Finite Group Databasebeta

← C2×#11736958 #14230388

Subgroups — C2×#11736958 #14230388

Order 1792.

2158 conjugacy classes of subgroups.

The subgroup lattice has 796 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#90234C211yesmaximal, characteristic, complemented
2C2×#90243C211yesmaximal, characteristic
3C2×C7×#435C211yesmaximal, characteristic, complemented
4C2×#89909C211yesmaximal, characteristic, complemented
5C2×#89905C211yesmaximal, characteristic, complemented
6C22×#6390C211yesmaximal, characteristic, complemented
7C2×#89886C211yesmaximal, characteristic, complemented
8#11736958C2116yesmaximal, direct product factor
9C2×#89623C211yesmaximal, characteristic, complemented
10C2×#89617C211yesmaximal, characteristic, complemented
11C2×#89511C211yesmaximal, characteristic, complemented
12C2×#89505C211yesmaximal, characteristic, complemented
13C2×#89507C211yesmaximal, characteristic, complemented
14C2×#89493C211yesmaximal, characteristic, complemented
15C2×#89488C211yesmaximal, characteristic, complemented
16C2×#89486C211yesmaximal, characteristic, complemented
17C22×#1157C2211yescharacteristic
18C23×Dic14C2211yescharacteristic
19C22×C7×M16C2211yescharacteristic
20C23×C7×C8C2211yescharacteristic
21C2×C4×C7×D4C2211yescharacteristic
22C2×#6502—21no—
23C2×D4×Dic7—21no—
24C2×#6493C2211yescharacteristic
25C22×C4⋊Dic7C2211yescharacteristic
26C22×C4⋊Dic7C2211yescharacteristic
27C2×#6487C2211yescharacteristic
28C2×#6487C2211yescharacteristic
29C2×#6487C2211yescharacteristic
30C22×Dic28C2211yescharacteristic
31C22×Dic28C2211yescharacteristic
32C22×#1132C2211yescharacteristic
33#90243—24no—
34#90243C2218yes—
35#90234—24no—
36#90234C2218yescomplemented
37C2×#6459—21no—
38C2×#6453—21no—
39C2×#6448—21no—
40C2×(C22⋊D7)⋊C4—21no—
41C2×#6441—21no—
42C2×#6441—21no—
43C2×#6438C2211yescharacteristic
44C2×#6432C2211yescharacteristic
45C2×C4×Dic14C2211yescharacteristic
46C2×C4×Dic14C2211yescharacteristic
47C7×#435C2218yescomplemented
48C2×C7×C4⋊C8C2211yescharacteristic
49C2×C7×C22⋊C8C2211yescharacteristic
50C2×C7×C22⋊C8C2211yescharacteristic
51C2×C7×#97C2211yescharacteristic
52#89909C2218yescomplemented
53#89905C2218yescomplemented
54#89886C2218yescomplemented
55C2×#6395C2211yescharacteristic
56C2×#6395C2211yescharacteristic
57C2×#6395C2211yescharacteristic
58C2×#6391C2211yescharacteristic
59C2×#6391C2211yescharacteristic
60C2×#6391C2211yescharacteristic
61C2×#6390C2211yescharacteristic
62C2×#6390C2211yescharacteristic
63C2×#6390C2211yescharacteristic
64C2×#6390C2211yescharacteristic
65C2×#6390C2211yescharacteristic
66C2×#6390C2211yescharacteristic
67C2×#6390C2211yescharacteristic
68C2×#6390C2218yescomplemented
69#89623C2218yescomplemented
70#89617C2218yescomplemented
71#89511C2218yescomplemented
72#89507C2218yescomplemented
73#89505C2218yescomplemented
74#89493C2218yescomplemented
75#89488C2218yescomplemented
76#89486C2218yescomplemented
77C2×#3316—71nomaximal, Sylow
78C22×C7×D4D411yescharacteristic
79C23×C4×C7C2311yescharacteristic
80C23×C4×C7C2311yescharacteristic
81C22×C22⋊D7—21no—
82C22×C22⋊D7—21no—
83C23×Dic7—21no—
84C23×Dic7—21no—
85C23×Dic7—21no—
86C2×#1157—22no—
87C2×#1157—24no—
88C2×#1157—42no—
89C2×#1157C2314yes—
90C22×D28C2311yescharacteristic
91C22×C4×D7—21no—
92C22×Dic14—24no—
93C22×Dic14—21no—
94C22×Dic14—22no—
95C22×Dic14—21no—
96C22×Dic14—42no—
97C22×Dic14C2311yescharacteristic
98C22×Dic14C2311yescharacteristic
99C22×Dic14C2314yes—
100C22×Dic14C2311yescharacteristic
101C2×C7×M16—42no—
102C2×C7×M16C2314yes—
103C22×C7×C8—42no—
104C22×C7×C8C2311yescharacteristic
105C22×C7×C8C2311yescharacteristic
106C22×C7×C8C2311yescharacteristic
107C22×C7×C8C2311yescharacteristic
108C22×C7×C8C2314yes—
109C4×C7×D4D414yes—
110C4×C7×D4C2314yes—
111C2×C7×C4⋊C4D411yescharacteristic
112C2×C7×C22⋊C4D411yescharacteristic
113C2×C7×C22⋊C4D411yescharacteristic
114C2×C42×C7C2311yescharacteristic
115C2×C22⋊Dic7—21no—
116C2×C22⋊Dic7—21no—
117C2×C22⋊Dic7—21no—
118#6502—28no—
119D4×Dic7—28no—
120#6493—22no—
121#6493C2314yes—
122C2×(C2×D7)⋊C4—21no—
123C2×(C2×D7)⋊C4—21no—
124C2×(C2×D7)⋊C4—21no—
125C2×C4⋊Dic7—21no—
126C2×C4⋊Dic7—21no—
127C2×C4⋊Dic7—21no—
128C2×C4⋊Dic7—22no—
129C2×C4⋊Dic7—22no—
130C2×C4⋊Dic7C2311yescharacteristic
131C2×C4⋊Dic7C2311yescharacteristic
132C2×C4⋊Dic7C2311yescharacteristic
133C2×C4⋊Dic7C2311yescharacteristic
134C2×C4⋊Dic7C2314yes—
135C2×C4⋊Dic7C2314yes—
136#6487—22no—
137#6487—22no—
138#6487—22no—
139#6487C2314yes—
140#6487C2314yes—
141#6487C2314yes—
142C2×Dic7⋊C4—21no—
143C2×Dic7⋊C4—21no—
144C2×Dic7⋊C4—21no—
145C2×Dic7⋊C4—21no—
146C2×Dic7⋊C4—21no—
147C2×C4×Dic7—21no—
148C2×C4×Dic7—21no—
149C2×Dic28—24no—
150C2×Dic28—42no—
151C2×Dic28C2314yes—
152C2×Dic28C2314yes—
153C2×#1132—42no—
154C2×#1132C2314yes—
155#6459—28no—
156#6453—28no—
157#6448—28no—
158(C22⋊D7)⋊C4—28no—
159#6441—28no—
160#6441—28no—
161#6438—22no—
162#6438C2314yes—
163#6432—22no—
164#6432C2314yes—
165C4×Dic14—22no—
166C4×Dic14—22no—
167C4×Dic14C2314yes—
168C4×Dic14C2314yes—
169C7×C4⋊C8C2314yes—
170C7×C22⋊C8C2314yes—
171C7×C22⋊C8C2314yes—
172C7×#97C2314yes—
173#6395C2314yes—
174#6395C2314yes—
175#6395C2314yes—
176#6391C2314yes—
177#6391C2314yes—
178#6391C2314yes—
179#6390C2314yes—
180#6390C2314yes—
181#6390C2314yes—
182#6390C2314yes—
183#6390C2314yes—
184#6390C2314yes—
185#6390C2314yes—
186C2×#554—71no—
187C2×#548—71no—
188#3316—716no—
189C2×#489—71no—
190C2×#481—71no—
191C2×#483—71no—
192C2×#475—71no—
193C2×#470—71no—
194C2×#465—71no—
195C2×#464—71no—
196C2×#452—71no—
197C2×#451—71no—
198C2×#441—71no—
199C2×#435D711yescharacteristic, complemented
200C2×#417—71no—
201C22×#103—71no—
202C24×C7C2×D411yescharacteristic
203C24×C7C2×D411yescharacteristic
204C23×D7—21no—
205C2×C7×D4—24no—
206C2×C7×D4C2×D414yes—
207C22×C4×C7—22no—
208C22×C4×C7—22no—
209C22×C4×C7—22no—
210C22×C4×C7—22no—
211C22×C4×C7C2×D411yescharacteristic
212C22×C4×C7C2×D411yescharacteristic
213C22×C4×C7C2×D411yescharacteristic
214C22×C4×C7C2×D411yescharacteristic
215C22×C4×C7C2×D412yes—
216C22×C4×C7C2×D412yes—
217C22×C4×C7C2412yes—
218C22×C4×C7C2412yes—
219C22×C4×C7C2411yescharacteristic
220C2×C22⋊D7—24no—
221C2×C22⋊D7—24no—
222C2×C22⋊D7—44no—
223C2×C22⋊D7—44no—
224C22×Dic7—21no—
225C22×Dic7—24no—
226C22×Dic7—21no—
227C22×Dic7—21no—
228C22×Dic7—21no—
229C22×Dic7—21no—
230C22×Dic7—21no—
231C22×Dic7—21no—
232C22×Dic7—24no—
233C22×Dic7—24no—
234C22×Dic7—44no—
235C22×Dic7—82no—
236C22×Dic7—82no—
237#1157—28no—
238#1157—44no—
239#1157—48no—
240C2×D28—22no—
241C2×D28—22no—
242C2×D28—21no—
243C2×D28C2412yes—
244C2×C4×D7—24no—
245C2×C4×D7—44no—
246C2×Dic14—21no—
247C2×Dic14—22no—
248C2×Dic14—22no—
249C2×Dic14—22no—
250C2×Dic14—22no—
251C2×Dic14—22no—
252C2×Dic14—28no—
253C2×Dic14—21no—
254C2×Dic14—21no—
255C2×Dic14—24no—
256C2×Dic14—24no—
257C2×Dic14—44no—
258C2×Dic14—48no—
259C2×Dic14—44no—
260C2×Dic14—82no—
261C2×Dic14#4114yes—
262C2×Dic14C2412yes—
263C2×Dic14C2412yes—
264C2×Dic14C2412yes—
265C7×M16—44no—
266C2×C7×C8—22no—
267C2×C7×C8—22no—
268C2×C7×C8—22no—
269C2×C7×C8—22no—
270C2×C7×C8—44no—
271C2×C7×C8C2412yes—
272C2×C7×C8C2412yes—
273C2×C7×C8C2412yes—
274C2×C7×C8C2412yes—
275C7×C4⋊C4C2×D414yes—
276C7×C22⋊C4C2×D414yes—
277C7×C22⋊C4C2×D414yes—
278C42×C7C2×D412yes—
279C42×C7C2412yes—
280C22⋊Dic7—24no—
281C22⋊Dic7—24no—
282C22⋊Dic7—24no—
283(C2×D7)⋊C4—24no—
284(C2×D7)⋊C4—24no—
285(C2×D7)⋊C4—24no—
286C4⋊Dic7—21no—
287C4⋊Dic7—21no—
288C4⋊Dic7—21no—
289C4⋊Dic7—21no—
290C4⋊Dic7—24no—
291C4⋊Dic7—24no—
292C4⋊Dic7—24no—
293C4⋊Dic7C2412yes—
294C4⋊Dic7C2412yes—
295C4⋊Dic7C2412yes—
296C4⋊Dic7C2412yes—
297Dic7⋊C4—24no—
298Dic7⋊C4—24no—
299Dic7⋊C4—24no—
300Dic7⋊C4—24no—
301Dic7⋊C4—24no—
302C4×Dic7—24no—
303C4×Dic7—24no—
304Dic28—28no—
305Dic28—44no—
306#1132—44no—
307C22×#41—71no—
308C23×Q8—71no—
309C22×Q16—71no—
310C22×Q16—71no—
311C22×SD16—71no—
312C22×M16C2×D711yescharacteristic
313C23×C8C2×D711yescharacteristic
314#554—78no—
315#554—144no—
316#548—78no—
317#548—144no—
318C2×C4⋊Q8—71no—
319C2×#125—141no—
320C2×#124—71no—
321C2×#124—141no—
322C2×C22⋊Q8—71no—
323C2×C22⋊Q8—71no—
324C2×C22⋊Q8—71no—
325C2×C22⋊Q8—141no—
326C2×C22⋊Q8—141no—
327C2×C22⋊Q8—141no—
328C2×#121—71no—
329C2×#121—141no—
330C2×C4×Q8—71no—
331C2×C4×Q8—71no—
332C2×C4×D4—141no—
333C2×C4×D4—141no—
334C2×C4×D4C2×D711yescharacteristic
335C22×C4⋊C4—71no—
336C22×C4⋊C4—71no—
337#489—78no—
338#483—78no—
339#481—78no—
340#475—78no—
341#470—78no—
342#465—78no—
343#464—78no—
344#452—78no—
345#451—78no—
346#441—78no—
347#435C2×D718yescomplemented
348C2×#106—71no—
349C2×#106—71no—
350C2×#106—71no—
351C2×C4⋊C8C2×D711yescharacteristic
352#417—78no—
353C2×#103—71no—
354C2×#103—71no—
355C2×#103—71no—
356C2×#103—71no—
357C2×#103—71no—
358C2×#103—71no—
359C2×#103—71no—
360C2×#103—78no—
361C2×#102—71no—
362C2×#102—71no—
363C2×#102—71no—
364C2×C22⋊C8C2×D711yescharacteristic
365C2×C22⋊C8C2×D711yescharacteristic
366C2×#97C2×D711yescharacteristic
367C23×C7—22no—
368C23×C7—22no—
369C23×C7—22no—
370C23×C7—22no—
371C23×C7—22no—
372C23×C7#13714yes—
373C23×C7C22×D412yes—
374C23×C7C22×D412yes—
375C23×C7C22×D411yescharacteristic
376C22×D7—22no—
377C22×D7—42no—
378C22×D7—42no—
379C22×D7—42no—
380C7×D4—28no—
381C2×C4×C7—22no—
382C2×C4×C7—22no—
383C2×C4×C7—22no—
384C2×C4×C7—22no—
385C2×C4×C7—24no—
386C2×C4×C7—24no—
387C2×C4×C7—22no—
388C2×C4×C7—22no—
389C2×C4×C7—22no—
390C2×C4×C7—22no—
391C2×C4×C7C22×D412yes—
392C2×C4×C7C22×D412yes—
393C2×C4×C7C22×D412yes—
394C2×C4×C7C22×D412yes—
395C2×C4×C7C22×D411yescharacteristic
396C2×C4×C7C2×#4112yes—
397C2×C4×C7H(5,𝔽2)12yes—
398C2×C4×C7C2511yescharacteristic
399C22⋊D7—48no—
400C22⋊D7—48no—
401C2×Dic7—24no—
402C2×Dic7—22no—
403C2×Dic7—22no—
404C2×Dic7—22no—
405C2×Dic7—22no—
406C2×Dic7—22no—
407C2×Dic7—22no—
408C2×Dic7—22no—
409C2×Dic7—48no—
410C2×Dic7—42no—
411C2×Dic7—42no—
412C2×Dic7—42no—
413C2×Dic7—42no—
414C2×Dic7—42no—
415C2×Dic7—42no—
416C2×Dic7—84no—
417C2×Dic7—84no—
418D28—22no—
419D28—22no—
420D28—42no—
421C4×D7—48no—
422Dic14—24no—
423Dic14—22no—
424Dic14—22no—
425Dic14—22no—
426Dic14—22no—
427Dic14—22no—
428Dic14—48no—
429Dic14—42no—
430Dic14—42no—
431Dic14—84no—
432Dic14C2×#4114yes—
433C7×C8—22no—
434C7×C8—22no—
435C7×C8—22no—
436C7×C8—22no—
437C2×#41—74no—
438C2×#41—144no—
439C2×#41—142no—
440C2×#41—282no—
441C22×Q8—71no—
442C22×Q8—71no—
443C22×Q8—71no—
444C22×Q8—74no—
445C22×Q8—144no—
446C22×Q8—141no—
447C22×Q8—142no—
448C22×Q8—141no—
449C22×Q8—282no—
450C22×D4—71no—
451C22×D4—141no—
452C22×D4—141no—
453C22×D4D2811yescharacteristic
454C23×C4—141no—
455C23×C4—141no—
456C23×C4—141no—
457C23×C4—141no—
458C23×C4C22×D711yescharacteristic
459C23×C4C22×D711yescharacteristic
460C2×Q16—74no—
461C2×Q16—74no—
462C2×Q16—144no—
463C2×Q16—282no—
464C2×SD16—74no—
465C2×SD16—282no—
466C2×M16—42no—
467C2×M16C22×D714yes—
468C22×C8—42no—
469C22×C8C22×D711yescharacteristic
470C22×C8C22×D711yescharacteristic
471C22×C8C22×D711yescharacteristic
472C22×C8C22×D711yescharacteristic
473C22×C8C22×D714yes—
474C4⋊Q8—74no—
475C4⋊Q8—142no—
476#125—148no—
477#124—74no—
478#124—148no—
479#124—142no—
480C22⋊Q8—74no—
481C22⋊Q8—74no—
482C22⋊Q8—74no—
483C22⋊Q8—142no—
484C22⋊Q8—142no—
485C22⋊Q8—142no—
486C22⋊Q8—148no—
487C22⋊Q8—148no—
488C22⋊Q8—148no—
489#121—74no—
490#121—148no—
491#121—142no—
492C4×Q8—74no—
493C4×Q8—74no—
494C4×Q8—142no—
495C4×Q8—142no—
496C4×D4—148no—
497C4×D4—148no—
498C4×D4D2814yes—
499C4×D4C22×D714yes—
500C2×C4⋊C4—71no—
501C2×C4⋊C4—71no—
502C2×C4⋊C4—71no—
503C2×C4⋊C4—74no—
504C2×C4⋊C4—74no—
505C2×C4⋊C4—71no—
506C2×C4⋊C4—141no—
507C2×C4⋊C4—141no—
508C2×C4⋊C4—142no—
509C2×C4⋊C4—142no—
510C2×C4⋊C4—141no—
511C2×C4⋊C4—141no—
512C2×C4⋊C4—141no—
513C2×C4⋊C4—141no—
514C2×C4⋊C4—141no—
515C2×C4⋊C4—141no—
516C2×C4⋊C4D2811yescharacteristic
517C2×C22⋊C4—141no—
518C2×C22⋊C4—141no—
519C2×C22⋊C4—141no—
520C2×C22⋊C4—141no—
521C2×C22⋊C4—141no—
522C2×C22⋊C4—141no—
523C2×C22⋊C4D2811yescharacteristic
524C2×C22⋊C4D2811yescharacteristic
525C2×C42—141no—
526C2×C42—141no—
527C2×C42C22×D711yescharacteristic
528#106—74no—
529#106—74no—
530#106—74no—
531C4⋊C8C22×D714yes—
532#103—74no—
533#103—74no—
534#103—74no—
535#103—74no—
536#103—74no—
537#103—74no—
538#103—74no—
539#102—74no—
540#102—74no—
541#102—74no—
542C22⋊C8C22×D714yes—
543C22⋊C8C22×D714yes—
544#97C22×D714yes—
545C22×C7—22no—
546C22×C7—28no—
547C22×C7—22no—
548C22×C7—22no—
549C22×C7—22no—
550C22×C7—22no—
551C22×C7—44no—
552C22×C7#54612yes—
553C22×C7C2×#13714yes—
554C22×C7C2×#13712yes—
555C22×C7#57712yes—
556C22×C7C23×D411yescharacteristic
557C2×D7—42no—
558C2×D7—42no—
559C2×D7—42no—
560C2×D7—84no—
561C4×C7—22no—
562C4×C7—22no—
563C4×C7—22no—
564C4×C7—22no—
565C4×C7#54612yes—
566C4×C7C22×#4111yescharacteristic
567C4×C7C2×H(5,𝔽2)11yescharacteristic
568Dic7—24no—
569Dic7—42no—
570Dic7—42no—
571Dic7—42no—
572Dic7—42no—
573Dic7—42no—
574Dic7—42no—
575C24—141no—
576C24C2×D2811yescharacteristic
577C24C2×D2811yescharacteristic
578#41—148no—
579#41—284no—
580#41—288no—
581C2×Q8—74no—
582C2×Q8—72no—
583C2×Q8—72no—
584C2×Q8—72no—
585C2×Q8—148no—
586C2×Q8—141no—
587C2×Q8—141no—
588C2×Q8—144no—
589C2×Q8—141no—
590C2×Q8—144no—
591C2×Q8—142no—
592C2×Q8—142no—
593C2×Q8—142no—
594C2×Q8—142no—
595C2×Q8—142no—
596C2×Q8—284no—
597C2×Q8—284no—
598C2×Q8—288no—
599C2×Q8—562no—
600C2×D4—24no—
601C2×D4—72no—
602C2×D4—144no—
603C2×D4—144no—
604C2×D4—141no—
605C2×D4—142no—
606C2×D4—142no—
607C2×D4—284no—
608C2×D4—284no—
609C2×D4C2×D2814yes—
610C22×C4—22no—
611C22×C4—22no—
612C22×C4—22no—
613C22×C4—22no—
614C22×C4—141no—
615C22×C4—144no—
616C22×C4—141no—
617C22×C4—141no—
618C22×C4—141no—
619C22×C4—141no—
620C22×C4—141no—
621C22×C4—141no—
622C22×C4—144no—
623C22×C4—144no—
624C22×C4—144no—
625C22×C4—284no—
626C22×C4—284no—
627C22×C4—562no—
628C22×C4—562no—
629C22×C4C2×D2812yes—
630C22×C4C2×D2812yes—
631C22×C4C2×D2811yescharacteristic
632C22×C4C2×D2811yescharacteristic
633C22×C4C2×D2811yescharacteristic
634C22×C4C2×D2811yescharacteristic
635C22×C4C23×D712yes—
636C22×C4C23×D712yes—
637C22×C4C23×D711yescharacteristic
638Q16—148no—
639Q16—284no—
640SD16—284no—
641M16—44no—
642C2×C8—22no—
643C2×C8—22no—
644C2×C8—22no—
645C2×C8—22no—
646C2×C8—44no—
647C2×C8C23×D712yes—
648C2×C8C23×D712yes—
649C2×C8C23×D712yes—
650C2×C8C23×D712yes—
651C4⋊C4—72no—
652C4⋊C4—72no—
653C4⋊C4—72no—
654C4⋊C4—72no—
655C4⋊C4—144no—
656C4⋊C4—144no—
657C4⋊C4—144no—
658C4⋊C4—144no—
659C4⋊C4—144no—
660C4⋊C4—141no—
661C4⋊C4—144no—
662C4⋊C4—144no—
663C4⋊C4—141no—
664C4⋊C4—141no—
665C4⋊C4—141no—
666C4⋊C4—144no—
667C4⋊C4C2×D2814yes—
668C22⋊C4—144no—
669C22⋊C4—144no—
670C22⋊C4—144no—
671C22⋊C4—144no—
672C22⋊C4—144no—
673C22⋊C4—144no—
674C22⋊C4C2×D2814yes—
675C22⋊C4C2×D2814yes—
676C42—144no—
677C42—144no—
678C42C2×D2812yes—
679C42C23×D712yes—
680C2×C7—24no—
681C2×C7—42no—
682C2×C7#331614yescomplemented
683C2×C7C2×#54611yescharacteristic
684C2×C7C22×#13711yescharacteristic
685C2×C7C2×#57711yescharacteristic
686D7—82no—
687C23—22no—
688C23—22no—
689C23—22no—
690C23—22no—
691C23—22no—
692C23—142no—
693C23—282no—
694C23—282no—
695C23—282no—
696C23#647214yes—
697C23C22×D2812yes—
698C23C22×D2812yes—
699C23C22×D2811yescharacteristic
700Q8—74no—
701Q8—144no—
702Q8—142no—
703Q8—142no—
704Q8—142no—
705Q8—142no—
706Q8—142no—
707Q8—288no—
708Q8—282no—
709Q8—282no—
710Q8—564no—
711D4—28no—
712D4—142no—
713D4—142no—
714D4—288no—
715D4—288no—
716D4—282no—
717C2×C4—22no—
718C2×C4—22no—
719C2×C4—22no—
720C2×C4—22no—
721C2×C4—24no—
722C2×C4—24no—
723C2×C4—22no—
724C2×C4—22no—
725C2×C4—22no—
726C2×C4—22no—
727C2×C4—144no—
728C2×C4—142no—
729C2×C4—142no—
730C2×C4—142no—
731C2×C4—142no—
732C2×C4—142no—
733C2×C4—142no—
734C2×C4—142no—
735C2×C4—288no—
736C2×C4—288no—
737C2×C4—282no—
738C2×C4—282no—
739C2×C4—282no—
740C2×C4—282no—
741C2×C4—282no—
742C2×C4—282no—
743C2×C4—564no—
744C2×C4—564no—
745C2×C4C22×D2812yes—
746C2×C4C22×D2812yes—
747C2×C4C22×D2812yes—
748C2×C4C22×D2812yes—
749C2×C4C22×D2811yescharacteristic
750C2×C4#654812yes—
751C2×C4D7×#4112yes—
752C2×C4C24×D711yescharacteristic
753C8—22no—
754C8—22no—
755C8—22no—
756C8—22no—
757C7C2×#331611yescharacteristic, complemented, Sylow
758C22—28no—
759C22—22no—
760C22—22no—
761C22—22no—
762C22—22no—
763C22—22no—
764C22—44no—
765C22—282no—
766C22—282no—
767C22—282no—
768C22—564no—
769C22#9024512yes—
770C22C2×#647214yes—
771C22C2×#647212yes—
772C22#9044212yes—
773C22C23×D2811yescharacteristic
774C4—22no—
775C4—22no—
776C4—22no—
777C4—22no—
778C4—144no—
779C4—282no—
780C4—282no—
781C4—282no—
782C4—282no—
783C4—282no—
784C4—282no—
785C4#9024512yes—
786C4C2×#654811yescharacteristic
787C4C2×D7×#4111yescharacteristic
788C2—24no—
789C2—42no—
790C2—562no—
791C2#1173695814yesdirect product factor
792C2C2×#9024511yescharacteristic
793C2C22×#647211yescharacteristic
794C2C2×#9044211yescharacteristic
subgroupG/H
centerC23C22×D28
commutator, cosocleC2×C4×C7C25
FrattiniC2×C4C24×D7
FittingC2×C7×#435C2
socleC23×C7C22×D4
prime radicalC2×#90243C2
hypercenterC2×#435D7
hypocenterC7C2×#3316
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×#90234C2semidirect
3. C2×C7×#435C2semidirect
4. C2×#89909C2semidirect
5. C2×#89905C2semidirect
6. C22×#6390C2semidirect
7. C2×#89886C2semidirect
8. #11736958C2direct (N × H)
9. C2×#89623C2semidirect
10. C2×#89617C2semidirect
11. C2×#89511C2semidirect
12. C2×#89505C2semidirect
13. C2×#89507C2semidirect
14. C2×#89493C2semidirect
15. C2×#89488C2semidirect
16. C2×#89486C2semidirect
36. #90234C22semidirect
47. C7×#435C22semidirect
52. #89909C22semidirect
53. #89905C22semidirect
54. #89886C22semidirect
68. C2×#6390C22semidirect
69. #89623C22semidirect
70. #89617C22semidirect
71. #89511C22semidirect
72. #89507C22semidirect
73. #89505C22semidirect
74. #89493C22semidirect
75. #89488C22semidirect
76. #89486C22semidirect
199. C2×#435D7semidirect
347. #435C2×D7semidirect
682. C2×C7#3316semidirect
757. C7C2×#3316semidirect
791. C2#11736958direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#902342
C2×#902432
C2×C7×#4352
C2×#899092
C2×#899052
C22×#63902
C2×#898862
#117369582
C2×#896232
C2×#896172
C2×#895112
C2×#895052
C2×#895072
C2×#894932
C2×#894882
C2×#894862
C2×#33167