Finite Group Databasebeta

← #13358707

Subgroups — #13358707

Order 1792.

826 conjugacy classes of subgroups.

The subgroup lattice has 596 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C7×#433C211yesmaximal, characteristic
2#11739676C211yesmaximal, characteristic
3#11739668C211yesmaximal, characteristic
4#11728209C211yesmaximal, characteristic, complemented
5#11728209C211yesmaximal, characteristic, complemented
6#11728208C211yesmaximal, characteristic, complemented
7#11728207C211yesmaximal, characteristic, complemented
8#11727683C211yesmaximal, characteristic
9#11727683C211yesmaximal, characteristic
10#11727682C211yesmaximal, characteristic
11#11727681C211yesmaximal, characteristic
12#11727568C211yesmaximal, characteristic, complemented
13#11727568C211yesmaximal, characteristic, complemented
14C4×#6392C211yesmaximal, characteristic, complemented
15C4×#6391C211yesmaximal, characteristic, complemented
16C2×C7×#117C2211yescharacteristic
17C2×#6489C2211yescharacteristic
18C22×C4⋊Dic7C2211yescharacteristic
19C7×#433C418yescomplemented
20C2×C7×C4⋊C8C2211yescharacteristic
21C2×C7×C4⋊C8C2211yescharacteristic
22C2×C7×C22⋊C8C2211yescharacteristic
23C2×C7×C22⋊C8C2211yescharacteristic
24C2×C7×#97C2211yescharacteristic
25C2×C4×C7×C8C2211yescharacteristic
26#89984C2211yescharacteristic
27#89984C2211yescharacteristic
28C2×#6392C2211yescharacteristic
29C2×#6392C2211yescharacteristic
30C2×#6392C2211yescharacteristic
31C2×#6392C2211yescharacteristic
32C2×#6391C2211yescharacteristic
33C2×#6391C2211yescharacteristic
34C2×#6391C2211yescharacteristic
35C2×#6391C2211yescharacteristic
36#89753—21no—
37#89753—21no—
38C4⋊C4×Dic7—21no—
39C4⋊C4×Dic7—21no—
40#89723—21no—
41#89723—21no—
42C22⋊C4×Dic7—21no—
43C22⋊C4×Dic7—21no—
44#89708C2211yescharacteristic
45#89707C2211yescharacteristic
46C4×C4⋊Dic7C2211yescharacteristic
47C4×C4⋊Dic7C2211yescharacteristic
48C4×C4⋊Dic7C2211yescharacteristic
49C4×C4⋊Dic7C2211yescharacteristic
50C4×C4⋊Dic7C2211yescharacteristic
51C4×C4⋊Dic7C2211yescharacteristic
52#89346C2211yescharacteristic
53#89346C2211yescharacteristic
54#89346C2211yescharacteristic
55#89346C2211yescharacteristic
56#89346C2211yescharacteristic
57#89346C2211yescharacteristic
58#89346C2211yescharacteristic
59#89346C2211yescharacteristic
60#21367—71nomaximal, Sylow
61C23×C4×C7C2311yescharacteristic
62C23×Dic7—21no—
63C22×C7×C8C2311yescharacteristic
64C22×C7×C8C2311yescharacteristic
65C22×C7×C8C2311yescharacteristic
66C22×C7×C8C2311yescharacteristic
67C7×#117C2×C414yes—
68C7×#117Q814yes—
69C2×C7×C4⋊C4D411yescharacteristic
70C2×C7×C4⋊C4D411yescharacteristic
71C2×C7×C22⋊C4D411yescharacteristic
72C2×C7×C22⋊C4D411yescharacteristic
73C2×C42×C7C2311yescharacteristic
74C2×C42×C7C2311yescharacteristic
75C2×C22⋊Dic7—21no—
76C2×C22⋊Dic7—21no—
77C2×C22⋊Dic7—21no—
78#6489—22no—
79#6489—22no—
80C2×C4⋊Dic7—21no—
81C2×C4⋊Dic7—22no—
82C2×C4⋊Dic7—22no—
83C2×C4⋊Dic7—21no—
84C2×C4⋊Dic7—21no—
85C2×C4⋊Dic7C2311yescharacteristic
86C2×C4⋊Dic7C2311yescharacteristic
87C2×C4⋊Dic7C2311yescharacteristic
88C2×C4⋊Dic7C2311yescharacteristic
89C2×C4⋊Dic7C2311yescharacteristic
90C2×C4⋊Dic7C2311yescharacteristic
91C2×C4⋊Dic7C2311yescharacteristic
92C2×C4⋊Dic7C2311yescharacteristic
93C2×C4×Dic7—21no—
94C2×C4×Dic7—21no—
95C2×C4×Dic7—21no—
96C2×C4×Dic7—21no—
97C2×C4×Dic7—21no—
98C2×C4×Dic7—21no—
99C2×C4×Dic7—21no—
100C7×C4⋊C8C2×C414yescomplemented
101C7×C4⋊C8C2×C414yescomplemented
102C7×C22⋊C8C2×C414yes—
103C7×C22⋊C8C2×C414yes—
104C7×#97C2×C414yescomplemented
105C4×C7×C8C2×C414yescomplemented
106C7⋊#95—21no—
107C7⋊#95—21no—
108C7⋊#95—21no—
109C7⋊#95—21no—
110C7⋊#95—21no—
111C7⋊#95—21no—
112C7⋊#95—21no—
113C7⋊#95—21no—
114C7⋊#95—21no—
115C7⋊#95—21no—
116#6392—22no—
117#6392—22no—
118#6392—22no—
119#6392—22no—
120#6391—22no—
121#6391—22no—
122#6391—22no—
123#6391—22no—
124C2×#433D711yescharacteristic
125#2314—71no—
126#2274—71no—
127#1949—71no—
128#1949—71no—
129#1948—71no—
130#1947—71no—
131#1854—71no—
132#1854—71no—
133#1853—71no—
134#1852—71no—
135#1776—71no—
136#1776—71no—
137C4×#107—71no—
138C4×#106—71no—
139C24×C7C2×D411yescharacteristic
140C22×C4×C7—21no—
141C22×C4×C7—21no—
142C22×C4×C7—21no—
143C22×C4×C7—21no—
144C22×C4×C7C22×C412yes—
145C22×C4×C7C2×D411yescharacteristic
146C22×C4×C7C2×D411yescharacteristic
147C22×C4×C7C2×D411yescharacteristic
148C22×C4×C7C2×D411yescharacteristic
149C22×C4×C7C2×D411yescharacteristic
150C22×C4×C7C2×Q812yes—
151C22×C4×C7C2411yescharacteristic
152C22×Dic7—21no—
153C22×Dic7—21no—
154C22×Dic7—21no—
155C22×Dic7—21no—
156C22×Dic7—24no—
157C22×Dic7—21no—
158C22×Dic7—21no—
159C22×Dic7—21no—
160C22×Dic7—21no—
161C22×Dic7—81no—
162C22×Dic7—81no—
163C2×C7×C8—21no—
164C2×C7×C8—21no—
165C2×C7×C8—21no—
166C2×C7×C8—21no—
167C2×C7×C8—21no—
168C2×C7×C8—21no—
169C2×C7×C8—21no—
170C2×C7×C8—21no—
171C2×C7×C8C22×C412yes—
172C2×C7×C8C22×C412yes—
173C2×C7×C8C22×C412yes—
174C2×C7×C8C22×C412yes—
175C7×C4⋊C4C4⋊C414yes—
176C7×C4⋊C4C4⋊C414yes—
177C7×C22⋊C4C4⋊C414yes—
178C7×C22⋊C4C4⋊C414yes—
179C42×C7C22×C412yes—
180C42×C7C22×C412yes—
181C42×C7C2×Q812yes—
182C42×C7C2×Q812yes—
183C22⋊Dic7—24no—
184C22⋊Dic7—81no—
185C22⋊Dic7—81no—
186C4⋊Dic7—24no—
187C4⋊Dic7—21no—
188C4⋊Dic7—21no—
189C4⋊Dic7—21no—
190C4⋊Dic7—21no—
191C4⋊Dic7—21no—
192C4⋊Dic7—21no—
193C4⋊Dic7—21no—
194C4⋊Dic7—21no—
195C4⋊Dic7—21no—
196C4⋊Dic7—21no—
197C4⋊Dic7—21no—
198C4⋊Dic7—21no—
199C4⋊Dic7—81no—
200C4⋊Dic7—81no—
201C4⋊Dic7#4112yes—
202C4⋊Dic7#4112yes—
203C4⋊Dic7#4112yes—
204C4⋊Dic7#4112yes—
205C4×Dic7—24no—
206C4×Dic7—81no—
207C4×Dic7—81no—
208C4×Dic7—81no—
209C4×Dic7—81no—
210C4×Dic7—81no—
211C4×Dic7—81no—
212C2×#117—71no—
213C2×#117C2×D711yescharacteristic
214C22×C4⋊C4—71no—
215#433Dic718yescomplemented
216C2×#107—71no—
217C2×#107—71no—
218C2×#107—71no—
219C2×#107—71no—
220C2×#106—71no—
221C2×#106—71no—
222C2×#106—71no—
223C2×#106—71no—
224C2×C4⋊C8C2×D711yescharacteristic
225C2×C4⋊C8C2×D711yescharacteristic
226C2×C22⋊C8C2×D711yescharacteristic
227C2×C22⋊C8C2×D711yescharacteristic
228C2×#97C2×D711yescharacteristic
229C2×C4×C8C2×D711yescharacteristic
230#388—141no—
231#388—141no—
232#387—141no—
233#387—141no—
234#384—71no—
235#382—71no—
236#380—71no—
237#380—71no—
238C4×C4⋊C4—71no—
239C4×C4⋊C4—71no—
240C4×C4⋊C4—71no—
241C4×C4⋊C4—71no—
242C4×C4⋊C4—71no—
243C4×C4⋊C4—71no—
244C4×C4⋊C4—141no—
245C4×C4⋊C4—141no—
246C4×C22⋊C4—141no—
247C4×C22⋊C4—141no—
248#340—71no—
249#340—71no—
250#340—71no—
251#340—71no—
252#340—71no—
253#340—71no—
254#340—71no—
255#340—71no—
256C23×C7—21no—
257C23×C7—21no—
258C23×C7—21no—
259C23×C7—21no—
260C23×C7—21no—
261C23×C7—21no—
262C23×C7C2×C4⋊C412yes—
263C23×C7C22×D411yescharacteristic
264C2×C4×C7—21no—
265C2×C4×C7—21no—
266C2×C4×C7—21no—
267C2×C4×C7—21no—
268C2×C4×C7—21no—
269C2×C4×C7—21no—
270C2×C4×C7—21no—
271C2×C4×C7—21no—
272C2×C4×C7—21no—
273C2×C4×C7—21no—
274C2×C4×C7—22no—
275C2×C4×C7—22no—
276C2×C4×C7—22no—
277C2×C4×C7—22no—
278C2×C4×C7C2×C4⋊C412yes—
279C2×C4×C7C2×C4⋊C412yes—
280C2×C4×C7C2×C4⋊C412yes—
281C2×C4×C7C2×C4⋊C412yes—
282C2×C4×C7C2×C4⋊C412yes—
283C2×C4×C7C23×C411yescharacteristic
284C2×C4×C7C22×Q811yescharacteristic
285C2×C4×C7C2×#4111yescharacteristic
286C2×C4×C7C2×#4111yescharacteristic
287C2×C4×C7C2×#4111yescharacteristic
288C2×C4×C7C2×#4111yescharacteristic
289C2×Dic7—22no—
290C2×Dic7—22no—
291C2×Dic7—22no—
292C2×Dic7—22no—
293C2×Dic7—41no—
294C2×Dic7—41no—
295C2×Dic7—41no—
296C2×Dic7—41no—
297C2×Dic7—41no—
298C2×Dic7—41no—
299C2×Dic7—41no—
300C2×Dic7—41no—
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—84no—
314C7×C8—22no—
315C7×C8—22no—
316C7×C8—22no—
317C7×C8—22no—
318C23×C4—141no—
319C23×C4C22×D711yescharacteristic
320C22×C8C22×D711yescharacteristic
321C22×C8C22×D711yescharacteristic
322C22×C8C22×D711yescharacteristic
323C22×C8C22×D711yescharacteristic
324#117—142no—
325#117—142no—
326#117Dic1414yes—
327#117C2×Dic714yes—
328C2×C4⋊C4—71no—
329C2×C4⋊C4—71no—
330C2×C4⋊C4—71no—
331C2×C4⋊C4—71no—
332C2×C4⋊C4—71no—
333C2×C4⋊C4—71no—
334C2×C4⋊C4—71no—
335C2×C4⋊C4—71no—
336C2×C4⋊C4—142no—
337C2×C4⋊C4—142no—
338C2×C4⋊C4—141no—
339C2×C4⋊C4—141no—
340C2×C4⋊C4—141no—
341C2×C4⋊C4D2811yescharacteristic
342C2×C4⋊C4D2811yescharacteristic
343C2×C22⋊C4—141no—
344C2×C22⋊C4—141no—
345C2×C22⋊C4—141no—
346C2×C22⋊C4D2811yescharacteristic
347C2×C22⋊C4D2811yescharacteristic
348C2×C42—141no—
349C2×C42—141no—
350C2×C42—141no—
351C2×C42—141no—
352C2×C42—141no—
353C2×C42—141no—
354C2×C42—141no—
355C2×C42C22×D711yescharacteristic
356C2×C42C22×D711yescharacteristic
357#107—142no—
358#107—142no—
359#107—142no—
360#107—142no—
361#106—142no—
362#106—142no—
363#106—142no—
364#106—142no—
365C4⋊C8C2×Dic714yescomplemented
366C4⋊C8C2×Dic714yescomplemented
367C22⋊C8C2×Dic714yes—
368C22⋊C8C2×Dic714yes—
369#97C2×Dic714yescomplemented
370C4×C8C2×Dic714yescomplemented
371#95—141no—
372#95—141no—
373#95—141no—
374#95—141no—
375#95—141no—
376#95—141no—
377#95—141no—
378#95—141no—
379#95—141no—
380#95—141no—
381C22×C7—22no—
382C22×C7—22no—
383C22×C7—22no—
384C22×C7—41no—
385C22×C7—41no—
386C22×C7—41no—
387C22×C7—41no—
388C22×C7C22×C4⋊C411yescharacteristic
389C22×C7#52511yescharacteristic
390C22×C7#52511yescharacteristic
391C22×C7#57611yescharacteristic
392C22×C7#57711yescharacteristic
393C22×C7#57711yescharacteristic
394C22×C7#57811yescharacteristic
395C4×C7—22no—
396C4×C7—22no—
397C4×C7—22no—
398C4×C7—22no—
399C4×C7—22no—
400C4×C7C4×#4111yescharacteristic
401C4×C7C4×#4111yescharacteristic
402C4×C7#53311yescharacteristic
403C4×C7#53311yescharacteristic
404Dic7—42no—
405Dic7—42no—
406Dic7—42no—
407Dic7—42no—
408Dic7—81no—
409Dic7—81no—
410Dic7—81no—
411Dic7—81no—
412C24C2×D2811yescharacteristic
413C22×C4—21no—
414C22×C4—21no—
415C22×C4—21no—
416C22×C4—21no—
417C22×C4—141no—
418C22×C4—141no—
419C22×C4—141no—
420C22×C4—141no—
421C22×C4—144no—
422C22×C4—141no—
423C22×C4—141no—
424C22×C4—141no—
425C22×C4—141no—
426C22×C4—561no—
427C22×C4—561no—
428C22×C4C2×Dic1412yes—
429C22×C4C2×D2811yescharacteristic
430C22×C4C2×D2811yescharacteristic
431C22×C4C2×D2811yescharacteristic
432C22×C4C2×D2811yescharacteristic
433C22×C4C2×D2811yescharacteristic
434C22×C4C22×Dic712yes—
435C22×C4C23×D711yescharacteristic
436C2×C8—21no—
437C2×C8—21no—
438C2×C8—21no—
439C2×C8—21no—
440C2×C8—21no—
441C2×C8—21no—
442C2×C8—21no—
443C2×C8—21no—
444C2×C8C22×Dic712yes—
445C2×C8C22×Dic712yes—
446C2×C8C22×Dic712yes—
447C2×C8C22×Dic712yes—
448C4⋊C4—72no—
449C4⋊C4—72no—
450C4⋊C4—72no—
451C4⋊C4—72no—
452C4⋊C4—144no—
453C4⋊C4—141no—
454C4⋊C4—141no—
455C4⋊C4—141no—
456C4⋊C4—141no—
457C4⋊C4—141no—
458C4⋊C4—141no—
459C4⋊C4—141no—
460C4⋊C4—141no—
461C4⋊C4—141no—
462C4⋊C4—141no—
463C4⋊C4—141no—
464C4⋊C4—141no—
465C4⋊C4—561no—
466C4⋊C4—561no—
467C4⋊C4C4⋊Dic714yes—
468C4⋊C4C4⋊Dic714yes—
469C22⋊C4—144no—
470C22⋊C4—561no—
471C22⋊C4—561no—
472C22⋊C4C4⋊Dic714yes—
473C22⋊C4C4⋊Dic714yes—
474C42—144no—
475C42—561no—
476C42—561no—
477C42—561no—
478C42—561no—
479C42—561no—
480C42—561no—
481C42C2×Dic1412yes—
482C42C2×Dic1412yes—
483C42C22×Dic712yes—
484C42C22×Dic712yes—
485C2×C7—42no—
486C2×C7#229611yescharacteristic
487C2×C7#291211yescharacteristic
488C2×C7#291311yescharacteristic
489C2×C7#311811yescharacteristic
490C2×C7#311911yescharacteristic
491C2×C7#312011yescharacteristic
492C2×C7#312111yescharacteristic
493C23—21no—
494C23—21no—
495C23—21no—
496C23—21no—
497C23—21no—
498C23—21no—
499C23C2×C4⋊Dic712yes—
500C23C22×D2811yescharacteristic
501C2×C4—21no—
502C2×C4—21no—
503C2×C4—21no—
504C2×C4—21no—
505C2×C4—21no—
506C2×C4—21no—
507C2×C4—21no—
508C2×C4—21no—
509C2×C4—21no—
510C2×C4—21no—
511C2×C4—22no—
512C2×C4—22no—
513C2×C4—22no—
514C2×C4—22no—
515C2×C4—142no—
516C2×C4—142no—
517C2×C4—142no—
518C2×C4—142no—
519C2×C4—281no—
520C2×C4—281no—
521C2×C4—281no—
522C2×C4—281no—
523C2×C4—281no—
524C2×C4—281no—
525C2×C4—281no—
526C2×C4—281no—
527C2×C4—281no—
528C2×C4—281no—
529C2×C4—281no—
530C2×C4—281no—
531C2×C4—281no—
532C2×C4—281no—
533C2×C4—281no—
534C2×C4—281no—
535C2×C4—281no—
536C2×C4—281no—
537C2×C4—281no—
538C2×C4—281no—
539C2×C4—564no—
540C2×C4C2×C4⋊Dic712yes—
541C2×C4C2×C4⋊Dic712yes—
542C2×C4C2×C4⋊Dic712yes—
543C2×C4C2×C4⋊Dic712yes—
544C2×C4C2×C4⋊Dic712yes—
545C2×C4C22×Dic1411yescharacteristic
546C2×C4D7×#4111yescharacteristic
547C2×C4D7×#4111yescharacteristic
548C2×C4D7×#4111yescharacteristic
549C2×C4D7×#4111yescharacteristic
550C2×C4C23×Dic711yescharacteristic
551C8—22no—
552C8—22no—
553C8—22no—
554C8—22no—
555C7#2136711yescharacteristic, complemented, Sylow
556C22—22no—
557C22—22no—
558C22—22no—
559C22—41no—
560C22—41no—
561C22—41no—
562C22—41no—
563C22#9021511yescharacteristic
564C22#9021511yescharacteristic
565C22#9044211yescharacteristic
566C22#9044211yescharacteristic
567C22#9044311yescharacteristic
568C22#9044411yescharacteristic
569C22C22×C4⋊Dic711yescharacteristic
570C4—22no—
571C4—22no—
572C4—22no—
573C4—22no—
574C4—22no—
575C4—282no—
576C4—282no—
577C4—282no—
578C4—282no—
579C4—561no—
580C4—561no—
581C4—561no—
582C4—561no—
583C4#9020811yescharacteristic
584C4#9020811yescharacteristic
585C4#41×Dic711yescharacteristic
586C4#41×Dic711yescharacteristic
587C2—42no—
588C2#1173682811yescharacteristic
589C2#1173682911yescharacteristic
590C2#1173683011yescharacteristic
591C2#1173683911yescharacteristic
592C2#1173967211yescharacteristic
593C2#1174122911yescharacteristic
594C2#1174123011yescharacteristic
subgroupG/H
centerC23C22×D28
commutatorC2×C4×C7C23×C4
FrattiniC22×C4C23×D7
FittingC2×C7×#433C2
socleC23×C7C22×D4
prime radicalC24×C7C2×D4
cosocleC22×C4×C7C24
hypercenterC2×#433D7
hypocenterC7#21367
LCSG ▷ C2×C4×C7 ▷ C2×C7 ▷ C7
UCSC1 ◁ C23 ◁ C2×#117 ◁ C2×#433

Complements

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

NH ≅ G/Ntype
4. #11728209C2semidirect
5. #11728209C2semidirect
6. #11728208C2semidirect
7. #11728207C2semidirect
12. #11727568C2semidirect
13. #11727568C2semidirect
14. C4×#6392C2semidirect
15. C4×#6391C2semidirect
19. C7×#433C4semidirect
100. C7×C4⋊C8C2×C4semidirect
101. C7×C4⋊C8C2×C4semidirect
104. C7×#97C2×C4semidirect
105. C4×C7×C8C2×C4semidirect
215. #433Dic7semidirect
365. C4⋊C8C2×Dic7semidirect
366. C4⋊C8C2×Dic7semidirect
369. #97C2×Dic7semidirect
370. C4×C8C2×Dic7semidirect
555. C7#21367semidirect

Maximal subgroups

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

subgroupindex
C2×C7×#4332
#117396762
#117396682
#117282092
#117282082
#117282072
#117276832
#117276822
#117276812
#117275682
C4×#63922
C4×#63912
#213677