Finite Group Databasebeta

← #14224553

Subgroups — #14224553

Order 1792.

2342 conjugacy classes of subgroups.

The subgroup lattice has 1008 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C7×C22⋊Q8C211yesmaximal, characteristic, complemented
2C2×#90482C211yesmaximal, characteristic
3#11741504C212yesmaximal, complemented
4C2×#89979C211yesmaximal, characteristic, complemented
5#11740187C212yesmaximal, complemented
6#11740186C212yesmaximal, complemented
7#11740184C214yesmaximal, complemented
8#11740183C212yesmaximal, complemented
9#11740182C214yesmaximal, complemented
10#11740181C212yesmaximal, complemented
11#11740180C212yesmaximal, complemented
12#11740177C214yesmaximal, complemented
13#11740172C212yesmaximal, complemented
14#11739584C212yesmaximal, complemented
15C23×C7×Q8C2211yescharacteristic, complemented
16C24×C4×C7C2211yescharacteristic
17C22×#1157C2211yescharacteristic
18C2×C7×C22⋊Q8—21no—
19C2×C7×C22⋊Q8—21no—
20C2×C7×C22⋊Q8—21no—
21C2×C7×C22⋊Q8—21no—
22C2×C7×C22⋊Q8—21no—
23C2×C7×C22⋊Q8—21no—
24C2×C7×C22⋊Q8C2212yes—
25C2×C7×C22⋊Q8C2212yes—
26C2×C7×C22⋊Q8C2212yes—
27C2×C7×C22⋊Q8C2212yescomplemented
28C2×C7×C22⋊Q8C2212yescomplemented
29C2×C7×C22⋊Q8C2212yescomplemented
30C22×C7×C4⋊C4—21no—
31C22×C7×C4⋊C4C2211yescharacteristic, complemented
32C22×C7×C22⋊C4—21no—
33C2×#6516—21no—
34C2×#6505C2214yescomplemented
35#90482—21no—
36#90482—21no—
37#90482—21no—
38#90482—21no—
39#90482C2212yes—
40#90482C2212yes—
41#90482C2212yes—
42#90482C2212yes—
43C2×#6493C2211yescharacteristic
44C2×#6493C2211yescharacteristic
45C2×#6492—21no—
46C2×C4×C22⋊D7—21no—
47C2×C4×C22⋊D7—21no—
48C2×#6489C2211yescharacteristic
49C2×#6487C2211yescharacteristic
50C2×#6487C2211yescharacteristic
51C22×#1136C2212yescomplemented
52#90000C2214yescomplemented
53#90000C2214yescomplemented
54#89999C2214yescomplemented
55#89999C2214yescomplemented
56#89997C2214yescomplemented
57#89979C2212yes—
58#89979C2212yes—
59#89979C2212yescomplemented
60#89979C2212yescomplemented
61C2×C22⋊(C7⋊C8)C2212yes—
62C2×C22⋊(C7⋊C8)C2212yescomplemented
63#89824C2218yescomplemented
64#89823C2218yescomplemented
65#89822C2214yescomplemented
66#89821C2218yescomplemented
67#89820C2218yescomplemented
68#89819C2218yescomplemented
69#89818C2214yescomplemented
70#89817C2218yescomplemented
71#89816C2214yescomplemented
72#89815C2214yescomplemented
73#89743C2214yescomplemented
74#89742C2214yescomplemented
75#89740C2214yescomplemented
76#89739C2214yescomplemented
77#89738C2214yescomplemented
78#89736C2214yescomplemented
79#60751—71nomaximal, Sylow
80C25×C7D411yescharacteristic
81C22×C7×Q8—21no—
82C22×C7×Q8—21no—
83C22×C7×Q8—21no—
84C22×C7×Q8—44no—
85C22×C7×Q8C2312yes—
86C22×C7×Q8C2312yes—
87C22×C7×Q8C2312yes—
88C23×C4×C7—21no—
89C23×C4×C7—21no—
90C23×C4×C7—44no—
91C23×C4×C7D411yescharacteristic
92C23×C4×C7D411yescharacteristic
93C23×C4×C7D411yescharacteristic
94C23×C4×C7D411yescharacteristic
95C23×C4×C7D411yescharacteristic
96C23×C4×C7D411yescharacteristic
97C23×C4×C7D411yescharacteristic
98C23×C4×C7C2311yescharacteristic
99C23×C4×C7C2311yescharacteristic
100C23×C4×C7C2311yescharacteristic
101C23×C4×C7C2311yescharacteristic
102C23×C4×C7C2311yescharacteristic
103C23×C4×C7C2311yescharacteristic
104C23×C4×C7C2311yescharacteristic
105C22×C22⋊D7—21no—
106C22×C22⋊D7—21no—
107C22×C22⋊D7—21no—
108C2×#1157—21no—
109C2×#1157—21no—
110C2×#1157—44no—
111C2×#1157C2312yes—
112C2×#1157C2312yes—
113C22×D28C2311yescharacteristic
114C22×C4×D7—21no—
115C22×Dic14C2311yescharacteristic
116C7×C22⋊Q8—22no—
117C7×C22⋊Q8—22no—
118C7×C22⋊Q8—22no—
119C7×C22⋊Q8—22no—
120C7×C22⋊Q8—22no—
121C7×C22⋊Q8—22no—
122C7×C22⋊Q8—22no—
123C7×C22⋊Q8—22no—
124C7×C22⋊Q8—22no—
125C7×C22⋊Q8—22no—
126C7×C22⋊Q8—22no—
127C7×C22⋊Q8—22no—
128C7×C22⋊Q8C2314yes—
129C7×C22⋊Q8C2314yes—
130C7×C22⋊Q8C2314yes—
131C7×C22⋊Q8C2314yes—
132C2×C7×C4⋊C4—22no—
133C2×C7×C4⋊C4—22no—
134C2×C7×C4⋊C4—22no—
135C2×C7×C4⋊C4—22no—
136C2×C7×C4⋊C4—22no—
137C2×C7×C4⋊C4—22no—
138C2×C7×C4⋊C4—21no—
139C2×C7×C4⋊C4—21no—
140C2×C7×C4⋊C4—21no—
141C2×C7×C4⋊C4C2312yes—
142C2×C7×C4⋊C4C2312yes—
143C2×C7×C4⋊C4C2312yes—
144C2×C7×C22⋊C4—22no—
145C2×C7×C22⋊C4—22no—
146C2×C7×C22⋊C4—22no—
147C2×C7×C22⋊C4—22no—
148C2×C7×C22⋊C4—22no—
149C2×C7×C22⋊C4—22no—
150#6516—22no—
151#6516—22no—
152#6516—22no—
153#6516—22no—
154C2×C22⋊Dic7—21no—
155C2×C22⋊Dic7—21no—
156C2×C22⋊Dic7—21no—
157C2×#1144C2318yescomplemented
158#6505—48no—
159C2×#1143C2318yescomplemented
160#6493—21no—
161#6493—21no—
162#6493—21no—
163#6493—21no—
164#6493C2312yes—
165#6493C2312yes—
166#6493C2312yes—
167#6493C2312yes—
168#6492—22no—
169#6492—22no—
170#6492—22no—
171#6492—22no—
172C4×C22⋊D7—22no—
173C4×C22⋊D7—22no—
174C4×C22⋊D7—22no—
175C4×C22⋊D7—22no—
176C4×C22⋊D7—22no—
177C4×C22⋊D7—22no—
178C4×C22⋊D7—22no—
179C4×C22⋊D7—22no—
180C2×(C2×D7)⋊C4—21no—
181C2×(C2×D7)⋊C4—21no—
182#6489—21no—
183#6489—21no—
184#6489C2312yes—
185#6489C2312yes—
186C2×C4⋊Dic7C2311yescharacteristic
187C2×C4⋊Dic7C2311yescharacteristic
188#6487—21no—
189#6487—21no—
190#6487—21no—
191#6487—21no—
192#6487C2312yes—
193#6487C2312yes—
194#6487C2312yes—
195#6487C2312yes—
196C2×Dic7⋊C4—21no—
197C2×Dic7⋊C4—21no—
198C2×C4×Dic7—21no—
199C2×#1136—44no—
200C2×#1136C2314yes—
201C2×#1136C2314yes—
202C22×C7⋊C8C2314yes—
203#6409C2318yescomplemented
204#6409C2318yescomplemented
205C22⋊(C7⋊C8)C2314yes—
206C22⋊(C7⋊C8)C2314yes—
207C22⋊(C7⋊C8)C2314yes—
208C22⋊(C7⋊C8)C2314yes—
209#6384C2318yescomplemented
210#6383C2318yescomplemented
211#6382C2318yescomplemented
212#6381C2318yescomplemented
213C2×#525—71no—
214C22×C22⋊Q8D711yescharacteristic, complemented
215#3196—74no—
216#3195—72no—
217#3193—72no—
218#3190—74no—
219#3189—72no—
220#3187—72no—
221#3095—72no—
222#3092—72no—
223#3056—74no—
224#3007—72no—
225#3004—72no—
226C2×#407—71no—
227C24×C7—24no—
228C24×C7—42no—
229C24×C7—42no—
230C24×C7C2×D411yescharacteristic
231C24×C7C2×D411yescharacteristic
232C24×C7C2×D411yescharacteristic
233C24×C7C2×D411yescharacteristic
234C24×C7C2×D411yescharacteristic
235C24×C7C2×D411yescharacteristic
236C24×C7C2×D411yescharacteristic
237C23×D7—21no—
238C2×C7×Q8—22no—
239C2×C7×Q8—22no—
240C2×C7×Q8—22no—
241C2×C7×Q8—28no—
242C2×C7×Q8—44no—
243C2×C7×Q8—44no—
244C2×C7×Q8—44no—
245C2×C7×Q8—44no—
246C2×C7×Q8—44no—
247C2×C7×Q8C2414yes—
248C22×C4×C7—24no—
249C22×C4×C7—24no—
250C22×C4×C7—24no—
251C22×C4×C7—22no—
252C22×C4×C7—22no—
253C22×C4×C7—22no—
254C22×C4×C7—22no—
255C22×C4×C7—22no—
256C22×C4×C7—22no—
257C22×C4×C7—42no—
258C22×C4×C7—42no—
259C22×C4×C7—42no—
260C22×C4×C7—42no—
261C22×C4×C7—42no—
262C22×C4×C7—42no—
263C22×C4×C7—42no—
264C22×C4×C7—42no—
265C22×C4×C7—42no—
266C22×C4×C7—42no—
267C22×C4×C7—42no—
268C22×C4×C7—44no—
269C22×C4×C7—44no—
270C22×C4×C7C2×D411yescharacteristic
271C22×C4×C7C2×D411yescharacteristic
272C22×C4×C7C2×D411yescharacteristic
273C22×C4×C7C2×D411yescharacteristic
274C22×C4×C7C2×D411yescharacteristic
275C22×C4×C7C2×D411yescharacteristic
276C22×C4×C7C2×D411yescharacteristic
277C22×C4×C7C2×D411yescharacteristic
278C22×C4×C7C2×D411yescharacteristic
279C22×C4×C7C2×D411yescharacteristic
280C22×C4×C7C2×D411yescharacteristic
281C22×C4×C7C2×D411yescharacteristic
282C22×C4×C7C2×D411yescharacteristic
283C22×C4×C7C2×D411yescharacteristic
284C22×C4×C7C2×D411yescharacteristic
285C22×C4×C7C2×D411yescharacteristic
286C22×C4×C7C2×D411yescharacteristic
287C22×C4×C7C2×D411yescharacteristic
288C22×C4×C7C2×D411yescharacteristic
289C22×C4×C7C2×D411yescharacteristic
290C22×C4×C7C2×D411yescharacteristic
291C22×C4×C7C2411yescharacteristic
292C22×C4×C7C2411yescharacteristic
293C22×C4×C7C2411yescharacteristic
294C22×C4×C7C2411yescharacteristic
295C22×C4×C7C2411yescharacteristic
296C22×C4×C7C2411yescharacteristic
297C22×C4×C7C2411yescharacteristic
298C2×C22⋊D7—22no—
299C2×C22⋊D7—22no—
300C2×C22⋊D7—22no—
301C2×C22⋊D7—22no—
302C2×C22⋊D7—22no—
303C2×C22⋊D7—22no—
304C2×C22⋊D7—44no—
305C2×C22⋊D7—44no—
306C2×C22⋊D7—44no—
307C22×Dic7—21no—
308C22×Dic7—21no—
309C22×Dic7—21no—
310#1157—28no—
311#1157—44no—
312#1157—44no—
313#1157—44no—
314C2×D28—21no—
315C2×D28—42no—
316C2×D28C2412yes—
317C2×C4×D7—22no—
318C2×C4×D7—22no—
319C2×C4×D7—44no—
320C2×Dic14—21no—
321C2×Dic14—42no—
322C2×Dic14C2412yes—
323C7×C4⋊C4—24no—
324C7×C4⋊C4—24no—
325C7×C4⋊C4—24no—
326C7×C4⋊C4—24no—
327C7×C4⋊C4—22no—
328C7×C4⋊C4—22no—
329C7×C4⋊C4—22no—
330C7×C4⋊C4C2414yes—
331C7×C22⋊C4—24no—
332C7×C22⋊C4—24no—
333C7×C22⋊C4—24no—
334C7×C22⋊C4—24no—
335C22⋊Dic7—22no—
336C22⋊Dic7—22no—
337C22⋊Dic7—22no—
338C22⋊Dic7—22no—
339C22⋊Dic7—22no—
340C22⋊Dic7—22no—
341#1144—48no—
342#1143—48no—
343(C2×D7)⋊C4—22no—
344(C2×D7)⋊C4—22no—
345(C2×D7)⋊C4—22no—
346(C2×D7)⋊C4—22no—
347C4⋊Dic7—21no—
348C4⋊Dic7—21no—
349C4⋊Dic7C2412yes—
350C4⋊Dic7C2412yes—
351Dic7⋊C4—22no—
352Dic7⋊C4—22no—
353Dic7⋊C4—22no—
354Dic7⋊C4—22no—
355C4×Dic7—22no—
356C4×Dic7—22no—
357#1136—28no—
358#1136—44no—
359C2×C7⋊C8—44no—
360C2×C7⋊C8C2418yes—
361C22×#41—71no—
362C23×Q8C2×D711yescharacteristic, complemented
363C24×C4C2×D711yescharacteristic
364C2×#137—74no—
365C22×M16—72no—
366#525—72no—
367#525—72no—
368#525—72no—
369#525—72no—
370#525—141no—
371#525—141no—
372#525—141no—
373#525—141no—
374C2×#123—141no—
375C2×C22⋊Q8—21no—
376C2×C22⋊Q8—21no—
377C2×C22⋊Q8—21no—
378C2×C22⋊Q8—21no—
379C2×C22⋊Q8—21no—
380C2×C22⋊Q8—21no—
381C2×C22⋊Q8—71no—
382C2×C22⋊Q8—71no—
383C2×C22⋊Q8C2×D712yes—
384C2×C22⋊Q8C2×D712yes—
385C2×C22⋊Q8C2×D712yes—
386C2×C22⋊Q8C2×D712yescomplemented
387C2×C22⋊Q8C2×D712yescomplemented
388C2×C22⋊Q8C2×D712yescomplemented
389C2×#121—71no—
390C2×#121—71no—
391C2×#120—141no—
392C2×C4×D4—141no—
393C2×C4×D4—141no—
394C2×#117—71no—
395C22×C4⋊C4—21no—
396C22×C4⋊C4C2×D711yescharacteristic, complemented
397C22×C22⋊C4—21no—
398#485—78no—
399#484—74no—
400#484—74no—
401#483—74no—
402#483—74no—
403#481—74no—
404#480—74no—
405#470—78no—
406#468—78no—
407#467—78no—
408#465—78no—
409#452—78no—
410#451—74no—
411#451—74no—
412#451—74no—
413#450—74no—
414#448—74no—
415#448—74no—
416#428—74no—
417#419—74no—
418#417—74no—
419#407—72no—
420#407—72no—
421#407—72no—
422#407—72no—
423C2×C22⋊C8—72no—
424C2×C22⋊C8—72no—
425C23×C7—22no—
426C23×C7—22no—
427C23×C7—22no—
428C23×C7—22no—
429C23×C7—22no—
430C23×C7—22no—
431C23×C7—22no—
432C23×C7—22no—
433C23×C7—22no—
434C23×C7—22no—
435C23×C7—22no—
436C23×C7—22no—
437C23×C7—41no—
438C23×C7—41no—
439C23×C7—41no—
440C23×C7—41no—
441C23×C7—41no—
442C23×C7—41no—
443C23×C7—41no—
444C23×C7—41no—
445C23×C7—416no—
446C23×C7#13714yescomplemented
447C23×C7C22×D411yescharacteristic
448C23×C7C22×D411yescharacteristic
449C23×C7C22×D411yescharacteristic
450C23×C7C22×D411yescharacteristic
451C23×C7C22×D411yescharacteristic
452C23×C7C22×D411yescharacteristic
453C23×C7C22×D411yescharacteristic
454C22×D7—22no—
455C22×D7—42no—
456C22×D7—42no—
457C22×D7—42no—
458C7×Q8—28no—
459C7×Q8—44no—
460C7×Q8—44no—
461C7×Q8—44no—
462C2×C4×C7—22no—
463C2×C4×C7—22no—
464C2×C4×C7—22no—
465C2×C4×C7—22no—
466C2×C4×C7—22no—
467C2×C4×C7—22no—
468C2×C4×C7—22no—
469C2×C4×C7—22no—
470C2×C4×C7—22no—
471C2×C4×C7—22no—
472C2×C4×C7—22no—
473C2×C4×C7—22no—
474C2×C4×C7—22no—
475C2×C4×C7—22no—
476C2×C4×C7—22no—
477C2×C4×C7—24no—
478C2×C4×C7—24no—
479C2×C4×C7—41no—
480C2×C4×C7—41no—
481C2×C4×C7—41no—
482C2×C4×C7—41no—
483C2×C4×C7—41no—
484C2×C4×C7—41no—
485C2×C4×C7—41no—
486C2×C4×C7—41no—
487C2×C4×C7—41no—
488C2×C4×C7—41no—
489C2×C4×C7—41no—
490C2×C4×C7—41no—
491C2×C4×C7—44no—
492C2×C4×C7—44no—
493C2×C4×C7—44no—
494C2×C4×C7—44no—
495C2×C4×C7—44no—
496C2×C4×C7—44no—
497C2×C4×C7C22×D411yescharacteristic
498C2×C4×C7C22×D411yescharacteristic
499C2×C4×C7C22×D411yescharacteristic
500C2×C4×C7C22×D411yescharacteristic
501C2×C4×C7C22×D411yescharacteristic
502C2×C4×C7C22×D411yescharacteristic
503C2×C4×C7C22×D411yescharacteristic
504C2×C4×C7H(5,𝔽2)14yes—
505C2×C4×C7C2511yescharacteristic
506C22⋊D7—44no—
507C22⋊D7—44no—
508C22⋊D7—44no—
509C22⋊D7—44no—
510C22⋊D7—44no—
511C22⋊D7—44no—
512C2×Dic7—22no—
513C2×Dic7—22no—
514C2×Dic7—22no—
515C2×Dic7—42no—
516C2×Dic7—42no—
517C2×Dic7—42no—
518D28—24no—
519D28—42no—
520C4×D7—44no—
521C4×D7—44no—
522Dic14—24no—
523Dic14—42no—
524C7⋊C8—28no—
525C25C22⋊D711yescharacteristic
526C2×#41—72no—
527C2×#41—72no—
528C2×#41—141no—
529C2×#41—141no—
530C2×#41—284no—
531C22×Q8—21no—
532C22×Q8—21no—
533C22×Q8—21no—
534C22×Q8—44no—
535C22×Q8—71no—
536C22×Q8C22×D712yes—
537C22×Q8C22×D712yes—
538C22×Q8C22×D712yes—
539C22×D4—71no—
540C22×D4—141no—
541C22×D4—141no—
542C22×D4—141no—
543C23×C4—21no—
544C23×C4—21no—
545C23×C4—44no—
546C23×C4—141no—
547C23×C4C22⋊D711yescharacteristic
548C23×C4C22⋊D711yescharacteristic
549C23×C4C22⋊D711yescharacteristic
550C23×C4C22⋊D711yescharacteristic
551C23×C4C22⋊D711yescharacteristic
552C23×C4C22⋊D711yescharacteristic
553C23×C4C22⋊D711yescharacteristic
554C23×C4C22×D711yescharacteristic
555C23×C4C22×D711yescharacteristic
556C23×C4C22×D711yescharacteristic
557C23×C4C22×D711yescharacteristic
558C23×C4C22×D711yescharacteristic
559C23×C4C22×D711yescharacteristic
560C23×C4C22×D711yescharacteristic
561#137—288no—
562C2×Q16—78no—
563C2×SD16—78no—
564C2×M16—74no—
565C2×M16—74no—
566C2×M16—284no—
567C22×C8—74no—
568#123—142no—
569#123—142no—
570#123—142no—
571#123—142no—
572C22⋊Q8—22no—
573C22⋊Q8—22no—
574C22⋊Q8—22no—
575C22⋊Q8—22no—
576C22⋊Q8—22no—
577C22⋊Q8—22no—
578C22⋊Q8—22no—
579C22⋊Q8—22no—
580C22⋊Q8—22no—
581C22⋊Q8—22no—
582C22⋊Q8—22no—
583C22⋊Q8—22no—
584C22⋊Q8—72no—
585C22⋊Q8—72no—
586C22⋊Q8—72no—
587C22⋊Q8—72no—
588C22⋊Q8—141no—
589C22⋊Q8—141no—
590C22⋊Q8—141no—
591C22⋊Q8—141no—
592C22⋊Q8C22×D714yes—
593C22⋊Q8C22×D714yes—
594C22⋊Q8C22×D714yes—
595C22⋊Q8C22×D714yes—
596#121—72no—
597#121—72no—
598#121—72no—
599#121—72no—
600#121—141no—
601#121—141no—
602#121—141no—
603#121—141no—
604#120—142no—
605#120—142no—
606#120—142no—
607#120—142no—
608C4×D4—142no—
609C4×D4—142no—
610C4×D4—142no—
611C4×D4—142no—
612C4×D4—142no—
613C4×D4—142no—
614C4×D4—142no—
615C4×D4—142no—
616#117—72no—
617#117—72no—
618#117—141no—
619#117—141no—
620C2×C4⋊C4—22no—
621C2×C4⋊C4—22no—
622C2×C4⋊C4—22no—
623C2×C4⋊C4—22no—
624C2×C4⋊C4—22no—
625C2×C4⋊C4—22no—
626C2×C4⋊C4—21no—
627C2×C4⋊C4—21no—
628C2×C4⋊C4—21no—
629C2×C4⋊C4—71no—
630C2×C4⋊C4—71no—
631C2×C4⋊C4—141no—
632C2×C4⋊C4—141no—
633C2×C4⋊C4C22×D712yes—
634C2×C4⋊C4C22×D712yes—
635C2×C4⋊C4C22×D712yes—
636C2×C22⋊C4—22no—
637C2×C22⋊C4—22no—
638C2×C22⋊C4—22no—
639C2×C22⋊C4—22no—
640C2×C22⋊C4—22no—
641C2×C22⋊C4—22no—
642C2×C22⋊C4—141no—
643C2×C22⋊C4—141no—
644C2×C22⋊C4—141no—
645C2×C22⋊C4—141no—
646C2×C22⋊C4—141no—
647C2×C42—141no—
648#107—78no—
649#106—78no—
650#103—78no—
651#103—78no—
652#103—78no—
653#102—78no—
654C22⋊C8—74no—
655C22⋊C8—74no—
656C22⋊C8—74no—
657C22⋊C8—74no—
658C22×C7—28no—
659C22×C7—21no—
660C22×C7—21no—
661C22×C7—21no—
662C22×C7—21no—
663C22×C7—21no—
664C22×C7—21no—
665C22×C7—21no—
666C22×C7—21no—
667C22×C7—21no—
668C22×C7—21no—
669C22×C7—21no—
670C22×C7—21no—
671C22×C7—21no—
672C22×C7—21no—
673C22×C7—21no—
674C22×C7—21no—
675C22×C7—44no—
676C22×C7—44no—
677C22×C7—44no—
678C22×C7—44no—
679C22×C7—44no—
680C22×C7—44no—
681C22×C7#53412yes—
682C22×C7C2×#13712yes—
683C22×C7C2×#13712yes—
684C22×C7C2×#13712yes—
685C22×C7#57512yes—
686C22×C7C23×D411yescharacteristic
687C2×D7—42no—
688C2×D7—42no—
689C2×D7—42no—
690C2×D7—84no—
691C4×C7—21no—
692C4×C7—21no—
693C4×C7—21no—
694C4×C7—21no—
695C4×C7—21no—
696C4×C7—21no—
697C4×C7—44no—
698C4×C7—44no—
699C4×C7#53412yes—
700C4×C7C2×H(5,𝔽2)12yes—
701Dic7—42no—
702Dic7—42no—
703Dic7—42no—
704C24—24no—
705C24—42no—
706C24—42no—
707C24—141no—
708C24C2×C22⋊D711yescharacteristic
709C24C2×C22⋊D711yescharacteristic
710C24C2×C22⋊D711yescharacteristic
711C24C2×C22⋊D711yescharacteristic
712C24C2×C22⋊D711yescharacteristic
713C24C2×C22⋊D711yescharacteristic
714C24C2×C22⋊D711yescharacteristic
715#41—148no—
716#41—284no—
717#41—284no—
718#41—284no—
719C2×Q8—22no—
720C2×Q8—22no—
721C2×Q8—22no—
722C2×Q8—28no—
723C2×Q8—44no—
724C2×Q8—44no—
725C2×Q8—44no—
726C2×Q8—44no—
727C2×Q8—44no—
728C2×Q8—72no—
729C2×Q8—141no—
730C2×Q8—282no—
731C2×Q8C23×D714yes—
732C2×D4—72no—
733C2×D4—142no—
734C2×D4—142no—
735C2×D4—142no—
736C2×D4—142no—
737C2×D4—142no—
738C2×D4—142no—
739C2×D4—141no—
740C2×D4—282no—
741C2×D4—284no—
742C2×D4—284no—
743C2×D4—284no—
744C22×C4—24no—
745C22×C4—24no—
746C22×C4—24no—
747C22×C4—22no—
748C22×C4—22no—
749C22×C4—22no—
750C22×C4—22no—
751C22×C4—22no—
752C22×C4—22no—
753C22×C4—42no—
754C22×C4—42no—
755C22×C4—42no—
756C22×C4—42no—
757C22×C4—42no—
758C22×C4—42no—
759C22×C4—42no—
760C22×C4—42no—
761C22×C4—42no—
762C22×C4—42no—
763C22×C4—42no—
764C22×C4—44no—
765C22×C4—44no—
766C22×C4—141no—
767C22×C4—141no—
768C22×C4—141no—
769C22×C4—142no—
770C22×C4—142no—
771C22×C4—284no—
772C22×C4C2×C22⋊D711yescharacteristic
773C22×C4C2×C22⋊D711yescharacteristic
774C22×C4C2×C22⋊D711yescharacteristic
775C22×C4C2×C22⋊D711yescharacteristic
776C22×C4C2×C22⋊D711yescharacteristic
777C22×C4C2×C22⋊D711yescharacteristic
778C22×C4C2×C22⋊D711yescharacteristic
779C22×C4C2×C22⋊D711yescharacteristic
780C22×C4C2×C22⋊D711yescharacteristic
781C22×C4C2×C22⋊D711yescharacteristic
782C22×C4C2×C22⋊D711yescharacteristic
783C22×C4C2×C22⋊D711yescharacteristic
784C22×C4C2×C22⋊D711yescharacteristic
785C22×C4C2×C22⋊D711yescharacteristic
786C22×C4C2×C22⋊D711yescharacteristic
787C22×C4C2×C22⋊D711yescharacteristic
788C22×C4C2×C22⋊D711yescharacteristic
789C22×C4C2×C22⋊D711yescharacteristic
790C22×C4C2×C22⋊D711yescharacteristic
791C22×C4C2×C22⋊D711yescharacteristic
792C22×C4C2×C22⋊D711yescharacteristic
793C22×C4C23×D711yescharacteristic
794C22×C4C23×D711yescharacteristic
795C22×C4C23×D711yescharacteristic
796C22×C4C23×D711yescharacteristic
797C22×C4C23×D711yescharacteristic
798C22×C4C23×D711yescharacteristic
799C22×C4C23×D711yescharacteristic
800Q16—288no—
801SD16—288no—
802M16—148no—
803M16—284no—
804C2×C8—78no—
805C2×C8—284no—
806C4⋊C4—24no—
807C4⋊C4—24no—
808C4⋊C4—24no—
809C4⋊C4—24no—
810C4⋊C4—22no—
811C4⋊C4—22no—
812C4⋊C4—22no—
813C4⋊C4—72no—
814C4⋊C4—72no—
815C4⋊C4—142no—
816C4⋊C4—142no—
817C4⋊C4—142no—
818C4⋊C4—142no—
819C4⋊C4—141no—
820C4⋊C4—141no—
821C4⋊C4C23×D714yes—
822C22⋊C4—24no—
823C22⋊C4—24no—
824C22⋊C4—24no—
825C22⋊C4—24no—
826C22⋊C4—142no—
827C22⋊C4—142no—
828C22⋊C4—142no—
829C22⋊C4—142no—
830C22⋊C4—142no—
831C22⋊C4—142no—
832C22⋊C4—142no—
833C22⋊C4—142no—
834C22⋊C4—142no—
835C22⋊C4—142no—
836C42—142no—
837C42—142no—
838C2×C7—22no—
839C2×C7—22no—
840C2×C7—22no—
841C2×C7—22no—
842C2×C7—22no—
843C2×C7—41no—
844C2×C7—41no—
845C2×C7C2×#53411yescharacteristic
846C2×C7C22×#13711yescharacteristic
847C2×C7C2×#57511yescharacteristic
848D7—82no—
849C23—22no—
850C23—22no—
851C23—22no—
852C23—22no—
853C23—22no—
854C23—22no—
855C23—22no—
856C23—22no—
857C23—22no—
858C23—22no—
859C23—22no—
860C23—22no—
861C23—41no—
862C23—41no—
863C23—41no—
864C23—41no—
865C23—41no—
866C23—41no—
867C23—41no—
868C23—41no—
869C23—416no—
870C23—142no—
871C23—282no—
872C23—282no—
873C23—282no—
874C23#650514yescomplemented
875C23C22×C22⋊D711yescharacteristic
876C23C22×C22⋊D711yescharacteristic
877C23C22×C22⋊D711yescharacteristic
878C23C22×C22⋊D711yescharacteristic
879C23C22×C22⋊D711yescharacteristic
880C23C22×C22⋊D711yescharacteristic
881C23C22×C22⋊D711yescharacteristic
882Q8—28no—
883Q8—44no—
884Q8—44no—
885Q8—44no—
886Q8—144no—
887Q8—282no—
888D4—144no—
889D4—282no—
890D4—284no—
891D4—284no—
892D4—284no—
893D4—284no—
894D4—284no—
895D4—284no—
896C2×C4—22no—
897C2×C4—22no—
898C2×C4—22no—
899C2×C4—22no—
900C2×C4—22no—
901C2×C4—22no—
902C2×C4—22no—
903C2×C4—22no—
904C2×C4—22no—
905C2×C4—22no—
906C2×C4—22no—
907C2×C4—22no—
908C2×C4—22no—
909C2×C4—22no—
910C2×C4—22no—
911C2×C4—24no—
912C2×C4—24no—
913C2×C4—41no—
914C2×C4—41no—
915C2×C4—41no—
916C2×C4—41no—
917C2×C4—41no—
918C2×C4—41no—
919C2×C4—41no—
920C2×C4—41no—
921C2×C4—41no—
922C2×C4—41no—
923C2×C4—41no—
924C2×C4—41no—
925C2×C4—44no—
926C2×C4—44no—
927C2×C4—44no—
928C2×C4—44no—
929C2×C4—44no—
930C2×C4—44no—
931C2×C4—142no—
932C2×C4—142no—
933C2×C4—142no—
934C2×C4—284no—
935C2×C4—282no—
936C2×C4—282no—
937C2×C4—282no—
938C2×C4—284no—
939C2×C4#654814yes—
940C2×C4C22×C22⋊D711yescharacteristic
941C2×C4C22×C22⋊D711yescharacteristic
942C2×C4C22×C22⋊D711yescharacteristic
943C2×C4C22×C22⋊D711yescharacteristic
944C2×C4C22×C22⋊D711yescharacteristic
945C2×C4C22×C22⋊D711yescharacteristic
946C2×C4C22×C22⋊D711yescharacteristic
947C2×C4C24×D711yescharacteristic
948C8—148no—
949C7#6075111yescharacteristic, complemented, Sylow
950C22—28no—
951C22—21no—
952C22—21no—
953C22—21no—
954C22—21no—
955C22—21no—
956C22—21no—
957C22—21no—
958C22—21no—
959C22—21no—
960C22—21no—
961C22—21no—
962C22—21no—
963C22—21no—
964C22—21no—
965C22—21no—
966C22—21no—
967C22—44no—
968C22—44no—
969C22—44no—
970C22—44no—
971C22—44no—
972C22—44no—
973C22—282no—
974C22—282no—
975C22—282no—
976C22—564no—
977C22#9049512yes—
978C22C2×#650512yes—
979C22C2×#650512yes—
980C22C2×#650512yes—
981C22#9051312yes—
982C22C23×C22⋊D711yescharacteristic
983C4—21no—
984C4—21no—
985C4—21no—
986C4—21no—
987C4—21no—
988C4—21no—
989C4—44no—
990C4—44no—
991C4—282no—
992C4—282no—
993C4—282no—
994C4#9049512yes—
995C4C2×#654812yes—
996C2—22no—
997C2—22no—
998C2—22no—
999C2—22no—
1000C2—22no—
1001C2—41no—
1002C2—41no—
1003C2—562no—
1004C2C2×#9049511yescharacteristic
1005C2C22×#650511yescharacteristic
1006C2C2×#9051311yescharacteristic
subgroupG/H
centerC22C23×C22⋊D7
commutator, cosocleC2×C4×C7C25
FrattiniC2×C4C24×D7
FittingC22×C7×C22⋊Q8C2
socleC22×C7C23×D4
prime radicalC2×#90482C2
hypercenterC22×C22⋊Q8D7
hypocenterC7#60751
LCSG ▷ C2×C4×C7 ▷ C2×C7 ▷ C7
UCSC1 ◁ C22 ◁ C24×C4 ◁ C22×C22⋊Q8

Complements

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

NH ≅ G/Ntype
1. C22×C7×C22⋊Q8C2semidirect
3. #11741504C2semidirect
4. C2×#89979C2semidirect
5. #11740187C2semidirect
6. #11740186C2semidirect
7. #11740184C2semidirect
8. #11740183C2semidirect
9. #11740182C2semidirect
10. #11740181C2semidirect
11. #11740180C2semidirect
12. #11740177C2semidirect
13. #11740172C2semidirect
14. #11739584C2semidirect
15. C23×C7×Q8C22semidirect
27. C2×C7×C22⋊Q8C22semidirect
28. C2×C7×C22⋊Q8C22semidirect
29. C2×C7×C22⋊Q8C22semidirect
31. C22×C7×C4⋊C4C22semidirect
34. C2×#6505C22semidirect
51. C22×#1136C22semidirect
52. #90000C22semidirect
53. #90000C22semidirect
54. #89999C22semidirect
55. #89999C22semidirect
56. #89997C22semidirect
59. #89979C22semidirect
60. #89979C22semidirect
62. C2×C22⋊(C7⋊C8)C22semidirect
63. #89824C22semidirect
64. #89823C22semidirect
65. #89822C22semidirect
66. #89821C22semidirect
67. #89820C22semidirect
68. #89819C22semidirect
69. #89818C22semidirect
70. #89817C22semidirect
71. #89816C22semidirect
72. #89815C22semidirect
73. #89743C22semidirect
74. #89742C22semidirect
75. #89740C22semidirect
76. #89739C22semidirect
77. #89738C22semidirect
78. #89736C22semidirect
157. C2×#1144C23semidirect
159. C2×#1143C23semidirect
203. #6409C23semidirect
204. #6409C23semidirect
209. #6384C23semidirect
210. #6383C23semidirect
211. #6382C23semidirect
212. #6381C23semidirect
214. C22×C22⋊Q8D7semidirect
362. C23×Q8C2×D7semidirect
386. C2×C22⋊Q8C2×D7semidirect
387. C2×C22⋊Q8C2×D7semidirect
388. C2×C22⋊Q8C2×D7semidirect
396. C22×C4⋊C4C2×D7semidirect
446. C23×C7#137semidirect
874. C23#6505semidirect
949. C7#60751semidirect

Maximal subgroups

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

subgroupindex
C22×C7×C22⋊Q82
C2×#904822
#117415042
C2×#899792
#117401872
#117401862
#117401842
#117401832
#117401822
#117401812
#117401802
#117401772
#117401722
#117395842
#607517