Finite Group Databasebeta

← #13319850

Subgroups — #13319850

Order 1792.

940 conjugacy classes of subgroups.

The subgroup lattice has 642 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#90401C211yesmaximal, characteristic
2#11736759C211yesmaximal, characteristic, complemented
3#11736708C211yesmaximal, characteristic, complemented
4C7×#1473C211yesmaximal, characteristic, complemented
5#11729499C211yesmaximal, characteristic, complemented
6#11728582C211yesmaximal, characteristic, complemented
7#11728538C211yesmaximal, characteristic, complemented
8#11725883C212yesmaximal, complemented
9#11725878C212yesmaximal, complemented
10#11725858C212yesmaximal, complemented
11#11725855C212yesmaximal, complemented
12C2×C7×#126C2211yescharacteristic
13#90401—22no—
14#90401—22no—
15#90401—22no—
16#90401—22no—
17C2×#6461C2211yescharacteristic
18C2×#6460C411yescharacteristic
19C2×#6459C411yescharacteristic
20C2×#6457C411yescharacteristic
21C2×#6455C2211yescharacteristic
22C2×#6451C411yescharacteristic
23C2×#6449C411yescharacteristic
24C2×#6448C411yescharacteristic
25C2×#6448C2211yescharacteristic
26C2×#6447C411yescharacteristic
27C2×(C22⋊D7)⋊C4C2211yescharacteristic
28C2×#6441C411yescharacteristic
29C2×#6438C2211yescharacteristic
30C2×C4×Dic14C2211yescharacteristic
31C7×#432C2211yescharacteristic
32C7×#431C2211yescharacteristic
33#89698C2211yescharacteristic
34#89697C2211yescharacteristic
35#89602—22no—
36#89600—22no—
37#89491C2212yes—
38#89490C2212yes—
39#89490C2212yes—
40#89490C2212yes—
41#89473—22no—
42C8×Dic14—22no—
43C7×#324C2212yes—
44C7×#323C2212yes—
45#89323C2212yes—
46#89320C2212yes—
47#89263C2212yes—
48#89263C2212yes—
49#89263C2212yes—
50#89263C2212yes—
51#17390—71nomaximal, Sylow
52C22×C22⋊D7C2×C411yescharacteristic
53C22×C22⋊D7C2×C411yescharacteristic
54C23×Dic7C2×C411yescharacteristic
55C22×D28C2×C411yescharacteristic
56C22×C4×D7C2×C411yescharacteristic
57C22×C4×D7C2×C411yescharacteristic
58C22×Dic14C2×C411yescharacteristic
59C22×Dic14C2×C411yescharacteristic
60C22×Dic14C2×C411yescharacteristic
61C7×#126—21no—
62C7×#126—21no—
63C7×#126—21no—
64C7×#126—21no—
65C2×C7×C4⋊C4C2×C411yescharacteristic
66C2×C7×C4⋊C4C2×C411yescharacteristic
67C2×C7×C4⋊C4C2311yescharacteristic
68C2×C7×C22⋊C4C2×C411yescharacteristic
69C2×C7×C22⋊C4C2×C411yescharacteristic
70C2×C7×C22⋊C4C2311yescharacteristic
71C2×C42×C7C2311yescharacteristic
72C2×C22⋊Dic7C2×C411yescharacteristic
73C2×(C2×D7)⋊C4C2×C411yescharacteristic
74C2×(C2×D7)⋊C4C2×C411yescharacteristic
75C2×(C2×D7)⋊C4C2×C411yescharacteristic
76C2×(C2×D7)⋊C4C2×C411yescharacteristic
77C2×(C2×D7)⋊C4C2×C411yescharacteristic
78C2×(C2×D7)⋊C4C2×C411yescharacteristic
79C2×(C2×D7)⋊C4C2311yescharacteristic
80C2×(C2×D7)⋊C4C2311yescharacteristic
81C2×C4⋊Dic7C2×C411yescharacteristic
82C2×C4⋊Dic7C2×C411yescharacteristic
83C2×C4⋊Dic7C2×C411yescharacteristic
84C2×Dic7⋊C4C2×C411yescharacteristic
85C2×Dic7⋊C4C2×C411yescharacteristic
86C2×Dic7⋊C4C2×C411yescharacteristic
87C2×Dic7⋊C4C2×C411yescharacteristic
88C2×C4×Dic7C2×C411yescharacteristic
89C2×C4×Dic7C2311yescharacteristic
90C2×C4×Dic7C2311yescharacteristic
91#6461—22no—
92#6461—22no—
93#6460—22no—
94#6460—22no—
95#6459—22no—
96#6459—22no—
97#6457—22no—
98#6457—22no—
99#6455—22no—
100#6455—22no—
101#6451—22no—
102#6451—22no—
103#6449—22no—
104#6449—22no—
105#6448—22no—
106#6448—22no—
107#6448—22no—
108#6448—22no—
109#6447—22no—
110#6447—22no—
111(C22⋊D7)⋊C4—22no—
112(C22⋊D7)⋊C4—22no—
113#6441—22no—
114#6441—22no—
115#6438—21no—
116#6438—21no—
117#6438—21no—
118#6438—21no—
119C4×Dic14D412yes—
120C4×Dic14D412yes—
121C4×Dic14D412yes—
122C4×Dic14D412yes—
123C7×C4⋊C8—21no—
124C7×C4⋊C8—21no—
125C7×C22⋊C8C2312yes—
126C7×C22⋊C8C2312yes—
127C7×#97—21no—
128C4×C7×C8—21no—
129C22⋊(C7⋊C8)C2312yes—
130C22⋊(C7⋊C8)C2312yes—
131#6389—22no—
132Dic7⋊C8—22no—
133Dic7⋊C8—22no—
134Dic7⋊C8—22no—
135Dic7⋊C8—22no—
136C8×Dic7—22no—
137C8×Dic7—22no—
138C8×Dic7—22no—
139C4⋊(C7⋊C8)—21no—
140C4⋊(C7⋊C8)—21no—
141#6377—21no—
142C4×C7⋊C8—21no—
143C2×#542—71no—
144#2983—71no—
145#2982—71no—
146#1473—72no—
147#1473—71no—
148#1473D711yescharacteristic, complemented
149#1469—71no—
150#1469—71no—
151#1469—72no—
152#1460—72no—
153#1458—72no—
154C24×C7C22×C411yescharacteristic
155C23×D7C22×C411yescharacteristic
156C23×D7C22×C411yescharacteristic
157C22×C4×C7C22×C411yescharacteristic
158C22×C4×C7C22×C411yescharacteristic
159C22×C4×C7C22×C411yescharacteristic
160C22×C4×C7C22×C411yescharacteristic
161C22×C4×C7C22×C411yescharacteristic
162C22×C4×C7C2411yescharacteristic
163C2×C22⋊D7—22no—
164C2×C22⋊D7—22no—
165C2×C22⋊D7—24no—
166C2×C22⋊D7—81no—
167C22×Dic7—22no—
168C22×Dic7—81no—
169C22×Dic7C22×C411yescharacteristic
170C22×Dic7C22×C411yescharacteristic
171C22×Dic7C22×C411yescharacteristic
172C22×Dic7C22×C411yescharacteristic
173C22×Dic7C22×C411yescharacteristic
174C22×Dic7C22×C411yescharacteristic
175C2×D28—21no—
176C2×D28—21no—
177C2×D28—81no—
178C2×C4×D7—22no—
179C2×C4×D7—24no—
180C2×C4×D7—22no—
181C2×C4×D7—81no—
182C2×Dic14—24no—
183C2×Dic14—21no—
184C2×Dic14—21no—
185C2×Dic14—22no—
186C2×Dic14—81no—
187C2×Dic14—81no—
188C2×Dic14C22⋊C412yes—
189C2×Dic14C22⋊C412yes—
190C2×C7×C8—22no—
191C2×C7×C8—22no—
192C7×C4⋊C4—21no—
193C7×C4⋊C4—21no—
194C7×C4⋊C4—21no—
195C7×C4⋊C4—21no—
196C7×C4⋊C4—21no—
197C7×C4⋊C4—21no—
198C7×C22⋊C4—21no—
199C7×C22⋊C4—21no—
200C7×C22⋊C4—21no—
201C7×C22⋊C4—21no—
202C7×C22⋊C4—21no—
203C7×C22⋊C4—21no—
204C42×C7C2×D411yescharacteristic
205C42×C7C2×D411yescharacteristic
206C42×C7C2×D411yescharacteristic
207C42×C7C2×D411yescharacteristic
208C22⋊Dic7—22no—
209(C2×D7)⋊C4—21no—
210(C2×D7)⋊C4—21no—
211(C2×D7)⋊C4—21no—
212(C2×D7)⋊C4—21no—
213(C2×D7)⋊C4—21no—
214(C2×D7)⋊C4—21no—
215(C2×D7)⋊C4—21no—
216(C2×D7)⋊C4—21no—
217(C2×D7)⋊C4—22no—
218(C2×D7)⋊C4—22no—
219(C2×D7)⋊C4—22no—
220(C2×D7)⋊C4—22no—
221C4⋊Dic7—22no—
222C4⋊Dic7—22no—
223C4⋊Dic7C22⋊C412yes—
224C4⋊Dic7C22⋊C412yes—
225Dic7⋊C4—22no—
226Dic7⋊C4—22no—
227Dic7⋊C4C22⋊C412yes—
228Dic7⋊C4C22⋊C412yes—
229Dic7⋊C4C22⋊C412yes—
230Dic7⋊C4C22⋊C412yes—
231C4×Dic7—22no—
232C4×Dic7C2×D412yes—
233C4×Dic7C2×D412yes—
234C4×Dic7C2×D412yes—
235C4×Dic7C2×D412yes—
236C2×C7⋊C8—22no—
237C2×C7⋊C8—22no—
238#542—142no—
239#542—142no—
240#542—142no—
241#542—142no—
242C2×C4⋊Q8—71no—
243C2×#126—71no—
244C2×#126C2×D711yescharacteristic
245C2×#124—71no—
246C2×#124—71no—
247C2×#124—71no—
248C2×#123—71no—
249C2×#123—71no—
250C2×C22⋊Q8—71no—
251C2×C22⋊Q8—71no—
252C2×C22⋊Q8—71no—
253C2×#121—71no—
254C2×C4×Q8—71no—
255C2×C4×D4—71no—
256C2×#117—71no—
257#446—142no—
258#446—142no—
259C8×Q8—142no—
260C8×Q8—142no—
261#432—71no—
262#432—72no—
263#432C2×D711yescharacteristic
264#431—71no—
265#431—72no—
266#431—72no—
267#431—72no—
268#431C2×D711yescharacteristic
269#324—72no—
270#324C2×D712yes—
271#323—72no—
272#323—72no—
273#323—72no—
274#323—72no—
275#323—72no—
276#323C2×D712yes—
277C23×C7—21no—
278C23×C7—22no—
279C23×C7—41no—
280C23×C7—41no—
281C23×C7C23×C411yescharacteristic
282C22×D7—21no—
283C22×D7—21no—
284C22×D7—22no—
285C22×D7—22no—
286C22×D7—41no—
287C22×D7—41no—
288C22×D7—41no—
289C22×D7—41no—
290C2×C4×C7—22no—
291C2×C4×C7—21no—
292C2×C4×C7—21no—
293C2×C4×C7—21no—
294C2×C4×C7—22no—
295C2×C4×C7—41no—
296C2×C4×C7—41no—
297C2×C4×C7—41no—
298C2×C4×C7—41no—
299C2×C4×C7C2×C22⋊C411yescharacteristic
300C2×C4×C7C2×C22⋊C411yescharacteristic
301C2×C4×C7C2×C22⋊C411yescharacteristic
302C2×C4×C7C2×C22⋊C411yescharacteristic
303C2×C4×C7C22×D411yescharacteristic
304C2×C4×C7C22×D411yescharacteristic
305C22⋊D7—44no—
306C22⋊D7—82no—
307C2×Dic7—22no—
308C2×Dic7—21no—
309C2×Dic7—21no—
310C2×Dic7—41no—
311C2×Dic7—41no—
312C2×Dic7—41no—
313C2×Dic7—41no—
314C2×Dic7—82no—
315C2×Dic7C2×C22⋊C412yes—
316C2×Dic7C2×C22⋊C412yes—
317C2×Dic7C2×C22⋊C412yes—
318C2×Dic7C2×C22⋊C412yes—
319C2×Dic7#13114yes—
320D28—81no—
321D28—81no—
322C4×D7—44no—
323C4×D7—82no—
324Dic14—24no—
325Dic14—24no—
326Dic14—82no—
327Dic14—81no—
328Dic14—81no—
329C7×C8—42no—
330C7×C8—42no—
331C7⋊C8—42no—
332C7⋊C8—42no—
333C22×Q8—71no—
334C22×Q8—71no—
335C22×Q8—71no—
336C22×D4—71no—
337C22×D4—71no—
338C22×D4—71no—
339C23×C4—71no—
340C23×C4—71no—
341C23×C4—71no—
342C4⋊Q8—142no—
343C4⋊Q8—142no—
344#126—21no—
345#126—21no—
346#126—21no—
347#126—21no—
348#126—142no—
349#126—142no—
350#124—142no—
351#124—142no—
352#124—142no—
353#124—142no—
354#124—141no—
355#124—141no—
356#124—141no—
357#124—141no—
358#123—142no—
359#123—142no—
360#123—142no—
361#123—142no—
362C22⋊Q8—142no—
363C22⋊Q8—142no—
364C22⋊Q8—142no—
365C22⋊Q8—142no—
366C22⋊Q8—142no—
367C22⋊Q8—142no—
368#121—142no—
369#121—142no—
370C4×Q8—72no—
371C4×Q8—72no—
372C4×Q8—72no—
373C4×Q8—72no—
374C4×D4—142no—
375C4×D4—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⋊C4—71no—
384C2×C4⋊C4—71no—
385C2×C4⋊C4C4×D711yescharacteristic
386C2×C4⋊C4C4×D711yescharacteristic
387C2×C4⋊C4C22×D711yescharacteristic
388C2×C22⋊C4—71no—
389C2×C22⋊C4—71no—
390C2×C22⋊C4—71no—
391C2×C22⋊C4—71no—
392C2×C22⋊C4—71no—
393C2×C22⋊C4—71no—
394C2×C22⋊C4—71no—
395C2×C22⋊C4—71no—
396C2×C22⋊C4—71no—
397C2×C22⋊C4C4×D711yescharacteristic
398C2×C22⋊C4C4×D711yescharacteristic
399C2×C22⋊C4C22×D711yescharacteristic
400C2×C42—71no—
401C2×C42—71no—
402C2×C42—71no—
403C2×C42C22×D711yescharacteristic
404C4⋊C8—21no—
405C4⋊C8—21no—
406C4⋊C8—142no—
407C4⋊C8—142no—
408C4⋊C8—142no—
409C4⋊C8—142no—
410C4⋊C8—141no—
411C4⋊C8—141no—
412C22⋊C8—72no—
413C22⋊C8—72no—
414C22⋊C8C22×D712yes—
415C22⋊C8C22×D712yes—
416#97—21no—
417#97—142no—
418#97—141no—
419C4×C8—21no—
420C4×C8—142no—
421C4×C8—142no—
422C4×C8—142no—
423C4×C8—141no—
424C22×C7—21no—
425C22×C7—21no—
426C22×C7—41no—
427C22×C7—41no—
428C22×C7—41no—
429C22×C7—82no—
430C22×C7C22×C22⋊C411yescharacteristic
431C22×C7C2×#13112yes—
432C2×D7—41no—
433C2×D7—41no—
434C2×D7—41no—
435C2×D7—41no—
436C2×D7—41no—
437C2×D7—41no—
438C2×D7—82no—
439C2×D7—82no—
440C4×C7—21no—
441C4×C7—21no—
442C4×C7—21no—
443C4×C7—21no—
444C4×C7—21no—
445C4×C7—21no—
446C4×C7—41no—
447C4×C7—41no—
448C4×C7—41no—
449Dic7—22no—
450Dic7—22no—
451Dic7—22no—
452Dic7—41no—
453Dic7—41no—
454Dic7#40814yes—
455C24—71no—
456C24—71no—
457C24C2×C4×D711yescharacteristic
458C2×Q8—72no—
459C2×Q8—72no—
460C2×Q8—144no—
461C2×Q8—142no—
462C2×Q8—141no—
463C2×Q8—141no—
464C2×Q8—561no—
465C2×Q8—561no—
466C2×D4—142no—
467C2×D4—144no—
468C2×D4—142no—
469C2×D4—141no—
470C2×D4—141no—
471C2×D4—561no—
472C2×D4—561no—
473C22×C4—71no—
474C22×C4—71no—
475C22×C4—71no—
476C22×C4—71no—
477C22×C4—71no—
478C22×C4—71no—
479C22×C4—142no—
480C22×C4—144no—
481C22×C4—142no—
482C22×C4—142no—
483C22×C4—561no—
484C22×C4—561no—
485C22×C4C2×C4×D711yescharacteristic
486C22×C4C2×C4×D711yescharacteristic
487C22×C4C2×C4×D711yescharacteristic
488C22×C4C2×C4×D711yescharacteristic
489C22×C4C2×C4×D711yescharacteristic
490C22×C4C23×D711yescharacteristic
491C2×C8—22no—
492C2×C8—22no—
493C2×C8—142no—
494C2×C8—142no—
495C4⋊C4—21no—
496C4⋊C4—21no—
497C4⋊C4—21no—
498C4⋊C4—21no—
499C4⋊C4—21no—
500C4⋊C4—21no—
501C4⋊C4—72no—
502C4⋊C4—72no—
503C4⋊C4—72no—
504C4⋊C4—72no—
505C4⋊C4—72no—
506C4⋊C4—72no—
507C4⋊C4—142no—
508C4⋊C4—142no—
509C4⋊C4—142no—
510C4⋊C4—142no—
511C22⋊C4—21no—
512C22⋊C4—21no—
513C22⋊C4—21no—
514C22⋊C4—21no—
515C22⋊C4—21no—
516C22⋊C4—21no—
517C22⋊C4—142no—
518C22⋊C4—142no—
519C22⋊C4—142no—
520C22⋊C4—142no—
521C22⋊C4—142no—
522C22⋊C4—141no—
523C22⋊C4—141no—
524C22⋊C4—141no—
525C22⋊C4—141no—
526C22⋊C4—141no—
527C22⋊C4—141no—
528C22⋊C4—141no—
529C22⋊C4—141no—
530C42—72no—
531C42—72no—
532C42—72no—
533C42—72no—
534C42—142no—
535C42D4×D711yescharacteristic
536C42D4×D711yescharacteristic
537C42D4×D711yescharacteristic
538C42D4×D711yescharacteristic
539C2×C7—22no—
540C2×C7—81no—
541C2×C7C2×#40811yescharacteristic
542C2×C7#288411yescharacteristic
543C2×C7#288811yescharacteristic
544D7—81no—
545D7—81no—
546C23—21no—
547C23—22no—
548C23—41no—
549C23—41no—
550C23—141no—
551C23—141no—
552C23—142no—
553C23—142no—
554C23—281no—
555C23—281no—
556C23—281no—
557C23—281no—
558C23C22×C4×D711yescharacteristic
559Q8—144no—
560Q8—144no—
561Q8—561no—
562Q8—561no—
563Q8—562no—
564D4—284no—
565D4—561no—
566D4—561no—
567D4—562no—
568C2×C4—22no—
569C2×C4—21no—
570C2×C4—21no—
571C2×C4—21no—
572C2×C4—22no—
573C2×C4—41no—
574C2×C4—41no—
575C2×C4—41no—
576C2×C4—41no—
577C2×C4—72no—
578C2×C4—74no—
579C2×C4—72no—
580C2×C4—72no—
581C2×C4—72no—
582C2×C4—142no—
583C2×C4—141no—
584C2×C4—141no—
585C2×C4—284no—
586C2×C4—281no—
587C2×C4—281no—
588C2×C4—281no—
589C2×C4—281no—
590C2×C4—562no—
591C2×C4—562no—
592C2×C4D7×C22⋊C411yescharacteristic
593C2×C4D7×C22⋊C411yescharacteristic
594C2×C4D7×C22⋊C411yescharacteristic
595C2×C4D7×C22⋊C411yescharacteristic
596C2×C4C2×D4×D711yescharacteristic
597C2×C4C2×D4×D711yescharacteristic
598C8—42no—
599C8—42no—
600C8—282no—
601C8—282no—
602C7#1739011yescharacteristic, complemented, Sylow
603C22—21no—
604C22—21no—
605C22—41no—
606C22—41no—
607C22—41no—
608C22—82no—
609C22—281no—
610C22—281no—
611C22—281no—
612C22—281no—
613C22—281no—
614C22—281no—
615C22—562no—
616C22—562no—
617C22C2×D7×C22⋊C411yescharacteristic
618C22D7×#13112yes—
619C4—21no—
620C4—21no—
621C4—21no—
622C4—21no—
623C4—21no—
624C4—21no—
625C4—41no—
626C4—41no—
627C4—41no—
628C4—74no—
629C4—142no—
630C4—142no—
631C4—142no—
632C4—281no—
633C4—281no—
634C2—22no—
635C2—81no—
636C2—561no—
637C2—561no—
638C2D7×#40811yescharacteristic
639C2#1173613411yescharacteristic
640C2#1173615911yescharacteristic
subgroupG/H
centerC22C2×D7×C22⋊C4
commutatorC23×C7C23×C4
FrattiniC22×C4C23×D7
FittingC7×#1473C2
socleC22×C7C22×C22⋊C4
prime radicalC2×#6447C4
cosocleC22×C4×C7C24
hypercenter#1473D7
hypocenterC7#17390
LCSG ▷ C23×C7 ▷ C2×C7 ▷ C7
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1473

Complements

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

NH ≅ G/Ntype
2. #11736759C2semidirect
3. #11736708C2semidirect
4. C7×#1473C2semidirect
5. #11729499C2semidirect
6. #11728582C2semidirect
7. #11728538C2semidirect
8. #11725883C2semidirect
9. #11725878C2semidirect
10. #11725858C2semidirect
11. #11725855C2semidirect
148. #1473D7semidirect
602. C7#17390semidirect

Maximal subgroups

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

subgroupindex
C2×#904012
#117367592
#117367082
C7×#14732
#117294992
#117285822
#117285382
#117258832
#117258782
#117258582
#117258552
#173907