Finite Group Databasebeta

← #13321457

Subgroups — #13321457

Order 1792.

944 conjugacy classes of subgroups.

The subgroup lattice has 892 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#11742795C211yesmaximal, characteristic
2C7×#2343C211yesmaximal, characteristic, complemented
3#11739655C211yesmaximal, characteristic, complemented
4#11727320C211yesmaximal, characteristic, complemented
5#11727319C211yesmaximal, characteristic, complemented
6#11727300C211yesmaximal, characteristic, complemented
7#11727298C211yesmaximal, characteristic, complemented
8#11727287C211yesmaximal, characteristic, complemented
9#11727286C211yesmaximal, characteristic
10#11727225C211yesmaximal, characteristic, complemented
11#11727224C211yesmaximal, characteristic, complemented
12#11727187C211yesmaximal, characteristic, complemented
13#11727185C211yesmaximal, characteristic, complemented
14C2×#89247C211yesmaximal, characteristic, complemented
15#11727152C211yesmaximal, characteristic
16C2×C7×#117C2211yescharacteristic
17#90482C2211yescharacteristic
18C2×#6487C2211yescharacteristic
19#90225C411yescharacteristic, complemented
20#90225C411yescharacteristic, complemented
21#90224—21no—
22#90222—21no—
23#90222—21no—
24#90220—21no—
25#90217C411yescharacteristic, complemented
26#90214C411yescharacteristic, complemented
27#90210C411yescharacteristic, complemented
28#90209C411yescharacteristic, complemented
29#90209C411yescharacteristic, complemented
30#90207C411yescharacteristic, complemented
31#90204—21no—
32#90202—21no—
33#90186—21no—
34#90186—21no—
35#90170C2211yescharacteristic
36#90170C2211yescharacteristic
37#90161C2211yescharacteristic
38#90161C2211yescharacteristic
39C7×#387—21no—
40C7×#387—21no—
41C7×#385—21no—
42C7×#383C2211yescharacteristic
43C7×#382C2211yescharacteristic
44C7×#381C2211yescharacteristic
45C4×C7×C4⋊C4C2211yescharacteristic
46C4×C7×C22⋊C4—21no—
47C7×#376C2211yescharacteristic
48C2×C7×#95C2211yescharacteristic
49#89979C2211yescharacteristic
50C2×C22⋊(C7⋊C8)C2211yescharacteristic
51#89772—21no—
52#89772—21no—
53#89771—21no—
54#89769—21no—
55#89698C2211yescharacteristic
56#89698C2211yescharacteristic
57#89697C2211yescharacteristic
58#89697C2211yescharacteristic
59#89247C2211yescharacteristic
60#89247C2211yescharacteristic
61#89247C2211yescharacteristic
62#89247C2211yescharacteristic
63#89247C2211yescharacteristic
64#89247C2211yescharacteristic
65#89247C2211yescharacteristic
66#89247C2211yescharacteristic
67#89247C2211yescharacteristic
68#89247C2211yescharacteristic
69#89247C2211yescharacteristic
70#89247C2211yescharacteristic
71#89246C2211yescharacteristic
72#89246C2211yescharacteristic
73#89246C2211yescharacteristic
74#89246C2211yescharacteristic
75#17609—71nomaximal, Sylow
76C23×C4×C7—21no—
77C23×C4×C7C2311yescharacteristic
78C2×#1157C2×C411yescharacteristic
79C22×Dic14C2×C411yescharacteristic
80C7×#117C2×C411yescharacteristic
81C7×#117C2×C411yescharacteristic
82C7×#117C2×C411yescharacteristic
83C7×#117C2×C411yescharacteristic
84C7×#117D411yescharacteristic
85C7×#117D411yescharacteristic
86C7×#117D411yescharacteristic
87C7×#117D411yescharacteristic
88C2×C7×C4⋊C4—21no—
89C2×C7×C4⋊C4—21no—
90C2×C7×C4⋊C4D411yescharacteristic
91C2×C7×C4⋊C4D411yescharacteristic
92C2×C7×C22⋊C4—21no—
93C2×C7×C22⋊C4D411yescharacteristic
94C2×C7×C22⋊C4D411yescharacteristic
95C2×C42×C7—21no—
96C2×C42×C7—21no—
97C2×C42×C7C2311yescharacteristic
98C2×C42×C7C2311yescharacteristic
99#6516—21no—
100C2×C22⋊Dic7—21no—
101#6493C2×C411yescharacteristic
102#6493C2311yescharacteristic
103#6492—21no—
104#6492—21no—
105#6492—21no—
106C4×C22⋊D7—21no—
107C4×C22⋊D7—21no—
108C4×C22⋊D7—21no—
109C4×C22⋊D7—21no—
110#6489—21no—
111#6489—21no—
112#6489C2×C411yescharacteristic
113C2×C4⋊Dic7C2×C411yescharacteristic
114#6487—21no—
115#6487—21no—
116#6487—21no—
117#6487—21no—
118#6487C2×C411yescharacteristic
119#6487C2×C411yescharacteristic
120#6487C2×C411yescharacteristic
121#6487C2311yescharacteristic
122#6487C2311yescharacteristic
123#6487C2311yescharacteristic
124C2×Dic7⋊C4—21no—
125C2×#1136—21no—
126C22×C7⋊C8—21no—
127#6461—21no—
128#6461—21no—
129#6460—21no—
130#6460—21no—
131#6459—21no—
132#6459—21no—
133#6455—21no—
134D7×C4⋊C4—21no—
135#6453—21no—
136#6452—21no—
137#6452—21no—
138#6452—21no—
139#6452—21no—
140#6451—21no—
141#6450—21no—
142#6450—21no—
143#6449—21no—
144#6449—21no—
145#6448—21no—
146#6448—21no—
147#6446—21no—
148#6446—21no—
149(C22⋊D7)⋊C4—21no—
150(C22⋊D7)⋊C4—21no—
151#6442—21no—
152#6442—21no—
153#6442—21no—
154#6442—21no—
155#6441—21no—
156#6441—21no—
157#6440—21no—
158#6440—21no—
159#6439—21no—
160#6439—21no—
161#6438C2×C411yescharacteristic, complemented
162#6438C2×C411yescharacteristic, complemented
163C4×D28C2×C411yescharacteristic, complemented
164C4×D28C2×C411yescharacteristic, complemented
165#6435—21no—
166#6435—21no—
167#6433—21no—
168#6433—21no—
169#6433C2×C411yescharacteristic, complemented
170#6433C2×C411yescharacteristic, complemented
171#6432C2×C411yescharacteristic, complemented
172#6432C2×C411yescharacteristic, complemented
173#6432C2×C411yescharacteristic, complemented
174#6432C2×C411yescharacteristic, complemented
175C4×Dic14—21no—
176C4×Dic14—21no—
177C4×Dic14C2×C411yescharacteristic, complemented
178C4×Dic14C2×C411yescharacteristic, complemented
179C4×Dic14C2×C411yescharacteristic, complemented
180C4×Dic14C2×C411yescharacteristic, complemented
181C4×Dic14C2×C411yescharacteristic, complemented
182C4×Dic14C2×C411yescharacteristic, complemented
183C7×#95—21no—
184C7×#95—21no—
185C7×#95—21no—
186C7×#95—21no—
187C7×#95—21no—
188C7×#95—21no—
189C7×#95C2311yescharacteristic
190C7×#95C2311yescharacteristic
191C7×#95C2311yescharacteristic
192C7×#95C2311yescharacteristic
193C22⋊(C7⋊C8)—21no—
194C22⋊(C7⋊C8)—21no—
195C22⋊(C7⋊C8)C2311yescharacteristic
196C22⋊(C7⋊C8)C2311yescharacteristic
197C22⋊(C7⋊C8)C2311yescharacteristic
198C22⋊(C7⋊C8)C2311yescharacteristic
199C4⋊(C7⋊C8)—21no—
200C4⋊(C7⋊C8)—21no—
201C4⋊(C7⋊C8)—21no—
202C4⋊(C7⋊C8)—21no—
203#6377—21no—
204#6377—21no—
205C4×C7⋊C8—21no—
206C4×C7⋊C8—21no—
207#3495—71no—
208#2924—71no—
209#2343D711yescharacteristic, complemented
210#1521—71no—
211#1518—71no—
212#1516—71no—
213#1515—71no—
214#1512—71no—
215#1511—71no—
216#1509—71no—
217#1506—71no—
218#1504—71no—
219#1503—71no—
220#1500—71no—
221C2×#328—71no—
222C24×C7C2×D411yescharacteristic
223C22×C4×C7—21no—
224C22×C4×C7—21no—
225C22×C4×C7—21no—
226C22×C4×C7—21no—
227C22×C4×C7—42no—
228C22×C4×C7—42no—
229C22×C4×C7—42no—
230C22×C4×C7—81no—
231C22×C4×C7C22×C411yescharacteristic
232C22×C4×C7C22×C411yescharacteristic
233C22×C4×C7C2×D411yescharacteristic
234C22×C4×C7C2×D411yescharacteristic
235C22×C4×C7C2×D411yescharacteristic
236C22×C4×C7C2×D411yescharacteristic
237C22×C4×C7C2×D411yescharacteristic
238C22×C4×C7C2×D411yescharacteristic
239C22×C4×C7C2×D411yescharacteristic
240C22×C4×C7C2411yescharacteristic
241C2×C22⋊D7—21no—
242C2×C22⋊D7—21no—
243C2×C22⋊D7—21no—
244C22×Dic7—21no—
245C22×Dic7—21no—
246#1157—42no—
247C2×D28C22×C411yescharacteristic
248C2×C4×D7—21no—
249C2×C4×D7—21no—
250C2×C4×D7—21no—
251C2×Dic14—21no—
252C2×Dic14—21no—
253C2×Dic14—21no—
254C2×Dic14—42no—
255C2×Dic14C22×C411yescharacteristic
256C2×Dic14C22×C411yescharacteristic
257C2×Dic14C22×C411yescharacteristic
258C7×C4⋊C4—42no—
259C7×C4⋊C4—81no—
260C7×C4⋊C4C22⋊C411yescharacteristic
261C7×C4⋊C4C22⋊C411yescharacteristic
262C7×C4⋊C4C22⋊C411yescharacteristic
263C7×C4⋊C4C22⋊C411yescharacteristic
264C7×C4⋊C4C22⋊C411yescharacteristic
265C7×C4⋊C4C22⋊C411yescharacteristic
266C7×C4⋊C4C22⋊C411yescharacteristic
267C7×C4⋊C4C22⋊C411yescharacteristic
268C7×C22⋊C4—42no—
269C7×C22⋊C4C22⋊C411yescharacteristic
270C7×C22⋊C4C22⋊C411yescharacteristic
271C7×C22⋊C4C22⋊C411yescharacteristic
272C7×C22⋊C4C22⋊C411yescharacteristic
273C7×C22⋊C4C22⋊C411yescharacteristic
274C7×C22⋊C4C22⋊C411yescharacteristic
275C7×C22⋊C4C22⋊C411yescharacteristic
276C7×C22⋊C4C22⋊C411yescharacteristic
277C42×C7—42no—
278C42×C7—81no—
279C42×C7C22×C411yescharacteristic
280C42×C7C22×C411yescharacteristic
281C42×C7C22×C411yescharacteristic
282C42×C7C22×C411yescharacteristic
283C42×C7C2×D411yescharacteristic
284C42×C7C2×D411yescharacteristic
285C42×C7C2×D411yescharacteristic
286C42×C7C2×D411yescharacteristic
287C22⋊Dic7—21no—
288C22⋊Dic7—21no—
289C22⋊Dic7—21no—
290C22⋊Dic7—21no—
291C22⋊Dic7—21no—
292C22⋊Dic7—21no—
293C22⋊Dic7—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—
302C4⋊Dic7—21no—
303C4⋊Dic7—21no—
304C4⋊Dic7—21no—
305C4⋊Dic7—21no—
306C4⋊Dic7—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—
325Dic7⋊C4—21no—
326Dic7⋊C4—21no—
327Dic7⋊C4—21no—
328Dic7⋊C4—21no—
329C4×Dic7—21no—
330C4×Dic7—21no—
331C4×Dic7—21no—
332C4×Dic7—21no—
333C4×Dic7—21no—
334C4×Dic7—21no—
335C4×Dic7—21no—
336#1136—42no—
337C2×C7⋊C8—21no—
338C2×C7⋊C8—21no—
339C2×C7⋊C8—21no—
340C2×C7⋊C8—21no—
341C2×C7⋊C8—42no—
342#556—141no—
343#554—141no—
344#552—141no—
345#552—141no—
346#552—141no—
347#552—141no—
348#551—141no—
349#551—141no—
350#544—71no—
351#542—71no—
352#542—71no—
353#541—71no—
354#541—71no—
355#536—71no—
356#533—71no—
357#533—71no—
358#529—71no—
359#529—71no—
360#525—71no—
361C2×C22⋊Q8—71no—
362#520—71no—
363#519—71no—
364C2×#117C2×D711yescharacteristic
365#433—141no—
366#433—141no—
367#432—71no—
368#432—71no—
369#431—71no—
370#431—71no—
371#424—141no—
372#407—71no—
373C2×C22⋊C8—71no—
374#405—141no—
375#387—21no—
376#387—21no—
377#385—21no—
378#383C2×D711yescharacteristic
379#382C2×D711yescharacteristic
380#381C2×D711yescharacteristic
381C4×C4⋊C4C2×D711yescharacteristic
382C4×C22⋊C4—21no—
383#376C2×D711yescharacteristic
384C2×#95C2×D711yescharacteristic
385#328—71no—
386#328—71no—
387#328—71no—
388#328—71no—
389#328—71no—
390#328—71no—
391#328—71no—
392#328—71no—
393#328—71no—
394#328—71no—
395#328—71no—
396#328—71no—
397#327—71no—
398#327—71no—
399#327—71no—
400#327—71no—
401C23×C7—21no—
402C23×C7—21no—
403C23×C7—22no—
404C23×C7—41no—
405C23×C7C2×C22⋊C411yescharacteristic
406C23×C7C2×C22⋊C411yescharacteristic
407C23×C7C22×D411yescharacteristic
408C22×D7—21no—
409C2×C4×C7—21no—
410C2×C4×C7—21no—
411C2×C4×C7—21no—
412C2×C4×C7—21no—
413C2×C4×C7—22no—
414C2×C4×C7—22no—
415C2×C4×C7—22no—
416C2×C4×C7—41no—
417C2×C4×C7—41no—
418C2×C4×C7—41no—
419C2×C4×C7—41no—
420C2×C4×C7—41no—
421C2×C4×C7—41no—
422C2×C4×C7—41no—
423C2×C4×C7—41no—
424C2×C4×C7—41no—
425C2×C4×C7—41no—
426C2×C4×C7—41no—
427C2×C4×C7—41no—
428C2×C4×C7—41no—
429C2×C4×C7—41no—
430C2×C4×C7—41no—
431C2×C4×C7—41no—
432C2×C4×C7—41no—
433C2×C4×C7—84no—
434C2×C4×C7C2×C22⋊C411yescharacteristic
435C2×C4×C7C2×C22⋊C411yescharacteristic
436C2×C4×C7C2×C22⋊C411yescharacteristic
437C2×C4×C7C2×C22⋊C411yescharacteristic
438C2×C4×C7C2×C22⋊C411yescharacteristic
439C2×C4×C7C2×C22⋊C411yescharacteristic
440C2×C4×C7C2×C22⋊C411yescharacteristic
441C2×C4×C7C2×C22⋊C411yescharacteristic
442C2×C4×C7C2×C22⋊C411yescharacteristic
443C2×C4×C7C2×C22⋊C411yescharacteristic
444C2×C4×C7C23×C411yescharacteristic
445C2×C4×C7C22×D411yescharacteristic
446C22⋊D7—41no—
447C22⋊D7—41no—
448C22⋊D7—42no—
449C22⋊D7—81no—
450C2×Dic7—21no—
451C2×Dic7—21no—
452C2×Dic7—21no—
453C2×Dic7—21no—
454C2×Dic7—21no—
455C2×Dic7—21no—
456C2×Dic7—21no—
457C2×Dic7—42no—
458C2×Dic7—81no—
459D28—41no—
460C4×D7—42no—
461C4×D7—81no—
462C4×D7—81no—
463Dic14—42no—
464Dic14—41no—
465Dic14—41no—
466Dic14—41no—
467Dic14—81no—
468Dic14—81no—
469C7⋊C8—41no—
470C7⋊C8—41no—
471C7⋊C8—41no—
472C7⋊C8—41no—
473C2×#41—71no—
474C22×Q8—71no—
475C23×C4—21no—
476C23×C4C22×D711yescharacteristic
477C2×M16—141no—
478C22×C8—141no—
479C4⋊Q8—71no—
480C4⋊Q8—71no—
481C4⋊Q8—71no—
482C4⋊Q8—71no—
483C4⋊Q8—141no—
484#126—141no—
485#126—141no—
486#126—141no—
487#126—141no—
488#126—141no—
489#126—141no—
490#126—141no—
491#126—141no—
492#125—71no—
493#125—71no—
494#125—141no—
495#125—141no—
496#125—141no—
497#125—141no—
498#125—141no—
499#125—141no—
500#125—141no—
501#124—71no—
502#124—71no—
503#124—141no—
504#124—141no—
505#123—141no—
506#123—141no—
507#123—141no—
508#123—141no—
509#123—141no—
510#123—141no—
511#123—141no—
512C22⋊Q8—71no—
513C22⋊Q8—71no—
514C22⋊Q8—71no—
515C22⋊Q8—71no—
516C22⋊Q8—71no—
517C22⋊Q8—71no—
518C22⋊Q8—141no—
519C22⋊Q8—141no—
520C22⋊Q8—141no—
521C22⋊Q8—141no—
522C22⋊Q8—141no—
523C22⋊Q8—141no—
524C22⋊Q8—141no—
525C22⋊Q8—141no—
526C22⋊Q8—141no—
527C22⋊Q8—141no—
528#121—71no—
529#121—71no—
530#120—141no—
531C4×Q8—71no—
532C4×Q8—71no—
533C4×Q8—71no—
534C4×Q8—71no—
535C4×Q8—71no—
536C4×Q8—71no—
537C4×Q8—141no—
538C4×Q8—141no—
539C4×Q8—141no—
540C4×Q8—141no—
541C4×D4—71no—
542C4×D4—71no—
543C4×D4—141no—
544C4×D4—141no—
545C4×D4—141no—
546C4×D4—141no—
547C4×D4—141no—
548C4×D4—141no—
549#117—71no—
550#117—141no—
551#117—141no—
552#117—141no—
553#117—141no—
554#117—141no—
555#117—141no—
556#117—141no—
557#117C4×D711yescharacteristic
558#117C4×D711yescharacteristic
559#117C4×D711yescharacteristic
560#117C4×D711yescharacteristic
561#117D2811yescharacteristic
562#117D2811yescharacteristic
563#117D2811yescharacteristic
564#117D2811yescharacteristic
565C2×C4⋊C4—21no—
566C2×C4⋊C4—21no—
567C2×C4⋊C4—71no—
568C2×C4⋊C4—141no—
569C2×C4⋊C4—141no—
570C2×C4⋊C4C22⋊D711yescharacteristic
571C2×C4⋊C4C22⋊D711yescharacteristic
572C2×C22⋊C4—21no—
573C2×C22⋊C4—141no—
574C2×C22⋊C4C22⋊D711yescharacteristic
575C2×C22⋊C4C22⋊D711yescharacteristic
576C2×C42—21no—
577C2×C42—21no—
578C2×C42C22×D711yescharacteristic
579C2×C42C22×D711yescharacteristic
580C4⋊C8—141no—
581C4⋊C8—141no—
582C4⋊C8—141no—
583C4⋊C8—141no—
584C22⋊C8—71no—
585C22⋊C8—71no—
586C22⋊C8—71no—
587C22⋊C8—71no—
588C22⋊C8—141no—
589C22⋊C8—141no—
590#97—141no—
591#97—141no—
592C4×C8—141no—
593C4×C8—141no—
594#95—21no—
595#95—21no—
596#95—21no—
597#95—21no—
598#95—21no—
599#95—21no—
600#95C22×D711yescharacteristic
601#95C22×D711yescharacteristic
602#95C22×D711yescharacteristic
603#95C22×D711yescharacteristic
604C22×C7—21no—
605C22×C7—21no—
606C22×C7—21no—
607C22×C7—21no—
608C22×C7—21no—
609C22×C7—21no—
610C22×C7—21no—
611C22×C7—42no—
612C22×C7—42no—
613C22×C7#41012yes—
614C22×C7C22×C22⋊C411yescharacteristic
615C22×C7#57711yescharacteristic
616C22×C7#57811yescharacteristic
617C2×D7—41no—
618C2×D7—41no—
619C2×D7—41no—
620C4×C7—21no—
621C4×C7—21no—
622C4×C7—21no—
623C4×C7—21no—
624C4×C7—21no—
625C4×C7—21no—
626C4×C7—21no—
627C4×C7—21no—
628C4×C7—21no—
629C4×C7—21no—
630C4×C7—21no—
631C4×C7—21no—
632C4×C7—42no—
633C4×C7—81no—
634C4×C7—81no—
635C4×C7—81no—
636Dic7—41no—
637Dic7—41no—
638Dic7—41no—
639Dic7—41no—
640Dic7—41no—
641Dic7—41no—
642Dic7—41no—
643C24C2×C22⋊D711yescharacteristic
644#41—282no—
645C2×Q8—71no—
646C2×Q8—71no—
647C2×Q8—71no—
648C2×Q8—141no—
649C2×Q8—141no—
650C2×Q8—141no—
651C2×Q8—282no—
652C2×D4—71no—
653C2×D4—141no—
654C2×D4—141no—
655C2×D4—141no—
656C22×C4—21no—
657C22×C4—21no—
658C22×C4—21no—
659C22×C4—21no—
660C22×C4—42no—
661C22×C4—42no—
662C22×C4—42no—
663C22×C4—81no—
664C22×C4—141no—
665C22×C4—141no—
666C22×C4—141no—
667C22×C4—141no—
668C22×C4—141no—
669C22×C4C2×C4×D711yescharacteristic
670C22×C4C2×C4×D711yescharacteristic
671C22×C4C2×D2811yescharacteristic
672C22×C4C2×D2811yescharacteristic
673C22×C4C2×C22⋊D711yescharacteristic
674C22×C4C2×C22⋊D711yescharacteristic
675C22×C4C2×C22⋊D711yescharacteristic
676C22×C4C2×C22⋊D711yescharacteristic
677C22×C4C2×C22⋊D711yescharacteristic
678C22×C4C23×D711yescharacteristic
679M16—282no—
680C2×C8—141no—
681C2×C8—141no—
682C2×C8—141no—
683C2×C8—141no—
684C2×C8—282no—
685C4⋊C4—42no—
686C4⋊C4—71no—
687C4⋊C4—71no—
688C4⋊C4—71no—
689C4⋊C4—71no—
690C4⋊C4—81no—
691C4⋊C4—141no—
692C4⋊C4—141no—
693C4⋊C4—141no—
694C4⋊C4—141no—
695C4⋊C4—141no—
696C4⋊C4—141no—
697C4⋊C4—141no—
698C4⋊C4—141no—
699C4⋊C4—141no—
700C4⋊C4—141no—
701C4⋊C4—141no—
702C4⋊C4—141no—
703C4⋊C4—141no—
704C4⋊C4—141no—
705C4⋊C4—141no—
706C4⋊C4—141no—
707C4⋊C4—141no—
708C4⋊C4—141no—
709C4⋊C4—141no—
710C4⋊C4—141no—
711C4⋊C4—141no—
712C4⋊C4—141no—
713C4⋊C4—141no—
714C4⋊C4(C2×D7)⋊C411yescharacteristic
715C4⋊C4(C2×D7)⋊C411yescharacteristic
716C4⋊C4(C2×D7)⋊C411yescharacteristic
717C4⋊C4(C2×D7)⋊C411yescharacteristic
718C4⋊C4(C2×D7)⋊C411yescharacteristic
719C4⋊C4(C2×D7)⋊C411yescharacteristic
720C4⋊C4(C2×D7)⋊C411yescharacteristic
721C4⋊C4(C2×D7)⋊C411yescharacteristic
722C22⋊C4—42no—
723C22⋊C4—141no—
724C22⋊C4—141no—
725C22⋊C4—141no—
726C22⋊C4—141no—
727C22⋊C4—141no—
728C22⋊C4—141no—
729C22⋊C4—141no—
730C22⋊C4—141no—
731C22⋊C4—141no—
732C22⋊C4—141no—
733C22⋊C4—141no—
734C22⋊C4—141no—
735C22⋊C4—141no—
736C22⋊C4—141no—
737C22⋊C4—141no—
738C22⋊C4(C2×D7)⋊C411yescharacteristic
739C22⋊C4(C2×D7)⋊C411yescharacteristic
740C22⋊C4(C2×D7)⋊C411yescharacteristic
741C22⋊C4(C2×D7)⋊C411yescharacteristic
742C22⋊C4(C2×D7)⋊C411yescharacteristic
743C22⋊C4(C2×D7)⋊C411yescharacteristic
744C22⋊C4(C2×D7)⋊C411yescharacteristic
745C22⋊C4(C2×D7)⋊C411yescharacteristic
746C42—42no—
747C42—81no—
748C42—141no—
749C42—141no—
750C42—141no—
751C42—141no—
752C42—141no—
753C42—141no—
754C42—141no—
755C42C2×C4×D711yescharacteristic
756C42C2×C4×D711yescharacteristic
757C42C2×C4×D711yescharacteristic
758C42C2×C4×D711yescharacteristic
759C42C2×D2811yescharacteristic
760C42C2×D2811yescharacteristic
761C42C2×D2811yescharacteristic
762C42C2×D2811yescharacteristic
763C2×C7—21no—
764C2×C7—21no—
765C2×C7—22no—
766C2×C7—41no—
767C2×C7C2×#41011yescharacteristic
768C2×C7#289811yescharacteristic
769C2×C7#290111yescharacteristic
770D7—81no—
771C23—21no—
772C23—21no—
773C23—22no—
774C23—41no—
775C23—141no—
776C23C2×(C2×D7)⋊C411yescharacteristic
777C23C2×(C2×D7)⋊C411yescharacteristic
778C23C22×C22⋊D711yescharacteristic
779Q8—281no—
780Q8—281no—
781Q8—281no—
782Q8—282no—
783Q8—561no—
784Q8—561no—
785D4—281no—
786D4—281no—
787D4—281no—
788D4—282no—
789D4—561no—
790C2×C4—21no—
791C2×C4—21no—
792C2×C4—21no—
793C2×C4—21no—
794C2×C4—22no—
795C2×C4—22no—
796C2×C4—22no—
797C2×C4—41no—
798C2×C4—41no—
799C2×C4—41no—
800C2×C4—41no—
801C2×C4—41no—
802C2×C4—41no—
803C2×C4—41no—
804C2×C4—41no—
805C2×C4—41no—
806C2×C4—41no—
807C2×C4—41no—
808C2×C4—41no—
809C2×C4—41no—
810C2×C4—41no—
811C2×C4—41no—
812C2×C4—41no—
813C2×C4—41no—
814C2×C4—84no—
815C2×C4—141no—
816C2×C4—141no—
817C2×C4—141no—
818C2×C4—141no—
819C2×C4—141no—
820C2×C4—141no—
821C2×C4—141no—
822C2×C4—282no—
823C2×C4—282no—
824C2×C4—561no—
825C2×C4—561no—
826C2×C4—561no—
827C2×C4C2×(C2×D7)⋊C411yescharacteristic
828C2×C4C2×(C2×D7)⋊C411yescharacteristic
829C2×C4C2×(C2×D7)⋊C411yescharacteristic
830C2×C4C2×(C2×D7)⋊C411yescharacteristic
831C2×C4C2×(C2×D7)⋊C411yescharacteristic
832C2×C4C2×(C2×D7)⋊C411yescharacteristic
833C2×C4C2×(C2×D7)⋊C411yescharacteristic
834C2×C4C2×(C2×D7)⋊C411yescharacteristic
835C2×C4C2×(C2×D7)⋊C411yescharacteristic
836C2×C4C2×(C2×D7)⋊C411yescharacteristic
837C2×C4C22×C4×D711yescharacteristic
838C2×C4C22×D2811yescharacteristic
839C8—281no—
840C8—281no—
841C8—281no—
842C8—281no—
843C7#1760911yescharacteristic, complemented, Sylow
844C22—21no—
845C22—21no—
846C22—21no—
847C22—21no—
848C22—21no—
849C22—21no—
850C22—21no—
851C22—42no—
852C22—42no—
853C22—281no—
854C22—281no—
855C22—281no—
856C22#8977812yes—
857C22C22×(C2×D7)⋊C411yescharacteristic
858C22#9052711yescharacteristic
859C22#9052911yescharacteristic
860C4—21no—
861C4—21no—
862C4—21no—
863C4—21no—
864C4—21no—
865C4—21no—
866C4—21no—
867C4—21no—
868C4—21no—
869C4—21no—
870C4—21no—
871C4—21no—
872C4—42no—
873C4—81no—
874C4—81no—
875C4—81no—
876C4—281no—
877C4—281no—
878C4—281no—
879C4—281no—
880C4—281no—
881C4—281no—
882C4—281no—
883C2—21no—
884C2—21no—
885C2—22no—
886C2—41no—
887C2—561no—
888C2C2×#8977811yescharacteristic
889C2#1173998111yescharacteristic
890C2#1174001511yescharacteristic
subgroupG/H
centerC22C22×(C2×D7)⋊C4
commutatorC2×C4×C7C23×C4
FrattiniC22×C4C23×D7
FittingC7×#2343C2
socleC22×C7C22×C22⋊C4
prime radical#90482C22
cosocleC22×C4×C7C24
hypercenter#2343D7
hypocenterC7#17609
LCSG ▷ C2×C4×C7 ▷ C22×C7 ▷ C7
UCSC1 ◁ C22 ◁ C2×#117 ◁ #2343

Complements

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

NH ≅ G/Ntype
2. C7×#2343C2semidirect
3. #11739655C2semidirect
4. #11727320C2semidirect
5. #11727319C2semidirect
6. #11727300C2semidirect
7. #11727298C2semidirect
8. #11727287C2semidirect
10. #11727225C2semidirect
11. #11727224C2semidirect
12. #11727187C2semidirect
13. #11727185C2semidirect
14. C2×#89247C2semidirect
19. #90225C4semidirect
20. #90225C4semidirect
25. #90217C4semidirect
26. #90214C4semidirect
27. #90210C4semidirect
28. #90209C4semidirect
29. #90209C4semidirect
30. #90207C4semidirect
161. #6438C2×C4semidirect
162. #6438C2×C4semidirect
163. C4×D28C2×C4semidirect
164. C4×D28C2×C4semidirect
169. #6433C2×C4semidirect
170. #6433C2×C4semidirect
171. #6432C2×C4semidirect
172. #6432C2×C4semidirect
173. #6432C2×C4semidirect
174. #6432C2×C4semidirect
177. C4×Dic14C2×C4semidirect
178. C4×Dic14C2×C4semidirect
179. C4×Dic14C2×C4semidirect
180. C4×Dic14C2×C4semidirect
181. C4×Dic14C2×C4semidirect
182. C4×Dic14C2×C4semidirect
209. #2343D7semidirect
843. C7#17609semidirect

Maximal subgroups

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

subgroupindex
#117427952
C7×#23432
#117396552
#117273202
#117273192
#117273002
#117272982
#117272872
#117272862
#117272252
#117272242
#117271872
#117271852
C2×#892472
#117271522
#176097