Finite Group Databasebeta

← C2×#11736945 #14230436

Subgroups — C2×#11736945 #14230436

Order 1792.

2190 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×#90242C211yesmaximal, characteristic, complemented
2C2×#90256C211yesmaximal, characteristic, complemented
3C2×C7×#435C211yesmaximal, characteristic, complemented
4C2×#89906C211yesmaximal, characteristic, complemented
5C2×#89905C211yesmaximal, characteristic, complemented
6C2×#89886C211yesmaximal, characteristic, complemented
7C2×#89885C211yesmaximal, characteristic, complemented
8#11736945C2116yesmaximal, direct product factor
9C2×#89619C211yesmaximal, characteristic, complemented
10C2×#89613C211yesmaximal, characteristic, complemented
11C2×#89506C211yesmaximal, characteristic, complemented
12C2×#89506C211yesmaximal, characteristic, complemented
13C2×#89495C211yesmaximal, characteristic, complemented
14C2×#89493C211yesmaximal, characteristic, complemented
15C2×#89475C211yesmaximal, characteristic, complemented
16C2×#89483C211yesmaximal, characteristic, complemented
17C22×#1157C2211yescharacteristic
18C22×#1157C2211yescharacteristic
19C22×C7×M16C2211yescharacteristic
20C23×C7×C8C2211yescharacteristic
21C2×C4×C7×D4C2211yescharacteristic
22C2×#6502—21no—
23C2×#6501—21no—
24C2×#6493C2211yescharacteristic
25C2×#6493C2211yescharacteristic
26C2×#6489C2211yescharacteristic
27C22×C4⋊Dic7C2211yescharacteristic
28C2×#6487C2211yescharacteristic
29C2×#6487C2211yescharacteristic
30C22×D56C2211yescharacteristic
31C22×#1132C2211yescharacteristic
32C22×#1132C2211yescharacteristic
33#90256—24no—
34#90256C2218yescomplemented
35#90242—24no—
36#90242C2218yescomplemented
37C2×#6461—21no—
38C2×D7×C4⋊C4—21no—
39C2×#6446—21no—
40C2×#6446—21no—
41C2×#6446—21no—
42C2×(C22⋊D7)⋊C4—21no—
43C2×C4×D28C2211yescharacteristic
44C2×C4×D28C2211yescharacteristic
45C2×#6433C2211yescharacteristic
46C2×#6432C2211yescharacteristic
47C7×#435C2218yescomplemented
48C2×C7×C4⋊C8C2211yescharacteristic
49C2×C7×C22⋊C8C2211yescharacteristic
50C2×C7×C22⋊C8C2211yescharacteristic
51C2×C7×#97C2211yescharacteristic
52#89906C2218yescomplemented
53#89905C2218yescomplemented
54#89886C2218yescomplemented
55#89885C2218yescomplemented
56C2×#6395C2211yescharacteristic
57C2×#6395C2211yescharacteristic
58C2×#6395C2211yescharacteristic
59C2×#6395C2211yescharacteristic
60C2×#6392C2211yescharacteristic
61C2×#6391C2211yescharacteristic
62C2×#6391C2211yescharacteristic
63C2×#6390C2211yescharacteristic
64C2×#6390C2211yescharacteristic
65C2×#6390C2211yescharacteristic
66C2×#6390C2211yescharacteristic
67C2×#6390C2211yescharacteristic
68C2×#6390C2211yescharacteristic
69#89619C2218yescomplemented
70#89613C2218yescomplemented
71#89506C2218yescomplemented
72#89506C2218yescomplemented
73#89495C2218yescomplemented
74#89493C2218yescomplemented
75#89483C2218yescomplemented
76#89475C2218yescomplemented
77C2×#3307—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—
86C2×#1157—22no—
87C2×#1157—22no—
88C2×#1157—24no—
89C2×#1157—24no—
90C2×#1157—42no—
91C2×#1157—42no—
92C2×#1157C2314yes—
93C2×#1157C2314yes—
94C22×D28C2311yescharacteristic
95C22×D28C2311yescharacteristic
96C22×C4×D7—21no—
97C22×C4×D7—21no—
98C22×C4×D7—21no—
99C22×C4×D7—21no—
100C22×Dic14C2311yescharacteristic
101C22×Dic14C2311yescharacteristic
102C2×C7×M16—42no—
103C2×C7×M16C2314yes—
104C22×C7×C8—42no—
105C22×C7×C8C2311yescharacteristic
106C22×C7×C8C2311yescharacteristic
107C22×C7×C8C2311yescharacteristic
108C22×C7×C8C2311yescharacteristic
109C22×C7×C8C2314yes—
110C4×C7×D4D414yes—
111C4×C7×D4C2314yes—
112C2×C7×C4⋊C4D411yescharacteristic
113C2×C7×C22⋊C4D411yescharacteristic
114C2×C7×C22⋊C4D411yescharacteristic
115C2×C42×C7C2311yescharacteristic
116C2×C22⋊Dic7—21no—
117C2×C22⋊Dic7—21no—
118C2×C22⋊Dic7—21no—
119#6502—28no—
120#6501—28no—
121#6493—22no—
122#6493—22no—
123#6493C2314yes—
124#6493C2314yes—
125C2×(C2×D7)⋊C4—21no—
126C2×(C2×D7)⋊C4—21no—
127C2×(C2×D7)⋊C4—21no—
128C2×(C2×D7)⋊C4—21no—
129#6489—22no—
130#6489C2314yes—
131C2×C4⋊Dic7—21no—
132C2×C4⋊Dic7—21no—
133C2×C4⋊Dic7—21no—
134C2×C4⋊Dic7—22no—
135C2×C4⋊Dic7C2311yescharacteristic
136C2×C4⋊Dic7C2311yescharacteristic
137C2×C4⋊Dic7C2311yescharacteristic
138C2×C4⋊Dic7C2311yescharacteristic
139C2×C4⋊Dic7C2314yes—
140#6487—22no—
141#6487—22no—
142#6487C2314yes—
143#6487C2314yes—
144C2×Dic7⋊C4—21no—
145C2×Dic7⋊C4—21no—
146C2×Dic7⋊C4—21no—
147C2×Dic7⋊C4—21no—
148C2×C4×Dic7—21no—
149C2×D56—24no—
150C2×D56C2314yes—
151C2×#1132—42no—
152C2×#1132—42no—
153C2×#1132C2314yes—
154C2×#1132C2314yes—
155#6461—28no—
156D7×C4⋊C4—28no—
157#6446—28no—
158#6446—28no—
159#6446—28no—
160(C22⋊D7)⋊C4—28no—
161C4×D28—22no—
162C4×D28—22no—
163C4×D28C2314yes—
164C4×D28C2314yes—
165#6433—22no—
166#6433C2314yes—
167#6432—22no—
168#6432C2314yes—
169C7×C4⋊C8C2314yes—
170C7×C22⋊C8C2314yes—
171C7×C22⋊C8C2314yes—
172C7×#97C2314yes—
173#6395C2314yes—
174#6395C2314yes—
175#6395C2314yes—
176#6395C2314yes—
177#6392C2314yes—
178#6391C2314yes—
179#6391C2314yes—
180#6390C2314yes—
181#6390C2314yes—
182#6390C2314yes—
183#6390C2314yes—
184#6390C2314yes—
185#6390C2314yes—
186C2×#553—71no—
187C2×#547—71no—
188#3307—716no—
189C2×#491—71no—
190C2×#485—71no—
191C2×#483—71no—
192C2×#478—71no—
193C2×#468—71no—
194C2×#465—71no—
195C2×#461—71no—
196C2×#449—71no—
197C2×#449—71no—
198C2×#442—71no—
199C2×#435D711yescharacteristic, complemented
200C2×#417—71no—
201C2×#416—71no—
202C24×C7C2×D411yescharacteristic
203C24×C7C2×D411yescharacteristic
204C23×D7—21no—
205C23×D7—21no—
206C2×C7×D4—42no—
207C2×C7×D4C2×D414yes—
208C22×C4×C7—22no—
209C22×C4×C7—22no—
210C22×C4×C7—22no—
211C22×C4×C7—22no—
212C22×C4×C7C2×D411yescharacteristic
213C22×C4×C7C2×D411yescharacteristic
214C22×C4×C7C2×D411yescharacteristic
215C22×C4×C7C2×D411yescharacteristic
216C22×C4×C7C2×D412yes—
217C22×C4×C7C2×D412yes—
218C22×C4×C7C2412yes—
219C22×C4×C7C2412yes—
220C22×C4×C7C2411yescharacteristic
221C2×C22⋊D7—24no—
222C2×C22⋊D7—24no—
223C2×C22⋊D7—24no—
224C2×C22⋊D7—24no—
225C2×C22⋊D7—44no—
226C2×C22⋊D7—44no—
227C2×C22⋊D7—44no—
228C2×C22⋊D7—82no—
229C22×Dic7—21no—
230C22×Dic7—21no—
231C22×Dic7—21no—
232C22×Dic7—21no—
233C22×Dic7—21no—
234C22×Dic7—21no—
235C22×Dic7—24no—
236C22×Dic7—82no—
237#1157—28no—
238#1157—28no—
239#1157—44no—
240#1157—44no—
241#1157—48no—
242#1157—48no—
243C2×D28—21no—
244C2×D28—22no—
245C2×D28—22no—
246C2×D28—22no—
247C2×D28—21no—
248C2×D28#4114yes—
249C2×D28C2412yes—
250C2×D28C2412yes—
251C2×C4×D7—24no—
252C2×C4×D7—24no—
253C2×C4×D7—24no—
254C2×C4×D7—24no—
255C2×C4×D7—44no—
256C2×C4×D7—44no—
257C2×C4×D7—44no—
258C2×C4×D7—82no—
259C2×Dic14—22no—
260C2×Dic14—22no—
261C2×Dic14—22no—
262C2×Dic14—22no—
263C2×Dic14—21no—
264C2×Dic14—21no—
265C2×Dic14C2412yes—
266C2×Dic14C2412yes—
267C7×M16—44no—
268C2×C7×C8—22no—
269C2×C7×C8—22no—
270C2×C7×C8—22no—
271C2×C7×C8—22no—
272C2×C7×C8—44no—
273C2×C7×C8C2412yes—
274C2×C7×C8C2412yes—
275C2×C7×C8C2412yes—
276C2×C7×C8C2412yes—
277C7×C4⋊C4C2×D414yes—
278C7×C22⋊C4C2×D414yes—
279C7×C22⋊C4C2×D414yes—
280C42×C7C2×D412yes—
281C42×C7C2412yes—
282C22⋊Dic7—24no—
283C22⋊Dic7—24no—
284C22⋊Dic7—24no—
285(C2×D7)⋊C4—24no—
286(C2×D7)⋊C4—24no—
287(C2×D7)⋊C4—24no—
288(C2×D7)⋊C4—24no—
289C4⋊Dic7—24no—
290C4⋊Dic7—24no—
291C4⋊Dic7—21no—
292C4⋊Dic7—21no—
293C4⋊Dic7—21no—
294C4⋊Dic7—21no—
295C4⋊Dic7—24no—
296C4⋊Dic7C2412yes—
297C4⋊Dic7C2412yes—
298C4⋊Dic7C2412yes—
299C4⋊Dic7C2412yes—
300Dic7⋊C4—24no—
301Dic7⋊C4—24no—
302Dic7⋊C4—24no—
303Dic7⋊C4—24no—
304C4×Dic7—24no—
305D56—28no—
306#1132—44no—
307#1132—44no—
308C22×#41—71no—
309C22×#41—71no—
310C22×SD16—71no—
311C22×SD16—71no—
312C22×D8—71no—
313C22×M16C2×D711yescharacteristic
314C23×C8C2×D711yescharacteristic
315#553—78no—
316#553—144no—
317#547—78no—
318#547—144no—
319C2×C4⋊Q8—71no—
320C2×#126—141no—
321C2×#125—71no—
322C2×#123—141no—
323C2×#123—141no—
324C2×#123—141no—
325C2×C22⋊Q8—71no—
326C2×C22⋊Q8—71no—
327C2×#121—71no—
328C2×#121—71no—
329C2×#121—141no—
330C2×#121—141no—
331C2×C4×D4—71no—
332C2×C4×D4—71no—
333C2×C4×D4—141no—
334C2×C4×D4C2×D711yescharacteristic
335C2×#117—71no—
336C22×C4⋊C4—71no—
337C22×C4⋊C4—141no—
338#491—78no—
339#485—78no—
340#483—78no—
341#478—78no—
342#468—78no—
343#465—78no—
344#461—78no—
345#449—78no—
346#449—78no—
347#442—78no—
348#435C2×D718yescomplemented
349C2×#107—71no—
350C2×#106—71no—
351C2×#106—71no—
352C2×C4⋊C8C2×D711yescharacteristic
353#417—78no—
354#416—78no—
355C2×#103—71no—
356C2×#103—71no—
357C2×#103—71no—
358C2×#103—71no—
359C2×#103—71no—
360C2×#103—71no—
361C2×#102—71no—
362C2×#102—71no—
363C2×#102—71no—
364C2×#102—71no—
365C2×C22⋊C8C2×D711yescharacteristic
366C2×C22⋊C8C2×D711yescharacteristic
367C2×#97C2×D711yescharacteristic
368C23×C7—22no—
369C23×C7—22no—
370C23×C7—22no—
371C23×C7—22no—
372C23×C7—22no—
373C23×C7—22no—
374C23×C7C22×D412yes—
375C23×C7C22×D412yes—
376C23×C7C22×D411yescharacteristic
377C22×D7—24no—
378C22×D7—22no—
379C22×D7—22no—
380C22×D7—42no—
381C22×D7—42no—
382C22×D7—42no—
383C22×D7—42no—
384C22×D7—42no—
385C7×D4—44no—
386C2×C4×C7—22no—
387C2×C4×C7—22no—
388C2×C4×C7—22no—
389C2×C4×C7—22no—
390C2×C4×C7—24no—
391C2×C4×C7—24no—
392C2×C4×C7—22no—
393C2×C4×C7—22no—
394C2×C4×C7—22no—
395C2×C4×C7—22no—
396C2×C4×C7C22×D412yes—
397C2×C4×C7C22×D412yes—
398C2×C4×C7C22×D412yes—
399C2×C4×C7C22×D412yes—
400C2×C4×C7C22×D411yescharacteristic
401C2×C4×C7C2×#4112yes—
402C2×C4×C7H(5,𝔽2)12yes—
403C2×C4×C7C2511yescharacteristic
404C22⋊D7—48no—
405C22⋊D7—48no—
406C22⋊D7—48no—
407C22⋊D7—84no—
408C2×Dic7—22no—
409C2×Dic7—22no—
410C2×Dic7—22no—
411C2×Dic7—22no—
412C2×Dic7—22no—
413C2×Dic7—22no—
414C2×Dic7—42no—
415C2×Dic7—42no—
416C2×Dic7—42no—
417C2×Dic7—42no—
418C2×Dic7—42no—
419C2×Dic7—42no—
420C2×Dic7—84no—
421D28—24no—
422D28—22no—
423D28—22no—
424D28—22no—
425D28—42no—
426D28C2×#4114yes—
427C4×D7—48no—
428C4×D7—48no—
429C4×D7—48no—
430C4×D7—84no—
431Dic14—22no—
432Dic14—22no—
433Dic14—22no—
434Dic14—22no—
435Dic14—42no—
436Dic14—42no—
437C7×C8—22no—
438C7×C8—22no—
439C7×C8—22no—
440C7×C8—22no—
441C2×#41—74no—
442C2×#41—74no—
443C2×#41—144no—
444C2×#41—144no—
445C2×#41—142no—
446C2×#41—142no—
447C2×#41—282no—
448C2×#41—282no—
449C22×Q8—71no—
450C22×Q8—71no—
451C22×D4—71no—
452C22×D4—71no—
453C22×D4—141no—
454C22×D4—141no—
455C22×D4—141no—
456C22×D4—141no—
457C22×D4D2811yescharacteristic
458C23×C4—141no—
459C23×C4—141no—
460C23×C4—141no—
461C23×C4—141no—
462C23×C4—141no—
463C23×C4C22×D711yescharacteristic
464C23×C4C22×D711yescharacteristic
465C2×SD16—74no—
466C2×SD16—74no—
467C2×SD16—282no—
468C2×SD16—282no—
469C2×D8—74no—
470C2×D8—144no—
471C2×M16—42no—
472C2×M16C22×D714yes—
473C22×C8—42no—
474C22×C8C22×D711yescharacteristic
475C22×C8C22×D711yescharacteristic
476C22×C8C22×D711yescharacteristic
477C22×C8C22×D711yescharacteristic
478C22×C8C22×D714yes—
479C4⋊Q8—74no—
480C4⋊Q8—142no—
481#126—148no—
482#125—74no—
483#125—142no—
484#123—148no—
485#123—148no—
486#123—148no—
487C22⋊Q8—74no—
488C22⋊Q8—74no—
489C22⋊Q8—142no—
490C22⋊Q8—142no—
491#121—74no—
492#121—74no—
493#121—148no—
494#121—148no—
495#121—142no—
496#121—142no—
497C4×D4—74no—
498C4×D4—74no—
499C4×D4—148no—
500C4×D4—142no—
501C4×D4—142no—
502C4×D4D2814yes—
503C4×D4C22×D714yes—
504#117—74no—
505#117—142no—
506C2×C4⋊C4—71no—
507C2×C4⋊C4—71no—
508C2×C4⋊C4—74no—
509C2×C4⋊C4—71no—
510C2×C4⋊C4—71no—
511C2×C4⋊C4—141no—
512C2×C4⋊C4—142no—
513C2×C4⋊C4—141no—
514C2×C4⋊C4—141no—
515C2×C4⋊C4—141no—
516C2×C4⋊C4—141no—
517C2×C4⋊C4—141no—
518C2×C4⋊C4—141no—
519C2×C4⋊C4—148no—
520C2×C4⋊C4D2811yescharacteristic
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⋊C4D2811yescharacteristic
529C2×C22⋊C4D2811yescharacteristic
530C2×C42—141no—
531C2×C42C22×D711yescharacteristic
532#107—74no—
533#106—74no—
534#106—74no—
535C4⋊C8C22×D714yes—
536#103—74no—
537#103—74no—
538#103—74no—
539#103—74no—
540#103—74no—
541#103—74no—
542#102—74no—
543#102—74no—
544#102—74no—
545#102—74no—
546C22⋊C8C22×D714yes—
547C22⋊C8C22×D714yes—
548#97C22×D714yes—
549C22×C7—22no—
550C22×C7—22no—
551C22×C7—22no—
552C22×C7—22no—
553C22×C7—22no—
554C22×C7—22no—
555C22×C7—44no—
556C22×C7—44no—
557C22×C7#54612yes—
558C22×C7#57512yes—
559C22×C7#57712yes—
560C22×C7C23×D411yescharacteristic
561C2×D7—24no—
562C2×D7—48no—
563C2×D7—42no—
564C2×D7—42no—
565C2×D7—42no—
566C2×D7—42no—
567C2×D7—42no—
568C2×D7—84no—
569C4×C7—22no—
570C4×C7—22no—
571C4×C7—22no—
572C4×C7—22no—
573C4×C7#54612yes—
574C4×C7C22×#4111yescharacteristic
575C4×C7C2×H(5,𝔽2)11yescharacteristic
576Dic7—42no—
577Dic7—42no—
578Dic7—42no—
579Dic7—42no—
580Dic7—42no—
581Dic7—42no—
582C24—141no—
583C24—141no—
584C24C2×D2811yescharacteristic
585C24C2×D2811yescharacteristic
586#41—148no—
587#41—148no—
588#41—284no—
589#41—284no—
590#41—288no—
591#41—288no—
592C2×Q8—72no—
593C2×Q8—72no—
594C2×Q8—141no—
595C2×Q8—141no—
596C2×Q8—142no—
597C2×Q8—142no—
598C2×Q8—142no—
599C2×Q8—142no—
600C2×D4—42no—
601C2×D4—74no—
602C2×D4—72no—
603C2×D4—72no—
604C2×D4—144no—
605C2×D4—144no—
606C2×D4—144no—
607C2×D4—144no—
608C2×D4—141no—
609C2×D4—141no—
610C2×D4—142no—
611C2×D4—142no—
612C2×D4—142no—
613C2×D4—284no—
614C2×D4—284no—
615C2×D4—284no—
616C2×D4—562no—
617C2×D4C2×D2814yes—
618C22×C4—22no—
619C22×C4—22no—
620C22×C4—22no—
621C22×C4—22no—
622C22×C4—141no—
623C22×C4—141no—
624C22×C4—141no—
625C22×C4—141no—
626C22×C4—141no—
627C22×C4—141no—
628C22×C4—144no—
629C22×C4—144no—
630C22×C4—144no—
631C22×C4—144no—
632C22×C4—144no—
633C22×C4—284no—
634C22×C4—284no—
635C22×C4—284no—
636C22×C4—562no—
637C22×C4—562no—
638C22×C4C2×D2812yes—
639C22×C4C2×D2812yes—
640C22×C4C2×D2811yescharacteristic
641C22×C4C2×D2811yescharacteristic
642C22×C4C2×D2811yescharacteristic
643C22×C4C2×D2811yescharacteristic
644C22×C4C23×D712yes—
645C22×C4C23×D712yes—
646C22×C4C23×D711yescharacteristic
647SD16—284no—
648SD16—284no—
649D8—148no—
650M16—44no—
651C2×C8—22no—
652C2×C8—22no—
653C2×C8—22no—
654C2×C8—22no—
655C2×C8—44no—
656C2×C8C23×D712yes—
657C2×C8C23×D712yes—
658C2×C8C23×D712yes—
659C2×C8C23×D712yes—
660C4⋊C4—72no—
661C4⋊C4—72no—
662C4⋊C4—72no—
663C4⋊C4—72no—
664C4⋊C4—144no—
665C4⋊C4—144no—
666C4⋊C4—144no—
667C4⋊C4—144no—
668C4⋊C4—141no—
669C4⋊C4—141no—
670C4⋊C4—144no—
671C4⋊C4—141no—
672C4⋊C4—141no—
673C4⋊C4—144no—
674C4⋊C4—144no—
675C4⋊C4C2×D2814yes—
676C22⋊C4—144no—
677C22⋊C4—144no—
678C22⋊C4—144no—
679C22⋊C4—144no—
680C22⋊C4—144no—
681C22⋊C4—144no—
682C22⋊C4—144no—
683C22⋊C4C2×D2814yes—
684C22⋊C4C2×D2814yes—
685C42—144no—
686C42C2×D2812yes—
687C42C23×D712yes—
688C2×C7—42no—
689C2×C7—42no—
690C2×C7#330714yescomplemented
691C2×C7C2×#54611yescharacteristic
692C2×C7C2×#57511yescharacteristic
693C2×C7C2×#57711yescharacteristic
694D7—44no—
695D7—82no—
696C23—22no—
697C23—22no—
698C23—22no—
699C23—22no—
700C23—22no—
701C23—22no—
702C23—144no—
703C23—142no—
704C23—142no—
705C23—282no—
706C23—282no—
707C23—282no—
708C23—282no—
709C23—282no—
710C23C22×D2812yes—
711C23C22×D2812yes—
712C23C22×D2811yescharacteristic
713Q8—142no—
714Q8—142no—
715Q8—142no—
716Q8—142no—
717Q8—282no—
718Q8—282no—
719D4—44no—
720D4—74no—
721D4—144no—
722D4—142no—
723D4—142no—
724D4—142no—
725D4—288no—
726D4—288no—
727D4—288no—
728D4—282no—
729D4—564no—
730C2×C4—22no—
731C2×C4—22no—
732C2×C4—22no—
733C2×C4—22no—
734C2×C4—24no—
735C2×C4—24no—
736C2×C4—22no—
737C2×C4—22no—
738C2×C4—22no—
739C2×C4—22no—
740C2×C4—142no—
741C2×C4—142no—
742C2×C4—142no—
743C2×C4—142no—
744C2×C4—142no—
745C2×C4—142no—
746C2×C4—288no—
747C2×C4—288no—
748C2×C4—288no—
749C2×C4—282no—
750C2×C4—282no—
751C2×C4—282no—
752C2×C4—282no—
753C2×C4—282no—
754C2×C4—282no—
755C2×C4—564no—
756C2×C4—564no—
757C2×C4C22×D2812yes—
758C2×C4C22×D2812yes—
759C2×C4C22×D2812yes—
760C2×C4C22×D2812yes—
761C2×C4C22×D2811yescharacteristic
762C2×C4#654812yes—
763C2×C4D7×#4112yes—
764C2×C4C24×D711yescharacteristic
765C8—22no—
766C8—22no—
767C8—22no—
768C8—22no—
769C7C2×#330711yescharacteristic, complemented, Sylow
770C22—22no—
771C22—22no—
772C22—22no—
773C22—22no—
774C22—22no—
775C22—22no—
776C22—44no—
777C22—44no—
778C22—144no—
779C22—288no—
780C22—282no—
781C22—282no—
782C22—282no—
783C22—282no—
784C22—282no—
785C22—564no—
786C22#9024512yes—
787C22#9043912yes—
788C22#9044212yes—
789C22C23×D2811yescharacteristic
790C4—22no—
791C4—22no—
792C4—22no—
793C4—22no—
794C4—282no—
795C4—282no—
796C4—282no—
797C4—282no—
798C4—282no—
799C4—282no—
800C4#9024512yes—
801C4C2×#654811yescharacteristic
802C4C2×D7×#4111yescharacteristic
803C2—42no—
804C2—42no—
805C2—284no—
806C2—562no—
807C2#1173694514yesdirect product factor
808C2C2×#9024511yescharacteristic
809C2C2×#9043911yescharacteristic
810C2C2×#9044211yescharacteristic
subgroupG/H
centerC23C22×D28
commutator, cosocleC2×C4×C7C25
FrattiniC2×C4C24×D7
FittingC2×C7×#435C2
socleC23×C7C22×D4
hypercenterC2×#435D7
hypocenterC7C2×#3307
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×#90242C2semidirect
2. C2×#90256C2semidirect
3. C2×C7×#435C2semidirect
4. C2×#89906C2semidirect
5. C2×#89905C2semidirect
6. C2×#89886C2semidirect
7. C2×#89885C2semidirect
8. #11736945C2direct (N × H)
9. C2×#89619C2semidirect
10. C2×#89613C2semidirect
11. C2×#89506C2semidirect
12. C2×#89506C2semidirect
13. C2×#89495C2semidirect
14. C2×#89493C2semidirect
15. C2×#89475C2semidirect
16. C2×#89483C2semidirect
34. #90256C22semidirect
36. #90242C22semidirect
47. C7×#435C22semidirect
52. #89906C22semidirect
53. #89905C22semidirect
54. #89886C22semidirect
55. #89885C22semidirect
69. #89619C22semidirect
70. #89613C22semidirect
71. #89506C22semidirect
72. #89506C22semidirect
73. #89495C22semidirect
74. #89493C22semidirect
75. #89483C22semidirect
76. #89475C22semidirect
199. C2×#435D7semidirect
348. #435C2×D7semidirect
690. C2×C7#3307semidirect
769. C7C2×#3307semidirect
807. C2#11736945direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#902422
C2×#902562
C2×C7×#4352
C2×#899062
C2×#899052
C2×#898862
C2×#898852
#117369452
C2×#896192
C2×#896132
C2×#895062
C2×#894952
C2×#894932
C2×#894752
C2×#894832
C2×#33077