Finite Group Databasebeta

← #13319604

Subgroups — #13319604

Order 1792.

1314 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×C4×#1159C211yesmaximal, characteristic
2C2×#89490C212yesmaximal, complemented
3C7×#1459C211yesmaximal, characteristic, complemented
4#11729354C211yesmaximal, characteristic, complemented
5#11727673C212yesmaximal, complemented
6#11725879C212yesmaximal, complemented
7#11725878C212yesmaximal, complemented
8#11725855C212yesmaximal, complemented
9#11725854C212yesmaximal, complemented
10C22×#1159C411yescharacteristic
11C2×C4×C7×D4C2211yescharacteristic
12C2×D4×Dic7C411yescharacteristic
13C2×C4×C22⋊D7C411yescharacteristic
14C2×C4×C22⋊D7C2211yescharacteristic
15C22×C4×Dic7C411yescharacteristic
16C22×C4×Dic7C2211yescharacteristic
17C4×#1159—22no—
18C4×#1159—22no—
19C4×#1159—22no—
20C4×#1159—22no—
21C2×#6455C2211yescharacteristic
22C2×#6450C2211yescharacteristic
23C2×(C22⋊D7)⋊C4C411yescharacteristic
24C2×(C22⋊D7)⋊C4C2211yescharacteristic
25C2×#6440C411yescharacteristic
26C2×#6440C2211yescharacteristic
27C2×C42×D7C411yescharacteristic
28C2×C4×Dic14C411yescharacteristic
29C2×C7×C22⋊C8C2212yes—
30C2×C22⋊(C7⋊C8)C2212yes—
31C2×Dic7⋊C8—22no—
32C2×C8×Dic7—22no—
33#89490—22no—
34#89490—22no—
35#89490C2214yes—
36#89490C2214yes—
37C7×#324C2212yes—
38C7×#323C2212yes—
39#89323C2212yes—
40#89320C2212yes—
41#89264C2214yes—
42#89263C2214yes—
43#17349—71nomaximal, Sylow
44C22×C7×D4C2×C411yescharacteristic
45C23×C4×C7C2×C411yescharacteristic
46C23×C4×C7C2311yescharacteristic
47C22×C22⋊D7C2×C411yescharacteristic
48C22×C22⋊D7C2×C411yescharacteristic
49C23×Dic7C2×C411yescharacteristic
50C23×Dic7C2×C411yescharacteristic
51C23×Dic7C2×C411yescharacteristic
52C23×Dic7C2×C411yescharacteristic
53C2×#1159—22no—
54C2×#1159—22no—
55C2×#1159—24no—
56C2×#1159C818yescomplemented
57C22×C4×D7C2×C411yescharacteristic
58C22×C4×D7C2×C411yescharacteristic
59C22×C4×D7C2×C411yescharacteristic
60C22×Dic14C2×C411yescharacteristic
61C22×C7×C8—22no—
62C4×C7×D4—22no—
63C4×C7×D4—22no—
64C2×C7×C4⋊C4C2311yescharacteristic
65C2×C7×C22⋊C4C2×C411yescharacteristic
66C2×C7×C22⋊C4C2311yescharacteristic
67C2×C42×C7C2×C411yescharacteristic
68C2×C22⋊Dic7C2×C411yescharacteristic
69C2×C22⋊Dic7C2×C411yescharacteristic
70D4×Dic7—22no—
71D4×Dic7—22no—
72C4×C22⋊D7—22no—
73C4×C22⋊D7—22no—
74C4×C22⋊D7—22no—
75C4×C22⋊D7—22no—
76C2×(C2×D7)⋊C4C2×C411yescharacteristic
77C2×(C2×D7)⋊C4C2311yescharacteristic
78C2×C4⋊Dic7C2×C411yescharacteristic
79C2×Dic7⋊C4C2×C411yescharacteristic
80C2×Dic7⋊C4C2×C411yescharacteristic
81C2×Dic7⋊C4C2×C411yescharacteristic
82C2×Dic7⋊C4C2311yescharacteristic
83C2×C4×Dic7—21no—
84C2×C4×Dic7—21no—
85C2×C4×Dic7—21no—
86C2×C4×Dic7—21no—
87C2×C4×Dic7C2×C411yescharacteristic
88C2×C4×Dic7C2×C411yescharacteristic
89C2×C4×Dic7C2×C411yescharacteristic
90C2×C4×Dic7C2×C411yescharacteristic
91C2×C4×Dic7C2×C411yescharacteristic
92C2×C4×Dic7C2×C411yescharacteristic
93C2×C4×Dic7C2×C411yescharacteristic
94C2×C4×Dic7D412yes—
95C2×C4×Dic7D412yes—
96C2×C4×Dic7D412yes—
97C2×C4×Dic7D412yes—
98C2×C4×Dic7C2311yescharacteristic
99C2×C4×Dic7C2311yescharacteristic
100C22×C7⋊C8—22no—
101#6455—22no—
102#6455—22no—
103#6450—22no—
104#6450—22no—
105(C22⋊D7)⋊C4—22no—
106(C22⋊D7)⋊C4—22no—
107(C22⋊D7)⋊C4—22no—
108(C22⋊D7)⋊C4—22no—
109#6440—22no—
110#6440—22no—
111#6440—22no—
112#6440—22no—
113C42×D7—21no—
114C42×D7—21no—
115C42×D7—21no—
116C42×D7—21no—
117C4×Dic14—22no—
118C4×Dic14—22no—
119C7×C22⋊C8—22no—
120C7×C22⋊C8C2314yes—
121C22⋊(C7⋊C8)—22no—
122C22⋊(C7⋊C8)C2314yes—
123Dic7⋊C8—24no—
124Dic7⋊C8—24no—
125C8×Dic7—24no—
126C8×Dic7—24no—
127C2×C4×#41—71no—
128C2×#431—72no—
129#1461—72no—
130#1460—72no—
131#1459—72no—
132#1459—71no—
133#1459D711yescharacteristic, complemented
134#1458—72no—
135#1458—72no—
136C24×C7C22×C411yescharacteristic
137C24×C7C22×C411yescharacteristic
138C23×D7C22×C411yescharacteristic
139C2×C7×D4—22no—
140C2×C7×D4—22no—
141C2×C7×D4C2×C814yes—
142C22×C4×C7—21no—
143C22×C4×C7—21no—
144C22×C4×C7—42no—
145C22×C4×C7—42no—
146C22×C4×C7C22×C411yescharacteristic
147C22×C4×C7C22×C411yescharacteristic
148C22×C4×C7C22×C411yescharacteristic
149C22×C4×C7C22×C411yescharacteristic
150C22×C4×C7C2×D412yes—
151C22×C4×C7C2×D412yes—
152C22×C4×C7C2411yescharacteristic
153C2×C22⋊D7—22no—
154C2×C22⋊D7—22no—
155C2×C22⋊D7—22no—
156C2×C22⋊D7—22no—
157C2×C22⋊D7C2×C814yes—
158C2×C22⋊D7C2×C814yescomplemented
159C22×Dic7—21no—
160C22×Dic7—21no—
161C22×Dic7—22no—
162C22×Dic7—21no—
163C22×Dic7—21no—
164C22×Dic7—42no—
165C22×Dic7—42no—
166C22×Dic7C22⋊C412yes—
167C22×Dic7C22⋊C412yes—
168C22×Dic7C22⋊C412yes—
169C22×Dic7C22⋊C412yes—
170C22×Dic7C2×C814yes—
171C22×Dic7C2×C814yescomplemented
172C22×Dic7M1614yes—
173C22×Dic7C22×C411yescharacteristic
174C22×Dic7C22×C411yescharacteristic
175C22×Dic7C22×C411yescharacteristic
176C22×Dic7C22×C411yescharacteristic
177C22×Dic7C22×C411yescharacteristic
178C22×Dic7C22×C411yescharacteristic
179C22×Dic7C22×C411yescharacteristic
180#1159—216no—
181#1159—216no—
182C2×C4×D7—21no—
183C2×C4×D7—21no—
184C2×C4×D7—22no—
185C2×C4×D7—21no—
186C2×C4×D7—21no—
187C2×C4×D7—21no—
188C2×C4×D7—21no—
189C2×C4×D7—42no—
190C2×C4×D7—42no—
191C2×C4×D7C2×C814yescomplemented
192C2×Dic14—22no—
193C2×Dic14—22no—
194C2×Dic14C2×C814yescomplemented
195C2×C7×C8—24no—
196C2×C7×C8—44no—
197C7×C4⋊C4—22no—
198C7×C22⋊C4—22no—
199C7×C22⋊C4—22no—
200C42×C7—21no—
201C42×C7—21no—
202C22⋊Dic7—22no—
203C22⋊Dic7—22no—
204(C2×D7)⋊C4—22no—
205(C2×D7)⋊C4—22no—
206C4⋊Dic7—22no—
207Dic7⋊C4—22no—
208Dic7⋊C4—22no—
209Dic7⋊C4—22no—
210Dic7⋊C4—22no—
211C4×Dic7—21no—
212C4×Dic7—21no—
213C4×Dic7—21no—
214C4×Dic7—21no—
215C4×Dic7—21no—
216C4×Dic7—21no—
217C4×Dic7—21no—
218C4×Dic7—21no—
219C4×Dic7—21no—
220C4×Dic7—21no—
221C4×Dic7C22⋊C412yes—
222C4×Dic7C22⋊C412yes—
223C4×Dic7C22⋊C411yescharacteristic
224C4×Dic7C22⋊C411yescharacteristic
225C4×Dic7C22⋊C411yescharacteristic
226C4×Dic7C22⋊C411yescharacteristic
227C4×Dic7C2×D412yes—
228C4×Dic7C2×D412yes—
229C4×Dic7C2×D412yes—
230C4×Dic7C2×D412yes—
231C2×C7⋊C8—24no—
232C2×C7⋊C8—44no—
233C22×#41—71no—
234C4×#41—142no—
235C4×#41—142no—
236C4×#41—142no—
237C4×#41—142no—
238C2×C4×Q8—71no—
239C2×C4×Q8—71no—
240C2×C4×D4—71no—
241C2×C4×D4—71no—
242C2×C4×D4—71no—
243C2×C4×D4—71no—
244C2×C4×D4—71no—
245C2×C4×D4C2×D711yescharacteristic
246C2×#117—71no—
247C2×#117—71no—
248C2×#117—71no—
249C22×C42—71no—
250C22×C42—71no—
251C22×C42—71no—
252#431—74no—
253#431—74no—
254#431—142no—
255#431—142no—
256C2×C4⋊C8—142no—
257C2×C22⋊C8—72no—
258C2×C22⋊C8C2×D712yes—
259C2×C4×C8—142no—
260#324—72no—
261#324—74no—
262#324C2×D712yes—
263#323—72no—
264#323—74no—
265#323C2×D712yes—
266C23×C7—21no—
267C23×C7—21no—
268C23×C7—41no—
269C23×C7—41no—
270C23×C7—41no—
271C23×C7—41no—
272C23×C7C2×C22⋊C412yes—
273C23×C7C22×C812yes—
274C23×C7C22×C812yes—
275C23×C7C2×M1612yes—
276C23×C7C23×C411yescharacteristic
277C22×D7—21no—
278C22×D7—21no—
279C22×D7—41no—
280C22×D7—41no—
281C22×D7C22×C812yes—
282C7×D4—28no—
283C2×C4×C7—21no—
284C2×C4×C7—21no—
285C2×C4×C7—24no—
286C2×C4×C7—22no—
287C2×C4×C7—21no—
288C2×C4×C7—21no—
289C2×C4×C7—42no—
290C2×C4×C7—41no—
291C2×C4×C7—42no—
292C2×C4×C7—42no—
293C2×C4×C7—41no—
294C2×C4×C7—41no—
295C2×C4×C7C2×C22⋊C411yescharacteristic
296C2×C4×C7C2×C22⋊C411yescharacteristic
297C2×C4×C7C22×C812yes—
298C2×C4×C7C22×D412yes—
299C22⋊D7—28no—
300C22⋊D7—28no—
301C2×Dic7—21no—
302C2×Dic7—21no—
303C2×Dic7—24no—
304C2×Dic7—24no—
305C2×Dic7—22no—
306C2×Dic7—24no—
307C2×Dic7—21no—
308C2×Dic7—21no—
309C2×Dic7—42no—
310C2×Dic7—41no—
311C2×Dic7—42no—
312C2×Dic7—42no—
313C2×Dic7—41no—
314C2×Dic7—41no—
315C2×Dic7C22⋊C818yes—
316C2×Dic7C22⋊C818yes—
317C2×Dic7C2×C22⋊C411yescharacteristic
318C2×Dic7C2×C22⋊C412yes—
319C2×Dic7C2×C22⋊C411yescharacteristic
320C2×Dic7C2×C22⋊C411yescharacteristic
321C2×Dic7C2×C22⋊C412yes—
322C2×Dic7C2×C22⋊C411yescharacteristic
323C2×Dic7C22×C812yes—
324C2×Dic7C22×C812yes—
325C2×Dic7C22×C812yes—
326C2×Dic7C2×M1612yes—
327C2×Dic7C2×M1612yes—
328C4×D7—24no—
329C4×D7—24no—
330C4×D7—42no—
331C4×D7—42no—
332C4×D7—42no—
333C4×D7—42no—
334Dic14—28no—
335C7×C8—44no—
336C7⋊C8—44no—
337C2×#41—78no—
338C2×#41—142no—
339C2×#41—142no—
340C2×#41—144no—
341C22×Q8—71no—
342C22×D4—71no—
343C22×D4—71no—
344C22×D4C4×D711yescharacteristic
345C23×C4—71no—
346C23×C4—71no—
347C23×C4—71no—
348C23×C4—71no—
349C23×C4—71no—
350C23×C4—71no—
351C23×C4—71no—
352C23×C4C4×D711yescharacteristic
353C23×C4C22×D711yescharacteristic
354C22×C8—22no—
355C22×C8—142no—
356C4×Q8—142no—
357C4×Q8—142no—
358C4×Q8—142no—
359C4×Q8—142no—
360C4×D4—22no—
361C4×D4—22no—
362C4×D4—142no—
363C4×D4—142no—
364C4×D4—142no—
365C4×D4—142no—
366C4×D4—142no—
367C4×D4—142no—
368C4×D4—142no—
369C4×D4—142no—
370C4×D4—142no—
371C4×D4—142no—
372#117—142no—
373#117—142no—
374#117—142no—
375#117—142no—
376#117—142no—
377#117—142no—
378C2×C4⋊C4—71no—
379C2×C4⋊C4—71no—
380C2×C4⋊C4—71no—
381C2×C4⋊C4—71no—
382C2×C4⋊C4—71no—
383C2×C4⋊C4C22×D711yescharacteristic
384C2×C22⋊C4—71no—
385C2×C22⋊C4—71no—
386C2×C22⋊C4—71no—
387C2×C22⋊C4—71no—
388C2×C22⋊C4C4×D711yescharacteristic
389C2×C22⋊C4C22×D711yescharacteristic
390C2×C42—71no—
391C2×C42—71no—
392C2×C42—72no—
393C2×C42—72no—
394C2×C42—72no—
395C2×C42—72no—
396C2×C42—71no—
397C2×C42—71no—
398C2×C42—71no—
399C2×C42—71no—
400C2×C42—71no—
401C2×C42—71no—
402C2×C42—71no—
403C2×C42—141no—
404C2×C42—141no—
405C2×C42—141no—
406C2×C42—141no—
407C2×C42—141no—
408C2×C42—141no—
409C2×C42—141no—
410C2×C42—141no—
411C2×C42C4×D711yescharacteristic
412C4⋊C8—144no—
413C4⋊C8—144no—
414C22⋊C8—22no—
415C22⋊C8—74no—
416C22⋊C8—142no—
417C22⋊C8C22×D714yes—
418C4×C8—144no—
419C4×C8—144no—
420C22×C7—21no—
421C22×C7—22no—
422C22×C7—21no—
423C22×C7—22no—
424C22×C7—22no—
425C22×C7—42no—
426C22×C7—42no—
427C22×C7—42no—
428C22×C7—42no—
429C22×C7—41no—
430C22×C7—41no—
431C22×C7C2×C22⋊C814yes—
432C22×C7C22×C22⋊C411yescharacteristic
433C22×C7C23×C811yescharacteristic
434C22×C7C22×M1611yescharacteristic
435C2×D7—22no—
436C2×D7—42no—
437C2×D7—41no—
438C2×D7—41no—
439C2×D7—42no—
440C4×C7—22no—
441C4×C7—22no—
442C4×C7—21no—
443C4×C7—41no—
444C4×C7—41no—
445C4×C7#41012yes—
446Dic7—22no—
447Dic7—21no—
448Dic7—22no—
449Dic7—41no—
450Dic7—41no—
451Dic7C2×C22⋊C814yes—
452Dic7C2×C22⋊C812yes—
453Dic7C2×C22⋊C812yes—
454Dic7#41312yes—
455C24—71no—
456C24C2×C4×D711yescharacteristic
457C24C2×C4×D711yescharacteristic
458#41—1416no—
459#41—1416no—
460C2×Q8—74no—
461C2×Q8—142no—
462C2×Q8—142no—
463C2×D4—22no—
464C2×D4—22no—
465C2×D4—74no—
466C2×D4—74no—
467C2×D4—142no—
468C2×D4—142no—
469C2×D4—142no—
470C2×D4—142no—
471C2×D4C8×D714yes—
472C22×C4—21no—
473C22×C4—21no—
474C22×C4—42no—
475C22×C4—42no—
476C22×C4—72no—
477C22×C4—72no—
478C22×C4—74no—
479C22×C4—74no—
480C22×C4—71no—
481C22×C4—71no—
482C22×C4—72no—
483C22×C4—74no—
484C22×C4—71no—
485C22×C4—71no—
486C22×C4—72no—
487C22×C4—71no—
488C22×C4—74no—
489C22×C4—71no—
490C22×C4—71no—
491C22×C4—141no—
492C22×C4—141no—
493C22×C4—142no—
494C22×C4—141no—
495C22×C4—141no—
496C22×C4—141no—
497C22×C4—141no—
498C22×C4—142no—
499C22×C4—141no—
500C22×C4—141no—
501C22×C4—141no—
502C22×C4—141no—
503C22×C4—282no—
504C22×C4—282no—
505C22×C4—282no—
506C22×C4—282no—
507C22×C4C2×C4×D711yescharacteristic
508C22×C4C2×C4×D711yescharacteristic
509C22×C4C2×C4×D711yescharacteristic
510C22×C4C2×C4×D711yescharacteristic
511C22×C4D4×D712yes—
512C22×C4D4×D712yes—
513C22×C4C23×D711yescharacteristic
514C2×C8—24no—
515C2×C8—44no—
516C2×C8—144no—
517C2×C8—284no—
518C4⋊C4—22no—
519C4⋊C4—142no—
520C4⋊C4—142no—
521C4⋊C4—142no—
522C4⋊C4—142no—
523C4⋊C4—142no—
524C22⋊C4—22no—
525C22⋊C4—22no—
526C22⋊C4—142no—
527C22⋊C4—142no—
528C22⋊C4—142no—
529C22⋊C4—142no—
530C42—21no—
531C42—21no—
532C42—71no—
533C42—71no—
534C42—72no—
535C42—71no—
536C42—71no—
537C42—72no—
538C42—72no—
539C42—72no—
540C42—72no—
541C42—72no—
542C42—141no—
543C42—141no—
544C42—141no—
545C42—141no—
546C42—141no—
547C42—141no—
548C42—141no—
549C42—141no—
550C42—141no—
551C42—141no—
552C2×C7—21no—
553C2×C7—21no—
554C2×C7—24no—
555C2×C7—42no—
556C2×C7C22×C22⋊C811yescharacteristic
557C2×C7C2×#41011yescharacteristic
558C2×C7C2×#41311yescharacteristic
559D7—42no—
560C23—21no—
561C23—21no—
562C23—41no—
563C23—41no—
564C23—41no—
565C23—41no—
566C23—72no—
567C23—141no—
568C23—141no—
569C23—281no—
570C23—281no—
571C23D7×C22⋊C412yes—
572C23C2×C8×D712yes—
573C23C2×C8×D712yes—
574C23D7×M1612yes—
575C23C22×C4×D711yescharacteristic
576Q8—148no—
577D4—28no—
578D4—148no—
579D4—148no—
580C2×C4—21no—
581C2×C4—21no—
582C2×C4—24no—
583C2×C4—22no—
584C2×C4—21no—
585C2×C4—21no—
586C2×C4—42no—
587C2×C4—41no—
588C2×C4—42no—
589C2×C4—42no—
590C2×C4—41no—
591C2×C4—41no—
592C2×C4—72no—
593C2×C4—72no—
594C2×C4—71no—
595C2×C4—71no—
596C2×C4—71no—
597C2×C4—72no—
598C2×C4—72no—
599C2×C4—72no—
600C2×C4—78no—
601C2×C4—78no—
602C2×C4—72no—
603C2×C4—71no—
604C2×C4—72no—
605C2×C4—144no—
606C2×C4—144no—
607C2×C4—144no—
608C2×C4—144no—
609C2×C4—144no—
610C2×C4—142no—
611C2×C4—141no—
612C2×C4—141no—
613C2×C4—141no—
614C2×C4—141no—
615C2×C4—282no—
616C2×C4—282no—
617C2×C4—282no—
618C2×C4—282no—
619C2×C4—282no—
620C2×C4—281no—
621C2×C4—282no—
622C2×C4—282no—
623C2×C4—281no—
624C2×C4—281no—
625C2×C4D7×C22⋊C411yescharacteristic
626C2×C4D7×C22⋊C411yescharacteristic
627C2×C4C2×C8×D712yes—
628C2×C4C2×D4×D712yes—
629C8—44no—
630C8—284no—
631C7#1734911yescharacteristic, complemented, Sylow
632C22—21no—
633C22—22no—
634C22—21no—
635C22—22no—
636C22—22no—
637C22—42no—
638C22—42no—
639C22—42no—
640C22—42no—
641C22—41no—
642C22—41no—
643C22—142no—
644C22—282no—
645C22—282no—
646C22—281no—
647C22—281no—
648C22D7×C22⋊C814yes—
649C22C2×D7×C22⋊C411yescharacteristic
650C22C22×C8×D711yescharacteristic
651C22C2×D7×M1611yescharacteristic
652C4—22no—
653C4—21no—
654C4—22no—
655C4—41no—
656C4—41no—
657C4—72no—
658C4—72no—
659C4—72no—
660C4—74no—
661C4—141no—
662C4—142no—
663C4—142no—
664C4—281no—
665C4—281no—
666C4#8951212yes—
667C2—21no—
668C2—21no—
669C2—24no—
670C2—42no—
671C2—282no—
672C2C2×D7×C22⋊C811yescharacteristic
673C2C2×#8951211yescharacteristic
674C2D7×#41311yescharacteristic
subgroupG/H
centerC2×C4D7×C22⋊C4
commutatorC22×C7C23×C8
FrattiniC22×C4C23×D7
FittingC7×#1459C2
socleC22×C7C22×C22⋊C4
prime radicalC22×#1159C4
cosocleC22×C4×C7C24
hypercenter#1459D7
hypocenterC7#17349
LCSG ▷ C22×C7 ▷ C2×C7 ▷ C7
UCSC1 ◁ C2×C4 ◁ C23×C4 ◁ #1459

Complements

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

NH ≅ G/Ntype
2. C2×#89490C2semidirect
3. C7×#1459C2semidirect
4. #11729354C2semidirect
5. #11727673C2semidirect
6. #11725879C2semidirect
7. #11725878C2semidirect
8. #11725855C2semidirect
9. #11725854C2semidirect
56. C2×#1159C8semidirect
133. #1459D7semidirect
158. C2×C22⋊D7C2×C8semidirect
171. C22×Dic7C2×C8semidirect
191. C2×C4×D7C2×C8semidirect
194. C2×Dic14C2×C8semidirect
631. C7#17349semidirect

Maximal subgroups

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

subgroupindex
C2×C4×#11592
C2×#894902
C7×#14592
#117293542
#117276732
#117258792
#117258782
#117258552
#117258542
#173497