Finite Group Databasebeta

← C2×#11741017 #14230498

Subgroups — C2×#11741017 #14230498

Order 1792.

2242 conjugacy classes of subgroups.

The subgroup lattice has 836 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C7×#550C211yesmaximal, characteristic, complemented
2C2×#90256C211yesmaximal, characteristic, complemented
3C2×#90010C211yesmaximal, characteristic, complemented
4C2×#90010C211yesmaximal, characteristic, complemented
5C2×#90004C211yesmaximal, characteristic, complemented
6C2×#90005C211yesmaximal, characteristic, complemented
7#11741017C2116yesmaximal, direct product factor
8C2×#89844C211yesmaximal, characteristic, complemented
9C2×#89843C211yesmaximal, characteristic, complemented
10C2×#89811C211yesmaximal, characteristic, complemented
11C2×#89810C211yesmaximal, characteristic, complemented
12C2×#89807C211yesmaximal, characteristic, complemented
13C2×#89805C211yesmaximal, characteristic, complemented
14C2×#89798C211yesmaximal, characteristic, complemented
15C2×#89794C211yesmaximal, characteristic, complemented
16C2×#89783C211yesmaximal, characteristic, complemented
17C22×C7×#41C2211yescharacteristic
18C22×C7×#41C2211yescharacteristic
19C7×#550—24no—
20C7×#550C2218yescomplemented
21C2×C7×#127—21no—
22C2×C7×#127C2211yescharacteristic
23C2×C7×#121—21no—
24C2×C7×#121—21no—
25C2×C7×#121C2211yescharacteristic
26C2×C7×#121C2211yescharacteristic
27C2×C4×C7×Q8C2211yescharacteristic
28C2×C4×C7×D4—21no—
29C2×C4×C7×D4C2211yescharacteristic
30C22×#1143C2211yescharacteristic
31C2×#6502—21no—
32C22×#1141C2211yescharacteristic
33C22×#1141C2211yescharacteristic
34C2×#6493C2211yescharacteristic
35C2×#6493C2211yescharacteristic
36C2×#6489C2211yescharacteristic
37C22×C4⋊Dic7C2211yescharacteristic
38C22×#1136C2211yescharacteristic
39C23×C7⋊C8C2211yescharacteristic
40#90256—24no—
41#90256C2218yescomplemented
42C2×#6461—21no—
43C2×#6446—21no—
44C2×(C22⋊D7)⋊C4—21no—
45C2×C4×D28C2211yescharacteristic
46C2×#6433C2211yescharacteristic
47#90010C2218yescomplemented
48#90010C2218yescomplemented
49#90005C2218yescomplemented
50#90004C2218yescomplemented
51C2×#6409C2211yescharacteristic
52C2×#6409C2211yescharacteristic
53C2×#6409C2211yescharacteristic
54C2×#6406C2211yescharacteristic
55C2×#6406C2211yescharacteristic
56C2×#6406C2211yescharacteristic
57C2×#6406C2211yescharacteristic
58C2×#6406C2211yescharacteristic
59C2×#6406C2211yescharacteristic
60C2×C22⋊(C7⋊C8)C2211yescharacteristic
61C2×C22⋊(C7⋊C8)C2211yescharacteristic
62#89844C2218yescomplemented
63#89843C2218yescomplemented
64#89811C2218yescomplemented
65#89810C2218yescomplemented
66#89807C2218yescomplemented
67#89805C2218yescomplemented
68#89798C2218yescomplemented
69#89794C2218yescomplemented
70#89783C2218yescomplemented
71C2×#6383C2211yescharacteristic
72C2×#6382C2211yescharacteristic
73C2×#6381C2211yescharacteristic
74C2×#6381C2211yescharacteristic
75C2×C4⋊(C7⋊C8)C2211yescharacteristic
76C2×#6377C2211yescharacteristic
77C2×#3309—71nomaximal, Sylow
78C2×C7×#41—22no—
79C2×C7×#41—22no—
80C2×C7×#41—24no—
81C2×C7×#41—24no—
82C2×C7×#41—42no—
83C2×C7×#41—42no—
84C2×C7×#41C2314yes—
85C2×C7×#41C2314yes—
86C22×C7×Q8C2311yescharacteristic
87C22×C7×D4—21no—
88C22×C7×D4—21no—
89C22×C7×D4—21no—
90C22×C7×D4—21no—
91C22×C7×D4—21no—
92C22×C7×D4—21no—
93C22×C7×D4D411yescharacteristic
94C22×C7×D4C2311yescharacteristic
95C22×C7×D4C2311yescharacteristic
96C23×C4×C7—21no—
97C23×C4×C7—21no—
98C23×C4×C7C2311yescharacteristic
99C23×C4×C7C2311yescharacteristic
100C22×C22⋊D7—21no—
101C22×C22⋊D7—21no—
102C23×Dic7—21no—
103C22×D28C2311yescharacteristic
104C22×C4×D7—21no—
105C7×#127—28no—
106C7×#127—22no—
107C7×#127C2314yes—
108C7×#121—22no—
109C7×#121—22no—
110C7×#121—28no—
111C7×#121—28no—
112C7×#121C2314yes—
113C7×#121C2314yes—
114C4×C7×Q8—22no—
115C4×C7×Q8C2314yes—
116C4×C7×D4—28no—
117C4×C7×D4D414yes—
118C4×C7×D4C2314yes—
119C2×C7×C4⋊C4—21no—
120C2×C7×C4⋊C4D411yescharacteristic
121C2×C7×C4⋊C4C2311yescharacteristic
122C2×C7×C22⋊C4—21no—
123C2×C7×C22⋊C4—21no—
124C2×C7×C22⋊C4D411yescharacteristic
125C2×C7×C22⋊C4D411yescharacteristic
126C2×C42×C7—21no—
127C2×C42×C7C2311yescharacteristic
128C2×C22⋊Dic7—21no—
129C2×#1143—24no—
130C2×#1143C2314yes—
131#6502—28no—
132C2×#1141—42no—
133C2×#1141—42no—
134C2×#1141C2314yes—
135C2×#1141C2314yes—
136#6493—22no—
137#6493—22no—
138#6493C2314yes—
139#6493C2314yes—
140C2×(C2×D7)⋊C4—21no—
141C2×(C2×D7)⋊C4—21no—
142C2×(C2×D7)⋊C4—21no—
143#6489—22no—
144#6489C2314yes—
145C2×C4⋊Dic7—21no—
146C2×C4⋊Dic7—22no—
147C2×C4⋊Dic7C2311yescharacteristic
148C2×C4⋊Dic7C2311yescharacteristic
149C2×C4⋊Dic7C2311yescharacteristic
150C2×C4⋊Dic7C2314yes—
151C2×Dic7⋊C4—21no—
152C2×Dic7⋊C4—21no—
153C2×C4×Dic7—21no—
154C2×#1136—42no—
155C2×#1136C2314yes—
156C22×C7⋊C8—42no—
157C22×C7⋊C8C2311yescharacteristic
158C22×C7⋊C8C2311yescharacteristic
159C22×C7⋊C8C2311yescharacteristic
160C22×C7⋊C8C2311yescharacteristic
161C22×C7⋊C8C2314yes—
162#6461—28no—
163#6446—28no—
164(C22⋊D7)⋊C4—28no—
165C4×D28—22no—
166C4×D28C2314yes—
167#6433—22no—
168#6433C2314yes—
169#6409C2314yes—
170#6409C2314yes—
171#6409C2314yes—
172#6406C2314yes—
173#6406C2314yes—
174#6406C2314yes—
175#6406C2314yes—
176#6406C2314yes—
177#6406C2314yes—
178C22⋊(C7⋊C8)C2314yes—
179C22⋊(C7⋊C8)C2314yes—
180#6383C2314yes—
181#6382C2314yes—
182#6381C2314yes—
183#6381C2314yes—
184C4⋊(C7⋊C8)C2314yes—
185#6377C2314yes—
186C2×#553—71no—
187C2×#550D711yescharacteristic, complemented
188#3309—716no—
189C2×#490—71no—
190C2×#482—71no—
191C2×#480—71no—
192C2×#479—71no—
193C2×#469—71no—
194C2×#466—71no—
195C2×#459—71no—
196C2×#449—71no—
197C2×#449—71no—
198C2×#440—71no—
199C2×#435—71no—
200C2×#417—71no—
201C2×#416—71no—
202C24×C7—21no—
203C24×C7—21no—
204C24×C7C2×D411yescharacteristic
205C24×C7C2×D411yescharacteristic
206C23×D7—21no—
207C7×#41—28no—
208C7×#41—28no—
209C7×#41—44no—
210C7×#41—44no—
211C7×#41—48no—
212C7×#41—48no—
213C2×C7×Q8—21no—
214C2×C7×Q8—22no—
215C2×C7×Q8#4114yes—
216C2×C7×Q8C2412yes—
217C2×C7×D4—24no—
218C2×C7×D4—24no—
219C2×C7×D4—24no—
220C2×C7×D4—24no—
221C2×C7×D4—24no—
222C2×C7×D4—21no—
223C2×C7×D4—21no—
224C2×C7×D4—24no—
225C2×C7×D4—22no—
226C2×C7×D4—22no—
227C2×C7×D4—22no—
228C2×C7×D4—22no—
229C2×C7×D4—42no—
230C2×C7×D4—44no—
231C2×C7×D4—44no—
232C2×C7×D4—44no—
233C2×C7×D4—82no—
234C2×C7×D4—82no—
235C2×C7×D4—82no—
236C2×C7×D4C2×D414yes—
237C2×C7×D4C2412yes—
238C2×C7×D4C2412yes—
239C22×C4×C7—21no—
240C22×C4×C7—22no—
241C22×C4×C7—22no—
242C22×C4×C7—22no—
243C22×C4×C7—22no—
244C22×C4×C7—21no—
245C22×C4×C7—24no—
246C22×C4×C7—24no—
247C22×C4×C7—44no—
248C22×C4×C7—44no—
249C22×C4×C7C2×D411yescharacteristic
250C22×C4×C7C2×D411yescharacteristic
251C22×C4×C7C2×D411yescharacteristic
252C22×C4×C7C2×D411yescharacteristic
253C22×C4×C7C2×D412yes—
254C22×C4×C7C2×D412yes—
255C22×C4×C7C2412yes—
256C22×C4×C7C2412yes—
257C22×C4×C7C2411yescharacteristic
258C2×C22⋊D7—24no—
259C2×C22⋊D7—24no—
260C2×C22⋊D7—44no—
261C2×C22⋊D7—82no—
262C22×Dic7—21no—
263C22×Dic7—21no—
264C22×Dic7—21no—
265C22×Dic7—24no—
266C22×Dic7—82no—
267C2×D28—22no—
268C2×D28—22no—
269C2×D28—21no—
270C2×D28C2412yes—
271C2×C4×D7—24no—
272C2×C4×D7—82no—
273C7×C4⋊C4—24no—
274C7×C4⋊C4—21no—
275C7×C4⋊C4C2×D414yes—
276C7×C4⋊C4C2412yes—
277C7×C22⋊C4—24no—
278C7×C22⋊C4—24no—
279C7×C22⋊C4C2×D414yes—
280C7×C22⋊C4C2×D414yes—
281C42×C7—24no—
282C42×C7C2×D412yes—
283C42×C7C2412yes—
284C22⋊Dic7—24no—
285#1143—28no—
286#1141—44no—
287#1141—44no—
288(C2×D7)⋊C4—24no—
289(C2×D7)⋊C4—24no—
290(C2×D7)⋊C4—24no—
291C4⋊Dic7—21no—
292C4⋊Dic7—21no—
293C4⋊Dic7—21no—
294C4⋊Dic7—24no—
295C4⋊Dic7C2412yes—
296C4⋊Dic7C2412yes—
297C4⋊Dic7C2412yes—
298Dic7⋊C4—24no—
299Dic7⋊C4—24no—
300C4×Dic7—24no—
301#1136—44no—
302C2×C7⋊C8—22no—
303C2×C7⋊C8—22no—
304C2×C7⋊C8—22no—
305C2×C7⋊C8—22no—
306C2×C7⋊C8—44no—
307C2×C7⋊C8C2412yes—
308C2×C7⋊C8C2412yes—
309C2×C7⋊C8C2412yes—
310C2×C7⋊C8C2412yes—
311C22×#41C2×D711yescharacteristic
312C22×#41C2×D711yescharacteristic
313C22×SD16—71no—
314C22×D8—71no—
315C22×D8—71no—
316C22×M16—71no—
317C23×C8—71no—
318#553—78no—
319#553—144no—
320#550—24no—
321#550C2×D718yescomplemented
322C2×#127—21no—
323C2×#127C2×D711yescharacteristic
324C2×#126—141no—
325C2×#125—71no—
326C2×#123—141no—
327C2×#121—21no—
328C2×#121—21no—
329C2×#121—71no—
330C2×#121—71no—
331C2×#121—141no—
332C2×#121C2×D711yescharacteristic
333C2×#121C2×D711yescharacteristic
334C2×C4×Q8C2×D711yescharacteristic
335C2×C4×D4—21no—
336C2×C4×D4—71no—
337C2×C4×D4—141no—
338C2×C4×D4C2×D711yescharacteristic
339C2×#117—71no—
340C22×C4⋊C4—71no—
341#490—78no—
342#482—78no—
343#480—78no—
344#479—78no—
345#469—78no—
346#466—78no—
347#459—78no—
348#449—78no—
349#449—78no—
350#440—78no—
351#435—78no—
352C2×#107—71no—
353C2×#107—71no—
354C2×#106—71no—
355C2×C4⋊C8—71no—
356#417—78no—
357#416—78no—
358C2×#103—71no—
359C2×#103—71no—
360C2×#103—71no—
361C2×#102—71no—
362C2×#102—71no—
363C2×#102—71no—
364C2×#102—71no—
365C2×#102—71no—
366C2×#102—71no—
367C2×#102—71no—
368C2×C22⋊C8—71no—
369C2×C22⋊C8—71no—
370C2×#97—71no—
371C23×C7—22no—
372C23×C7—22no—
373C23×C7—22no—
374C23×C7—22no—
375C23×C7—22no—
376C23×C7—22no—
377C23×C7—22no—
378C23×C7—22no—
379C23×C7—42no—
380C23×C7—42no—
381C23×C7—42no—
382C23×C7—42no—
383C23×C7—42no—
384C23×C7—42no—
385C23×C7C22×D412yes—
386C23×C7C22×D412yes—
387C23×C7C22×D411yescharacteristic
388C22×D7—22no—
389C22×D7—42no—
390C22×D7—42no—
391C22×D7—42no—
392C7×Q8—24no—
393C7×Q8—22no—
394C7×Q8C2×#4114yes—
395C7×D4—22no—
396C7×D4—22no—
397C7×D4—22no—
398C7×D4—22no—
399C7×D4—44no—
400C7×D4—48no—
401C7×D4—48no—
402C7×D4—48no—
403C7×D4—42no—
404C7×D4—42no—
405C7×D4—84no—
406C7×D4—84no—
407C7×D4—84no—
408C2×C4×C7—22no—
409C2×C4×C7—22no—
410C2×C4×C7—24no—
411C2×C4×C7—22no—
412C2×C4×C7—22no—
413C2×C4×C7—22no—
414C2×C4×C7—24no—
415C2×C4×C7—24no—
416C2×C4×C7—22no—
417C2×C4×C7—22no—
418C2×C4×C7—22no—
419C2×C4×C7—22no—
420C2×C4×C7—22no—
421C2×C4×C7—48no—
422C2×C4×C7—48no—
423C2×C4×C7—42no—
424C2×C4×C7C22×D412yes—
425C2×C4×C7C22×D412yes—
426C2×C4×C7C22×D412yes—
427C2×C4×C7C22×D412yes—
428C2×C4×C7C22×D411yescharacteristic
429C2×C4×C7C2×#4112yes—
430C2×C4×C7H(5,𝔽2)12yes—
431C2×C4×C7C2511yescharacteristic
432C22⋊D7—48no—
433C22⋊D7—84no—
434C2×Dic7—22no—
435C2×Dic7—22no—
436C2×Dic7—22no—
437C2×Dic7—42no—
438C2×Dic7—42no—
439C2×Dic7—42no—
440C2×Dic7—84no—
441D28—22no—
442D28—22no—
443D28—42no—
444C4×D7—84no—
445C7⋊C8—22no—
446C7⋊C8—22no—
447C7⋊C8—22no—
448C7⋊C8—22no—
449C2×#41—22no—
450C2×#41—22no—
451C2×#41—24no—
452C2×#41—24no—
453C2×#41—42no—
454C2×#41—42no—
455C2×#41C22×D714yes—
456C2×#41C22×D714yes—
457C22×Q8C22×D711yescharacteristic
458C22×D4—21no—
459C22×D4—21no—
460C22×D4—21no—
461C22×D4—21no—
462C22×D4—21no—
463C22×D4—21no—
464C22×D4—71no—
465C22×D4—141no—
466C22×D4—141no—
467C22×D4C22⋊D711yescharacteristic
468C22×D4C22×D711yescharacteristic
469C22×D4C22×D711yescharacteristic
470C23×C4—21no—
471C23×C4—21no—
472C23×C4—141no—
473C23×C4—141no—
474C23×C4C22×D711yescharacteristic
475C23×C4C22×D711yescharacteristic
476C2×SD16—74no—
477C2×SD16—144no—
478C2×D8—74no—
479C2×D8—74no—
480C2×D8—282no—
481C2×D8—282no—
482C2×M16—74no—
483C2×M16—282no—
484C22×C8—71no—
485C22×C8—71no—
486C22×C8—71no—
487C22×C8—71no—
488C22×C8—74no—
489C22×C8—282no—
490#127—28no—
491#127—22no—
492#127C22×D714yes—
493#126—148no—
494#125—74no—
495#125—142no—
496#123—148no—
497#121—22no—
498#121—22no—
499#121—28no—
500#121—28no—
501#121—74no—
502#121—74no—
503#121—148no—
504#121—142no—
505#121—142no—
506#121C22×D714yes—
507#121C22×D714yes—
508C4×Q8—22no—
509C4×Q8C22×D714yes—
510C4×D4—28no—
511C4×D4—74no—
512C4×D4—148no—
513C4×D4—142no—
514C4×D4C22⋊D714yes—
515C4×D4C22×D714yes—
516#117—74no—
517#117—142no—
518C2×C4⋊C4—21no—
519C2×C4⋊C4—71no—
520C2×C4⋊C4—71no—
521C2×C4⋊C4—74no—
522C2×C4⋊C4—71no—
523C2×C4⋊C4—141no—
524C2×C4⋊C4—142no—
525C2×C4⋊C4—141no—
526C2×C4⋊C4—141no—
527C2×C4⋊C4C22⋊D711yescharacteristic
528C2×C4⋊C4C22×D711yescharacteristic
529C2×C22⋊C4—21no—
530C2×C22⋊C4—21no—
531C2×C22⋊C4—141no—
532C2×C22⋊C4—141no—
533C2×C22⋊C4—141no—
534C2×C22⋊C4—141no—
535C2×C22⋊C4C22⋊D711yescharacteristic
536C2×C22⋊C4C22⋊D711yescharacteristic
537C2×C42—21no—
538C2×C42—141no—
539C2×C42C22×D711yescharacteristic
540#107—74no—
541#107—74no—
542#106—74no—
543C4⋊C8—74no—
544#103—74no—
545#103—74no—
546#103—74no—
547#102—74no—
548#102—74no—
549#102—74no—
550#102—74no—
551#102—74no—
552#102—74no—
553#102—74no—
554C22⋊C8—74no—
555C22⋊C8—74no—
556#97—74no—
557C22×C7—22no—
558C22×C7—22no—
559C22×C7—22no—
560C22×C7—22no—
561C22×C7—22no—
562C22×C7—22no—
563C22×C7—44no—
564C22×C7—44no—
565C22×C7—42no—
566C22×C7—42no—
567C22×C7—42no—
568C22×C7—42no—
569C22×C7—42no—
570C22×C7—42no—
571C22×C7—84no—
572C22×C7—84no—
573C22×C7#54612yes—
574C22×C7#57512yes—
575C22×C7#57612yes—
576C22×C7C23×D411yescharacteristic
577C2×D7—42no—
578C2×D7—42no—
579C2×D7—42no—
580C2×D7—84no—
581C4×C7—22no—
582C4×C7—22no—
583C4×C7—24no—
584C4×C7—22no—
585C4×C7—22no—
586C4×C7—42no—
587C4×C7#54612yes—
588C4×C7C22×#4111yescharacteristic
589C4×C7C2×H(5,𝔽2)11yescharacteristic
590Dic7—42no—
591Dic7—42no—
592Dic7—42no—
593C24—21no—
594C24—21no—
595C24—141no—
596C24C2×C22⋊D711yescharacteristic
597C24C2×C22⋊D711yescharacteristic
598#41—28no—
599#41—28no—
600#41—44no—
601#41—44no—
602#41—48no—
603#41—48no—
604C2×Q8—22no—
605C2×Q8—21no—
606C2×Q8#115914yes—
607C2×Q8C23×D712yes—
608C2×D4—24no—
609C2×D4—24no—
610C2×D4—24no—
611C2×D4—24no—
612C2×D4—22no—
613C2×D4—22no—
614C2×D4—22no—
615C2×D4—22no—
616C2×D4—24no—
617C2×D4—21no—
618C2×D4—21no—
619C2×D4—24no—
620C2×D4—42no—
621C2×D4—44no—
622C2×D4—44no—
623C2×D4—44no—
624C2×D4—72no—
625C2×D4—82no—
626C2×D4—82no—
627C2×D4—82no—
628C2×D4—144no—
629C2×D4—144no—
630C2×D4—142no—
631C2×D4—142no—
632C2×D4—141no—
633C2×D4—284no—
634C2×D4—562no—
635C2×D4C2×C22⋊D714yes—
636C2×D4C23×D712yes—
637C2×D4C23×D712yes—
638C22×C4—21no—
639C22×C4—22no—
640C22×C4—22no—
641C22×C4—22no—
642C22×C4—22no—
643C22×C4—21no—
644C22×C4—24no—
645C22×C4—24no—
646C22×C4—44no—
647C22×C4—44no—
648C22×C4—141no—
649C22×C4—141no—
650C22×C4—141no—
651C22×C4—144no—
652C22×C4—144no—
653C22×C4—562no—
654C22×C4—562no—
655C22×C4C2×C22⋊D712yes—
656C22×C4C2×C22⋊D712yes—
657C22×C4C2×C22⋊D711yescharacteristic
658C22×C4C2×C22⋊D711yescharacteristic
659C22×C4C2×C22⋊D711yescharacteristic
660C22×C4C2×C22⋊D711yescharacteristic
661C22×C4C23×D712yes—
662C22×C4C23×D712yes—
663C22×C4C23×D711yescharacteristic
664SD16—148no—
665D8—284no—
666D8—284no—
667M16—284no—
668C2×C8—72no—
669C2×C8—72no—
670C2×C8—72no—
671C2×C8—72no—
672C2×C8—142no—
673C2×C8—142no—
674C2×C8—142no—
675C2×C8—142no—
676C2×C8—284no—
677C4⋊C4—24no—
678C4⋊C4—21no—
679C4⋊C4—72no—
680C4⋊C4—72no—
681C4⋊C4—72no—
682C4⋊C4—144no—
683C4⋊C4—144no—
684C4⋊C4—141no—
685C4⋊C4—141no—
686C4⋊C4—144no—
687C4⋊C4—141no—
688C4⋊C4C2×C22⋊D714yes—
689C4⋊C4C23×D712yes—
690C22⋊C4—24no—
691C22⋊C4—24no—
692C22⋊C4—144no—
693C22⋊C4—144no—
694C22⋊C4—144no—
695C22⋊C4—144no—
696C22⋊C4C2×C22⋊D714yes—
697C22⋊C4C2×C22⋊D714yes—
698C42—24no—
699C42—144no—
700C42C2×C22⋊D712yes—
701C42C23×D712yes—
702C2×C7—42no—
703C2×C7—42no—
704C2×C7—82no—
705C2×C7—82no—
706C2×C7#330914yescomplemented
707C2×C7C2×#54611yescharacteristic
708C2×C7C2×#57511yescharacteristic
709C2×C7C2×#57611yescharacteristic
710D7—82no—
711C23—22no—
712C23—22no—
713C23—22no—
714C23—22no—
715C23—22no—
716C23—22no—
717C23—22no—
718C23—22no—
719C23—42no—
720C23—42no—
721C23—42no—
722C23—42no—
723C23—42no—
724C23—42no—
725C23—142no—
726C23—282no—
727C23—282no—
728C23—282no—
729C23C22×C22⋊D712yes—
730C23C22×C22⋊D712yes—
731C23C22×C22⋊D711yescharacteristic
732Q8—24no—
733Q8—22no—
734Q8C2×#115914yes—
735D4—22no—
736D4—22no—
737D4—22no—
738D4—22no—
739D4—44no—
740D4—48no—
741D4—48no—
742D4—48no—
743D4—42no—
744D4—42no—
745D4—84no—
746D4—84no—
747D4—84no—
748D4—142no—
749D4—142no—
750D4—288no—
751D4—282no—
752D4—564no—
753C2×C4—22no—
754C2×C4—22no—
755C2×C4—24no—
756C2×C4—22no—
757C2×C4—22no—
758C2×C4—22no—
759C2×C4—24no—
760C2×C4—24no—
761C2×C4—22no—
762C2×C4—22no—
763C2×C4—22no—
764C2×C4—22no—
765C2×C4—22no—
766C2×C4—48no—
767C2×C4—48no—
768C2×C4—42no—
769C2×C4—142no—
770C2×C4—142no—
771C2×C4—142no—
772C2×C4—282no—
773C2×C4—282no—
774C2×C4—282no—
775C2×C4—564no—
776C2×C4—564no—
777C2×C4C2×#115912yes—
778C2×C4#654812yes—
779C2×C4C22×C22⋊D712yes—
780C2×C4C22×C22⋊D712yes—
781C2×C4C22×C22⋊D712yes—
782C2×C4C22×C22⋊D712yes—
783C2×C4C22×C22⋊D711yescharacteristic
784C2×C4C24×D711yescharacteristic
785C8—142no—
786C8—142no—
787C8—142no—
788C8—142no—
789C7C2×#330911yescharacteristic, complemented, Sylow
790C22—22no—
791C22—22no—
792C22—22no—
793C22—22no—
794C22—22no—
795C22—22no—
796C22—44no—
797C22—44no—
798C22—42no—
799C22—42no—
800C22—42no—
801C22—42no—
802C22—42no—
803C22—42no—
804C22—84no—
805C22—84no—
806C22—282no—
807C22—282no—
808C22—282no—
809C22—564no—
810C22#9049712yes—
811C22#9051312yes—
812C22#9052612yes—
813C22C23×C22⋊D711yescharacteristic
814C4—22no—
815C4—22no—
816C4—24no—
817C4—22no—
818C4—22no—
819C4—42no—
820C4—282no—
821C4—282no—
822C4—282no—
823C4#9049712yes—
824C4C22×#115911yescharacteristic
825C4C2×#654811yescharacteristic
826C2—42no—
827C2—42no—
828C2—82no—
829C2—82no—
830C2—562no—
831C2#1174101714yesdirect product factor
832C2C2×#9049711yescharacteristic
833C2C2×#9051311yescharacteristic
834C2C2×#9052611yescharacteristic
subgroupG/H
centerC23C22×C22⋊D7
commutator, cosocleC2×C4×C7C25
FrattiniC2×C4C24×D7
FittingC2×C7×#550C2
socleC23×C7C22×D4
hypercenterC2×#550D7
hypocenterC7C2×#3309
LCSG ▷ C2×C4×C7 ▷ C2×C7 ▷ C7
UCSC1 ◁ C23 ◁ C2×C4×D4 ◁ C2×#550

Complements

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

NH ≅ G/Ntype
1. C2×C7×#550C2semidirect
2. C2×#90256C2semidirect
3. C2×#90010C2semidirect
4. C2×#90010C2semidirect
5. C2×#90004C2semidirect
6. C2×#90005C2semidirect
7. #11741017C2direct (N × H)
8. C2×#89844C2semidirect
9. C2×#89843C2semidirect
10. C2×#89811C2semidirect
11. C2×#89810C2semidirect
12. C2×#89807C2semidirect
13. C2×#89805C2semidirect
14. C2×#89798C2semidirect
15. C2×#89794C2semidirect
16. C2×#89783C2semidirect
20. C7×#550C22semidirect
41. #90256C22semidirect
47. #90010C22semidirect
48. #90010C22semidirect
49. #90005C22semidirect
50. #90004C22semidirect
62. #89844C22semidirect
63. #89843C22semidirect
64. #89811C22semidirect
65. #89810C22semidirect
66. #89807C22semidirect
67. #89805C22semidirect
68. #89798C22semidirect
69. #89794C22semidirect
70. #89783C22semidirect
187. C2×#550D7semidirect
321. #550C2×D7semidirect
706. C2×C7#3309semidirect
789. C7C2×#3309semidirect
831. C2#11741017direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C7×#5502
C2×#902562
C2×#900102
C2×#900042
C2×#900052
#117410172
C2×#898442
C2×#898432
C2×#898112
C2×#898102
C2×#898072
C2×#898052
C2×#897982
C2×#897942
C2×#897832
C2×#33097