Finite Group Databasebeta

← #13319930

Subgroups — #13319930

Order 1792.

960 conjugacy classes of subgroups.

The subgroup lattice has 626 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#90313C211yesmaximal, characteristic
2#11736064C211yesmaximal, characteristic
3C2×#89491C211yesmaximal, characteristic
4C7×#1472C211yesmaximal, characteristic
5#11729445C211yesmaximal, characteristic
6#11727726C211yesmaximal, characteristic
7#11727677C211yesmaximal, characteristic
8#11725882C214yesmaximal, complemented
9#11725881C214yesmaximal, complemented
10C2×C7×C22⋊Q8C2211yescharacteristic
11C2×Q8×Dic7C411yescharacteristic
12C2×#6507C411yescharacteristic
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×#6452C2212yes—
24C2×#6451C411yescharacteristic
25C2×#6450C411yescharacteristic
26C2×#6450C2212yes—
27C2×#6441C412yes—
28C2×#6440C412yes—
29C7×#407C2211yescharacteristic
30C2×C7×C22⋊C8C2211yescharacteristic
31#89979C2211yescharacteristic
32C2×C22⋊(C7⋊C8)C2211yescharacteristic
33#89890—21no—
34M16×Dic7—21no—
35C2×#6389—21no—
36C2×Dic7⋊C8—21no—
37#89491—21no—
38#89491—21no—
39#89491—21no—
40#89491C2212yes—
41#89491C2212yes—
42#89491C2212yes—
43#89490—21no—
44#89490C2212yes—
45C7×#324C2214yes—
46#89323C2214yes—
47#89264C2214yes—
48#89264C2214yes—
49#17404—71nomaximal, Sylow
50C22×C7×Q8C2×C411yescharacteristic
51C23×C4×C7C2311yescharacteristic
52C23×Dic7C2×C411yescharacteristic
53C23×Dic7C2×C411yescharacteristic
54C22×Dic14C2×C412yes—
55C22×Dic14C2×C411yescharacteristic
56C2×C7×M16—21no—
57C22×C7×C8—21no—
58C7×C22⋊Q8—21no—
59C7×C22⋊Q8—21no—
60C7×C22⋊Q8—21no—
61C7×C22⋊Q8—21no—
62C2×C7×C4⋊C4C2×C411yescharacteristic
63C2×C7×C4⋊C4C2312yes—
64C2×C7×C22⋊C4C2×C412yes—
65C2×C22⋊Dic7C2×C412yes—
66Q8×Dic7—21no—
67Q8×Dic7—21no—
68Q8×Dic7—21no—
69Q8×Dic7—21no—
70#6507—21no—
71#6507—21no—
72#6507—21no—
73#6507—21no—
74C2×C4⋊Dic7C2×C412yes—
75C2×C4⋊Dic7C2×C411yescharacteristic
76#6487—21no—
77#6487—21no—
78#6487—21no—
79#6487—21no—
80C2×Dic7⋊C4C2×C412yes—
81C2×Dic7⋊C4C2×C412yes—
82C2×Dic7⋊C4C2×C412yes—
83C2×Dic7⋊C4C2×C412yes—
84C2×Dic7⋊C4C2312yes—
85C2×C4×Dic7C2×C412yes—
86C2×C4×Dic7C2×C412yes—
87C2×C4×Dic7C2×C411yescharacteristic
88C2×C4×Dic7C2×C411yescharacteristic
89C2×C4×Dic7D411yescharacteristic
90C2×C4×Dic7D411yescharacteristic
91C2×C4×Dic7D411yescharacteristic
92C2×C4×Dic7D411yescharacteristic
93C2×C4×Dic7D411yescharacteristic
94C2×C4×Dic7D411yescharacteristic
95C2×C4×Dic7D411yescharacteristic
96C2×C4×Dic7D411yescharacteristic
97C2×C4×Dic7C2311yescharacteristic
98C2×C4×Dic7C2311yescharacteristic
99C2×#1136—21no—
100C22×C7⋊C8—21no—
101#6452—22no—
102#6452—22no—
103#6452—22no—
104#6452—22no—
105#6451—21no—
106#6451—21no—
107#6451—21no—
108#6451—21no—
109#6450—21no—
110#6450—21no—
111#6450—21no—
112#6450—21no—
113#6450—22no—
114#6450—22no—
115#6450—22no—
116#6450—22no—
117#6441—22no—
118#6441—22no—
119#6441—22no—
120#6441—22no—
121#6440—22no—
122#6440—22no—
123#6440—22no—
124#6440—22no—
125C7×C22⋊C8—21no—
126C7×C22⋊C8—21no—
127C7×C22⋊C8C2312yes—
128C7×C22⋊C8C2312yes—
129C22⋊(C7⋊C8)—21no—
130C22⋊(C7⋊C8)—21no—
131C22⋊(C7⋊C8)C2312yes—
132C22⋊(C7⋊C8)C2312yes—
133#6389—22no—
134#6389—22no—
135#6389—22no—
136Dic7⋊C8—22no—
137Dic7⋊C8—22no—
138Dic7⋊C8—22no—
139Dic7⋊C8—22no—
140C8×Dic7—22no—
141C2×#533—71no—
142#2920—71no—
143C2×#432—71no—
144#1472—71no—
145#1472—71no—
146#1472—71no—
147#1472D711yescharacteristic
148#1470—74no—
149#1467—74no—
150C24×C7C22×C411yescharacteristic
151C2×C7×Q8—21no—
152C2×C7×Q8—21no—
153C2×C7×Q8—42no—
154C22×C4×C7—42no—
155C22×C4×C7C22×C412yes—
156C22×C4×C7C22×C411yescharacteristic
157C22×C4×C7C22×C412yes—
158C22×C4×C7C2×D411yescharacteristic
159C22×C4×C7C2×D411yescharacteristic
160C22×C4×C7C2×D411yescharacteristic
161C22×C4×C7C2×D411yescharacteristic
162C22×C4×C7C2411yescharacteristic
163C22×Dic7—24no—
164C22×Dic7—42no—
165C22×Dic7C22⋊C411yescharacteristic
166C22×Dic7C22⋊C411yescharacteristic
167C22×Dic7C22⋊C411yescharacteristic
168C22×Dic7C22⋊C411yescharacteristic
169C22×Dic7C22⋊C411yescharacteristic
170C22×Dic7C22⋊C411yescharacteristic
171C22×Dic7C22⋊C411yescharacteristic
172C22×Dic7C22⋊C411yescharacteristic
173C22×Dic7C22×C412yes—
174C22×Dic7C22×C411yescharacteristic
175C22×Dic7C22×C411yescharacteristic
176C22×Dic7C22×C411yescharacteristic
177C22×Dic7C22×C411yescharacteristic
178C22×Dic7C22×C412yes—
179C2×Dic14—21no—
180C2×Dic14—21no—
181C2×Dic14—22no—
182C2×Dic14—22no—
183C2×Dic14—44no—
184C2×Dic14—42no—
185C7×M16—42no—
186C2×C7×C8—22no—
187C2×C7×C8—22no—
188C2×C7×C8—42no—
189C7×C4⋊C4—21no—
190C7×C4⋊C4—21no—
191C7×C4⋊C4—22no—
192C7×C4⋊C4—22no—
193C7×C22⋊C4—22no—
194C7×C22⋊C4—22no—
195C22⋊Dic7—22no—
196C22⋊Dic7—22no—
197C4⋊Dic7—21no—
198C4⋊Dic7—21no—
199C4⋊Dic7—22no—
200C4⋊Dic7—22no—
201Dic7⋊C4—22no—
202Dic7⋊C4—22no—
203Dic7⋊C4—22no—
204Dic7⋊C4—22no—
205Dic7⋊C4—22no—
206Dic7⋊C4—22no—
207Dic7⋊C4—22no—
208Dic7⋊C4—22no—
209Dic7⋊C4—22no—
210Dic7⋊C4—22no—
211C4×Dic7—22no—
212C4×Dic7—22no—
213C4×Dic7—22no—
214C4×Dic7—22no—
215C4×Dic7C22⋊C411yescharacteristic
216C4×Dic7C22⋊C411yescharacteristic
217C4×Dic7C22⋊C411yescharacteristic
218C4×Dic7C22⋊C411yescharacteristic
219C4×Dic7C22⋊C411yescharacteristic
220C4×Dic7C22⋊C411yescharacteristic
221C4×Dic7C22⋊C411yescharacteristic
222C4×Dic7C22⋊C411yescharacteristic
223C4×Dic7C2×D411yescharacteristic
224C4×Dic7C2×D411yescharacteristic
225C4×Dic7C2×D411yescharacteristic
226C4×Dic7C2×D411yescharacteristic
227C4×Dic7C2×D411yescharacteristic
228C4×Dic7C2×D411yescharacteristic
229C4×Dic7C2×D411yescharacteristic
230C4×Dic7C2×D411yescharacteristic
231#1136—42no—
232C2×C7⋊C8—22no—
233C2×C7⋊C8—22no—
234C2×C7⋊C8—42no—
235#533—141no—
236#533—141no—
237#533—141no—
238#533—141no—
239#533—141no—
240#533—141no—
241#533—141no—
242#533—141no—
243C2×C4⋊Q8—71no—
244C2×C4⋊Q8—71no—
245C2×#125—72no—
246C2×C22⋊Q8—71no—
247C2×C22⋊Q8—72no—
248C2×C22⋊Q8C2×D711yescharacteristic
249C2×C4×Q8—71no—
250C2×C4×Q8—71no—
251C2×C4×Q8—72no—
252C2×#117—72no—
253C22×C42—71no—
254#432—72no—
255#432—72no—
256#432—72no—
257#432—141no—
258#432—141no—
259#432—141no—
260#431—72no—
261#431—141no—
262#423—141no—
263C2×C4⋊C8—141no—
264#407—71no—
265#407C2×D711yescharacteristic
266C2×C22⋊C8—71no—
267C2×C22⋊C8C2×D711yescharacteristic
268C4×M16—141no—
269C2×#97—141no—
270#324—74no—
271#324—74no—
272#324—74no—
273#324C2×D714yes—
274C23×C7—22no—
275C23×C7—22no—
276C23×C7—41no—
277C23×C7C2×C22⋊C411yescharacteristic
278C23×C7C2×C22⋊C411yescharacteristic
279C23×C7C23×C411yescharacteristic
280C7×Q8—42no—
281C7×Q8—42no—
282C2×C4×C7—22no—
283C2×C4×C7—22no—
284C2×C4×C7—22no—
285C2×C4×C7—22no—
286C2×C4×C7—22no—
287C2×C4×C7—24no—
288C2×C4×C7—41no—
289C2×C4×C7—41no—
290C2×C4×C7—41no—
291C2×C4×C7—42no—
292C2×C4×C7C2×C22⋊C411yescharacteristic
293C2×C4×C7C2×C22⋊C411yescharacteristic
294C2×C4×C7C22×D411yescharacteristic
295C2×C4×C7C22×D411yescharacteristic
296C2×Dic7—22no—
297C2×Dic7—22no—
298C2×Dic7—22no—
299C2×Dic7—22no—
300C2×Dic7—22no—
301C2×Dic7—22no—
302C2×Dic7—22no—
303C2×Dic7—22no—
304C2×Dic7—22no—
305C2×Dic7—24no—
306C2×Dic7—41no—
307C2×Dic7—41no—
308C2×Dic7—41no—
309C2×Dic7—41no—
310C2×Dic7—42no—
311C2×Dic7#10114yes—
312C2×Dic7C2×C22⋊C411yescharacteristic
313C2×Dic7C2×C22⋊C411yescharacteristic
314C2×Dic7C2×C22⋊C411yescharacteristic
315C2×Dic7C2×C22⋊C411yescharacteristic
316C2×Dic7C2×C22⋊C411yescharacteristic
317C2×Dic7C2×C22⋊C411yescharacteristic
318C2×Dic7C2×C22⋊C411yescharacteristic
319C2×Dic7C2×C22⋊C411yescharacteristic
320Dic14—44no—
321Dic14—44no—
322Dic14—42no—
323Dic14—42no—
324C7×C8—42no—
325C7×C8—42no—
326C7⋊C8—42no—
327C7⋊C8—42no—
328C22×Q8—72no—
329C22×Q8—71no—
330C22×Q8C4×D711yescharacteristic
331C23×C4—71no—
332C23×C4—71no—
333C23×C4C22×D711yescharacteristic
334C2×M16—21no—
335C2×M16—141no—
336C22×C8—21no—
337C22×C8—141no—
338C4⋊Q8—141no—
339C4⋊Q8—141no—
340C4⋊Q8—141no—
341C4⋊Q8—141no—
342C4⋊Q8—141no—
343C4⋊Q8—141no—
344C4⋊Q8—141no—
345C4⋊Q8—141no—
346#125—142no—
347#125—142no—
348#125—142no—
349#125—142no—
350C22⋊Q8—21no—
351C22⋊Q8—21no—
352C22⋊Q8—21no—
353C22⋊Q8—21no—
354C22⋊Q8—142no—
355C22⋊Q8—142no—
356C22⋊Q8—142no—
357C22⋊Q8—142no—
358C22⋊Q8—141no—
359C22⋊Q8—141no—
360C22⋊Q8—141no—
361C22⋊Q8—141no—
362C4×Q8—141no—
363C4×Q8—141no—
364C4×Q8—141no—
365C4×Q8—141no—
366C4×Q8—142no—
367C4×Q8—142no—
368C4×Q8—142no—
369C4×Q8—142no—
370C4×Q8—141no—
371C4×Q8—141no—
372C4×Q8—141no—
373C4×Q8—141no—
374#117—142no—
375#117—142no—
376#117—142no—
377#117—142no—
378C2×C4⋊C4—72no—
379C2×C4⋊C4—72no—
380C2×C4⋊C4—72no—
381C2×C4⋊C4—72no—
382C2×C4⋊C4—72no—
383C2×C4⋊C4—71no—
384C2×C4⋊C4—72no—
385C2×C4⋊C4C4×D711yescharacteristic
386C2×C4⋊C4C22×D712yes—
387C2×C22⋊C4—72no—
388C2×C22⋊C4C4×D712yes—
389C2×C42—71no—
390C2×C42—71no—
391C2×C42—71no—
392C2×C42—71no—
393C2×C42—71no—
394C2×C42—71no—
395C2×C42—71no—
396C2×C42—71no—
397C2×C42—71no—
398C2×C42—71no—
399C2×C42—71no—
400C2×C42—71no—
401C2×C42—72no—
402C2×C42—72no—
403C4⋊C8—142no—
404C4⋊C8—142no—
405C4⋊C8—142no—
406C4⋊C8—142no—
407C22⋊C8—21no—
408C22⋊C8—21no—
409C22⋊C8—72no—
410C22⋊C8—72no—
411C22⋊C8—141no—
412C22⋊C8—141no—
413C22⋊C8C22×D712yes—
414C22⋊C8C22×D712yes—
415#97—142no—
416#97—142no—
417#97—142no—
418C4×C8—142no—
419C22×C7—21no—
420C22×C7—21no—
421C22×C7—21no—
422C22×C7—21no—
423C22×C7—21no—
424C22×C7—21no—
425C22×C7—21no—
426C22×C7—44no—
427C22×C7C2×#10112yes—
428C22×C7C22×C22⋊C411yescharacteristic
429C22×C7#56812yes—
430C4×C7—21no—
431C4×C7—21no—
432C4×C7—21no—
433C4×C7—42no—
434C4×C7—42no—
435C4×C7#41012yes—
436Dic7—21no—
437Dic7—21no—
438Dic7—21no—
439Dic7—21no—
440Dic7—21no—
441Dic7—21no—
442Dic7—42no—
443Dic7—42no—
444Dic7C2×#10112yes—
445Dic7C2×#10112yes—
446C24C2×C4×D711yescharacteristic
447C2×Q8—21no—
448C2×Q8—21no—
449C2×Q8—42no—
450C2×Q8—142no—
451C2×Q8—142no—
452C2×Q8—141no—
453C2×Q8—141no—
454C2×Q8—284no—
455C2×Q8—282no—
456C22×C4—42no—
457C22×C4—71no—
458C22×C4—71no—
459C22×C4—71no—
460C22×C4—71no—
461C22×C4—71no—
462C22×C4—71no—
463C22×C4—71no—
464C22×C4—71no—
465C22×C4—71no—
466C22×C4—71no—
467C22×C4—71no—
468C22×C4—71no—
469C22×C4—72no—
470C22×C4—72no—
471C22×C4—144no—
472C22×C4—282no—
473C22×C4C2×C4×D712yes—
474C22×C4C2×C4×D711yescharacteristic
475C22×C4C2×C4×D712yes—
476C22×C4D4×D711yescharacteristic
477C22×C4D4×D711yescharacteristic
478C22×C4D4×D711yescharacteristic
479C22×C4D4×D711yescharacteristic
480C22×C4C23×D711yescharacteristic
481M16—42no—
482M16—282no—
483C2×C8—22no—
484C2×C8—22no—
485C2×C8—42no—
486C2×C8—142no—
487C2×C8—142no—
488C2×C8—282no—
489C4⋊C4—21no—
490C4⋊C4—21no—
491C4⋊C4—22no—
492C4⋊C4—22no—
493C4⋊C4—142no—
494C4⋊C4—142no—
495C4⋊C4—142no—
496C4⋊C4—142no—
497C4⋊C4—142no—
498C4⋊C4—142no—
499C4⋊C4—142no—
500C4⋊C4—142no—
501C4⋊C4—142no—
502C4⋊C4—142no—
503C4⋊C4—141no—
504C4⋊C4—141no—
505C4⋊C4—142no—
506C4⋊C4—142no—
507C22⋊C4—22no—
508C22⋊C4—22no—
509C22⋊C4—142no—
510C22⋊C4—142no—
511C42—71no—
512C42—71no—
513C42—71no—
514C42—71no—
515C42—71no—
516C42—71no—
517C42—71no—
518C42—71no—
519C42—71no—
520C42—71no—
521C42—71no—
522C42—71no—
523C42—71no—
524C42—71no—
525C42—71no—
526C42—71no—
527C42—142no—
528C42—142no—
529C42—142no—
530C42—142no—
531C2×C7—22no—
532C2×C7—22no—
533C2×C7—41no—
534C2×C7#287911yescharacteristic
535C2×C7C2×#41011yescharacteristic
536C2×C7C22×#10111yescharacteristic
537C23—22no—
538C23—22no—
539C23—41no—
540C23D7×C22⋊C411yescharacteristic
541C23D7×C22⋊C411yescharacteristic
542C23C22×C4×D711yescharacteristic
543Q8—42no—
544Q8—42no—
545Q8—282no—
546Q8—284no—
547Q8—284no—
548Q8—282no—
549C2×C4—22no—
550C2×C4—22no—
551C2×C4—22no—
552C2×C4—22no—
553C2×C4—22no—
554C2×C4—24no—
555C2×C4—41no—
556C2×C4—41no—
557C2×C4—41no—
558C2×C4—42no—
559C2×C4—71no—
560C2×C4—71no—
561C2×C4—74no—
562C2×C4—71no—
563C2×C4—71no—
564C2×C4—71no—
565C2×C4—71no—
566C2×C4—71no—
567C2×C4—71no—
568C2×C4—142no—
569C2×C4—142no—
570C2×C4—142no—
571C2×C4—142no—
572C2×C4—142no—
573C2×C4—142no—
574C2×C4—142no—
575C2×C4—142no—
576C2×C4—142no—
577C2×C4—144no—
578C2×C4—281no—
579C2×C4—281no—
580C2×C4—281no—
581C2×C4—281no—
582C2×C4—282no—
583C2×C4D7×C22⋊C411yescharacteristic
584C2×C4D7×C22⋊C411yescharacteristic
585C2×C4C2×D4×D711yescharacteristic
586C2×C4C2×D4×D711yescharacteristic
587C8—42no—
588C8—42no—
589C8—282no—
590C8—282no—
591C7#1740411yescharacteristic, complemented, Sylow
592C22—21no—
593C22—21no—
594C22—21no—
595C22—21no—
596C22—21no—
597C22—21no—
598C22—21no—
599C22—44no—
600C22D7×#10112yes—
601C22C2×D7×C22⋊C411yescharacteristic
602C22#9044112yes—
603C4—21no—
604C4—21no—
605C4—21no—
606C4—42no—
607C4—42no—
608C4—72no—
609C4—72no—
610C4—141no—
611C4—141no—
612C4—141no—
613C4—141no—
614C4—141no—
615C4—141no—
616C4—282no—
617C4—282no—
618C4#8951212yes—
619C2—22no—
620C2—22no—
621C2—41no—
622C2#1173610711yescharacteristic
623C2C2×#8951211yescharacteristic
624C2C2×D7×#10111yescharacteristic
subgroupG/H
centerC22C2×D7×C22⋊C4
commutatorC23×C7C23×C4
FrattiniC22×C4C23×D7
FittingC7×#1472C2
socleC22×C7C22×C22⋊C4
prime radicalC24×C7C22×C4
cosocleC22×C4×C7C24
hypercenter#1472D7
hypocenterC7#17404
LCSG ▷ C23×C7 ▷ C2×C7 ▷ C7
UCSC1 ◁ C22 ◁ C23×C4 ◁ #1472

Complements

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

NH ≅ G/Ntype
8. #11725882C2semidirect
9. #11725881C2semidirect
591. C7#17404semidirect

Maximal subgroups

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

subgroupindex
C2×#903132
#117360642
C2×#894912
C7×#14722
#117294452
#117277262
#117276772
#117258822
#117258812
#174047