Finite Group Databasebeta

← C4×#90239 #13512324

Subgroups — C4×#90239 #13512324

Order 1792.

3526 conjugacy classes of subgroups.

The subgroup lattice has 790 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#90239C211yesmaximal, characteristic
2C2×C4×#1157C212yesmaximal, complemented
3C42×C7×D4C211yesmaximal, characteristic, complemented
4C4×#6501C212yesmaximal, complemented
5C4×#6503C212yesmaximal, complemented
6#11739764C211yesmaximal, characteristic, complemented
7C42×C22⋊D7C212yesmaximal, complemented
8C4×#6458C212yesmaximal, complemented
9#11731198C211yesmaximal, characteristic, complemented
10C4×#6451C212yesmaximal, complemented
11#11731062C211yesmaximal, characteristic, complemented
12C4×#6447C214yesmaximal, complemented
13#11731008C212yesmaximal, complemented
14C4×#6448C214yesmaximal, complemented
15#11730884C212yesmaximal, complemented
16C43×D7C211yesmaximal, characteristic, complemented
17C42×D28C211yesmaximal, characteristic, complemented
18C22×#1157C2212yes—
19C2×C4×C7×D4C2212yes—
20C2×C4×C7×D4C2211yescharacteristic
21C22×C42×C7C2212yes—
22C2×#6503C2211yescharacteristic
23C2×#6501C2211yescharacteristic
24C2×C4×C22⋊D7C2214yes—
25C2×C4×C22⋊D7C2214yes—
26C2×C4×C22⋊D7C2214yes—
27C2×C4×C22⋊D7C2212yes—
28C2×#6489C2212yes—
29#90239C4116yesdirect product factor
30C2×#6458C2211yescharacteristic
31C2×#6451C2211yescharacteristic
32C2×#6448C2212yes—
33C2×#6447C2212yes—
34C4×#1157—216no—
35C2×C4×D28C2214yes—
36C2×C4×D28C2212yes—
37C2×C4×D28C2211yescharacteristic
38C2×#6435C2212yes—
39C2×#6435C2212yes—
40C2×C42×D7C2212yes—
41C2×C42×D7C2212yes—
42C2×C42×D7C2211yescharacteristic
43C2×C42×D7C2212yes—
44C2×C42×D7C2211yescharacteristic
45C2×C42×D7C2211yescharacteristic
46C2×C4×Dic14C2214yes—
47C4×C7×C4⋊C4C2212yes—
48C4×C7×C4⋊C4C2211yescharacteristic
49C4×C7×C22⋊C4C2212yes—
50C4×C7×C22⋊C4C2214yes—
51C43×C7C2211yescharacteristic
52#89993C2212yes—
53C4×C22⋊Dic7C2212yes—
54C4×C22⋊Dic7C2214yes—
55#89760C2212yes—
56#89759C2212yes—
57#89757C2212yes—
58#89748C2212yes—
59#89745C2212yes—
60#89729C2214yes—
61#89729C2214yes—
62#89728C2214yes—
63#89723C2214yes—
64#89716C2214yes—
65C4×(C2×D7)⋊C4C2214yes—
66C4×(C2×D7)⋊C4C2212yes—
67C4×(C2×D7)⋊C4C2214yes—
68C4×(C2×D7)⋊C4C2212yes—
69C4×C4⋊Dic7C2211yescharacteristic
70C4×C4⋊Dic7C2212yes—
71C4×Dic7⋊C4C2214yes—
72C4×Dic7⋊C4C2212yes—
73C42×Dic7C2211yescharacteristic
74C42×Dic7C2211yescharacteristic
75C42×Dic7C2212yes—
76C42×Dic7C2211yescharacteristic
77C42×Dic7C2212yes—
78#89442C2214yes—
79#89441C2214yes—
80#89439C2212yes—
81#89437C2214yes—
82#89422C2212yes—
83#89419C2214yes—
84#89418C2214yes—
85C4×#532—71nomaximal, Sylow
86C22×C7×D4C2311yescharacteristic
87C23×C4×C7C2314yes—
88C23×C4×C7C2312yes—
89C22×C22⋊D7C2312yes—
90C22×C22⋊D7C2312yes—
91C22×C22⋊D7C2312yes—
92C2×#1157—28no—
93C2×#1157—28no—
94C2×#1157C2×C4116yescomplemented
95C22×D28C2311yescharacteristic
96C22×D28C2312yes—
97C22×C4×D7C2312yes—
98C22×C4×D7C2314yes—
99C22×C4×D7C2311yescharacteristic
100C22×C4×D7C2311yescharacteristic
101C22×C4×D7C2312yes—
102C22×C4×D7C2312yes—
103C22×C4×D7C2311yescharacteristic
104C22×Dic14C2312yes—
105C4×C7×D4—28no—
106C4×C7×D4C2×C418yescomplemented
107C2×C7×C4⋊C4C2312yes—
108C2×C7×C4⋊C4C2311yescharacteristic
109C2×C7×C22⋊C4C2314yes—
110C2×C7×C22⋊C4C2312yes—
111C2×C42×C7—28no—
112C2×C42×C7C2314yes—
113C2×C42×C7C2312yes—
114C2×C42×C7C2311yescharacteristic
115C2×C42×C7C2312yes—
116C2×C42×C7C2311yescharacteristic
117C2×C42×C7C2312yes—
118C2×C42×C7C2311yescharacteristic
119C2×C22⋊Dic7C2314yes—
120C2×C22⋊Dic7C2314yes—
121C2×C22⋊Dic7C2312yes—
122#6503C2×C418yescomplemented
123#6501C2×C418yescomplemented
124C4×C22⋊D7—216no—
125C4×C22⋊D7—216no—
126C4×C22⋊D7—216no—
127C4×C22⋊D7C2×C4116yescomplemented
128C2×(C2×D7)⋊C4C2314yes—
129C2×(C2×D7)⋊C4C2314yes—
130C2×(C2×D7)⋊C4C2314yes—
131C2×(C2×D7)⋊C4C2314yes—
132C2×(C2×D7)⋊C4C2312yes—
133C2×(C2×D7)⋊C4C2312yes—
134#6489—28no—
135C2×C4⋊Dic7C2314yes—
136C2×C4⋊Dic7C2312yes—
137C2×C4⋊Dic7C2311yescharacteristic
138C2×Dic7⋊C4C2314yes—
139C2×Dic7⋊C4C2314yes—
140C2×Dic7⋊C4C2314yes—
141C2×Dic7⋊C4C2312yes—
142C2×C4×Dic7C2314yes—
143C2×C4×Dic7C2312yes—
144C2×C4×Dic7C2312yes—
145C2×C4×Dic7C2312yes—
146C2×C4×Dic7C2312yes—
147C2×C4×Dic7C2312yes—
148C2×C4×Dic7C2312yes—
149C2×C4×Dic7C2311yescharacteristic
150C2×C4×Dic7C2312yes—
151C2×C4×Dic7C2311yescharacteristic
152C2×C4×Dic7C2311yescharacteristic
153C2×C4×Dic7C2311yescharacteristic
154C2×C4×Dic7C2312yes—
155C2×C4×Dic7C2311yescharacteristic
156C2×C4×Dic7C2312yes—
157#6458C2×C418yescomplemented
158#6451C2×C418yescomplemented
159#6448C2×C4116yescomplemented
160#6447C2×C4116yescomplemented
161C4×D28—216no—
162C4×D28—28no—
163C4×D28C2×C418yescomplemented
164#6435—28no—
165#6435—28no—
166C42×D7—24no—
167C42×D7—28no—
168C42×D7—28no—
169C42×D7—28no—
170C42×D7C2×C418yescomplemented
171C42×D7D418yescomplemented
172C4×Dic14—216no—
173C7×#95C2314yes—
174C7×#95C2312yes—
175C7⋊#95C2314yes—
176C7⋊#95C2314yes—
177C7⋊#95C2314yes—
178C7⋊#95C2312yes—
179C7⋊#95C2314yes—
180C2×#532—71no—
181C2×C4×#41—72no—
182C4×C4⋊Q8—72no—
183C4×#127—72no—
184C4×#124—74no—
185C4×#121—72no—
186C4×#121—74no—
187C4×#121—72no—
188#2297—72no—
189#2293—71no—
190#2293—72no—
191#2293—71no—
192#2285—71no—
193C42×D4—72no—
194C42×D4—71no—
195C42×D4D711yescharacteristic, complemented
196C2×C43—71no—
197C24×C7C2412yes—
198C23×D7C2412yes—
199C23×D7C2411yescharacteristic
200C2×C7×D4—24no—
201C2×C7×D4C22×C414yes—
202C22×C4×C7—24no—
203C22×C4×C7—24no—
204C22×C4×C7—28no—
205C22×C4×C7—28no—
206C22×C4×C7—28no—
207C22×C4×C7C22×C418yes—
208C22×C4×C7C2414yes—
209C22×C4×C7C2411yescharacteristic
210C22×C4×C7C2412yes—
211C22×C4×C7C2412yes—
212C22×C4×C7C2411yescharacteristic
213C22×C4×C7C2411yescharacteristic
214C22×C4×C7C2412yes—
215C2×C22⋊D7—24no—
216C2×C22⋊D7—24no—
217C2×C22⋊D7—24no—
218C2×C22⋊D7—28no—
219C2×C22⋊D7—24no—
220C2×C22⋊D7C22×C418yes—
221C2×C22⋊D7C22×C418yes—
222C2×C22⋊D7C22×C418yes—
223C22×Dic7C2414yes—
224C22×Dic7C2411yescharacteristic
225C22×Dic7C2412yes—
226C22×Dic7C2412yes—
227C22×Dic7C2412yes—
228C22×Dic7C2411yescharacteristic
229C22×Dic7C2411yescharacteristic
230#1157—264no—
231C2×D28—24no—
232C2×D28—24no—
233C2×D28—24no—
234C2×D28C22×C414yes—
235C2×D28C22×C418yes—
236C2×C4×D7—24no—
237C2×C4×D7—24no—
238C2×C4×D7—24no—
239C2×C4×D7—24no—
240C2×C4×D7—24no—
241C2×C4×D7—24no—
242C2×C4×D7—24no—
243C2×C4×D7—24no—
244C2×C4×D7—24no—
245C2×C4×D7—28no—
246C2×C4×D7—28no—
247C2×C4×D7—28no—
248C2×C4×D7C22×C414yes—
249C2×C4×D7C22×C414yes—
250C2×C4×D7C22×C418yes—
251C2×C4×D7C22×C414yes—
252C2×C4×D7C2×D418yes—
253C2×C4×D7C2×D414yes—
254C2×C4×D7#4114yes—
255C2×Dic14—24no—
256C2×Dic14—24no—
257C2×Dic14C22×C418yes—
258C7×C4⋊C4—24no—
259C7×C4⋊C4C22×C414yes—
260C7×C22⋊C4—28no—
261C7×C22⋊C4C22×C418yes—
262C42×C7—28no—
263C42×C7—24no—
264C42×C7—22no—
265C42×C7—24no—
266C42×C7C22×C414yes—
267C42×C7C2×D414yes—
268C42×C7#4118yescomplemented
269C22⋊Dic7—28no—
270C22⋊Dic7—28no—
271C22⋊Dic7C22×C418yes—
272(C2×D7)⋊C4—28no—
273(C2×D7)⋊C4—28no—
274(C2×D7)⋊C4—28no—
275(C2×D7)⋊C4—28no—
276(C2×D7)⋊C4C22×C418yes—
277(C2×D7)⋊C4C22×C418yes—
278C4⋊Dic7—24no—
279C4⋊Dic7—28no—
280C4⋊Dic7C22×C414yes—
281Dic7⋊C4—28no—
282Dic7⋊C4—28no—
283Dic7⋊C4—28no—
284Dic7⋊C4C22×C418yes—
285C4×Dic7—28no—
286C4×Dic7—24no—
287C4×Dic7—24no—
288C4×Dic7—24no—
289C4×Dic7—24no—
290C4×Dic7—22no—
291C4×Dic7—24no—
292C4×Dic7—24no—
293C4×Dic7—24no—
294C4×Dic7C22×C414yes—
295C4×Dic7C22×C414yes—
296C4×Dic7C22×C414yes—
297C4×Dic7C2×D418yes—
298C4×Dic7C2×D414yes—
299C4×Dic7#4118yescomplemented
300C22×#41—72no—
301#532—716no—
302C2×C4⋊Q8—71no—
303C2×#127—71no—
304C2×#124—72no—
305C2×#121—71no—
306C2×#121—71no—
307C2×#121—72no—
308C4×#41—1416no—
309C2×C4×Q8—74no—
310C2×C4×D4—72no—
311C2×C4×D4—74no—
312C2×C4×D4—74no—
313C2×C4×D4—74no—
314C2×C4×D4—71no—
315C2×C4×D4—72no—
316C2×C4×D4—74no—
317C2×C4×D4C2×D712yes—
318C2×C4×D4C2×D711yescharacteristic
319C2×#117—72no—
320C2×#117—72no—
321C2×#117—72no—
322C22×C42—71no—
323C22×C42—71no—
324C22×C42—71no—
325C22×C42—72no—
326C22×C42—72no—
327C22×C42—72no—
328C22×C42C2×D712yes—
329#391—74no—
330#390—72no—
331#390—72no—
332#390—74no—
333#390—74no—
334#389—72no—
335#389—72no—
336#389—74no—
337#388—74no—
338#388—74no—
339#388—74no—
340#388—74no—
341#386—74no—
342#386—74no—
343#384—72no—
344#382—72no—
345#380—72no—
346#380—72no—
347C4×C4⋊C4—74no—
348C4×C4⋊C4—72no—
349C4×C4⋊C4—72no—
350C4×C4⋊C4—71no—
351C4×C4⋊C4C2×D712yes—
352C4×C4⋊C4C2×D711yescharacteristic
353C4×C22⋊C4—72no—
354C4×C22⋊C4—74no—
355C4×C22⋊C4—72no—
356C4×C22⋊C4—72no—
357C4×C22⋊C4—74no—
358C4×C22⋊C4—74no—
359C4×C22⋊C4C2×D712yes—
360C4×C22⋊C4C2×D714yes—
361C43—72no—
362C43—71no—
363C43—71no—
364C43—72no—
365C43—71no—
366C43C2×D711yescharacteristic
367C23×C7—22no—
368C23×C7—24no—
369C23×C7—24no—
370C23×C7—22no—
371C23×C7C23×C414yes—
372C23×C7C2511yescharacteristic
373C22×D7—22no—
374C22×D7—22no—
375C22×D7—22no—
376C22×D7—24no—
377C22×D7—24no—
378C22×D7—22no—
379C22×D7C23×C414yes—
380C22×D7C23×C412yes—
381C22×D7C22×D412yes—
382C22×D7C2×#4112yes—
383C7×D4—28no—
384C2×C4×C7—22no—
385C2×C4×C7—22no—
386C2×C4×C7—22no—
387C2×C4×C7—22no—
388C2×C4×C7—22no—
389C2×C4×C7—216no—
390C2×C4×C7—24no—
391C2×C4×C7—24no—
392C2×C4×C7—24no—
393C2×C4×C7—416no—
394C2×C4×C7C23×C412yes—
395C2×C4×C7C23×C414yes—
396C2×C4×C7C23×C412yes—
397C2×C4×C7C23×C412yes—
398C2×C4×C7C22×D412yes—
399C2×C4×C7C22×D414yes—
400C2×C4×C7C2×#4114yes—
401C2×C4×C7C2×#4114yes—
402C2×C4×C7C2×#4114yes—
403C2×C4×C7C2×#4112yes—
404C2×C4×C7C2×#4114yes—
405C22⋊D7—216no—
406C22⋊D7—216no—
407C22⋊D7—216no—
408C2×Dic7—22no—
409C2×Dic7—22no—
410C2×Dic7—22no—
411C2×Dic7—22no—
412C2×Dic7—22no—
413C2×Dic7—22no—
414C2×Dic7—22no—
415C2×Dic7—24no—
416C2×Dic7—24no—
417C2×Dic7—24no—
418C2×Dic7C23×C412yes—
419C2×Dic7C23×C414yes—
420C2×Dic7C23×C412yes—
421C2×Dic7C23×C412yes—
422C2×Dic7C22×D414yes—
423C2×Dic7C22×D412yes—
424C2×Dic7C2×#4114yes—
425C2×Dic7C2×#4112yes—
426C2×Dic7C2×#4114yes—
427D28—216no—
428D28—28no—
429C4×D7—216no—
430C4×D7—216no—
431C4×D7—28no—
432C4×D7—216no—
433C4×D7—28no—
434C4×D7—416no—
435C4×D7C4×D4116yescomplemented
436Dic14—216no—
437C2×#41—716no—
438C2×#41—148no—
439C2×#41—148no—
440C22×Q8—72no—
441C22×D4—72no—
442C22×D4—72no—
443C22×D4—72no—
444C22×D4—71no—
445C22×D4—72no—
446C22×D4C22×D711yescharacteristic
447C23×C4—71no—
448C23×C4—72no—
449C23×C4—72no—
450C23×C4—71no—
451C23×C4—71no—
452C23×C4—74no—
453C23×C4—72no—
454C23×C4C22×D714yes—
455C23×C4C22×D712yes—
456C4⋊Q8—78no—
457#127—78no—
458#124—716no—
459#121—78no—
460#121—78no—
461#121—716no—
462C4×Q8—1416no—
463C4×D4—28no—
464C4×D4—716no—
465C4×D4—78no—
466C4×D4—1416no—
467C4×D4—1416no—
468C4×D4—1416no—
469C4×D4—1416no—
470C4×D4—148no—
471C4×D4C4×D718yescomplemented
472#117—148no—
473#117—148no—
474#117—148no—
475C2×C4⋊C4—72no—
476C2×C4⋊C4—71no—
477C2×C4⋊C4—74no—
478C2×C4⋊C4—74no—
479C2×C4⋊C4—74no—
480C2×C4⋊C4—74no—
481C2×C4⋊C4—72no—
482C2×C4⋊C4C22×D712yes—
483C2×C4⋊C4C22×D711yescharacteristic
484C2×C22⋊C4—72no—
485C2×C22⋊C4—72no—
486C2×C22⋊C4—72no—
487C2×C22⋊C4—74no—
488C2×C22⋊C4—74no—
489C2×C22⋊C4—74no—
490C2×C22⋊C4—74no—
491C2×C22⋊C4—74no—
492C2×C22⋊C4—74no—
493C2×C22⋊C4C22×D714yes—
494C2×C22⋊C4C22×D712yes—
495C2×C42—28no—
496C2×C42—71no—
497C2×C42—72no—
498C2×C42—71no—
499C2×C42—72no—
500C2×C42—71no—
501C2×C42—71no—
502C2×C42—78no—
503C2×C42—78no—
504C2×C42—72no—
505C2×C42—74no—
506C2×C42—72no—
507C2×C42—71no—
508C2×C42—72no—
509C2×C42—72no—
510C2×C42—72no—
511C2×C42—72no—
512C2×C42—72no—
513C2×C42—148no—
514C2×C42—144no—
515C2×C42—148no—
516C2×C42—148no—
517C2×C42C22×D712yes—
518C2×C42C22×D714yes—
519C2×C42C22×D712yes—
520C2×C42C22×D711yescharacteristic
521C2×C42C22×D711yescharacteristic
522C2×C42C22×D712yes—
523C2×C42C22×D711yescharacteristic
524#95—74no—
525#95—72no—
526#95—74no—
527#95—74no—
528#95—74no—
529#95C22×D712yes—
530#95C22×D714yes—
531C22×C7—24no—
532C22×C7—24no—
533C22×C7—24no—
534C22×C7—44no—
535C22×C7—44no—
536C22×C7C24×C411yescharacteristic
537C22×C7C23×D411yescharacteristic
538C22×C7C22×#4112yes—
539C22×C7C22×#4111yescharacteristic
540C22×C7C22×#4112yes—
541C2×D7—22no—
542C2×D7—22no—
543C2×D7—24no—
544C2×D7—24no—
545C2×D7—24no—
546C2×D7—24no—
547C2×D7—24no—
548C2×D7—44no—
549C2×D7—44no—
550C2×D7C2×C4×D414yes—
551C4×C7—24no—
552C4×C7—22no—
553C4×C7—24no—
554C4×C7—44no—
555C4×C7C2×C4×D414yes—
556C4×C7C4×#4114yescomplemented
557C4×C7#53218yescomplemented
558Dic7—24no—
559Dic7—22no—
560Dic7—24no—
561Dic7—24no—
562Dic7—44no—
563Dic7C2×C4×D414yes—
564Dic7C4×#4114yescomplemented
565C24—71no—
566C24—72no—
567C24C23×D712yes—
568#41—1464no—
569C2×Q8—78no—
570C2×Q8—144no—
571C2×Q8—144no—
572C2×D4—24no—
573C2×D4—78no—
574C2×D4—78no—
575C2×D4—78no—
576C2×D4—74no—
577C2×D4—78no—
578C2×D4—144no—
579C2×D4—144no—
580C2×D4—144no—
581C2×D4—148no—
582C2×D4—144no—
583C2×D4—144no—
584C2×D4—144no—
585C2×D4—144no—
586C2×D4C2×C4×D714yes—
587C22×C4—24no—
588C22×C4—24no—
589C22×C4—28no—
590C22×C4—28no—
591C22×C4—28no—
592C22×C4—71no—
593C22×C4—71no—
594C22×C4—74no—
595C22×C4—74no—
596C22×C4—74no—
597C22×C4—71no—
598C22×C4—72no—
599C22×C4—72no—
600C22×C4—72no—
601C22×C4—74no—
602C22×C4—74no—
603C22×C4—78no—
604C22×C4—78no—
605C22×C4—74no—
606C22×C4—144no—
607C22×C4—144no—
608C22×C4—144no—
609C22×C4—144no—
610C22×C4—144no—
611C22×C4—144no—
612C22×C4—144no—
613C22×C4—144no—
614C22×C4—144no—
615C22×C4—148no—
616C22×C4—148no—
617C22×C4—148no—
618C22×C4C2×C4×D718yes—
619C22×C4C23×D714yes—
620C22×C4C23×D711yescharacteristic
621C22×C4C23×D712yes—
622C22×C4C23×D712yes—
623C22×C4C23×D711yescharacteristic
624C22×C4C23×D711yescharacteristic
625C22×C4C23×D712yes—
626C4⋊C4—24no—
627C4⋊C4—78no—
628C4⋊C4—74no—
629C4⋊C4—148no—
630C4⋊C4—148no—
631C4⋊C4—148no—
632C4⋊C4—148no—
633C4⋊C4—144no—
634C4⋊C4C2×C4×D714yes—
635C22⋊C4—28no—
636C22⋊C4—78no—
637C22⋊C4—78no—
638C22⋊C4—78no—
639C22⋊C4—148no—
640C22⋊C4—148no—
641C22⋊C4—148no—
642C22⋊C4—148no—
643C22⋊C4—148no—
644C22⋊C4—148no—
645C22⋊C4C2×C4×D718yes—
646C42—24no—
647C42—28no—
648C42—22no—
649C42—24no—
650C42—74no—
651C42—74no—
652C42—74no—
653C42—74no—
654C42—78no—
655C42—78no—
656C42—144no—
657C42—144no—
658C42—144no—
659C42—144no—
660C42—144no—
661C42—144no—
662C42—144no—
663C42—148no—
664C42—142no—
665C42C2×C4×D714yes—
666C42#115718yescomplemented
667C42D4×D714yes—
668C2×C7—44no—
669C2×C7C22×C4×D411yescharacteristic
670C2×C7C2×C4×#4111yescharacteristic
671C2×C7C2×C4×#4111yescharacteristic
672C2×C7C2×#53212yes—
673C2×C7#344412yes—
674D7—24no—
675D7—44no—
676C23—24no—
677C23—22no—
678C23—24no—
679C23—22no—
680C23—72no—
681C23—72no—
682C23—72no—
683C23—74no—
684C23—142no—
685C23—142no—
686C23—144no—
687C23—142no—
688C23—144no—
689C23—142no—
690C23C22×C4×D714yes—
691C23C24×D711yescharacteristic
692Q8—1416no—
693D4—28no—
694D4—1416no—
695D4—1416no—
696D4—1416no—
697D4—1416no—
698D4—148no—
699C2×C4—22no—
700C2×C4—22no—
701C2×C4—22no—
702C2×C4—22no—
703C2×C4—22no—
704C2×C4—216no—
705C2×C4—24no—
706C2×C4—24no—
707C2×C4—24no—
708C2×C4—416no—
709C2×C4—72no—
710C2×C4—72no—
711C2×C4—72no—
712C2×C4—74no—
713C2×C4—72no—
714C2×C4—716no—
715C2×C4—72no—
716C2×C4—74no—
717C2×C4—74no—
718C2×C4—74no—
719C2×C4—148no—
720C2×C4—1416no—
721C2×C4—142no—
722C2×C4—142no—
723C2×C4—142no—
724C2×C4—142no—
725C2×C4—142no—
726C2×C4—142no—
727C2×C4—142no—
728C2×C4—148no—
729C2×C4—1416no—
730C2×C4—1416no—
731C2×C4—144no—
732C2×C4—144no—
733C2×C4—144no—
734C2×C4—2816no—
735C2×C4C22×C4×D712yes—
736C2×C4C22×C4×D714yes—
737C2×C4C22×C4×D712yes—
738C2×C4C22×C4×D712yes—
739C2×C4C2×#115714yes—
740C2×C4C2×#115714yes—
741C2×C4C2×#115714yes—
742C2×C4C2×D4×D712yes—
743C2×C4C2×D4×D714yes—
744C2×C4D7×#4112yes—
745C2×C4D7×#4114yes—
746C7C4×#53211yescharacteristic, complemented, Sylow
747C22—24no—
748C22—24no—
749C22—24no—
750C22—44no—
751C22—44no—
752C22—74no—
753C22—142no—
754C22—144no—
755C22—142no—
756C22—144no—
757C22—144no—
758C22—144no—
759C22—144no—
760C22—284no—
761C22—284no—
762C22C23×C4×D711yescharacteristic
763C22C22×#115712yes—
764C22C22×D4×D711yescharacteristic
765C22C2×D7×#4111yescharacteristic
766C22C2×D7×#4112yes—
767C4—24no—
768C4—22no—
769C4—24no—
770C4—44no—
771C4—74no—
772C4—74no—
773C4—142no—
774C4—144no—
775C4—144no—
776C4—144no—
777C4—284no—
778C4C4×#115714yescomplemented
779C4C4×D4×D714yes—
780C4#9023918yesdirect product factor
781C2—44no—
782C2—144no—
783C2—284no—
784C2C2×C4×#115711yescharacteristic
785C2C2×C4×D4×D711yescharacteristic
786C2C2×#9023912yes—
787C2C4×D7×#4111yescharacteristic
788C2#1174290412yes—
subgroupG/H
centerC2×C42C22×D7
commutatorC22×C7C24×C4
FrattiniC23C24×D7
FittingC42×C7×D4C2
socle, cosocleC23×C7C25
prime radicalC2×#90239C2
hypercenterC42×D4D7
hypocenterC7C4×#532
LCSG ▷ C22×C7 ▷ C7
UCSC1 ◁ C2×C42 ◁ C42×D4

Complements

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

NH ≅ G/Ntype
2. C2×C4×#1157C2semidirect
3. C42×C7×D4C2semidirect
4. C4×#6501C2semidirect
5. C4×#6503C2semidirect
6. #11739764C2semidirect
7. C42×C22⋊D7C2semidirect
8. C4×#6458C2semidirect
9. #11731198C2semidirect
10. C4×#6451C2semidirect
11. #11731062C2semidirect
12. C4×#6447C2semidirect
13. #11731008C2semidirect
14. C4×#6448C2semidirect
15. #11730884C2semidirect
16. C43×D7C2semidirect
17. C42×D28C2semidirect
29. #90239C4direct (N × H)
94. C2×#1157C2×C4semidirect
106. C4×C7×D4C2×C4semidirect
122. #6503C2×C4semidirect
123. #6501C2×C4semidirect
127. C4×C22⋊D7C2×C4semidirect
157. #6458C2×C4semidirect
158. #6451C2×C4semidirect
159. #6448C2×C4semidirect
160. #6447C2×C4semidirect
163. C4×D28C2×C4semidirect
170. C42×D7C2×C4semidirect
171. C42×D7D4semidirect
195. C42×D4D7semidirect
268. C42×C7#41semidirect
299. C4×Dic7#41semidirect
435. C4×D7C4×D4semidirect
471. C4×D4C4×D7semidirect
556. C4×C7C4×#41semidirect
557. C4×C7#532semidirect
564. Dic7C4×#41semidirect
666. C42#1157semidirect
746. C7C4×#532semidirect
778. C4C4×#1157semidirect
780. C4#90239direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#902392
C2×C4×#11572
C42×C7×D42
C4×#65012
C4×#65032
#117397642
C42×C22⋊D72
C4×#64582
#117311982
C4×#64512
#117310622
C4×#64472
#117310082
C4×#64482
#117308842
C43×D72
C42×D282
C4×#5327