Finite Group Databasebeta

← #13370595

Subgroups — #13370595

Order 1792.

1074 conjugacy classes of subgroups.

The subgroup lattice has 676 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#90362C211yesmaximal, characteristic
2C2×#89602C211yesmaximal, characteristic, complemented
3#11731087C211yesmaximal, characteristic, complemented
4C7×#1983C211yesmaximal, characteristic
5#11729479C211yesmaximal, characteristic
6#11728240C211yesmaximal, characteristic, complemented
7#11727983C211yesmaximal, characteristic, complemented
8#11727979C211yesmaximal, characteristic, complemented
9#11727976C211yesmaximal, characteristic, complemented
10Dic7×#103C211yesmaximal, characteristic, complemented
11#11727916C211yesmaximal, characteristic
12#11727912C211yesmaximal, characteristic
13#11727907C211yesmaximal, characteristic
14Dic7×#102C211yesmaximal, characteristic
15C4×#6384C211yesmaximal, characteristic, complemented
16C2×C7×#124C2211yescharacteristic
17C2×Q8×Dic7C2211yescharacteristic
18C2×#6507C2211yescharacteristic
19C2×#6499C2211yescharacteristic
20C2×D4×Dic7C2211yescharacteristic
21#90362—24no—
22#90362C418yescomplemented
23C2×#6442—21no—
24C2×#6442—21no—
25C2×#6441—21no—
26C2×#6440—21no—
27C2×C4×Dic14C2211yescharacteristic
28C2×C4×Dic14C2211yescharacteristic
29C2×C7×C4⋊C8C2211yescharacteristic
30C2×C7×#103C2211yescharacteristic
31C2×C7×#103C2211yescharacteristic
32C2×C7×#102C2211yescharacteristic
33C2×C7×#102C2211yescharacteristic
34C4×C7×C4⋊C4C2211yescharacteristic
35C2×#6409C2211yescharacteristic
36C2×#6409C2211yescharacteristic
37C2×#6406C2211yescharacteristic
38C2×#6406C2211yescharacteristic
39C2×#6390C2211yescharacteristic
40C2×#6390C2211yescharacteristic
41C2×Dic7⋊C8C2211yescharacteristic
42C2×Dic7⋊C8C2211yescharacteristic
43C2×C8×Dic7C2211yescharacteristic
44C2×C8×Dic7C2211yescharacteristic
45#89749C2211yescharacteristic
46#89748C2211yescharacteristic
47C4⋊C4×Dic7C2211yescharacteristic
48C4⋊C4×Dic7C2211yescharacteristic
49C2×#6384C2211yescharacteristic
50C2×#6384C2211yescharacteristic
51#89708C2211yescharacteristic
52#89705—21no—
53C4×Dic7⋊C4—21no—
54C2×C4×C7⋊C8C2211yescharacteristic
55#89602—24no—
56#89426—21no—
57#89418—21no—
58#89346C2211yescharacteristic
59#89346C2211yescharacteristic
60#89324C2211yescharacteristic
61#89324C2211yescharacteristic
62#22541—71nomaximal, Sylow
63C22×C7×Q8C2311yescharacteristic
64C22×C7×D4C2311yescharacteristic
65C23×Dic7—21no—
66C22×Dic14D411yescharacteristic
67C22×Dic14C2311yescharacteristic
68C22×C7×C8C2311yescharacteristic
69C22×C7×C8C2311yescharacteristic
70C7×#124—22no—
71C7×#124C2×C414yes—
72C2×C7×C4⋊C4C2311yescharacteristic
73C2×C7×C4⋊C4C2311yescharacteristic
74C2×C7×C22⋊C4—21no—
75C2×C7×C22⋊C4—21no—
76C2×C42×C7—21no—
77C2×C42×C7C2311yescharacteristic
78C2×C22⋊Dic7—21no—
79C2×C22⋊Dic7—21no—
80C2×C22⋊Dic7—21no—
81Q8×Dic7—22no—
82Q8×Dic7C2×C414yes—
83#6507—22no—
84#6507C2×C414yes—
85#6499—22no—
86#6499C2×C414yes—
87D4×Dic7—22no—
88D4×Dic7C2×C414yes—
89C2×C4⋊Dic7—21no—
90C2×C4⋊Dic7D411yescharacteristic
91C2×C4⋊Dic7C2311yescharacteristic
92C2×C4⋊Dic7C2311yescharacteristic
93C2×C4⋊Dic7C2311yescharacteristic
94C2×Dic7⋊C4—21no—
95C2×Dic7⋊C4—21no—
96C2×Dic7⋊C4—21no—
97C2×Dic7⋊C4—21no—
98C2×Dic7⋊C4—21no—
99C2×Dic7⋊C4D411yescharacteristic
100C2×Dic7⋊C4D411yescharacteristic
101C2×C4×Dic7—21no—
102C2×C4×Dic7—21no—
103C2×C4×Dic7—21no—
104C2×C4×Dic7—21no—
105C2×C4×Dic7C2311yescharacteristic
106C2×C4×Dic7C2311yescharacteristic
107C22×C7⋊C8C2311yescharacteristic
108C22×C7⋊C8C2311yescharacteristic
109#6442—28no—
110#6442—28no—
111#6441—28no—
112#6440—28no—
113C4×Dic14—22no—
114C4×Dic14C2×C414yes—
115C4×Dic14C2×C414yes—
116C4×Dic14D414yes—
117C7×C4⋊C8—22no—
118C7×#103—22no—
119C7×#103—41no—
120C7×#102—22no—
121C7×#102—41no—
122C7×#95—21no—
123#6409—22no—
124#6409—41no—
125#6406—22no—
126#6406—41no—
127C7⋊#95—21no—
128C7⋊#95—21no—
129C7⋊#95—21no—
130C7⋊#95—21no—
131C7⋊#95—21no—
132C7⋊#95—21no—
133#6390—41no—
134#6390—41no—
135Dic7⋊C8—22no—
136Dic7⋊C8—22no—
137C8×Dic7—22no—
138C8×Dic7—22no—
139#6384—22no—
140#6384—22no—
141C4×C7⋊C8—22no—
142C2×#556—71no—
143C2×C8×Q8—71no—
144#2355—71no—
145#1983—71no—
146#1983D711yescharacteristic
147#1981—71no—
148#1958—71no—
149#1958—71no—
150#1956—71no—
151#1805—71no—
152#1805—71no—
153#1802—71no—
154C4×#103—71no—
155C4×#103—71no—
156C4×#102—71no—
157C24×C7—21no—
158C2×C7×Q8—21no—
159C2×C7×Q8—21no—
160C2×C7×Q8—21no—
161C2×C7×Q8—21no—
162C2×C7×Q8—21no—
163C2×C7×Q8C22×C412yes—
164C2×C7×D4—21no—
165C2×C7×D4—21no—
166C2×C7×D4—21no—
167C2×C7×D4—21no—
168C2×C7×D4—21no—
169C2×C7×D4C22×C412yes—
170C22×C4×C7—21no—
171C22×C4×C7—21no—
172C22×C4×C7—21no—
173C22×C4×C7C2×D411yescharacteristic
174C22×C4×C7C2×D411yescharacteristic
175C22×C4×C7C2411yescharacteristic
176C22×Dic7—21no—
177C22×Dic7—21no—
178C22×Dic7—24no—
179C22×Dic7—21no—
180C22×Dic7—21no—
181C22×Dic7—42no—
182C22×Dic7—42no—
183C22×Dic7C2×D411yescharacteristic
184C22×Dic7C2×D411yescharacteristic
185C22×Dic7C2×D411yescharacteristic
186C22×Dic7C2×D411yescharacteristic
187C2×Dic14—22no—
188C2×Dic14—22no—
189C2×Dic14—21no—
190C2×Dic14—21no—
191C2×Dic14—21no—
192C2×Dic14—21no—
193C2×Dic14—21no—
194C2×Dic14C22⋊C414yes—
195C2×Dic14C22×C412yes—
196C2×C7×C8—21no—
197C2×C7×C8—21no—
198C2×C7×C8—21no—
199C2×C7×C8—21no—
200C2×C7×C8—21no—
201C2×C7×C8—21no—
202C7×C4⋊C4—21no—
203C7×C4⋊C4—21no—
204C7×C4⋊C4—21no—
205C7×C4⋊C4#4112yes—
206C7×C22⋊C4—24no—
207C7×C22⋊C4—24no—
208C42×C7—81no—
209C42×C7C22×C412yes—
210C42×C7C2×D412yes—
211C22⋊Dic7—24no—
212C22⋊Dic7—24no—
213C22⋊Dic7—24no—
214C4⋊Dic7—21no—
215C4⋊Dic7—24no—
216C4⋊Dic7—21no—
217C4⋊Dic7—21no—
218C4⋊Dic7—21no—
219C4⋊Dic7—21no—
220C4⋊Dic7C22⋊C414yes—
221C4⋊Dic7C22×C412yes—
222Dic7⋊C4—24no—
223Dic7⋊C4—24no—
224Dic7⋊C4—24no—
225Dic7⋊C4—42no—
226Dic7⋊C4—81no—
227Dic7⋊C4C22⋊C414yes—
228Dic7⋊C4C22⋊C414yes—
229C4×Dic7—24no—
230C4×Dic7—24no—
231C4×Dic7—42no—
232C4×Dic7—81no—
233C4×Dic7C22×C412yes—
234C4×Dic7C22×C412yes—
235C4×Dic7C2×D412yes—
236C4×Dic7C2×D412yes—
237C2×C7⋊C8—21no—
238C2×C7⋊C8—21no—
239C2×C7⋊C8—21no—
240C2×C7⋊C8—21no—
241C2×C7⋊C8—21no—
242C2×C7⋊C8#4112yes—
243#556—78no—
244#556—144no—
245C2×C4⋊Q8—71no—
246C2×#126—141no—
247C2×#126—141no—
248C2×#124—71no—
249C2×#124C2×D711yescharacteristic
250C2×C22⋊Q8—141no—
251C2×C4×Q8—71no—
252C2×C4×Q8—71no—
253C2×C4×Q8—71no—
254C2×C4×D4—71no—
255C2×#117—141no—
256C8×Q8—144no—
257C2×C4⋊C8—71no—
258C2×C4⋊C8—71no—
259C2×C4⋊C8C2×D711yescharacteristic
260C2×#103—71no—
261C2×#103—71no—
262C2×#103—71no—
263C2×#103—71no—
264C2×#103—71no—
265C2×#103—71no—
266C2×#103C2×D711yescharacteristic
267C2×#103C2×D711yescharacteristic
268C2×#102—71no—
269C2×#102—71no—
270C2×#102C2×D711yescharacteristic
271C2×#102C2×D711yescharacteristic
272C2×C4×C8—71no—
273C2×C4×C8—71no—
274C2×C4×C8—71no—
275#391—141no—
276#387—141no—
277#387—141no—
278#384—71no—
279#382—71no—
280#382—71no—
281C4×C4⋊C4—71no—
282C4×C4⋊C4—71no—
283C4×C4⋊C4—141no—
284C4×C4⋊C4C2×D711yescharacteristic
285#340—71no—
286#340—71no—
287#340—71no—
288#340—71no—
289C23×C7—22no—
290C23×C7—41no—
291C23×C7—41no—
292C23×C7—41no—
293C23×C7—41no—
294C23×C7—41no—
295C23×C7—41no—
296C23×C7C22×D411yescharacteristic
297C7×Q8—22no—
298C7×Q8—22no—
299C7×Q8—41no—
300C7×Q8—41no—
301C7×D4—22no—
302C7×D4—22no—
303C7×D4—41no—
304C7×D4—41no—
305C2×C4×C7—21no—
306C2×C4×C7—21no—
307C2×C4×C7—21no—
308C2×C4×C7—21no—
309C2×C4×C7—22no—
310C2×C4×C7—22no—
311C2×C4×C7—41no—
312C2×C4×C7—41no—
313C2×C4×C7—41no—
314C2×C4×C7—41no—
315C2×C4×C7—41no—
316C2×C4×C7—41no—
317C2×C4×C7—41no—
318C2×C4×C7C2×C22⋊C412yes—
319C2×C4×C7C2×C22⋊C412yes—
320C2×C4×C7C23×C411yescharacteristic
321C2×C4×C7C22×D411yescharacteristic
322C2×C4×C7C2×#4111yescharacteristic
323C2×C4×C7C2×#4111yescharacteristic
324C2×C4×C7H(5,𝔽2)11yescharacteristic
325C2×C4×C72−1+411yescharacteristic
326C2×Dic7—21no—
327C2×Dic7—21no—
328C2×Dic7—21no—
329C2×Dic7—21no—
330C2×Dic7—21no—
331C2×Dic7—21no—
332C2×Dic7—22no—
333C2×Dic7—22no—
334C2×Dic7—41no—
335C2×Dic7—41no—
336C2×Dic7—41no—
337C2×Dic7—41no—
338C2×Dic7—48no—
339C2×Dic7—41no—
340C2×Dic7—41no—
341C2×Dic7—41no—
342C2×Dic7—41no—
343C2×Dic7—41no—
344C2×Dic7—41no—
345C2×Dic7C2×C22⋊C412yes—
346C2×Dic7C2×C22⋊C412yes—
347C2×Dic7C2×C22⋊C412yes—
348C2×Dic7C2×C22⋊C412yes—
349C2×Dic7#13512yes—
350C2×Dic7#13512yes—
351Dic14—28no—
352Dic14—22no—
353Dic14—22no—
354Dic14—41no—
355Dic14—41no—
356C7×C8—41no—
357C7×C8—41no—
358C7⋊C8—22no—
359C7⋊C8—41no—
360C22×Q8—71no—
361C22×Q8—71no—
362C22×Q8C22×D711yescharacteristic
363C22×D4C22×D711yescharacteristic
364C23×C4—141no—
365C22×C8—71no—
366C22×C8—71no—
367C22×C8C22×D711yescharacteristic
368C22×C8C22×D711yescharacteristic
369C4⋊Q8—74no—
370C4⋊Q8—142no—
371#126—148no—
372#126—148no—
373#124—22no—
374#124—74no—
375#124—142no—
376#124C4×D714yes—
377C22⋊Q8—148no—
378C4×Q8—74no—
379C4×Q8—74no—
380C4×Q8—74no—
381C4×Q8—74no—
382C4×Q8—142no—
383C4×Q8—142no—
384C4×D4—74no—
385C4×D4—142no—
386#117—148no—
387C2×C4⋊C4—71no—
388C2×C4⋊C4—71no—
389C2×C4⋊C4—71no—
390C2×C4⋊C4—71no—
391C2×C4⋊C4—71no—
392C2×C4⋊C4—71no—
393C2×C4⋊C4—141no—
394C2×C4⋊C4—141no—
395C2×C4⋊C4—141no—
396C2×C4⋊C4—141no—
397C2×C4⋊C4—141no—
398C2×C4⋊C4—141no—
399C2×C4⋊C4C22×D711yescharacteristic
400C2×C4⋊C4C22×D711yescharacteristic
401C2×C22⋊C4—21no—
402C2×C22⋊C4—21no—
403C2×C22⋊C4—141no—
404C2×C22⋊C4—141no—
405C2×C22⋊C4—141no—
406C2×C42—21no—
407C2×C42—71no—
408C2×C42—71no—
409C2×C42—141no—
410C2×C42—141no—
411C2×C42—141no—
412C2×C42—141no—
413C2×C42C22×D711yescharacteristic
414C4⋊C8—22no—
415C4⋊C8—142no—
416C4⋊C8—142no—
417#103—22no—
418#103—41no—
419#103—142no—
420#103—142no—
421#103—142no—
422#103—281no—
423#103—281no—
424#103—281no—
425#102—22no—
426#102—41no—
427#102—142no—
428#102—281no—
429C4×C8—142no—
430C4×C8—142no—
431C4×C8—142no—
432#95—21no—
433#95—141no—
434#95—141no—
435#95—141no—
436#95—141no—
437#95—141no—
438#95—141no—
439C22×C7—42no—
440C22×C7—42no—
441C22×C7—42no—
442C22×C7—81no—
443C22×C7—81no—
444C22×C7—81no—
445C22×C7—81no—
446C22×C7C22×C22⋊C411yescharacteristic
447C22×C7#54811yescharacteristic
448C22×C7#55011yescharacteristic
449C22×C7C2×#13511yescharacteristic
450C22×C7C2×#13511yescharacteristic
451C22×C7#57711yescharacteristic
452C22×C7#57811yescharacteristic
453C4×C7—22no—
454C4×C7—22no—
455C4×C7—42no—
456C4×C7—42no—
457C4×C7—81no—
458C4×C7C4×#4111yescharacteristic
459C4×C7#52011yescharacteristic
460C4×C7#54811yescharacteristic
461C4×C7#55011yescharacteristic
462Dic7—22no—
463Dic7—22no—
464Dic7—22no—
465Dic7—42no—
466Dic7—42no—
467Dic7—81no—
468Dic7—81no—
469Dic7#41614yes—
470C24—21no—
471C2×Q8—21no—
472C2×Q8—21no—
473C2×Q8—21no—
474C2×Q8—21no—
475C2×Q8—21no—
476C2×Q8—74no—
477C2×Q8—72no—
478C2×Q8—142no—
479C2×Q8—142no—
480C2×Q8—141no—
481C2×Q8—141no—
482C2×Q8—141no—
483C2×Q8—141no—
484C2×Q8—141no—
485C2×Q8C2×C4×D712yes—
486C2×D4—21no—
487C2×D4—21no—
488C2×D4—21no—
489C2×D4—21no—
490C2×D4—21no—
491C2×D4C2×C4×D712yes—
492C22×C4—21no—
493C22×C4—21no—
494C22×C4—21no—
495C22×C4—71no—
496C22×C4—71no—
497C22×C4—71no—
498C22×C4—71no—
499C22×C4—144no—
500C22×C4—141no—
501C22×C4—141no—
502C22×C4—141no—
503C22×C4—141no—
504C22×C4—282no—
505C22×C4—282no—
506C22×C4D4×D711yescharacteristic
507C22×C4D4×D711yescharacteristic
508C22×C4C23×D711yescharacteristic
509C2×C8—21no—
510C2×C8—21no—
511C2×C8—21no—
512C2×C8—21no—
513C2×C8—21no—
514C2×C8—21no—
515C2×C8—72no—
516C2×C8—141no—
517C2×C8—141no—
518C2×C8—141no—
519C2×C8—141no—
520C2×C8—141no—
521C4⋊C4—21no—
522C4⋊C4—21no—
523C4⋊C4—21no—
524C4⋊C4—74no—
525C4⋊C4—74no—
526C4⋊C4—74no—
527C4⋊C4—72no—
528C4⋊C4—144no—
529C4⋊C4—144no—
530C4⋊C4—144no—
531C4⋊C4—144no—
532C4⋊C4—141no—
533C4⋊C4—141no—
534C4⋊C4—141no—
535C4⋊C4—141no—
536C4⋊C4—141no—
537C4⋊C4—282no—
538C4⋊C4—561no—
539C4⋊C4#115912yes—
540C22⋊C4—24no—
541C22⋊C4—24no—
542C22⋊C4—144no—
543C22⋊C4—144no—
544C22⋊C4—144no—
545C42—72no—
546C42—72no—
547C42—72no—
548C42—72no—
549C42—81no—
550C42—144no—
551C42—144no—
552C42—282no—
553C42—561no—
554C42C2×C4×D712yes—
555C42D4×D712yes—
556C2×C7—82no—
557C2×C7#234111yescharacteristic
558C2×C7C2×#41611yescharacteristic
559C2×C7#289811yescharacteristic
560C2×C7#336011yescharacteristic
561C2×C7#336411yescharacteristic
562C2×C7#339311yescharacteristic
563C2×C7#339411yescharacteristic
564C23—22no—
565C23—41no—
566C23—41no—
567C23—41no—
568C23—41no—
569C23—41no—
570C23—41no—
571C23C2×D4×D711yescharacteristic
572Q8—22no—
573Q8—22no—
574Q8—41no—
575Q8—41no—
576Q8—148no—
577Q8—142no—
578Q8—142no—
579Q8—281no—
580Q8—281no—
581D4—22no—
582D4—22no—
583D4—41no—
584D4—41no—
585C2×C4—21no—
586C2×C4—21no—
587C2×C4—21no—
588C2×C4—21no—
589C2×C4—22no—
590C2×C4—22no—
591C2×C4—41no—
592C2×C4—41no—
593C2×C4—41no—
594C2×C4—41no—
595C2×C4—41no—
596C2×C4—41no—
597C2×C4—41no—
598C2×C4—72no—
599C2×C4—72no—
600C2×C4—72no—
601C2×C4—72no—
602C2×C4—72no—
603C2×C4—72no—
604C2×C4—141no—
605C2×C4—141no—
606C2×C4—141no—
607C2×C4—141no—
608C2×C4—141no—
609C2×C4—141no—
610C2×C4—142no—
611C2×C4—142no—
612C2×C4—288no—
613C2×C4—281no—
614C2×C4—281no—
615C2×C4—281no—
616C2×C4—281no—
617C2×C4—281no—
618C2×C4—281no—
619C2×C4—281no—
620C2×C4—281no—
621C2×C4—281no—
622C2×C4—281no—
623C2×C4D7×C22⋊C412yes—
624C2×C4D7×C22⋊C412yes—
625C2×C4C22×C4×D711yescharacteristic
626C2×C4C2×D4×D711yescharacteristic
627C2×C4C2×#115911yescharacteristic
628C2×C4#654811yescharacteristic
629C2×C4D7×#4111yescharacteristic
630C2×C4#655411yescharacteristic
631C8—41no—
632C8—41no—
633C8—142no—
634C8—281no—
635C7#2254111yescharacteristic, complemented, Sylow
636C22—42no—
637C22—42no—
638C22—42no—
639C22—81no—
640C22—81no—
641C22—81no—
642C22—81no—
643C22C2×D7×C22⋊C411yescharacteristic
644C22#9028911yescharacteristic
645C22#9029011yescharacteristic
646C22D7×#13511yescharacteristic
647C22D7×#13511yescharacteristic
648C22#9046611yescharacteristic
649C22#9047011yescharacteristic
650C4—22no—
651C4—22no—
652C4—42no—
653C4—42no—
654C4—74no—
655C4—81no—
656C4—142no—
657C4—142no—
658C4—142no—
659C4—282no—
660C4—282no—
661C4—561no—
662C4—561no—
663C4C4×#115911yescharacteristic
664C4#9023711yescharacteristic
665C4#9036811yescharacteristic
666C4#9040911yescharacteristic
667C2—82no—
668C2#1173374611yescharacteristic
669C2D7×#41611yescharacteristic
670C2#1173632811yescharacteristic
671C2#1173796111yescharacteristic
672C2#1173796911yescharacteristic
673C2#1173802511yescharacteristic
674C2#1173803311yescharacteristic
subgroupG/H
centerC23C2×D4×D7
commutatorC2×C4×C7C23×C4
FrattiniC22×C4C23×D7
FittingC7×#1983C2
socleC23×C7C22×D4
prime radicalC22×C7×D4C23
cosocleC22×C4×C7C24
hypercenter#1983D7
hypocenterC7#22541
LCSG ▷ C2×C4×C7 ▷ C2×C7 ▷ C7
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1983

Complements

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

NH ≅ G/Ntype
2. C2×#89602C2semidirect
3. #11731087C2semidirect
6. #11728240C2semidirect
7. #11727983C2semidirect
8. #11727979C2semidirect
9. #11727976C2semidirect
10. Dic7×#103C2semidirect
15. C4×#6384C2semidirect
22. #90362C4semidirect
635. C7#22541semidirect

Maximal subgroups

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

subgroupindex
C2×#903622
C2×#896022
#117310872
C7×#19832
#117294792
#117282402
#117279832
#117279792
#117279762
Dic7×#1032
#117279162
#117279122
#117279072
Dic7×#1022
C4×#63842
#225417