C2×Dic7—21no—
326C2×Dic7—41no—
327C2×Dic7—41no—
328C2×Dic7—41no—
329C2×Dic7—41no—
330C2×Dic7—41no—
331C2×Dic7—41no—
332C2×Dic7—41no—
333C2×Dic7—41no—
334C2×Dic7—41no—
335C2×Dic7—41no—
336C2×Dic7#12112yes—
337C2×Dic7#12112yes—
338C7×C8—22no—
339C7×C8—22no—
340C7⋊C8—41no—
341C7⋊C8—41no—
342C22×Q8C22×D711yescharacteristic
343C22×Q8C22×D711yescharacteristic
344C22×Q8C22×D711yescharacteristic
345C2×Q16—22no—
346C2×Q16—22no—
347C2×Q16—22no—
348C2×Q16—22no—
349C2×Q16C2×Dic714yes—
350C2×Q16C2×Dic714yes—
351C22×C8—71no—
352C22×C8—71no—
353C22×C8C22×D711yescharacteristic
354C22×C8C22×D711yescharacteristic
355C4⋊Q8—22no—
356C4⋊Q8C2×Dic714yes—
357C4×Q8—22no—
358C4×Q8—74no—
359C4×Q8—142no—
360C4×Q8—142no—
361C4×Q8—142no—
362C4×Q8—142no—
363C4×Q8—142no—
364C4×Q8—142no—
365C4×Q8—142no—
366C4×Q8C2×Dic714yes—
367C2×C4⋊C4—21no—
368C2×C4⋊C4—21no—
369C2×C4⋊C4—21no—
370C2×C4⋊C4—71no—
371C2×C4⋊C4—71no—
372C2×C4⋊C4—71no—
373C2×C4⋊C4—71no—
374C2×C4⋊C4—141no—
375C2×C4⋊C4—141no—
376C2×C4⋊C4—141no—
377C2×C4⋊C4—141no—
378C2×C4⋊C4C22×D711yescharacteristic
379C2×C42—21no—
380C2×C42—71no—
381C2×C42—71no—
382C2×C42—141no—
383C2×C42—141no—
384C2×C42—141no—
385C2×C42—141no—
386C2×C42—141no—
387C2×C42—141no—
388C2×C42—141no—
389C2×C42C22×D711yescharacteristic
390#107—142no—
391#106—142no—
392C4⋊C8—142no—
393C4⋊C8C2×Dic714yes—
394#103—142no—
395#103—142no—
396#103—142no—
397#103—142no—
398#103—142no—
399#103—142no—
400#103C2×Dic714yes—
401#103C2×Dic714yes—
402#97—142no—
403C4×C8—142no—
404#95—71no—
405#95—71no—
406#95—71no—
407#95—71no—
408#95—141no—
409#95—141no—
410#95—141no—
411#95—141no—
412#95—141no—
413#95—141no—
414#95—141no—
415#95—141no—
416#95—141no—
417C22×C7C2×C4×D411yescharacteristic
418C22×C7C2×#12111yescharacteristic
419C22×C7#52511yescharacteristic
420C22×C7#57711yescharacteristic
421C22×C7#57811yescharacteristic
422C22×C7#57811yescharacteristic
423C22×C7#57811yescharacteristic
424C4×C7—22no—
425C4×C7—22no—
426C4×C7—24no—
427C4×C7—42no—
428C4×C7—42no—
429C4×C7—42no—
430C4×C7C2×C4×D411yescharacteristic
431C4×C7C4×#4111yescharacteristic
432C4×C7#52911yescharacteristic
433C4×C7#53211yescharacteristic
434Dic7—22no—
435Dic7—22no—
436Dic7—41no—
437Dic7—42no—
438Dic7—41no—
439Dic7—42no—
440Dic7—81no—
441Dic7—81no—
442C2×Q8—21no—
443C2×Q8—21no—
444C2×Q8—21no—
445C2×Q8—21no—
446C2×Q8—21no—
447C2×Q8—21no—
448C2×Q8—21no—
449C2×Q8—21no—
450C2×Q8—21no—
451C2×Q8—21no—
452C2×Q8—21no—
453C2×Q8—21no—
454C2×Q8—21no—
455C2×Q8D4×D712yes—
456C2×Q8#115912yes—
457C2×Q8C22×Dic712yes—
458C2×Q8C22×Dic712yes—
459C2×Q8C22×Dic712yes—
460C22×C4—21no—
461C22×C4—21no—
462C22×C4—21no—
463C22×C4—21no—
464C22×C4—71no—
465C22×C4—71no—
466C22×C4—71no—
467C22×C4—71no—
468C22×C4—141no—
469C22×C4—141no—
470C22×C4—141no—
471C22×C4—141no—
472C22×C4D4×D711yescharacteristic
473C22×C4D4×D711yescharacteristic
474C22×C4C23×D711yescharacteristic
475Q16—28no—
476Q16—28no—
477C2×C8—21no—
478C2×C8—21no—
479C2×C8—21no—
480C2×C8—21no—
481C2×C8—141no—
482C2×C8—141no—
483C2×C8—141no—
484C2×C8—141no—
485C2×C8—141no—
486C2×C8—141no—
487C2×C8C22×Dic712yes—
488C2×C8C22×Dic712yes—
489C4⋊C4—24no—
490C4⋊C4—24no—
491C4⋊C4—24no—
492C4⋊C4—21no—
493C4⋊C4—72no—
494C4⋊C4—72no—
495C4⋊C4—144no—
496C4⋊C4—144no—
497C4⋊C4—141no—
498C4⋊C4—141no—
499C4⋊C4—141no—
500C4⋊C4—141no—
501C4⋊C4—141no—
502C4⋊C4—141no—
503C4⋊C4—282no—
504C4⋊C4—282no—
505C4⋊C4C22×Dic712yes—
506C42—24no—
507C42—72no—
508C42—72no—
509C42—144no—
510C42—144no—
511C42—141no—
512C42—141no—
513C42—282no—
514C42—282no—
515C42—561no—
516C42—561no—
517C42—561no—
518C42#115912yes—
519C42C22×Dic712yes—
520C2×C7C4×#12111yescharacteristic
521C2×C7#294711yescharacteristic
522C2×C7#295011yescharacteristic
523C2×C7#304411yescharacteristic
524C2×C7#304611yescharacteristic
525C2×C7#312011yescharacteristic
526C2×C7#312711yescharacteristic
527C23C2×D4×D711yescharacteristic
528Q8—22no—
529Q8—22no—
530Q8—22no—
531Q8—22no—
532Q8—22no—
533Q8—22no—
534Q8—22no—
535Q8—41no—
536Q8—41no—
537Q8—41no—
538Q8—41no—
539Q8D4×Dic714yes—
540C2×C4—21no—
541C2×C4—21no—
542C2×C4—21no—
543C2×C4—21no—
544C2×C4—22no—
545C2×C4—22no—
546C2×C4—22no—
547C2×C4—22no—
548C2×C4—22no—
549C2×C4—22no—
550C2×C4—41no—
551C2×C4—41no—
552C2×C4—41no—
553C2×C4—41no—
554C2×C4—41no—
555C2×C4—41no—
556C2×C4—72no—
557C2×C4—72no—
558C2×C4—141no—
559C2×C4—141no—
560C2×C4—141no—
561C2×C4—141no—
562C2×C4—141no—
563C2×C4—141no—
564C2×C4—141no—
565C2×C4—141no—
566C2×C4—142no—
567C2×C4—141no—
568C2×C4—142no—
569C2×C4—141no—
570C2×C4—281no—
571C2×C4—281no—
572C2×C4—281no—
573C2×C4—281no—
574C2×C4—281no—
575C2×C4—281no—
576C2×C4—281no—
577C2×C4—281no—
578C2×C4—281no—
579C2×C4—281no—
580C2×C4D4×Dic712yes—
581C2×C4D4×Dic712yes—
582C2×C4C2×D4×D711yescharacteristic
583C2×C4C2×#115911yescharacteristic
584C2×C4C2×#115911yescharacteristic
585C2×C4D7×#4111yescharacteristic
586C2×C4D7×#4111yescharacteristic
587C2×C4C23×Dic711yescharacteristic
588C8—22no—
589C8—22no—
590C8—281no—
591C8—281no—
592C7#2151611yescharacteristic, complemented, Sylow
593C22D7×#12111yescharacteristic
594C22#9029711yescharacteristic
595C22#9045711yescharacteristic
596C22#9045711yescharacteristic
597C22#9046911yescharacteristic
598C22#9047011yescharacteristic
599C22C2×D4×Dic711yescharacteristic
600C4—22no—
601C4—24no—
602C4—22no—
603C4—42no—
604C4—42no—
605C4—42no—
606C4—142no—
607C4—142no—
608C4—281no—
609C4—282no—
610C4—281no—
611C4—282no—
612C4—561no—
613C4—561no—
614C4#9028711yescharacteristic
615C4#9029111yescharacteristic
616C4C2×D4×Dic711yescharacteristic
617C4#41×Dic711yescharacteristic
618C2#1173790511yescharacteristic
619C2#1173790611yescharacteristic
620C2#1173792311yescharacteristic
621C2#1173792411yescharacteristic
622C2Dic7×#12111yescharacteristic
623C2#1174131911yescharacteristic
624C2#1174141011yescharacteristic
subgroupG/H
centerC23C2×D4×D7
commutatorC2×C4×C7C23×C4
FrattiniC22×C4C23×D7
FittingC2×C7×#462C2
socle, prime radicalC23×C7C22×D4
cosocleC22×C4×C7C24
hypercenterC2×#462D7
hypocenterC7#21516
LCSG ▷ C2×C4×C7 ▷ C2×C7 ▷ C7
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#462

Complements

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

NH ≅ G/Ntype
24. C7×#462C4semidirect
239. #462Dic7semidirect
592. C7#21516semidirect

Maximal subgroups

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

subgroupindex
C2×C7×#4622
C2×#899562
C2×Q16×Dic72
#117406722
#117398952
#117298192
#117295322
#117293812
#117282092
#117281962
#117279782
#117279772
#117279742
Dic7×#1032
#215167