Finite Group Databasebeta

← C2×#11736253 #14230215

Subgroups — C2×#11736253 #14230215

Order 1792.

2210 conjugacy classes of subgroups.

The subgroup lattice has 812 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#90508C211yesmaximal, characteristic, complemented
2C2×#90205C211yesmaximal, characteristic, complemented
3C22×C7×#103C211yesmaximal, characteristic, complemented
4C2×#89999C211yesmaximal, characteristic, complemented
5C2×#89887C211yesmaximal, characteristic, complemented
6C2×C8×C22⋊D7C211yesmaximal, characteristic, complemented
7C2×#89740C211yesmaximal, characteristic, complemented
8C2×#89591C211yesmaximal, characteristic, complemented
9#11736253C2116yesmaximal, direct product factor
10C2×#89579C211yesmaximal, characteristic, complemented
11C2×#89583C211yesmaximal, characteristic, complemented
12C2×#89576C211yesmaximal, characteristic, complemented
13C2×#89572C211yesmaximal, characteristic, complemented
14C2×#89586C211yesmaximal, characteristic, complemented
15C2×#89568C211yesmaximal, characteristic, complemented
16C2×#89560C211yesmaximal, characteristic, complemented
17C23×C7×Q8C2211yescharacteristic
18C22×#1161C2211yescharacteristic
19C23×C7×C8C2211yescharacteristic
20C22×C7×C4⋊C4C2211yescharacteristic
21#90508—24no—
22#90508C2218yescomplemented
23C2×#6510—21no—
24C2×#6510C2211yescharacteristic
25C2×#6509—21no—
26C2×#6509C2211yescharacteristic
27C2×Q8×Dic7C2211yescharacteristic
28C22×#1143C2211yescharacteristic
29C22×#1143C2211yescharacteristic
30C2×#6493—21no—
31C2×#6493—21no—
32C2×#6493C2211yescharacteristic
33C2×#6493C2211yescharacteristic
34C2×C4×C22⋊D7—21no—
35C2×C4×C22⋊D7—21no—
36C2×C4×C22⋊D7C2211yescharacteristic
37C22×D56C2211yescharacteristic
38C22×C8×D7C2211yescharacteristic
39#90205—24no—
40#90205C2218yescomplemented
41C2×#6461—21no—
42C2×#6458C2211yescharacteristic
43C2×#6457—21no—
44C2×#6456C2211yescharacteristic
45C2×#6455C2211yescharacteristic
46C2×#6453C2211yescharacteristic
47C2×C7×#103C2211yescharacteristic
48C2×C7×#103C2211yescharacteristic
49C2×C7×#103C2211yescharacteristic
50C2×C7×#103C2211yescharacteristic
51C2×C7×#103C2218yescomplemented
52#89999C2218yescomplemented
53C2×#6409C2211yescharacteristic
54C2×#6409C2211yescharacteristic
55C2×C22⋊(C7⋊C8)C2211yescharacteristic
56#89887C2218yescomplemented
57C2×#6395C2211yescharacteristic
58C2×#6395C2211yescharacteristic
59C8×C22⋊D7C2218yescomplemented
60C2×(C2×D7)⋊C8C2211yescharacteristic
61C2×#6392C2211yescharacteristic
62C2×Dic7⋊C8C2211yescharacteristic
63C2×C8×Dic7C2211yescharacteristic
64#89740C2218yescomplemented
65C2×#6383C2211yescharacteristic
66C2×#6383C2211yescharacteristic
67C2×#6382C2211yescharacteristic
68C2×#6382C2211yescharacteristic
69#89591C2218yescomplemented
70#89586C2218yescomplemented
71#89583C2218yescomplemented
72#89579C2218yescomplemented
73#89576C2218yescomplemented
74#89572C2218yescomplemented
75#89568C2218yescomplemented
76#89560C2218yescomplemented
77C2×#3301—71nomaximal, Sylow
78C22×C7×Q8—21no—
79C22×C7×Q8—22no—
80C22×C7×Q8—24no—
81C22×C7×Q8—42no—
82C22×C7×Q8C2311yescharacteristic
83C22×C7×Q8C2314yes—
84C22×C7×Q8C2311yescharacteristic
85C23×C4×C7—21no—
86C23×C4×C7—21no—
87C23×C4×C7C2311yescharacteristic
88C22×C22⋊D7—21no—
89C22×C22⋊D7—21no—
90C22×C22⋊D7D411yescharacteristic
91C2×#1161—22no—
92C2×#1161—24no—
93C2×#1161—42no—
94C2×#1161C2314yes—
95C22×D28—21no—
96C22×D28—21no—
97C22×D28C2311yescharacteristic
98C22×D28C2311yescharacteristic
99C22×C4×D7—21no—
100C22×C4×D7—21no—
101C22×C4×D7C2311yescharacteristic
102C22×C7×C8—42no—
103C22×C7×C8C2311yescharacteristic
104C22×C7×C8C2311yescharacteristic
105C22×C7×C8C2314yes—
106C2×C7×C4⋊C4—21no—
107C2×C7×C4⋊C4—22no—
108C2×C7×C4⋊C4C2311yescharacteristic
109C2×C7×C4⋊C4C2311yescharacteristic
110C2×C7×C4⋊C4C2314yes—
111C2×C22⋊Dic7D411yescharacteristic
112#6510—28no—
113#6510—22no—
114#6510C2314yes—
115#6509—22no—
116#6509—28no—
117#6509C2314yes—
118Q8×Dic7—22no—
119Q8×Dic7C2314yes—
120C2×#1143—24no—
121C2×#1143—42no—
122C2×#1143C2314yes—
123C2×#1143C2314yes—
124#6493—22no—
125#6493—22no—
126#6493—28no—
127#6493—28no—
128#6493C2314yes—
129#6493C2314yes—
130C4×C22⋊D7—28no—
131C4×C22⋊D7—28no—
132C4×C22⋊D7D414yes—
133C4×C22⋊D7C2314yes—
134C2×(C2×D7)⋊C4—21no—
135C2×(C2×D7)⋊C4—21no—
136C2×(C2×D7)⋊C4—21no—
137C2×(C2×D7)⋊C4—21no—
138C2×(C2×D7)⋊C4—21no—
139C2×(C2×D7)⋊C4—21no—
140C2×(C2×D7)⋊C4—21no—
141C2×(C2×D7)⋊C4—21no—
142C2×(C2×D7)⋊C4D411yescharacteristic
143C2×C4⋊Dic7—21no—
144C2×C4⋊Dic7—21no—
145C2×C4⋊Dic7C2311yescharacteristic
146C2×C4⋊Dic7C2311yescharacteristic
147C2×Dic7⋊C4—21no—
148C2×Dic7⋊C4—21no—
149C2×Dic7⋊C4D411yescharacteristic
150C2×C4×Dic7—21no—
151C2×C4×Dic7—21no—
152C2×C4×Dic7C2311yescharacteristic
153C22×C7⋊C8C2311yescharacteristic
154C22×C7⋊C8C2311yescharacteristic
155C2×D56—42no—
156C2×D56C2314yes—
157C2×C8×D7—42no—
158C2×C8×D7C2314yes—
159#6461—28no—
160#6458—22no—
161#6458C2314yes—
162#6457—28no—
163#6456—22no—
164#6456C2314yes—
165#6455—22no—
166#6455C2314yes—
167#6453—22no—
168#6453C2314yes—
169C7×#103C2314yes—
170C7×#103C2314yes—
171C7×#103C2314yes—
172C7×#103C2314yes—
173#6409C2314yes—
174#6409C2314yes—
175C22⋊(C7⋊C8)C2314yes—
176#6395C2314yes—
177#6395C2314yes—
178(C2×D7)⋊C8C2314yes—
179#6392C2314yes—
180Dic7⋊C8C2314yes—
181C8×Dic7C2314yes—
182#6383C2314yes—
183#6383C2314yes—
184#6382C2314yes—
185#6382C2314yes—
186C2×#553—71no—
187C2×#548—71no—
188#3301—716no—
189C2×#488—71no—
190C2×#481—71no—
191C2×#485—71no—
192C2×#479—71no—
193C2×#466—71no—
194C2×#465—71no—
195C2×#463—71no—
196C2×#449—71no—
197C2×#448—71no—
198C2×C4×SD16—71no—
199C2×C8×D4—71no—
200C2×#416—71no—
201C22×#103D711yescharacteristic, complemented
202C24×C7C2×D411yescharacteristic
203C23×D7—21no—
204C23×D7—21no—
205C23×D7C2×D411yescharacteristic
206C2×C7×Q8—21no—
207C2×C7×Q8—24no—
208C2×C7×Q8—21no—
209C2×C7×Q8—22no—
210C2×C7×Q8—28no—
211C2×C7×Q8—22no—
212C2×C7×Q8—22no—
213C2×C7×Q8—44no—
214C2×C7×Q8—44no—
215C2×C7×Q8—48no—
216C2×C7×Q8#4114yes—
217C2×C7×Q8C2412yes—
218C2×C7×Q8C2412yes—
219C22×C4×C7—21no—
220C22×C4×C7—22no—
221C22×C4×C7—22no—
222C22×C4×C7—21no—
223C22×C4×C7—21no—
224C22×C4×C7—21no—
225C22×C4×C7—24no—
226C22×C4×C7—24no—
227C22×C4×C7—44no—
228C22×C4×C7—82no—
229C22×C4×C7C2×D411yescharacteristic
230C22×C4×C7C2×D412yes—
231C22×C4×C7C2412yes—
232C22×C4×C7C2411yescharacteristic
233C2×C22⋊D7—24no—
234C2×C22⋊D7—24no—
235C2×C22⋊D7—24no—
236C2×C22⋊D7—44no—
237C2×C22⋊D7—44no—
238C2×C22⋊D7C2×D414yes—
239C22×Dic7—21no—
240C22×Dic7—21no—
241C22×Dic7C2×D411yescharacteristic
242C22×Dic7C2×D411yescharacteristic
243C22×Dic7C2×D411yescharacteristic
244#1161—28no—
245#1161—44no—
246#1161—48no—
247C2×D28—22no—
248C2×D28—22no—
249C2×D28—22no—
250C2×D28—22no—
251C2×D28—24no—
252C2×D28—21no—
253C2×D28—21no—
254C2×D28—24no—
255C2×D28—44no—
256C2×D28—82no—
257C2×D28C2412yes—
258C2×D28C2412yes—
259C2×C4×D7—22no—
260C2×C4×D7—22no—
261C2×C4×D7—24no—
262C2×C4×D7—24no—
263C2×C4×D7—44no—
264C2×C4×D7—82no—
265C2×C4×D7C2×D412yes—
266C2×C4×D7C2412yes—
267C2×C7×C8—22no—
268C2×C7×C8—22no—
269C2×C7×C8—44no—
270C2×C7×C8C2412yes—
271C2×C7×C8C2412yes—
272C7×C4⋊C4—21no—
273C7×C4⋊C4—21no—
274C7×C4⋊C4—24no—
275C7×C4⋊C4C2412yes—
276C7×C4⋊C4C2412yes—
277C22⋊Dic7C2×D414yes—
278#1143—28no—
279#1143—44no—
280(C2×D7)⋊C4—24no—
281(C2×D7)⋊C4—24no—
282(C2×D7)⋊C4—24no—
283(C2×D7)⋊C4—24no—
284(C2×D7)⋊C4—24no—
285(C2×D7)⋊C4—24no—
286(C2×D7)⋊C4—24no—
287(C2×D7)⋊C4—24no—
288(C2×D7)⋊C4C2×D414yes—
289C4⋊Dic7—21no—
290C4⋊Dic7—21no—
291C4⋊Dic7—24no—
292C4⋊Dic7—24no—
293C4⋊Dic7C2412yes—
294C4⋊Dic7C2412yes—
295Dic7⋊C4—24no—
296Dic7⋊C4—24no—
297Dic7⋊C4C2×D414yes—
298C4×Dic7—24no—
299C4×Dic7—24no—
300C4×Dic7C2×D412yes—
301C4×Dic7C2412yes—
302C2×C7⋊C8—22no—
303C2×C7⋊C8—22no—
304C2×C7⋊C8C2412yes—
305C2×C7⋊C8C2412yes—
306D56—44no—
307C8×D7—44no—
308C22×#41—71no—
309C23×Q8C2×D711yescharacteristic
310C22×SD16—71no—
311C22×SD16—71no—
312C22×D8—71no—
313C23×C8—71no—
314C23×C8C2×D711yescharacteristic
315#553—78no—
316#553—144no—
317#548—78no—
318#548—144no—
319C2×#126—141no—
320C2×#125—71no—
321C2×#124—71no—
322C2×#124—141no—
323C2×#123—141no—
324C2×C22⋊Q8—71no—
325C2×C22⋊Q8—141no—
326C2×#121—71no—
327C2×#121—71no—
328C2×#121—71no—
329C2×#121—141no—
330C2×#121—141no—
331C2×C4×Q8—71no—
332C2×C4×D4—71no—
333C2×C4×D4—71no—
334C2×C4×D4—141no—
335C2×C4×D4—141no—
336C2×#117—71no—
337C22×C4⋊C4C2×D711yescharacteristic
338#488—78no—
339#485—78no—
340#481—78no—
341#479—78no—
342#466—78no—
343#465—78no—
344#463—78no—
345#449—78no—
346#448—78no—
347C4×SD16—78no—
348C8×D4—78no—
349C2×#107—71no—
350C2×#106—71no—
351C2×#106—71no—
352C2×C4⋊C8—71no—
353#416—78no—
354C2×#103—71no—
355C2×#103—71no—
356C2×#103C2×D711yescharacteristic
357C2×#103C2×D711yescharacteristic
358C2×#103C2×D711yescharacteristic
359C2×#103C2×D711yescharacteristic
360C2×#103C2×D718yescomplemented
361C2×#102—71no—
362C2×#102—71no—
363C2×#102—71no—
364C2×#102—71no—
365C2×C22⋊C8—71no—
366C2×C22⋊C8—71no—
367C2×C4×C8—71no—
368C23×C7—22no—
369C23×C7—22no—
370C23×C7#13514yes—
371C23×C7C22×D412yes—
372C23×C7C22×D411yescharacteristic
373C22×D7—22no—
374C22×D7—22no—
375C22×D7—22no—
376C22×D7—22no—
377C22×D7—22no—
378C22×D7—42no—
379C22×D7—42no—
380C22×D7—42no—
381C22×D7—42no—
382C22×D7—42no—
383C22×D7—42no—
384C22×D7C22×D412yes—
385C7×Q8—24no—
386C7×Q8—22no—
387C7×Q8—22no—
388C7×Q8—22no—
389C7×Q8—48no—
390C7×Q8—42no—
391C7×Q8C2×#4114yes—
392C2×C4×C7—24no—
393C2×C4×C7—22no—
394C2×C4×C7—22no—
395C2×C4×C7—24no—
396C2×C4×C7—22no—
397C2×C4×C7—22no—
398C2×C4×C7—22no—
399C2×C4×C7—22no—
400C2×C4×C7—22no—
401C2×C4×C7—48no—
402C2×C4×C7—42no—
403C2×C4×C7—42no—
404C2×C4×C7—42no—
405C2×C4×C7—84no—
406C2×C4×C7C22×D412yes—
407C2×C4×C7C22×D411yescharacteristic
408C2×C4×C7C2×#4112yes—
409C2×C4×C7H(5,𝔽2)12yes—
410C2×C4×C7C2511yescharacteristic
411C22⋊D7—28no—
412C22⋊D7—48no—
413C22⋊D7—48no—
414C2×Dic7—22no—
415C2×Dic7—22no—
416C2×Dic7—22no—
417C2×Dic7—22no—
418C2×Dic7—22no—
419C2×Dic7—42no—
420C2×Dic7—42no—
421C2×Dic7C22×D412yes—
422C2×Dic7C22×D412yes—
423C2×Dic7C22×D412yes—
424D28—22no—
425D28—22no—
426D28—22no—
427D28—22no—
428D28—48no—
429D28—42no—
430D28—42no—
431D28—84no—
432C4×D7—24no—
433C4×D7—22no—
434C4×D7—22no—
435C4×D7—48no—
436C4×D7—84no—
437C7×C8—22no—
438C7×C8—22no—
439C7⋊C8—22no—
440C7⋊C8—22no—
441C2×#41—74no—
442C2×#41—142no—
443C2×#41—144no—
444C2×#41—282no—
445C22×Q8—21no—
446C22×Q8—22no—
447C22×Q8—24no—
448C22×Q8—42no—
449C22×Q8C22×D711yescharacteristic
450C22×Q8C22×D714yes—
451C22×Q8C22×D711yescharacteristic
452C22×D4—71no—
453C22×D4—71no—
454C22×D4—71no—
455C22×D4—141no—
456C22×D4—141no—
457C22×D4—141no—
458C22×D4—141no—
459C23×C4—21no—
460C23×C4—21no—
461C23×C4—71no—
462C23×C4—141no—
463C23×C4—141no—
464C23×C4C22×D711yescharacteristic
465C2×SD16—74no—
466C2×SD16—74no—
467C2×SD16—144no—
468C2×SD16—282no—
469C2×D8—74no—
470C2×D8—282no—
471C22×C8—42no—
472C22×C8—71no—
473C22×C8—71no—
474C22×C8—74no—
475C22×C8—282no—
476C22×C8C22×D711yescharacteristic
477C22×C8C22×D711yescharacteristic
478C22×C8C22×D714yes—
479#126—148no—
480#125—74no—
481#125—142no—
482#124—74no—
483#124—142no—
484#124—148no—
485#123—148no—
486C22⋊Q8—74no—
487C22⋊Q8—148no—
488C22⋊Q8—142no—
489#121—74no—
490#121—74no—
491#121—74no—
492#121—142no—
493#121—148no—
494#121—148no—
495#121—142no—
496#121—142no—
497C4×Q8—74no—
498C4×Q8—142no—
499C4×D4—74no—
500C4×D4—74no—
501C4×D4—74no—
502C4×D4—142no—
503C4×D4—148no—
504C4×D4—148no—
505#117—74no—
506#117—142no—
507C2×C4⋊C4—21no—
508C2×C4⋊C4—22no—
509C2×C4⋊C4—71no—
510C2×C4⋊C4—71no—
511C2×C4⋊C4—71no—
512C2×C4⋊C4—141no—
513C2×C4⋊C4—141no—
514C2×C4⋊C4—141no—
515C2×C4⋊C4—141no—
516C2×C4⋊C4C22×D711yescharacteristic
517C2×C4⋊C4C22×D711yescharacteristic
518C2×C4⋊C4C22×D714yes—
519C2×C22⋊C4—71no—
520C2×C22⋊C4—71no—
521C2×C22⋊C4—141no—
522C2×C22⋊C4—141no—
523C2×C22⋊C4—141no—
524C2×C22⋊C4—141no—
525C2×C22⋊C4—141no—
526C2×C22⋊C4—141no—
527C2×C22⋊C4—141no—
528C2×C22⋊C4—141no—
529C2×C42—71no—
530C2×C42—141no—
531C2×C42—141no—
532#107—74no—
533#106—74no—
534#106—74no—
535C4⋊C8—74no—
536#103—74no—
537#103—74no—
538#103C22×D714yes—
539#103C22×D714yes—
540#103C22×D714yes—
541#103C22×D714yes—
542#102—74no—
543#102—74no—
544#102—74no—
545#102—74no—
546C22⋊C8—74no—
547C22⋊C8—74no—
548C4×C8—74no—
549C22×C7—22no—
550C22×C7—28no—
551C22×C7—22no—
552C22×C7#54612yes—
553C22×C7C2×#13514yes—
554C22×C7C2×#13512yes—
555C22×C7#57712yes—
556C22×C7C23×D411yescharacteristic
557C2×D7—22no—
558C2×D7—22no—
559C2×D7—22no—
560C2×D7—44no—
561C2×D7—42no—
562C2×D7—42no—
563C2×D7—42no—
564C2×D7—42no—
565C2×D7—42no—
566C2×D7—42no—
567C2×D7—84no—
568C2×D7—84no—
569C4×C7—24no—
570C4×C7—22no—
571C4×C7—42no—
572C4×C7—42no—
573C4×C7—42no—
574C4×C7#54612yes—
575C4×C7C22×#4111yescharacteristic
576C4×C7C2×H(5,𝔽2)11yescharacteristic
577Dic7—22no—
578Dic7—22no—
579Dic7—22no—
580Dic7—42no—
581Dic7—42no—
582C24—71no—
583C24—141no—
584C24—141no—
585C24D4×D711yescharacteristic
586#41—148no—
587#41—284no—
588#41—288no—
589C2×Q8—21no—
590C2×Q8—24no—
591C2×Q8—21no—
592C2×Q8—22no—
593C2×Q8—28no—
594C2×Q8—22no—
595C2×Q8—22no—
596C2×Q8—44no—
597C2×Q8—44no—
598C2×Q8—48no—
599C2×Q8#115714yes—
600C2×Q8C23×D712yes—
601C2×Q8C23×D712yes—
602C2×D4—74no—
603C2×D4—72no—
604C2×D4—72no—
605C2×D4—144no—
606C2×D4—144no—
607C2×D4—144no—
608C2×D4—144no—
609C2×D4—144no—
610C2×D4—142no—
611C2×D4—142no—
612C2×D4—141no—
613C2×D4—141no—
614C2×D4—142no—
615C2×D4—142no—
616C2×D4—284no—
617C2×D4—284no—
618C2×D4—284no—
619C2×D4—562no—
620C22×C4—21no—
621C22×C4—22no—
622C22×C4—22no—
623C22×C4—24no—
624C22×C4—21no—
625C22×C4—21no—
626C22×C4—21no—
627C22×C4—24no—
628C22×C4—44no—
629C22×C4—71no—
630C22×C4—71no—
631C22×C4—71no—
632C22×C4—72no—
633C22×C4—72no—
634C22×C4—82no—
635C22×C4—144no—
636C22×C4—144no—
637C22×C4—142no—
638C22×C4—142no—
639C22×C4—141no—
640C22×C4—141no—
641C22×C4—284no—
642C22×C4—562no—
643C22×C4D4×D712yes—
644C22×C4D4×D711yescharacteristic
645C22×C4C23×D712yes—
646C22×C4C23×D711yescharacteristic
647SD16—148no—
648SD16—284no—
649D8—284no—
650C2×C8—22no—
651C2×C8—22no—
652C2×C8—44no—
653C2×C8—72no—
654C2×C8—72no—
655C2×C8—142no—
656C2×C8—142no—
657C2×C8—284no—
658C2×C8C23×D712yes—
659C2×C8C23×D712yes—
660C4⋊C4—21no—
661C4⋊C4—21no—
662C4⋊C4—24no—
663C4⋊C4—74no—
664C4⋊C4—72no—
665C4⋊C4—72no—
666C4⋊C4—144no—
667C4⋊C4—144no—
668C4⋊C4—144no—
669C4⋊C4—144no—
670C4⋊C4—141no—
671C4⋊C4—141no—
672C4⋊C4C23×D712yes—
673C4⋊C4C23×D712yes—
674C22⋊C4—74no—
675C22⋊C4—74no—
676C22⋊C4—144no—
677C22⋊C4—144no—
678C22⋊C4—144no—
679C22⋊C4—144no—
680C22⋊C4—144no—
681C22⋊C4—144no—
682C22⋊C4—144no—
683C22⋊C4—144no—
684C42—72no—
685C42—72no—
686C42—144no—
687C42—144no—
688C2×C7—24no—
689C2×C7#330114yescomplemented
690C2×C7C2×#54611yescharacteristic
691C2×C7C22×#13511yescharacteristic
692C2×C7C2×#57711yescharacteristic
693D7—42no—
694D7—82no—
695D7—82no—
696C23—22no—
697C23—22no—
698C23—72no—
699C23—142no—
700C23—142no—
701C23—142no—
702C23—142no—
703C23—142no—
704C23—282no—
705C23—282no—
706C23—282no—
707C23—282no—
708C23—282no—
709C23—282no—
710C23#648214yes—
711C23C2×D4×D712yes—
712C23C2×D4×D711yescharacteristic
713Q8—24no—
714Q8—22no—
715Q8—22no—
716Q8—22no—
717Q8—48no—
718Q8—42no—
719Q8C2×#115714yes—
720D4—148no—
721D4—142no—
722D4—142no—
723D4—142no—
724D4—142no—
725D4—288no—
726D4—288no—
727D4—288no—
728D4—282no—
729D4—282no—
730D4—564no—
731C2×C4—22no—
732C2×C4—24no—
733C2×C4—22no—
734C2×C4—24no—
735C2×C4—22no—
736C2×C4—22no—
737C2×C4—22no—
738C2×C4—22no—
739C2×C4—22no—
740C2×C4—48no—
741C2×C4—42no—
742C2×C4—42no—
743C2×C4—42no—
744C2×C4—72no—
745C2×C4—72no—
746C2×C4—72no—
747C2×C4—84no—
748C2×C4—142no—
749C2×C4—142no—
750C2×C4—142no—
751C2×C4—144no—
752C2×C4—142no—
753C2×C4—142no—
754C2×C4—142no—
755C2×C4—142no—
756C2×C4—288no—
757C2×C4—282no—
758C2×C4—282no—
759C2×C4—564no—
760C2×C4C2×#115712yes—
761C2×C4C2×D4×D712yes—
762C2×C4C2×D4×D711yescharacteristic
763C2×C4#654812yes—
764C2×C4C24×D711yescharacteristic
765C8—22no—
766C8—22no—
767C8—142no—
768C8—142no—
769C7C2×#330111yescharacteristic, complemented, Sylow
770C22—22no—
771C22—28no—
772C22—22no—
773C22—142no—
774C22—142no—
775C22—142no—
776C22—284no—
777C22—282no—
778C22—282no—
779C22—282no—
780C22—282no—
781C22—282no—
782C22—282no—
783C22—564no—
784C22—564no—
785C22#9018112yes—
786C22#9045312yes—
787C22C2×#648214yes—
788C22C2×#648212yes—
789C22C22×D4×D711yescharacteristic
790C4—22no—
791C4—24no—
792C4—42no—
793C4—42no—
794C4—42no—
795C4—142no—
796C4—142no—
797C4—142no—
798C4—282no—
799C4—282no—
800C4#9018112yes—
801C4C22×#115711yescharacteristic
802C4C2×#654811yescharacteristic
803C2—24no—
804C2—282no—
805C2—562no—
806C2—562no—
807C2#1173625314yesdirect product factor
808C2C2×#9018111yescharacteristic
809C2C2×#9045311yescharacteristic
810C2C22×#648211yescharacteristic
subgroupG/H
centerC23C2×D4×D7
commutator, cosocleC2×C4×C7C25
FrattiniC2×C4C24×D7
FittingC22×C7×#103C2
socleC23×C7C22×D4
hypercenterC22×#103D7
hypocenterC7C2×#3301
LCSG ▷ C2×C4×C7 ▷ C2×C7 ▷ C7
UCSC1 ◁ C23 ◁ C23×C4 ◁ C22×#103

Complements

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

NH ≅ G/Ntype
1. C2×#90508C2semidirect
2. C2×#90205C2semidirect
3. C22×C7×#103C2semidirect
4. C2×#89999C2semidirect
5. C2×#89887C2semidirect
6. C2×C8×C22⋊D7C2semidirect
7. C2×#89740C2semidirect
8. C2×#89591C2semidirect
9. #11736253C2direct (N × H)
10. C2×#89579C2semidirect
11. C2×#89583C2semidirect
12. C2×#89576C2semidirect
13. C2×#89572C2semidirect
14. C2×#89586C2semidirect
15. C2×#89568C2semidirect
16. C2×#89560C2semidirect
22. #90508C22semidirect
40. #90205C22semidirect
51. C2×C7×#103C22semidirect
52. #89999C22semidirect
56. #89887C22semidirect
59. C8×C22⋊D7C22semidirect
64. #89740C22semidirect
69. #89591C22semidirect
70. #89586C22semidirect
71. #89583C22semidirect
72. #89579C22semidirect
73. #89576C22semidirect
74. #89572C22semidirect
75. #89568C22semidirect
76. #89560C22semidirect
201. C22×#103D7semidirect
360. C2×#103C2×D7semidirect
689. C2×C7#3301semidirect
769. C7C2×#3301semidirect
807. C2#11736253direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#905082
C2×#902052
C22×C7×#1032
C2×#899992
C2×#898872
C2×C8×C22⋊D72
C2×#897402
C2×#895912
#117362532
C2×#895792
C2×#895832
C2×#895762
C2×#895722
C2×#895862
C2×#895682
C2×#895602
C2×#33017