Finite Group Databasebeta

← #14222183

Subgroups — #14222183

Order 1792.

2570 conjugacy classes of subgroups.

The subgroup lattice has 904 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C4×C7×D4C211yesmaximal, characteristic, complemented
2#11742748C211yesmaximal, characteristic, complemented
3#11741483C212yesmaximal, complemented
4#11739760C212yesmaximal, complemented
5#11739759C212yesmaximal, complemented
6#11739756C214yesmaximal, complemented
7#11739755C212yesmaximal, complemented
8#11739754C214yesmaximal, complemented
9#11739753C212yesmaximal, complemented
10#11739752C212yesmaximal, complemented
11#11739741C212yesmaximal, complemented
12C4×#6495C214yesmaximal, complemented
13#11739584C212yesmaximal, complemented
14#11739494C211yesmaximal, characteristic, complemented
15C23×C7×D4C2211yescharacteristic
16C24×C4×C7—21no—
17C2×C4×C7×D4—21no—
18C2×C4×C7×D4—21no—
19C2×C4×C7×D4—21no—
20C2×C4×C7×D4—21no—
21C2×C4×C7×D4—21no—
22C2×C4×C7×D4—21no—
23C2×C4×C7×D4C2212yes—
24C2×C4×C7×D4C2212yes—
25C2×C4×C7×D4C2212yes—
26C2×C4×C7×D4C2212yes—
27C2×C4×C7×D4C2212yes—
28C2×C4×C7×D4C2212yes—
29C22×C7×C4⋊C4C2211yescharacteristic
30C22×C7×C22⋊C4—21no—
31C22×C42×C7C2211yescharacteristic
32C2×#6495C2214yes—
33#90482—21no—
34#90482—21no—
35#90482C2212yes—
36#90170—21no—
37#90170—21no—
38#90170—21no—
39#90170—21no—
40#90170C2212yescomplemented
41#90170C2212yescomplemented
42#90168C2211yescharacteristic, complemented
43#90168C2211yescharacteristic, complemented
44#90168C2211yescharacteristic, complemented
45C4×#1157—21no—
46C4×#1157—21no—
47C4×#1157C2212yescomplemented
48#90161C2211yescharacteristic, complemented
49#90161C2211yescharacteristic, complemented
50#90161C2211yescharacteristic, complemented
51#89990C2214yes—
52#89990C2214yes—
53#89989C2214yes—
54#89989C2214yes—
55#89987C2214yes—
56#89979C2212yes—
57#89791C2214yescomplemented
58#89790C2218yescomplemented
59C4×#1142C2218yescomplemented
60#89788C2218yescomplemented
61#89787C2214yescomplemented
62#89786C2218yescomplemented
63C4×#1141C2218yescomplemented
64#89781C2218yescomplemented
65#89780C2214yescomplemented
66#89779C2214yescomplemented
67#89743C2214yescomplemented
68#89742C2214yescomplemented
69#89740C2214yescomplemented
70#89739C2214yescomplemented
71#89738C2214yescomplemented
72#89736C2214yescomplemented
73#89698C2212yescomplemented
74#89698C2212yescomplemented
75#89697C2212yescomplemented
76#89697C2212yescomplemented
77#89696C2212yescomplemented
78C4×#1136C2212yescomplemented
79#60558—71nomaximal, Sylow
80C25×C7—21no—
81C22×C7×D4—28no—
82C22×C7×D4—21no—
83C22×C7×D4—21no—
84C22×C7×D4—21no—
85C22×C7×D4C2312yes—
86C22×C7×D4C2312yes—
87C22×C7×D4C2312yes—
88C23×C4×C7—21no—
89C23×C4×C7—22no—
90C23×C4×C7—22no—
91C23×C4×C7—22no—
92C23×C4×C7—22no—
93C23×C4×C7—22no—
94C23×C4×C7—22no—
95C23×C4×C7—48no—
96C23×C4×C7D411yescharacteristic
97C23×C4×C7D411yescharacteristic
98C23×C4×C7C2311yescharacteristic
99C2×#1157—21no—
100C2×#1157—21no—
101C2×#1157C2312yes—
102C4×C7×D4—22no—
103C4×C7×D4—22no—
104C4×C7×D4—22no—
105C4×C7×D4—22no—
106C4×C7×D4—22no—
107C4×C7×D4—22no—
108C4×C7×D4—22no—
109C4×C7×D4—22no—
110C4×C7×D4—22no—
111C4×C7×D4—22no—
112C4×C7×D4—22no—
113C4×C7×D4—22no—
114C4×C7×D4C2314yes—
115C4×C7×D4C2314yes—
116C4×C7×D4C2314yes—
117C4×C7×D4C2314yes—
118C2×C7×C4⋊C4—21no—
119C2×C7×C4⋊C4—21no—
120C2×C7×C4⋊C4—21no—
121C2×C7×C4⋊C4C2312yes—
122C2×C7×C4⋊C4C2312yes—
123C2×C7×C4⋊C4C2312yes—
124C2×C7×C22⋊C4—22no—
125C2×C7×C22⋊C4—22no—
126C2×C7×C22⋊C4—22no—
127C2×C7×C22⋊C4—22no—
128C2×C7×C22⋊C4—22no—
129C2×C7×C22⋊C4—22no—
130C2×C42×C7D411yescharacteristic
131C2×C42×C7D411yescharacteristic
132C2×C42×C7D411yescharacteristic
133C2×C42×C7D411yescharacteristic
134C2×C42×C7D411yescharacteristic
135C2×C42×C7D411yescharacteristic
136C2×C42×C7C2311yescharacteristic
137C2×C42×C7C2311yescharacteristic
138C2×C42×C7C2311yescharacteristic
139C2×C42×C7C2311yescharacteristic
140C2×C42×C7C2311yescharacteristic
141C2×C42×C7C2311yescharacteristic
142#6516—22no—
143C2×#1142C2318yes—
144#6495—216no—
145C2×#1141C2318yes—
146#6493—21no—
147#6493—21no—
148#6493—21no—
149#6493—21no—
150#6493C2312yes—
151#6493C2312yes—
152#6492—22no—
153#6492—22no—
154#6492—22no—
155C4×C22⋊D7—22no—
156C4×C22⋊D7—22no—
157C4×C22⋊D7—22no—
158C4×C22⋊D7—22no—
159C4×C22⋊D7—22no—
160C4×C22⋊D7—22no—
161#6489—21no—
162#6489—21no—
163#6489C2312yes—
164#6487—21no—
165#6487—21no—
166#6487—21no—
167#6487—21no—
168#6487C2312yes—
169#6487C2312yes—
170C2×#1136C2314yes—
171#6439—22no—
172#6439—22no—
173#6438—21no—
174#6438—21no—
175#6438C2312yescomplemented
176#6437C2311yescharacteristic, complemented
177C4×D28—21no—
178C4×D28—21no—
179C4×D28—21no—
180C4×D28—21no—
181C4×D28C2312yescomplemented
182C4×D28C2312yescomplemented
183#6435—22no—
184#6435—22no—
185#6435—22no—
186C42×D7—22no—
187#6433—21no—
188#6433—21no—
189#6433C2312yescomplemented
190#6432C2311yescharacteristic, complemented
191#6432C2311yescharacteristic, complemented
192#6432C2311yescharacteristic, complemented
193C4×Dic14—21no—
194C4×Dic14—21no—
195C4×Dic14—21no—
196C4×Dic14—21no—
197C4×Dic14C2312yescomplemented
198C4×Dic14C2312yescomplemented
199#6406C2318yes—
200#6406C2318yes—
201C22⋊(C7⋊C8)C2314yes—
202C22⋊(C7⋊C8)C2314yes—
203#6384C2318yescomplemented
204#6383C2318yescomplemented
205#6382C2318yescomplemented
206#6381C2318yescomplemented
207C4⋊(C7⋊C8)C2314yescomplemented
208C4⋊(C7⋊C8)C2314yescomplemented
209#6377C2314yescomplemented
210C4×C7⋊C8C2314yescomplemented
211#3444—71no—
212C22×C4×D4D711yescharacteristic, complemented
213#3114—74no—
214#3110—72no—
215#3109—72no—
216#3105—74no—
217#3101—72no—
218#3100—72no—
219#3092—72no—
220#3077—72no—
221#3036—72no—
222#3003—72no—
223C4×AGL(1,ℤ/8)—74no—
224#2920—71no—
225C24×C7—28no—
226C24×C7—22no—
227C24×C7—22no—
228C24×C7—22no—
229C24×C7—44no—
230C24×C7—44no—
231C24×C7C2×D411yescharacteristic
232C2×C7×D4—28no—
233C2×C7×D4—28no—
234C2×C7×D4—28no—
235C2×C7×D4—28no—
236C2×C7×D4—28no—
237C2×C7×D4—22no—
238C2×C7×D4—22no—
239C2×C7×D4—22no—
240C2×C7×D4—24no—
241C2×C7×D4#4118yescomplemented
242C2×C7×D4C2414yes—
243C22×C4×C7—24no—
244C22×C4×C7—24no—
245C22×C4×C7—22no—
246C22×C4×C7—22no—
247C22×C4×C7—22no—
248C22×C4×C7—24no—
249C22×C4×C7—24no—
250C22×C4×C7—24no—
251C22×C4×C7—24no—
252C22×C4×C7—42no—
253C22×C4×C7—48no—
254C22×C4×C7—48no—
255C22×C4×C7—48no—
256C22×C4×C7—48no—
257C22×C4×C7—48no—
258C22×C4×C7—44no—
259C22×C4×C7—48no—
260C22×C4×C7C2×D411yescharacteristic
261C22×C4×C7C2×D411yescharacteristic
262C22×C4×C7C2×D411yescharacteristic
263C22×C4×C7C2×D411yescharacteristic
264C22×C4×C7C2×D411yescharacteristic
265C22×C4×C7C2×D411yescharacteristic
266C22×C4×C7C2×D411yescharacteristic
267C22×C4×C7C2×D411yescharacteristic
268C22×C4×C7C2×D411yescharacteristic
269C22×C4×C7C2×D411yescharacteristic
270C22×C4×C7C2×D411yescharacteristic
271C22×C4×C7C2×D411yescharacteristic
272C22×C4×C7C2×D411yescharacteristic
273C22×C4×C7C2×D411yescharacteristic
274C22×C4×C7C2×D411yescharacteristic
275C22×C4×C7C2411yescharacteristic
276C22×C4×C7C2411yescharacteristic
277C22×C4×C7C2411yescharacteristic
278C2×C22⋊D7—22no—
279C2×C22⋊D7—22no—
280C2×C22⋊D7—22no—
281#1157—28no—
282#1157—44no—
283#1157—44no—
284C2×D28—21no—
285C2×D28—21no—
286C2×D28C2412yes—
287C2×C4×D7—22no—
288C2×C4×D7—22no—
289C2×C4×D7—22no—
290C2×Dic14—21no—
291C2×Dic14—21no—
292C2×Dic14C2412yes—
293C7×C4⋊C4—22no—
294C7×C4⋊C4—22no—
295C7×C4⋊C4—22no—
296C7×C4⋊C4C2414yes—
297C7×C22⋊C4—24no—
298C7×C22⋊C4—24no—
299C7×C22⋊C4—24no—
300C7×C22⋊C4—24no—
301C42×C7C2×D411yescharacteristic
302C42×C7C2×D411yescharacteristic
303C42×C7C2×D411yescharacteristic
304C42×C7C2×D411yescharacteristic
305C42×C7C2×D411yescharacteristic
306C42×C7C2×D411yescharacteristic
307C42×C7C2×D411yescharacteristic
308C42×C7C2×D411yescharacteristic
309C42×C7C2×D411yescharacteristic
310C42×C7C2×D411yescharacteristic
311C42×C7C2×D411yescharacteristic
312C42×C7C2×D411yescharacteristic
313C42×C7C2411yescharacteristic
314C42×C7C2411yescharacteristic
315C42×C7C2411yescharacteristic
316C42×C7C2411yescharacteristic
317C22⋊Dic7—22no—
318C22⋊Dic7—22no—
319C22⋊Dic7—22no—
320#1142—216no—
321#1141—216no—
322(C2×D7)⋊C4—22no—
323(C2×D7)⋊C4—22no—
324(C2×D7)⋊C4—22no—
325(C2×D7)⋊C4—22no—
326(C2×D7)⋊C4—22no—
327(C2×D7)⋊C4—22no—
328C4⋊Dic7—21no—
329C4⋊Dic7—21no—
330C4⋊Dic7—21no—
331C4⋊Dic7—21no—
332C4⋊Dic7C2412yes—
333C4⋊Dic7C2412yes—
334Dic7⋊C4—22no—
335Dic7⋊C4—22no—
336Dic7⋊C4—22no—
337Dic7⋊C4—22no—
338Dic7⋊C4—22no—
339Dic7⋊C4—22no—
340C4×Dic7—22no—
341C4×Dic7—22no—
342C4×Dic7—22no—
343#1136—28no—
344C2×C7⋊C8C2418yes—
345C23×D4C2×D711yescharacteristic
346C24×C4—21no—
347C2×AGL(1,ℤ/8)—74no—
348#533—71no—
349#533—71no—
350#533—71no—
351#532—71no—
352#532—71no—
353#532—71no—
354#529—72no—
355#529—72no—
356#529—141no—
357#529—141no—
358#529—141no—
359#529—141no—
360#525—72no—
361#525—141no—
362#525—141no—
363C4×#41—72no—
364C4×#41—141no—
365C4×#41—141no—
366C2×C4×D4—21no—
367C2×C4×D4—21no—
368C2×C4×D4—21no—
369C2×C4×D4—21no—
370C2×C4×D4—21no—
371C2×C4×D4—21no—
372C2×C4×D4C2×D712yes—
373C2×C4×D4C2×D712yes—
374C2×C4×D4C2×D712yes—
375C2×C4×D4C2×D712yes—
376C2×C4×D4C2×D712yes—
377C2×C4×D4C2×D712yes—
378C22×C4⋊C4C2×D711yescharacteristic
379C22×C22⋊C4—21no—
380C22×C42C2×D711yescharacteristic
381#484—74no—
382#483—74no—
383#481—74no—
384#480—74no—
385#478—78no—
386#476—74no—
387#474—74no—
388#463—78no—
389#461—74no—
390#459—74no—
391#450—74no—
392#450—74no—
393#447—74no—
394#447—74no—
395#442—78no—
396#440—78no—
397C4×SD16—78no—
398C4×D8—78no—
399#432—72no—
400#432—72no—
401#431—72no—
402#431—72no—
403#428—74no—
404#423—72no—
405#418—74no—
406#417—74no—
407#407—72no—
408C4×M16—72no—
409C23×C7—22no—
410C23×C7—22no—
411C23×C7—22no—
412C23×C7—28no—
413C23×C7—28no—
414C23×C7—28no—
415C23×C7—24no—
416C23×C7—44no—
417C23×C7—44no—
418C23×C7—432no—
419C23×C7—44no—
420C23×C7—44no—
421C23×C7—44no—
422C23×C7—44no—
423C23×C7C22×D411yescharacteristic
424C23×C7C22×D411yescharacteristic
425C23×C7C22×D411yescharacteristic
426C22×D7—22no—
427C7×D4—28no—
428C7×D4—28no—
429C7×D4—28no—
430C7×D4—24no—
431C7×D4C2×#4118yes—
432C2×C4×C7—22no—
433C2×C4×C7—22no—
434C2×C4×C7—22no—
435C2×C4×C7—22no—
436C2×C4×C7—22no—
437C2×C4×C7—22no—
438C2×C4×C7—22no—
439C2×C4×C7—22no—
440C2×C4×C7—22no—
441C2×C4×C7—22no—
442C2×C4×C7—22no—
443C2×C4×C7—22no—
444C2×C4×C7—24no—
445C2×C4×C7—41no—
446C2×C4×C7—41no—
447C2×C4×C7—41no—
448C2×C4×C7—41no—
449C2×C4×C7—48no—
450C2×C4×C7—48no—
451C2×C4×C7—44no—
452C2×C4×C7—44no—
453C2×C4×C7—44no—
454C2×C4×C7—48no—
455C2×C4×C7—48no—
456C2×C4×C7AGL(1,ℤ/8)14yescomplemented
457C2×C4×C7C22×D411yescharacteristic
458C2×C4×C7C22×D411yescharacteristic
459C2×C4×C7C22×D411yescharacteristic
460C2×C4×C7C22×D411yescharacteristic
461C2×C4×C7C22×D411yescharacteristic
462C2×C4×C7C22×D411yescharacteristic
463C2×C4×C7C22×D411yescharacteristic
464C2×C4×C7C22×D411yescharacteristic
465C2×C4×C7C22×D411yescharacteristic
466C2×C4×C7C22×D411yescharacteristic
467C2×C4×C7C22×D411yescharacteristic
468C2×C4×C7C2×#4114yes—
469C2×C4×C7C2511yescharacteristic
470C22⋊D7—44no—
471C22⋊D7—44no—
472C22⋊D7—44no—
473C2×Dic7—22no—
474C2×Dic7—22no—
475C2×Dic7—22no—
476D28—24no—
477D28—42no—
478D28—42no—
479C4×D7—44no—
480C4×D7—44no—
481C4×D7—44no—
482Dic14—24no—
483Dic14—42no—
484Dic14—42no—
485C7⋊C8—28no—
486C25—21no—
487C2×#41—72no—
488C2×#41—141no—
489C2×#41—141no—
490C22×D4—28no—
491C22×D4—21no—
492C22×D4—21no—
493C22×D4—21no—
494C22×D4C22×D712yes—
495C22×D4C22×D712yes—
496C22×D4C22×D712yes—
497C23×C4—21no—
498C23×C4—22no—
499C23×C4—22no—
500C23×C4—22no—
501C23×C4—22no—
502C23×C4—22no—
503C23×C4—22no—
504C23×C4—48no—
505C23×C4C22⋊D711yescharacteristic
506C23×C4C22⋊D711yescharacteristic
507C23×C4C22×D711yescharacteristic
508AGL(1,ℤ/8)—1416no—
509C2×SD16—78no—
510C2×D8—78no—
511C2×M16—74no—
512C4⋊Q8—71no—
513C4⋊Q8—71no—
514C4⋊Q8—71no—
515#127—71no—
516#126—142no—
517#126—142no—
518#125—72no—
519#125—141no—
520#125—141no—
521#124—72no—
522#124—141no—
523#124—141no—
524#123—142no—
525#123—142no—
526#123—142no—
527C22⋊Q8—72no—
528C22⋊Q8—72no—
529C22⋊Q8—141no—
530C22⋊Q8—141no—
531C22⋊Q8—141no—
532C22⋊Q8—141no—
533#121—72no—
534#121—72no—
535#121—141no—
536#121—141no—
537#121—141no—
538#121—141no—
539#120—142no—
540C4×Q8—72no—
541C4×Q8—72no—
542C4×Q8—141no—
543C4×Q8—141no—
544C4×Q8—141no—
545C4×Q8—141no—
546C4×D4—22no—
547C4×D4—22no—
548C4×D4—22no—
549C4×D4—22no—
550C4×D4—22no—
551C4×D4—22no—
552C4×D4—22no—
553C4×D4—22no—
554C4×D4—22no—
555C4×D4—22no—
556C4×D4—22no—
557C4×D4—22no—
558C4×D4—72no—
559C4×D4—72no—
560C4×D4—142no—
561C4×D4—142no—
562C4×D4—142no—
563C4×D4—142no—
564C4×D4—142no—
565C4×D4—142no—
566C4×D4—141no—
567C4×D4—141no—
568C4×D4—141no—
569C4×D4—141no—
570C4×D4C22×D714yes—
571C4×D4C22×D714yes—
572C4×D4C22×D714yes—
573C4×D4C22×D714yes—
574#117—72no—
575#117—141no—
576#117—141no—
577#117—142no—
578#117—142no—
579#117—142no—
580C2×C4⋊C4—21no—
581C2×C4⋊C4—21no—
582C2×C4⋊C4—21no—
583C2×C4⋊C4C22×D712yes—
584C2×C4⋊C4C22×D712yes—
585C2×C4⋊C4C22×D712yes—
586C2×C22⋊C4—22no—
587C2×C22⋊C4—22no—
588C2×C22⋊C4—22no—
589C2×C22⋊C4—22no—
590C2×C22⋊C4—22no—
591C2×C22⋊C4—22no—
592C2×C42—142no—
593C2×C42C22⋊D711yescharacteristic
594C2×C42C22⋊D711yescharacteristic
595C2×C42C22⋊D711yescharacteristic
596C2×C42C22⋊D711yescharacteristic
597C2×C42C22⋊D711yescharacteristic
598C2×C42C22⋊D711yescharacteristic
599C2×C42C22×D711yescharacteristic
600C2×C42C22×D711yescharacteristic
601C2×C42C22×D711yescharacteristic
602C2×C42C22×D711yescharacteristic
603C2×C42C22×D711yescharacteristic
604C2×C42C22×D711yescharacteristic
605#107—78no—
606#106—78no—
607C4⋊C8—74no—
608C4⋊C8—74no—
609#103—78no—
610#102—78no—
611#102—78no—
612#102—78no—
613C22⋊C8—74no—
614C22⋊C8—74no—
615#97—74no—
616C4×C8—74no—
617C22×C7—28no—
618C22×C7—21no—
619C22×C7—21no—
620C22×C7—21no—
621C22×C7—21no—
622C22×C7—21no—
623C22×C7—21no—
624C22×C7—28no—
625C22×C7—416no—
626C22×C7—416no—
627C22×C7—416no—
628C22×C7—44no—
629C22×C7—44no—
630C22×C7#52512yes—
631C22×C7C2×AGL(1,ℤ/8)12yes—
632C22×C7#57512yes—
633C22×C7C23×D411yescharacteristic
634C2×D7—42no—
635C2×D7—42no—
636C2×D7—42no—
637C4×C7—21no—
638C4×C7—21no—
639C4×C7—21no—
640C4×C7—21no—
641C4×C7—21no—
642C4×C7—21no—
643C4×C7—21no—
644C4×C7—21no—
645C4×C7—44no—
646C4×C7#52512yes—
647C4×C7C2×AGL(1,ℤ/8)12yes—
648C4×C7C2×AGL(1,ℤ/8)12yes—
649C4×C7C22×#4112yes—
650Dic7—42no—
651Dic7—42no—
652Dic7—42no—
653C24—28no—
654C24—22no—
655C24—22no—
656C24—22no—
657C24—44no—
658C24—44no—
659C24C2×C22⋊D711yescharacteristic
660#41—148no—
661#41—284no—
662#41—284no—
663C2×Q8—72no—
664C2×Q8—141no—
665C2×Q8—141no—
666C2×D4—28no—
667C2×D4—28no—
668C2×D4—28no—
669C2×D4—28no—
670C2×D4—28no—
671C2×D4—24no—
672C2×D4—22no—
673C2×D4—22no—
674C2×D4—22no—
675C2×D4—72no—
676C2×D4—142no—
677C2×D4—142no—
678C2×D4—142no—
679C2×D4—141no—
680C2×D4—141no—
681C2×D4#115718yescomplemented
682C2×D4C23×D714yes—
683C22×C4—24no—
684C22×C4—24no—
685C22×C4—22no—
686C22×C4—22no—
687C22×C4—22no—
688C22×C4—24no—
689C22×C4—24no—
690C22×C4—24no—
691C22×C4—24no—
692C22×C4—42no—
693C22×C4—48no—
694C22×C4—48no—
695C22×C4—48no—
696C22×C4—48no—
697C22×C4—48no—
698C22×C4—44no—
699C22×C4—48no—
700C22×C4—142no—
701C22×C4—142no—
702C22×C4—142no—
703C22×C4C2×C22⋊D711yescharacteristic
704C22×C4C2×C22⋊D711yescharacteristic
705C22×C4C2×C22⋊D711yescharacteristic
706C22×C4C2×C22⋊D711yescharacteristic
707C22×C4C2×C22⋊D711yescharacteristic
708C22×C4C2×C22⋊D711yescharacteristic
709C22×C4C2×C22⋊D711yescharacteristic
710C22×C4C2×C22⋊D711yescharacteristic
711C22×C4C2×C22⋊D711yescharacteristic
712C22×C4C2×C22⋊D711yescharacteristic
713C22×C4C2×C22⋊D711yescharacteristic
714C22×C4C2×C22⋊D711yescharacteristic
715C22×C4C2×C22⋊D711yescharacteristic
716C22×C4C2×C22⋊D711yescharacteristic
717C22×C4C2×C22⋊D711yescharacteristic
718C22×C4C23×D711yescharacteristic
719C22×C4C23×D711yescharacteristic
720C22×C4C23×D711yescharacteristic
721SD16—1416no—
722D8—1416no—
723M16—148no—
724C2×C8—78no—
725C4⋊C4—22no—
726C4⋊C4—22no—
727C4⋊C4—22no—
728C4⋊C4—72no—
729C4⋊C4—72no—
730C4⋊C4—142no—
731C4⋊C4—142no—
732C4⋊C4—142no—
733C4⋊C4—142no—
734C4⋊C4—142no—
735C4⋊C4—142no—
736C4⋊C4—141no—
737C4⋊C4—141no—
738C4⋊C4—141no—
739C4⋊C4—141no—
740C4⋊C4C23×D714yes—
741C22⋊C4—24no—
742C22⋊C4—24no—
743C22⋊C4—24no—
744C22⋊C4—24no—
745C22⋊C4—142no—
746C22⋊C4—142no—
747C22⋊C4—142no—
748C22⋊C4—142no—
749C22⋊C4—142no—
750C22⋊C4—142no—
751C22⋊C4—142no—
752C22⋊C4—142no—
753C22⋊C4—142no—
754C42—142no—
755C42—142no—
756C42—142no—
757C42C2×C22⋊D711yescharacteristic
758C42C2×C22⋊D711yescharacteristic
759C42C2×C22⋊D711yescharacteristic
760C42C2×C22⋊D711yescharacteristic
761C42C2×C22⋊D711yescharacteristic
762C42C2×C22⋊D711yescharacteristic
763C42C2×C22⋊D711yescharacteristic
764C42C2×C22⋊D711yescharacteristic
765C42C2×C22⋊D711yescharacteristic
766C42C2×C22⋊D711yescharacteristic
767C42C2×C22⋊D711yescharacteristic
768C42C2×C22⋊D711yescharacteristic
769C42C23×D711yescharacteristic
770C42C23×D711yescharacteristic
771C42C23×D711yescharacteristic
772C42C23×D711yescharacteristic
773C2×C7—22no—
774C2×C7—22no—
775C2×C7—22no—
776C2×C7—48no—
777C2×C7C2×#52511yescharacteristic
778C2×C7C22×AGL(1,ℤ/8)11yescharacteristic
779C2×C7C2×#57511yescharacteristic
780D7—82no—
781C23—22no—
782C23—22no—
783C23—22no—
784C23—28no—
785C23—28no—
786C23—28no—
787C23—24no—
788C23—44no—
789C23—44no—
790C23—432no—
791C23—44no—
792C23—44no—
793C23—44no—
794C23—44no—
795C23—142no—
796C23C22×C22⋊D711yescharacteristic
797C23C22×C22⋊D711yescharacteristic
798C23C22×C22⋊D711yescharacteristic
799Q8—144no—
800Q8—282no—
801Q8—282no—
802D4—28no—
803D4—28no—
804D4—28no—
805D4—24no—
806D4—144no—
807D4—282no—
808D4—284no—
809D4—284no—
810D4—284no—
811D4—282no—
812D4C2×#115718yes—
813C2×C4—22no—
814C2×C4—22no—
815C2×C4—22no—
816C2×C4—22no—
817C2×C4—22no—
818C2×C4—22no—
819C2×C4—22no—
820C2×C4—22no—
821C2×C4—22no—
822C2×C4—22no—
823C2×C4—22no—
824C2×C4—22no—
825C2×C4—24no—
826C2×C4—41no—
827C2×C4—41no—
828C2×C4—41no—
829C2×C4—41no—
830C2×C4—48no—
831C2×C4—48no—
832C2×C4—44no—
833C2×C4—44no—
834C2×C4—44no—
835C2×C4—48no—
836C2×C4—48no—
837C2×C4—142no—
838C2×C4—142no—
839C2×C4—142no—
840C2×C4—284no—
841C2×C4—284no—
842C2×C4—284no—
843C2×C4#649514yescomplemented
844C2×C4C2×#115714yes—
845C2×C4C22×C22⋊D711yescharacteristic
846C2×C4C22×C22⋊D711yescharacteristic
847C2×C4C22×C22⋊D711yescharacteristic
848C2×C4C22×C22⋊D711yescharacteristic
849C2×C4C22×C22⋊D711yescharacteristic
850C2×C4C22×C22⋊D711yescharacteristic
851C2×C4C22×C22⋊D711yescharacteristic
852C2×C4C22×C22⋊D711yescharacteristic
853C2×C4C22×C22⋊D711yescharacteristic
854C2×C4C22×C22⋊D711yescharacteristic
855C2×C4C22×C22⋊D711yescharacteristic
856C2×C4C24×D711yescharacteristic
857C8—148no—
858C7#6055811yescharacteristic, complemented, Sylow
859C22—28no—
860C22—21no—
861C22—21no—
862C22—21no—
863C22—21no—
864C22—21no—
865C22—21no—
866C22—28no—
867C22—416no—
868C22—416no—
869C22—416no—
870C22—44no—
871C22—44no—
872C22—282no—
873C22—282no—
874C22—282no—
875C22#9048212yes—
876C22C2×#649512yes—
877C22#9051312yes—
878C22C23×C22⋊D711yescharacteristic
879C4—21no—
880C4—21no—
881C4—21no—
882C4—21no—
883C4—21no—
884C4—21no—
885C4—21no—
886C4—21no—
887C4—44no—
888C4—282no—
889C4—282no—
890C4—282no—
891C4#9048212yes—
892C4C2×#649512yes—
893C4C2×#649512yes—
894C4C22×#115712yes—
895C2—22no—
896C2—22no—
897C2—22no—
898C2—48no—
899C2—562no—
900C2C2×#9048211yescharacteristic
901C2C22×#649511yescharacteristic
902C2C2×#9051311yescharacteristic
subgroupG/H
centerC2×C4C22×C22⋊D7
commutator, cosocleC2×C4×C7C25
FrattiniC2×C4C24×D7
FittingC22×C4×C7×D4C2
socleC22×C7C23×D4
hypercenterC22×C4×D4D7
hypocenterC7#60558
LCSG ▷ C2×C4×C7 ▷ C2×C7 ▷ C7
UCSC1 ◁ C2×C4 ◁ C22×C42 ◁ C22×C4×D4

Complements

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

NH ≅ G/Ntype
1. C22×C4×C7×D4C2semidirect
2. #11742748C2semidirect
3. #11741483C2semidirect
4. #11739760C2semidirect
5. #11739759C2semidirect
6. #11739756C2semidirect
7. #11739755C2semidirect
8. #11739754C2semidirect
9. #11739753C2semidirect
10. #11739752C2semidirect
11. #11739741C2semidirect
12. C4×#6495C2semidirect
13. #11739584C2semidirect
14. #11739494C2semidirect
40. #90170C22semidirect
41. #90170C22semidirect
42. #90168C22semidirect
43. #90168C22semidirect
44. #90168C22semidirect
47. C4×#1157C22semidirect
48. #90161C22semidirect
49. #90161C22semidirect
50. #90161C22semidirect
57. #89791C22semidirect
58. #89790C22semidirect
59. C4×#1142C22semidirect
60. #89788C22semidirect
61. #89787C22semidirect
62. #89786C22semidirect
63. C4×#1141C22semidirect
64. #89781C22semidirect
65. #89780C22semidirect
66. #89779C22semidirect
67. #89743C22semidirect
68. #89742C22semidirect
69. #89740C22semidirect
70. #89739C22semidirect
71. #89738C22semidirect
72. #89736C22semidirect
73. #89698C22semidirect
74. #89698C22semidirect
75. #89697C22semidirect
76. #89697C22semidirect
77. #89696C22semidirect
78. C4×#1136C22semidirect
175. #6438C23semidirect
176. #6437C23semidirect
181. C4×D28C23semidirect
182. C4×D28C23semidirect
189. #6433C23semidirect
190. #6432C23semidirect
191. #6432C23semidirect
192. #6432C23semidirect
197. C4×Dic14C23semidirect
198. C4×Dic14C23semidirect
203. #6384C23semidirect
204. #6383C23semidirect
205. #6382C23semidirect
206. #6381C23semidirect
207. C4⋊(C7⋊C8)C23semidirect
208. C4⋊(C7⋊C8)C23semidirect
209. #6377C23semidirect
210. C4×C7⋊C8C23semidirect
212. C22×C4×D4D7semidirect
241. C2×C7×D4#41semidirect
456. C2×C4×C7AGL(1,ℤ/8)semidirect
681. C2×D4#1157semidirect
843. C2×C4#6495semidirect
858. C7#60558semidirect

Maximal subgroups

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

subgroupindex
C22×C4×C7×D42
#117427482
#117414832
#117397602
#117397592
#117397562
#117397552
#117397542
#117397532
#117397522
#117397412
C4×#64952
#117395842
#117394942
#605587