Finite Group Databasebeta

← #13525669

Subgroups — #13525669

Order 1792.

3578 conjugacy classes of subgroups.

The subgroup lattice has 1240 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#90347C211yesmaximal, characteristic, complemented
2C2×#90277C211yesmaximal, characteristic, complemented
3C2×C4×#1159C211yesmaximal, characteristic, complemented
4C22×(C22⋊D7)⋊C4C211yesmaximal, characteristic, complemented
5C7×#2534C211yesmaximal, characteristic, complemented
6#11740301C211yesmaximal, characteristic, complemented
7#11740027C211yesmaximal, characteristic, complemented
8#11739859C211yesmaximal, characteristic, complemented
9#11739574C211yesmaximal, characteristic, complemented
10#11734759C212yesmaximal, complemented
11#11734726C212yesmaximal, complemented
12#11734389C212yesmaximal, complemented
13#11734335C212yesmaximal, complemented
14#11733037C212yesmaximal, complemented
15#11732897C212yesmaximal, complemented
16#11732196C212yesmaximal, complemented
17#11732105C212yesmaximal, complemented
18#11731520C211yesmaximal, characteristic, complemented
19#11731495C211yesmaximal, characteristic, complemented
20#11731474C211yesmaximal, characteristic, complemented
21#11731309C211yesmaximal, characteristic, complemented
22#11731269C211yesmaximal, characteristic, complemented
23#11731262C211yesmaximal, characteristic, complemented
24C23×C22⋊D7C2211yescharacteristic
25C24×Dic7C2211yescharacteristic
26C22×#1159C2211yescharacteristic
27C23×C4×D7C2211yescharacteristic
28C2×C7×#123C2211yescharacteristic
29C2×C7×#120C2211yescharacteristic
30C2×C4×C7×D4C2211yescharacteristic
31C22×C7×C22⋊C4C2211yescharacteristic
32C2×#6516C2211yescharacteristic
33C2×#6502C2212yes—
34C2×#6502C2212yescomplemented
35C2×#6500C2211yescharacteristic
36C2×#6498C2211yescharacteristic
37C2×D4×Dic7C2211yescharacteristic
38C2×D4×Dic7C2212yescomplemented
39C2×#6492C2211yescharacteristic
40C2×C4×C22⋊D7C2211yescharacteristic
41C2×C4×C22⋊D7C2211yescharacteristic, complemented
42C22×(C2×D7)⋊C4C2211yescharacteristic
43C22×Dic7⋊C4C2211yescharacteristic
44C22×C4×Dic7C2211yescharacteristic
45C22×C4×Dic7C2211yescharacteristic, complemented
46#90347—28no—
47#90277—28no—
48C4×#1159—28no—
49C2×#6459C2212yescomplemented
50C2×#6456C2212yescomplemented
51C2×#6455C2211yescharacteristic, complemented
52C2×#6450C2211yescharacteristic, complemented
53C2×#6449C2211yescharacteristic
54C2×#6447C2212yes—
55C2×#6447C2212yescomplemented
56C2×#6445C2211yescharacteristic
57C2×(C22⋊D7)⋊C4—28no—
58C2×(C22⋊D7)⋊C4C2212yes—
59C2×(C22⋊D7)⋊C4C2212yes—
60C2×(C22⋊D7)⋊C4C2212yes—
61C2×(C22⋊D7)⋊C4C2212yes—
62C2×(C22⋊D7)⋊C4C2211yescharacteristic
63C2×(C22⋊D7)⋊C4C2212yescomplemented
64C2×(C22⋊D7)⋊C4C2212yescomplemented
65C2×(C22⋊D7)⋊C4C2211yescharacteristic, complemented
66C2×#6441C2212yescomplemented
67C2×#6440C2211yescharacteristic
68C2×#6440C2211yescharacteristic
69C2×#6440C2211yescharacteristic
70C2×#6440C2211yescharacteristic, complemented
71C2×C42×D7C2211yescharacteristic, complemented
72C2×C4×Dic14C2211yescharacteristic, complemented
73C7×#396C2212yescomplemented
74C7×#394C2212yescomplemented
75C7×#388C2212yescomplemented
76C7×#386C2212yescomplemented
77C7×#381C2211yescharacteristic
78C7×#380C2211yescharacteristic
79C7×#379C2211yescharacteristic
80#90019C2211yescharacteristic
81#89995C2212yes—
82#89985C2212yescomplemented
83#89984C2211yescharacteristic
84#89983C2211yescharacteristic
85#89766C2212yescomplemented
86#89766C2212yescomplemented
87#89763C2212yescomplemented
88#89756C2212yescomplemented
89#89748C2212yescomplemented
90C4⋊C4×Dic7C2212yescomplemented
91#89744C2212yescomplemented
92#89733C2212yes—
93#89733C2212yescomplemented
94#89733C2212yescomplemented
95#89732C2212yes—
96#89731C2212yes—
97#89729C2212yes—
98#89729C2212yes—
99#89728C2212yescomplemented
100#89727C2211yescharacteristic
101#89727C2211yescharacteristic
102#89724C2212yescomplemented
103#89720C2212yescomplemented
104#89716C2212yescomplemented
105#89715C2211yescharacteristic
106#89715C2211yescharacteristic
107#89714C2211yescharacteristic
108#89714C2211yescharacteristic
109#89714C2212yescomplemented
110#89714C2212yescomplemented
111#89714C2212yescomplemented
112C22⋊C4×Dic7C2212yescomplemented
113C22⋊C4×Dic7C2212yescomplemented
114#89712C2212yescomplemented
115#89447C2212yescomplemented
116#89442C2212yescomplemented
117#89439C2212yescomplemented
118#89439C2212yescomplemented
119#89439C2212yescomplemented
120#89438C2212yescomplemented
121#89438C2212yescomplemented
122#89437C2212yescomplemented
123#89429C2212yescomplemented
124#89422C2212yescomplemented
125#89421C2212yescomplemented
126#89419C2212yescomplemented
127#34935—71nomaximal, Sylow
128C25×C7C2311yescharacteristic
129C24×D7C2311yescharacteristic
130C22×C7×D4C2312yes—
131C22×C7×D4C2311yescharacteristic
132C23×C4×C7C2311yescharacteristic
133C23×C4×C7C2311yescharacteristic
134C23×C4×C7C2311yescharacteristic
135C22×C22⋊D7—28no—
136C22×C22⋊D7—24no—
137C22×C22⋊D7C2312yes—
138C22×C22⋊D7C2312yes—
139C22×C22⋊D7C2312yes—
140C22×C22⋊D7C2311yescharacteristic
141C22×C22⋊D7C2311yescharacteristic
142C22×C22⋊D7C2312yes—
143C23×Dic7—24no—
144C23×Dic7—24no—
145C23×Dic7—24no—
146C23×Dic7C2312yes—
147C23×Dic7C2312yes—
148C23×Dic7C2311yescharacteristic
149C23×Dic7C2311yescharacteristic
150C23×Dic7C2311yescharacteristic
151C23×Dic7C2311yescharacteristic
152C23×Dic7C2311yescharacteristic
153C2×#1159—24no—
154C2×#1159—24no—
155C2×#1159D418yescomplemented
156C22×D28C2312yes—
157C22×C4×D7—24no—
158C22×C4×D7—24no—
159C22×C4×D7—24no—
160C22×C4×D7C2311yescharacteristic
161C22×C4×D7C2312yes—
162C22×C4×D7C2312yes—
163C22×C4×D7C2311yescharacteristic
164C22×C4×D7C2311yescharacteristic
165C22×Dic14C2311yescharacteristic
166C7×#123—24no—
167C7×#120—24no—
168C4×C7×D4—24no—
169C2×C7×C4⋊C4C2311yescharacteristic
170C2×C7×C4⋊C4C2312yes—
171C2×C7×C4⋊C4C2312yes—
172C2×C7×C22⋊C4—24no—
173C2×C7×C22⋊C4C2311yescharacteristic
174C2×C7×C22⋊C4C2311yescharacteristic
175C2×C7×C22⋊C4C2311yescharacteristic
176C2×C7×C22⋊C4C2311yescharacteristic
177C2×C7×C22⋊C4C2312yes—
178C2×C7×C22⋊C4C2312yes—
179C2×C7×C22⋊C4C2312yes—
180C2×C7×C22⋊C4C2312yes—
181C2×C7×C22⋊C4C2312yes—
182C2×C7×C22⋊C4C2312yes—
183C2×C42×C7C2311yescharacteristic
184#6516—24no—
185C2×C22⋊Dic7C2311yescharacteristic
186C2×C22⋊Dic7C2311yescharacteristic
187C2×C22⋊Dic7C2311yescharacteristic
188C2×C22⋊Dic7C2311yescharacteristic
189C2×C22⋊Dic7C2312yes—
190C2×C22⋊Dic7C2312yes—
191C2×C22⋊Dic7C2312yes—
192C2×C22⋊Dic7C2312yes—
193#6502—28no—
194#6502—28no—
195#6500—24no—
196#6498—24no—
197D4×Dic7—24no—
198D4×Dic7—28no—
199#6492—24no—
200C4×C22⋊D7—24no—
201C4×C22⋊D7—24no—
202C2×(C2×D7)⋊C4—24no—
203C2×(C2×D7)⋊C4C2312yes—
204C2×(C2×D7)⋊C4C2312yes—
205C2×(C2×D7)⋊C4C2311yescharacteristic
206C2×(C2×D7)⋊C4C2312yes—
207C2×(C2×D7)⋊C4C2312yes—
208C2×(C2×D7)⋊C4C2311yescharacteristic
209C2×(C2×D7)⋊C4C2312yes—
210C2×(C2×D7)⋊C4C2312yes—
211C2×(C2×D7)⋊C4C2312yes—
212C2×(C2×D7)⋊C4C2312yes—
213C2×(C2×D7)⋊C4C2312yes—
214C2×(C2×D7)⋊C4C2312yes—
215C2×C4⋊Dic7C2311yescharacteristic
216C2×C4⋊Dic7C2312yes—
217C2×C4⋊Dic7C2312yes—
218C2×Dic7⋊C4—24no—
219C2×Dic7⋊C4C2311yescharacteristic
220C2×Dic7⋊C4C2311yescharacteristic
221C2×Dic7⋊C4C2312yes—
222C2×Dic7⋊C4C2312yes—
223C2×Dic7⋊C4C2311yescharacteristic
224C2×Dic7⋊C4C2311yescharacteristic
225C2×Dic7⋊C4C2312yes—
226C2×Dic7⋊C4C2312yes—
227C2×Dic7⋊C4C2312yes—
228C2×Dic7⋊C4C2312yes—
229C2×Dic7⋊C4C2312yes—
230C2×Dic7⋊C4C2312yes—
231C2×C4×Dic7—24no—
232C2×C4×Dic7D418yescomplemented
233C2×C4×Dic7C2311yescharacteristic
234C2×C4×Dic7C2311yescharacteristic
235C2×C4×Dic7C2311yescharacteristic
236C2×C4×Dic7C2312yes—
237C2×C4×Dic7C2312yes—
238C2×C4×Dic7C2311yescharacteristic
239C2×C4×Dic7C2311yescharacteristic
240C2×C4×Dic7C2311yescharacteristic
241C2×C4×Dic7C2311yescharacteristic
242C2×C4×Dic7C2311yescharacteristic
243C2×C4×Dic7C2311yescharacteristic
244#6459—28no—
245#6456—28no—
246#6455—24no—
247#6450—24no—
248#6449—24no—
249#6447—28no—
250#6447—28no—
251#6445—24no—
252(C22⋊D7)⋊C4—24no—
253(C22⋊D7)⋊C4—28no—
254(C22⋊D7)⋊C4—28no—
255(C22⋊D7)⋊C4—28no—
256(C22⋊D7)⋊C4—28no—
257(C22⋊D7)⋊C4—28no—
258(C22⋊D7)⋊C4—28no—
259(C22⋊D7)⋊C4—24no—
260#6441—28no—
261#6440—24no—
262#6440—24no—
263#6440—24no—
264#6440—24no—
265C42×D7—24no—
266C4×Dic14—24no—
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—
281C2×C4×#41—71no—
282C22×C4×D4—71no—
283#2538—72no—
284#2537—72no—
285#2536—72no—
286#2535—72no—
287#2534—71no—
288#2534—71no—
289#2534—71no—
290#2534D711yescharacteristic, complemented
291#2486—71no—
292#2486—71no—
293#2408—71no—
294#2408—71no—
295#2392—72no—
296#2392—72no—
297C4×#121—72no—
298C4×#121—72no—
299#2285—71no—
300#2280—71no—
301#2280—71no—
302C24×C7—22no—
303C24×C7—24no—
304C24×C7—22no—
305C24×C7—22no—
306C24×C7—42no—
307C24×C7C2411yescharacteristic
308C24×C7C2412yes—
309C24×C7C2411yescharacteristic
310C23×D7—22no—
311C23×D7—24no—
312C23×D7—22no—
313C23×D7—22no—
314C23×D7—42no—
315C23×D7C2411yescharacteristic
316C23×D7C2412yes—
317C2×C7×D4—22no—
318C2×C7×D4—22no—
319C2×C7×D4—24no—
320C2×C7×D4—24no—
321C2×C7×D4—42no—
322C2×C7×D4C2×D414yes—
323C22×C4×C7—22no—
324C22×C4×C7—22no—
325C22×C4×C7—22no—
326C22×C4×C7—22no—
327C22×C4×C7—42no—
328C22×C4×C7—42no—
329C22×C4×C7C2×D414yes—
330C22×C4×C7C2412yes—
331C22×C4×C7C2411yescharacteristic
332C22×C4×C7C2411yescharacteristic
333C22×C4×C7C2412yes—
334C22×C4×C7C2412yes—
335C22×C4×C7C2411yescharacteristic
336C22×C4×C7C2411yescharacteristic
337C22×C4×C7C2411yescharacteristic
338C2×C22⋊D7—232no—
339C2×C22⋊D7—22no—
340C2×C22⋊D7—22no—
341C2×C22⋊D7—24no—
342C2×C22⋊D7—24no—
343C2×C22⋊D7—24no—
344C2×C22⋊D7—24no—
345C2×C22⋊D7—24no—
346C2×C22⋊D7—24no—
347C2×C22⋊D7—24no—
348C2×C22⋊D7—24no—
349C2×C22⋊D7—22no—
350C2×C22⋊D7—22no—
351C2×C22⋊D7—24no—
352C2×C22⋊D7—42no—
353C2×C22⋊D7—42no—
354C2×C22⋊D7C2×D414yes—
355C2×C22⋊D7C2×D414yescomplemented
356C2×C22⋊D7#4118yescomplemented
357C22×Dic7—22no—
358C22×Dic7—22no—
359C22×Dic7—24no—
360C22×Dic7—22no—
361C22×Dic7—22no—
362C22×Dic7—22no—
363C22×Dic7—24no—
364C22×Dic7—24no—
365C22×Dic7—24no—
366C22×Dic7—22no—
367C22×Dic7—24no—
368C22×Dic7—24no—
369C22×Dic7—24no—
370C22×Dic7—24no—
371C22×Dic7—416no—
372C22×Dic7C2×D414yes—
373C22×Dic7C2×D414yes—
374C22×Dic7C2×D414yes—
375C22×Dic7C2×D414yescomplemented
376C22×Dic7#4114yes—
377C22×Dic7C2411yescharacteristic
378C22×Dic7C2411yescharacteristic
379C22×Dic7C2412yes—
380C22×Dic7C2412yes—
381C22×Dic7C2412yes—
382C22×Dic7C2411yescharacteristic
383C22×Dic7C2411yescharacteristic
384C22×Dic7C2411yescharacteristic
385C22×Dic7C2411yescharacteristic
386C22×Dic7C2411yescharacteristic
387#1159—232no—
388C2×D28—24no—
389C2×D28—24no—
390C2×D28—42no—
391C2×C4×D7—22no—
392C2×C4×D7—22no—
393C2×C4×D7—22no—
394C2×C4×D7—22no—
395C2×C4×D7—24no—
396C2×C4×D7—24no—
397C2×C4×D7—24no—
398C2×C4×D7—24no—
399C2×C4×D7—24no—
400C2×C4×D7—24no—
401C2×C4×D7—24no—
402C2×C4×D7—42no—
403C2×C4×D7—416no—
404C2×C4×D7C2×D414yescomplemented
405C2×Dic14—22no—
406C2×Dic14—22no—
407C2×Dic14C2×D414yescomplemented
408C7×C4⋊C4—22no—
409C7×C4⋊C4—24no—
410C7×C4⋊C4—42no—
411C7×C22⋊C4—22no—
412C7×C22⋊C4—22no—
413C7×C22⋊C4—22no—
414C7×C22⋊C4—24no—
415C7×C22⋊C4—24no—
416C7×C22⋊C4—22no—
417C7×C22⋊C4—24no—
418C7×C22⋊C4—24no—
419C7×C22⋊C4—24no—
420C7×C22⋊C4—42no—
421C42×C7—22no—
422C22⋊Dic7—22no—
423C22⋊Dic7—22no—
424C22⋊Dic7—22no—
425C22⋊Dic7—24no—
426C22⋊Dic7—24no—
427C22⋊Dic7—22no—
428C22⋊Dic7—24no—
429C22⋊Dic7—42no—
430(C2×D7)⋊C4—24no—
431(C2×D7)⋊C4—24no—
432(C2×D7)⋊C4—24no—
433(C2×D7)⋊C4—24no—
434(C2×D7)⋊C4—24no—
435(C2×D7)⋊C4—24no—
436(C2×D7)⋊C4—22no—
437(C2×D7)⋊C4—24no—
438(C2×D7)⋊C4—24no—
439(C2×D7)⋊C4—22no—
440(C2×D7)⋊C4—42no—
441(C2×D7)⋊C4—42no—
442C4⋊Dic7—22no—
443C4⋊Dic7—24no—
444C4⋊Dic7—42no—
445Dic7⋊C4—22no—
446Dic7⋊C4—24no—
447Dic7⋊C4—22no—
448Dic7⋊C4—22no—
449Dic7⋊C4—24no—
450Dic7⋊C4—24no—
451Dic7⋊C4—22no—
452Dic7⋊C4—24no—
453Dic7⋊C4—24no—
454Dic7⋊C4—24no—
455Dic7⋊C4—24no—
456Dic7⋊C4—24no—
457C4×Dic7—22no—
458C4×Dic7—22no—
459C4×Dic7—22no—
460C4×Dic7—24no—
461C4×Dic7—24no—
462C4×Dic7—22no—
463C4×Dic7—22no—
464C4×Dic7C2×D414yes—
465C4×Dic7C2×D414yes—
466C4×Dic7C2×D414yes—
467C4×Dic7C2×D414yes—
468C22×#41—71no—
469C23×D4—71no—
470C24×C4—71no—
471C24×C4—71no—
472#525—148no—
473#525—148no—
474C2×#123—71no—
475C2×#123—71no—
476C2×#123—71no—
477C2×#123C2×D711yescharacteristic
478C2×C22⋊Q8—72no—
479C2×C22⋊Q8—72no—
480C2×#121—72no—
481C2×#121—72no—
482C2×#121—72no—
483C2×#121—72no—
484C2×#120—71no—
485C2×#120—71no—
486C2×#120—71no—
487C2×#120C2×D711yescharacteristic
488C4×#41—148no—
489C2×C4×Q8—71no—
490C2×C4×Q8—71no—
491C2×C4×D4—72no—
492C2×C4×D4—71no—
493C2×C4×D4—71no—
494C2×C4×D4—71no—
495C2×C4×D4—72no—
496C2×C4×D4—72no—
497C2×C4×D4—72no—
498C2×C4×D4—72no—
499C2×C4×D4—72no—
500C2×C4×D4—71no—
501C2×C4×D4—72no—
502C2×C4×D4—72no—
503C2×C4×D4—71no—
504C2×C4×D4—148no—
505C2×C4×D4C2×D711yescharacteristic
506C2×#117—71no—
507C2×#117—71no—
508C2×#117—71no—
509C2×#117—71no—
510C2×#117—71no—
511C22×C4⋊C4—71no—
512C22×C22⋊C4—71no—
513C22×C22⋊C4C2×D711yescharacteristic
514C22×C42—71no—
515C22×C42—71no—
516C22×C42—71no—
517#398—72no—
518#398—72no—
519#397—72no—
520#397—72no—
521#396—72no—
522#396—72no—
523#396—72no—
524#396C2×D712yescomplemented
525#394—72no—
526#394—72no—
527#394—72no—
528#394—72no—
529#394—72no—
530#394C2×D712yescomplemented
531#392—72no—
532#392—72no—
533#390—72no—
534#390—72no—
535#389—72no—
536#389—72no—
537#388—72no—
538#388—72no—
539#388—72no—
540#388C2×D712yescomplemented
541#386—72no—
542#386—72no—
543#386—72no—
544#386C2×D712yescomplemented
545#384—72no—
546#382—72no—
547#381—71no—
548#381—71no—
549#381—71no—
550#381C2×D711yescharacteristic
551#380—71no—
552#380—71no—
553#380—71no—
554#380—72no—
555#380—72no—
556#380—72no—
557#380—72no—
558#380—72no—
559#380—72no—
560#380C2×D711yescharacteristic
561#379—71no—
562#379—71no—
563#379—71no—
564#379C2×D711yescharacteristic
565C4×C4⋊C4—72no—
566C4×C4⋊C4—72no—
567C4×C22⋊C4—72no—
568C4×C22⋊C4—72no—
569C4×C22⋊C4—72no—
570C4×C22⋊C4—72no—
571C23×C7—22no—
572C23×C7—22no—
573C23×C7—28no—
574C23×C7—21no—
575C23×C7—22no—
576C23×C7—22no—
577C23×C7—22no—
578C23×C7—21no—
579C23×C7—22no—
580C23×C7—22no—
581C23×C7—22no—
582C23×C7—22no—
583C23×C7—22no—
584C23×C7—48no—
585C23×C7—48no—
586C23×C7—44no—
587C23×C7—44no—
588C23×C7C22×D412yes—
589C23×C7C22×D412yes—
590C23×C7C22×D412yes—
591C23×C7C2×#4114yes—
592C23×C7C2×#4112yes—
593C23×C7C2511yescharacteristic
594C22×D7—28no—
595C22×D7—21no—
596C22×D7—22no—
597C22×D7—22no—
598C22×D7—22no—
599C22×D7—22no—
600C22×D7—21no—
601C22×D7—22no—
602C22×D7—22no—
603C22×D7—22no—
604C22×D7—22no—
605C22×D7—48no—
606C22×D7—48no—
607C22×D7—44no—
608C22×D7—44no—
609C22×D7C22×D412yes—
610C22×D7C2×#4114yes—
611C7×D4—28no—
612C7×D4—48no—
613C2×C4×C7—21no—
614C2×C4×C7—21no—
615C2×C4×C7—22no—
616C2×C4×C7—22no—
617C2×C4×C7—21no—
618C2×C4×C7—21no—
619C2×C4×C7—22no—
620C2×C4×C7—22no—
621C2×C4×C7—22no—
622C2×C4×C7—22no—
623C2×C4×C7—22no—
624C2×C4×C7—22no—
625C2×C4×C7—22no—
626C2×C4×C7—22no—
627C2×C4×C7—22no—
628C2×C4×C7—22no—
629C2×C4×C7—22no—
630C2×C4×C7—44no—
631C2×C4×C7—44no—
632C2×C4×C7—44no—
633C2×C4×C7C22×D412yes—
634C2×C4×C7C22×D412yes—
635C2×C4×C7C22×D412yes—
636C22⋊D7—216no—
637C22⋊D7—28no—
638C22⋊D7—28no—
639C22⋊D7—216no—
640C22⋊D7—48no—
641C22⋊D7—48no—
642C2×Dic7—21no—
643C2×Dic7—21no—
644C2×Dic7—22no—
645C2×Dic7—28no—
646C2×Dic7—28no—
647C2×Dic7—21no—
648C2×Dic7—21no—
649C2×Dic7—22no—
650C2×Dic7—22no—
651C2×Dic7—22no—
652C2×Dic7—22no—
653C2×Dic7—22no—
654C2×Dic7—22no—
655C2×Dic7—22no—
656C2×Dic7—22no—
657C2×Dic7—22no—
658C2×Dic7—22no—
659C2×Dic7—22no—
660C2×Dic7—44no—
661C2×Dic7—48no—
662C2×Dic7—48no—
663C2×Dic7—44no—
664C2×Dic7#121116yescomplemented
665C2×Dic7C22×D412yes—
666C2×Dic7C22×D412yes—
667C2×Dic7C22×D412yes—
668C2×Dic7C22×D412yes—
669C2×Dic7C22×D412yes—
670C2×Dic7C22×D412yes—
671C2×Dic7C22×D412yes—
672C2×Dic7C2×#4112yes—
673C2×Dic7C2×#4112yes—
674C2×Dic7C2×#4114yes—
675D28—48no—
676C4×D7—28no—
677C4×D7—44no—
678C4×D7—48no—
679C4×D7—48no—
680C4×D7—44no—
681Dic14—28no—
682C25—71no—
683C25C22×D711yescharacteristic
684C2×#41—78no—
685C2×#41—144no—
686C2×#41—144no—
687C22×Q8—71no—
688C22×D4—71no—
689C22×D4—71no—
690C22×D4—72no—
691C22×D4—72no—
692C22×D4—72no—
693C22×D4—72no—
694C22×D4—72no—
695C22×D4—144no—
696C22×D4—148no—
697C22×D4C22×D712yes—
698C22×D4C22×D711yescharacteristic
699C23×C4—71no—
700C23×C4—71no—
701C23×C4—71no—
702C23×C4—71no—
703C23×C4—71no—
704C23×C4—72no—
705C23×C4—71no—
706C23×C4—72no—
707C23×C4—72no—
708C23×C4—71no—
709C23×C4—72no—
710C23×C4—71no—
711C23×C4—144no—
712C23×C4—144no—
713C23×C4—144no—
714C23×C4—144no—
715C23×C4—144no—
716C23×C4—144no—
717C23×C4C22×D711yescharacteristic
718C23×C4C22×D711yescharacteristic
719C23×C4C22×D711yescharacteristic
720#123—24no—
721#123—144no—
722#123—144no—
723#123—144no—
724C22⋊Q8—148no—
725C22⋊Q8—148no—
726#121—148no—
727#121—148no—
728#121—148no—
729#121—148no—
730#120—24no—
731#120—144no—
732#120—144no—
733#120—144no—
734C4×Q8—144no—
735C4×Q8—144no—
736C4×D4—24no—
737C4×D4—148no—
738C4×D4—148no—
739C4×D4—148no—
740C4×D4—148no—
741C4×D4—144no—
742C4×D4—144no—
743C4×D4—144no—
744C4×D4—148no—
745C4×D4—148no—
746C4×D4—148no—
747C4×D4—144no—
748C4×D4—148no—
749C4×D4—144no—
750#117—144no—
751#117—144no—
752#117—144no—
753#117—144no—
754#117—144no—
755C2×C4⋊C4—72no—
756C2×C4⋊C4—72no—
757C2×C4⋊C4—71no—
758C2×C4⋊C4—71no—
759C2×C4⋊C4—71no—
760C2×C4⋊C4—71no—
761C2×C4⋊C4—71no—
762C2×C4⋊C4—72no—
763C2×C4⋊C4—72no—
764C2×C4⋊C4—72no—
765C2×C4⋊C4—72no—
766C2×C4⋊C4—72no—
767C2×C4⋊C4—72no—
768C2×C4⋊C4—72no—
769C2×C4⋊C4—72no—
770C2×C4⋊C4—144no—
771C2×C4⋊C4C22×D711yescharacteristic
772C2×C4⋊C4C22×D712yes—
773C2×C4⋊C4C22×D712yes—
774C2×C22⋊C4—24no—
775C2×C22⋊C4—71no—
776C2×C22⋊C4—71no—
777C2×C22⋊C4—71no—
778C2×C22⋊C4—71no—
779C2×C22⋊C4—72no—
780C2×C22⋊C4—72no—
781C2×C22⋊C4—72no—
782C2×C22⋊C4—72no—
783C2×C22⋊C4—72no—
784C2×C22⋊C4—71no—
785C2×C22⋊C4—71no—
786C2×C22⋊C4—72no—
787C2×C22⋊C4—72no—
788C2×C22⋊C4—72no—
789C2×C22⋊C4—72no—
790C2×C22⋊C4—72no—
791C2×C22⋊C4—72no—
792C2×C22⋊C4—72no—
793C2×C22⋊C4—72no—
794C2×C22⋊C4—72no—
795C2×C22⋊C4—144no—
796C2×C22⋊C4C22×D712yes—
797C2×C22⋊C4C22×D712yes—
798C2×C22⋊C4C22×D711yescharacteristic
799C2×C22⋊C4C22×D711yescharacteristic
800C2×C22⋊C4C22×D711yescharacteristic
801C2×C22⋊C4C22×D711yescharacteristic
802C2×C22⋊C4C22×D712yes—
803C2×C22⋊C4C22×D712yes—
804C2×C22⋊C4C22×D712yes—
805C2×C22⋊C4C22×D712yes—
806C2×C42—78no—
807C2×C42—71no—
808C2×C42—71no—
809C2×C42—71no—
810C2×C42—71no—
811C2×C42—71no—
812C2×C42—71no—
813C2×C42—72no—
814C2×C42—72no—
815C2×C42—71no—
816C2×C42—71no—
817C2×C42—71no—
818C2×C42—144no—
819C2×C42—144no—
820C2×C42C22×D711yescharacteristic
821#95—72no—
822#95—72no—
823#95—72no—
824#95—72no—
825#95—72no—
826#95—72no—
827#95—72no—
828#95—72no—
829#95—72no—
830#95C22×D712yes—
831#95C22×D712yes—
832#95C22×D712yes—
833C22×C7—22no—
834C22×C7—22no—
835C22×C7—24no—
836C22×C7—24no—
837C22×C7—22no—
838C22×C7—24no—
839C22×C7—24no—
840C22×C7—24no—
841C22×C7—24no—
842C22×C7—416no—
843C22×C7—42no—
844C22×C7—41no—
845C22×C7—41no—
846C22×C7—42no—
847C22×C7—42no—
848C22×C7—42no—
849C22×C7—42no—
850C22×C7C2×#12114yes—
851C22×C7C23×D411yescharacteristic
852C22×C7C23×D411yescharacteristic
853C22×C7C22×#4111yescharacteristic
854C22×C7C22×#4112yes—
855C22×C7#58512yes—
856C2×D7—22no—
857C2×D7—24no—
858C2×D7—24no—
859C2×D7—24no—
860C2×D7—24no—
861C2×D7—416no—
862C2×D7—42no—
863C2×D7—41no—
864C2×D7—41no—
865C2×D7—42no—
866C2×D7—42no—
867C2×D7—42no—
868C2×D7—42no—
869C4×C7—22no—
870C4×C7—22no—
871C4×C7—22no—
872C4×C7—42no—
873C4×C7—41no—
874C4×C7—41no—
875C4×C7—42no—
876C4×C7—42no—
877Dic7—22no—
878Dic7—22no—
879Dic7—42no—
880Dic7—41no—
881Dic7—41no—
882Dic7—42no—
883Dic7—42no—
884Dic7C2×#12114yes—
885Dic7C2×#12114yes—
886Dic7#52514yescomplemented
887C24—22no—
888C24—24no—
889C24—22no—
890C24—22no—
891C24—42no—
892C24—72no—
893C24—71no—
894C24—144no—
895C24—142no—
896C24—142no—
897C24—142no—
898C24—282no—
899C24C23×D711yescharacteristic
900C24C23×D712yes—
901C24C23×D711yescharacteristic
902#41—1432no—
903C2×Q8—74no—
904C2×Q8—142no—
905C2×Q8—142no—
906C2×D4—22no—
907C2×D4—22no—
908C2×D4—24no—
909C2×D4—24no—
910C2×D4—42no—
911C2×D4—74no—
912C2×D4—74no—
913C2×D4—78no—
914C2×D4—144no—
915C2×D4—144no—
916C2×D4—144no—
917C2×D4—144no—
918C2×D4—142no—
919C2×D4—144no—
920C2×D4—142no—
921C2×D4—144no—
922C2×D4—1432no—
923C2×D4—142no—
924C2×D4—144no—
925C2×D4—142no—
926C2×D4—144no—
927C2×D4—144no—
928C2×D4—144no—
929C2×D4—144no—
930C2×D4—282no—
931C2×D4—282no—
932C2×D4—282no—
933C2×D4D4×D714yes—
934C22×C4—22no—
935C22×C4—22no—
936C22×C4—22no—
937C22×C4—22no—
938C22×C4—42no—
939C22×C4—42no—
940C22×C4—74no—
941C22×C4—74no—
942C22×C4—74no—
943C22×C4—71no—
944C22×C4—71no—
945C22×C4—71no—
946C22×C4—74no—
947C22×C4—74no—
948C22×C4—71no—
949C22×C4—71no—
950C22×C4—74no—
951C22×C4—71no—
952C22×C4—71no—
953C22×C4—72no—
954C22×C4—72no—
955C22×C4—72no—
956C22×C4—142no—
957C22×C4—142no—
958C22×C4—142no—
959C22×C4—144no—
960C22×C4—144no—
961C22×C4—144no—
962C22×C4—144no—
963C22×C4—144no—
964C22×C4—144no—
965C22×C4—144no—
966C22×C4—142no—
967C22×C4—144no—
968C22×C4—142no—
969C22×C4—142no—
970C22×C4—144no—
971C22×C4—144no—
972C22×C4—144no—
973C22×C4—144no—
974C22×C4—144no—
975C22×C4—144no—
976C22×C4—144no—
977C22×C4—142no—
978C22×C4—142no—
979C22×C4—142no—
980C22×C4—142no—
981C22×C4—282no—
982C22×C4—2816no—
983C22×C4—2816no—
984C22×C4D4×D714yes—
985C22×C4C23×D712yes—
986C22×C4C23×D711yescharacteristic
987C22×C4C23×D711yescharacteristic
988C22×C4C23×D712yes—
989C22×C4C23×D712yes—
990C22×C4C23×D711yescharacteristic
991C22×C4C23×D711yescharacteristic
992C22×C4C23×D711yescharacteristic
993C4⋊C4—22no—
994C4⋊C4—24no—
995C4⋊C4—42no—
996C4⋊C4—144no—
997C4⋊C4—144no—
998C4⋊C4—142no—
999C4⋊C4—142no—
1000C4⋊C4—142no—
1001C4⋊C4—144no—
1002C4⋊C4—144no—
1003C4⋊C4—144no—
1004C4⋊C4—144no—
1005C4⋊C4—144no—
1006C4⋊C4—142no—
1007C4⋊C4—144no—
1008C4⋊C4—142no—
1009C4⋊C4—144no—
1010C4⋊C4—282no—
1011C22⋊C4—22no—
1012C22⋊C4—22no—
1013C22⋊C4—22no—
1014C22⋊C4—24no—
1015C22⋊C4—24no—
1016C22⋊C4—24no—
1017C22⋊C4—24no—
1018C22⋊C4—22no—
1019C22⋊C4—24no—
1020C22⋊C4—42no—
1021C22⋊C4—142no—
1022C22⋊C4—144no—
1023C22⋊C4—144no—
1024C22⋊C4—144no—
1025C22⋊C4—144no—
1026C22⋊C4—144no—
1027C22⋊C4—142no—
1028C22⋊C4—144no—
1029C22⋊C4—142no—
1030C22⋊C4—142no—
1031C22⋊C4—142no—
1032C22⋊C4—144no—
1033C22⋊C4—144no—
1034C22⋊C4—144no—
1035C22⋊C4—144no—
1036C22⋊C4—142no—
1037C22⋊C4—144no—
1038C22⋊C4—282no—
1039C22⋊C4—282no—
1040C22⋊C4—282no—
1041C42—22no—
1042C42—74no—
1043C42—74no—
1044C42—74no—
1045C42—74no—
1046C42—142no—
1047C42—142no—
1048C42—142no—
1049C42—142no—
1050C42—144no—
1051C42—144no—
1052C42—142no—
1053C2×C7—24no—
1054C2×C7—42no—
1055C2×C7—44no—
1056C2×C7C22×#12111yescharacteristic
1057C2×C7C2×#52511yescharacteristic
1058C2×C7#344911yescharacteristic
1059C2×C7D4×#4112yes—
1060C2×C7#347512yes—
1061D7—42no—
1062D7—44no—
1063C23—22no—
1064C23—22no—
1065C23—28no—
1066C23—22no—
1067C23—21no—
1068C23—22no—
1069C23—22no—
1070C23—21no—
1071C23—22no—
1072C23—22no—
1073C23—22no—
1074C23—22no—
1075C23—22no—
1076C23—48no—
1077C23—48no—
1078C23—44no—
1079C23—44no—
1080C23—72no—
1081C23—74no—
1082C23—148no—
1083C23—141no—
1084C23—142no—
1085C23—142no—
1086C23—142no—
1087C23—141no—
1088C23—142no—
1089C23—142no—
1090C23—142no—
1091C23—142no—
1092C23—142no—
1093C23—288no—
1094C23—288no—
1095C23—284no—
1096C23—284no—
1097C23C2×D4×D712yes—
1098C23C2×D4×D712yes—
1099C23C2×D4×D712yes—
1100C23D7×#4114yes—
1101C23D7×#4112yes—
1102C23C24×D711yescharacteristic
1103Q8—148no—
1104D4—28no—
1105D4—48no—
1106D4—1416no—
1107D4—148no—
1108D4—1416no—
1109D4—148no—
1110D4—288no—
1111D4—288no—
1112D4—288no—
1113C2×C4—21no—
1114C2×C4—21no—
1115C2×C4—22no—
1116C2×C4—22no—
1117C2×C4—21no—
1118C2×C4—21no—
1119C2×C4—22no—
1120C2×C4—22no—
1121C2×C4—22no—
1122C2×C4—22no—
1123C2×C4—22no—
1124C2×C4—22no—
1125C2×C4—22no—
1126C2×C4—22no—
1127C2×C4—22no—
1128C2×C4—22no—
1129C2×C4—22no—
1130C2×C4—44no—
1131C2×C4—44no—
1132C2×C4—44no—
1133C2×C4—716no—
1134C2×C4—72no—
1135C2×C4—72no—
1136C2×C4—72no—
1137C2×C4—72no—
1138C2×C4—72no—
1139C2×C4—74no—
1140C2×C4—72no—
1141C2×C4—72no—
1142C2×C4—72no—
1143C2×C4—72no—
1144C2×C4—148no—
1145C2×C4—148no—
1146C2×C4—148no—
1147C2×C4—141no—
1148C2×C4—142no—
1149C2×C4—141no—
1150C2×C4—141no—
1151C2×C4—141no—
1152C2×C4—142no—
1153C2×C4—142no—
1154C2×C4—142no—
1155C2×C4—142no—
1156C2×C4—142no—
1157C2×C4—142no—
1158C2×C4—142no—
1159C2×C4—142no—
1160C2×C4—142no—
1161C2×C4—142no—
1162C2×C4—142no—
1163C2×C4—284no—
1164C2×C4—284no—
1165C2×C4—288no—
1166C2×C4—288no—
1167C2×C4—284no—
1168C2×C4—288no—
1169C2×C4—288no—
1170C2×C4—284no—
1171C2×C4C2×D4×D712yes—
1172C2×C4C2×D4×D712yes—
1173C2×C4C2×D4×D712yes—
1174C7#3493511yescharacteristic, complemented, Sylow
1175C22—24no—
1176C22—22no—
1177C22—22no—
1178C22—24no—
1179C22—22no—
1180C22—24no—
1181C22—24no—
1182C22—24no—
1183C22—24no—
1184C22—416no—
1185C22—42no—
1186C22—42no—
1187C22—42no—
1188C22—41no—
1189C22—41no—
1190C22—42no—
1191C22—42no—
1192C22—142no—
1193C22—144no—
1194C22—144no—
1195C22—144no—
1196C22—144no—
1197C22—2816no—
1198C22—282no—
1199C22—282no—
1200C22—282no—
1201C22—281no—
1202C22—281no—
1203C22—282no—
1204C22—282no—
1205C22D7×#12114yes—
1206C22C22×D4×D711yescharacteristic
1207C22C22×D4×D711yescharacteristic
1208C22C2×D7×#4111yescharacteristic
1209C22C2×D7×#4112yes—
1210C22#9061812yes—
1211C4—22no—
1212C4—22no—
1213C4—22no—
1214C4—42no—
1215C4—41no—
1216C4—41no—
1217C4—42no—
1218C4—42no—
1219C4—74no—
1220C4—74no—
1221C4—74no—
1222C4—142no—
1223C4—142no—
1224C4—282no—
1225C4—281no—
1226C4—281no—
1227C4—282no—
1228C4—282no—
1229C2—24no—
1230C2—44no—
1231C2—42no—
1232C2—284no—
1233C2—282no—
1234C2C2×D7×#12111yescharacteristic
1235C2D7×#52511yescharacteristic
1236C2#1174336211yescharacteristic
1237C2#1174369412yes—
1238C2#1174385812yes—
subgroupG/H
center, FrattiniC23C24×D7
commutator, socle, cosocleC23×C7C25
FittingC7×#2534C2
hypercenter#2534D7
hypocenterC7#34935
LCSG ▷ C23×C7 ▷ C7
UCSC1 ◁ C23 ◁ #2534

Complements

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

NH ≅ G/Ntype
1. C2×#90347C2semidirect
2. C2×#90277C2semidirect
3. C2×C4×#1159C2semidirect
4. C22×(C22⋊D7)⋊C4C2semidirect
5. C7×#2534C2semidirect
6. #11740301C2semidirect
7. #11740027C2semidirect
8. #11739859C2semidirect
9. #11739574C2semidirect
10. #11734759C2semidirect
11. #11734726C2semidirect
12. #11734389C2semidirect
13. #11734335C2semidirect
14. #11733037C2semidirect
15. #11732897C2semidirect
16. #11732196C2semidirect
17. #11732105C2semidirect
18. #11731520C2semidirect
19. #11731495C2semidirect
20. #11731474C2semidirect
21. #11731309C2semidirect
22. #11731269C2semidirect
23. #11731262C2semidirect
34. C2×#6502C22semidirect
38. C2×D4×Dic7C22semidirect
41. C2×C4×C22⋊D7C22semidirect
45. C22×C4×Dic7C22semidirect
49. C2×#6459C22semidirect
50. C2×#6456C22semidirect
51. C2×#6455C22semidirect
52. C2×#6450C22semidirect
55. C2×#6447C22semidirect
63. C2×(C22⋊D7)⋊C4C22semidirect
64. C2×(C22⋊D7)⋊C4C22semidirect
65. C2×(C22⋊D7)⋊C4C22semidirect
66. C2×#6441C22semidirect
70. C2×#6440C22semidirect
71. C2×C42×D7C22semidirect
72. C2×C4×Dic14C22semidirect
73. C7×#396C22semidirect
74. C7×#394C22semidirect
75. C7×#388C22semidirect
76. C7×#386C22semidirect
82. #89985C22semidirect
85. #89766C22semidirect
86. #89766C22semidirect
87. #89763C22semidirect
88. #89756C22semidirect
89. #89748C22semidirect
90. C4⋊C4×Dic7C22semidirect
91. #89744C22semidirect
93. #89733C22semidirect
94. #89733C22semidirect
99. #89728C22semidirect
102. #89724C22semidirect
103. #89720C22semidirect
104. #89716C22semidirect
109. #89714C22semidirect
110. #89714C22semidirect
111. #89714C22semidirect
112. C22⋊C4×Dic7C22semidirect
113. C22⋊C4×Dic7C22semidirect
114. #89712C22semidirect
115. #89447C22semidirect
116. #89442C22semidirect
117. #89439C22semidirect
118. #89439C22semidirect
119. #89439C22semidirect
120. #89438C22semidirect
121. #89438C22semidirect
122. #89437C22semidirect
123. #89429C22semidirect
124. #89422C22semidirect
125. #89421C22semidirect
126. #89419C22semidirect
155. C2×#1159D4semidirect
232. C2×C4×Dic7D4semidirect
290. #2534D7semidirect
355. C2×C22⋊D7C2×D4semidirect
356. C2×C22⋊D7#41semidirect
375. C22×Dic7C2×D4semidirect
404. C2×C4×D7C2×D4semidirect
407. C2×Dic14C2×D4semidirect
524. #396C2×D7semidirect
530. #394C2×D7semidirect
540. #388C2×D7semidirect
544. #386C2×D7semidirect
664. C2×Dic7#121semidirect
886. Dic7#525semidirect
1174. C7#34935semidirect

Maximal subgroups

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

subgroupindex
C2×#903472
C2×#902772
C2×C4×#11592
C22×(C22⋊D7)⋊C42
C7×#25342
#117403012
#117400272
#117398592
#117395742
#117347592
#117347262
#117343892
#117343352
#117330372
#117328972
#117321962
#117321052
#117315202
#117314952
#117314742
#117313092
#117312692
#117312622
#349357