Finite Group Databasebeta

← #13320633

Subgroups — #13320633

Order 1792.

954 conjugacy classes of subgroups.

The subgroup lattice has 910 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#11742906C211yesmaximal, characteristic
2C7×#2965C211yesmaximal, characteristic, complemented
3#11739966C211yesmaximal, characteristic, complemented
4#11728519C211yesmaximal, characteristic, complemented
5#11728518C211yesmaximal, characteristic, complemented
6#11728517C211yesmaximal, characteristic, complemented
7#11728516C211yesmaximal, characteristic, complemented
8#11728514C211yesmaximal, characteristic, complemented
9#11728512C211yesmaximal, characteristic, complemented
10#11727609C211yesmaximal, characteristic, complemented
11#11727608C211yesmaximal, characteristic, complemented
12#11727607C211yesmaximal, characteristic, complemented
13#11727606C211yesmaximal, characteristic, complemented
14#11727490C211yesmaximal, characteristic, complemented
15#11727489C211yesmaximal, characteristic, complemented
16C4×C7×#41C2211yescharacteristic
17#90524C411yescharacteristic
18#90521C411yescharacteristic
19#90273—21no—
20#90271—21no—
21#90253—21no—
22#90251—21no—
23#90251—21no—
24#90239—21no—
25#90238—21no—
26#90238—21no—
27#90226C411yescharacteristic
28#90226C411yescharacteristic
29#90225C411yescharacteristic
30#90225C411yescharacteristic
31#90216C411yescharacteristic
32#90210C411yescharacteristic
33#90170C2211yescharacteristic
34#90170C2211yescharacteristic
35#90168C2211yescharacteristic
36#90168C2211yescharacteristic
37C4×#1157C2211yescharacteristic
38C2×C4×D28C2211yescharacteristic
39C7×#446—21no—
40C7×#436—21no—
41C7×#435—21no—
42C7×#435—21no—
43C7×#431C2211yescharacteristic
44C7×#431C2211yescharacteristic, complemented
45C7×#431C2211yescharacteristic, complemented
46C4×C7×M16C2211yescharacteristic
47C4×C7×M16C2211yescharacteristic, complemented
48C2×C4×C7×C8C2211yescharacteristic, complemented
49#89796—21no—
50#89784—21no—
51#89783—21no—
52#89783—21no—
53#89698C2211yescharacteristic
54#89698C2211yescharacteristic, complemented
55#89697C2211yescharacteristic, complemented
56#89696C2211yescharacteristic
57#89696C2211yescharacteristic, complemented
58C2×C4⋊(C7⋊C8)C2211yescharacteristic, complemented
59#89254C2211yescharacteristic
60#89254C2211yescharacteristic
61#89254C2211yescharacteristic
62#89254C2211yescharacteristic
63#89254C2211yescharacteristic
64#89254C2211yescharacteristic
65#89254C2211yescharacteristic
66#89254C2211yescharacteristic
67#89254C2211yescharacteristic, complemented
68#89254C2211yescharacteristic, complemented
69#89254C2211yescharacteristic, complemented
70#89254C2211yescharacteristic, complemented
71#89251C2211yescharacteristic, complemented
72#89251C2211yescharacteristic, complemented
73#89251C2211yescharacteristic, complemented
74#89251C2211yescharacteristic, complemented
75#17505—71nomaximal, Sylow
76C2×C7×#41C2×C411yescharacteristic
77C2×#1157—21no—
78C2×#1157—21no—
79C2×#1157C2×C411yescharacteristic
80C22×D28C2×C411yescharacteristic
81C22×C4×D7—21no—
82C2×C7×M16—21no—
83C2×C7×M16—21no—
84C22×C7×C8—21no—
85C4×C7×Q8D411yescharacteristic
86C4×C7×Q8D411yescharacteristic
87C4×C7×D4D411yescharacteristic
88C4×C7×D4D411yescharacteristic
89C4×C7×D4D411yescharacteristic
90C4×C7×D4D411yescharacteristic
91C4×C7×D4D411yescharacteristic
92C4×C7×D4D411yescharacteristic
93C7×#117C2×C411yescharacteristic
94C7×#117C2×C411yescharacteristic
95C7×#117C2×C411yescharacteristic
96C2×C42×C7C2311yescharacteristic
97C2×C42×C7C2311yescharacteristic
98C2×C42×C7C2311yescharacteristic
99#6510—21no—
100#6509—21no—
101#6503—21no—
102#6502—21no—
103#6502—21no—
104#6501—21no—
105#6500—21no—
106#6500—21no—
107#6493—21no—
108#6493—21no—
109#6493C2×C411yescharacteristic
110#6493C2×C411yescharacteristic
111#6493C2×C411yescharacteristic
112#6493C2×C411yescharacteristic
113#6493C2×C411yescharacteristic
114#6493C2×C411yescharacteristic
115#6492—21no—
116#6492—21no—
117C4×C22⋊D7—21no—
118C4×C22⋊D7—21no—
119C4×C22⋊D7—21no—
120C4×C22⋊D7—21no—
121C2×(C2×D7)⋊C4—21no—
122#6489C2×C411yescharacteristic
123C2×C4⋊Dic7C2×C411yescharacteristic
124#6487C2×C411yescharacteristic
125#6487C2×C411yescharacteristic
126C2×#1136—21no—
127C2×#1136—21no—
128C22×C7⋊C8—21no—
129#6461—21no—
130#6461—21no—
131#6459—21no—
132#6459—21no—
133#6458—21no—
134#6458—21no—
135#6457—21no—
136#6457—21no—
137#6457—21no—
138#6457—21no—
139#6453—21no—
140#6451—21no—
141#6448—21no—
142#6448—21no—
143#6447—21no—
144#6447—21no—
145#6447—21no—
146#6447—21no—
147#6446—21no—
148#6446—21no—
149#6445—21no—
150#6445—21no—
151#6441—21no—
152#6441—21no—
153#6439—21no—
154#6439—21no—
155#6438—21no—
156#6438—21no—
157#6438C2×C411yescharacteristic
158#6438C2×C411yescharacteristic
159#6437C2×C411yescharacteristic
160#6437C2×C411yescharacteristic
161C4×D28—21no—
162C4×D28—21no—
163C4×D28—21no—
164C4×D28—21no—
165C4×D28C2×C411yescharacteristic
166C4×D28C2×C411yescharacteristic
167C4×D28C2×C411yescharacteristic
168C4×D28C2311yescharacteristic
169C4×D28C2311yescharacteristic
170C4×D28C2311yescharacteristic
171#6435—21no—
172#6435—21no—
173#6435—21no—
174C42×D7—21no—
175#6433C2×C411yescharacteristic
176#6433C2×C411yescharacteristic
177#6432C2×C411yescharacteristic
178#6432C2×C411yescharacteristic
179C4×Dic14C2×C411yescharacteristic
180C4×Dic14C2311yescharacteristic
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—
189C4×C7×C8—21no—
190C4×C7×C8C2311yescharacteristic
191C4×C7×C8C2311yescharacteristic
192C4×C7×C8C2311yescharacteristic
193C4×C7×C8C2311yescharacteristic
194C22⋊(C7⋊C8)—21no—
195C22⋊(C7⋊C8)—21no—
196C22⋊(C7⋊C8)—21no—
197C4⋊(C7⋊C8)—21no—
198C4⋊(C7⋊C8)—21no—
199C4⋊(C7⋊C8)—21no—
200C4⋊(C7⋊C8)C2311yescharacteristic
201C4⋊(C7⋊C8)C2311yescharacteristic
202C4⋊(C7⋊C8)C2311yescharacteristic
203C4⋊(C7⋊C8)C2311yescharacteristic
204#6377—21no—
205#6377—21no—
206C4×C7⋊C8—21no—
207#3460—71no—
208#2989—71no—
209#2965D711yescharacteristic, complemented
210#1496—71no—
211#1495—71no—
212#1494—71no—
213#1492—71no—
214#1490—71no—
215#1489—71no—
216#1488—71no—
217#1486—71no—
218#1484—71no—
219#1483—71no—
220#1482—71no—
221#1480—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—
241C2×C22⋊D7—21no—
242C2×C22⋊D7—21no—
243C2×C22⋊D7—21no—
244C22×Dic7—21no—
245#1157—42no—
246#1157—81no—
247#1157—81no—
248#1157—81no—
249#1157—81no—
250C2×D28—21no—
251C2×D28—21no—
252C2×D28—21no—
253C2×D28—21no—
254C2×D28—21no—
255C2×D28—42no—
256C2×D28C22×C411yescharacteristic
257C2×D28C22×C411yescharacteristic
258C2×D28C22×C411yescharacteristic
259C2×C4×D7—21no—
260C2×C4×D7—21no—
261C2×C4×D7—21no—
262C2×C4×D7—21no—
263C2×C4×D7—21no—
264C2×C4×D7—21no—
265C2×C4×D7—21no—
266C2×C4×D7—81no—
267C2×C4×D7—81no—
268C2×Dic14—21no—
269C2×Dic14—21no—
270C2×Dic14C22×C411yescharacteristic
271C7×M16—42no—
272C7×M16—42no—
273C2×C7×C8—21no—
274C2×C7×C8—21no—
275C2×C7×C8—21no—
276C2×C7×C8—21no—
277C2×C7×C8—42no—
278C7×C4⋊C4C22⋊C411yescharacteristic
279C7×C4⋊C4C22⋊C411yescharacteristic
280C7×C4⋊C4C22⋊C411yescharacteristic
281C7×C4⋊C4C22⋊C411yescharacteristic
282C7×C4⋊C4C22⋊C411yescharacteristic
283C7×C4⋊C4C22⋊C411yescharacteristic
284C7×C22⋊C4C22⋊C411yescharacteristic
285C7×C22⋊C4C22⋊C411yescharacteristic
286C7×C22⋊C4C22⋊C411yescharacteristic
287C7×C22⋊C4C22⋊C411yescharacteristic
288C7×C22⋊C4C22⋊C411yescharacteristic
289C7×C22⋊C4C22⋊C411yescharacteristic
290C42×C7C22×C411yescharacteristic
291C42×C7C22×C411yescharacteristic
292C42×C7C22×C411yescharacteristic
293C42×C7C2×D411yescharacteristic
294C42×C7C2×D411yescharacteristic
295C42×C7C2×D411yescharacteristic
296C42×C7C2×D411yescharacteristic
297C42×C7C2×D411yescharacteristic
298C42×C7C2×D411yescharacteristic
299C42×C7C2411yescharacteristic
300C22⋊Dic7—21no—
301C22⋊Dic7—21no—
302C22⋊Dic7—21no—
303(C2×D7)⋊C4—21no—
304(C2×D7)⋊C4—21no—
305(C2×D7)⋊C4—21no—
306(C2×D7)⋊C4—21no—
307(C2×D7)⋊C4—21no—
308(C2×D7)⋊C4—21no—
309(C2×D7)⋊C4—21no—
310(C2×D7)⋊C4—21no—
311(C2×D7)⋊C4—21no—
312(C2×D7)⋊C4—21no—
313(C2×D7)⋊C4—21no—
314(C2×D7)⋊C4—21no—
315(C2×D7)⋊C4—21no—
316(C2×D7)⋊C4—21no—
317(C2×D7)⋊C4—21no—
318(C2×D7)⋊C4—21no—
319C4⋊Dic7—21no—
320C4⋊Dic7—21no—
321C4⋊Dic7—21no—
322C4⋊Dic7C22×C411yescharacteristic
323C4⋊Dic7C22×C411yescharacteristic
324C4⋊Dic7C22×C411yescharacteristic
325C4⋊Dic7C22×C411yescharacteristic
326Dic7⋊C4—21no—
327Dic7⋊C4—21no—
328Dic7⋊C4—21no—
329Dic7⋊C4—21no—
330Dic7⋊C4—21no—
331Dic7⋊C4—21no—
332Dic7⋊C4—21no—
333Dic7⋊C4—21no—
334C4×Dic7—21no—
335C4×Dic7—21no—
336C4×Dic7—21no—
337#1136—81no—
338#1136—81no—
339C2×C7⋊C8—21no—
340C2×C7⋊C8—21no—
341C2×C7⋊C8—21no—
342C2×C7⋊C8—21no—
343C2×C7⋊C8—81no—
344#544—71no—
345#542—71no—
346#542—71no—
347#542—141no—
348#540—71no—
349#540—71no—
350#540—141no—
351#538—141no—
352#538—141no—
353#537—71no—
354#535—71no—
355#535—71no—
356#532—71no—
357#532—71no—
358#532—141no—
359#529—71no—
360#529—71no—
361#529—141no—
362#525—141no—
363#525—141no—
364C4×#41—71no—
365C4×#41C2×D711yescharacteristic
366C2×C4×D4—71no—
367#446—21no—
368#446—141no—
369#436—21no—
370#436—141no—
371#435—21no—
372#435—21no—
373#435—141no—
374#435—141no—
375#432—71no—
376#432—71no—
377#431—71no—
378#431C2×D711yescharacteristic
379#431C2×D711yescharacteristic, complemented
380#431C2×D711yescharacteristic, complemented
381#423—71no—
382#423—71no—
383C2×C4⋊C8—71no—
384C4×M16C2×D711yescharacteristic
385C4×M16C2×D711yescharacteristic, complemented
386C2×C4×C8C2×D711yescharacteristic, complemented
387Q8⋊C8—71no—
388Q8⋊C8—71no—
389Q8⋊C8—71no—
390Q8⋊C8—71no—
391D4⋊C8—71no—
392D4⋊C8—71no—
393D4⋊C8—71no—
394D4⋊C8—71no—
395D4⋊C8—71no—
396D4⋊C8—71no—
397D4⋊C8—71no—
398D4⋊C8—71no—
399D4⋊C8—71no—
400D4⋊C8—71no—
401D4⋊C8—71no—
402D4⋊C8—71no—
403C23×C7C2×C22⋊C411yescharacteristic
404C23×C7C2×C22⋊C411yescharacteristic
405C23×C7C2×C22⋊C411yescharacteristic
406C22×D7—21no—
407C22×D7—21no—
408C22×D7—21no—
409C22×D7—42no—
410C22×D7—81no—
411C22×D7—81no—
412C7×Q8—41no—
413C7×D4—41no—
414C7×D4—41no—
415C7×D4—41no—
416C2×C4×C7—22no—
417C2×C4×C7—22no—
418C2×C4×C7—22no—
419C2×C4×C7—21no—
420C2×C4×C7—21no—
421C2×C4×C7—21no—
422C2×C4×C7—21no—
423C2×C4×C7—21no—
424C2×C4×C7—21no—
425C2×C4×C7—41no—
426C2×C4×C7—41no—
427C2×C4×C7—41no—
428C2×C4×C7C2×C22⋊C411yescharacteristic
429C2×C4×C7C2×C22⋊C411yescharacteristic
430C2×C4×C7C2×C22⋊C411yescharacteristic
431C2×C4×C7C2×C22⋊C411yescharacteristic
432C2×C4×C7C2×C22⋊C411yescharacteristic
433C2×C4×C7C2×C22⋊C411yescharacteristic
434C2×C4×C7C2×C22⋊C411yescharacteristic
435C2×C4×C7C2×C22⋊C411yescharacteristic
436C2×C4×C7C2×C22⋊C411yescharacteristic
437C2×C4×C7C23×C411yescharacteristic
438C2×C4×C7C22×D411yescharacteristic
439C2×C4×C7C22×D411yescharacteristic
440C22⋊D7—42no—
441C22⋊D7—81no—
442C22⋊D7—81no—
443C22⋊D7—81no—
444C22⋊D7—81no—
445C22⋊D7—81no—
446C22⋊D7—81no—
447C2×Dic7—21no—
448C2×Dic7—21no—
449C2×Dic7—21no—
450C2×Dic7—21no—
451C2×Dic7—21no—
452C2×Dic7—81no—
453D28—22no—
454D28—22no—
455D28—22no—
456D28—42no—
457D28—81no—
458D28—81no—
459D28—81no—
460D28—81no—
461C4×D7—42no—
462C4×D7—41no—
463C4×D7—41no—
464C4×D7—41no—
465C4×D7—41no—
466C4×D7—41no—
467C4×D7—41no—
468C4×D7—81no—
469C4×D7—81no—
470C4×D7—81no—
471Dic14—22no—
472Dic14—81no—
473Dic14—81no—
474C7×C8—22no—
475C7×C8—41no—
476C7×C8—41no—
477C7×C8—41no—
478C7⋊C8—41no—
479C7⋊C8—41no—
480C7⋊C8—41no—
481C7⋊C8—41no—
482C2×#41—71no—
483C2×#41—141no—
484C2×#41—141no—
485C2×#41C4×D711yescharacteristic
486C22×D4—71no—
487C23×C4—141no—
488C2×M16—21no—
489C2×M16—21no—
490C2×M16—141no—
491C2×M16—141no—
492C22×C8—21no—
493C22×C8—141no—
494C4⋊Q8—71no—
495C4⋊Q8—71no—
496C4⋊Q8—141no—
497#127—71no—
498#127—71no—
499#127—141no—
500#126—141no—
501#126—141no—
502#126—141no—
503#126—141no—
504#125—71no—
505#125—71no—
506#125—141no—
507#124—71no—
508#124—71no—
509#124—141no—
510#124—141no—
511#124—141no—
512#124—141no—
513#124—141no—
514#123—141no—
515#123—141no—
516#123—141no—
517#123—141no—
518#123—141no—
519#123—141no—
520#123—141no—
521#123—141no—
522C22⋊Q8—71no—
523C22⋊Q8—71no—
524C22⋊Q8—141no—
525C22⋊Q8—141no—
526C22⋊Q8—141no—
527C22⋊Q8—141no—
528C22⋊Q8—141no—
529#121—71no—
530#121—71no—
531#121—71no—
532#121—71no—
533#121—71no—
534#121—71no—
535#121—141no—
536#121—141no—
537#121—141no—
538#121—141no—
539#121—141no—
540#121—141no—
541#121—141no—
542#121—141no—
543#121—141no—
544#121—141no—
545#121—141no—
546#120—141no—
547#120—141no—
548#120—141no—
549#120—141no—
550C4×Q8—71no—
551C4×Q8—71no—
552C4×Q8D2811yescharacteristic
553C4×Q8C22⋊D711yescharacteristic
554C4×D4—71no—
555C4×D4—71no—
556C4×D4—71no—
557C4×D4—71no—
558C4×D4—71no—
559C4×D4—71no—
560C4×D4—141no—
561C4×D4—141no—
562C4×D4—141no—
563C4×D4—141no—
564C4×D4—141no—
565C4×D4—141no—
566C4×D4—141no—
567C4×D4—141no—
568C4×D4D2811yescharacteristic
569C4×D4D2811yescharacteristic
570C4×D4D2811yescharacteristic
571C4×D4C22⋊D711yescharacteristic
572C4×D4C22⋊D711yescharacteristic
573C4×D4C22⋊D711yescharacteristic
574#117—71no—
575#117—141no—
576#117—141no—
577#117—141no—
578#117C4×D711yescharacteristic
579#117C4×D711yescharacteristic
580#117C4×D711yescharacteristic
581C2×C4⋊C4—71no—
582C2×C22⋊C4—141no—
583C2×C42—141no—
584C2×C42C22×D711yescharacteristic
585C2×C42C22×D711yescharacteristic
586C2×C42C22×D711yescharacteristic
587C4⋊C8—21no—
588C4⋊C8—21no—
589C4⋊C8—21no—
590C4⋊C8—71no—
591C4⋊C8—71no—
592C4⋊C8—71no—
593C4⋊C8—71no—
594C4⋊C8—141no—
595C4⋊C8—141no—
596C4⋊C8—141no—
597C22⋊C8—21no—
598C22⋊C8—21no—
599C22⋊C8—21no—
600C22⋊C8—141no—
601C22⋊C8—141no—
602C22⋊C8—141no—
603#97—21no—
604#97—21no—
605#97—141no—
606#97—141no—
607C4×C8—21no—
608C4×C8—141no—
609C4×C8C22×D711yescharacteristic
610C4×C8C22×D711yescharacteristic
611C4×C8C22×D711yescharacteristic
612C4×C8C22×D711yescharacteristic
613C22×C7—21no—
614C22×C7—21no—
615C22×C7—21no—
616C22×C7—21no—
617C22×C7—21no—
618C22×C7—21no—
619C22×C7—21no—
620C22×C7—21no—
621C22×C7—21no—
622C22×C7C22×C22⋊C411yescharacteristic
623C2×D7—41no—
624C2×D7—41no—
625C2×D7—41no—
626C2×D7—41no—
627C2×D7—41no—
628C2×D7—41no—
629C2×D7—41no—
630C2×D7—41no—
631C2×D7—41no—
632C2×D7—84no—
633C4×C7—21no—
634C4×C7—21no—
635C4×C7—21no—
636C4×C7—21no—
637C4×C7—21no—
638C4×C7—21no—
639C4×C7—21no—
640C4×C7—21no—
641C4×C7—21no—
642C4×C7—21no—
643C4×C7#56812yes—
644C4×C7#57611yescharacteristic
645C4×C7#57711yescharacteristic
646Dic7—41no—
647Dic7—41no—
648Dic7—41no—
649Dic7—41no—
650Dic7—41no—
651C24—141no—
652#41—42no—
653#41—282no—
654#41—561no—
655#41—561no—
656#41—561no—
657#41—561no—
658C2×Q8—71no—
659C2×Q8—141no—
660C2×Q8—141no—
661C2×Q8(C2×D7)⋊C411yescharacteristic
662C2×D4—71no—
663C2×D4—71no—
664C2×D4—71no—
665C2×D4—141no—
666C2×D4—141no—
667C2×D4—141no—
668C2×D4—141no—
669C2×D4—141no—
670C2×D4—141no—
671C2×D4—141no—
672C2×D4—141no—
673C2×D4—141no—
674C2×D4—141no—
675C2×D4—141no—
676C2×D4—141no—
677C2×D4—282no—
678C2×D4(C2×D7)⋊C411yescharacteristic
679C2×D4(C2×D7)⋊C411yescharacteristic
680C2×D4(C2×D7)⋊C411yescharacteristic
681C22×C4—141no—
682C22×C4—141no—
683C22×C4—141no—
684C22×C4—141no—
685C22×C4—141no—
686C22×C4—141no—
687C22×C4—141no—
688C22×C4—141no—
689C22×C4—561no—
690C22×C4—561no—
691C22×C4C2×C4×D711yescharacteristic
692C22×C4C2×C4×D711yescharacteristic
693C22×C4C2×C4×D711yescharacteristic
694C22×C4C2×D2811yescharacteristic
695C22×C4C2×D2811yescharacteristic
696C22×C4C2×D2811yescharacteristic
697C22×C4C2×C22⋊D711yescharacteristic
698C22×C4C2×C22⋊D711yescharacteristic
699C22×C4C2×C22⋊D711yescharacteristic
700M16—42no—
701M16—42no—
702M16—561no—
703M16—561no—
704C2×C8—21no—
705C2×C8—21no—
706C2×C8—21no—
707C2×C8—21no—
708C2×C8—42no—
709C2×C8—141no—
710C2×C8—141no—
711C2×C8—141no—
712C2×C8—141no—
713C2×C8—561no—
714C4⋊C4—71no—
715C4⋊C4—71no—
716C4⋊C4—71no—
717C4⋊C4—71no—
718C4⋊C4—141no—
719C4⋊C4—141no—
720C4⋊C4—141no—
721C4⋊C4—141no—
722C4⋊C4—141no—
723C4⋊C4—141no—
724C4⋊C4—141no—
725C4⋊C4—141no—
726C4⋊C4—141no—
727C4⋊C4—141no—
728C4⋊C4—141no—
729C4⋊C4(C2×D7)⋊C411yescharacteristic
730C4⋊C4(C2×D7)⋊C411yescharacteristic
731C4⋊C4(C2×D7)⋊C411yescharacteristic
732C4⋊C4(C2×D7)⋊C411yescharacteristic
733C4⋊C4(C2×D7)⋊C411yescharacteristic
734C4⋊C4(C2×D7)⋊C411yescharacteristic
735C22⋊C4—141no—
736C22⋊C4—141no—
737C22⋊C4—141no—
738C22⋊C4—141no—
739C22⋊C4—141no—
740C22⋊C4—141no—
741C22⋊C4—141no—
742C22⋊C4—141no—
743C22⋊C4—141no—
744C22⋊C4—141no—
745C22⋊C4—141no—
746C22⋊C4—141no—
747C22⋊C4—141no—
748C22⋊C4—141no—
749C22⋊C4—141no—
750C22⋊C4—141no—
751C22⋊C4—141no—
752C22⋊C4—141no—
753C22⋊C4—141no—
754C22⋊C4(C2×D7)⋊C411yescharacteristic
755C22⋊C4(C2×D7)⋊C411yescharacteristic
756C22⋊C4(C2×D7)⋊C411yescharacteristic
757C22⋊C4(C2×D7)⋊C411yescharacteristic
758C22⋊C4(C2×D7)⋊C411yescharacteristic
759C22⋊C4(C2×D7)⋊C411yescharacteristic
760C42—141no—
761C42—141no—
762C42—141no—
763C42C2×C4×D711yescharacteristic
764C42C2×C4×D711yescharacteristic
765C42C2×C4×D711yescharacteristic
766C42C2×D2811yescharacteristic
767C42C2×D2811yescharacteristic
768C42C2×D2811yescharacteristic
769C42C2×C22⋊D711yescharacteristic
770C42C2×C22⋊D711yescharacteristic
771C42C2×C22⋊D711yescharacteristic
772C42C23×D711yescharacteristic
773C2×C7—41no—
774C2×C7—41no—
775C2×C7—41no—
776C2×C7#287911yescharacteristic
777C2×C7#289711yescharacteristic
778C2×C7#290111yescharacteristic
779D7—81no—
780D7—81no—
781D7—81no—
782C23—141no—
783C23—141no—
784C23—141no—
785C23—282no—
786C23—561no—
787C23—561no—
788C23C2×(C2×D7)⋊C411yescharacteristic
789C23C2×(C2×D7)⋊C411yescharacteristic
790C23C2×(C2×D7)⋊C411yescharacteristic
791Q8—41no—
792Q8—142no—
793Q8—561no—
794Q8—561no—
795D4—41no—
796D4—41no—
797D4—41no—
798D4—142no—
799D4—142no—
800D4—142no—
801D4—282no—
802D4—282no—
803D4—561no—
804D4—561no—
805D4—561no—
806D4—561no—
807D4—561no—
808D4—561no—
809D4—561no—
810D4—561no—
811D4—561no—
812D4—561no—
813C2×C4—22no—
814C2×C4—22no—
815C2×C4—22no—
816C2×C4—21no—
817C2×C4—21no—
818C2×C4—21no—
819C2×C4—21no—
820C2×C4—21no—
821C2×C4—21no—
822C2×C4—41no—
823C2×C4—41no—
824C2×C4—41no—
825C2×C4—141no—
826C2×C4—141no—
827C2×C4—141no—
828C2×C4—141no—
829C2×C4—141no—
830C2×C4—282no—
831C2×C4—281no—
832C2×C4—281no—
833C2×C4—281no—
834C2×C4—281no—
835C2×C4—281no—
836C2×C4—281no—
837C2×C4—561no—
838C2×C4—561no—
839C2×C4—561no—
840C2×C4—561no—
841C2×C4C2×(C2×D7)⋊C411yescharacteristic
842C2×C4C2×(C2×D7)⋊C411yescharacteristic
843C2×C4C2×(C2×D7)⋊C411yescharacteristic
844C2×C4C2×(C2×D7)⋊C411yescharacteristic
845C2×C4C2×(C2×D7)⋊C411yescharacteristic
846C2×C4C2×(C2×D7)⋊C411yescharacteristic
847C2×C4C2×(C2×D7)⋊C411yescharacteristic
848C2×C4C2×(C2×D7)⋊C411yescharacteristic
849C2×C4C2×(C2×D7)⋊C411yescharacteristic
850C2×C4C22×C4×D711yescharacteristic
851C2×C4C22×D2811yescharacteristic
852C2×C4C22×C22⋊D711yescharacteristic
853C8—22no—
854C8—41no—
855C8—41no—
856C8—41no—
857C8—281no—
858C8—281no—
859C8—281no—
860C8—281no—
861C7#1750511yescharacteristic, complemented, Sylow
862C22—21no—
863C22—21no—
864C22—21no—
865C22—21no—
866C22—21no—
867C22—21no—
868C22—21no—
869C22—21no—
870C22—21no—
871C22—281no—
872C22—281no—
873C22—281no—
874C22—281no—
875C22—281no—
876C22—281no—
877C22—281no—
878C22—281no—
879C22—281no—
880C22—564no—
881C22C22×(C2×D7)⋊C411yescharacteristic
882C4—21no—
883C4—21no—
884C4—21no—
885C4—21no—
886C4—21no—
887C4—21no—
888C4—21no—
889C4—21no—
890C4—21no—
891C4—21no—
892C4—281no—
893C4—281no—
894C4—281no—
895C4—281no—
896C4—281no—
897C4#9043612yes—
898C4#9044211yescharacteristic
899C4#9044311yescharacteristic
900C2—41no—
901C2—41no—
902C2—41no—
903C2—561no—
904C2—561no—
905C2—561no—
906C2#1173998111yescharacteristic
907C2#1174120711yescharacteristic
908C2#1174124211yescharacteristic
subgroupG/H
centerC2×C4C22×D28
commutatorC2×C4×C7C23×C4
FrattiniC42C23×D7
FittingC7×#2965C2
socleC22×C7C22×C22⋊C4
prime radical#11742906C2
cosocleC42×C7C24
hypercenter#2965D7
hypocenterC7#17505
LCSG ▷ C2×C4×C7 ▷ C2×C7 ▷ C7
UCSC1 ◁ C2×C4 ◁ C4×#41 ◁ #2965

Complements

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

NH ≅ G/Ntype
2. C7×#2965C2semidirect
3. #11739966C2semidirect
4. #11728519C2semidirect
5. #11728518C2semidirect
6. #11728517C2semidirect
7. #11728516C2semidirect
8. #11728514C2semidirect
9. #11728512C2semidirect
10. #11727609C2semidirect
11. #11727608C2semidirect
12. #11727607C2semidirect
13. #11727606C2semidirect
14. #11727490C2semidirect
15. #11727489C2semidirect
44. C7×#431C22semidirect
45. C7×#431C22semidirect
47. C4×C7×M16C22semidirect
48. C2×C4×C7×C8C22semidirect
54. #89698C22semidirect
55. #89697C22semidirect
57. #89696C22semidirect
58. C2×C4⋊(C7⋊C8)C22semidirect
67. #89254C22semidirect
68. #89254C22semidirect
69. #89254C22semidirect
70. #89254C22semidirect
71. #89251C22semidirect
72. #89251C22semidirect
73. #89251C22semidirect
74. #89251C22semidirect
209. #2965D7semidirect
379. #431C2×D7semidirect
380. #431C2×D7semidirect
385. C4×M16C2×D7semidirect
386. C2×C4×C8C2×D7semidirect
861. C7#17505semidirect

Maximal subgroups

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

subgroupindex
#117429062
C7×#29652
#117399662
#117285192
#117285182
#117285172
#117285162
#117285142
#117285122
#117276092
#117276082
#117276072
#117276062
#117274902
#117274892
#175057