Finite Group Databasebeta

← #13322018

Subgroups — #13322018

Order 1792.

902 conjugacy classes of subgroups.

The subgroup lattice has 860 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#11742917C211yesmaximal, characteristic
2C7×#2970C211yesmaximal, characteristic, complemented
3#11739963C211yesmaximal, characteristic, complemented
4#11728567C211yesmaximal, characteristic, complemented
5#11728564C211yesmaximal, characteristic, complemented
6#11728563C211yesmaximal, characteristic, complemented
7#11728562C211yesmaximal, characteristic, complemented
8#11728561C211yesmaximal, characteristic, complemented
9#11728559C211yesmaximal, characteristic, complemented
10#11727615C211yesmaximal, characteristic, complemented
11#11727612C211yesmaximal, characteristic, complemented
12#11727555C211yesmaximal, characteristic, complemented
13#11727553C211yesmaximal, characteristic, complemented
14#11727551C211yesmaximal, characteristic, complemented
15C2×#89259C211yesmaximal, characteristic, complemented
16C4×C7×#41C2211yescharacteristic
17#90521C411yescharacteristic
18#90516C411yescharacteristic
19#90259—21no—
20#90259—21no—
21#90250—21no—
22#90250—21no—
23#90247—21no—
24#90247—21no—
25#90247—21no—
26#90247—21no—
27#90225C411yescharacteristic
28#90225C411yescharacteristic
29#90225C411yescharacteristic
30#90225C411yescharacteristic
31#90212C411yescharacteristic
32#90207C411yescharacteristic
33#90170C2211yescharacteristic
34#90170C2211yescharacteristic
35#90170C2211yescharacteristic
36#90170C2211yescharacteristic
37C2×#6438C2211yescharacteristic
38#90161C2211yescharacteristic
39C7×#446—21no—
40C7×#435—21no—
41C7×#435—21no—
42C7×C8×D4—21no—
43C7×#432C2211yescharacteristic
44C7×#432C2211yescharacteristic, complemented
45C7×#432C2211yescharacteristic, complemented
46C4×C7×M16C2211yescharacteristic, complemented
47C2×C7×#97C2211yescharacteristic
48C2×C7×#97C2211yescharacteristic, complemented
49#89796—21no—
50#89783—21no—
51#89783—21no—
52D4×C7⋊C8—21no—
53#89698C2211yescharacteristic
54#89698C2211yescharacteristic, complemented
55#89698C2211yescharacteristic, complemented
56C4×#1136C2211yescharacteristic, complemented
57C2×#6377C2211yescharacteristic
58C2×#6377C2211yescharacteristic, complemented
59#89260C2211yescharacteristic, complemented
60#89260C2211yescharacteristic, complemented
61#89260C2211yescharacteristic, complemented
62#89260C2211yescharacteristic, complemented
63#89260C2211yescharacteristic, complemented
64#89260C2211yescharacteristic, complemented
65#89260C2211yescharacteristic, complemented
66#89260C2211yescharacteristic, complemented
67#89259C2211yescharacteristic
68#89259C2211yescharacteristic
69#89259C2211yescharacteristic
70#89259C2211yescharacteristic
71#89259C2211yescharacteristic
72#89259C2211yescharacteristic
73#89259C2211yescharacteristic
74#89259C2211yescharacteristic
75#17686—71nomaximal, Sylow
76C2×C7×#41C2×C411yescharacteristic
77C22×D28C2×C411yescharacteristic
78C22×Dic14C2×C411yescharacteristic
79C2×C7×M16—21no—
80C22×C7×C8—21no—
81C22×C7×C8—21no—
82C4×C7×Q8D411yescharacteristic
83C4×C7×Q8D411yescharacteristic
84C4×C7×D4D411yescharacteristic
85C4×C7×D4D411yescharacteristic
86C4×C7×D4D411yescharacteristic
87C4×C7×D4D411yescharacteristic
88C4×C7×D4D411yescharacteristic
89C4×C7×D4D411yescharacteristic
90C7×#117C2×C411yescharacteristic
91C7×#117C2×C411yescharacteristic
92C7×#117C2×C411yescharacteristic
93C2×C42×C7C2311yescharacteristic
94C2×C42×C7C2311yescharacteristic
95C2×C42×C7C2311yescharacteristic
96#6510—21no—
97#6507—21no—
98#6503—21no—
99#6500—21no—
100#6500—21no—
101#6499—21no—
102#6498—21no—
103#6498—21no—
104#6493C2×C411yescharacteristic
105#6493C2×C411yescharacteristic
106#6493C2×C411yescharacteristic
107#6493C2×C411yescharacteristic
108#6492—21no—
109#6492—21no—
110#6492—21no—
111#6492—21no—
112C4×C22⋊D7—21no—
113C4×C22⋊D7—21no—
114C4×C22⋊D7—21no—
115C4×C22⋊D7—21no—
116C2×(C2×D7)⋊C4—21no—
117C2×(C2×D7)⋊C4—21no—
118#6489C2×C411yescharacteristic
119#6489C2×C411yescharacteristic
120#6487—21no—
121#6487—21no—
122#6487C2×C411yescharacteristic
123#6487C2×C411yescharacteristic
124#6487C2×C411yescharacteristic
125#6487C2×C411yescharacteristic
126C2×#1136—21no—
127C22×C7⋊C8—21no—
128C22×C7⋊C8—21no—
129#6461—21no—
130#6461—21no—
131#6461—21no—
132#6461—21no—
133#6459—21no—
134#6459—21no—
135#6459—21no—
136#6459—21no—
137#6456—21no—
138#6456—21no—
139#6450—21no—
140#6450—21no—
141#6448—21no—
142#6448—21no—
143#6448—21no—
144#6448—21no—
145#6446—21no—
146#6446—21no—
147#6446—21no—
148#6446—21no—
149D7×C22⋊C4—21no—
150D7×C22⋊C4—21no—
151#6440—21no—
152#6440—21no—
153#6439—21no—
154#6439—21no—
155#6439—21no—
156#6439—21no—
157#6438—21no—
158#6438—21no—
159#6438C2×C411yescharacteristic
160#6438C2×C411yescharacteristic
161#6438C2311yescharacteristic
162#6438C2311yescharacteristic
163C4×D28C2×C411yescharacteristic
164C4×D28C2×C411yescharacteristic
165C4×D28C2×C411yescharacteristic
166C4×D28C2×C411yescharacteristic
167#6435—21no—
168#6435—21no—
169#6435—21no—
170#6435—21no—
171#6433C2311yescharacteristic
172#6433C2311yescharacteristic
173#6432C2×C411yescharacteristic
174#6432C2×C411yescharacteristic
175C4×Dic14—21no—
176C4×Dic14—21no—
177C4×Dic14C2×C411yescharacteristic
178C4×Dic14C2×C411yescharacteristic
179C4×Dic14C2×C411yescharacteristic
180C4×Dic14C2×C411yescharacteristic
181C7×C4⋊C8—21no—
182C7×C4⋊C8—21no—
183C7×C4⋊C8—21no—
184C7×C22⋊C8—21no—
185C7×C22⋊C8—21no—
186C7×C22⋊C8—21no—
187C7×#97—21no—
188C7×#97—21no—
189C7×#97C2311yescharacteristic
190C7×#97C2311yescharacteristic
191C7×#97C2311yescharacteristic
192C7×#97C2311yescharacteristic
193C4×C7×C8—21no—
194C22⋊(C7⋊C8)—21no—
195C22⋊(C7⋊C8)—21no—
196C22⋊(C7⋊C8)—21no—
197C4⋊(C7⋊C8)—21no—
198C4⋊(C7⋊C8)—21no—
199C4⋊(C7⋊C8)—21no—
200#6377—21no—
201#6377—21no—
202#6377C2311yescharacteristic
203#6377C2311yescharacteristic
204#6377C2311yescharacteristic
205#6377C2311yescharacteristic
206C4×C7⋊C8—21no—
207#3510—71no—
208#2970—71no—
209#2970D711yescharacteristic, complemented
210#1535—71no—
211#1535—71no—
212#1533—71no—
213#1532—71no—
214#1532—71no—
215#1531—71no—
216#1531—71no—
217#1529—71no—
218#1529—71no—
219#1524—71no—
220#1524—71no—
221C2×#329—71no—
222C23×D7—21no—
223C7×#41—42no—
224C2×C7×Q8C22⋊C411yescharacteristic
225C2×C7×D4C22⋊C411yescharacteristic
226C2×C7×D4C22⋊C411yescharacteristic
227C2×C7×D4C22⋊C411yescharacteristic
228C22×C4×C7C22×C411yescharacteristic
229C22×C4×C7C22×C411yescharacteristic
230C22×C4×C7C22×C411yescharacteristic
231C22×C4×C7C2×D411yescharacteristic
232C22×C4×C7C2×D411yescharacteristic
233C22×C4×C7C2×D411yescharacteristic
234C22×C4×C7C2×D411yescharacteristic
235C22×C4×C7C2×D411yescharacteristic
236C22×C4×C7C2×D411yescharacteristic
237C2×C22⋊D7—21no—
238C2×C22⋊D7—21no—
239C2×C22⋊D7—21no—
240C2×C22⋊D7—21no—
241C22×Dic7—21no—
242C2×D28—21no—
243C2×D28—42no—
244C2×D28C22×C411yescharacteristic
245C2×D28C22×C411yescharacteristic
246C2×C4×D7—21no—
247C2×C4×D7—21no—
248C2×C4×D7—21no—
249C2×C4×D7—21no—
250C2×Dic14—21no—
251C2×Dic14—21no—
252C2×Dic14—21no—
253C2×Dic14—42no—
254C2×Dic14C22×C411yescharacteristic
255C2×Dic14C22×C411yescharacteristic
256C7×M16—42no—
257C2×C7×C8—21no—
258C2×C7×C8—21no—
259C2×C7×C8—21no—
260C2×C7×C8—21no—
261C2×C7×C8—42no—
262C2×C7×C8—42no—
263C7×C4⋊C4C22⋊C411yescharacteristic
264C7×C4⋊C4C22⋊C411yescharacteristic
265C7×C4⋊C4C22⋊C411yescharacteristic
266C7×C4⋊C4C22⋊C411yescharacteristic
267C7×C4⋊C4C22⋊C411yescharacteristic
268C7×C4⋊C4C22⋊C411yescharacteristic
269C7×C22⋊C4C22⋊C411yescharacteristic
270C7×C22⋊C4C22⋊C411yescharacteristic
271C7×C22⋊C4C22⋊C411yescharacteristic
272C7×C22⋊C4C22⋊C411yescharacteristic
273C7×C22⋊C4C22⋊C411yescharacteristic
274C7×C22⋊C4C22⋊C411yescharacteristic
275C42×C7C22×C411yescharacteristic
276C42×C7C22×C411yescharacteristic
277C42×C7C22×C411yescharacteristic
278C42×C7C2×D411yescharacteristic
279C42×C7C2×D411yescharacteristic
280C42×C7C2×D411yescharacteristic
281C42×C7C2×D411yescharacteristic
282C42×C7C2×D411yescharacteristic
283C42×C7C2×D411yescharacteristic
284C42×C7C2411yescharacteristic
285C22⋊Dic7—21no—
286C22⋊Dic7—21no—
287C22⋊Dic7—21no—
288C22⋊Dic7—21no—
289C22⋊Dic7—21no—
290C22⋊Dic7—21no—
291(C2×D7)⋊C4—21no—
292(C2×D7)⋊C4—21no—
293(C2×D7)⋊C4—21no—
294(C2×D7)⋊C4—21no—
295(C2×D7)⋊C4—21no—
296(C2×D7)⋊C4—21no—
297(C2×D7)⋊C4—21no—
298(C2×D7)⋊C4—21no—
299(C2×D7)⋊C4—21no—
300(C2×D7)⋊C4—21no—
301(C2×D7)⋊C4—21no—
302(C2×D7)⋊C4—21no—
303(C2×D7)⋊C4—21no—
304(C2×D7)⋊C4—21no—
305(C2×D7)⋊C4—21no—
306(C2×D7)⋊C4—21no—
307C4⋊Dic7—21no—
308C4⋊Dic7—21no—
309C4⋊Dic7C22×C411yescharacteristic
310C4⋊Dic7C22×C411yescharacteristic
311C4⋊Dic7C22×C411yescharacteristic
312C4⋊Dic7C22×C411yescharacteristic
313Dic7⋊C4—21no—
314Dic7⋊C4—21no—
315Dic7⋊C4—21no—
316Dic7⋊C4—21no—
317Dic7⋊C4—21no—
318Dic7⋊C4—21no—
319Dic7⋊C4—21no—
320Dic7⋊C4—21no—
321Dic7⋊C4—21no—
322Dic7⋊C4—21no—
323Dic7⋊C4—21no—
324Dic7⋊C4—21no—
325C4×Dic7—21no—
326C4×Dic7—21no—
327C4×Dic7—21no—
328C4×Dic7—21no—
329C4×Dic7—21no—
330C4×Dic7—21no—
331#1136—42no—
332C2×C7⋊C8—21no—
333C2×C7⋊C8—21no—
334C2×C7⋊C8—21no—
335C2×C7⋊C8—21no—
336C2×C7⋊C8—42no—
337C2×C7⋊C8—42no—
338#559—141no—
339#559—141no—
340#556—141no—
341#556—141no—
342#551—141no—
343#551—141no—
344#551—141no—
345#551—141no—
346#542—71no—
347#542—71no—
348#542—71no—
349#542—71no—
350#536—71no—
351#535—71no—
352#533—71no—
353#529—71no—
354#529—71no—
355#529—71no—
356#529—71no—
357C2×#124—71no—
358#519—71no—
359#518—71no—
360C4×#41C2×D711yescharacteristic
361#446—21no—
362#446—141no—
363#435—21no—
364#435—21no—
365#435—141no—
366#435—141no—
367C8×D4—21no—
368C8×D4—141no—
369#432—71no—
370#432—71no—
371#432—71no—
372#432C2×D711yescharacteristic
373#432C2×D711yescharacteristic, complemented
374#432C2×D711yescharacteristic, complemented
375C4×M16—71no—
376C4×M16C2×D711yescharacteristic, complemented
377C2×#97—71no—
378C2×#97—71no—
379C2×#97C2×D711yescharacteristic
380C2×#97C2×D711yescharacteristic, complemented
381#330—71no—
382#330—71no—
383#330—71no—
384#330—71no—
385#330—71no—
386#330—71no—
387#330—71no—
388#330—71no—
389#329—71no—
390#329—71no—
391#329—71no—
392#329—71no—
393#329—71no—
394#329—71no—
395#329—71no—
396#329—71no—
397C23×C7C2×C22⋊C411yescharacteristic
398C23×C7C2×C22⋊C411yescharacteristic
399C23×C7C2×C22⋊C411yescharacteristic
400C22×D7—21no—
401C22×D7—21no—
402C22×D7—42no—
403C22×D7—81no—
404C22×D7—81no—
405C7×Q8—41no—
406C7×D4—22no—
407C7×D4—22no—
408C7×D4—41no—
409C2×C4×C7—22no—
410C2×C4×C7—41no—
411C2×C4×C7—41no—
412C2×C4×C7—41no—
413C2×C4×C7—41no—
414C2×C4×C7—41no—
415C2×C4×C7—41no—
416C2×C4×C7—41no—
417C2×C4×C7—41no—
418C2×C4×C7C2×C22⋊C411yescharacteristic
419C2×C4×C7C2×C22⋊C411yescharacteristic
420C2×C4×C7C2×C22⋊C411yescharacteristic
421C2×C4×C7C2×C22⋊C411yescharacteristic
422C2×C4×C7C2×C22⋊C411yescharacteristic
423C2×C4×C7C2×C22⋊C411yescharacteristic
424C2×C4×C7C2×C22⋊C411yescharacteristic
425C2×C4×C7C2×C22⋊C411yescharacteristic
426C2×C4×C7C2×C22⋊C411yescharacteristic
427C2×C4×C7C23×C411yescharacteristic
428C2×C4×C7C22×D411yescharacteristic
429C2×C4×C7C22×D411yescharacteristic
430C22⋊D7—81no—
431C22⋊D7—81no—
432C22⋊D7—81no—
433C22⋊D7—81no—
434C2×Dic7—21no—
435C2×Dic7—21no—
436C2×Dic7—21no—
437C2×Dic7—21no—
438C2×Dic7—21no—
439C2×Dic7—21no—
440C2×Dic7—42no—
441D28—41no—
442D28—41no—
443D28—42no—
444C4×D7—81no—
445C4×D7—81no—
446C4×D7—81no—
447C4×D7—81no—
448Dic14—42no—
449Dic14—41no—
450Dic14—41no—
451Dic14—81no—
452Dic14—81no—
453C7×C8—22no—
454C7×C8—41no—
455C7×C8—41no—
456C7×C8—41no—
457C7⋊C8—22no—
458C7⋊C8—41no—
459C7⋊C8—41no—
460C7⋊C8—41no—
461C2×#41C4×D711yescharacteristic
462C22×Q8—71no—
463C22×D4—71no—
464C2×M16—21no—
465C2×M16—141no—
466C22×C8—21no—
467C22×C8—21no—
468C22×C8—141no—
469C22×C8—141no—
470C4⋊Q8—71no—
471C4⋊Q8—71no—
472C4⋊Q8—141no—
473#127—141no—
474#126—141no—
475#126—141no—
476#126—141no—
477#126—141no—
478#126—141no—
479#126—141no—
480#126—141no—
481#126—141no—
482#125—71no—
483#125—71no—
484#124—71no—
485#124—71no—
486#124—71no—
487#124—71no—
488#124—141no—
489#124—141no—
490#124—141no—
491#124—141no—
492#124—141no—
493#124—141no—
494#124—141no—
495#124—141no—
496#123—141no—
497#123—141no—
498#123—141no—
499#123—141no—
500#123—141no—
501#123—141no—
502#123—141no—
503#123—141no—
504#123—141no—
505#123—141no—
506C22⋊Q8—71no—
507C22⋊Q8—71no—
508C22⋊Q8—71no—
509C22⋊Q8—71no—
510C22⋊Q8—141no—
511C22⋊Q8—141no—
512C22⋊Q8—141no—
513C22⋊Q8—141no—
514C22⋊Q8—141no—
515C22⋊Q8—141no—
516#121—71no—
517#121—71no—
518#121—71no—
519#121—71no—
520#120—141no—
521#120—141no—
522C4×Q8—71no—
523C4×Q8—71no—
524C4×Q8—71no—
525C4×Q8—71no—
526C4×Q8—141no—
527C4×Q8—141no—
528C4×Q8—141no—
529C4×Q8—141no—
530C4×Q8D2811yescharacteristic
531C4×Q8C22⋊D711yescharacteristic
532C4×D4—71no—
533C4×D4—71no—
534C4×D4—71no—
535C4×D4—71no—
536C4×D4—141no—
537C4×D4—141no—
538C4×D4—141no—
539C4×D4—141no—
540C4×D4—141no—
541C4×D4—141no—
542C4×D4D2811yescharacteristic
543C4×D4D2811yescharacteristic
544C4×D4D2811yescharacteristic
545C4×D4C22⋊D711yescharacteristic
546C4×D4C22⋊D711yescharacteristic
547C4×D4C22⋊D711yescharacteristic
548#117—71no—
549#117—71no—
550#117—141no—
551#117—141no—
552#117—141no—
553#117—141no—
554#117—141no—
555#117—141no—
556#117C4×D711yescharacteristic
557#117C4×D711yescharacteristic
558#117C4×D711yescharacteristic
559C2×C22⋊C4—141no—
560C2×C22⋊C4—141no—
561C2×C22⋊C4—141no—
562C2×C22⋊C4—141no—
563C2×C42C22×D711yescharacteristic
564C2×C42C22×D711yescharacteristic
565C2×C42C22×D711yescharacteristic
566C4⋊C8—21no—
567C4⋊C8—21no—
568C4⋊C8—21no—
569C4⋊C8—141no—
570C4⋊C8—141no—
571C4⋊C8—141no—
572C22⋊C8—21no—
573C22⋊C8—21no—
574C22⋊C8—21no—
575C22⋊C8—141no—
576C22⋊C8—141no—
577C22⋊C8—141no—
578#97—21no—
579#97—21no—
580#97—71no—
581#97—71no—
582#97—71no—
583#97—71no—
584#97—141no—
585#97—141no—
586#97C22×D711yescharacteristic
587#97C22×D711yescharacteristic
588#97C22×D711yescharacteristic
589#97C22×D711yescharacteristic
590C4×C8—21no—
591C4×C8—141no—
592C22×C7—21no—
593C22×C7—21no—
594C22×C7—21no—
595C22×C7—21no—
596C22×C7—21no—
597C22×C7—21no—
598C22×C7—21no—
599C22×C7—21no—
600C22×C7#41312yes—
601C22×C7C22×C22⋊C411yescharacteristic
602C2×D7—41no—
603C2×D7—41no—
604C2×D7—41no—
605C2×D7—41no—
606C2×D7—41no—
607C2×D7—41no—
608C2×D7—162no—
609C4×C7—21no—
610C4×C7—21no—
611C4×C7—21no—
612C4×C7—21no—
613C4×C7—21no—
614C4×C7—21no—
615C4×C7—21no—
616C4×C7—21no—
617C4×C7—21no—
618C4×C7—21no—
619C4×C7—21no—
620C4×C7—21no—
621Dic7—41no—
622Dic7—41no—
623Dic7—41no—
624Dic7—41no—
625Dic7—41no—
626Dic7—41no—
627C24—141no—
628#41—42no—
629C2×Q8—71no—
630C2×Q8—71no—
631C2×Q8—141no—
632C2×Q8—141no—
633C2×Q8—141no—
634C2×Q8—282no—
635C2×Q8(C2×D7)⋊C411yescharacteristic
636C2×D4—71no—
637C2×D4—71no—
638C2×D4—141no—
639C2×D4—141no—
640C2×D4—141no—
641C2×D4—141no—
642C2×D4—141no—
643C2×D4—282no—
644C2×D4(C2×D7)⋊C411yescharacteristic
645C2×D4(C2×D7)⋊C411yescharacteristic
646C2×D4(C2×D7)⋊C411yescharacteristic
647C22×C4—141no—
648C22×C4—141no—
649C22×C4—141no—
650C22×C4—141no—
651C22×C4—141no—
652C22×C4C2×C4×D711yescharacteristic
653C22×C4C2×C4×D711yescharacteristic
654C22×C4C2×C4×D711yescharacteristic
655C22×C4C2×D2811yescharacteristic
656C22×C4C2×D2811yescharacteristic
657C22×C4C2×D2811yescharacteristic
658C22×C4C2×C22⋊D711yescharacteristic
659C22×C4C2×C22⋊D711yescharacteristic
660C22×C4C2×C22⋊D711yescharacteristic
661M16—42no—
662M16—282no—
663C2×C8—21no—
664C2×C8—21no—
665C2×C8—21no—
666C2×C8—21no—
667C2×C8—42no—
668C2×C8—42no—
669C2×C8—141no—
670C2×C8—141no—
671C2×C8—141no—
672C2×C8—141no—
673C2×C8—282no—
674C2×C8—282no—
675C4⋊C4—71no—
676C4⋊C4—71no—
677C4⋊C4—71no—
678C4⋊C4—71no—
679C4⋊C4—141no—
680C4⋊C4—141no—
681C4⋊C4—141no—
682C4⋊C4—141no—
683C4⋊C4—141no—
684C4⋊C4—141no—
685C4⋊C4—141no—
686C4⋊C4—141no—
687C4⋊C4—141no—
688C4⋊C4—141no—
689C4⋊C4—141no—
690C4⋊C4—141no—
691C4⋊C4—141no—
692C4⋊C4—141no—
693C4⋊C4(C2×D7)⋊C411yescharacteristic
694C4⋊C4(C2×D7)⋊C411yescharacteristic
695C4⋊C4(C2×D7)⋊C411yescharacteristic
696C4⋊C4(C2×D7)⋊C411yescharacteristic
697C4⋊C4(C2×D7)⋊C411yescharacteristic
698C4⋊C4(C2×D7)⋊C411yescharacteristic
699C22⋊C4—141no—
700C22⋊C4—141no—
701C22⋊C4—141no—
702C22⋊C4—141no—
703C22⋊C4—141no—
704C22⋊C4—141no—
705C22⋊C4—141no—
706C22⋊C4—141no—
707C22⋊C4—141no—
708C22⋊C4—141no—
709C22⋊C4—141no—
710C22⋊C4—141no—
711C22⋊C4—141no—
712C22⋊C4—141no—
713C22⋊C4—141no—
714C22⋊C4—141no—
715C22⋊C4—141no—
716C22⋊C4—141no—
717C22⋊C4—141no—
718C22⋊C4—141no—
719C22⋊C4—141no—
720C22⋊C4—141no—
721C22⋊C4(C2×D7)⋊C411yescharacteristic
722C22⋊C4(C2×D7)⋊C411yescharacteristic
723C22⋊C4(C2×D7)⋊C411yescharacteristic
724C22⋊C4(C2×D7)⋊C411yescharacteristic
725C22⋊C4(C2×D7)⋊C411yescharacteristic
726C22⋊C4(C2×D7)⋊C411yescharacteristic
727C42—141no—
728C42—141no—
729C42—141no—
730C42—141no—
731C42—141no—
732C42—141no—
733C42C2×C4×D711yescharacteristic
734C42C2×C4×D711yescharacteristic
735C42C2×C4×D711yescharacteristic
736C42C2×D2811yescharacteristic
737C42C2×D2811yescharacteristic
738C42C2×D2811yescharacteristic
739C42C2×C22⋊D711yescharacteristic
740C42C2×C22⋊D711yescharacteristic
741C42C2×C22⋊D711yescharacteristic
742C42C23×D711yescharacteristic
743C2×C7—22no—
744C2×C7—41no—
745C2×C7—41no—
746C2×C7C2×#41311yescharacteristic
747C2×C7#290111yescharacteristic
748C2×C7#290111yescharacteristic
749D7—81no—
750D7—81no—
751C23—141no—
752C23—141no—
753C23—282no—
754C23—561no—
755C23—561no—
756C23C2×(C2×D7)⋊C411yescharacteristic
757C23C2×(C2×D7)⋊C411yescharacteristic
758C23C2×(C2×D7)⋊C411yescharacteristic
759Q8—41no—
760Q8—281no—
761Q8—281no—
762Q8—282no—
763Q8—561no—
764Q8—561no—
765D4—22no—
766D4—22no—
767D4—41no—
768D4—281no—
769D4—281no—
770D4—282no—
771D4—561no—
772D4—561no—
773D4—561no—
774D4—561no—
775C2×C4—22no—
776C2×C4—41no—
777C2×C4—41no—
778C2×C4—41no—
779C2×C4—41no—
780C2×C4—41no—
781C2×C4—41no—
782C2×C4—41no—
783C2×C4—41no—
784C2×C4—141no—
785C2×C4—141no—
786C2×C4—141no—
787C2×C4—141no—
788C2×C4—141no—
789C2×C4—141no—
790C2×C4—282no—
791C2×C4—561no—
792C2×C4—561no—
793C2×C4—561no—
794C2×C4—561no—
795C2×C4C2×(C2×D7)⋊C411yescharacteristic
796C2×C4C2×(C2×D7)⋊C411yescharacteristic
797C2×C4C2×(C2×D7)⋊C411yescharacteristic
798C2×C4C2×(C2×D7)⋊C411yescharacteristic
799C2×C4C2×(C2×D7)⋊C411yescharacteristic
800C2×C4C2×(C2×D7)⋊C411yescharacteristic
801C2×C4C2×(C2×D7)⋊C411yescharacteristic
802C2×C4C2×(C2×D7)⋊C411yescharacteristic
803C2×C4C2×(C2×D7)⋊C411yescharacteristic
804C2×C4C22×C4×D711yescharacteristic
805C2×C4C22×D2811yescharacteristic
806C2×C4C22×C22⋊D711yescharacteristic
807C8—22no—
808C8—41no—
809C8—41no—
810C8—41no—
811C8—142no—
812C8—281no—
813C8—281no—
814C8—281no—
815C7#1768611yescharacteristic, complemented, Sylow
816C22—21no—
817C22—21no—
818C22—21no—
819C22—21no—
820C22—21no—
821C22—21no—
822C22—21no—
823C22—21no—
824C22—281no—
825C22—281no—
826C22—281no—
827C22—281no—
828C22—281no—
829C22—281no—
830C22—1122no—
831C22#8990412yes—
832C22C22×(C2×D7)⋊C411yescharacteristic
833C4—21no—
834C4—21no—
835C4—21no—
836C4—21no—
837C4—21no—
838C4—21no—
839C4—21no—
840C4—21no—
841C4—21no—
842C4—21no—
843C4—21no—
844C4—21no—
845C4—281no—
846C4—281no—
847C4—281no—
848C4—281no—
849C4—281no—
850C4—281no—
851C2—22no—
852C2—41no—
853C2—41no—
854C2—561no—
855C2—561no—
856C2#1173998111yescharacteristic
857C2C2×#8990411yescharacteristic
858C2#1174126211yescharacteristic
subgroupG/H
centerC22C22×(C2×D7)⋊C4
commutatorC2×C4×C7C23×C4
FrattiniC42C23×D7
FittingC7×#2970C2
socleC22×C7C22×C22⋊C4
prime radical#90521C4
cosocleC42×C7C24
hypercenter#2970D7
hypocenterC7#17686
LCSG ▷ C2×C4×C7 ▷ C22×C7 ▷ C7
UCSC1 ◁ C22 ◁ C4×#41 ◁ #2970

Complements

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

NH ≅ G/Ntype
2. C7×#2970C2semidirect
3. #11739963C2semidirect
4. #11728567C2semidirect
5. #11728564C2semidirect
6. #11728563C2semidirect
7. #11728562C2semidirect
8. #11728561C2semidirect
9. #11728559C2semidirect
10. #11727615C2semidirect
11. #11727612C2semidirect
12. #11727555C2semidirect
13. #11727553C2semidirect
14. #11727551C2semidirect
15. C2×#89259C2semidirect
44. C7×#432C22semidirect
45. C7×#432C22semidirect
46. C4×C7×M16C22semidirect
48. C2×C7×#97C22semidirect
54. #89698C22semidirect
55. #89698C22semidirect
56. C4×#1136C22semidirect
58. C2×#6377C22semidirect
59. #89260C22semidirect
60. #89260C22semidirect
61. #89260C22semidirect
62. #89260C22semidirect
63. #89260C22semidirect
64. #89260C22semidirect
65. #89260C22semidirect
66. #89260C22semidirect
209. #2970D7semidirect
373. #432C2×D7semidirect
374. #432C2×D7semidirect
376. C4×M16C2×D7semidirect
380. C2×#97C2×D7semidirect
815. C7#17686semidirect

Maximal subgroups

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

subgroupindex
#117429172
C7×#29702
#117399632
#117285672
#117285642
#117285632
#117285622
#117285612
#117285592
#117276152
#117276122
#117275552
#117275532
#117275512
C2×#892592
#176867