Finite Group Databasebeta

← C2×#11736126 #14224484

Subgroups — C2×#11736126 #14224484

Order 1792.

2186 conjugacy classes of subgroups.

The subgroup lattice has 840 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#90524C211yesmaximal, characteristic
2C2×#90516C211yesmaximal, characteristic, complemented
3C2×C7×#408C211yesmaximal, characteristic, complemented
4C2×#89909C211yesmaximal, characteristic, complemented
5C2×#89906C211yesmaximal, characteristic, complemented
6C2×#89888C211yesmaximal, characteristic, complemented
7C2×#89886C211yesmaximal, characteristic, complemented
8#11736126C2116yesmaximal, direct product factor
9C2×#89511C211yesmaximal, characteristic, complemented
10C2×#89510C211yesmaximal, characteristic, complemented
11C2×#89505C211yesmaximal, characteristic, complemented
12C2×#89505C211yesmaximal, characteristic, complemented
13C2×#89494C211yesmaximal, characteristic, complemented
14C2×#89495C211yesmaximal, characteristic, complemented
15C2×#89509C211yesmaximal, characteristic, complemented
16C2×#89493C211yesmaximal, characteristic, complemented
17C22×C7×#41C2211yescharacteristic
18C22×#1157C2211yescharacteristic
19C23×Dic14C2211yescharacteristic
20C22×C7×M16C2211yescharacteristic
21C23×C7×C8C2211yescharacteristic
22#90524—24no—
23#90524C2218yes—
24#90516—24no—
25#90516C2218yescomplemented
26C2×#6509—21no—
27C2×#6507—21no—
28C2×#6502—21no—
29C2×#6502—21no—
30C2×#6501—21no—
31C2×#6499—21no—
32C2×#6498—21no—
33C2×#6498—21no—
34C2×#6493C2211yescharacteristic
35C2×#6493C2211yescharacteristic
36C2×#6489C2211yescharacteristic
37C22×C4⋊Dic7C2211yescharacteristic
38C2×#6487C2211yescharacteristic
39C2×#6487C2211yescharacteristic
40C2×#6487C2211yescharacteristic
41C2×#6487C2211yescharacteristic
42C2×#6487C2211yescharacteristic
43C2×#6487C2211yescharacteristic
44C22×Dic28C2211yescharacteristic
45C22×Dic28C2211yescharacteristic
46C22×#1132C2211yescharacteristic
47C22×#1132C2211yescharacteristic
48C7×#408C2218yescomplemented
49C2×C7×C22⋊C8C2211yescharacteristic
50C2×C7×C22⋊C8C2211yescharacteristic
51C2×C7×C22⋊C8C2211yescharacteristic
52C2×C7×C22⋊C8C2211yescharacteristic
53#89909C2218yescomplemented
54#89906C2218yescomplemented
55#89888C2218yescomplemented
56#89886C2218yescomplemented
57C2×#6395C2211yescharacteristic
58C2×#6395C2211yescharacteristic
59C2×#6392C2211yescharacteristic
60C2×#6392C2211yescharacteristic
61C2×#6391C2211yescharacteristic
62C2×#6391C2211yescharacteristic
63C2×#6390C2211yescharacteristic
64C2×#6390C2211yescharacteristic
65C2×#6390C2211yescharacteristic
66C2×#6390C2211yescharacteristic
67C2×#6390C2211yescharacteristic
68C2×#6390C2211yescharacteristic
69#89511C2218yescomplemented
70#89510C2218yescomplemented
71#89509C2218yescomplemented
72#89505C2218yescomplemented
73#89505C2218yescomplemented
74#89495C2218yescomplemented
75#89494C2218yescomplemented
76#89493C2218yescomplemented
77C2×#3201—71nomaximal, Sylow
78C2×C7×#41—42no—
79C2×C7×#41—42no—
80C2×C7×#41D414yes—
81C2×C7×#41C2314yes—
82C22×C7×Q8D411yescharacteristic
83C22×C7×D4D411yescharacteristic
84C22×C7×D4D411yescharacteristic
85C22×C7×D4D411yescharacteristic
86C23×C4×C7C2311yescharacteristic
87C23×C4×C7C2311yescharacteristic
88C23×C4×C7C2311yescharacteristic
89C22×C22⋊D7—21no—
90C22×C22⋊D7—21no—
91C22×C22⋊D7—21no—
92C23×Dic7—21no—
93C23×Dic7—21no—
94C2×#1157—22no—
95C2×#1157—42no—
96C2×#1157—42no—
97C2×#1157C2314yes—
98C22×D28C2311yescharacteristic
99C22×C4×D7—21no—
100C22×Dic14—21no—
101C22×Dic14—22no—
102C22×Dic14—42no—
103C22×Dic14—42no—
104C22×Dic14C2311yescharacteristic
105C22×Dic14C2311yescharacteristic
106C22×Dic14C2311yescharacteristic
107C22×Dic14C2314yes—
108C2×C7×M16—42no—
109C2×C7×M16C2314yes—
110C22×C7×C8—42no—
111C22×C7×C8C2311yescharacteristic
112C22×C7×C8C2311yescharacteristic
113C22×C7×C8C2311yescharacteristic
114C22×C7×C8C2311yescharacteristic
115C22×C7×C8C2314yes—
116C2×C22⋊Dic7—21no—
117C2×C22⋊Dic7—21no—
118C2×C22⋊Dic7—21no—
119C2×C22⋊Dic7—21no—
120C2×C22⋊Dic7—21no—
121C2×C22⋊Dic7—21no—
122C2×C22⋊Dic7—21no—
123#6509—28no—
124#6507—28no—
125#6502—28no—
126#6502—28no—
127#6501—28no—
128#6499—28no—
129#6498—28no—
130#6498—28no—
131#6493—22no—
132#6493—22no—
133#6493C2314yes—
134#6493C2314yes—
135C2×(C2×D7)⋊C4—21no—
136C2×(C2×D7)⋊C4—21no—
137#6489—22no—
138#6489C2314yes—
139C2×C4⋊Dic7—21no—
140C2×C4⋊Dic7—22no—
141C2×C4⋊Dic7C2311yescharacteristic
142C2×C4⋊Dic7C2311yescharacteristic
143C2×C4⋊Dic7C2311yescharacteristic
144C2×C4⋊Dic7C2311yescharacteristic
145C2×C4⋊Dic7C2314yes—
146#6487—22no—
147#6487—22no—
148#6487—22no—
149#6487—22no—
150#6487—22no—
151#6487—22no—
152#6487C2314yes—
153#6487C2314yes—
154#6487C2314yes—
155#6487C2314yes—
156#6487C2314yes—
157#6487C2314yes—
158C2×Dic7⋊C4—21no—
159C2×Dic7⋊C4—21no—
160C2×Dic7⋊C4—21no—
161C2×Dic7⋊C4—21no—
162C2×Dic7⋊C4—21no—
163C2×Dic7⋊C4—21no—
164C2×C4×Dic7—21no—
165C2×Dic28—42no—
166C2×Dic28—42no—
167C2×Dic28C2314yes—
168C2×Dic28C2314yes—
169C2×#1132—42no—
170C2×#1132—42no—
171C2×#1132C2314yes—
172C2×#1132C2314yes—
173C7×C22⋊C8C2314yes—
174C7×C22⋊C8C2314yes—
175C7×C22⋊C8C2314yes—
176C7×C22⋊C8C2314yes—
177#6395C2314yes—
178#6395C2314yes—
179#6392C2314yes—
180#6392C2314yes—
181#6391C2314yes—
182#6391C2314yes—
183#6390C2314yes—
184#6390C2314yes—
185#6390C2314yes—
186#6390C2314yes—
187#6390C2314yes—
188#6390C2314yes—
189C2×#537—71no—
190C2×#536—71no—
191#3201—716no—
192C2×#484—71no—
193C2×#485—71no—
194C2×#482—71no—
195C2×#483—71no—
196C2×#470—71no—
197C2×#468—71no—
198C2×#467—71no—
199C2×#465—71no—
200C2×#452—71no—
201C2×#452—71no—
202C2×#451—71no—
203C2×#448—71no—
204C2×#408D711yescharacteristic, complemented
205C24×C7C2×D411yescharacteristic
206C24×C7C2×D411yescharacteristic
207C24×C7C2×D411yescharacteristic
208C23×D7—21no—
209C7×#41—48no—
210C7×#41—44no—
211C7×#41—44no—
212C2×C7×Q8—42no—
213C2×C7×Q8C2×D414yes—
214C2×C7×D4—42no—
215C2×C7×D4—42no—
216C2×C7×D4—42no—
217C2×C7×D4C2×D414yes—
218C2×C7×D4C2×D414yes—
219C2×C7×D4C2×D414yes—
220C22×C4×C7—22no—
221C22×C4×C7—22no—
222C22×C4×C7—22no—
223C22×C4×C7—22no—
224C22×C4×C7—22no—
225C22×C4×C7—22no—
226C22×C4×C7C2×D411yescharacteristic
227C22×C4×C7C2×D411yescharacteristic
228C22×C4×C7C2×D411yescharacteristic
229C22×C4×C7C2×D412yes—
230C22×C4×C7C2×D412yes—
231C22×C4×C7C2×D412yes—
232C22×C4×C7C2412yes—
233C22×C4×C7C2412yes—
234C22×C4×C7C2412yes—
235C22×C4×C7C2411yescharacteristic
236C2×C22⋊D7—24no—
237C2×C22⋊D7—24no—
238C2×C22⋊D7—24no—
239C2×C22⋊D7—44no—
240C2×C22⋊D7—82no—
241C2×C22⋊D7—82no—
242C22×Dic7—21no—
243C22×Dic7—21no—
244C22×Dic7—21no—
245C22×Dic7—21no—
246C22×Dic7—21no—
247C22×Dic7—21no—
248C22×Dic7—21no—
249C22×Dic7—24no—
250C22×Dic7—24no—
251C22×Dic7—44no—
252C22×Dic7—82no—
253#1157—44no—
254#1157—44no—
255#1157—48no—
256C2×D28—22no—
257C2×D28—22no—
258C2×D28—21no—
259C2×D28C2412yes—
260C2×C4×D7—24no—
261C2×C4×D7—44no—
262C2×Dic14—22no—
263C2×Dic14—22no—
264C2×Dic14—22no—
265C2×Dic14—22no—
266C2×Dic14—22no—
267C2×Dic14—22no—
268C2×Dic14—21no—
269C2×Dic14—21no—
270C2×Dic14—21no—
271C2×Dic14—24no—
272C2×Dic14—44no—
273C2×Dic14—44no—
274C2×Dic14—44no—
275C2×Dic14—48no—
276C2×Dic14C2412yes—
277C2×Dic14C2412yes—
278C2×Dic14C2412yes—
279C7×M16—44no—
280C2×C7×C8—22no—
281C2×C7×C8—22no—
282C2×C7×C8—22no—
283C2×C7×C8—22no—
284C2×C7×C8—44no—
285C2×C7×C8C2412yes—
286C2×C7×C8C2412yes—
287C2×C7×C8C2412yes—
288C2×C7×C8C2412yes—
289C22⋊Dic7—24no—
290C22⋊Dic7—24no—
291C22⋊Dic7—24no—
292C22⋊Dic7—24no—
293C22⋊Dic7—24no—
294C22⋊Dic7—24no—
295C22⋊Dic7—24no—
296(C2×D7)⋊C4—24no—
297(C2×D7)⋊C4—24no—
298C4⋊Dic7—21no—
299C4⋊Dic7—21no—
300C4⋊Dic7—21no—
301C4⋊Dic7—21no—
302C4⋊Dic7—24no—
303C4⋊Dic7C2412yes—
304C4⋊Dic7C2412yes—
305C4⋊Dic7C2412yes—
306C4⋊Dic7C2412yes—
307Dic7⋊C4—24no—
308Dic7⋊C4—24no—
309Dic7⋊C4—24no—
310Dic7⋊C4—24no—
311Dic7⋊C4—24no—
312Dic7⋊C4—24no—
313C4×Dic7—24no—
314Dic28—44no—
315Dic28—44no—
316#1132—44no—
317#1132—44no—
318C22×#41—71no—
319C22×#41C2×D711yescharacteristic
320C23×Q8—71no—
321C22×Q16—71no—
322C22×Q16—71no—
323C22×SD16—71no—
324C22×SD16—71no—
325C22×M16C2×D711yescharacteristic
326C23×C8C2×D711yescharacteristic
327#537—78no—
328#537—144no—
329#536—78no—
330#536—144no—
331C2×C4⋊Q8—141no—
332C2×#124—141no—
333C2×#123—141no—
334C2×#123—141no—
335C2×C22⋊Q8—71no—
336C2×C22⋊Q8—71no—
337C2×C22⋊Q8—71no—
338C2×C22⋊Q8—71no—
339C2×C22⋊Q8—71no—
340C2×C22⋊Q8—71no—
341C2×C22⋊Q8—141no—
342C2×#121—71no—
343C2×#121—71no—
344C2×#121—141no—
345C2×#121—141no—
346C2×#121—141no—
347C2×#117—71no—
348C22×C4⋊C4—71no—
349#485—78no—
350#484—78no—
351#483—78no—
352#482—78no—
353#470—78no—
354#468—78no—
355#467—78no—
356#465—78no—
357#452—78no—
358#452—78no—
359#451—78no—
360#448—78no—
361C2×#107—71no—
362C2×#107—71no—
363C2×#106—71no—
364C2×#106—71no—
365C2×#103—71no—
366C2×#103—71no—
367C2×#103—71no—
368C2×#103—71no—
369C2×#103—71no—
370C2×#103—71no—
371C2×#102—71no—
372C2×#102—71no—
373#408C2×D718yescomplemented
374C2×C22⋊C8C2×D711yescharacteristic
375C2×C22⋊C8C2×D711yescharacteristic
376C2×C22⋊C8C2×D711yescharacteristic
377C2×C22⋊C8C2×D711yescharacteristic
378C23×C7—22no—
379C23×C7—22no—
380C23×C7—22no—
381C23×C7—22no—
382C23×C7—22no—
383C23×C7—22no—
384C23×C7—22no—
385C23×C7—22no—
386C23×C7—22no—
387C23×C7C22×D412yes—
388C23×C7C22×D412yes—
389C23×C7C22×D412yes—
390C23×C7C22×D411yescharacteristic
391C22×D7—22no—
392C22×D7—42no—
393C22×D7—42no—
394C22×D7—42no—
395C7×Q8—44no—
396C7×D4—44no—
397C7×D4—44no—
398C7×D4—44no—
399C2×C4×C7—22no—
400C2×C4×C7—22no—
401C2×C4×C7—22no—
402C2×C4×C7—24no—
403C2×C4×C7—24no—
404C2×C4×C7—24no—
405C2×C4×C7—22no—
406C2×C4×C7—22no—
407C2×C4×C7—22no—
408C2×C4×C7—22no—
409C2×C4×C7—22no—
410C2×C4×C7—22no—
411C2×C4×C7C22×D412yes—
412C2×C4×C7C22×D412yes—
413C2×C4×C7C22×D412yes—
414C2×C4×C7C22×D411yescharacteristic
415C2×C4×C7H(5,𝔽2)12yes—
416C2×C4×C7H(5,𝔽2)12yes—
417C2×C4×C7C2511yescharacteristic
418C22⋊D7—48no—
419C22⋊D7—84no—
420C22⋊D7—84no—
421C2×Dic7—22no—
422C2×Dic7—22no—
423C2×Dic7—22no—
424C2×Dic7—22no—
425C2×Dic7—22no—
426C2×Dic7—22no—
427C2×Dic7—22no—
428C2×Dic7—48no—
429C2×Dic7—42no—
430C2×Dic7—42no—
431C2×Dic7—42no—
432C2×Dic7—42no—
433C2×Dic7—42no—
434C2×Dic7—42no—
435C2×Dic7—42no—
436C2×Dic7—84no—
437D28—22no—
438D28—22no—
439D28—42no—
440C4×D7—48no—
441Dic14—22no—
442Dic14—22no—
443Dic14—22no—
444Dic14—22no—
445Dic14—22no—
446Dic14—22no—
447Dic14—48no—
448Dic14—42no—
449Dic14—42no—
450Dic14—42no—
451C7×C8—22no—
452C7×C8—22no—
453C7×C8—22no—
454C7×C8—22no—
455C2×#41—42no—
456C2×#41—42no—
457C2×#41—74no—
458C2×#41—142no—
459C2×#41—282no—
460C2×#41—282no—
461C2×#41D2814yes—
462C2×#41C22×D714yes—
463C22×Q8—71no—
464C22×Q8—71no—
465C22×Q8—71no—
466C22×Q8—74no—
467C22×Q8—141no—
468C22×Q8—142no—
469C22×Q8—282no—
470C22×Q8—282no—
471C22×Q8D2811yescharacteristic
472C22×D4—71no—
473C22×D4—141no—
474C22×D4—141no—
475C22×D4—141no—
476C22×D4D2811yescharacteristic
477C22×D4D2811yescharacteristic
478C22×D4D2811yescharacteristic
479C23×C4—141no—
480C23×C4—141no—
481C23×C4—141no—
482C23×C4C22×D711yescharacteristic
483C23×C4C22×D711yescharacteristic
484C23×C4C22×D711yescharacteristic
485C2×Q16—74no—
486C2×Q16—74no—
487C2×Q16—282no—
488C2×Q16—282no—
489C2×SD16—74no—
490C2×SD16—74no—
491C2×SD16—282no—
492C2×SD16—282no—
493C2×M16—42no—
494C2×M16C22×D714yes—
495C22×C8—42no—
496C22×C8C22×D711yescharacteristic
497C22×C8C22×D711yescharacteristic
498C22×C8C22×D711yescharacteristic
499C22×C8C22×D711yescharacteristic
500C22×C8C22×D714yes—
501C4⋊Q8—148no—
502#124—148no—
503#123—148no—
504#123—148no—
505C22⋊Q8—74no—
506C22⋊Q8—74no—
507C22⋊Q8—74no—
508C22⋊Q8—74no—
509C22⋊Q8—74no—
510C22⋊Q8—74no—
511C22⋊Q8—148no—
512C22⋊Q8—142no—
513C22⋊Q8—142no—
514C22⋊Q8—142no—
515C22⋊Q8—142no—
516C22⋊Q8—142no—
517C22⋊Q8—142no—
518#121—74no—
519#121—74no—
520#121—148no—
521#121—148no—
522#121—148no—
523#121—142no—
524#121—142no—
525#117—74no—
526#117—142no—
527C2×C4⋊C4—71no—
528C2×C4⋊C4—71no—
529C2×C4⋊C4—74no—
530C2×C4⋊C4—71no—
531C2×C4⋊C4—71no—
532C2×C4⋊C4—141no—
533C2×C4⋊C4—142no—
534C2×C4⋊C4—141no—
535C2×C4⋊C4—141no—
536C2×C4⋊C4—141no—
537C2×C4⋊C4—141no—
538C2×C4⋊C4—141no—
539C2×C4⋊C4—141no—
540C2×C22⋊C4—141no—
541C2×C22⋊C4—141no—
542C2×C22⋊C4—141no—
543C2×C22⋊C4—141no—
544C2×C22⋊C4—141no—
545C2×C22⋊C4—141no—
546C2×C22⋊C4—141no—
547C2×C22⋊C4—141no—
548C2×C22⋊C4—141no—
549C2×C42—141no—
550#107—74no—
551#107—74no—
552#106—74no—
553#106—74no—
554#103—74no—
555#103—74no—
556#103—74no—
557#103—74no—
558#103—74no—
559#103—74no—
560#102—74no—
561#102—74no—
562C22⋊C8C22×D714yes—
563C22⋊C8C22×D714yes—
564C22⋊C8C22×D714yes—
565C22⋊C8C22×D714yes—
566C22×C7—22no—
567C22×C7—22no—
568C22×C7—22no—
569C22×C7—22no—
570C22×C7—22no—
571C22×C7—22no—
572C22×C7—22no—
573C22×C7—22no—
574C22×C7—22no—
575C22×C7—44no—
576C22×C7—44no—
577C22×C7—44no—
578C22×C7#53412yes—
579C22×C7#57712yes—
580C22×C7#57812yes—
581C22×C7C23×D411yescharacteristic
582C2×D7—42no—
583C2×D7—42no—
584C2×D7—42no—
585C2×D7—84no—
586C4×C7—22no—
587C4×C7—22no—
588C4×C7—22no—
589C4×C7#53412yes—
590C4×C7C2×H(5,𝔽2)11yescharacteristic
591C4×C7C2×H(5,𝔽2)11yescharacteristic
592Dic7—42no—
593Dic7—42no—
594Dic7—42no—
595Dic7—42no—
596Dic7—42no—
597Dic7—42no—
598Dic7—42no—
599C24—141no—
600C24C2×D2811yescharacteristic
601C24C2×D2811yescharacteristic
602C24C2×D2811yescharacteristic
603#41—48no—
604#41—44no—
605#41—44no—
606#41—284no—
607#41—284no—
608#41—288no—
609C2×Q8—42no—
610C2×Q8—72no—
611C2×Q8—72no—
612C2×Q8—72no—
613C2×Q8—141no—
614C2×Q8—141no—
615C2×Q8—141no—
616C2×Q8—144no—
617C2×Q8—142no—
618C2×Q8—142no—
619C2×Q8—142no—
620C2×Q8—142no—
621C2×Q8—142no—
622C2×Q8—142no—
623C2×Q8—284no—
624C2×Q8—284no—
625C2×Q8—284no—
626C2×Q8—288no—
627C2×Q8C2×D2814yes—
628C2×D4—42no—
629C2×D4—42no—
630C2×D4—42no—
631C2×D4—72no—
632C2×D4—144no—
633C2×D4—144no—
634C2×D4—144no—
635C2×D4—141no—
636C2×D4—142no—
637C2×D4—142no—
638C2×D4—284no—
639C2×D4—562no—
640C2×D4—562no—
641C2×D4C2×D2814yes—
642C2×D4C2×D2814yes—
643C2×D4C2×D2814yes—
644C22×C4—22no—
645C22×C4—22no—
646C22×C4—22no—
647C22×C4—22no—
648C22×C4—22no—
649C22×C4—22no—
650C22×C4—144no—
651C22×C4—141no—
652C22×C4—141no—
653C22×C4—141no—
654C22×C4—141no—
655C22×C4—141no—
656C22×C4—141no—
657C22×C4—141no—
658C22×C4—144no—
659C22×C4—144no—
660C22×C4—284no—
661C22×C4—284no—
662C22×C4—562no—
663C22×C4C2×D2812yes—
664C22×C4C2×D2812yes—
665C22×C4C2×D2812yes—
666C22×C4C2×D2811yescharacteristic
667C22×C4C2×D2811yescharacteristic
668C22×C4C2×D2811yescharacteristic
669C22×C4C23×D712yes—
670C22×C4C23×D712yes—
671C22×C4C23×D712yes—
672C22×C4C23×D711yescharacteristic
673Q16—284no—
674Q16—284no—
675SD16—284no—
676SD16—284no—
677M16—44no—
678C2×C8—22no—
679C2×C8—22no—
680C2×C8—22no—
681C2×C8—22no—
682C2×C8—44no—
683C2×C8C23×D712yes—
684C2×C8C23×D712yes—
685C2×C8C23×D712yes—
686C2×C8C23×D712yes—
687C4⋊C4—72no—
688C4⋊C4—72no—
689C4⋊C4—72no—
690C4⋊C4—72no—
691C4⋊C4—144no—
692C4⋊C4—144no—
693C4⋊C4—144no—
694C4⋊C4—144no—
695C4⋊C4—144no—
696C4⋊C4—144no—
697C4⋊C4—144no—
698C4⋊C4—141no—
699C4⋊C4—141no—
700C4⋊C4—141no—
701C4⋊C4—141no—
702C22⋊C4—144no—
703C22⋊C4—144no—
704C22⋊C4—144no—
705C22⋊C4—144no—
706C22⋊C4—144no—
707C22⋊C4—144no—
708C22⋊C4—144no—
709C22⋊C4—144no—
710C22⋊C4—144no—
711C42—144no—
712C2×C7—42no—
713C2×C7—42no—
714C2×C7—42no—
715C2×C7#320114yescomplemented
716C2×C7C2×#53411yescharacteristic
717C2×C7C2×#57711yescharacteristic
718C2×C7C2×#57811yescharacteristic
719D7—82no—
720C23—22no—
721C23—22no—
722C23—22no—
723C23—22no—
724C23—22no—
725C23—22no—
726C23—22no—
727C23—22no—
728C23—22no—
729C23—142no—
730C23—282no—
731C23—282no—
732C23—282no—
733C23C22×D2812yes—
734C23C22×D2812yes—
735C23C22×D2812yes—
736C23C22×D2811yescharacteristic
737Q8—44no—
738Q8—142no—
739Q8—142no—
740Q8—142no—
741Q8—142no—
742Q8—142no—
743Q8—142no—
744Q8—288no—
745Q8—282no—
746Q8—282no—
747Q8—282no—
748D4—44no—
749D4—44no—
750D4—44no—
751D4—142no—
752D4—142no—
753D4—288no—
754D4—282no—
755D4—564no—
756D4—564no—
757C2×C4—22no—
758C2×C4—22no—
759C2×C4—22no—
760C2×C4—24no—
761C2×C4—24no—
762C2×C4—24no—
763C2×C4—22no—
764C2×C4—22no—
765C2×C4—22no—
766C2×C4—22no—
767C2×C4—22no—
768C2×C4—22no—
769C2×C4—142no—
770C2×C4—142no—
771C2×C4—142no—
772C2×C4—142no—
773C2×C4—142no—
774C2×C4—142no—
775C2×C4—142no—
776C2×C4—288no—
777C2×C4—288no—
778C2×C4—282no—
779C2×C4—282no—
780C2×C4—282no—
781C2×C4—282no—
782C2×C4—282no—
783C2×C4—282no—
784C2×C4—282no—
785C2×C4—564no—
786C2×C4C22×D2812yes—
787C2×C4C22×D2812yes—
788C2×C4C22×D2812yes—
789C2×C4C22×D2811yescharacteristic
790C2×C4#654812yes—
791C2×C4#654812yes—
792C2×C4C24×D711yescharacteristic
793C8—22no—
794C8—22no—
795C8—22no—
796C8—22no—
797C7C2×#320111yescharacteristic, complemented, Sylow
798C22—22no—
799C22—22no—
800C22—22no—
801C22—22no—
802C22—22no—
803C22—22no—
804C22—22no—
805C22—22no—
806C22—22no—
807C22—44no—
808C22—44no—
809C22—44no—
810C22—282no—
811C22—282no—
812C22—282no—
813C22—564no—
814C22#9018412yes—
815C22#9044212yes—
816C22#9044412yes—
817C22C23×D2811yescharacteristic
818C4—22no—
819C4—22no—
820C4—22no—
821C4—282no—
822C4—282no—
823C4—282no—
824C4—282no—
825C4—282no—
826C4—282no—
827C4—282no—
828C4#9018412yes—
829C4C2×#654811yescharacteristic
830C4C2×#654811yescharacteristic
831C2—42no—
832C2—42no—
833C2—42no—
834C2—562no—
835C2#1173612614yesdirect product factor
836C2C2×#9018411yescharacteristic
837C2C2×#9044211yescharacteristic
838C2C2×#9044411yescharacteristic
subgroupG/H
centerC23C22×D28
commutator, cosocleC2×C4×C7C25
FrattiniC2×C4C24×D7
FittingC2×C7×#408C2
socleC23×C7C22×D4
prime radicalC2×#90524C2
hypercenterC2×#408D7
hypocenterC7C2×#3201
LCSG ▷ C2×C4×C7 ▷ C2×C7 ▷ C7
UCSC1 ◁ C23 ◁ C22×#41 ◁ C2×#408

Complements

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

NH ≅ G/Ntype
2. C2×#90516C2semidirect
3. C2×C7×#408C2semidirect
4. C2×#89909C2semidirect
5. C2×#89906C2semidirect
6. C2×#89888C2semidirect
7. C2×#89886C2semidirect
8. #11736126C2direct (N × H)
9. C2×#89511C2semidirect
10. C2×#89510C2semidirect
11. C2×#89505C2semidirect
12. C2×#89505C2semidirect
13. C2×#89494C2semidirect
14. C2×#89495C2semidirect
15. C2×#89509C2semidirect
16. C2×#89493C2semidirect
25. #90516C22semidirect
48. C7×#408C22semidirect
53. #89909C22semidirect
54. #89906C22semidirect
55. #89888C22semidirect
56. #89886C22semidirect
69. #89511C22semidirect
70. #89510C22semidirect
71. #89509C22semidirect
72. #89505C22semidirect
73. #89505C22semidirect
74. #89495C22semidirect
75. #89494C22semidirect
76. #89493C22semidirect
204. C2×#408D7semidirect
373. #408C2×D7semidirect
715. C2×C7#3201semidirect
797. C7C2×#3201semidirect
835. C2#11736126direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#905242
C2×#905162
C2×C7×#4082
C2×#899092
C2×#899062
C2×#898882
C2×#898862
#117361262
C2×#895112
C2×#895102
C2×#895052
C2×#894942
C2×#894952
C2×#895092
C2×#894932
C2×#32017