Finite Group Databasebeta

← #13372002

Subgroups — #13372002

Order 1792.

970 conjugacy classes of subgroups.

The subgroup lattice has 672 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#89633C211yesmaximal, characteristic, complemented
2C2×#89632C211yesmaximal, characteristic, complemented
3C2×#89608C211yesmaximal, characteristic
4#11731769C211yesmaximal, characteristic
5#11731216C211yesmaximal, characteristic
6C7×#1948C211yesmaximal, characteristic, complemented
7#11728334C211yesmaximal, characteristic, complemented
8#11728333C211yesmaximal, characteristic, complemented
9#11728209C211yesmaximal, characteristic, complemented
10#11727332C211yesmaximal, characteristic, complemented
11#11727235C211yesmaximal, characteristic, complemented
12#11726631C211yesmaximal, characteristic, complemented
13#11726630C211yesmaximal, characteristic, complemented
14#11726624C211yesmaximal, characteristic, complemented
15#11726622C211yesmaximal, characteristic, complemented
16C22×#1131C2211yescharacteristic
17C22×C8×D7C2211yescharacteristic
18C2×#6455C2211yescharacteristic
19C2×#6455C2211yescharacteristic
20C2×#6455C2211yescharacteristic
21C2×D7×C4⋊C4C2211yescharacteristic
22C2×C4×D28C2211yescharacteristic
23C2×C7×#106C2211yescharacteristic
24C2×C7×#106C2211yescharacteristic
25C2×C7×C4⋊C8C2211yescharacteristic
26C7×#384C2211yescharacteristic
27C4×C7×C4⋊C4C2211yescharacteristic
28C2×(C2×D7)⋊C8C2211yescharacteristic
29C2×(C2×D7)⋊C8C2211yescharacteristic
30C2×#6392C2211yescharacteristic
31C2×#6391C2211yescharacteristic
32#89762—21no—
33#89762—21no—
34#89760—21no—
35#89759C2211yescharacteristic
36#89759C2211yescharacteristic
37#89759C2211yescharacteristic
38#89759C2211yescharacteristic
39C4⋊C4×Dic7—21no—
40C2×#6382C2211yescharacteristic
41C2×#6382C2211yescharacteristic
42C2×#6382C2211yescharacteristic
43C2×#6381C2211yescharacteristic
44C2×#6381C2211yescharacteristic
45C2×#6381C2211yescharacteristic
46#89712—21no—
47C4×(C2×D7)⋊C4—21no—
48#89708C2211yescharacteristic
49C4×C4⋊Dic7C2211yescharacteristic
50C2×#6377C2211yescharacteristic
51#89633—24no—
52#89632—24no—
53#89608C418yescomplemented
54#89437—21no—
55#89425—21no—
56C7×#340C2211yescharacteristic
57C7×#340C2211yescharacteristic
58#89346C2211yescharacteristic
59#89346C2211yescharacteristic
60#89324C2211yescharacteristic
61#89324C2211yescharacteristic
62#22662—71nomaximal, Sylow
63C22×D28D411yescharacteristic
64C22×C4×D7—21no—
65C22×C4×D7C2311yescharacteristic
66C22×C4×D7C2311yescharacteristic
67C22×C7×C8C2311yescharacteristic
68C22×C7×C8C2311yescharacteristic
69C2×C7×C4⋊C4—21no—
70C2×C7×C4⋊C4—21no—
71C2×C7×C4⋊C4C2311yescharacteristic
72C2×C7×C4⋊C4C2311yescharacteristic
73C2×C7×C4⋊C4C2311yescharacteristic
74C2×C7×C4⋊C4C2311yescharacteristic
75C2×C42×C7—21no—
76C2×C42×C7C2311yescharacteristic
77C2×(C2×D7)⋊C4—21no—
78C2×(C2×D7)⋊C4—21no—
79C2×(C2×D7)⋊C4—21no—
80C2×(C2×D7)⋊C4—21no—
81C2×(C2×D7)⋊C4—21no—
82C2×(C2×D7)⋊C4—21no—
83C2×(C2×D7)⋊C4—21no—
84C2×(C2×D7)⋊C4D411yescharacteristic
85C2×(C2×D7)⋊C4D411yescharacteristic
86C2×C4⋊Dic7D411yescharacteristic
87C2×C4⋊Dic7C2311yescharacteristic
88C2×C4⋊Dic7C2311yescharacteristic
89C2×C4⋊Dic7C2311yescharacteristic
90C2×C4⋊Dic7C2311yescharacteristic
91C2×Dic7⋊C4—21no—
92C2×C4×Dic7—21no—
93C2×C4×Dic7—21no—
94C2×C4×Dic7—21no—
95C2×C4×Dic7—21no—
96C22×C7⋊C8C2311yescharacteristic
97C22×C7⋊C8C2311yescharacteristic
98C2×#1131—22no—
99C2×#1131—22no—
100C2×#1131C2×C414yes—
101C2×C8×D7—22no—
102C2×C8×D7—22no—
103C2×C8×D7C2×C414yescomplemented
104#6455—22no—
105#6455—22no—
106#6455—22no—
107#6455—41no—
108#6455—41no—
109#6455—41no—
110D7×C4⋊C4—22no—
111D7×C4⋊C4—41no—
112C4×D28C2×C414yes—
113C4×D28Q814yes—
114C7×#106—22no—
115C7×#106—22no—
116C7×C4⋊C8C2×C414yescomplemented
117C7×#95—21no—
118C7⋊#95—21no—
119C7⋊#95—21no—
120C7⋊#95—21no—
121C7⋊#95—21no—
122C7⋊#95—21no—
123C7⋊#95—21no—
124C7⋊#95—21no—
125(C2×D7)⋊C8C2×C414yes—
126(C2×D7)⋊C8C2×C414yescomplemented
127#6392—22no—
128#6391—22no—
129#6382—22no—
130#6382—22no—
131#6382—41no—
132#6381—22no—
133#6381—41no—
134#6381D414yescomplemented
135#6377C2×C414yescomplemented
136C2×#435—71no—
137C2×#428—71no—
138C2×#427—71no—
139#2354—71no—
140#2352—71no—
141#1949—71no—
142#1948D711yescharacteristic, complemented
143#1854—71no—
144#1854—71no—
145#1854—71no—
146#1853—71no—
147#1847—71no—
148#1809—71no—
149#1807—71no—
150#1776—71no—
151C23×D7C2×D411yescharacteristic
152C23×D7C2×D411yescharacteristic
153C22×C4×C7—21no—
154C22×C4×C7—21no—
155C22×C4×C7—21no—
156C22×C4×C7—21no—
157C22×C4×C7C2×D411yescharacteristic
158C22×C4×C7C2×D411yescharacteristic
159C22×C4×C7C2411yescharacteristic
160C22×Dic7—21no—
161C22×Dic7—21no—
162C22×Dic7—21no—
163C22×Dic7—21no—
164C22×Dic7C2×D411yescharacteristic
165C22×Dic7C2×D411yescharacteristic
166C2×D28—41no—
167C2×D28—41no—
168C2×D28C4⋊C414yes—
169C2×C4×D7—21no—
170C2×C4×D7—21no—
171C2×C4×D7—21no—
172C2×C4×D7—21no—
173C2×C4×D7—21no—
174C2×C4×D7—21no—
175C2×C4×D7—21no—
176C2×C4×D7—21no—
177C2×C4×D7—42no—
178C2×C4×D7—42no—
179C2×C4×D7—81no—
180C2×C4×D7C22×C412yes—
181C2×C4×D7C22×C412yes—
182C2×C4×D7C2×Q812yes—
183C2×C4×D7C2×Q812yes—
184C2×C7×C8—21no—
185C2×C7×C8—21no—
186C2×C7×C8—21no—
187C2×C7×C8—21no—
188C2×C7×C8C22×C412yes—
189C2×C7×C8C22×C412yes—
190C7×C4⋊C4—21no—
191C7×C4⋊C4—21no—
192C7×C4⋊C4—21no—
193C7×C4⋊C4—21no—
194C7×C4⋊C4—21no—
195C7×C4⋊C4—21no—
196C7×C4⋊C4—21no—
197C7×C4⋊C4—42no—
198C7×C4⋊C4—81no—
199C7×C4⋊C4C2×D412yes—
200C42×C7—81no—
201C42×C7C22×C412yes—
202C42×C7C2×Q812yes—
203(C2×D7)⋊C4—42no—
204(C2×D7)⋊C4—42no—
205(C2×D7)⋊C4—42no—
206(C2×D7)⋊C4—42no—
207(C2×D7)⋊C4—81no—
208(C2×D7)⋊C4—81no—
209(C2×D7)⋊C4—81no—
210(C2×D7)⋊C4C4⋊C414yes—
211(C2×D7)⋊C4C4⋊C414yes—
212C4⋊Dic7—21no—
213C4⋊Dic7—21no—
214C4⋊Dic7—21no—
215C4⋊Dic7—21no—
216C4⋊Dic7—21no—
217C4⋊Dic7—21no—
218C4⋊Dic7—21no—
219C4⋊Dic7C4⋊C414yes—
220C4⋊Dic7C2×D412yes—
221Dic7⋊C4—42no—
222C4×Dic7—42no—
223C4×Dic7—42no—
224C4×Dic7—42no—
225C4×Dic7—42no—
226C2×C7⋊C8—21no—
227C2×C7⋊C8—21no—
228C2×C7⋊C8C22×C412yes—
229C2×C7⋊C8C22×C412yes—
230C2×C7⋊C8C2×D412yes—
231C2×C7⋊C8#4112yes—
232#1131—28no—
233C8×D7—28no—
234C22×M16—71no—
235C23×C8—71no—
236C2×C4×D4—71no—
237C2×#117—71no—
238C2×#117—71no—
239C2×#117—71no—
240C22×C4⋊C4—71no—
241#435—78no—
242#428—144no—
243#427—144no—
244C2×#107—71no—
245C2×#107—71no—
246C2×#107—71no—
247C2×#107—71no—
248C2×#106—71no—
249C2×#106—71no—
250C2×#106—71no—
251C2×#106—71no—
252C2×#106C2×D711yescharacteristic
253C2×#106C2×D711yescharacteristic
254C2×C4⋊C8C2×D711yescharacteristic
255C2×C22⋊C8—71no—
256C2×C22⋊C8—71no—
257C2×#97—71no—
258#390—141no—
259#388—141no—
260#388—141no—
261#388—141no—
262#387—141no—
263#386—141no—
264#384C2×D711yescharacteristic
265#382—71no—
266#380—71no—
267#380—71no—
268#380—71no—
269#380—71no—
270C4×C4⋊C4—71no—
271C4×C4⋊C4—141no—
272C4×C4⋊C4C2×D711yescharacteristic
273C4×C22⋊C4—141no—
274#340—71no—
275#340—71no—
276#340—71no—
277#340—71no—
278#340C2×D711yescharacteristic
279#340C2×D711yescharacteristic
280C23×C7C22×D411yescharacteristic
281C22×D7—21no—
282C22×D7—21no—
283C22×D7—21no—
284C22×D7—21no—
285C22×D7—21no—
286C22×D7—21no—
287C22×D7—21no—
288C22×D7—21no—
289C22×D7—21no—
290C22×D7—21no—
291C22×D7—21no—
292C22×D7—21no—
293C22×D7C2×C4⋊C412yes—
294C22×D7C2×C4⋊C412yes—
295C2×C4×C7—21no—
296C2×C4×C7—21no—
297C2×C4×C7—21no—
298C2×C4×C7—21no—
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×C7—41no—
307C2×C4×C7—41no—
308C2×C4×C7—41no—
309C2×C4×C7—41no—
310C2×C4×C7—41no—
311C2×C4×C7C2×C4⋊C412yes—
312C2×C4×C7C2×C4⋊C412yes—
313C2×C4×C7C23×C411yescharacteristic
314C2×C4×C7C22×D411yescharacteristic
315C2×C4×C7C22×Q811yescharacteristic
316C2×C4×C7C2×#4111yescharacteristic
317C2×C4×C7H(5,𝔽2)11yescharacteristic
318C2×C4×C72−1+411yescharacteristic
319C2×Dic7—21no—
320C2×Dic7—21no—
321C2×Dic7—21no—
322C2×Dic7—21no—
323C2×Dic7—22no—
324C2×Dic7—41no—
325C2×Dic7—41no—
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×Dic7C2×C4⋊C412yes—
336C2×Dic7C2×C4⋊C412yes—
337D28—44no—
338C4×D7—22no—
339C4×D7—22no—
340C4×D7—22no—
341C4×D7—22no—
342C4×D7—22no—
343C4×D7—22no—
344C4×D7—22no—
345C4×D7—22no—
346C4×D7—84no—
347C7×C8—22no—
348C7×C8—22no—
349C7⋊C8—22no—
350C7⋊C8C4×D414yes—
351C22×D4—71no—
352C23×C4—71no—
353C23×C4—71no—
354C23×C4—141no—
355C2×M16—74no—
356C2×M16—142no—
357C2×M16—142no—
358C22×C8—71no—
359C22×C8—71no—
360C22×C8—74no—
361C22×C8—142no—
362C22×C8—142no—
363C22×C8C22×D711yescharacteristic
364C22×C8C22×D711yescharacteristic
365C4×D4—74no—
366C4×D4—74no—
367#117—142no—
368#117—142no—
369#117—142no—
370#117—281no—
371#117—281no—
372#117—281no—
373C2×C4⋊C4—21no—
374C2×C4⋊C4—21no—
375C2×C4⋊C4—71no—
376C2×C4⋊C4—71no—
377C2×C4⋊C4—71no—
378C2×C4⋊C4—71no—
379C2×C4⋊C4—71no—
380C2×C4⋊C4—142no—
381C2×C4⋊C4—141no—
382C2×C4⋊C4—281no—
383C2×C4⋊C4C22×D711yescharacteristic
384C2×C4⋊C4C22×D711yescharacteristic
385C2×C4⋊C4C22×D711yescharacteristic
386C2×C4⋊C4C22×D711yescharacteristic
387C2×C22⋊C4—71no—
388C2×C22⋊C4—71no—
389C2×C22⋊C4—141no—
390C2×C22⋊C4—141no—
391C2×C22⋊C4—141no—
392C2×C22⋊C4—141no—
393C2×C22⋊C4—141no—
394C2×C22⋊C4—141no—
395C2×C22⋊C4—141no—
396C2×C42—21no—
397C2×C42—141no—
398C2×C42—141no—
399C2×C42—141no—
400C2×C42—141no—
401C2×C42C22×D711yescharacteristic
402#107—74no—
403#107—142no—
404#107—142no—
405#107—281no—
406#106—22no—
407#106—22no—
408#106—142no—
409#106—142no—
410#106—142no—
411#106—281no—
412C4⋊C8C4×D714yescomplemented
413C22⋊C8—74no—
414C22⋊C8—74no—
415#97—74no—
416#95—21no—
417#95—141no—
418#95—141no—
419#95—141no—
420#95—141no—
421#95—141no—
422#95—141no—
423#95—141no—
424C22×C7C22×C4⋊C411yescharacteristic
425C22×C7D4211yescharacteristic
426C22×C7#54711yescharacteristic
427C22×C7#57511yescharacteristic
428C22×C7#57511yescharacteristic
429C22×C7#57711yescharacteristic
430C22×C7#57711yescharacteristic
431C2×D7—22no—
432C2×D7—22no—
433C2×D7—22no—
434C2×D7—22no—
435C2×D7—22no—
436C2×D7—22no—
437C2×D7—41no—
438C2×D7—41no—
439C2×D7—41no—
440C2×D7—41no—
441C2×D7—41no—
442C2×D7—41no—
443C2×D7—41no—
444C2×D7—41no—
445C4×C7—22no—
446C4×C7—22no—
447C4×C7—42no—
448C4×C7—81no—
449C4×C7—81no—
450C4×C7—81no—
451C4×C7C2×C4×D411yescharacteristic
452C4×C7#52011yescharacteristic
453C4×C7D4×Q811yescharacteristic
454C4×C7#55411yescharacteristic
455Dic7—22no—
456Dic7—22no—
457Dic7—42no—
458Dic7—81no—
459Dic7—81no—
460Dic7—81no—
461C24—71no—
462C24—71no—
463C2×D4—74no—
464C2×D4—281no—
465C2×D4—281no—
466C22×C4—21no—
467C22×C4—21no—
468C22×C4—21no—
469C22×C4—21no—
470C22×C4—71no—
471C22×C4—71no—
472C22×C4—72no—
473C22×C4—72no—
474C22×C4—72no—
475C22×C4—72no—
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—282no—
489C22×C4—282no—
490C22×C4—561no—
491C22×C4D4×D711yescharacteristic
492C22×C4D4×D711yescharacteristic
493C22×C4C23×D711yescharacteristic
494M16—148no—
495C2×C8—21no—
496C2×C8—21no—
497C2×C8—21no—
498C2×C8—21no—
499C2×C8—72no—
500C2×C8—72no—
501C2×C8—72no—
502C2×C8—72no—
503C2×C8—148no—
504C2×C8—141no—
505C2×C8—141no—
506C2×C8C2×C4×D712yes—
507C2×C8C2×C4×D712yes—
508C4⋊C4—21no—
509C4⋊C4—21no—
510C4⋊C4—21no—
511C4⋊C4—21no—
512C4⋊C4—21no—
513C4⋊C4—21no—
514C4⋊C4—21no—
515C4⋊C4—42no—
516C4⋊C4—74no—
517C4⋊C4—72no—
518C4⋊C4—81no—
519C4⋊C4—141no—
520C4⋊C4—141no—
521C4⋊C4—141no—
522C4⋊C4—141no—
523C4⋊C4—141no—
524C4⋊C4—141no—
525C4⋊C4—141no—
526C4⋊C4—282no—
527C4⋊C4D4×D712yes—
528C22⋊C4—74no—
529C22⋊C4—74no—
530C22⋊C4—282no—
531C22⋊C4—282no—
532C22⋊C4—282no—
533C22⋊C4—282no—
534C22⋊C4—561no—
535C22⋊C4—561no—
536C22⋊C4—561no—
537C42—81no—
538C42—282no—
539C42—282no—
540C42—282no—
541C42—282no—
542C42C2×C4×D712yes—
543C42Q8×D712yes—
544C2×C7D4×C4⋊C411yescharacteristic
545C2×C7#291111yescharacteristic
546C2×C7#291211yescharacteristic
547C2×C7#326711yescharacteristic
548C2×C7#327111yescharacteristic
549C2×C7#334811yescharacteristic
550C2×C7#335011yescharacteristic
551D7—42no—
552D7—42no—
553C23—72no—
554C23—72no—
555C23—141no—
556C23—141no—
557C23—141no—
558C23—141no—
559C23—141no—
560C23—141no—
561C23—141no—
562C23—141no—
563C23—141no—
564C23—141no—
565C23—141no—
566C23—141no—
567C23C2×D4×D711yescharacteristic
568D4—284no—
569C2×C4—21no—
570C2×C4—21no—
571C2×C4—21no—
572C2×C4—21no—
573C2×C4—22no—
574C2×C4—41no—
575C2×C4—41no—
576C2×C4—41no—
577C2×C4—41no—
578C2×C4—41no—
579C2×C4—41no—
580C2×C4—41no—
581C2×C4—41no—
582C2×C4—41no—
583C2×C4—41no—
584C2×C4—41no—
585C2×C4—72no—
586C2×C4—72no—
587C2×C4—141no—
588C2×C4—141no—
589C2×C4—141no—
590C2×C4—141no—
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—281no—
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—564no—
612C2×C4D7×C4⋊C412yes—
613C2×C4D7×C4⋊C412yes—
614C2×C4C22×C4×D711yescharacteristic
615C2×C4C2×D4×D711yescharacteristic
616C2×C4C2×Q8×D711yescharacteristic
617C2×C4#655111yescharacteristic
618C2×C4D7×#4111yescharacteristic
619C2×C4#655311yescharacteristic
620C8—22no—
621C8—22no—
622C8—74no—
623C8—142no—
624C7#2266211yescharacteristic, complemented, Sylow
625C22—142no—
626C22—142no—
627C22—142no—
628C22—142no—
629C22—142no—
630C22—142no—
631C22—281no—
632C22—281no—
633C22—281no—
634C22—281no—
635C22—281no—
636C22—281no—
637C22—281no—
638C22—281no—
639C22C2×D7×C4⋊C411yescharacteristic
640C22#9030011yescharacteristic
641C22#9032211yescharacteristic
642C22#9045311yescharacteristic
643C22#9045311yescharacteristic
644C22#9046411yescharacteristic
645C22#9046811yescharacteristic
646C4—22no—
647C4—22no—
648C4—42no—
649C4—81no—
650C4—81no—
651C4—81no—
652C4—142no—
653C4—142no—
654C4—282no—
655C4—561no—
656C4—561no—
657C4—561no—
658C4C4×D4×D711yescharacteristic
659C4#9026511yescharacteristic
660C4#9038111yescharacteristic
661C4#9041811yescharacteristic
662C2—282no—
663C2—282no—
664C2#1173364711yescharacteristic
665C2#1173656111yescharacteristic
666C2#1173665311yescharacteristic
667C2#1173785211yescharacteristic
668C2#1173789011yescharacteristic
669C2#1173847611yescharacteristic
670C2#1173852911yescharacteristic
subgroupG/H
centerC23C2×D4×D7
commutatorC2×C4×C7C23×C4
FrattiniC22×C4C23×D7
FittingC7×#1948C2
socleC23×C7C22×D4
prime radicalC22×D28D4
cosocleC22×C4×C7C24
hypercenter#1948D7
hypocenterC7#22662
LCSG ▷ C2×C4×C7 ▷ C2×C7 ▷ C7
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1948

Complements

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

NH ≅ G/Ntype
1. C2×#89633C2semidirect
2. C2×#89632C2semidirect
6. C7×#1948C2semidirect
7. #11728334C2semidirect
8. #11728333C2semidirect
9. #11728209C2semidirect
10. #11727332C2semidirect
11. #11727235C2semidirect
12. #11726631C2semidirect
13. #11726630C2semidirect
14. #11726624C2semidirect
15. #11726622C2semidirect
53. #89608C4semidirect
103. C2×C8×D7C2×C4semidirect
116. C7×C4⋊C8C2×C4semidirect
126. (C2×D7)⋊C8C2×C4semidirect
134. #6381D4semidirect
135. #6377C2×C4semidirect
142. #1948D7semidirect
412. C4⋊C8C4×D7semidirect
624. C7#22662semidirect

Maximal subgroups

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

subgroupindex
C2×#896332
C2×#896322
C2×#896082
#117317692
#117312162
C7×#19482
#117283342
#117283332
#117282092
#117273322
#117272352
#117266312
#117266302
#117266242
#117266222
#226627