Finite Group Databasebeta

← #14219762

Subgroups — #14219762

Order 1792.

1894 conjugacy classes of subgroups.

The subgroup lattice has 1180 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#11743221C211yesmaximal, characteristic
2C7×#2994C211yesmaximal, characteristic, complemented
3#11740571C211yesmaximal, characteristic, complemented
4#11737389C211yesmaximal, characteristic, complemented
5#11737387C211yesmaximal, characteristic, complemented
6#11737353C211yesmaximal, characteristic, complemented
7#11737350C211yesmaximal, characteristic, complemented
8#11736988C211yesmaximal, characteristic, complemented
9#11736986C211yesmaximal, characteristic, complemented
10#11736930C212yesmaximal, complemented
11#11736926C212yesmaximal, complemented
12#11736876C211yesmaximal, characteristic, complemented
13#11736873C212yesmaximal, complemented
14D4×#1131C211yesmaximal, characteristic, complemented
15D4×#1131C212yesmaximal, complemented
16#11736823C212yesmaximal, complemented
17#11736812C212yesmaximal, complemented
18#11736732C211yesmaximal, characteristic, complemented
19#11736722C211yesmaximal, characteristic, complemented
20#11736530C212yesmaximal, complemented
21#11736519C212yesmaximal, complemented
22#11736460C211yesmaximal, characteristic, complemented
23C2×#89610C211yesmaximal, characteristic, complemented
24C7×#529C2211yescharacteristic
25C2×#6470C2212yescomplemented
26C22×#1131C2212yescomplemented
27C22×#1131C2212yescomplemented
28#90400C412yes—
29#90396C412yes—
30#90386C411yescharacteristic
31#90381C411yescharacteristic
32#90372C411yescharacteristic
33#90367C411yescharacteristic
34#90349C412yes—
35#90345C412yes—
36#90326C411yescharacteristic
37#90321C411yescharacteristic
38#90309C411yescharacteristic
39#90300C411yescharacteristic
40#90271C2211yescharacteristic
41C4×#1161C2211yescharacteristic
42#90239C2211yescharacteristic
43#90238C2212yes—
44C4×D4×D7C2212yes—
45C4×D4×D7C2211yescharacteristic
46#90219C2212yes—
47#90215C2212yes—
48C4×#1157C2211yescharacteristic
49C2×C4×D28C2211yescharacteristic
50C7×#446C2211yescharacteristic, complemented
51C7×C8×Q8C2211yescharacteristic, complemented
52C7×#436C2211yescharacteristic, complemented
53C7×#435C2212yescomplemented
54C7×C8×D4C2212yescomplemented
55C7×C8×D4C2211yescharacteristic, complemented
56C7×#433C2212yescomplemented
57C7×#431C2211yescharacteristic, complemented
58C7×#424C2212yescomplemented
59C2×C7×C4⋊C8C2211yescharacteristic, complemented
60#89900C2212yescomplemented
61#89899C2212yescomplemented
62#89898C2212yescomplemented
63#89883C2212yes—
64#89883C2212yescomplemented
65#89883C2212yescomplemented
66#89882C2212yescomplemented
67C8×C22⋊D7C2212yescomplemented
68C2×(C2×D7)⋊C8C2212yescomplemented
69#89796C2211yescharacteristic, complemented
70Q8×C7⋊C8C2211yescharacteristic, complemented
71#89784C2211yescharacteristic, complemented
72#89783C2212yescomplemented
73D4×C7⋊C8C2212yescomplemented
74D4×C7⋊C8C2211yescharacteristic, complemented
75#89772C2212yescomplemented
76#89769C2212yescomplemented
77#89698C2211yescharacteristic, complemented
78C2×C4×C7⋊C8C2211yescharacteristic, complemented
79#89612C2212yescomplemented
80#89611C2212yescomplemented
81#89610C2211yescharacteristic
82#89610C2211yescharacteristic
83#89610C2212yescomplemented
84#89610C2211yescharacteristic, complemented
85#89610C2212yescomplemented
86#89610C2211yescharacteristic, complemented
87#89610C2212yescomplemented
88#89610C2212yescomplemented
89#89610C2211yescharacteristic, complemented
90#89610C2211yescharacteristic, complemented
91#89609C2211yescharacteristic, complemented
92#89609C2212yescomplemented
93#89608C2212yescomplemented
94#89608C2212yescomplemented
95#89608C2212yescomplemented
96#89608C2212yescomplemented
97#89608C2212yescomplemented
98#89607C2211yescharacteristic, complemented
99#89607C2212yescomplemented
100#89605C2211yescharacteristic, complemented
101D7×C4⋊C8C2211yescharacteristic, complemented
102#89603C2211yescharacteristic, complemented
103#89603C2211yescharacteristic, complemented
104#89600C2212yescomplemented
105#89502C2211yescharacteristic
106#89502C2211yescharacteristic
107#89502C2212yescomplemented
108#89502C2212yescomplemented
109#89502C2211yescharacteristic, complemented
110#89502C2211yescharacteristic, complemented
111#89501C2212yescomplemented
112#89500C2212yescomplemented
113#89499C2212yescomplemented
114#89499C2212yescomplemented
115#89498C2212yescomplemented
116#89498C2212yescomplemented
117#89498C2212yescomplemented
118D7×C22⋊C8C2212yescomplemented
119#89480C2212yescomplemented
120#89478C2212yescomplemented
121#89478C2212yescomplemented
122#89477C2212yescomplemented
123#89462C2212yescomplemented
124#89460C2211yescharacteristic
125#89460C2211yescharacteristic
126#89460C2212yescomplemented
127#89460C2212yescomplemented
128C4×#1131C2212yescomplemented
129C4×#1131C2211yescharacteristic, complemented
130C4×#1131C2211yescharacteristic, complemented
131C8×D28C2211yescharacteristic, complemented
132C8×D28C2211yescharacteristic, complemented
133#89457C2211yescharacteristic, complemented
134#89457C2211yescharacteristic, complemented
135#60324—71nomaximal, Sylow
136C2×#1161C2×C411yescharacteristic
137C2×D4×D7C2×C412yes—
138C2×D4×D7C2×C411yescharacteristic
139C2×#1157C2×C411yescharacteristic
140C2×#1157C2312yes—
141C22×D28C2×C411yescharacteristic
142C22×C4×D7C2312yes—
143C22×C4×D7C2312yes—
144C2×C7×M16C2312yes—
145C22×C7×C8C2312yes—
146C22×C7×C8C2312yes—
147C7×#126C2×C412yes—
148C7×#125C2×C411yescharacteristic
149C7×#124C2×C411yescharacteristic
150C7×#123C2×C412yes—
151C7×C22⋊Q8C2×C411yescharacteristic
152C7×#121C2×C411yescharacteristic
153C4×C7×Q8C2311yescharacteristic
154C4×C7×D4C2312yes—
155C4×C7×D4C2311yescharacteristic
156C7×#117C2312yes—
157C2×C42×C7C2311yescharacteristic
158#6510C2×C411yescharacteristic
159#6509C2×C411yescharacteristic
160Q8×Dic7C2×C411yescharacteristic
161#6503C2×C411yescharacteristic
162#6502C2×C412yes—
163#6501C2×C411yescharacteristic
164#6500C2×C412yes—
165D4×Dic7C2×C411yescharacteristic
166D4×Dic7C2×C412yes—
167C4×C22⋊D7C2×C411yescharacteristic
168C4×C22⋊D7C2×C411yescharacteristic
169C4×C22⋊D7C2311yescharacteristic
170C4×C22⋊D7C2311yescharacteristic
171C4×C22⋊D7C2312yes—
172C4×C22⋊D7C2312yes—
173C2×(C2×D7)⋊C4C2×C412yes—
174#6489C2×C411yescharacteristic
175C2×C4⋊Dic7C2×C411yescharacteristic
176C2×#1136C2312yes—
177C22×C7⋊C8C2311yescharacteristic
178C22×C7⋊C8C2312yes—
179C22×C7⋊C8C2311yescharacteristic
180#6470—44no—
181C2×#1131—44no—
182C2×#1131—44no—
183C2×#1131C2312yes—
184C2×#1131C2311yescharacteristic
185C2×#1131C2312yes—
186C2×#1131C2311yescharacteristic
187C2×#1131C2312yes—
188C2×#1131C2312yes—
189C2×#1131C2312yes—
190C2×#1131C2312yes—
191C2×#1131C2312yes—
192C2×#1131C2311yescharacteristic
193C2×#1131C2311yescharacteristic
194C2×C8×D7C2312yes—
195C2×C8×D7C2312yes—
196C2×C8×D7C2312yes—
197#6461C2×C412yes—
198#6461C2×C412yes—
199#6460C2×C412yes—
200#6460C2×C412yes—
201#6459C2×C412yes—
202#6459C2×C412yes—
203#6458C2×C412yes—
204#6458C2×C411yescharacteristic
205#6458C2×C411yescharacteristic
206#6458C2×C412yes—
207#6457C2×C412yes—
208#6457C2×C412yes—
209#6457C2×C412yes—
210#6456C2×C411yescharacteristic
211#6456C2×C411yescharacteristic
212#6456C2×C412yes—
213#6456C2×C412yes—
214#6455C2×C411yescharacteristic
215#6455C2×C412yes—
216D7×C4⋊C4C2×C412yes—
217D7×C4⋊C4C2×C411yescharacteristic
218#6453C2×C411yescharacteristic
219#6452C2×C412yes—
220#6451C2×C411yescharacteristic
221#6449C2×C412yes—
222#6449C2×C412yes—
223#6448C2×C412yes—
224#6448C2×C412yes—
225#6447C2×C412yes—
226#6447C2×C412yes—
227#6447C2×C412yes—
228#6446C2×C412yes—
229#6446C2×C412yes—
230#6445C2×C412yes—
231#6445C2×C412yes—
232#6445C2×C412yes—
233(C22⋊D7)⋊C4C2×C412yes—
234(C22⋊D7)⋊C4C2×C412yes—
235(C22⋊D7)⋊C4C2×C412yes—
236D7×C22⋊C4C2×C412yes—
237D7×C22⋊C4C2×C412yes—
238D7×C22⋊C4C2×C412yes—
239#6442C2×C412yes—
240#6441C2×C412yes—
241C4×D28C2×C411yescharacteristic
242C4×D28C2×C411yescharacteristic
243C4×D28C2×C411yescharacteristic
244C4×D28C2×C412yes—
245C4×D28C2312yes—
246C4×D28C2311yescharacteristic
247C4×D28C2312yes—
248C4×D28C2312yes—
249C4×D28C2311yescharacteristic
250C4×D28C2311yescharacteristic
251#6435C2×C411yescharacteristic
252#6435C2×C411yescharacteristic
253#6435C2312yes—
254C42×D7C2311yescharacteristic
255C42×D7C2311yescharacteristic
256C42×D7C2312yes—
257C4×Dic14C2×C411yescharacteristic
258C4×Dic14C2311yescharacteristic
259C7×C4⋊C8C2312yes—
260C7×C4⋊C8C2311yescharacteristic
261C7×C4⋊C8C2311yescharacteristic
262C7×C4⋊C8C2311yescharacteristic
263C7×C4⋊C8C2312yes—
264C7×C4⋊C8C2311yescharacteristic
265C7×C4⋊C8C2312yes—
266C7×C22⋊C8C2311yescharacteristic
267C7×C22⋊C8C2311yescharacteristic
268C7×C22⋊C8C2312yes—
269C7×C22⋊C8C2312yes—
270C7×#97C2312yes—
271C4×C7×C8C2311yescharacteristic
272C4×C7×C8C2311yescharacteristic
273C4×C7×C8C2312yes—
274C22⋊(C7⋊C8)C2312yes—
275C22⋊(C7⋊C8)C2312yes—
276C22⋊(C7⋊C8)C2312yes—
277(C2×D7)⋊C8C2312yes—
278(C2×D7)⋊C8C2312yes—
279(C2×D7)⋊C8C2312yes—
280(C2×D7)⋊C8C2312yes—
281(C2×D7)⋊C8C2311yescharacteristic
282(C2×D7)⋊C8C2311yescharacteristic
283(C2×D7)⋊C8C2312yes—
284(C2×D7)⋊C8C2312yes—
285(C2×D7)⋊C8C2312yes—
286(C2×D7)⋊C8C2312yes—
287(C2×D7)⋊C8C2312yes—
288(C2×D7)⋊C8C2312yes—
289(C2×D7)⋊C8C2311yescharacteristic
290(C2×D7)⋊C8C2311yescharacteristic
291#6389C2312yes—
292#6389C2311yescharacteristic
293#6389C2311yescharacteristic
294#6389C2311yescharacteristic
295#6389C2311yescharacteristic
296Dic7⋊C8C2312yes—
297Dic7⋊C8C2312yes—
298Dic7⋊C8C2311yescharacteristic
299Dic7⋊C8C2311yescharacteristic
300Dic7⋊C8C2311yescharacteristic
301Dic7⋊C8C2311yescharacteristic
302C8×Dic7C2312yes—
303C4⋊(C7⋊C8)C2311yescharacteristic
304C4⋊(C7⋊C8)C2311yescharacteristic
305C4⋊(C7⋊C8)C2312yes—
306C4⋊(C7⋊C8)C2312yes—
307#6377C2312yes—
308#6377C2312yes—
309C4×C7⋊C8C2311yescharacteristic
310C4×C7⋊C8C2311yescharacteristic
311C4×C7⋊C8C2311yescharacteristic
312C4×C7⋊C8C2311yescharacteristic
313C4×C7⋊C8C2312yes—
314#3481—71no—
315#2995—72no—
316#2994D711yescharacteristic, complemented
317#2993—71no—
318#2990—71no—
319#2989—71no—
320#2981—71no—
321#2978—72no—
322#2976—72no—
323#2975—71no—
324#2974—71no—
325#2973—72no—
326#2971—71no—
327#2969—71no—
328#2967—72no—
329#2966—71no—
330#2965—71no—
331#2935—71no—
332D4×M16—72no—
333D4×M16—71no—
334#2933—72no—
335#2930—72no—
336C2×#436—71no—
337C23×D7C22×C412yes—
338C23×D7C22×C412yes—
339C2×C7×Q8C22×C411yescharacteristic
340C2×C7×D4C22×C412yes—
341C2×C7×D4C22×C411yescharacteristic
342C22×C4×C7C22×C411yescharacteristic
343C22×C4×C7C22×C411yescharacteristic
344C22×C4×C7C2411yescharacteristic
345C22×C4×C7C2412yes—
346C2×C22⋊D7C22×C411yescharacteristic
347C2×C22⋊D7C22×C411yescharacteristic
348C2×C22⋊D7C22×C412yes—
349C2×C22⋊D7C22×C412yes—
350C2×C22⋊D7C22×C412yes—
351C2×C22⋊D7C22×C412yes—
352C22×Dic7C22×C412yes—
353C22×Dic7C22×C412yes—
354#1161—42no—
355D4×D7—42no—
356D4×D7—44no—
357#1157—42no—
358#1157—42no—
359#1157—42no—
360C2×D28—42no—
361C2×D28C22×C411yescharacteristic
362C2×D28C22×C411yescharacteristic
363C2×D28C22×C411yescharacteristic
364C2×D28C22×C412yes—
365C2×D28C22×C412yes—
366C2×D28C22×C412yes—
367C2×D28C22×C412yes—
368C2×C4×D7—42no—
369C2×C4×D7—42no—
370C2×C4×D7—42no—
371C2×C4×D7—42no—
372C2×C4×D7C22×C411yescharacteristic
373C2×C4×D7C22×C411yescharacteristic
374C2×C4×D7C22×C411yescharacteristic
375C2×C4×D7C22×C411yescharacteristic
376C2×C4×D7C22×C412yes—
377C2×C4×D7C22×C412yes—
378C2×C4×D7C22×C412yes—
379C2×C4×D7C22×C412yes—
380C2×C4×D7C22×C412yes—
381C2×C4×D7C22×C412yes—
382C2×C4×D7C2411yescharacteristic
383C2×C4×D7C2411yescharacteristic
384C2×C4×D7C2412yes—
385C2×C4×D7C2412yes—
386C2×Dic14C22×C411yescharacteristic
387C2×Dic14C22×C412yes—
388C7×M16—42no—
389C2×C7×C8—42no—
390C2×C7×C8—42no—
391C2×C7×C8C2411yescharacteristic
392C2×C7×C8C2411yescharacteristic
393C2×C7×C8C2411yescharacteristic
394C2×C7×C8C2411yescharacteristic
395C2×C7×C8C2412yes—
396C2×C7×C8C2412yes—
397C7×C4⋊C4C22×C411yescharacteristic
398C7×C4⋊C4C22×C412yes—
399C7×C4⋊C4C22×C411yescharacteristic
400C7×C4⋊C4C22×C412yes—
401C7×C4⋊C4C22×C412yes—
402C7×C4⋊C4C22×C412yes—
403C7×C22⋊C4C22×C412yes—
404C7×C22⋊C4C22×C412yes—
405C7×C22⋊C4C22×C412yes—
406C7×C22⋊C4C22×C412yes—
407C7×C22⋊C4C22×C412yes—
408C42×C7C22×C411yescharacteristic
409C42×C7C22×C411yescharacteristic
410C42×C7C2411yescharacteristic
411C42×C7C2412yes—
412C42×C7C2411yescharacteristic
413C22⋊Dic7C22×C411yescharacteristic
414C22⋊Dic7C22×C412yes—
415C22⋊Dic7C22×C412yes—
416C22⋊Dic7C22×C411yescharacteristic
417(C2×D7)⋊C4C22×C411yescharacteristic
418(C2×D7)⋊C4C22×C411yescharacteristic
419(C2×D7)⋊C4C22×C411yescharacteristic
420(C2×D7)⋊C4C22×C411yescharacteristic
421(C2×D7)⋊C4C22×C412yes—
422(C2×D7)⋊C4C22×C412yes—
423(C2×D7)⋊C4C22×C412yes—
424(C2×D7)⋊C4C22×C412yes—
425(C2×D7)⋊C4C22×C412yes—
426(C2×D7)⋊C4C22×C412yes—
427(C2×D7)⋊C4C22×C412yes—
428(C2×D7)⋊C4C22×C412yes—
429(C2×D7)⋊C4C22×C412yes—
430(C2×D7)⋊C4C22×C412yes—
431(C2×D7)⋊C4C22×C412yes—
432(C2×D7)⋊C4C22×C412yes—
433C4⋊Dic7C22×C411yescharacteristic
434C4⋊Dic7C22×C411yescharacteristic
435C4⋊Dic7C22×C412yes—
436C4⋊Dic7C22×C411yescharacteristic
437C4⋊Dic7C22×C411yescharacteristic
438C4⋊Dic7C22×C412yes—
439C4⋊Dic7C22×C412yes—
440Dic7⋊C4C22×C411yescharacteristic
441Dic7⋊C4C22×C411yescharacteristic
442Dic7⋊C4C22×C411yescharacteristic
443Dic7⋊C4C22×C411yescharacteristic
444Dic7⋊C4C22×C412yes—
445Dic7⋊C4C22×C412yes—
446Dic7⋊C4C22×C412yes—
447Dic7⋊C4C22×C412yes—
448C4×Dic7C22×C411yescharacteristic
449C4×Dic7C22×C411yescharacteristic
450C4×Dic7C22×C411yescharacteristic
451C4×Dic7C22×C411yescharacteristic
452C4×Dic7C22×C412yes—
453C4×Dic7C22×C412yes—
454C4×Dic7C2411yescharacteristic
455C4×Dic7C2411yescharacteristic
456#1136—42no—
457C2×C7⋊C8—22no—
458C2×C7⋊C8—24no—
459C2×C7⋊C8—41no—
460C2×C7⋊C8C2412yes—
461C2×C7⋊C8C2412yes—
462C2×C7⋊C8C2411yescharacteristic
463C2×C7⋊C8C2411yescharacteristic
464C2×C7⋊C8C2411yescharacteristic
465C2×C7⋊C8C2411yescharacteristic
466#1131—24no—
467#1131—22no—
468#1131—24no—
469#1131—22no—
470#1131—42no—
471#1131—42no—
472#1131—42no—
473#1131—42no—
474#1131—42no—
475#1131—41no—
476#1131—41no—
477C8×D7—42no—
478C8×D7—42no—
479C8×D7—42no—
480C2×#131—72no—
481C22×M16—72no—
482C22×M16—72no—
483#559—71no—
484#554—71no—
485#554—71no—
486#553—72no—
487#553—71no—
488#553—71no—
489#551—72no—
490#551—72no—
491#546—71no—
492#546—72no—
493#546—71no—
494D42—71no—
495#532—71no—
496#529—71no—
497#529—72no—
498#529C2×D711yescharacteristic
499#525—72no—
500#525—72no—
501C4×#41—71no—
502C4×#41—71no—
503C2×C4×D4—72no—
504C2×C4×D4—71no—
505C2×C4×D4—71no—
506#446—71no—
507#446—72no—
508#446—71no—
509#446—71no—
510#446C2×D711yescharacteristic, complemented
511C8×Q8—71no—
512C8×Q8C2×D711yescharacteristic, complemented
513#436—72no—
514#436—71no—
515#436—71no—
516#436—71no—
517#436—72no—
518#436—71no—
519#436—72no—
520#436—71no—
521#436—71no—
522#436—72no—
523#436—72no—
524#436—71no—
525#436—72no—
526#436—71no—
527#436—71no—
528#436—72no—
529#436—72no—
530#436C2×D711yescharacteristic, complemented
531#435—72no—
532#435—72no—
533#435—72no—
534#435—72no—
535#435—72no—
536#435—72no—
537#435—72no—
538#435—72no—
539#435—72no—
540#435—72no—
541#435—71no—
542#435—72no—
543#435—71no—
544#435—72no—
545#435—71no—
546#435—71no—
547#435—72no—
548#435—72no—
549#435—72no—
550#435C2×D712yescomplemented
551C8×D4—72no—
552C8×D4—72no—
553C8×D4—71no—
554C8×D4—71no—
555C8×D4—71no—
556C8×D4C2×D712yescomplemented
557C8×D4C2×D711yescharacteristic, complemented
558#433—72no—
559#433—72no—
560#433—72no—
561#433C2×D712yescomplemented
562#432—71no—
563#432—72no—
564#432—71no—
565#432—72no—
566#431—71no—
567#431—71no—
568#431—71no—
569#431C2×D711yescharacteristic, complemented
570#424—72no—
571#424C2×D712yescomplemented
572#423—72no—
573#423—71no—
574C2×C4⋊C8—71no—
575C2×C4⋊C8C2×D711yescharacteristic, complemented
576#408—72no—
577#408—72no—
578#408—72no—
579#407—72no—
580#407—72no—
581#407—72no—
582#407—72no—
583C2×C22⋊C8—72no—
584C2×C22⋊C8—72no—
585#405—72no—
586#405—72no—
587C4×M16—71no—
588C4×M16—72no—
589C4×M16—71no—
590C2×C4×C8—71no—
591C23×C7C23×C412yes—
592C23×C7C23×C411yescharacteristic
593C22×D7—24no—
594C22×D7—42no—
595C22×D7—42no—
596C22×D7—42no—
597C22×D7—42no—
598C22×D7—42no—
599C22×D7C23×C412yes—
600C22×D7C23×C411yescharacteristic
601C22×D7C23×C412yes—
602C22×D7C23×C411yescharacteristic
603C7×Q8—22no—
604C7×D4—24no—
605C7×D4—22no—
606C2×C4×C7—22no—
607C2×C4×C7—22no—
608C2×C4×C7—21no—
609C2×C4×C7—22no—
610C2×C4×C7—21no—
611C2×C4×C7—22no—
612C2×C4×C7C23×C411yescharacteristic
613C2×C4×C7C23×C412yes—
614C2×C4×C7C23×C412yes—
615C2×C4×C7C23×C411yescharacteristic
616C2×C4×C7C23×C411yescharacteristic
617C2×C4×C7C23×C412yes—
618C2×C4×C7C23×C411yescharacteristic
619C2×C4×C7C23×C411yescharacteristic
620C2×C4×C7C2511yescharacteristic
621C22⋊D7—22no—
622C22⋊D7—22no—
623C22⋊D7—42no—
624C22⋊D7—42no—
625C22⋊D7—42no—
626C22⋊D7—42no—
627C2×Dic7—42no—
628C2×Dic7—42no—
629C2×Dic7C23×C411yescharacteristic
630C2×Dic7C23×C411yescharacteristic
631C2×Dic7C23×C411yescharacteristic
632C2×Dic7C23×C411yescharacteristic
633C2×Dic7C23×C412yes—
634C2×Dic7C23×C411yescharacteristic
635C2×Dic7C23×C411yescharacteristic
636C2×Dic7C23×C412yes—
637D28—22no—
638D28—22no—
639D28—42no—
640D28—42no—
641D28—41no—
642D28—42no—
643D28—42no—
644C4×D7—22no—
645C4×D7—22no—
646C4×D7—21no—
647C4×D7—22no—
648C4×D7—22no—
649C4×D7—21no—
650C4×D7—22no—
651C4×D7—22no—
652C4×D7—21no—
653C4×D7—21no—
654C4×D7—42no—
655C4×D7—42no—
656C4×D7—42no—
657C4×D7—42no—
658C4×D7—41no—
659C4×D7—41no—
660C4×D7—42no—
661C4×D7—42no—
662Dic14—42no—
663Dic14—41no—
664C7×C8—21no—
665C7×C8—22no—
666C7×C8—22no—
667C7×C8—21no—
668C7×C8—21no—
669C7×C8—21no—
670C7⋊C8—22no—
671C7⋊C8—21no—
672C7⋊C8—22no—
673C7⋊C8—21no—
674C7⋊C8—21no—
675C7⋊C8H(5,𝔽2)12yes—
676C2×#41—71no—
677C2×#41—71no—
678C2×#41—72no—
679C22×D4—71no—
680C22×D4—72no—
681C22×D4—71no—
682C23×C4—72no—
683C23×C4—72no—
684#131—284no—
685C2×M16—72no—
686C2×M16—72no—
687C2×M16—71no—
688C2×M16—72no—
689C2×M16—71no—
690C2×M16—72no—
691C2×M16—72no—
692C2×M16—72no—
693C2×M16—72no—
694C2×M16—71no—
695C2×M16—72no—
696C2×M16—71no—
697C2×M16—284no—
698C2×M16—284no—
699C2×M16C22×D712yes—
700C22×C8—71no—
701C22×C8—72no—
702C22×C8—71no—
703C22×C8—72no—
704C22×C8—72no—
705C22×C8—72no—
706C22×C8C22×D712yes—
707C22×C8C22×D712yes—
708C4⋊Q8—71no—
709#127—71no—
710#126—72no—
711#126—72no—
712#126—72no—
713#126C4×D712yes—
714#125—72no—
715#125—71no—
716#125C4×D711yescharacteristic
717#124—71no—
718#124—72no—
719#124—72no—
720#124C4×D711yescharacteristic
721#123—72no—
722#123—72no—
723#123—72no—
724#123—72no—
725#123—72no—
726#123—72no—
727#123—72no—
728#123C4×D712yes—
729C22⋊Q8—71no—
730C22⋊Q8—72no—
731C22⋊Q8—72no—
732C22⋊Q8—72no—
733C22⋊Q8—72no—
734C22⋊Q8—72no—
735C22⋊Q8C4×D711yescharacteristic
736#121—72no—
737#121—71no—
738#121—72no—
739#121—72no—
740#121—71no—
741#121—71no—
742#121—72no—
743#121—72no—
744#121—72no—
745#121C4×D711yescharacteristic
746#120—72no—
747#120—72no—
748#120—72no—
749#120—72no—
750C4×Q8—71no—
751C4×Q8—71no—
752C4×Q8—71no—
753C4×Q8C22×D711yescharacteristic
754C4×D4—72no—
755C4×D4—71no—
756C4×D4—71no—
757C4×D4—71no—
758C4×D4—71no—
759C4×D4—72no—
760C4×D4—72no—
761C4×D4—71no—
762C4×D4—71no—
763C4×D4—72no—
764C4×D4—71no—
765C4×D4—72no—
766C4×D4—72no—
767C4×D4—72no—
768C4×D4—72no—
769C4×D4—71no—
770C4×D4—72no—
771C4×D4—71no—
772C4×D4—71no—
773C4×D4—71no—
774C4×D4—72no—
775C4×D4—72no—
776C4×D4—71no—
777C4×D4—71no—
778C4×D4—72no—
779C4×D4C22×D712yes—
780C4×D4C22×D711yescharacteristic
781#117—71no—
782#117—72no—
783#117—71no—
784#117—71no—
785#117—71no—
786#117—72no—
787#117C22×D712yes—
788C2×C4⋊C4—71no—
789C2×C4⋊C4—72no—
790C2×C4⋊C4—71no—
791C2×C22⋊C4—72no—
792C2×C22⋊C4—72no—
793C2×C22⋊C4—72no—
794C2×C22⋊C4—72no—
795C2×C42—71no—
796C2×C42—72no—
797C2×C42—71no—
798C2×C42C22×D711yescharacteristic
799C4⋊C8—72no—
800C4⋊C8—71no—
801C4⋊C8—72no—
802C4⋊C8—71no—
803C4⋊C8—71no—
804C4⋊C8—71no—
805C4⋊C8—71no—
806C4⋊C8—72no—
807C4⋊C8—71no—
808C4⋊C8—72no—
809C4⋊C8C22×D711yescharacteristic
810C4⋊C8C22×D711yescharacteristic
811C4⋊C8C22×D712yes—
812C4⋊C8C22×D712yes—
813C4⋊C8C22×D712yes—
814C4⋊C8C22×D711yescharacteristic
815C4⋊C8C22×D711yescharacteristic
816C22⋊C8—72no—
817C22⋊C8—72no—
818C22⋊C8—72no—
819C22⋊C8—72no—
820C22⋊C8—72no—
821C22⋊C8—72no—
822C22⋊C8—72no—
823C22⋊C8—72no—
824C22⋊C8—72no—
825C22⋊C8—72no—
826C22⋊C8—71no—
827C22⋊C8—71no—
828C22⋊C8—72no—
829C22⋊C8—72no—
830C22⋊C8—71no—
831C22⋊C8—71no—
832C22⋊C8—72no—
833C22⋊C8C22×D711yescharacteristic
834C22⋊C8C22×D711yescharacteristic
835C22⋊C8C22×D712yes—
836C22⋊C8C22×D712yes—
837#97—71no—
838#97—71no—
839#97—71no—
840#97—72no—
841#97—71no—
842#97—72no—
843#97—72no—
844#97C22×D712yes—
845C4×C8—72no—
846C4×C8—71no—
847C4×C8—71no—
848C4×C8—71no—
849C4×C8—71no—
850C4×C8—72no—
851C4×C8C22×D711yescharacteristic
852C4×C8C22×D711yescharacteristic
853C4×C8C22×D712yes—
854C22×C7—21no—
855C22×C7—21no—
856C22×C7—22no—
857C22×C7—22no—
858C22×C7—22no—
859C22×C7#56812yes—
860C22×C7C24×C411yescharacteristic
861C2×D7—21no—
862C2×D7—22no—
863C2×D7—22no—
864C2×D7—21no—
865C2×D7—21no—
866C2×D7—21no—
867C2×D7—22no—
868C2×D7—21no—
869C2×D7—21no—
870C2×D7—22no—
871C2×D7—22no—
872C2×D7—22no—
873C2×D7—84no—
874C2×D7—84no—
875C4×C7—22no—
876C4×C7—21no—
877C4×C7—21no—
878C4×C7—21no—
879C4×C7—22no—
880C4×C7—22no—
881C4×C7—21no—
882C4×C7#56812yes—
883C4×C7C2×H(5,𝔽2)11yescharacteristic
884C4×C7#58511yescharacteristic
885Dic7—21no—
886Dic7—22no—
887Dic7—21no—
888Dic7—22no—
889Dic7—21no—
890Dic7—21no—
891Dic7—21no—
892Dic7—21no—
893C24—72no—
894C24—72no—
895#41—282no—
896#41—282no—
897#41—282no—
898#41—282no—
899C2×Q8—71no—
900C2×Q8—72no—
901C2×Q8C2×C4×D711yescharacteristic
902C2×D4—71no—
903C2×D4—71no—
904C2×D4—72no—
905C2×D4—72no—
906C2×D4—72no—
907C2×D4—72no—
908C2×D4—71no—
909C2×D4—71no—
910C2×D4—72no—
911C2×D4—71no—
912C2×D4—72no—
913C2×D4—72no—
914C2×D4—72no—
915C2×D4—282no—
916C2×D4—282no—
917C2×D4—284no—
918C2×D4C2×C4×D712yes—
919C2×D4C2×C4×D711yescharacteristic
920C22×C4—72no—
921C22×C4—72no—
922C22×C4—71no—
923C22×C4—71no—
924C22×C4—71no—
925C22×C4—72no—
926C22×C4—71no—
927C22×C4—72no—
928C22×C4—72no—
929C22×C4—71no—
930C22×C4—72no—
931C22×C4—71no—
932C22×C4—72no—
933C22×C4—72no—
934C22×C4—72no—
935C22×C4—72no—
936C22×C4—282no—
937C22×C4—282no—
938C22×C4—282no—
939C22×C4—282no—
940C22×C4C2×C4×D711yescharacteristic
941C22×C4C2×C4×D711yescharacteristic
942C22×C4C23×D711yescharacteristic
943C22×C4C23×D712yes—
944M16—42no—
945M16—144no—
946M16—142no—
947M16—144no—
948M16—142no—
949M16—281no—
950M16—282no—
951M16—281no—
952M16—282no—
953M16—282no—
954M16—282no—
955M16—282no—
956M16—282no—
957C2×C8—42no—
958C2×C8—42no—
959C2×C8—71no—
960C2×C8—72no—
961C2×C8—71no—
962C2×C8—71no—
963C2×C8—71no—
964C2×C8—72no—
965C2×C8—142no—
966C2×C8—144no—
967C2×C8—282no—
968C2×C8—282no—
969C2×C8—282no—
970C2×C8—281no—
971C2×C8C23×D712yes—
972C2×C8C23×D711yescharacteristic
973C2×C8C23×D711yescharacteristic
974C2×C8C23×D711yescharacteristic
975C2×C8C23×D711yescharacteristic
976C2×C8C23×D712yes—
977C4⋊C4—71no—
978C4⋊C4—72no—
979C4⋊C4—72no—
980C4⋊C4—71no—
981C4⋊C4—71no—
982C4⋊C4—71no—
983C4⋊C4—72no—
984C4⋊C4—72no—
985C4⋊C4—71no—
986C4⋊C4—71no—
987C4⋊C4—72no—
988C4⋊C4—72no—
989C4⋊C4—72no—
990C4⋊C4—71no—
991C4⋊C4—71no—
992C4⋊C4C2×C4×D711yescharacteristic
993C4⋊C4C2×C4×D712yes—
994C4⋊C4C2×C4×D711yescharacteristic
995C4⋊C4C2×C4×D712yes—
996C4⋊C4C2×C4×D712yes—
997C4⋊C4C2×C4×D712yes—
998C22⋊C4—71no—
999C22⋊C4—72no—
1000C22⋊C4—72no—
1001C22⋊C4—71no—
1002C22⋊C4—71no—
1003C22⋊C4—72no—
1004C22⋊C4—72no—
1005C22⋊C4—72no—
1006C22⋊C4—72no—
1007C22⋊C4—72no—
1008C22⋊C4—72no—
1009C22⋊C4—72no—
1010C22⋊C4—72no—
1011C22⋊C4—72no—
1012C22⋊C4—71no—
1013C22⋊C4—71no—
1014C22⋊C4—72no—
1015C22⋊C4—71no—
1016C22⋊C4—72no—
1017C22⋊C4—72no—
1018C22⋊C4C2×C4×D712yes—
1019C22⋊C4C2×C4×D712yes—
1020C22⋊C4C2×C4×D712yes—
1021C22⋊C4C2×C4×D712yes—
1022C22⋊C4C2×C4×D712yes—
1023C42—71no—
1024C42—72no—
1025C42—71no—
1026C42—72no—
1027C42—71no—
1028C42—71no—
1029C42—71no—
1030C42—71no—
1031C42C2×C4×D711yescharacteristic
1032C42C2×C4×D711yescharacteristic
1033C42C23×D711yescharacteristic
1034C42C23×D711yescharacteristic
1035C42C23×D712yes—
1036C2×C7—22no—
1037C2×C7—42no—
1038C2×C7C4×H(5,𝔽2)11yescharacteristic
1039C2×C7C2×#56811yescharacteristic
1040C2×C7C2×#56811yescharacteristic
1041D7—41no—
1042D7—42no—
1043D7—41no—
1044D7—42no—
1045C23—72no—
1046C23—71no—
1047C23—72no—
1048C23—71no—
1049C23—144no—
1050C23—282no—
1051C23—282no—
1052C23—282no—
1053C23—282no—
1054C23—282no—
1055C23C22×C4×D712yes—
1056C23C22×C4×D711yescharacteristic
1057Q8—22no—
1058Q8—281no—
1059Q8—282no—
1060D4—24no—
1061D4—22no—
1062D4—142no—
1063D4—142no—
1064D4—142no—
1065D4—142no—
1066D4—282no—
1067D4—282no—
1068D4—281no—
1069D4—282no—
1070D4—282no—
1071D4—282no—
1072D4—282no—
1073D4—282no—
1074D4—282no—
1075C2×C4—22no—
1076C2×C4—22no—
1077C2×C4—21no—
1078C2×C4—22no—
1079C2×C4—21no—
1080C2×C4—22no—
1081C2×C4—71no—
1082C2×C4—71no—
1083C2×C4—71no—
1084C2×C4—71no—
1085C2×C4—71no—
1086C2×C4—72no—
1087C2×C4—71no—
1088C2×C4—72no—
1089C2×C4—142no—
1090C2×C4—142no—
1091C2×C4—141no—
1092C2×C4—142no—
1093C2×C4—141no—
1094C2×C4—142no—
1095C2×C4—142no—
1096C2×C4—141no—
1097C2×C4—142no—
1098C2×C4—141no—
1099C2×C4—282no—
1100C2×C4—282no—
1101C2×C4—282no—
1102C2×C4—282no—
1103C2×C4—282no—
1104C2×C4—281no—
1105C2×C4—281no—
1106C2×C4—282no—
1107C2×C4—282no—
1108C2×C4—282no—
1109C2×C4C22×C4×D711yescharacteristic
1110C2×C4C22×C4×D712yes—
1111C2×C4C22×C4×D712yes—
1112C2×C4C22×C4×D711yescharacteristic
1113C2×C4C22×C4×D711yescharacteristic
1114C2×C4C22×C4×D711yescharacteristic
1115C2×C4C22×C4×D712yes—
1116C2×C4C22×C4×D711yescharacteristic
1117C2×C4C24×D711yescharacteristic
1118C8—21no—
1119C8—22no—
1120C8—22no—
1121C8—21no—
1122C8—21no—
1123C8—21no—
1124C8—72no—
1125C8—142no—
1126C8—141no—
1127C8—142no—
1128C8—141no—
1129C8—141no—
1130C7#6032411yescharacteristic, complemented, Sylow
1131C22—21no—
1132C22—21no—
1133C22—22no—
1134C22—22no—
1135C22—22no—
1136C22—141no—
1137C22—141no—
1138C22—141no—
1139C22—142no—
1140C22—141no—
1141C22—142no—
1142C22—142no—
1143C22—142no—
1144C22—141no—
1145C22—142no—
1146C22—142no—
1147C22—141no—
1148C22—564no—
1149C22—564no—
1150C22#9044112yes—
1151C22C23×C4×D711yescharacteristic
1152C4—21no—
1153C4—21no—
1154C4—21no—
1155C4—22no—
1156C4—22no—
1157C4—21no—
1158C4—22no—
1159C4—141no—
1160C4—141no—
1161C4—141no—
1162C4—141no—
1163C4—141no—
1164C4—142no—
1165C4—142no—
1166C4—141no—
1167C4#9044112yes—
1168C4D7×H(5,𝔽2)11yescharacteristic
1169C4#9062011yescharacteristic
1170C2—22no—
1171C2—42no—
1172C2—281no—
1173C2—282no—
1174C2—282no—
1175C2—281no—
1176C2#1174295411yescharacteristic
1177C2C2×#9044111yescharacteristic
1178C2C2×#9044111yescharacteristic
subgroupG/H
center, FrattiniC2×C4C24×D7
commutator, socleC22×C7C24×C4
FittingC7×#2994C2
prime radical#11743221C2
cosocleC2×C4×C7C25
hypercenter#2994D7
hypocenterC7#60324
LCSG ▷ C22×C7 ▷ C7
UCSC1 ◁ C2×C4 ◁ #2994

Complements

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

NH ≅ G/Ntype
2. C7×#2994C2semidirect
3. #11740571C2semidirect
4. #11737389C2semidirect
5. #11737387C2semidirect
6. #11737353C2semidirect
7. #11737350C2semidirect
8. #11736988C2semidirect
9. #11736986C2semidirect
10. #11736930C2semidirect
11. #11736926C2semidirect
12. #11736876C2semidirect
13. #11736873C2semidirect
14. D4×#1131C2semidirect
15. D4×#1131C2semidirect
16. #11736823C2semidirect
17. #11736812C2semidirect
18. #11736732C2semidirect
19. #11736722C2semidirect
20. #11736530C2semidirect
21. #11736519C2semidirect
22. #11736460C2semidirect
23. C2×#89610C2semidirect
25. C2×#6470C22semidirect
26. C22×#1131C22semidirect
27. C22×#1131C22semidirect
50. C7×#446C22semidirect
51. C7×C8×Q8C22semidirect
52. C7×#436C22semidirect
53. C7×#435C22semidirect
54. C7×C8×D4C22semidirect
55. C7×C8×D4C22semidirect
56. C7×#433C22semidirect
57. C7×#431C22semidirect
58. C7×#424C22semidirect
59. C2×C7×C4⋊C8C22semidirect
60. #89900C22semidirect
61. #89899C22semidirect
62. #89898C22semidirect
64. #89883C22semidirect
65. #89883C22semidirect
66. #89882C22semidirect
67. C8×C22⋊D7C22semidirect
68. C2×(C2×D7)⋊C8C22semidirect
69. #89796C22semidirect
70. Q8×C7⋊C8C22semidirect
71. #89784C22semidirect
72. #89783C22semidirect
73. D4×C7⋊C8C22semidirect
74. D4×C7⋊C8C22semidirect
75. #89772C22semidirect
76. #89769C22semidirect
77. #89698C22semidirect
78. C2×C4×C7⋊C8C22semidirect
79. #89612C22semidirect
80. #89611C22semidirect
83. #89610C22semidirect
84. #89610C22semidirect
85. #89610C22semidirect
86. #89610C22semidirect
87. #89610C22semidirect
88. #89610C22semidirect
89. #89610C22semidirect
90. #89610C22semidirect
91. #89609C22semidirect
92. #89609C22semidirect
93. #89608C22semidirect
94. #89608C22semidirect
95. #89608C22semidirect
96. #89608C22semidirect
97. #89608C22semidirect
98. #89607C22semidirect
99. #89607C22semidirect
100. #89605C22semidirect
101. D7×C4⋊C8C22semidirect
102. #89603C22semidirect
103. #89603C22semidirect
104. #89600C22semidirect
107. #89502C22semidirect
108. #89502C22semidirect
109. #89502C22semidirect
110. #89502C22semidirect
111. #89501C22semidirect
112. #89500C22semidirect
113. #89499C22semidirect
114. #89499C22semidirect
115. #89498C22semidirect
116. #89498C22semidirect
117. #89498C22semidirect
118. D7×C22⋊C8C22semidirect
119. #89480C22semidirect
120. #89478C22semidirect
121. #89478C22semidirect
122. #89477C22semidirect
123. #89462C22semidirect
126. #89460C22semidirect
127. #89460C22semidirect
128. C4×#1131C22semidirect
129. C4×#1131C22semidirect
130. C4×#1131C22semidirect
131. C8×D28C22semidirect
132. C8×D28C22semidirect
133. #89457C22semidirect
134. #89457C22semidirect
316. #2994D7semidirect
510. #446C2×D7semidirect
512. C8×Q8C2×D7semidirect
530. #436C2×D7semidirect
550. #435C2×D7semidirect
556. C8×D4C2×D7semidirect
557. C8×D4C2×D7semidirect
561. #433C2×D7semidirect
569. #431C2×D7semidirect
571. #424C2×D7semidirect
575. C2×C4⋊C8C2×D7semidirect
1130. C7#60324semidirect

Maximal subgroups

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

subgroupindex
#117432212
C7×#29942
#117405712
#117373892
#117373872
#117373532
#117373502
#117369882
#117369862
#117369302
#117369262
#117368762
#117368732
D4×#11312
#117368232
#117368122
#117367322
#117367222
#117365302
#117365192
#117364602
C2×#896102
#603247