Finite Group Databasebeta

← #13382867

Subgroups — #13382867

Order 1792.

874 conjugacy classes of subgroups.

The subgroup lattice has 620 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×D7×#106C211yesmaximal, characteristic
2C2×#89611C211yesmaximal, characteristic
3#11733413C211yesmaximal, characteristic
4#11733413C211yesmaximal, characteristic
5C7×#2088C211yesmaximal, characteristic, complemented
6#11728322C211yesmaximal, characteristic, complemented
7#11728218C211yesmaximal, characteristic, complemented
8#11727378C211yesmaximal, characteristic, complemented
9#11727364C211yesmaximal, characteristic, complemented
10#11726621C211yesmaximal, characteristic
11#11726621C211yesmaximal, characteristic
12#11726620C211yesmaximal, characteristic
13#11726595C211yesmaximal, characteristic, complemented
14#11726594C211yesmaximal, characteristic, complemented
15#11726563C211yesmaximal, characteristic, complemented
16C22×#1131C2211yescharacteristic
17C22×C8×D7C2211yescharacteristic
18C2×#6455C2211yescharacteristic
19C2×#6455C2211yescharacteristic
20C2×D7×C4⋊C4C2211yescharacteristic
21C2×D7×C4⋊C4C2211yescharacteristic
22C2×#6435C2211yescharacteristic
23C2×C7×#106C2211yescharacteristic
24C2×C7×C4⋊C8C2211yescharacteristic
25C7×#389C2211yescharacteristic
26C7×#389C2211yescharacteristic
27C2×#6391C2211yescharacteristic
28C2×Dic7⋊C8C2211yescharacteristic
29C2×Dic7⋊C8C2211yescharacteristic
30#89761—21no—
31#89761—21no—
32#89757C2211yescharacteristic
33#89757C2211yescharacteristic
34#89748—21no—
35#89748—21no—
36#89745C2211yescharacteristic
37#89745C2211yescharacteristic
38C2×#6382C2211yescharacteristic
39C2×#6382C2211yescharacteristic
40#89700C2211yescharacteristic
41#89700C2211yescharacteristic
42C2×C4⋊(C7⋊C8)C2211yescharacteristic
43D7×#106—24no—
44#89611—24no—
45#89440—21no—
46#89440—21no—
47#89422—21no—
48#89422—21no—
49C7×#340C2211yescharacteristic
50C7×#340C2211yescharacteristic
51C7×#340C2211yescharacteristic
52#89346C2211yescharacteristic
53#89346C2211yescharacteristic
54#89346C2211yescharacteristic
55#89324C2211yescharacteristic
56#89324C2211yescharacteristic
57#89324C2211yescharacteristic
58#89324C2211yescharacteristic
59#89324C2211yescharacteristic
60#89324C2211yescharacteristic
61#23668—71nomaximal, Sylow
62C22×C4×D7—21no—
63C22×C4×D7—21no—
64C22×C4×D7C2311yescharacteristic
65C22×C7×C8C2311yescharacteristic
66C22×C7×C8C2311yescharacteristic
67C2×C7×C4⋊C4—21no—
68C2×C7×C4⋊C4—21no—
69C2×C7×C4⋊C4C2311yescharacteristic
70C2×C7×C4⋊C4C2311yescharacteristic
71C2×C7×C4⋊C4C2311yescharacteristic
72C2×C7×C4⋊C4C2311yescharacteristic
73C2×C42×C7C2311yescharacteristic
74C2×(C2×D7)⋊C4—21no—
75C2×(C2×D7)⋊C4—21no—
76C2×(C2×D7)⋊C4D411yescharacteristic
77C2×(C2×D7)⋊C4D411yescharacteristic
78C2×C4⋊Dic7—21no—
79C2×C4⋊Dic7—21no—
80C2×C4⋊Dic7C2311yescharacteristic
81C2×C4⋊Dic7C2311yescharacteristic
82C2×C4⋊Dic7C2311yescharacteristic
83C2×C4⋊Dic7C2311yescharacteristic
84C2×Dic7⋊C4—21no—
85C2×Dic7⋊C4—21no—
86C2×Dic7⋊C4—21no—
87C2×Dic7⋊C4—21no—
88C2×Dic7⋊C4—21no—
89C2×Dic7⋊C4—21no—
90C2×Dic7⋊C4D411yescharacteristic
91C2×Dic7⋊C4D411yescharacteristic
92C2×C4×Dic7—21no—
93C2×C4×Dic7—21no—
94C2×C4×Dic7C2311yescharacteristic
95C22×C7⋊C8C2311yescharacteristic
96C22×C7⋊C8C2311yescharacteristic
97C2×#1131—22no—
98C2×#1131—22no—
99C2×#1131—22no—
100C2×C8×D7—22no—
101C2×C8×D7—22no—
102C2×C8×D7D414yes—
103#6455—22no—
104#6455—22no—
105#6455Q814yes—
106#6455Q814yes—
107D7×C4⋊C4—22no—
108D7×C4⋊C4—22no—
109D7×C4⋊C4—22no—
110D7×C4⋊C4—22no—
111#6435—22no—
112#6435—22no—
113C7×#106—22no—
114C7×C4⋊C8—22no—
115C7×#95—21no—
116C7×#95—21no—
117C7⋊#95—21no—
118C7⋊#95—21no—
119C7⋊#95—21no—
120C7⋊#95—21no—
121C7⋊#95—21no—
122C7⋊#95—21no—
123#6391—22no—
124Dic7⋊C8—22no—
125Dic7⋊C8—22no—
126#6382—22no—
127#6382—22no—
128C4⋊(C7⋊C8)—22no—
129C22×#106—71no—
130C2×#424—71no—
131#2317—71no—
132#2317—71no—
133#2088—71no—
134#2088—71no—
135#2088—71no—
136#2088—71no—
137#2088—71no—
138#2088—71no—
139#2088—71no—
140#2088D711yescharacteristic, complemented
141#1736—71no—
142#1736—71no—
143#1735—71no—
144C23×D7C2×D411yescharacteristic
145C22×C4×C7—21no—
146C22×C4×C7—21no—
147C22×C4×C7—21no—
148C22×C4×C7—21no—
149C22×C4×C7C2×D411yescharacteristic
150C22×C4×C7C2×D411yescharacteristic
151C22×C4×C7C2411yescharacteristic
152C22×Dic7—21no—
153C22×Dic7—21no—
154C22×Dic7—21no—
155C22×Dic7—21no—
156C22×Dic7C2×D411yescharacteristic
157C22×Dic7C2×D411yescharacteristic
158C22×Dic7C2×D411yescharacteristic
159C2×C4×D7—42no—
160C2×C4×D7—42no—
161C2×C4×D7—81no—
162C2×C4×D7—81no—
163C2×C4×D7—81no—
164C2×C4×D7—81no—
165C2×C4×D7C2×D412yes—
166C2×C4×D7C2×Q812yes—
167C2×C4×D7C2×Q812yes—
168C2×C4×D7#4112yes—
169C2×C4×D7#4112yes—
170C2×C4×D7#4112yes—
171C2×C7×C8—21no—
172C2×C7×C8—21no—
173C2×C7×C8—21no—
174C2×C7×C8—21no—
175C2×C7×C8—21no—
176C2×C7×C8C2×D412yes—
177C7×C4⋊C4—21no—
178C7×C4⋊C4—21no—
179C7×C4⋊C4—21no—
180C7×C4⋊C4—21no—
181C7×C4⋊C4—21no—
182C7×C4⋊C4—21no—
183C7×C4⋊C4—81no—
184C7×C4⋊C4—81no—
185C7×C4⋊C4C2×Q812yes—
186C7×C4⋊C4C2×Q812yes—
187C42×C7—21no—
188C42×C7—21no—
189(C2×D7)⋊C4—22no—
190(C2×D7)⋊C4—22no—
191(C2×D7)⋊C4—24no—
192(C2×D7)⋊C4—24no—
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⋊Dic7C2×Q812yes—
202C4⋊Dic7C2×Q812yes—
203Dic7⋊C4—22no—
204Dic7⋊C4—22no—
205Dic7⋊C4—42no—
206Dic7⋊C4—42no—
207Dic7⋊C4—81no—
208Dic7⋊C4—81no—
209Dic7⋊C4—81no—
210Dic7⋊C4—81no—
211C4×Dic7—21no—
212C4×Dic7—21no—
213C4×Dic7—24no—
214C4×Dic7—24no—
215C2×C7⋊C8—21no—
216C2×C7⋊C8—21no—
217C2×C7⋊C8—21no—
218C2×C7⋊C8—21no—
219C2×C7⋊C8—21no—
220C2×C7⋊C8C2×D412yes—
221#1131—44no—
222C8×D7—28no—
223C22×M16—71no—
224C23×C8—71no—
225C2×#117—71no—
226C2×#117—71no—
227C2×#117—71no—
228C22×C4⋊C4—71no—
229C22×C4⋊C4—71no—
230C2×#106—71no—
231C2×#106—71no—
232C2×#106—71no—
233C2×#106—144no—
234C2×#106C2×D711yescharacteristic
235#424—144no—
236C2×C4⋊C8—71no—
237C2×C4⋊C8—71no—
238C2×C4⋊C8—71no—
239C2×C4⋊C8C2×D711yescharacteristic
240#389—71no—
241#389—71no—
242#389—71no—
243#389—71no—
244#389—71no—
245#389—71no—
246#389C2×D711yescharacteristic
247#389C2×D711yescharacteristic
248#385—141no—
249#385—141no—
250#385—141no—
251#385—141no—
252#384—141no—
253#384—141no—
254#382—141no—
255#382—141no—
256#340—71no—
257#340—71no—
258#340—71no—
259#340—71no—
260#340—71no—
261#340—71no—
262#340—71no—
263#340—71no—
264#340—71no—
265#340C2×D711yescharacteristic
266#340C2×D711yescharacteristic
267#340C2×D711yescharacteristic
268C23×C7C22×D411yescharacteristic
269C22×D7—21no—
270C22×D7—21no—
271C22×D7—21no—
272C22×D7—21no—
273C22×D7#12112yes—
274C22×D7C22⋊Q812yes—
275C22×D7C22⋊Q812yes—
276C2×C4×C7—21no—
277C2×C4×C7—21no—
278C2×C4×C7—22no—
279C2×C4×C7—22no—
280C2×C4×C7—21no—
281C2×C4×C7—21no—
282C2×C4×C7—21no—
283C2×C4×C7—21no—
284C2×C4×C7—41no—
285C2×C4×C7—41no—
286C2×C4×C7—41no—
287C2×C4×C7—41no—
288C2×C4×C7—41no—
289C2×C4×C7—41no—
290C2×C4×C7—41no—
291C2×C4×C7—41no—
292C2×C4×C7—41no—
293C2×C4×C7—41no—
294C2×C4×C7C22×D411yescharacteristic
295C2×C4×C7C22×Q811yescharacteristic
296C2×C4×C7C22×Q811yescharacteristic
297C2×C4×C7C2×#4111yescharacteristic
298C2×C4×C7C2×#4111yescharacteristic
299C2×C4×C7C2×#4111yescharacteristic
300C2×Dic7—21no—
301C2×Dic7—21no—
302C2×Dic7—22no—
303C2×Dic7—22no—
304C2×Dic7—21no—
305C2×Dic7—21no—
306C2×Dic7—21no—
307C2×Dic7—21no—
308C2×Dic7—41no—
309C2×Dic7—41no—
310C2×Dic7—41no—
311C2×Dic7—41no—
312C2×Dic7—41no—
313C2×Dic7—41no—
314C2×Dic7—41no—
315C2×Dic7—41no—
316C2×Dic7—41no—
317C2×Dic7—41no—
318C2×Dic7#12112yes—
319C2×Dic7C22⋊Q812yes—
320C2×Dic7C22⋊Q812yes—
321C4×D7—84no—
322C4×D7—84no—
323C4×D7#12314yes—
324C4×D7#12514yes—
325C4×D7#12514yes—
326C4×D7C4⋊Q814yes—
327C7×C8—22no—
328C7×C8—41no—
329C7⋊C8—22no—
330C7⋊C8—41no—
331C23×C4—71no—
332C23×C4—141no—
333C23×C4—141no—
334C2×M16—142no—
335C2×M16—142no—
336C2×M16—142no—
337C22×C8—71no—
338C22×C8—74no—
339C22×C8—71no—
340C22×C8—142no—
341C22×C8—142no—
342C22×C8C22×D711yescharacteristic
343C22×C8C22×D711yescharacteristic
344#117—74no—
345#117—74no—
346#117—142no—
347#117—142no—
348#117—142no—
349#117—142no—
350C2×C4⋊C4—21no—
351C2×C4⋊C4—21no—
352C2×C4⋊C4—71no—
353C2×C4⋊C4—71no—
354C2×C4⋊C4—71no—
355C2×C4⋊C4—71no—
356C2×C4⋊C4—71no—
357C2×C4⋊C4—71no—
358C2×C4⋊C4—142no—
359C2×C4⋊C4—142no—
360C2×C4⋊C4—142no—
361C2×C4⋊C4—142no—
362C2×C4⋊C4—141no—
363C2×C4⋊C4—141no—
364C2×C4⋊C4—141no—
365C2×C4⋊C4—141no—
366C2×C4⋊C4—141no—
367C2×C4⋊C4—141no—
368C2×C4⋊C4—141no—
369C2×C4⋊C4—141no—
370C2×C4⋊C4C22×D711yescharacteristic
371C2×C4⋊C4C22×D711yescharacteristic
372C2×C4⋊C4C22×D711yescharacteristic
373C2×C4⋊C4C22×D711yescharacteristic
374C2×C22⋊C4—71no—
375C2×C22⋊C4—71no—
376C2×C22⋊C4—141no—
377C2×C22⋊C4—141no—
378C2×C42—71no—
379C2×C42—141no—
380C2×C42—141no—
381C2×C42C22×D711yescharacteristic
382#106—22no—
383#106—142no—
384#106—142no—
385#106—142no—
386C4⋊C8—22no—
387C4⋊C8—142no—
388C4⋊C8—142no—
389C4⋊C8—142no—
390#95—21no—
391#95—21no—
392#95—141no—
393#95—141no—
394#95—141no—
395#95—141no—
396#95—141no—
397#95—141no—
398C22×C7C2×#12111yescharacteristic
399C22×C7C2×C22⋊Q811yescharacteristic
400C22×C7C2×C22⋊Q811yescharacteristic
401C22×C7#57711yescharacteristic
402C22×C7#57711yescharacteristic
403C22×C7#57711yescharacteristic
404C22×C7#57711yescharacteristic
405C2×D7—22no—
406C2×D7—22no—
407C2×D7—22no—
408C2×D7—22no—
409C2×D7—22no—
410C2×D7—22no—
411C2×D7#39814yes—
412C4×C7—42no—
413C4×C7—42no—
414C4×C7—41no—
415C4×C7—41no—
416C4×C7—81no—
417C4×C7—81no—
418C4×C7C2×#12311yescharacteristic
419C4×C7C2×#12511yescharacteristic
420C4×C7C2×#12511yescharacteristic
421C4×C7C2×C4⋊Q811yescharacteristic
422Dic7—42no—
423Dic7—42no—
424Dic7—41no—
425Dic7—41no—
426Dic7—81no—
427Dic7—81no—
428Dic7#39814yes—
429C24—71no—
430C22×C4—21no—
431C22×C4—21no—
432C22×C4—21no—
433C22×C4—21no—
434C22×C4—71no—
435C22×C4—72no—
436C22×C4—72no—
437C22×C4—72no—
438C22×C4—72no—
439C22×C4—72no—
440C22×C4—72no—
441C22×C4—71no—
442C22×C4—71no—
443C22×C4—141no—
444C22×C4—141no—
445C22×C4—141no—
446C22×C4—141no—
447C22×C4—282no—
448C22×C4—282no—
449C22×C4—561no—
450C22×C4—561no—
451C22×C4—561no—
452C22×C4—561no—
453C22×C4D4×D711yescharacteristic
454C22×C4D4×D711yescharacteristic
455C22×C4C23×D711yescharacteristic
456M16—284no—
457C2×C8—21no—
458C2×C8—21no—
459C2×C8—21no—
460C2×C8—21no—
461C2×C8—21no—
462C2×C8—72no—
463C2×C8—148no—
464C2×C8—141no—
465C2×C8—141no—
466C2×C8—141no—
467C2×C8—141no—
468C2×C8—141no—
469C2×C8D4×D712yes—
470C4⋊C4—21no—
471C4⋊C4—21no—
472C4⋊C4—21no—
473C4⋊C4—21no—
474C4⋊C4—21no—
475C4⋊C4—21no—
476C4⋊C4—72no—
477C4⋊C4—72no—
478C4⋊C4—81no—
479C4⋊C4—81no—
480C4⋊C4—142no—
481C4⋊C4—142no—
482C4⋊C4—141no—
483C4⋊C4—141no—
484C4⋊C4—141no—
485C4⋊C4—141no—
486C4⋊C4—141no—
487C4⋊C4—141no—
488C4⋊C4—282no—
489C4⋊C4—282no—
490C4⋊C4—561no—
491C4⋊C4—561no—
492C4⋊C4—561no—
493C4⋊C4—561no—
494C4⋊C4—561no—
495C4⋊C4—561no—
496C4⋊C4Q8×D712yes—
497C4⋊C4Q8×D712yes—
498C22⋊C4—142no—
499C22⋊C4—142no—
500C22⋊C4—144no—
501C22⋊C4—144no—
502C42—21no—
503C42—21no—
504C42—144no—
505C42—144no—
506C42—141no—
507C42—141no—
508C2×C7C2×#39811yescharacteristic
509C2×C7#305711yescharacteristic
510C2×C7#305711yescharacteristic
511C2×C7#308411yescharacteristic
512C2×C7#308411yescharacteristic
513C2×C7#308411yescharacteristic
514C2×C7#308411yescharacteristic
515D7—24no—
516C23—72no—
517C23—72no—
518C23—72no—
519C23—141no—
520C23—141no—
521C23—141no—
522C23—141no—
523C23C2×D4×D711yescharacteristic
524C2×C4—21no—
525C2×C4—21no—
526C2×C4—21no—
527C2×C4—21no—
528C2×C4—21no—
529C2×C4—21no—
530C2×C4—22no—
531C2×C4—22no—
532C2×C4—41no—
533C2×C4—41no—
534C2×C4—41no—
535C2×C4—41no—
536C2×C4—41no—
537C2×C4—41no—
538C2×C4—41no—
539C2×C4—41no—
540C2×C4—41no—
541C2×C4—41no—
542C2×C4—72no—
543C2×C4—72no—
544C2×C4—72no—
545C2×C4—74no—
546C2×C4—74no—
547C2×C4—74no—
548C2×C4—74no—
549C2×C4—141no—
550C2×C4—141no—
551C2×C4—141no—
552C2×C4—141no—
553C2×C4—141no—
554C2×C4—141no—
555C2×C4—142no—
556C2×C4—142no—
557C2×C4—281no—
558C2×C4—281no—
559C2×C4—281no—
560C2×C4—281no—
561C2×C4—281no—
562C2×C4—281no—
563C2×C4—281no—
564C2×C4—281no—
565C2×C4—281no—
566C2×C4—281no—
567C2×C4—564no—
568C2×C4—564no—
569C2×C4C2×D4×D711yescharacteristic
570C2×C4C2×Q8×D711yescharacteristic
571C2×C4C2×Q8×D711yescharacteristic
572C2×C4D7×#4111yescharacteristic
573C2×C4D7×#4111yescharacteristic
574C2×C4D7×#4111yescharacteristic
575C8—22no—
576C8—41no—
577C8—142no—
578C8—281no—
579C7#2366811yescharacteristic, complemented, Sylow
580C22—74no—
581C22—142no—
582C22—142no—
583C22—142no—
584C22—142no—
585C22—142no—
586C22—142no—
587C22D7×#12111yescharacteristic
588C22D7×C22⋊Q811yescharacteristic
589C22D7×C22⋊Q811yescharacteristic
590C22#9045311yescharacteristic
591C22#9046111yescharacteristic
592C22#9046611yescharacteristic
593C22#9046911yescharacteristic
594C4—41no—
595C4—42no—
596C4—41no—
597C4—42no—
598C4—74no—
599C4—81no—
600C4—81no—
601C4—282no—
602C4—282no—
603C4—281no—
604C4—281no—
605C4—561no—
606C4—561no—
607C4D7×#12311yescharacteristic
608C4D7×#12511yescharacteristic
609C4D7×#12511yescharacteristic
610C4D7×C4⋊Q811yescharacteristic
611C2—144no—
612C2D7×#39811yescharacteristic
613C2#1173810411yescharacteristic
614C2#1173825211yescharacteristic
615C2#1173845911yescharacteristic
616C2#1173850811yescharacteristic
617C2#1173861611yescharacteristic
618C2#1173868011yescharacteristic
subgroupG/H
centerC23C2×D4×D7
commutator, cosocleC22×C4×C7C24
FrattiniC22×C4C23×D7
FittingC7×#2088C2
socleC23×C7C22×D4
prime radicalC23×D7C2×D4
hypercenter#2088D7
hypocenterC7#23668
LCSG ▷ C22×C4×C7 ▷ C2×C7 ▷ C7
UCSC1 ◁ C23 ◁ C2×C42 ◁ #2088

Complements

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

NH ≅ G/Ntype
5. C7×#2088C2semidirect
6. #11728322C2semidirect
7. #11728218C2semidirect
8. #11727378C2semidirect
9. #11727364C2semidirect
13. #11726595C2semidirect
14. #11726594C2semidirect
15. #11726563C2semidirect
140. #2088D7semidirect
579. C7#23668semidirect

Maximal subgroups

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

subgroupindex
C2×D7×#1062
C2×#896112
#117334132
C7×#20882
#117283222
#117282182
#117273782
#117273642
#117266212
#117266202
#117265952
#117265942
#117265632
#236687