Finite Group Databasebeta

← #13522555

Subgroups — #13522555

Order 1792.

3578 conjugacy classes of subgroups.

The subgroup lattice has 1266 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#90347C211yesmaximal, characteristic, complemented
2C2×#90277C211yesmaximal, characteristic, complemented
3C22×(C22⋊D7)⋊C4C211yesmaximal, characteristic, complemented
4C22×#6440C211yesmaximal, characteristic, complemented
5C7×#2412C211yesmaximal, characteristic, complemented
6#11740287C211yesmaximal, characteristic, complemented
7#11740051C211yesmaximal, characteristic, complemented
8#11739572C211yesmaximal, characteristic, complemented
9#11739552C211yesmaximal, characteristic, complemented
10#11734907C212yesmaximal, complemented
11#11734902C212yesmaximal, complemented
12#11734341C212yesmaximal, complemented
13#11734335C212yesmaximal, complemented
14#11732334C211yesmaximal, characteristic, complemented
15#11732137C212yesmaximal, complemented
16#11732105C212yesmaximal, complemented
17#11732103C211yesmaximal, characteristic, complemented
18#11732047C211yesmaximal, characteristic, complemented
19#11731823C211yesmaximal, characteristic, complemented
20#11731509C211yesmaximal, characteristic, complemented
21#11731495C211yesmaximal, characteristic, complemented
22#11731334C212yesmaximal, complemented
23#11731310C212yesmaximal, complemented
24C23×C22⋊D7C2211yescharacteristic
25C24×Dic7C2211yescharacteristic
26C22×#1159C2211yescharacteristic
27C23×C4×D7C2211yescharacteristic
28C2×C7×#123C2211yescharacteristic
29C2×C7×#120C2211yescharacteristic
30C22×C7×C22⋊C4C2211yescharacteristic
31C22×C7×C22⋊C4C2211yescharacteristic
32C2×#6516C2211yescharacteristic
33C22×C22⋊Dic7C2211yescharacteristic
34C2×#6502C2212yes—
35C2×#6502C2211yescharacteristic, complemented
36C2×#6502C2211yescharacteristic, complemented
37C2×#6500C2211yescharacteristic
38C2×#6498C2211yescharacteristic
39C2×D4×Dic7C2211yescharacteristic, complemented
40C2×D4×Dic7C2211yescharacteristic, complemented
41C2×#6493C2212yes—
42C2×#6492C2211yescharacteristic
43C22×(C2×D7)⋊C4C2211yescharacteristic
44C22×Dic7⋊C4C2211yescharacteristic
45C22×Dic7⋊C4C2212yescomplemented
46C22×C4×Dic7C2211yescharacteristic
47C22×C4×Dic7C2212yescomplemented
48#90347—28no—
49#90277—28no—
50C2×#6459C2212yescomplemented
51C2×#6456C2212yescomplemented
52C2×#6449C2211yescharacteristic
53C2×#6447C2212yescomplemented
54C2×#6445C2211yescharacteristic
55C2×(C22⋊D7)⋊C4—28no—
56C2×(C22⋊D7)⋊C4C2212yes—
57C2×(C22⋊D7)⋊C4C2212yes—
58C2×(C22⋊D7)⋊C4C2212yes—
59C2×(C22⋊D7)⋊C4C2212yes—
60C2×(C22⋊D7)⋊C4C2211yescharacteristic, complemented
61C2×(C22⋊D7)⋊C4C2211yescharacteristic, complemented
62C2×(C22⋊D7)⋊C4C2212yescomplemented
63C2×#6441C2211yescharacteristic, complemented
64C2×#6441C2211yescharacteristic, complemented
65C2×#6440—28no—
66C2×#6440C2211yescharacteristic
67C2×#6440C2211yescharacteristic
68C2×#6440C2211yescharacteristic
69C2×#6440C2211yescharacteristic
70C2×#6440C2211yescharacteristic
71C2×#6440C2212yescomplemented
72C2×#6440C2212yescomplemented
73C7×#397C2212yescomplemented
74C7×#394C2212yescomplemented
75C7×#386C2211yescharacteristic
76C7×#386C2212yescomplemented
77C7×#385C2211yescharacteristic
78C7×#381C2211yescharacteristic
79C7×#380C2212yescomplemented
80#89995C2212yes—
81#89992C2211yescharacteristic
82#89985C2211yescharacteristic
83#89985C2212yes—
84#89983C2211yescharacteristic
85#89982C2211yescharacteristic
86#89766C2212yescomplemented
87#89760C2212yescomplemented
88#89752C2212yescomplemented
89C4⋊C4×Dic7C2212yescomplemented
90#89745C2212yescomplemented
91#89744C2212yescomplemented
92#89733C2212yes—
93#89732C2212yes—
94#89731C2212yes—
95#89731C2212yescomplemented
96#89731C2212yescomplemented
97#89730C2211yescharacteristic
98#89730C2212yes—
99#89730C2212yescomplemented
100#89729C2212yescomplemented
101#89729C2212yescomplemented
102#89727C2211yescharacteristic
103#89727C2211yescharacteristic
104#89724C2212yescomplemented
105#89722C2211yescharacteristic
106#89720C2212yescomplemented
107#89718C2211yescharacteristic
108#89716C2212yescomplemented
109#89714C2212yescomplemented
110C22⋊C4×Dic7C2212yescomplemented
111#89448C2212yescomplemented
112#89448C2212yescomplemented
113#89444C2212yescomplemented
114#89442C2212yescomplemented
115#89441C2212yescomplemented
116#89441C2212yescomplemented
117#89439C2212yescomplemented
118#89439C2212yescomplemented
119#89438C2212yescomplemented
120#89438C2212yescomplemented
121#89438C2212yescomplemented
122#89429C2212yescomplemented
123#89421C2212yescomplemented
124#89419C2212yescomplemented
125#89419C2212yescomplemented
126#89418C2212yescomplemented
127#34737—71nomaximal, Sylow
128C25×C7C2311yescharacteristic
129C24×D7C2311yescharacteristic
130C22×C7×D4C2311yescharacteristic
131C22×C7×D4C2311yescharacteristic
132C22×C7×D4C2311yescharacteristic
133C23×C4×C7C2311yescharacteristic
134C23×C4×C7C2312yes—
135C23×C4×C7C2311yescharacteristic
136C22×C22⋊D7—24no—
137C22×C22⋊D7—28no—
138C22×C22⋊D7C2312yes—
139C22×C22⋊D7C2311yescharacteristic
140C22×C22⋊D7C2311yescharacteristic
141C22×C22⋊D7C2311yescharacteristic
142C22×C22⋊D7C2312yes—
143C22×C22⋊D7C2312yes—
144C22×C22⋊D7C2311yescharacteristic
145C23×Dic7—24no—
146C23×Dic7—24no—
147C23×Dic7D418yescomplemented
148C23×Dic7C2311yescharacteristic
149C23×Dic7C2311yescharacteristic
150C23×Dic7C2312yes—
151C23×Dic7C2311yescharacteristic
152C23×Dic7C2311yescharacteristic
153C23×Dic7C2311yescharacteristic
154C23×Dic7C2311yescharacteristic
155C23×Dic7C2311yescharacteristic
156C23×Dic7C2311yescharacteristic
157C2×#1159—24no—
158C2×#1159—24no—
159C2×#1159—24no—
160C22×D28C2312yes—
161C22×C4×D7—24no—
162C22×C4×D7—24no—
163C22×C4×D7—24no—
164C22×C4×D7C2312yes—
165C22×C4×D7C2312yes—
166C22×C4×D7C2311yescharacteristic
167C22×Dic14C2311yescharacteristic
168C7×#123—24no—
169C7×#120—24no—
170C2×C7×C4⋊C4C2312yes—
171C2×C7×C4⋊C4C2312yes—
172C2×C7×C22⋊C4—24no—
173C2×C7×C22⋊C4—24no—
174C2×C7×C22⋊C4C2311yescharacteristic
175C2×C7×C22⋊C4C2311yescharacteristic
176C2×C7×C22⋊C4C2312yes—
177C2×C7×C22⋊C4C2311yescharacteristic
178C2×C7×C22⋊C4C2311yescharacteristic
179C2×C7×C22⋊C4C2312yes—
180C2×C7×C22⋊C4C2312yes—
181C2×C7×C22⋊C4C2312yes—
182C2×C7×C22⋊C4C2312yes—
183C2×C7×C22⋊C4C2311yescharacteristic
184#6516—24no—
185C2×C22⋊Dic7—24no—
186C2×C22⋊Dic7C2311yescharacteristic
187C2×C22⋊Dic7C2311yescharacteristic
188C2×C22⋊Dic7C2312yes—
189C2×C22⋊Dic7C2311yescharacteristic
190C2×C22⋊Dic7C2311yescharacteristic
191C2×C22⋊Dic7C2312yes—
192C2×C22⋊Dic7C2311yescharacteristic
193C2×C22⋊Dic7C2311yescharacteristic
194C2×C22⋊Dic7C2311yescharacteristic
195#6502—28no—
196#6502—24no—
197#6502—24no—
198#6500—24no—
199#6498—24no—
200D4×Dic7—24no—
201D4×Dic7—24no—
202#6493—28no—
203#6492—24no—
204C2×(C2×D7)⋊C4—24no—
205C2×(C2×D7)⋊C4C2312yes—
206C2×(C2×D7)⋊C4C2312yes—
207C2×(C2×D7)⋊C4C2312yes—
208C2×(C2×D7)⋊C4C2311yescharacteristic
209C2×(C2×D7)⋊C4C2311yescharacteristic
210C2×(C2×D7)⋊C4C2312yes—
211C2×(C2×D7)⋊C4C2312yes—
212C2×(C2×D7)⋊C4C2312yes—
213C2×(C2×D7)⋊C4C2312yes—
214C2×(C2×D7)⋊C4C2312yes—
215C2×(C2×D7)⋊C4C2312yes—
216C2×(C2×D7)⋊C4C2312yes—
217C2×(C2×D7)⋊C4C2312yes—
218C2×C4⋊Dic7C2311yescharacteristic
219C2×C4⋊Dic7C2311yescharacteristic
220C2×C4⋊Dic7C2312yes—
221C2×Dic7⋊C4—24no—
222C2×Dic7⋊C4—28no—
223C2×Dic7⋊C4C2312yes—
224C2×Dic7⋊C4C2312yes—
225C2×Dic7⋊C4C2312yes—
226C2×Dic7⋊C4C2311yescharacteristic
227C2×Dic7⋊C4C2311yescharacteristic
228C2×Dic7⋊C4C2311yescharacteristic
229C2×Dic7⋊C4C2311yescharacteristic
230C2×Dic7⋊C4C2312yes—
231C2×Dic7⋊C4C2312yes—
232C2×Dic7⋊C4C2312yes—
233C2×Dic7⋊C4C2312yes—
234C2×Dic7⋊C4C2312yes—
235C2×Dic7⋊C4C2312yes—
236C2×C4×Dic7—24no—
237C2×C4×Dic7—28no—
238C2×C4×Dic7C2312yes—
239C2×C4×Dic7C2312yes—
240C2×C4×Dic7C2312yes—
241C2×C4×Dic7C2311yescharacteristic
242C2×C4×Dic7C2311yescharacteristic
243C2×C4×Dic7C2312yes—
244C2×C4×Dic7C2312yes—
245C2×C4×Dic7C2312yes—
246#6459—28no—
247#6456—28no—
248#6449—24no—
249#6447—28no—
250#6445—24no—
251(C22⋊D7)⋊C4—28no—
252(C22⋊D7)⋊C4—28no—
253(C22⋊D7)⋊C4—28no—
254(C22⋊D7)⋊C4—28no—
255(C22⋊D7)⋊C4—24no—
256(C22⋊D7)⋊C4—24no—
257(C22⋊D7)⋊C4—28no—
258#6441—24no—
259#6441—24no—
260#6440—24no—
261#6440—24no—
262#6440—24no—
263#6440—24no—
264#6440—28no—
265#6440—28no—
266#6440D418yescomplemented
267C7×#95C2312yes—
268C7×#95C2312yes—
269C7×#95C2312yes—
270C7×#95C2312yes—
271C7⋊#95C2312yes—
272C7⋊#95C2312yes—
273C7⋊#95C2312yes—
274C7⋊#95C2312yes—
275C7⋊#95C2312yes—
276C7⋊#95C2312yes—
277C7⋊#95C2312yes—
278C7⋊#95C2312yes—
279C2×#525—71no—
280C2×#525—71no—
281C22×C4×D4—71no—
282C22×#117—71no—
283#2417—72no—
284#2416—72no—
285#2415—72no—
286#2414—72no—
287#2413—71no—
288#2413—71no—
289#2412—71no—
290#2412D711yescharacteristic, complemented
291#2411—71no—
292#2411—71no—
293#2410—71no—
294#2410—71no—
295#2392—72no—
296#2392—72no—
297C4×#121—72no—
298C4×#121—72no—
299#2297—71no—
300#2296—71no—
301#2280—71no—
302C24×C7—22no—
303C24×C7—22no—
304C24×C7—24no—
305C24×C7—42no—
306C24×C7C2×D414yes—
307C24×C7C2411yescharacteristic
308C24×C7C2411yescharacteristic
309C24×C7C2411yescharacteristic
310C24×C7C2411yescharacteristic
311C23×D7—22no—
312C23×D7—24no—
313C23×D7—22no—
314C23×D7—22no—
315C23×D7—42no—
316C23×D7C2411yescharacteristic
317C23×D7C2412yes—
318C2×C7×D4—22no—
319C2×C7×D4—22no—
320C2×C7×D4—22no—
321C2×C7×D4—22no—
322C2×C7×D4—24no—
323C2×C7×D4—22no—
324C2×C7×D4—42no—
325C22×C4×C7—22no—
326C22×C4×C7—22no—
327C22×C4×C7—22no—
328C22×C4×C7—24no—
329C22×C4×C7—22no—
330C22×C4×C7—24no—
331C22×C4×C7—42no—
332C22×C4×C7—42no—
333C22×C4×C7C2412yes—
334C22×C4×C7C2411yescharacteristic
335C22×C4×C7C2412yes—
336C22×C4×C7C2411yescharacteristic
337C22×C4×C7C2412yes—
338C22×C4×C7C2411yescharacteristic
339C22×C4×C7C2412yes—
340C2×C22⋊D7—232no—
341C2×C22⋊D7—24no—
342C2×C22⋊D7—24no—
343C2×C22⋊D7—24no—
344C2×C22⋊D7—24no—
345C2×C22⋊D7—22no—
346C2×C22⋊D7—22no—
347C2×C22⋊D7—22no—
348C2×C22⋊D7—22no—
349C2×C22⋊D7—24no—
350C2×C22⋊D7—22no—
351C2×C22⋊D7—24no—
352C2×C22⋊D7—24no—
353C2×C22⋊D7—22no—
354C2×C22⋊D7—22no—
355C2×C22⋊D7—24no—
356C2×C22⋊D7—22no—
357C2×C22⋊D7—42no—
358C2×C22⋊D7—42no—
359C2×C22⋊D7#4118yescomplemented
360C22×Dic7—22no—
361C22×Dic7—22no—
362C22×Dic7—22no—
363C22×Dic7—232no—
364C22×Dic7—22no—
365C22×Dic7—22no—
366C22×Dic7—22no—
367C22×Dic7—22no—
368C22×Dic7—22no—
369C22×Dic7—22no—
370C22×Dic7—22no—
371C22×Dic7—22no—
372C22×Dic7—24no—
373C22×Dic7—24no—
374C22×Dic7—22no—
375C22×Dic7—24no—
376C22×Dic7—22no—
377C22×Dic7—22no—
378C22×Dic7—42no—
379C22×Dic7C2×D414yes—
380C22×Dic7C2×D414yes—
381C22×Dic7C2×D414yes—
382C22×Dic7C2×D414yes—
383C22×Dic7C2×D414yes—
384C22×Dic7C2×D414yes—
385C22×Dic7C2×D414yes—
386C22×Dic7#4114yes—
387C22×Dic7C2412yes—
388C22×Dic7C2411yescharacteristic
389C22×Dic7C2411yescharacteristic
390C22×Dic7C2411yescharacteristic
391C22×Dic7C2412yes—
392C22×Dic7C2411yescharacteristic
393C22×Dic7C2411yescharacteristic
394C22×Dic7C2412yes—
395C22×Dic7C2411yescharacteristic
396C22×Dic7C2411yescharacteristic
397#1159—416no—
398C2×D28—24no—
399C2×D28—24no—
400C2×D28—42no—
401C2×C4×D7—24no—
402C2×C4×D7—24no—
403C2×C4×D7—22no—
404C2×C4×D7—24no—
405C2×C4×D7—24no—
406C2×C4×D7—22no—
407C2×C4×D7—24no—
408C2×C4×D7—24no—
409C2×C4×D7—22no—
410C2×C4×D7—416no—
411C2×Dic14—22no—
412C2×Dic14—22no—
413C2×Dic14—22no—
414C7×C4⋊C4—24no—
415C7×C4⋊C4—42no—
416C7×C22⋊C4—22no—
417C7×C22⋊C4—22no—
418C7×C22⋊C4—22no—
419C7×C22⋊C4—22no—
420C7×C22⋊C4—24no—
421C7×C22⋊C4—24no—
422C7×C22⋊C4—24no—
423C7×C22⋊C4—24no—
424C7×C22⋊C4—42no—
425C7×C22⋊C4C2×D414yes—
426C22⋊Dic7—22no—
427C22⋊Dic7—22no—
428C22⋊Dic7—22no—
429C22⋊Dic7—22no—
430C22⋊Dic7—24no—
431C22⋊Dic7—22no—
432C22⋊Dic7—22no—
433C22⋊Dic7—24no—
434C22⋊Dic7C2×D414yes—
435(C2×D7)⋊C4—24no—
436(C2×D7)⋊C4—24no—
437(C2×D7)⋊C4—24no—
438(C2×D7)⋊C4—24no—
439(C2×D7)⋊C4—24no—
440(C2×D7)⋊C4—22no—
441(C2×D7)⋊C4—22no—
442(C2×D7)⋊C4—24no—
443(C2×D7)⋊C4—24no—
444(C2×D7)⋊C4—24no—
445(C2×D7)⋊C4—42no—
446(C2×D7)⋊C4—42no—
447(C2×D7)⋊C4—42no—
448C4⋊Dic7—22no—
449C4⋊Dic7—22no—
450C4⋊Dic7—24no—
451Dic7⋊C4—24no—
452Dic7⋊C4—24no—
453Dic7⋊C4—24no—
454Dic7⋊C4—22no—
455Dic7⋊C4—22no—
456Dic7⋊C4—22no—
457Dic7⋊C4—22no—
458Dic7⋊C4—24no—
459Dic7⋊C4—24no—
460Dic7⋊C4—24no—
461Dic7⋊C4—24no—
462Dic7⋊C4—42no—
463Dic7⋊C4C2×D418yescomplemented
464C4×Dic7—24no—
465C4×Dic7—24no—
466C4×Dic7—24no—
467C4×Dic7—22no—
468C4×Dic7—22no—
469C4×Dic7—24no—
470C4×Dic7—24no—
471C4×Dic7C2×D418yescomplemented
472C22×#41—71no—
473C23×D4—71no—
474C24×C4—71no—
475C24×C4—71no—
476#525—148no—
477#525—148no—
478C2×#123—71no—
479C2×#123—71no—
480C2×#123—71no—
481C2×#123C2×D711yescharacteristic
482C2×C22⋊Q8—72no—
483C2×C22⋊Q8—71no—
484C2×C22⋊Q8—71no—
485C2×#121—72no—
486C2×#121—71no—
487C2×#121—71no—
488C2×#121—72no—
489C2×#121—72no—
490C2×#120—71no—
491C2×#120—71no—
492C2×#120—71no—
493C2×#120C2×D711yescharacteristic
494C2×C4×D4—71no—
495C2×C4×D4—71no—
496C2×C4×D4—72no—
497C2×C4×D4—72no—
498C2×C4×D4—72no—
499C2×C4×D4—72no—
500C2×C4×D4—72no—
501C2×C4×D4—71no—
502C2×C4×D4—72no—
503C2×C4×D4—71no—
504C2×C4×D4—148no—
505C2×#117—71no—
506C2×#117—71no—
507C2×#117—71no—
508C2×#117—71no—
509C2×#117—71no—
510C2×#117—72no—
511C2×#117—72no—
512C2×#117—148no—
513C22×C4⋊C4—72no—
514C22×C4⋊C4—71no—
515C22×C22⋊C4—71no—
516C22×C22⋊C4—71no—
517C22×C22⋊C4C2×D711yescharacteristic
518C22×C22⋊C4C2×D711yescharacteristic
519C22×C42—72no—
520C22×C42—71no—
521#398—72no—
522#398—72no—
523#397—72no—
524#397C2×D712yescomplemented
525#396—72no—
526#396—72no—
527#396—72no—
528#396—72no—
529#394—72no—
530#394—72no—
531#394—72no—
532#394—72no—
533#394—72no—
534#394C2×D712yescomplemented
535#392—72no—
536#392—72no—
537#391—72no—
538#390—72no—
539#390—72no—
540#390—72no—
541#389—72no—
542#389—72no—
543#389—72no—
544#389—72no—
545#388—72no—
546#388—72no—
547#388—72no—
548#388—72no—
549#386—71no—
550#386—72no—
551#386—71no—
552#386—71no—
553#386—72no—
554#386—72no—
555#386C2×D711yescharacteristic
556#386C2×D712yescomplemented
557#385—71no—
558#385—71no—
559#385—71no—
560#385C2×D711yescharacteristic
561#381—71no—
562#381C2×D711yescharacteristic
563#380—72no—
564#380—72no—
565#380—72no—
566#380C2×D712yescomplemented
567#379—71no—
568#379—71no—
569C4×C4⋊C4—72no—
570C4×C4⋊C4—72no—
571C4×C22⋊C4—72no—
572C4×C22⋊C4—72no—
573C4×C22⋊C4—72no—
574C4×C22⋊C4—72no—
575C23×C7—21no—
576C23×C7—21no—
577C23×C7—22no—
578C23×C7—22no—
579C23×C7—22no—
580C23×C7—28no—
581C23×C7—28no—
582C23×C7—21no—
583C23×C7—21no—
584C23×C7—22no—
585C23×C7—22no—
586C23×C7—21no—
587C23×C7—21no—
588C23×C7—22no—
589C23×C7—21no—
590C23×C7—22no—
591C23×C7—44no—
592C23×C7—48no—
593C23×C7—48no—
594C23×C7C22×D412yes—
595C23×C7C22×D412yes—
596C23×C7C22×D412yes—
597C23×C7C22×D412yes—
598C23×C7C2×#4112yes—
599C23×C7C2×#4114yes—
600C23×C7C2511yescharacteristic
601C22×D7—28no—
602C22×D7—22no—
603C22×D7—22no—
604C22×D7—22no—
605C22×D7—22no—
606C22×D7—22no—
607C22×D7—22no—
608C22×D7—21no—
609C22×D7—21no—
610C22×D7—22no—
611C22×D7—21no—
612C22×D7—22no—
613C22×D7—48no—
614C22×D7—48no—
615C22×D7—44no—
616C22×D7—44no—
617C22×D7C2×#4114yes—
618C7×D4—44no—
619C7×D4—44no—
620C7×D4—44no—
621C2×C4×C7—22no—
622C2×C4×C7—22no—
623C2×C4×C7—22no—
624C2×C4×C7—22no—
625C2×C4×C7—21no—
626C2×C4×C7—21no—
627C2×C4×C7—21no—
628C2×C4×C7—22no—
629C2×C4×C7—22no—
630C2×C4×C7—21no—
631C2×C4×C7—22no—
632C2×C4×C7—22no—
633C2×C4×C7—21no—
634C2×C4×C7—22no—
635C2×C4×C7—22no—
636C2×C4×C7—22no—
637C2×C4×C7—22no—
638C2×C4×C7—22no—
639C2×C4×C7—48no—
640C2×C4×C7—44no—
641C2×C4×C7—44no—
642C2×C4×C7C22×D414yes—
643C22⋊D7—216no—
644C22⋊D7—216no—
645C22⋊D7—48no—
646C22⋊D7—44no—
647C22⋊D7—44no—
648C22⋊D7—44no—
649C22⋊D7—44no—
650C2×Dic7—28no—
651C2×Dic7—28no—
652C2×Dic7—21no—
653C2×Dic7—22no—
654C2×Dic7—21no—
655C2×Dic7—22no—
656C2×Dic7—21no—
657C2×Dic7—21no—
658C2×Dic7—22no—
659C2×Dic7—22no—
660C2×Dic7—28no—
661C2×Dic7—28no—
662C2×Dic7—28no—
663C2×Dic7—28no—
664C2×Dic7—22no—
665C2×Dic7—21no—
666C2×Dic7—21no—
667C2×Dic7—21no—
668C2×Dic7—21no—
669C2×Dic7—22no—
670C2×Dic7—22no—
671C2×Dic7—21no—
672C2×Dic7—22no—
673C2×Dic7—22no—
674C2×Dic7—48no—
675C2×Dic7—44no—
676C2×Dic7#121116yescomplemented
677C2×Dic7C22×D414yes—
678C2×Dic7C22×D412yes—
679C2×Dic7C22×D412yes—
680C2×Dic7C22×D412yes—
681C2×Dic7C22×D412yes—
682C2×Dic7C22×D412yes—
683C2×Dic7C22×D412yes—
684C2×Dic7C2×#4114yes—
685C2×Dic7C2×#4112yes—
686C2×Dic7C2×#4112yes—
687D28—48no—
688C4×D7—48no—
689C4×D7—48no—
690C4×D7—44no—
691Dic14—44no—
692C25—71no—
693C25C22×D711yescharacteristic
694C2×#41—144no—
695C2×#41—144no—
696C2×#41—144no—
697C22×Q8—71no—
698C22×D4—72no—
699C22×D4—72no—
700C22×D4—71no—
701C22×D4—71no—
702C22×D4—71no—
703C22×D4—72no—
704C22×D4—71no—
705C22×D4—72no—
706C22×D4—148no—
707C22×D4—144no—
708C22×D4C22×D711yescharacteristic
709C22×D4C22×D711yescharacteristic
710C22×D4C22×D711yescharacteristic
711C23×C4—71no—
712C23×C4—78no—
713C23×C4—71no—
714C23×C4—71no—
715C23×C4—71no—
716C23×C4—71no—
717C23×C4—71no—
718C23×C4—71no—
719C23×C4—71no—
720C23×C4—72no—
721C23×C4—72no—
722C23×C4—71no—
723C23×C4—72no—
724C23×C4—144no—
725C23×C4—144no—
726C23×C4—144no—
727C23×C4—144no—
728C23×C4—144no—
729C23×C4C22×D711yescharacteristic
730C23×C4C22×D712yes—
731C23×C4C22×D711yescharacteristic
732#123—24no—
733#123—144no—
734#123—144no—
735#123—144no—
736C22⋊Q8—144no—
737C22⋊Q8—144no—
738C22⋊Q8—148no—
739#121—148no—
740#121—148no—
741#121—144no—
742#121—144no—
743#121—148no—
744#120—24no—
745#120—144no—
746#120—144no—
747#120—144no—
748C4×D4—148no—
749C4×D4—148no—
750C4×D4—148no—
751C4×D4—148no—
752C4×D4—148no—
753C4×D4—148no—
754C4×D4—144no—
755C4×D4—144no—
756C4×D4—144no—
757C4×D4—144no—
758#117—78no—
759#117—148no—
760#117—144no—
761#117—148no—
762#117—144no—
763#117—144no—
764#117—144no—
765C2×C4⋊C4—72no—
766C2×C4⋊C4—72no—
767C2×C4⋊C4—72no—
768C2×C4⋊C4—72no—
769C2×C4⋊C4—72no—
770C2×C4⋊C4—72no—
771C2×C4⋊C4—71no—
772C2×C4⋊C4—71no—
773C2×C4⋊C4—72no—
774C2×C4⋊C4—71no—
775C2×C4⋊C4—71no—
776C2×C4⋊C4—71no—
777C2×C4⋊C4—71no—
778C2×C4⋊C4—72no—
779C2×C4⋊C4—72no—
780C2×C4⋊C4—72no—
781C2×C4⋊C4—148no—
782C2×C4⋊C4—144no—
783C2×C4⋊C4C22×D712yes—
784C2×C4⋊C4C22×D712yes—
785C2×C22⋊C4—24no—
786C2×C22⋊C4—24no—
787C2×C22⋊C4—71no—
788C2×C22⋊C4—71no—
789C2×C22⋊C4—72no—
790C2×C22⋊C4—71no—
791C2×C22⋊C4—71no—
792C2×C22⋊C4—71no—
793C2×C22⋊C4—71no—
794C2×C22⋊C4—71no—
795C2×C22⋊C4—72no—
796C2×C22⋊C4—72no—
797C2×C22⋊C4—72no—
798C2×C22⋊C4—72no—
799C2×C22⋊C4—72no—
800C2×C22⋊C4—72no—
801C2×C22⋊C4—71no—
802C2×C22⋊C4—71no—
803C2×C22⋊C4—72no—
804C2×C22⋊C4—72no—
805C2×C22⋊C4—72no—
806C2×C22⋊C4—72no—
807C2×C22⋊C4—72no—
808C2×C22⋊C4—72no—
809C2×C22⋊C4—144no—
810C2×C22⋊C4—144no—
811C2×C22⋊C4C22×D711yescharacteristic
812C2×C22⋊C4C22×D712yes—
813C2×C22⋊C4C22×D712yes—
814C2×C22⋊C4C22×D712yes—
815C2×C22⋊C4C22×D711yescharacteristic
816C2×C22⋊C4C22×D711yescharacteristic
817C2×C22⋊C4C22×D711yescharacteristic
818C2×C22⋊C4C22×D712yes—
819C2×C22⋊C4C22×D712yes—
820C2×C22⋊C4C22×D711yescharacteristic
821C2×C42—72no—
822C2×C42—72no—
823C2×C42—72no—
824C2×C42—72no—
825C2×C42—71no—
826C2×C42—71no—
827C2×C42—72no—
828C2×C42—72no—
829C2×C42—148no—
830C2×C42—144no—
831#95—72no—
832#95—72no—
833#95—72no—
834#95—72no—
835#95—72no—
836#95—72no—
837#95—72no—
838#95—72no—
839#95C22×D712yes—
840#95C22×D712yes—
841#95C22×D712yes—
842#95C22×D712yes—
843C22×C7—22no—
844C22×C7—22no—
845C22×C7—22no—
846C22×C7—22no—
847C22×C7—24no—
848C22×C7—24no—
849C22×C7—24no—
850C22×C7—24no—
851C22×C7—22no—
852C22×C7—22no—
853C22×C7—22no—
854C22×C7—416no—
855C22×C7—42no—
856C22×C7—42no—
857C22×C7—41no—
858C22×C7—41no—
859C22×C7—41no—
860C22×C7—42no—
861C22×C7—42no—
862C22×C7C2×#12114yes—
863C22×C7#52514yescomplemented
864C22×C7C23×D411yescharacteristic
865C22×C7C23×D411yescharacteristic
866C22×C7C22×#4111yescharacteristic
867C22×C7C22×#4112yes—
868C22×C7#58512yes—
869C2×D7—24no—
870C2×D7—24no—
871C2×D7—24no—
872C2×D7—416no—
873C2×D7—42no—
874C2×D7—42no—
875C2×D7—42no—
876C2×D7—42no—
877C2×D7—41no—
878C2×D7—41no—
879C2×D7—41no—
880C2×D7—42no—
881C2×D7—42no—
882C4×C7—24no—
883C4×C7—41no—
884C4×C7—42no—
885C4×C7—41no—
886C4×C7—42no—
887C4×C7—41no—
888C4×C7—42no—
889Dic7—22no—
890Dic7—22no—
891Dic7—24no—
892Dic7—24no—
893Dic7—41no—
894Dic7—41no—
895Dic7—41no—
896Dic7—42no—
897Dic7C2×#12114yes—
898Dic7C2×#12114yes—
899C24—22no—
900C24—22no—
901C24—24no—
902C24—42no—
903C24—72no—
904C24—71no—
905C24—144no—
906C24—142no—
907C24—142no—
908C24—142no—
909C24—282no—
910C24D4×D714yes—
911C24C23×D711yescharacteristic
912C24C23×D711yescharacteristic
913C24C23×D711yescharacteristic
914C24C23×D711yescharacteristic
915#41—2816no—
916C2×Q8—142no—
917C2×Q8—142no—
918C2×Q8—142no—
919C2×D4—22no—
920C2×D4—22no—
921C2×D4—22no—
922C2×D4—22no—
923C2×D4—24no—
924C2×D4—22no—
925C2×D4—42no—
926C2×D4—78no—
927C2×D4—144no—
928C2×D4—144no—
929C2×D4—144no—
930C2×D4—142no—
931C2×D4—142no—
932C2×D4—142no—
933C2×D4—144no—
934C2×D4—1432no—
935C2×D4—144no—
936C2×D4—144no—
937C2×D4—144no—
938C2×D4—144no—
939C2×D4—142no—
940C2×D4—142no—
941C2×D4—142no—
942C2×D4—142no—
943C2×D4—144no—
944C2×D4—142no—
945C2×D4—144no—
946C2×D4—282no—
947C2×D4—282no—
948C2×D4—282no—
949C22×C4—22no—
950C22×C4—22no—
951C22×C4—22no—
952C22×C4—24no—
953C22×C4—22no—
954C22×C4—24no—
955C22×C4—42no—
956C22×C4—42no—
957C22×C4—74no—
958C22×C4—74no—
959C22×C4—74no—
960C22×C4—71no—
961C22×C4—71no—
962C22×C4—74no—
963C22×C4—74no—
964C22×C4—74no—
965C22×C4—74no—
966C22×C4—74no—
967C22×C4—72no—
968C22×C4—72no—
969C22×C4—71no—
970C22×C4—71no—
971C22×C4—72no—
972C22×C4—71no—
973C22×C4—71no—
974C22×C4—71no—
975C22×C4—144no—
976C22×C4—144no—
977C22×C4—144no—
978C22×C4—142no—
979C22×C4—142no—
980C22×C4—144no—
981C22×C4—144no—
982C22×C4—144no—
983C22×C4—142no—
984C22×C4—142no—
985C22×C4—142no—
986C22×C4—142no—
987C22×C4—142no—
988C22×C4—1432no—
989C22×C4—142no—
990C22×C4—142no—
991C22×C4—142no—
992C22×C4—142no—
993C22×C4—144no—
994C22×C4—144no—
995C22×C4—142no—
996C22×C4—142no—
997C22×C4—142no—
998C22×C4—142no—
999C22×C4—142no—
1000C22×C4—142no—
1001C22×C4—144no—
1002C22×C4—2816no—
1003C22×C4—282no—
1004C22×C4C23×D712yes—
1005C22×C4C23×D711yescharacteristic
1006C22×C4C23×D711yescharacteristic
1007C22×C4C23×D712yes—
1008C22×C4C23×D712yes—
1009C22×C4C23×D711yescharacteristic
1010C22×C4C23×D712yes—
1011C4⋊C4—24no—
1012C4⋊C4—42no—
1013C4⋊C4—78no—
1014C4⋊C4—144no—
1015C4⋊C4—144no—
1016C4⋊C4—144no—
1017C4⋊C4—144no—
1018C4⋊C4—142no—
1019C4⋊C4—142no—
1020C4⋊C4—142no—
1021C4⋊C4—142no—
1022C4⋊C4—144no—
1023C4⋊C4—144no—
1024C4⋊C4—142no—
1025C4⋊C4—142no—
1026C4⋊C4—144no—
1027C4⋊C4—144no—
1028C4⋊C4—282no—
1029C22⋊C4—22no—
1030C22⋊C4—24no—
1031C22⋊C4—24no—
1032C22⋊C4—22no—
1033C22⋊C4—22no—
1034C22⋊C4—22no—
1035C22⋊C4—24no—
1036C22⋊C4—24no—
1037C22⋊C4—42no—
1038C22⋊C4—74no—
1039C22⋊C4—144no—
1040C22⋊C4—144no—
1041C22⋊C4—144no—
1042C22⋊C4—142no—
1043C22⋊C4—142no—
1044C22⋊C4—144no—
1045C22⋊C4—144no—
1046C22⋊C4—144no—
1047C22⋊C4—144no—
1048C22⋊C4—144no—
1049C22⋊C4—142no—
1050C22⋊C4—142no—
1051C22⋊C4—144no—
1052C22⋊C4—142no—
1053C22⋊C4—142no—
1054C22⋊C4—142no—
1055C22⋊C4—142no—
1056C22⋊C4—144no—
1057C22⋊C4—282no—
1058C22⋊C4—282no—
1059C22⋊C4—282no—
1060C22⋊C4D4×D714yes—
1061C42—78no—
1062C42—144no—
1063C42—144no—
1064C42—144no—
1065C42—144no—
1066C42—142no—
1067C42—142no—
1068C42—144no—
1069C2×C7—24no—
1070C2×C7—24no—
1071C2×C7—42no—
1072C2×C7—81no—
1073C2×C7C22×#12111yescharacteristic
1074C2×C7C2×#52511yescharacteristic
1075C2×C7#344911yescharacteristic
1076C2×C7D4×#4112yes—
1077C2×C7#347512yes—
1078D7—44no—
1079D7—81no—
1080C23—21no—
1081C23—21no—
1082C23—22no—
1083C23—22no—
1084C23—22no—
1085C23—28no—
1086C23—28no—
1087C23—21no—
1088C23—21no—
1089C23—22no—
1090C23—22no—
1091C23—21no—
1092C23—21no—
1093C23—22no—
1094C23—21no—
1095C23—22no—
1096C23—44no—
1097C23—48no—
1098C23—48no—
1099C23—74no—
1100C23—148no—
1101C23—142no—
1102C23—142no—
1103C23—142no—
1104C23—142no—
1105C23—142no—
1106C23—142no—
1107C23—141no—
1108C23—141no—
1109C23—142no—
1110C23—141no—
1111C23—142no—
1112C23—288no—
1113C23—288no—
1114C23—284no—
1115C23—284no—
1116C23C2×D4×D712yes—
1117C23C2×D4×D712yes—
1118C23C2×D4×D712yes—
1119C23C2×D4×D712yes—
1120C23D7×#4112yes—
1121C23D7×#4114yes—
1122C23C24×D711yescharacteristic
1123Q8—284no—
1124D4—44no—
1125D4—44no—
1126D4—44no—
1127D4—1416no—
1128D4—1416no—
1129D4—288no—
1130D4—284no—
1131D4—288no—
1132D4—284no—
1133D4—284no—
1134D4—284no—
1135C2×C4—22no—
1136C2×C4—22no—
1137C2×C4—22no—
1138C2×C4—22no—
1139C2×C4—21no—
1140C2×C4—21no—
1141C2×C4—22no—
1142C2×C4—21no—
1143C2×C4—22no—
1144C2×C4—21no—
1145C2×C4—22no—
1146C2×C4—22no—
1147C2×C4—22no—
1148C2×C4—21no—
1149C2×C4—22no—
1150C2×C4—22no—
1151C2×C4—22no—
1152C2×C4—22no—
1153C2×C4—48no—
1154C2×C4—44no—
1155C2×C4—44no—
1156C2×C4—716no—
1157C2×C4—72no—
1158C2×C4—72no—
1159C2×C4—72no—
1160C2×C4—72no—
1161C2×C4—72no—
1162C2×C4—72no—
1163C2×C4—74no—
1164C2×C4—72no—
1165C2×C4—72no—
1166C2×C4—74no—
1167C2×C4—148no—
1168C2×C4—148no—
1169C2×C4—148no—
1170C2×C4—148no—
1171C2×C4—148no—
1172C2×C4—148no—
1173C2×C4—141no—
1174C2×C4—142no—
1175C2×C4—141no—
1176C2×C4—142no—
1177C2×C4—141no—
1178C2×C4—141no—
1179C2×C4—142no—
1180C2×C4—142no—
1181C2×C4—142no—
1182C2×C4—141no—
1183C2×C4—141no—
1184C2×C4—141no—
1185C2×C4—141no—
1186C2×C4—142no—
1187C2×C4—142no—
1188C2×C4—141no—
1189C2×C4—142no—
1190C2×C4—142no—
1191C2×C4—288no—
1192C2×C4—288no—
1193C2×C4—284no—
1194C2×C4—284no—
1195C2×C4—288no—
1196C2×C4C2×D4×D714yes—
1197C7#3473711yescharacteristic, complemented, Sylow
1198C22—22no—
1199C22—22no—
1200C22—24no—
1201C22—24no—
1202C22—22no—
1203C22—22no—
1204C22—24no—
1205C22—24no—
1206C22—22no—
1207C22—22no—
1208C22—22no—
1209C22—416no—
1210C22—42no—
1211C22—42no—
1212C22—41no—
1213C22—41no—
1214C22—42no—
1215C22—41no—
1216C22—42no—
1217C22—144no—
1218C22—144no—
1219C22—144no—
1220C22—2816no—
1221C22—282no—
1222C22—282no—
1223C22—282no—
1224C22—282no—
1225C22—281no—
1226C22—281no—
1227C22—282no—
1228C22—281no—
1229C22—282no—
1230C22D7×#12114yes—
1231C22#9034714yescomplemented
1232C22C22×D4×D711yescharacteristic
1233C22C22×D4×D711yescharacteristic
1234C22C2×D7×#4111yescharacteristic
1235C22C2×D7×#4112yes—
1236C22#9061812yes—
1237C4—24no—
1238C4—42no—
1239C4—41no—
1240C4—41no—
1241C4—42no—
1242C4—41no—
1243C4—42no—
1244C4—74no—
1245C4—74no—
1246C4—142no—
1247C4—142no—
1248C4—144no—
1249C4—144no—
1250C4—281no—
1251C4—281no—
1252C4—281no—
1253C4—282no—
1254C2—24no—
1255C2—24no—
1256C2—42no—
1257C2—81no—
1258C2—284no—
1259C2—561no—
1260C2C2×D7×#12111yescharacteristic
1261C2C2×#9034711yescharacteristic
1262C2#1174336211yescharacteristic
1263C2#1174369412yes—
1264C2#1174385812yes—
subgroupG/H
center, FrattiniC23C24×D7
commutator, socle, cosocleC23×C7C25
FittingC7×#2412C2
hypercenter#2412D7
hypocenterC7#34737
LCSG ▷ C23×C7 ▷ C7
UCSC1 ◁ C23 ◁ #2412

Complements

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

NH ≅ G/Ntype
1. C2×#90347C2semidirect
2. C2×#90277C2semidirect
3. C22×(C22⋊D7)⋊C4C2semidirect
4. C22×#6440C2semidirect
5. C7×#2412C2semidirect
6. #11740287C2semidirect
7. #11740051C2semidirect
8. #11739572C2semidirect
9. #11739552C2semidirect
10. #11734907C2semidirect
11. #11734902C2semidirect
12. #11734341C2semidirect
13. #11734335C2semidirect
14. #11732334C2semidirect
15. #11732137C2semidirect
16. #11732105C2semidirect
17. #11732103C2semidirect
18. #11732047C2semidirect
19. #11731823C2semidirect
20. #11731509C2semidirect
21. #11731495C2semidirect
22. #11731334C2semidirect
23. #11731310C2semidirect
35. C2×#6502C22semidirect
36. C2×#6502C22semidirect
39. C2×D4×Dic7C22semidirect
40. C2×D4×Dic7C22semidirect
45. C22×Dic7⋊C4C22semidirect
47. C22×C4×Dic7C22semidirect
50. C2×#6459C22semidirect
51. C2×#6456C22semidirect
53. C2×#6447C22semidirect
60. C2×(C22⋊D7)⋊C4C22semidirect
61. C2×(C22⋊D7)⋊C4C22semidirect
62. C2×(C22⋊D7)⋊C4C22semidirect
63. C2×#6441C22semidirect
64. C2×#6441C22semidirect
71. C2×#6440C22semidirect
72. C2×#6440C22semidirect
73. C7×#397C22semidirect
74. C7×#394C22semidirect
76. C7×#386C22semidirect
79. C7×#380C22semidirect
86. #89766C22semidirect
87. #89760C22semidirect
88. #89752C22semidirect
89. C4⋊C4×Dic7C22semidirect
90. #89745C22semidirect
91. #89744C22semidirect
95. #89731C22semidirect
96. #89731C22semidirect
99. #89730C22semidirect
100. #89729C22semidirect
101. #89729C22semidirect
104. #89724C22semidirect
106. #89720C22semidirect
108. #89716C22semidirect
109. #89714C22semidirect
110. C22⋊C4×Dic7C22semidirect
111. #89448C22semidirect
112. #89448C22semidirect
113. #89444C22semidirect
114. #89442C22semidirect
115. #89441C22semidirect
116. #89441C22semidirect
117. #89439C22semidirect
118. #89439C22semidirect
119. #89438C22semidirect
120. #89438C22semidirect
121. #89438C22semidirect
122. #89429C22semidirect
123. #89421C22semidirect
124. #89419C22semidirect
125. #89419C22semidirect
126. #89418C22semidirect
147. C23×Dic7D4semidirect
266. #6440D4semidirect
290. #2412D7semidirect
359. C2×C22⋊D7#41semidirect
463. Dic7⋊C4C2×D4semidirect
471. C4×Dic7C2×D4semidirect
524. #397C2×D7semidirect
534. #394C2×D7semidirect
556. #386C2×D7semidirect
566. #380C2×D7semidirect
676. C2×Dic7#121semidirect
863. C22×C7#525semidirect
1197. C7#34737semidirect
1231. C22#90347semidirect

Maximal subgroups

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

subgroupindex
C2×#903472
C2×#902772
C22×(C22⋊D7)⋊C42
C22×#64402
C7×#24122
#117402872
#117400512
#117395722
#117395522
#117349072
#117349022
#117343412
#117343352
#117323342
#117321372
#117321052
#117321032
#117320472
#117318232
#117315092
#117314952
#117313342
#117313102
#347377