Finite Group Databasebeta

← C2×#11737496 #14230374

Subgroups — C2×#11737496 #14230374

Order 1792.

2374 conjugacy classes of subgroups.

The subgroup lattice has 824 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#90508C211yesmaximal, characteristic, complemented
2C2×#90302C211yesmaximal, characteristic, complemented
3C2×C7×#448C211yesmaximal, characteristic, complemented
4C22×#6409C211yesmaximal, characteristic, complemented
5C2×#89946C211yesmaximal, characteristic, complemented
6C2×#89944C211yesmaximal, characteristic, complemented
7C2×#89937C211yesmaximal, characteristic, complemented
8C2×#89936C211yesmaximal, characteristic, complemented
9C2×#89810C211yesmaximal, characteristic, complemented
10#11737496C2116yesmaximal, direct product factor
11C2×#89581C211yesmaximal, characteristic, complemented
12C2×#89575C211yesmaximal, characteristic, complemented
13C2×#89567C211yesmaximal, characteristic, complemented
14C2×#89566C211yesmaximal, characteristic, complemented
15C2×#89502C211yesmaximal, characteristic, complemented
16C2×#89508C211yesmaximal, characteristic, complemented
17C23×C7×Q8C2211yescharacteristic
18C22×#1161C2211yescharacteristic
19C22×#1159—21no—
20C22×C7×SD16C2211yescharacteristic
21C22×C7×SD16C2211yescharacteristic
22C2×C7×#121C2211yescharacteristic
23#90508—24no—
24#90508C2218yescomplemented
25C2×#6510—21no—
26C2×#6510C2211yescharacteristic
27C2×#6509—21no—
28C2×#6509C2211yescharacteristic
29C2×Q8×Dic7C2211yescharacteristic
30C2×#6501C2211yescharacteristic
31C2×#6498—21no—
32C2×D4×Dic7C2211yescharacteristic
33C22×#1141C2211yescharacteristic
34C2×#6493—21no—
35C2×#6493C2211yescharacteristic
36C2×C4×C22⋊D7—21no—
37C2×C4×C22⋊D7C2211yescharacteristic
38C22×C4⋊Dic7C2211yescharacteristic
39C23×C7⋊C8C2211yescharacteristic
40C22×#1131C2211yescharacteristic
41#90302—24no—
42#90302C2218yescomplemented
43C2×D7×C4⋊C4C2211yescharacteristic
44C2×#6451C2211yescharacteristic
45C2×#6446—21no—
46C2×#6441—21no—
47C7×#448C2218yescomplemented
48C2×C7×#103C2211yescharacteristic
49C2×C7×#103C2211yescharacteristic
50C2×C7×C22⋊C8C2211yescharacteristic
51C2×#6409C2211yescharacteristic
52C2×#6409C2211yescharacteristic
53C2×#6409C2211yescharacteristic
54C2×#6409C2211yescharacteristic
55C2×#6409C2218yescomplemented
56C2×#6406C2211yescharacteristic
57#89946C2218yescomplemented
58#89944C2218yescomplemented
59#89937C2218yescomplemented
60#89936C2218yescomplemented
61C2×#6395C2211yescharacteristic
62C2×#6395C2211yescharacteristic
63C2×(C2×D7)⋊C8C2211yescharacteristic
64C2×#6392C2211yescharacteristic
65C2×#6392C2211yescharacteristic
66C2×#6389C2211yescharacteristic
67C2×Dic7⋊C8C2211yescharacteristic
68#89810C2218yescomplemented
69C2×#6383C2211yescharacteristic
70C2×#6381C2211yescharacteristic
71#89581C2218yescomplemented
72#89575C2218yescomplemented
73#89567C2218yescomplemented
74#89566C2218yescomplemented
75#89508C2218yescomplemented
76#89502C2218yescomplemented
77C2×#3308—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
85C22×C7×D4—21no—
86C22×C7×D4C2311yescharacteristic
87C23×C4×C7—21no—
88C23×C4×C7C2311yescharacteristic
89C22×C22⋊D7—21no—
90C22×C22⋊D7—21no—
91C22×C22⋊D7D411yescharacteristic
92C23×Dic7—21no—
93C23×Dic7—21no—
94C2×#1161—22no—
95C2×#1161—24no—
96C2×#1161—42no—
97C2×#1161C2314yes—
98C2×#1159—28no—
99C2×#1159—48no—
100C22×D28—21no—
101C22×D28C2311yescharacteristic
102C22×C4×D7—21no—
103C22×C4×D7—21no—
104C22×C4×D7C2311yescharacteristic
105C22×Dic14—21no—
106C2×C7×SD16—24no—
107C2×C7×SD16—42no—
108C2×C7×SD16C2314yes—
109C2×C7×SD16C2314yes—
110C22×C7×C8C2311yescharacteristic
111C22×C7×C8C2311yescharacteristic
112C7×#121—22no—
113C7×#121C2314yes—
114C2×C7×C4⋊C4C2311yescharacteristic
115C2×C7×C22⋊C4—21no—
116C2×C22⋊Dic7—21no—
117C2×C22⋊Dic7—21no—
118C2×C22⋊Dic7D411yescharacteristic
119#6510—28no—
120#6510—22no—
121#6510C2314yes—
122#6509—22no—
123#6509—28no—
124#6509C2314yes—
125Q8×Dic7—22no—
126Q8×Dic7C2314yes—
127#6501—22no—
128#6501C2314yes—
129#6498—28no—
130D4×Dic7—22no—
131D4×Dic7C2314yes—
132C2×#1141—42no—
133C2×#1141C2314yes—
134#6493—22no—
135#6493—28no—
136#6493C2314yes—
137C4×C22⋊D7—28no—
138C4×C22⋊D7D414yes—
139C4×C22⋊D7C2314yes—
140C2×(C2×D7)⋊C4—21no—
141C2×(C2×D7)⋊C4—21no—
142C2×(C2×D7)⋊C4—21no—
143C2×(C2×D7)⋊C4—21no—
144C2×(C2×D7)⋊C4D411yescharacteristic
145C2×C4⋊Dic7—21no—
146C2×C4⋊Dic7—22no—
147C2×C4⋊Dic7—21no—
148C2×C4⋊Dic7C2311yescharacteristic
149C2×C4⋊Dic7C2311yescharacteristic
150C2×C4⋊Dic7C2311yescharacteristic
151C2×C4⋊Dic7C2314yes—
152C2×Dic7⋊C4—21no—
153C2×Dic7⋊C4—21no—
154C2×Dic7⋊C4—21no—
155C2×Dic7⋊C4D411yescharacteristic
156C2×C4×Dic7—21no—
157C2×C4×Dic7C2311yescharacteristic
158C22×C7⋊C8—42no—
159C22×C7⋊C8C2311yescharacteristic
160C22×C7⋊C8C2311yescharacteristic
161C22×C7⋊C8C2314yes—
162C2×#1131—42no—
163C2×#1131C2314yes—
164D7×C4⋊C4—22no—
165D7×C4⋊C4C2314yes—
166#6451—22no—
167#6451C2314yes—
168#6446—28no—
169#6441—28no—
170C7×#103C2314yes—
171C7×#103C2314yes—
172C7×C22⋊C8C2314yes—
173#6409C2314yes—
174#6409C2314yes—
175#6409C2314yes—
176#6409C2314yes—
177#6406C2314yes—
178#6395C2314yes—
179#6395C2314yes—
180(C2×D7)⋊C8C2314yes—
181#6392C2314yes—
182#6392C2314yes—
183#6389C2314yes—
184Dic7⋊C8C2314yes—
185#6383C2314yes—
186#6381C2314yes—
187C2×#548—71no—
188C2×#547—71no—
189#3308—716no—
190C2×#489—71no—
191C2×#484—71no—
192C2×#480—71no—
193C2×#477—71no—
194C2×#468—71no—
195C2×#466—71no—
196C2×#463—71no—
197C2×#449—71no—
198C2×#448D711yescharacteristic, complemented
199C2×#440—71no—
200C2×#435—71no—
201C2×#417—71no—
202C22×#103—71no—
203C24×C7—21no—
204C24×C7C2×D411yescharacteristic
205C23×D7—21no—
206C23×D7C2×D411yescharacteristic
207C2×C7×Q8—21no—
208C2×C7×Q8—24no—
209C2×C7×Q8—21no—
210C2×C7×Q8—22no—
211C2×C7×Q8—28no—
212C2×C7×Q8—22no—
213C2×C7×Q8—22no—
214C2×C7×Q8—44no—
215C2×C7×Q8—44no—
216C2×C7×Q8—48no—
217C2×C7×Q8#4114yescomplemented
218C2×C7×Q8C2412yes—
219C2×C7×Q8C2412yes—
220C2×C7×D4—24no—
221C2×C7×D4—21no—
222C2×C7×D4—22no—
223C2×C7×D4—22no—
224C2×C7×D4—44no—
225C2×C7×D4C2412yes—
226C22×C4×C7—21no—
227C22×C4×C7—22no—
228C22×C4×C7—22no—
229C22×C4×C7—21no—
230C22×C4×C7—21no—
231C22×C4×C7—24no—
232C22×C4×C7—44no—
233C22×C4×C7C2×D411yescharacteristic
234C22×C4×C7C2×D412yes—
235C22×C4×C7C2412yes—
236C22×C4×C7C2411yescharacteristic
237C2×C22⋊D7—24no—
238C2×C22⋊D7—24no—
239C2×C22⋊D7—24no—
240C2×C22⋊D7—44no—
241C2×C22⋊D7—44no—
242C2×C22⋊D7C2×D414yes—
243C22×Dic7—21no—
244C22×Dic7—21no—
245C22×Dic7—21no—
246C22×Dic7—24no—
247C22×Dic7—24no—
248C22×Dic7—44no—
249C22×Dic7—44no—
250C22×Dic7C2×D411yescharacteristic
251C22×Dic7C2×D411yescharacteristic
252C22×Dic7C2×D411yescharacteristic
253#1161—28no—
254#1161—44no—
255#1161—48no—
256#1159—432no—
257C2×D28—22no—
258C2×D28—22no—
259C2×D28—24no—
260C2×D28—21no—
261C2×D28—44no—
262C2×D28C2412yes—
263C2×C4×D7—22no—
264C2×C4×D7—22no—
265C2×C4×D7—24no—
266C2×C4×D7—24no—
267C2×C4×D7—44no—
268C2×C4×D7—44no—
269C2×C4×D7C2×D412yes—
270C2×C4×D7C2412yes—
271C2×Dic14—24no—
272C2×Dic14—44no—
273C7×SD16—28no—
274C7×SD16—44no—
275C2×C7×C8—22no—
276C2×C7×C8—22no—
277C2×C7×C8C2412yes—
278C2×C7×C8C2412yes—
279C7×C4⋊C4—21no—
280C7×C4⋊C4C2412yes—
281C7×C22⋊C4—24no—
282C22⋊Dic7—24no—
283C22⋊Dic7—24no—
284C22⋊Dic7C2×D414yes—
285#1141—44no—
286(C2×D7)⋊C4—24no—
287(C2×D7)⋊C4—24no—
288(C2×D7)⋊C4—24no—
289(C2×D7)⋊C4—24no—
290(C2×D7)⋊C4C2×D414yes—
291C4⋊Dic7—24no—
292C4⋊Dic7—21no—
293C4⋊Dic7—21no—
294C4⋊Dic7—21no—
295C4⋊Dic7—24no—
296C4⋊Dic7C2412yes—
297C4⋊Dic7C2412yes—
298C4⋊Dic7C2412yes—
299Dic7⋊C4—24no—
300Dic7⋊C4—24no—
301Dic7⋊C4—24no—
302Dic7⋊C4C2×D414yes—
303C4×Dic7—24no—
304C4×Dic7C2×D412yes—
305C4×Dic7C2412yes—
306C2×C7⋊C8—22no—
307C2×C7⋊C8—22no—
308C2×C7⋊C8—44no—
309C2×C7⋊C8C2412yes—
310C2×C7⋊C8C2412yes—
311#1131—44no—
312C22×#41—71no—
313C22×#41—141no—
314C23×Q8C2×D711yescharacteristic
315C22×SD16C2×D711yescharacteristic
316C22×SD16C2×D711yescharacteristic
317C22×D8—71no—
318C22×M16—71no—
319C23×C8—71no—
320#548—78no—
321#548—144no—
322#547—78no—
323#547—144no—
324C2×C4⋊Q8—71no—
325C2×#124—71no—
326C2×#124—141no—
327C2×#123—141no—
328C2×#123—141no—
329C2×C22⋊Q8—71no—
330C2×C22⋊Q8—141no—
331C2×C22⋊Q8—141no—
332C2×#121—71no—
333C2×#121—71no—
334C2×#121—141no—
335C2×#121C2×D711yescharacteristic
336C2×C4×Q8—71no—
337C2×C4×D4—71no—
338C2×C4×D4—71no—
339C2×C4×D4—141no—
340C22×C4⋊C4—71no—
341C22×C4⋊C4—71no—
342#489—78no—
343#484—78no—
344#480—78no—
345#477—78no—
346#468—78no—
347#466—78no—
348#463—78no—
349#449—78no—
350#448C2×D718yescomplemented
351#440—78no—
352#435—78no—
353C2×#107—71no—
354C2×#107—71no—
355C2×#107—71no—
356C2×C4⋊C8—71no—
357#417—78no—
358C2×#103—71no—
359C2×#103—71no—
360C2×#103—71no—
361C2×#103—71no—
362C2×#103—78no—
363C2×#103C2×D711yescharacteristic
364C2×#103C2×D711yescharacteristic
365C2×#102—71no—
366C2×#102—71no—
367C2×#102—71no—
368C2×#102—71no—
369C2×C22⋊C8—71no—
370C2×C22⋊C8C2×D711yescharacteristic
371C2×#97—71no—
372C23×C7—22no—
373C23×C7—22no—
374C23×C7—22no—
375C23×C7—42no—
376C23×C7—42no—
377C23×C7—42no—
378C23×C7AGL(1,ℤ/8)14yes—
379C23×C7C22×D412yes—
380C23×C7C22×D411yescharacteristic
381C22×D7—22no—
382C22×D7—22no—
383C22×D7—22no—
384C22×D7—22no—
385C22×D7—42no—
386C22×D7—42no—
387C22×D7—42no—
388C22×D7C22×D412yes—
389C7×Q8—24no—
390C7×Q8—22no—
391C7×Q8—22no—
392C7×Q8—22no—
393C7×Q8—48no—
394C7×Q8—42no—
395C7×Q8C2×#4114yescomplemented
396C7×D4—22no—
397C7×D4—22no—
398C7×D4—48no—
399C7×D4—42no—
400C2×C4×C7—24no—
401C2×C4×C7—22no—
402C2×C4×C7—22no—
403C2×C4×C7—24no—
404C2×C4×C7—22no—
405C2×C4×C7—22no—
406C2×C4×C7—22no—
407C2×C4×C7—22no—
408C2×C4×C7—48no—
409C2×C4×C7—42no—
410C2×C4×C7—42no—
411C2×C4×C7C22×D412yes—
412C2×C4×C7C22×D411yescharacteristic
413C2×C4×C7C2×#4112yes—
414C2×C4×C7H(5,𝔽2)12yes—
415C2×C4×C7C2511yescharacteristic
416C22⋊D7—28no—
417C22⋊D7—48no—
418C22⋊D7—48no—
419C2×Dic7—22no—
420C2×Dic7—22no—
421C2×Dic7—22no—
422C2×Dic7—22no—
423C2×Dic7—22no—
424C2×Dic7—22no—
425C2×Dic7—48no—
426C2×Dic7—42no—
427C2×Dic7—42no—
428C2×Dic7—48no—
429C2×Dic7—42no—
430C2×Dic7C22×D412yes—
431C2×Dic7C22×D412yes—
432C2×Dic7C22×D412yes—
433D28—22no—
434D28—22no—
435D28—48no—
436D28—42no—
437C4×D7—24no—
438C4×D7—22no—
439C4×D7—22no—
440C4×D7—48no—
441C4×D7—48no—
442Dic14—48no—
443C7×C8—22no—
444C7×C8—22no—
445C7⋊C8—22no—
446C7⋊C8—22no—
447C2×#41—74no—
448C2×#41—142no—
449C2×#41—148no—
450C2×#41—144no—
451C2×#41—282no—
452C2×#41—288no—
453C22×Q8—21no—
454C22×Q8—22no—
455C22×Q8—24no—
456C22×Q8—42no—
457C22×Q8—141no—
458C22×Q8C22×D711yescharacteristic
459C22×Q8C22×D714yes—
460C22×Q8C22×D711yescharacteristic
461C22×D4—21no—
462C22×D4—71no—
463C22×D4—71no—
464C22×D4—141no—
465C22×D4—141no—
466C22×D4—141no—
467C22×D4C22×D711yescharacteristic
468C23×C4—21no—
469C23×C4—71no—
470C23×C4—141no—
471C23×C4—141no—
472C23×C4—141no—
473C23×C4—141no—
474C23×C4C22×D711yescharacteristic
475C2×SD16—24no—
476C2×SD16—42no—
477C2×SD16C22×D714yes—
478C2×SD16C22×D714yes—
479C2×D8—74no—
480C2×D8—282no—
481C2×M16—74no—
482C2×M16—282no—
483C22×C8—71no—
484C22×C8—71no—
485C22×C8—74no—
486C22×C8—282no—
487C22×C8C22×D711yescharacteristic
488C22×C8C22×D711yescharacteristic
489C4⋊Q8—74no—
490C4⋊Q8—142no—
491#124—74no—
492#124—142no—
493#124—148no—
494#123—148no—
495#123—148no—
496C22⋊Q8—74no—
497C22⋊Q8—148no—
498C22⋊Q8—148no—
499C22⋊Q8—142no—
500#121—22no—
501#121—74no—
502#121—74no—
503#121—148no—
504#121—142no—
505#121—142no—
506#121C22×D714yes—
507C4×Q8—74no—
508C4×Q8—142no—
509C4×D4—74no—
510C4×D4—74no—
511C4×D4—74no—
512C4×D4—142no—
513C4×D4—148no—
514C2×C4⋊C4—71no—
515C2×C4⋊C4—71no—
516C2×C4⋊C4—71no—
517C2×C4⋊C4—74no—
518C2×C4⋊C4—71no—
519C2×C4⋊C4—74no—
520C2×C4⋊C4—142no—
521C2×C4⋊C4—141no—
522C2×C4⋊C4—141no—
523C2×C4⋊C4—141no—
524C2×C4⋊C4—141no—
525C2×C4⋊C4—141no—
526C2×C4⋊C4—142no—
527C2×C4⋊C4C22×D711yescharacteristic
528C2×C22⋊C4—21no—
529C2×C22⋊C4—71no—
530C2×C22⋊C4—71no—
531C2×C22⋊C4—141no—
532C2×C22⋊C4—141no—
533C2×C22⋊C4—141no—
534C2×C22⋊C4—141no—
535C2×C22⋊C4—141no—
536C2×C22⋊C4—141no—
537C2×C42—71no—
538C2×C42—141no—
539#107—74no—
540#107—74no—
541#107—74no—
542C4⋊C8—74no—
543#103—74no—
544#103—74no—
545#103—74no—
546#103—74no—
547#103C22×D714yes—
548#103C22×D714yes—
549#102—74no—
550#102—74no—
551#102—74no—
552#102—74no—
553C22⋊C8—74no—
554C22⋊C8C22×D714yes—
555#97—74no—
556C22×C7—22no—
557C22×C7—28no—
558C22×C7—22no—
559C22×C7—42no—
560C22×C7—42no—
561C22×C7—42no—
562C22×C7—84no—
563C22×C7#54612yes—
564C22×C7C2×AGL(1,ℤ/8)14yes—
565C22×C7C2×AGL(1,ℤ/8)12yes—
566C22×C7#57812yes—
567C22×C7C23×D411yescharacteristic
568C2×D7—22no—
569C2×D7—22no—
570C2×D7—22no—
571C2×D7—44no—
572C2×D7—42no—
573C2×D7—42no—
574C2×D7—42no—
575C2×D7—84no—
576C4×C7—24no—
577C4×C7—22no—
578C4×C7—42no—
579C4×C7—42no—
580C4×C7#54612yes—
581C4×C7C22×#4111yescharacteristic
582C4×C7C2×H(5,𝔽2)11yescharacteristic
583Dic7—22no—
584Dic7—22no—
585Dic7—22no—
586Dic7—42no—
587Dic7—42no—
588Dic7—42no—
589C24—21no—
590C24—71no—
591C24—141no—
592C24D4×D711yescharacteristic
593#41—148no—
594#41—284no—
595#41—288no—
596#41—2832no—
597C2×Q8—21no—
598C2×Q8—24no—
599C2×Q8—21no—
600C2×Q8—22no—
601C2×Q8—28no—
602C2×Q8—22no—
603C2×Q8—22no—
604C2×Q8—44no—
605C2×Q8—44no—
606C2×Q8—48no—
607C2×Q8—144no—
608C2×Q8—284no—
609C2×Q8#115914yescomplemented
610C2×Q8C23×D712yes—
611C2×Q8C23×D712yes—
612C2×D4—24no—
613C2×D4—21no—
614C2×D4—22no—
615C2×D4—22no—
616C2×D4—44no—
617C2×D4—74no—
618C2×D4—72no—
619C2×D4—144no—
620C2×D4—144no—
621C2×D4—144no—
622C2×D4—144no—
623C2×D4—141no—
624C2×D4—142no—
625C2×D4—142no—
626C2×D4—284no—
627C2×D4—284no—
628C2×D4—284no—
629C2×D4C23×D712yes—
630C22×C4—21no—
631C22×C4—22no—
632C22×C4—22no—
633C22×C4—24no—
634C22×C4—21no—
635C22×C4—21no—
636C22×C4—44no—
637C22×C4—71no—
638C22×C4—71no—
639C22×C4—71no—
640C22×C4—72no—
641C22×C4—72no—
642C22×C4—144no—
643C22×C4—144no—
644C22×C4—144no—
645C22×C4—142no—
646C22×C4—142no—
647C22×C4—144no—
648C22×C4—141no—
649C22×C4—141no—
650C22×C4—141no—
651C22×C4—284no—
652C22×C4—284no—
653C22×C4—284no—
654C22×C4—284no—
655C22×C4D4×D712yes—
656C22×C4D4×D711yescharacteristic
657C22×C4C23×D712yes—
658C22×C4C23×D711yescharacteristic
659SD16—28no—
660SD16—44no—
661D8—284no—
662M16—284no—
663C2×C8—22no—
664C2×C8—22no—
665C2×C8—72no—
666C2×C8—72no—
667C2×C8—142no—
668C2×C8—142no—
669C2×C8—284no—
670C2×C8C23×D712yes—
671C2×C8C23×D712yes—
672C4⋊C4—21no—
673C4⋊C4—74no—
674C4⋊C4—72no—
675C4⋊C4—72no—
676C4⋊C4—72no—
677C4⋊C4—144no—
678C4⋊C4—144no—
679C4⋊C4—144no—
680C4⋊C4—144no—
681C4⋊C4—141no—
682C4⋊C4—141no—
683C4⋊C4—144no—
684C4⋊C4—141no—
685C4⋊C4C23×D712yes—
686C22⋊C4—24no—
687C22⋊C4—74no—
688C22⋊C4—74no—
689C22⋊C4—144no—
690C22⋊C4—144no—
691C22⋊C4—144no—
692C22⋊C4—144no—
693C22⋊C4—144no—
694C22⋊C4—144no—
695C42—72no—
696C42—72no—
697C42—144no—
698C2×C7—24no—
699C2×C7—82no—
700C2×C7#330814yescomplemented
701C2×C7C2×#54611yescharacteristic
702C2×C7C22×AGL(1,ℤ/8)11yescharacteristic
703C2×C7C2×#57811yescharacteristic
704D7—42no—
705D7—82no—
706C23—22no—
707C23—22no—
708C23—22no—
709C23—42no—
710C23—42no—
711C23—42no—
712C23—72no—
713C23—142no—
714C23—142no—
715C23—142no—
716C23—142no—
717C23—282no—
718C23—282no—
719C23—282no—
720C23#647714yes—
721C23C2×D4×D712yes—
722C23C2×D4×D711yescharacteristic
723Q8—24no—
724Q8—22no—
725Q8—22no—
726Q8—22no—
727Q8—48no—
728Q8—42no—
729Q8—288no—
730Q8C2×#115914yescomplemented
731D4—22no—
732D4—22no—
733D4—48no—
734D4—42no—
735D4—148no—
736D4—142no—
737D4—142no—
738D4—288no—
739D4—288no—
740D4—288no—
741D4—282no—
742C2×C4—22no—
743C2×C4—24no—
744C2×C4—22no—
745C2×C4—24no—
746C2×C4—22no—
747C2×C4—22no—
748C2×C4—22no—
749C2×C4—22no—
750C2×C4—48no—
751C2×C4—42no—
752C2×C4—42no—
753C2×C4—72no—
754C2×C4—72no—
755C2×C4—72no—
756C2×C4—142no—
757C2×C4—142no—
758C2×C4—142no—
759C2×C4—144no—
760C2×C4—142no—
761C2×C4—142no—
762C2×C4—142no—
763C2×C4—142no—
764C2×C4—142no—
765C2×C4—288no—
766C2×C4—288no—
767C2×C4—288no—
768C2×C4—282no—
769C2×C4—282no—
770C2×C4—288no—
771C2×C4—282no—
772C2×C4C2×D4×D712yes—
773C2×C4C2×D4×D711yescharacteristic
774C2×C4C2×#115912yes—
775C2×C4#654812yes—
776C2×C4C24×D711yescharacteristic
777C8—22no—
778C8—22no—
779C8—142no—
780C8—142no—
781C7C2×#330811yescharacteristic, complemented, Sylow
782C22—22no—
783C22—22no—
784C22—28no—
785C22—42no—
786C22—42no—
787C22—42no—
788C22—84no—
789C22—142no—
790C22—142no—
791C22—142no—
792C22—284no—
793C22—282no—
794C22—282no—
795C22—282no—
796C22—564no—
797C22#9028212yes—
798C22C2×#647714yes—
799C22C2×#647712yes—
800C22#9047012yes—
801C22C22×D4×D711yescharacteristic
802C4—22no—
803C4—24no—
804C4—42no—
805C4—42no—
806C4—142no—
807C4—142no—
808C4—142no—
809C4—282no—
810C4—282no—
811C4—282no—
812C4#9028212yes—
813C4C22×#115911yescharacteristic
814C4C2×#654811yescharacteristic
815C2—24no—
816C2—82no—
817C2—282no—
818C2—562no—
819C2#1173749614yesdirect product factor
820C2C2×#9028211yescharacteristic
821C2C22×#647711yescharacteristic
822C2C2×#9047011yescharacteristic
subgroupG/H
centerC23C2×D4×D7
commutator, cosocleC2×C4×C7C25
FrattiniC2×C4C24×D7
FittingC2×C7×#448C2
socleC23×C7C22×D4
hypercenterC2×#448D7
hypocenterC7C2×#3308
LCSG ▷ C2×C4×C7 ▷ C2×C7 ▷ C7
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#448

Complements

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

NH ≅ G/Ntype
1. C2×#90508C2semidirect
2. C2×#90302C2semidirect
3. C2×C7×#448C2semidirect
4. C22×#6409C2semidirect
5. C2×#89946C2semidirect
6. C2×#89944C2semidirect
7. C2×#89937C2semidirect
8. C2×#89936C2semidirect
9. C2×#89810C2semidirect
10. #11737496C2direct (N × H)
11. C2×#89581C2semidirect
12. C2×#89575C2semidirect
13. C2×#89567C2semidirect
14. C2×#89566C2semidirect
15. C2×#89502C2semidirect
16. C2×#89508C2semidirect
24. #90508C22semidirect
42. #90302C22semidirect
47. C7×#448C22semidirect
55. C2×#6409C22semidirect
57. #89946C22semidirect
58. #89944C22semidirect
59. #89937C22semidirect
60. #89936C22semidirect
68. #89810C22semidirect
71. #89581C22semidirect
72. #89575C22semidirect
73. #89567C22semidirect
74. #89566C22semidirect
75. #89508C22semidirect
76. #89502C22semidirect
198. C2×#448D7semidirect
217. C2×C7×Q8#41semidirect
350. #448C2×D7semidirect
395. C7×Q8C2×#41semidirect
609. C2×Q8#1159semidirect
700. C2×C7#3308semidirect
730. Q8C2×#1159semidirect
781. C7C2×#3308semidirect
819. C2#11737496direct (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×#903022
C2×C7×#4482
C22×#64092
C2×#899462
C2×#899442
C2×#899372
C2×#899362
C2×#898102
#117374962
C2×#895812
C2×#895752
C2×#895672
C2×#895662
C2×#895022
C2×#895082
C2×#33087