Finite Group Databasebeta

← C2×#11736954 #14230372

Subgroups — C2×#11736954 #14230372

Order 1792.

2374 conjugacy classes of subgroups.

The subgroup lattice has 824 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#90243C211yesmaximal, characteristic, complemented
2C2×#90246C211yesmaximal, characteristic, complemented
3C2×C7×#435C211yesmaximal, characteristic, complemented
4C2×#89906C211yesmaximal, characteristic, complemented
5C2×#89905C211yesmaximal, characteristic, complemented
6C22×#6390C211yesmaximal, characteristic, complemented
7C2×#89887C211yesmaximal, characteristic, complemented
8#11736954C2116yesmaximal, direct product factor
9C2×#89622C211yesmaximal, characteristic, complemented
10C2×#89616C211yesmaximal, characteristic, complemented
11C2×#89510C211yesmaximal, characteristic, complemented
12C2×#89506C211yesmaximal, characteristic, complemented
13C2×#89494C211yesmaximal, characteristic, complemented
14C2×#89508C211yesmaximal, characteristic, complemented
15C2×#89486C211yesmaximal, characteristic, complemented
16C2×#89482C211yesmaximal, characteristic, complemented
17C22×#1159—21no—
18C22×#1157C2211yescharacteristic
19C23×Dic14C2211yescharacteristic
20C22×C7×M16C2211yescharacteristic
21C23×C7×C8C2211yescharacteristic
22C2×C4×C7×D4C2211yescharacteristic
23C2×#6502—21no—
24C2×#6493C2211yescharacteristic
25C2×#6493C2211yescharacteristic
26C2×#6493C2211yescharacteristic
27C22×C4⋊Dic7C2211yescharacteristic
28C22×C4⋊Dic7C2211yescharacteristic
29C2×#6487C2211yescharacteristic
30C22×D56C2211yescharacteristic
31C22×#1132C2211yescharacteristic
32C22×#1132C2211yescharacteristic
33#90246—24no—
34#90246C2218yescomplemented
35#90243—24no—
36#90243C2218yescomplemented
37C2×#6460—21no—
38C2×#6459—21no—
39C2×#6449—21no—
40C2×#6449—21no—
41C2×#6448—21no—
42C2×(C22⋊D7)⋊C4—21no—
43C2×#6438C2211yescharacteristic
44C2×C4×D28C2211yescharacteristic
45C2×#6432C2211yescharacteristic
46C2×C4×Dic14C2211yescharacteristic
47C7×#435C2218yescomplemented
48C2×C7×C4⋊C8C2211yescharacteristic
49C2×C7×C22⋊C8C2211yescharacteristic
50C2×C7×C22⋊C8C2211yescharacteristic
51C2×C7×#97C2211yescharacteristic
52#89906C2218yescomplemented
53#89905C2218yescomplemented
54#89887C2218yescomplemented
55C2×#6395C2211yescharacteristic
56C2×#6395C2211yescharacteristic
57C2×#6395C2211yescharacteristic
58C2×#6395C2211yescharacteristic
59C2×#6392C2211yescharacteristic
60C2×#6392C2211yescharacteristic
61C2×#6392C2211yescharacteristic
62C2×#6390C2211yescharacteristic
63C2×#6390C2211yescharacteristic
64C2×#6390C2211yescharacteristic
65C2×#6390C2211yescharacteristic
66C2×#6390C2211yescharacteristic
67C2×#6390C2211yescharacteristic
68C2×#6390C2218yescomplemented
69#89622C2218yescomplemented
70#89616C2218yescomplemented
71#89510C2218yescomplemented
72#89508C2218yescomplemented
73#89506C2218yescomplemented
74#89494C2218yescomplemented
75#89486C2218yescomplemented
76#89482C2218yescomplemented
77C2×#3308—71nomaximal, Sylow
78C22×C7×D4D411yescharacteristic
79C23×C4×C7C2311yescharacteristic
80C23×C4×C7C2311yescharacteristic
81C22×C22⋊D7—21no—
82C22×C22⋊D7—21no—
83C22×C22⋊D7—21no—
84C22×C22⋊D7—21no—
85C23×Dic7—21no—
86C23×Dic7—21no—
87C23×Dic7—21no—
88C2×#1159—28no—
89C2×#1159—48no—
90C2×#1157—22no—
91C2×#1157—24no—
92C2×#1157—42no—
93C2×#1157C2314yes—
94C22×D28C2311yescharacteristic
95C22×D28C2311yescharacteristic
96C22×C4×D7—21no—
97C22×C4×D7—21no—
98C22×Dic14—24no—
99C22×Dic14—21no—
100C22×Dic14—21no—
101C22×Dic14—22no—
102C22×Dic14—42no—
103C22×Dic14C2311yescharacteristic
104C22×Dic14C2314yes—
105C22×Dic14C2311yescharacteristic
106C2×C7×M16—42no—
107C2×C7×M16C2314yes—
108C22×C7×C8—42no—
109C22×C7×C8C2311yescharacteristic
110C22×C7×C8C2311yescharacteristic
111C22×C7×C8C2311yescharacteristic
112C22×C7×C8C2311yescharacteristic
113C22×C7×C8C2314yes—
114C4×C7×D4D414yes—
115C4×C7×D4C2314yes—
116C2×C7×C4⋊C4D411yescharacteristic
117C2×C7×C22⋊C4D411yescharacteristic
118C2×C7×C22⋊C4D411yescharacteristic
119C2×C42×C7C2311yescharacteristic
120C2×C22⋊Dic7—21no—
121#6502—28no—
122#6493—22no—
123#6493—22no—
124#6493—22no—
125#6493C2314yes—
126#6493C2314yes—
127#6493C2314yes—
128C2×(C2×D7)⋊C4—21no—
129C2×(C2×D7)⋊C4—21no—
130C2×(C2×D7)⋊C4—21no—
131C2×(C2×D7)⋊C4—21no—
132C2×(C2×D7)⋊C4—21no—
133C2×(C2×D7)⋊C4—21no—
134C2×C4⋊Dic7—21no—
135C2×C4⋊Dic7—21no—
136C2×C4⋊Dic7—21no—
137C2×C4⋊Dic7—22no—
138C2×C4⋊Dic7—22no—
139C2×C4⋊Dic7C2311yescharacteristic
140C2×C4⋊Dic7C2311yescharacteristic
141C2×C4⋊Dic7C2311yescharacteristic
142C2×C4⋊Dic7C2314yes—
143C2×C4⋊Dic7C2311yescharacteristic
144C2×C4⋊Dic7C2314yes—
145#6487—22no—
146#6487C2314yes—
147C2×Dic7⋊C4—21no—
148C2×Dic7⋊C4—21no—
149C2×C4×Dic7—21no—
150C2×D56—42no—
151C2×D56C2314yes—
152C2×#1132—24no—
153C2×#1132—42no—
154C2×#1132C2314yes—
155C2×#1132C2314yes—
156#6460—28no—
157#6459—28no—
158#6449—28no—
159#6449—28no—
160#6448—28no—
161(C22⋊D7)⋊C4—28no—
162#6438—22no—
163#6438C2314yes—
164C4×D28—22no—
165C4×D28C2314yes—
166#6432—22no—
167#6432C2314yes—
168C4×Dic14—22no—
169C4×Dic14C2314yes—
170C7×C4⋊C8C2314yes—
171C7×C22⋊C8C2314yes—
172C7×C22⋊C8C2314yes—
173C7×#97C2314yes—
174#6395C2314yes—
175#6395C2314yes—
176#6395C2314yes—
177#6395C2314yes—
178#6392C2314yes—
179#6392C2314yes—
180#6392C2314yes—
181#6390C2314yes—
182#6390C2314yes—
183#6390C2314yes—
184#6390C2314yes—
185#6390C2314yes—
186#6390C2314yes—
187C2×#548—71no—
188C2×#547—71no—
189#3308—716no—
190C2×#489—71no—
191C2×#484—71no—
192C2×#480—71no—
193C2×#477—71no—
194C2×#468—71no—
195C2×#466—71no—
196C2×#463—71no—
197C2×#449—71no—
198C2×#448—71no—
199C2×#440—71no—
200C2×#435D711yescharacteristic, complemented
201C2×#417—71no—
202C22×#103—71no—
203C24×C7C2×D411yescharacteristic
204C24×C7C2×D411yescharacteristic
205C23×D7—21no—
206C23×D7—21no—
207C2×C7×D4—24no—
208C2×C7×D4C2×D414yes—
209C22×C4×C7—22no—
210C22×C4×C7—22no—
211C22×C4×C7—22no—
212C22×C4×C7—22no—
213C22×C4×C7C2×D411yescharacteristic
214C22×C4×C7C2×D411yescharacteristic
215C22×C4×C7C2×D411yescharacteristic
216C22×C4×C7C2×D412yes—
217C22×C4×C7C2×D411yescharacteristic
218C22×C4×C7C2×D412yes—
219C22×C4×C7C2412yes—
220C22×C4×C7C2412yes—
221C22×C4×C7C2411yescharacteristic
222C2×C22⋊D7—24no—
223C2×C22⋊D7—24no—
224C2×C22⋊D7—24no—
225C2×C22⋊D7—24no—
226C2×C22⋊D7—44no—
227C2×C22⋊D7—44no—
228C2×C22⋊D7—44no—
229C2×C22⋊D7—44no—
230C22×Dic7—21no—
231C22×Dic7—24no—
232C22×Dic7—24no—
233C22×Dic7—24no—
234C22×Dic7—21no—
235C22×Dic7—21no—
236C22×Dic7—21no—
237C22×Dic7—21no—
238C22×Dic7—21no—
239C22×Dic7—44no—
240C22×Dic7—44no—
241C22×Dic7—44no—
242#1159—432no—
243#1157—28no—
244#1157—44no—
245#1157—48no—
246C2×D28—22no—
247C2×D28—22no—
248C2×D28—22no—
249C2×D28—22no—
250C2×D28—21no—
251C2×D28—21no—
252C2×D28C2412yes—
253C2×D28C2412yes—
254C2×C4×D7—24no—
255C2×C4×D7—24no—
256C2×C4×D7—44no—
257C2×C4×D7—44no—
258C2×Dic14—21no—
259C2×Dic14—22no—
260C2×Dic14—22no—
261C2×Dic14—22no—
262C2×Dic14—28no—
263C2×Dic14—24no—
264C2×Dic14—21no—
265C2×Dic14—24no—
266C2×Dic14—44no—
267C2×Dic14—48no—
268C2×Dic14—44no—
269C2×Dic14—44no—
270C2×Dic14#4114yescomplemented
271C2×Dic14C2412yes—
272C2×Dic14C2412yes—
273C7×M16—44no—
274C2×C7×C8—22no—
275C2×C7×C8—22no—
276C2×C7×C8—22no—
277C2×C7×C8—22no—
278C2×C7×C8—44no—
279C2×C7×C8C2412yes—
280C2×C7×C8C2412yes—
281C2×C7×C8C2412yes—
282C2×C7×C8C2412yes—
283C7×C4⋊C4C2×D414yes—
284C7×C22⋊C4C2×D414yes—
285C7×C22⋊C4C2×D414yes—
286C42×C7C2×D412yes—
287C42×C7C2412yes—
288C22⋊Dic7—24no—
289(C2×D7)⋊C4—24no—
290(C2×D7)⋊C4—24no—
291(C2×D7)⋊C4—24no—
292(C2×D7)⋊C4—24no—
293(C2×D7)⋊C4—24no—
294(C2×D7)⋊C4—24no—
295C4⋊Dic7—21no—
296C4⋊Dic7—21no—
297C4⋊Dic7—21no—
298C4⋊Dic7—24no—
299C4⋊Dic7—21no—
300C4⋊Dic7—24no—
301C4⋊Dic7—24no—
302C4⋊Dic7C2412yes—
303C4⋊Dic7C2412yes—
304C4⋊Dic7C2412yes—
305C4⋊Dic7C2412yes—
306Dic7⋊C4—24no—
307Dic7⋊C4—24no—
308C4×Dic7—24no—
309D56—44no—
310#1132—28no—
311#1132—44no—
312C22×#41—71no—
313C22×#41—141no—
314C23×Q8—71no—
315C22×SD16—71no—
316C22×SD16—71no—
317C22×D8—71no—
318C22×M16C2×D711yescharacteristic
319C23×C8C2×D711yescharacteristic
320#548—78no—
321#548—144no—
322#547—78no—
323#547—144no—
324C2×C4⋊Q8—71no—
325C2×#124—71no—
326C2×#124—141no—
327C2×#123—141no—
328C2×#123—141no—
329C2×C22⋊Q8—71no—
330C2×C22⋊Q8—141no—
331C2×C22⋊Q8—141no—
332C2×#121—71no—
333C2×#121—71no—
334C2×#121—71no—
335C2×#121—141no—
336C2×C4×Q8—71no—
337C2×C4×D4—71no—
338C2×C4×D4—141no—
339C2×C4×D4C2×D711yescharacteristic
340C22×C4⋊C4—71no—
341C22×C4⋊C4—71no—
342#489—78no—
343#484—78no—
344#480—78no—
345#477—78no—
346#468—78no—
347#466—78no—
348#463—78no—
349#449—78no—
350#448—78no—
351#440—78no—
352#435C2×D718yescomplemented
353C2×#107—71no—
354C2×#107—71no—
355C2×#107—71no—
356C2×C4⋊C8C2×D711yescharacteristic
357#417—78no—
358C2×#103—71no—
359C2×#103—71no—
360C2×#103—71no—
361C2×#103—71no—
362C2×#103—71no—
363C2×#103—71no—
364C2×#103—78no—
365C2×#102—71no—
366C2×#102—71no—
367C2×#102—71no—
368C2×#102—71no—
369C2×C22⋊C8C2×D711yescharacteristic
370C2×C22⋊C8C2×D711yescharacteristic
371C2×#97C2×D711yescharacteristic
372C23×C7—22no—
373C23×C7—22no—
374C23×C7—22no—
375C23×C7—22no—
376C23×C7—22no—
377C23×C7AGL(1,ℤ/8)14yes—
378C23×C7C22×D412yes—
379C23×C7C22×D412yes—
380C23×C7C22×D411yescharacteristic
381C22×D7—22no—
382C22×D7—22no—
383C22×D7—42no—
384C22×D7—42no—
385C22×D7—42no—
386C22×D7—42no—
387C22×D7—42no—
388C22×D7—42no—
389C7×D4—28no—
390C2×C4×C7—22no—
391C2×C4×C7—22no—
392C2×C4×C7—22no—
393C2×C4×C7—22no—
394C2×C4×C7—24no—
395C2×C4×C7—24no—
396C2×C4×C7—22no—
397C2×C4×C7—22no—
398C2×C4×C7—22no—
399C2×C4×C7—22no—
400C2×C4×C7C22×D412yes—
401C2×C4×C7C22×D412yes—
402C2×C4×C7C22×D412yes—
403C2×C4×C7C22×D412yes—
404C2×C4×C7C22×D411yescharacteristic
405C2×C4×C7C2×#4112yes—
406C2×C4×C7H(5,𝔽2)12yes—
407C2×C4×C7C2511yescharacteristic
408C22⋊D7—48no—
409C22⋊D7—48no—
410C22⋊D7—48no—
411C22⋊D7—48no—
412C2×Dic7—24no—
413C2×Dic7—22no—
414C2×Dic7—22no—
415C2×Dic7—22no—
416C2×Dic7—22no—
417C2×Dic7—22no—
418C2×Dic7—22no—
419C2×Dic7—48no—
420C2×Dic7—48no—
421C2×Dic7—42no—
422C2×Dic7—42no—
423C2×Dic7—42no—
424C2×Dic7—42no—
425C2×Dic7—48no—
426C2×Dic7—42no—
427D28—22no—
428D28—22no—
429D28—22no—
430D28—22no—
431D28—42no—
432D28—42no—
433C4×D7—48no—
434C4×D7—48no—
435Dic14—24no—
436Dic14—22no—
437Dic14—22no—
438Dic14—22no—
439Dic14—48no—
440Dic14—48no—
441Dic14—42no—
442Dic14C2×#4114yescomplemented
443C7×C8—22no—
444C7×C8—22no—
445C7×C8—22no—
446C7×C8—22no—
447C2×#41—74no—
448C2×#41—144no—
449C2×#41—148no—
450C2×#41—142no—
451C2×#41—282no—
452C2×#41—288no—
453C22×Q8—71no—
454C22×Q8—71no—
455C22×Q8—74no—
456C22×Q8—144no—
457C22×Q8—141no—
458C22×Q8—141no—
459C22×Q8—142no—
460C22×Q8—282no—
461C22×D4—71no—
462C22×D4—71no—
463C22×D4—141no—
464C22×D4—141no—
465C22×D4—141no—
466C22×D4—141no—
467C22×D4D2811yescharacteristic
468C23×C4—141no—
469C23×C4—141no—
470C23×C4—141no—
471C23×C4—141no—
472C23×C4—141no—
473C23×C4C22×D711yescharacteristic
474C23×C4C22×D711yescharacteristic
475C2×SD16—74no—
476C2×SD16—74no—
477C2×SD16—144no—
478C2×SD16—282no—
479C2×D8—74no—
480C2×D8—282no—
481C2×M16—42no—
482C2×M16C22×D714yes—
483C22×C8—42no—
484C22×C8C22×D711yescharacteristic
485C22×C8C22×D711yescharacteristic
486C22×C8C22×D711yescharacteristic
487C22×C8C22×D711yescharacteristic
488C22×C8C22×D714yes—
489C4⋊Q8—74no—
490C4⋊Q8—142no—
491#124—74no—
492#124—148no—
493#124—142no—
494#123—148no—
495#123—148no—
496C22⋊Q8—74no—
497C22⋊Q8—142no—
498C22⋊Q8—148no—
499C22⋊Q8—148no—
500#121—74no—
501#121—74no—
502#121—74no—
503#121—148no—
504#121—142no—
505#121—142no—
506#121—142no—
507C4×Q8—74no—
508C4×Q8—142no—
509C4×D4—74no—
510C4×D4—148no—
511C4×D4—142no—
512C4×D4D2814yes—
513C4×D4C22×D714yes—
514C2×C4⋊C4—71no—
515C2×C4⋊C4—71no—
516C2×C4⋊C4—71no—
517C2×C4⋊C4—74no—
518C2×C4⋊C4—74no—
519C2×C4⋊C4—71no—
520C2×C4⋊C4—141no—
521C2×C4⋊C4—141no—
522C2×C4⋊C4—142no—
523C2×C4⋊C4—142no—
524C2×C4⋊C4—141no—
525C2×C4⋊C4—141no—
526C2×C4⋊C4—141no—
527C2×C4⋊C4D2811yescharacteristic
528C2×C22⋊C4—141no—
529C2×C22⋊C4—141no—
530C2×C22⋊C4—141no—
531C2×C22⋊C4—141no—
532C2×C22⋊C4—141no—
533C2×C22⋊C4—141no—
534C2×C22⋊C4—141no—
535C2×C22⋊C4D2811yescharacteristic
536C2×C22⋊C4D2811yescharacteristic
537C2×C42—141no—
538C2×C42C22×D711yescharacteristic
539#107—74no—
540#107—74no—
541#107—74no—
542C4⋊C8C22×D714yes—
543#103—74no—
544#103—74no—
545#103—74no—
546#103—74no—
547#103—74no—
548#103—74no—
549#102—74no—
550#102—74no—
551#102—74no—
552#102—74no—
553C22⋊C8C22×D714yes—
554C22⋊C8C22×D714yes—
555#97C22×D714yes—
556C22×C7—22no—
557C22×C7—28no—
558C22×C7—22no—
559C22×C7—22no—
560C22×C7—22no—
561C22×C7—22no—
562C22×C7—44no—
563C22×C7#54612yes—
564C22×C7C2×AGL(1,ℤ/8)14yes—
565C22×C7C2×AGL(1,ℤ/8)12yes—
566C22×C7#57812yes—
567C22×C7C23×D411yescharacteristic
568C2×D7—42no—
569C2×D7—42no—
570C2×D7—42no—
571C2×D7—42no—
572C2×D7—42no—
573C2×D7—42no—
574C2×D7—84no—
575C2×D7—84no—
576C4×C7—22no—
577C4×C7—22no—
578C4×C7—22no—
579C4×C7—22no—
580C4×C7#54612yes—
581C4×C7C22×#4111yescharacteristic
582C4×C7C2×H(5,𝔽2)11yescharacteristic
583Dic7—24no—
584Dic7—42no—
585Dic7—42no—
586Dic7—42no—
587Dic7—42no—
588Dic7—42no—
589C24—141no—
590C24—141no—
591C24C2×D2811yescharacteristic
592C24C2×D2811yescharacteristic
593#41—148no—
594#41—284no—
595#41—288no—
596#41—2832no—
597C2×Q8—74no—
598C2×Q8—72no—
599C2×Q8—72no—
600C2×Q8—148no—
601C2×Q8—141no—
602C2×Q8—144no—
603C2×Q8—141no—
604C2×Q8—144no—
605C2×Q8—142no—
606C2×Q8—142no—
607C2×Q8—142no—
608C2×Q8—284no—
609C2×Q8—284no—
610C2×Q8—288no—
611C2×Q8—284no—
612C2×D4—24no—
613C2×D4—72no—
614C2×D4—72no—
615C2×D4—144no—
616C2×D4—144no—
617C2×D4—144no—
618C2×D4—144no—
619C2×D4—141no—
620C2×D4—141no—
621C2×D4—142no—
622C2×D4—142no—
623C2×D4—142no—
624C2×D4—142no—
625C2×D4—284no—
626C2×D4—284no—
627C2×D4—284no—
628C2×D4—284no—
629C2×D4C2×D2814yes—
630C22×C4—22no—
631C22×C4—22no—
632C22×C4—22no—
633C22×C4—22no—
634C22×C4—141no—
635C22×C4—144no—
636C22×C4—144no—
637C22×C4—144no—
638C22×C4—141no—
639C22×C4—141no—
640C22×C4—141no—
641C22×C4—141no—
642C22×C4—141no—
643C22×C4—144no—
644C22×C4—144no—
645C22×C4—284no—
646C22×C4—284no—
647C22×C4—284no—
648C22×C4—284no—
649C22×C4—284no—
650C22×C4C2×D2812yes—
651C22×C4C2×D2812yes—
652C22×C4C2×D2811yescharacteristic
653C22×C4C2×D2811yescharacteristic
654C22×C4C2×D2811yescharacteristic
655C22×C4C2×D2811yescharacteristic
656C22×C4C23×D712yes—
657C22×C4C23×D712yes—
658C22×C4C23×D711yescharacteristic
659SD16—148no—
660SD16—284no—
661D8—284no—
662M16—44no—
663C2×C8—22no—
664C2×C8—22no—
665C2×C8—22no—
666C2×C8—22no—
667C2×C8—44no—
668C2×C8C23×D712yes—
669C2×C8C23×D712yes—
670C2×C8C23×D712yes—
671C2×C8C23×D712yes—
672C4⋊C4—72no—
673C4⋊C4—72no—
674C4⋊C4—72no—
675C4⋊C4—72no—
676C4⋊C4—144no—
677C4⋊C4—144no—
678C4⋊C4—141no—
679C4⋊C4—141no—
680C4⋊C4—141no—
681C4⋊C4—144no—
682C4⋊C4—144no—
683C4⋊C4—141no—
684C4⋊C4—144no—
685C4⋊C4C2×D2814yes—
686C22⋊C4—144no—
687C22⋊C4—144no—
688C22⋊C4—144no—
689C22⋊C4—144no—
690C22⋊C4—144no—
691C22⋊C4—144no—
692C22⋊C4—144no—
693C22⋊C4C2×D2814yes—
694C22⋊C4C2×D2814yes—
695C42—144no—
696C42C2×D2812yes—
697C42C23×D712yes—
698C2×C7—24no—
699C2×C7—42no—
700C2×C7#330814yescomplemented
701C2×C7C2×#54611yescharacteristic
702C2×C7C22×AGL(1,ℤ/8)11yescharacteristic
703C2×C7C2×#57811yescharacteristic
704D7—82no—
705D7—82no—
706C23—22no—
707C23—22no—
708C23—22no—
709C23—22no—
710C23—22no—
711C23—142no—
712C23—142no—
713C23—282no—
714C23—282no—
715C23—282no—
716C23—282no—
717C23—282no—
718C23—282no—
719C23#647114yes—
720C23C22×D2812yes—
721C23C22×D2812yes—
722C23C22×D2811yescharacteristic
723Q8—74no—
724Q8—144no—
725Q8—142no—
726Q8—142no—
727Q8—142no—
728Q8—288no—
729Q8—288no—
730Q8—282no—
731D4—28no—
732D4—142no—
733D4—142no—
734D4—142no—
735D4—142no—
736D4—288no—
737D4—288no—
738D4—288no—
739D4—288no—
740D4—282no—
741D4—282no—
742C2×C4—22no—
743C2×C4—22no—
744C2×C4—22no—
745C2×C4—22no—
746C2×C4—24no—
747C2×C4—24no—
748C2×C4—22no—
749C2×C4—22no—
750C2×C4—22no—
751C2×C4—22no—
752C2×C4—144no—
753C2×C4—142no—
754C2×C4—142no—
755C2×C4—142no—
756C2×C4—142no—
757C2×C4—142no—
758C2×C4—142no—
759C2×C4—288no—
760C2×C4—288no—
761C2×C4—288no—
762C2×C4—288no—
763C2×C4—282no—
764C2×C4—282no—
765C2×C4—282no—
766C2×C4—288no—
767C2×C4—282no—
768C2×C4—282no—
769C2×C4C22×D2812yes—
770C2×C4C22×D2812yes—
771C2×C4C22×D2812yes—
772C2×C4C22×D2812yes—
773C2×C4C22×D2811yescharacteristic
774C2×C4#654812yes—
775C2×C4D7×#4112yes—
776C2×C4C24×D711yescharacteristic
777C8—22no—
778C8—22no—
779C8—22no—
780C8—22no—
781C7C2×#330811yescharacteristic, complemented, Sylow
782C22—28no—
783C22—22no—
784C22—22no—
785C22—22no—
786C22—22no—
787C22—22no—
788C22—44no—
789C22—282no—
790C22—282no—
791C22—282no—
792C22—282no—
793C22—282no—
794C22—282no—
795C22—564no—
796C22—564no—
797C22#9024512yes—
798C22C2×#647114yes—
799C22C2×#647112yes—
800C22#9044412yes—
801C22C23×D2811yescharacteristic
802C4—22no—
803C4—22no—
804C4—22no—
805C4—22no—
806C4—144no—
807C4—282no—
808C4—282no—
809C4—282no—
810C4—282no—
811C4—282no—
812C4#9024512yes—
813C4C2×#654811yescharacteristic
814C4C2×D7×#4111yescharacteristic
815C2—24no—
816C2—42no—
817C2—562no—
818C2—562no—
819C2#1173695414yesdirect product factor
820C2C2×#9024511yescharacteristic
821C2C22×#647111yescharacteristic
822C2C2×#9044411yescharacteristic
subgroupG/H
centerC23C22×D28
commutator, cosocleC2×C4×C7C25
FrattiniC2×C4C24×D7
FittingC2×C7×#435C2
socleC23×C7C22×D4
hypercenterC2×#435D7
hypocenterC7C2×#3308
LCSG ▷ C2×C4×C7 ▷ C2×C7 ▷ C7
UCSC1 ◁ C23 ◁ C2×C4×D4 ◁ C2×#435

Complements

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

NH ≅ G/Ntype
1. C2×#90243C2semidirect
2. C2×#90246C2semidirect
3. C2×C7×#435C2semidirect
4. C2×#89906C2semidirect
5. C2×#89905C2semidirect
6. C22×#6390C2semidirect
7. C2×#89887C2semidirect
8. #11736954C2direct (N × H)
9. C2×#89622C2semidirect
10. C2×#89616C2semidirect
11. C2×#89510C2semidirect
12. C2×#89506C2semidirect
13. C2×#89494C2semidirect
14. C2×#89508C2semidirect
15. C2×#89486C2semidirect
16. C2×#89482C2semidirect
34. #90246C22semidirect
36. #90243C22semidirect
47. C7×#435C22semidirect
52. #89906C22semidirect
53. #89905C22semidirect
54. #89887C22semidirect
68. C2×#6390C22semidirect
69. #89622C22semidirect
70. #89616C22semidirect
71. #89510C22semidirect
72. #89508C22semidirect
73. #89506C22semidirect
74. #89494C22semidirect
75. #89486C22semidirect
76. #89482C22semidirect
200. C2×#435D7semidirect
270. C2×Dic14#41semidirect
352. #435C2×D7semidirect
442. Dic14C2×#41semidirect
700. C2×C7#3308semidirect
781. C7C2×#3308semidirect
819. C2#11736954direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#902432
C2×#902462
C2×C7×#4352
C2×#899062
C2×#899052
C22×#63902
C2×#898872
#117369542
C2×#896222
C2×#896162
C2×#895102
C2×#895062
C2×#894942
C2×#895082
C2×#894862
C2×#894822
C2×#33087