Finite Group Databasebeta

← #13358438

Subgroups — #13358438

Order 1792.

1202 conjugacy classes of subgroups.

The subgroup lattice has 694 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#90313C211yesmaximal, characteristic
2#11731309C211yesmaximal, characteristic
3C4×#6440C211yesmaximal, characteristic
4C7×#1996C211yesmaximal, characteristic
5#11729455C211yesmaximal, characteristic
6#11727283C211yesmaximal, characteristic
7#11727211C211yesmaximal, characteristic
8#11726709C214yesmaximal
9#11726705C214yesmaximal
10C2×C7×C22⋊Q8C2211yescharacteristic
11C2×Q8×Dic7C411yescharacteristic, complemented
12C2×#6507C411yescharacteristic, complemented
13C2×#6487C2211yescharacteristic
14C22×C4×Dic7C2211yescharacteristic
15#90313—21no—
16#90313—21no—
17#90313—21no—
18#90313—21no—
19#90313—21no—
20#90313—21no—
21#90313—21no—
22#90313—21no—
23C2×#6452C412yescomplemented
24C2×#6451C411yescharacteristic, complemented
25C2×#6450C411yescharacteristic, complemented
26C2×#6450C412yescomplemented
27C2×#6441C2212yes—
28C2×#6440C2212yes—
29C2×#6440C2212yes—
30C2×#6440C2212yes—
31C7×#380C2211yescharacteristic
32C4×C7×C22⋊C4C2211yescharacteristic
33#89984C2211yescharacteristic
34C4×C22⋊Dic7C2211yescharacteristic
35#89748—21no—
36C4⋊C4×Dic7—21no—
37#89714C2212yes—
38C22⋊C4×Dic7C2212yes—
39C4×Dic7⋊C4—21no—
40C42×Dic7—21no—
41#89422—21no—
42#89421—21no—
43#89421—21no—
44#89420—21no—
45C7×#342C2214yes—
46#89322C2214yes—
47#89322C2214yes—
48#89321C2214yes—
49#21332—71nomaximal, Sylow
50C22×C7×Q8C2×C411yescharacteristic
51C23×C4×C7C2311yescharacteristic
52C23×Dic7C2311yescharacteristic
53C23×Dic7C2311yescharacteristic
54C22×Dic14C2×C412yes—
55C22×Dic14C2×C411yescharacteristic
56C7×C22⋊Q8—21no—
57C7×C22⋊Q8—21no—
58C7×C22⋊Q8—21no—
59C7×C22⋊Q8—21no—
60C2×C7×C4⋊C4—21no—
61C2×C7×C4⋊C4C2×C411yescharacteristic
62C2×C7×C4⋊C4C2×C412yes—
63C2×C7×C22⋊C4C2312yes—
64C2×C7×C22⋊C4C2312yes—
65C2×C7×C22⋊C4C2312yes—
66C2×C42×C7—21no—
67C2×C22⋊Dic7C2312yes—
68C2×C22⋊Dic7C2312yes—
69C2×C22⋊Dic7C2312yes—
70Q8×Dic7—21no—
71Q8×Dic7—21no—
72Q8×Dic7—21no—
73Q8×Dic7—21no—
74#6507—21no—
75#6507—21no—
76#6507—21no—
77#6507—21no—
78C2×C4⋊Dic7—21no—
79C2×C4⋊Dic7C2×C412yes—
80C2×C4⋊Dic7C2×C411yescharacteristic
81#6487—21no—
82#6487—21no—
83#6487—21no—
84#6487—21no—
85C2×Dic7⋊C4—22no—
86C2×Dic7⋊C4—22no—
87C2×Dic7⋊C4—22no—
88C2×Dic7⋊C4C2×C412yes—
89C2×Dic7⋊C4C2×C412yes—
90C2×Dic7⋊C4C2×C412yes—
91C2×Dic7⋊C4C2×C412yes—
92C2×Dic7⋊C4C2×C412yes—
93C2×C4×Dic7—22no—
94C2×C4×Dic7—21no—
95C2×C4×Dic7—22no—
96C2×C4×Dic7—22no—
97C2×C4×Dic7C2×C412yes—
98C2×C4×Dic7C2×C412yes—
99C2×C4×Dic7C2×C411yescharacteristic
100C2×C4×Dic7C2×C411yescharacteristic
101C2×C4×Dic7C2×C411yescharacteristic
102C2×C4×Dic7C2×C411yescharacteristic
103C2×C4×Dic7D411yescharacteristic
104C2×C4×Dic7D411yescharacteristic
105C2×C4×Dic7D411yescharacteristic
106C2×C4×Dic7D411yescharacteristic
107C2×C4×Dic7D411yescharacteristic
108C2×C4×Dic7D411yescharacteristic
109C2×C4×Dic7D411yescharacteristic
110C2×C4×Dic7D411yescharacteristic
111#6452—22no—
112#6452—22no—
113#6452—22no—
114#6452—22no—
115#6451—21no—
116#6451—21no—
117#6451—21no—
118#6451—21no—
119#6450—21no—
120#6450—21no—
121#6450—21no—
122#6450—21no—
123#6450—22no—
124#6450—22no—
125#6450—22no—
126#6450—22no—
127#6441—22no—
128#6441—22no—
129#6441—22no—
130#6441—22no—
131#6440—22no—
132#6440—22no—
133#6440—22no—
134#6440—22no—
135#6440—24no—
136#6440—28no—
137#6440Q818yescomplemented
138C7×#95—21no—
139C7×#95—21no—
140C7⋊#95—21no—
141C7⋊#95—21no—
142C7⋊#95—22no—
143C7⋊#95—22no—
144C2×#533—71no—
145#2285—71no—
146C4×#117—71no—
147#1996—71no—
148#1996—71no—
149#1996—74no—
150#1996—71no—
151#1996D711yescharacteristic
152#1740—74no—
153C24×C7C2411yescharacteristic
154C2×C7×Q8—21no—
155C2×C7×Q8—21no—
156C2×C7×Q8—42no—
157C22×C4×C7—22no—
158C22×C4×C7—22no—
159C22×C4×C7—42no—
160C22×C4×C7C22×C411yescharacteristic
161C22×C4×C7C22×C412yes—
162C22×C4×C7C22×C412yes—
163C22×C4×C7C22×C411yescharacteristic
164C22×C4×C7C2×D411yescharacteristic
165C22×C4×C7C2×D411yescharacteristic
166C22×C4×C7C2×D411yescharacteristic
167C22×C4×C7C2×D411yescharacteristic
168C22×Dic7—22no—
169C22×Dic7—22no—
170C22×Dic7—42no—
171C22×Dic7C22×C411yescharacteristic
172C22×Dic7C22×C412yes—
173C22×Dic7C22×C412yes—
174C22×Dic7C22×C411yescharacteristic
175C22×Dic7C22×C411yescharacteristic
176C22×Dic7C22×C411yescharacteristic
177C22×Dic7C2×D411yescharacteristic
178C22×Dic7C2×D411yescharacteristic
179C22×Dic7C2×D411yescharacteristic
180C22×Dic7C2×D411yescharacteristic
181C22×Dic7C2×D411yescharacteristic
182C22×Dic7C2×D411yescharacteristic
183C22×Dic7C2×D411yescharacteristic
184C22×Dic7C2×D411yescharacteristic
185C22×Dic7C2×Q814yes—
186C22×Dic7#4114yes—
187C2×Dic14—21no—
188C2×Dic14—21no—
189C2×Dic14—22no—
190C2×Dic14—22no—
191C2×Dic14—44no—
192C2×Dic14—42no—
193C7×C4⋊C4—21no—
194C7×C4⋊C4—21no—
195C7×C4⋊C4—22no—
196C7×C4⋊C4—22no—
197C7×C4⋊C4—42no—
198C7×C22⋊C4—22no—
199C7×C22⋊C4—22no—
200C7×C22⋊C4—22no—
201C7×C22⋊C4—24no—
202C7×C22⋊C4C2×Q814yes—
203C42×C7—42no—
204C22⋊Dic7—22no—
205C22⋊Dic7—22no—
206C22⋊Dic7—22no—
207C22⋊Dic7—24no—
208C22⋊Dic7C2×Q814yes—
209C4⋊Dic7—21no—
210C4⋊Dic7—21no—
211C4⋊Dic7—22no—
212C4⋊Dic7—22no—
213C4⋊Dic7—42no—
214Dic7⋊C4—22no—
215Dic7⋊C4—22no—
216Dic7⋊C4—22no—
217Dic7⋊C4—22no—
218Dic7⋊C4—22no—
219Dic7⋊C4—22no—
220Dic7⋊C4—22no—
221Dic7⋊C4—22no—
222Dic7⋊C4—22no—
223Dic7⋊C4—22no—
224Dic7⋊C4—28no—
225Dic7⋊C4—44no—
226Dic7⋊C4—44no—
227C4×Dic7—22no—
228C4×Dic7—22no—
229C4×Dic7—22no—
230C4×Dic7—22no—
231C4×Dic7—28no—
232C4×Dic7—44no—
233C4×Dic7—42no—
234C4×Dic7—44no—
235C4×Dic7C22⋊C411yescharacteristic
236C4×Dic7C22⋊C411yescharacteristic
237C4×Dic7C22⋊C411yescharacteristic
238C4×Dic7C22⋊C411yescharacteristic
239C4×Dic7C22⋊C411yescharacteristic
240C4×Dic7C22⋊C411yescharacteristic
241C4×Dic7C22⋊C411yescharacteristic
242C4×Dic7C22⋊C411yescharacteristic
243C4×Dic7C22⋊C411yescharacteristic
244C4×Dic7C22⋊C411yescharacteristic
245C4×Dic7C22⋊C411yescharacteristic
246C4×Dic7C22⋊C411yescharacteristic
247C4×Dic7C22⋊C411yescharacteristic
248C4×Dic7C22⋊C411yescharacteristic
249C4×Dic7C22⋊C411yescharacteristic
250C4×Dic7C22⋊C411yescharacteristic
251#533—141no—
252#533—141no—
253#533—141no—
254#533—141no—
255#533—141no—
256#533—141no—
257#533—141no—
258#533—141no—
259C2×C4⋊Q8—71no—
260C2×C4⋊Q8—71no—
261C2×#125—72no—
262C2×C22⋊Q8—71no—
263C2×C22⋊Q8—72no—
264C2×C22⋊Q8C2×D711yescharacteristic
265C2×C4×Q8—71no—
266C2×C4×Q8—71no—
267C2×C4×Q8—72no—
268C2×#117—72no—
269C2×#117—72no—
270C2×#117—72no—
271C22×C42—71no—
272#384—141no—
273#382—141no—
274#380—71no—
275#380—72no—
276#380C2×D711yescharacteristic
277C4×C4⋊C4—141no—
278C4×C4⋊C4—141no—
279C4×C4⋊C4—141no—
280C4×C4⋊C4—141no—
281C4×C22⋊C4—71no—
282C4×C22⋊C4—72no—
283C4×C22⋊C4C2×D711yescharacteristic
284#376—141no—
285C43—141no—
286#342—74no—
287#342—74no—
288#342—74no—
289#342C2×D714yes—
290C23×C7—41no—
291C23×C7—41no—
292C23×C7C23×C411yescharacteristic
293C23×C7C22×D411yescharacteristic
294C23×C7C22×D411yescharacteristic
295C23×C7C22×Q812yes—
296C23×C7C2×#4112yes—
297C7×Q8—42no—
298C7×Q8—42no—
299C2×C4×C7—22no—
300C2×C4×C7—22no—
301C2×C4×C7—22no—
302C2×C4×C7—22no—
303C2×C4×C7—22no—
304C2×C4×C7—24no—
305C2×C4×C7—41no—
306C2×C4×C7—41no—
307C2×C4×C7—41no—
308C2×C4×C7—42no—
309C2×C4×C7—42no—
310C2×C4×C7—42no—
311C2×C4×C7—42no—
312C2×C4×C7—42no—
313C2×C4×C7—42no—
314C2×C4×C7—42no—
315C2×C4×C7C2×C22⋊C411yescharacteristic
316C2×C4×C7C2×C22⋊C411yescharacteristic
317C2×C4×C7C2×C22⋊C411yescharacteristic
318C2×C4×C7C2×C22⋊C411yescharacteristic
319C2×Dic7—22no—
320C2×Dic7—22no—
321C2×Dic7—22no—
322C2×Dic7—22no—
323C2×Dic7—22no—
324C2×Dic7—24no—
325C2×Dic7—41no—
326C2×Dic7—41no—
327C2×Dic7—41no—
328C2×Dic7—42no—
329C2×Dic7—42no—
330C2×Dic7—42no—
331C2×Dic7—42no—
332C2×Dic7—42no—
333C2×Dic7—42no—
334C2×Dic7—42no—
335C2×Dic7C2×C22⋊C411yescharacteristic
336C2×Dic7C2×C22⋊C411yescharacteristic
337C2×Dic7C2×C22⋊C411yescharacteristic
338C2×Dic7C2×C22⋊C411yescharacteristic
339C2×Dic7C2×C22⋊C411yescharacteristic
340C2×Dic7C2×C22⋊C411yescharacteristic
341C2×Dic7C2×C22⋊C411yescharacteristic
342C2×Dic7C2×C22⋊C411yescharacteristic
343C2×Dic7C4×Q814yes—
344C2×Dic7C4×Q814yes—
345C2×Dic7C22⋊Q814yes—
346C2×Dic7C22⋊Q814yes—
347C2×Dic7#12412yes—
348C2×Dic7#12412yes—
349C2×Dic7C4⋊Q812yes—
350C2×Dic7C4⋊Q812yes—
351Dic14—44no—
352Dic14—42no—
353Dic14—42no—
354Dic14—44no—
355C22×Q8—72no—
356C22×Q8—71no—
357C22×Q8C4×D711yescharacteristic
358C23×C4—71no—
359C23×C4—71no—
360C23×C4C22×D711yescharacteristic
361C4⋊Q8—141no—
362C4⋊Q8—141no—
363C4⋊Q8—141no—
364C4⋊Q8—141no—
365C4⋊Q8—141no—
366C4⋊Q8—141no—
367C4⋊Q8—141no—
368C4⋊Q8—141no—
369#125—142no—
370#125—142no—
371#125—142no—
372#125—142no—
373C22⋊Q8—21no—
374C22⋊Q8—21no—
375C22⋊Q8—21no—
376C22⋊Q8—21no—
377C22⋊Q8—142no—
378C22⋊Q8—142no—
379C22⋊Q8—142no—
380C22⋊Q8—142no—
381C22⋊Q8—141no—
382C22⋊Q8—141no—
383C22⋊Q8—141no—
384C22⋊Q8—141no—
385C4×Q8—142no—
386C4×Q8—142no—
387C4×Q8—142no—
388C4×Q8—142no—
389C4×Q8—141no—
390C4×Q8—141no—
391C4×Q8—141no—
392C4×Q8—141no—
393C4×Q8—141no—
394C4×Q8—141no—
395C4×Q8—141no—
396C4×Q8—141no—
397#117—78no—
398#117—142no—
399#117—142no—
400#117—142no—
401#117—142no—
402#117—144no—
403#117—148no—
404C2×C4⋊C4—21no—
405C2×C4⋊C4—72no—
406C2×C4⋊C4—72no—
407C2×C4⋊C4—72no—
408C2×C4⋊C4—72no—
409C2×C4⋊C4—72no—
410C2×C4⋊C4—72no—
411C2×C4⋊C4—71no—
412C2×C4⋊C4—142no—
413C2×C4⋊C4—142no—
414C2×C4⋊C4—142no—
415C2×C4⋊C4—141no—
416C2×C4⋊C4C4×D712yes—
417C2×C4⋊C4C4×D711yescharacteristic
418C2×C22⋊C4—72no—
419C2×C22⋊C4—72no—
420C2×C22⋊C4—72no—
421C2×C22⋊C4C22×D712yes—
422C2×C22⋊C4C22×D712yes—
423C2×C22⋊C4C22×D712yes—
424C2×C42—21no—
425C2×C42—71no—
426C2×C42—71no—
427C2×C42—71no—
428C2×C42—71no—
429C2×C42—71no—
430C2×C42—71no—
431C2×C42—71no—
432C2×C42—71no—
433C2×C42—71no—
434C2×C42—71no—
435C2×C42—71no—
436C2×C42—71no—
437C2×C42—72no—
438C2×C42—72no—
439C2×C42—142no—
440C2×C42—142no—
441C2×C42—142no—
442C2×C42—141no—
443#95—21no—
444#95—21no—
445#95—142no—
446#95—142no—
447#95—141no—
448#95—141no—
449C22×C7—21no—
450C22×C7—21no—
451C22×C7—21no—
452C22×C7—21no—
453C22×C7—21no—
454C22×C7—21no—
455C22×C7—42no—
456C22×C7—42no—
457C22×C7C22×C22⋊C411yescharacteristic
458C22×C7C2×C4×Q812yes—
459C22×C7C2×C22⋊Q812yes—
460C22×C7C2×#12411yescharacteristic
461C22×C7C2×C4⋊Q811yescharacteristic
462C4×C7—21no—
463C4×C7—21no—
464C4×C7—21no—
465C4×C7—44no—
466C4×C7—42no—
467C4×C7—42no—
468C4×C7—82no—
469C4×C7#41012yes—
470Dic7—21no—
471Dic7—21no—
472Dic7—21no—
473Dic7—44no—
474Dic7—42no—
475Dic7—42no—
476Dic7—82no—
477Dic7#39112yes—
478Dic7#39112yes—
479Dic7#39112yes—
480Dic7#39112yes—
481Dic7#41012yes—
482C24C23×D711yescharacteristic
483C2×Q8—21no—
484C2×Q8—21no—
485C2×Q8—42no—
486C2×Q8—142no—
487C2×Q8—142no—
488C2×Q8—141no—
489C2×Q8—141no—
490C2×Q8—282no—
491C2×Q8—284no—
492C22×C4—22no—
493C22×C4—22no—
494C22×C4—42no—
495C22×C4—71no—
496C22×C4—71no—
497C22×C4—71no—
498C22×C4—71no—
499C22×C4—71no—
500C22×C4—71no—
501C22×C4—74no—
502C22×C4—74no—
503C22×C4—71no—
504C22×C4—71no—
505C22×C4—71no—
506C22×C4—71no—
507C22×C4—71no—
508C22×C4—71no—
509C22×C4—72no—
510C22×C4—72no—
511C22×C4—142no—
512C22×C4—142no—
513C22×C4—282no—
514C22×C4C2×C4×D711yescharacteristic
515C22×C4C2×C4×D712yes—
516C22×C4C2×C4×D712yes—
517C22×C4C2×C4×D711yescharacteristic
518C22×C4D4×D711yescharacteristic
519C22×C4D4×D711yescharacteristic
520C22×C4D4×D711yescharacteristic
521C22×C4D4×D711yescharacteristic
522C4⋊C4—22no—
523C4⋊C4—22no—
524C4⋊C4—21no—
525C4⋊C4—21no—
526C4⋊C4—42no—
527C4⋊C4—142no—
528C4⋊C4—142no—
529C4⋊C4—142no—
530C4⋊C4—142no—
531C4⋊C4—142no—
532C4⋊C4—142no—
533C4⋊C4—142no—
534C4⋊C4—142no—
535C4⋊C4—148no—
536C4⋊C4—142no—
537C4⋊C4—142no—
538C4⋊C4—142no—
539C4⋊C4—142no—
540C4⋊C4—141no—
541C4⋊C4—141no—
542C4⋊C4—282no—
543C4⋊C4—284no—
544C4⋊C4—284no—
545C22⋊C4—22no—
546C22⋊C4—22no—
547C22⋊C4—22no—
548C22⋊C4—24no—
549C22⋊C4—74no—
550C22⋊C4—142no—
551C22⋊C4—142no—
552C22⋊C4—142no—
553C22⋊C4—144no—
554C22⋊C4Q8×D714yes—
555C42—42no—
556C42—71no—
557C42—71no—
558C42—71no—
559C42—71no—
560C42—71no—
561C42—71no—
562C42—71no—
563C42—71no—
564C42—71no—
565C42—71no—
566C42—71no—
567C42—71no—
568C42—71no—
569C42—71no—
570C42—71no—
571C42—71no—
572C42—142no—
573C42—142no—
574C42—142no—
575C42—142no—
576C42—148no—
577C42—282no—
578C42—284no—
579C42—284no—
580C2×C7—22no—
581C2×C7—21no—
582C2×C7—22no—
583C2×C7—21no—
584C2×C7C2×#39111yescharacteristic
585C2×C7C2×#41011yescharacteristic
586C2×C7C2×#41011yescharacteristic
587C23—41no—
588C23—41no—
589C23C22×C4×D711yescharacteristic
590C23C2×D4×D711yescharacteristic
591C23C2×D4×D711yescharacteristic
592C23C2×Q8×D712yes—
593C23D7×#4112yes—
594Q8—42no—
595Q8—42no—
596Q8—282no—
597Q8—284no—
598Q8—284no—
599Q8—282no—
600C2×C4—22no—
601C2×C4—22no—
602C2×C4—22no—
603C2×C4—22no—
604C2×C4—22no—
605C2×C4—24no—
606C2×C4—41no—
607C2×C4—41no—
608C2×C4—41no—
609C2×C4—42no—
610C2×C4—42no—
611C2×C4—42no—
612C2×C4—42no—
613C2×C4—42no—
614C2×C4—42no—
615C2×C4—42no—
616C2×C4—72no—
617C2×C4—72no—
618C2×C4—71no—
619C2×C4—71no—
620C2×C4—71no—
621C2×C4—71no—
622C2×C4—71no—
623C2×C4—74no—
624C2×C4—74no—
625C2×C4—74no—
626C2×C4—74no—
627C2×C4—72no—
628C2×C4—72no—
629C2×C4—71no—
630C2×C4—71no—
631C2×C4—71no—
632C2×C4—142no—
633C2×C4—142no—
634C2×C4—142no—
635C2×C4—142no—
636C2×C4—142no—
637C2×C4—144no—
638C2×C4—281no—
639C2×C4—281no—
640C2×C4—281no—
641C2×C4—282no—
642C2×C4—282no—
643C2×C4—282no—
644C2×C4—282no—
645C2×C4—282no—
646C2×C4—282no—
647C2×C4—282no—
648C2×C4D7×C22⋊C411yescharacteristic
649C2×C4D7×C22⋊C411yescharacteristic
650C2×C4D7×C22⋊C411yescharacteristic
651C2×C4D7×C22⋊C411yescharacteristic
652C7#2133211yescharacteristic, complemented, Sylow
653C22—21no—
654C22—21no—
655C22—21no—
656C22—21no—
657C22—21no—
658C22—21no—
659C22—42no—
660C22—42no—
661C22C2×D7×C22⋊C411yescharacteristic
662C22C4×Q8×D712yes—
663C22D7×C22⋊Q812yes—
664C22D7×#12411yescharacteristic
665C22D7×C4⋊Q811yescharacteristic
666C4—21no—
667C4—21no—
668C4—21no—
669C4—44no—
670C4—42no—
671C4—42no—
672C4—72no—
673C4—72no—
674C4—72no—
675C4—72no—
676C4—72no—
677C4—82no—
678C4—141no—
679C4—141no—
680C4—141no—
681C4—284no—
682C4—282no—
683C4—282no—
684C4—562no—
685C4#8951212yes—
686C2—22no—
687C2—21no—
688C2—21no—
689C2—22no—
690C2D7×#39111yescharacteristic
691C2C2×#8951211yescharacteristic
692C2D7×#41011yescharacteristic
subgroupG/H
centerC22C2×D7×C22⋊C4
commutatorC23×C7C23×C4
FrattiniC24C23×D7
FittingC7×#1996C2
socleC22×C7C22×C22⋊C4
prime radical, cosocleC24×C7C24
hypercenter#1996D7
hypocenterC7#21332
LCSG ▷ C23×C7 ▷ C2×C7 ▷ C7
UCSC1 ◁ C22 ◁ C23×C4 ◁ #1996

Complements

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

NH ≅ G/Ntype
11. C2×Q8×Dic7C4semidirect
12. C2×#6507C4semidirect
23. C2×#6452C4semidirect
24. C2×#6451C4semidirect
25. C2×#6450C4semidirect
26. C2×#6450C4semidirect
137. #6440Q8semidirect
652. C7#21332semidirect

Maximal subgroups

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

subgroupindex
C2×#903132
#117313092
C4×#64402
C7×#19962
#117294552
#117272832
#117272112
#117267092
#117267052
#213327