Finite Group Databasebeta

← C2×#11736341 #14230371

Subgroups — C2×#11736341 #14230371

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×#90522C211yesmaximal, characteristic, complemented
2C2×#90198C211yesmaximal, characteristic, complemented
3C2×C7×#417C211yesmaximal, characteristic, complemented
4C2×#90010C211yesmaximal, characteristic, complemented
5C2×#89906C211yesmaximal, characteristic, complemented
6C2×#89899C211yesmaximal, characteristic, complemented
7C2×#89742C211yesmaximal, characteristic, complemented
8#11736341C2116yesmaximal, direct product factor
9C2×#89578C211yesmaximal, characteristic, complemented
10C2×D7×#103C211yesmaximal, characteristic, complemented
11C2×#89566C211yesmaximal, characteristic, complemented
12C2×#89589C211yesmaximal, characteristic, complemented
13C2×#89559C211yesmaximal, characteristic, complemented
14C2×#89546C211yesmaximal, characteristic, complemented
15C2×#89547C211yesmaximal, characteristic, complemented
16C2×#89537C211yesmaximal, characteristic, complemented
17C22×C7×#41C2211yescharacteristic
18C22×Q8×D7C2211yescharacteristic
19C22×#1157—21no—
20C22×C7×M16C2211yescharacteristic
21C22×C7×C4⋊C4C2211yescharacteristic
22#90522—24no—
23#90522C2218yescomplemented
24C2×Q8×Dic7C2211yescharacteristic
25C22×#1143C2211yescharacteristic
26C2×#6501—21no—
27C2×#6501C2211yescharacteristic
28C2×#6499—21no—
29C2×#6499C2211yescharacteristic
30C22×#1141C2211yescharacteristic
31C2×#6493C2211yescharacteristic
32C2×#6492—21no—
33C2×C4×C22⋊D7—21no—
34C2×C4×C22⋊D7C2211yescharacteristic
35C2×#6487—21no—
36C2×#6487C2211yescharacteristic
37C22×#1132C2211yescharacteristic
38C22×C8×D7C2211yescharacteristic
39C2×#6459—21no—
40#90198—24no—
41#90198C2218yescomplemented
42C2×#6458C2211yescharacteristic
43C2×#6457—21no—
44C2×#6456C2211yescharacteristic
45C2×D7×C4⋊C4C2211yescharacteristic
46C2×#6451C2211yescharacteristic
47C7×#417C2218yescomplemented
48C2×C7×#103C2211yescharacteristic
49C2×C7×#103C2211yescharacteristic
50C2×C7×#102C2211yescharacteristic
51C2×C7×#102C2211yescharacteristic
52#90010C2218yescomplemented
53C2×#6409C2211yescharacteristic
54C2×#6406C2211yescharacteristic
55C2×C22⋊(C7⋊C8)C2211yescharacteristic
56#89906C2218yescomplemented
57#89899C2218yescomplemented
58C2×#6395C2211yescharacteristic
59C2×(C2×D7)⋊C8C2211yescharacteristic
60C2×#6392C2211yescharacteristic
61C2×#6390C2211yescharacteristic
62C2×#6389C2211yescharacteristic
63C2×Dic7⋊C8C2211yescharacteristic
64#89742C2218yescomplemented
65C2×#6384C2211yescharacteristic
66C2×#6384C2211yescharacteristic
67C2×#6381C2211yescharacteristic
68C2×#6381C2211yescharacteristic
69#89589C2218yescomplemented
70#89578C2218yescomplemented
71D7×#103C2218yescomplemented
72#89566C2218yescomplemented
73#89559C2218yescomplemented
74#89547C2218yescomplemented
75#89546C2218yescomplemented
76#89537C2218yescomplemented
77C2×#3308—71nomaximal, Sylow
78C2×C7×#41—22no—
79C2×C7×#41—24no—
80C2×C7×#41—42no—
81C2×C7×#41C2314yes—
82C22×C7×Q8C2311yescharacteristic
83C22×C7×D4—21no—
84C22×C7×D4C2311yescharacteristic
85C23×C4×C7—21no—
86C23×C4×C7—21no—
87C23×C4×C7C2311yescharacteristic
88C22×C22⋊D7—21no—
89C22×C22⋊D7—21no—
90C22×C22⋊D7D411yescharacteristic
91C2×Q8×D7—22no—
92C2×Q8×D7—24no—
93C2×Q8×D7—42no—
94C2×Q8×D7C2314yes—
95C2×#1157—28no—
96C2×#1157—48no—
97C22×D28—21no—
98C22×D28C2311yescharacteristic
99C22×C4×D7—21no—
100C22×C4×D7—21no—
101C22×C4×D7—21no—
102C22×C4×D7C2311yescharacteristic
103C22×Dic14—21no—
104C22×Dic14—21no—
105C22×Dic14C2311yescharacteristic
106C2×C7×M16—42no—
107C2×C7×M16C2314yes—
108C22×C7×C8C2311yescharacteristic
109C22×C7×C8C2311yescharacteristic
110C2×C7×C4⋊C4—21no—
111C2×C7×C4⋊C4—22no—
112C2×C7×C4⋊C4C2311yescharacteristic
113C2×C7×C4⋊C4C2311yescharacteristic
114C2×C7×C4⋊C4C2314yes—
115C2×C22⋊Dic7—21no—
116C2×C22⋊Dic7—21no—
117C2×C22⋊Dic7—21no—
118C2×C22⋊Dic7—21no—
119C2×C22⋊Dic7D411yescharacteristic
120Q8×Dic7—22no—
121Q8×Dic7C2314yes—
122C2×#1143—24no—
123C2×#1143C2314yes—
124#6501—28no—
125#6501—22no—
126#6501C2314yes—
127#6499—28no—
128#6499—22no—
129#6499C2314yes—
130C2×#1141—42no—
131C2×#1141C2314yes—
132#6493—22no—
133#6493C2314yes—
134#6492—28no—
135C4×C22⋊D7—28no—
136C4×C22⋊D7D414yes—
137C4×C22⋊D7C2314yes—
138C2×(C2×D7)⋊C4—21no—
139C2×(C2×D7)⋊C4—21no—
140C2×(C2×D7)⋊C4—21no—
141C2×(C2×D7)⋊C4D411yescharacteristic
142C2×C4⋊Dic7—21no—
143C2×C4⋊Dic7C2311yescharacteristic
144C2×C4⋊Dic7C2311yescharacteristic
145#6487—22no—
146#6487—28no—
147#6487C2314yes—
148C2×Dic7⋊C4—21no—
149C2×Dic7⋊C4—21no—
150C2×Dic7⋊C4—21no—
151C2×Dic7⋊C4D411yescharacteristic
152C2×C4×Dic7—21no—
153C2×C4×Dic7C2311yescharacteristic
154C22×C7⋊C8C2311yescharacteristic
155C22×C7⋊C8C2311yescharacteristic
156C2×#1132—42no—
157C2×#1132C2314yes—
158C2×C8×D7—42no—
159C2×C8×D7C2314yes—
160#6459—28no—
161#6458—22no—
162#6458C2314yes—
163#6457—28no—
164#6456—22no—
165#6456C2314yes—
166D7×C4⋊C4—22no—
167D7×C4⋊C4C2314yes—
168#6451—22no—
169#6451C2314yes—
170C7×#103C2314yes—
171C7×#103C2314yes—
172C7×#102C2314yes—
173C7×#102C2314yes—
174#6409C2314yes—
175#6406C2314yes—
176C22⋊(C7⋊C8)C2314yes—
177#6395C2314yes—
178(C2×D7)⋊C8C2314yes—
179#6392C2314yes—
180#6390C2314yes—
181#6389C2314yes—
182Dic7⋊C8C2314yes—
183#6384C2314yes—
184#6384C2314yes—
185#6381C2314yes—
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×#448—71no—
199C2×#440—71no—
200C2×#435—71no—
201C2×#417D711yescharacteristic, complemented
202C22×#103—71no—
203C24×C7—21no—
204C24×C7C2×D411yescharacteristic
205C23×D7—21no—
206C23×D7C2×D411yescharacteristic
207C7×#41—28no—
208C7×#41—44no—
209C7×#41—48no—
210C2×C7×Q8—21no—
211C2×C7×Q8—22no—
212C2×C7×Q8#4114yescomplemented
213C2×C7×Q8C2412yes—
214C2×C7×D4—24no—
215C2×C7×D4—21no—
216C2×C7×D4—22no—
217C2×C7×D4—22no—
218C2×C7×D4—44no—
219C2×C7×D4C2412yes—
220C22×C4×C7—21no—
221C22×C4×C7—22no—
222C22×C4×C7—22no—
223C22×C4×C7—21no—
224C22×C4×C7—21no—
225C22×C4×C7—24no—
226C22×C4×C7—24no—
227C22×C4×C7—44no—
228C22×C4×C7—44no—
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×Dic7—21no—
242C22×Dic7C2×D411yescharacteristic
243C22×Dic7C2×D411yescharacteristic
244C22×Dic7C2×D411yescharacteristic
245Q8×D7—28no—
246Q8×D7—44no—
247Q8×D7—48no—
248#1157—432no—
249C2×D28—22no—
250C2×D28—22no—
251C2×D28—24no—
252C2×D28—21no—
253C2×D28—44no—
254C2×D28C2412yes—
255C2×C4×D7—22no—
256C2×C4×D7—22no—
257C2×C4×D7—24no—
258C2×C4×D7—24no—
259C2×C4×D7—24no—
260C2×C4×D7—44no—
261C2×C4×D7—44no—
262C2×C4×D7—44no—
263C2×C4×D7C2×D412yes—
264C2×C4×D7C2412yes—
265C2×Dic14—22no—
266C2×Dic14—22no—
267C2×Dic14—21no—
268C2×Dic14—24no—
269C2×Dic14—24no—
270C2×Dic14—44no—
271C2×Dic14—44no—
272C2×Dic14C2412yes—
273C7×M16—44no—
274C2×C7×C8—22no—
275C2×C7×C8—22no—
276C2×C7×C8C2412yes—
277C2×C7×C8C2412yes—
278C7×C4⋊C4—21no—
279C7×C4⋊C4—21no—
280C7×C4⋊C4—24no—
281C7×C4⋊C4C2412yes—
282C7×C4⋊C4C2412yes—
283C22⋊Dic7—24no—
284C22⋊Dic7—24no—
285C22⋊Dic7—24no—
286C22⋊Dic7—24no—
287C22⋊Dic7C2×D414yes—
288#1143—28no—
289#1141—44no—
290(C2×D7)⋊C4—24no—
291(C2×D7)⋊C4—24no—
292(C2×D7)⋊C4—24no—
293(C2×D7)⋊C4C2×D414yes—
294C4⋊Dic7—21no—
295C4⋊Dic7—21no—
296C4⋊Dic7—24no—
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⋊C8C2412yes—
309C2×C7⋊C8C2412yes—
310#1132—44no—
311C8×D7—44no—
312C22×#41—141no—
313C22×#41C2×D711yescharacteristic
314C23×Q8—71no—
315C22×SD16—71no—
316C22×SD16—71no—
317C22×D8—71no—
318C22×M16C2×D711yescharacteristic
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—71no—
335C2×#121—141no—
336C2×C4×Q8—71no—
337C2×C4×D4—71no—
338C2×C4×D4—71no—
339C2×C4×D4—141no—
340C22×C4⋊C4—71no—
341C22×C4⋊C4C2×D711yescharacteristic
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#448—78no—
351#440—78no—
352#435—78no—
353C2×#107—71no—
354C2×#107—71no—
355C2×#107—71no—
356C2×C4⋊C8—71no—
357#417C2×D718yescomplemented
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×#102C2×D711yescharacteristic
368C2×#102C2×D711yescharacteristic
369C2×C22⋊C8—71no—
370C2×C22⋊C8—71no—
371C2×#97—71no—
372C23×C7—22no—
373C23×C7—22no—
374C23×C7—22no—
375C23×C7—22no—
376C23×C7—42no—
377C23×C7—42no—
378C23×C7—42no—
379C23×C7C22×D412yes—
380C23×C7C22×D411yescharacteristic
381C22×D7—22no—
382C22×D7—22no—
383C22×D7—22no—
384C22×D7—42no—
385C22×D7—42no—
386C22×D7—42no—
387C22×D7AGL(1,ℤ/8)14yes—
388C22×D7C22×D412yes—
389C7×Q8—24no—
390C7×Q8—22no—
391C7×Q8C2×#4114yescomplemented
392C7×D4—22no—
393C7×D4—22no—
394C7×D4—48no—
395C7×D4—42no—
396C2×C4×C7—24no—
397C2×C4×C7—22no—
398C2×C4×C7—22no—
399C2×C4×C7—24no—
400C2×C4×C7—22no—
401C2×C4×C7—22no—
402C2×C4×C7—22no—
403C2×C4×C7—22no—
404C2×C4×C7—48no—
405C2×C4×C7—48no—
406C2×C4×C7—42no—
407C2×C4×C7—42no—
408C2×C4×C7C22×D412yes—
409C2×C4×C7C22×D411yescharacteristic
410C2×C4×C7C2×#4112yes—
411C2×C4×C7H(5,𝔽2)12yes—
412C2×C4×C7C2511yescharacteristic
413C22⋊D7—28no—
414C22⋊D7—48no—
415C22⋊D7—48no—
416C2×Dic7—22no—
417C2×Dic7—22no—
418C2×Dic7—22no—
419C2×Dic7—22no—
420C2×Dic7—22no—
421C2×Dic7—22no—
422C2×Dic7—42no—
423C2×Dic7—42no—
424C2×Dic7—42no—
425C2×Dic7C22×D412yes—
426C2×Dic7C22×D412yes—
427C2×Dic7C22×D412yes—
428D28—22no—
429D28—22no—
430D28—48no—
431D28—42no—
432C4×D7—24no—
433C4×D7—22no—
434C4×D7—22no—
435C4×D7—48no—
436C4×D7—48no—
437C4×D7—48no—
438Dic14—22no—
439Dic14—22no—
440Dic14—48no—
441Dic14—48no—
442Dic14—42no—
443C7×C8—22no—
444C7×C8—22no—
445C7⋊C8—22no—
446C7⋊C8—22no—
447C2×#41—22no—
448C2×#41—24no—
449C2×#41—42no—
450C2×#41—148no—
451C2×#41—288no—
452C2×#41C22×D714yes—
453C22×Q8—74no—
454C22×Q8—71no—
455C22×Q8—141no—
456C22×Q8—141no—
457C22×Q8—142no—
458C22×Q8—144no—
459C22×Q8—282no—
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—21no—
470C23×C4—71no—
471C23×C4—141no—
472C23×C4—141no—
473C23×C4—141no—
474C23×C4C22×D711yescharacteristic
475C2×SD16—74no—
476C2×SD16—74no—
477C2×SD16—144no—
478C2×SD16—282no—
479C2×D8—74no—
480C2×D8—282no—
481C2×M16—42no—
482C2×M16C22×D714yes—
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—74no—
501#121—74no—
502#121—74no—
503#121—142no—
504#121—142no—
505#121—148no—
506#121—142no—
507C4×Q8—74no—
508C4×Q8—142no—
509C4×D4—74no—
510C4×D4—74no—
511C4×D4—74no—
512C4×D4—142no—
513C4×D4—148no—
514C2×C4⋊C4—21no—
515C2×C4⋊C4—22no—
516C2×C4⋊C4—71no—
517C2×C4⋊C4—71no—
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⋊C4C22×D711yescharacteristic
526C2×C4⋊C4C22×D711yescharacteristic
527C2×C4⋊C4C22×D714yes—
528C2×C22⋊C4—71no—
529C2×C22⋊C4—71no—
530C2×C22⋊C4—141no—
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#102C22×D714yes—
552#102C22×D714yes—
553C22⋊C8—74no—
554C22⋊C8—74no—
555#97—74no—
556C22×C7—22no—
557C22×C7—22no—
558C22×C7—22no—
559C22×C7—44no—
560C22×C7—42no—
561C22×C7—42no—
562C22×C7—42no—
563C22×C7—84no—
564C22×C7#54612yes—
565C22×C7C2×AGL(1,ℤ/8)12yes—
566C22×C7#57812yes—
567C22×C7C23×D411yescharacteristic
568C2×D7—22no—
569C2×D7—28no—
570C2×D7—22no—
571C2×D7—42no—
572C2×D7—42no—
573C2×D7—42no—
574C2×D7—84no—
575C2×D7C2×AGL(1,ℤ/8)14yes—
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—28no—
594#41—44no—
595#41—48no—
596#41—2832no—
597C2×Q8—21no—
598C2×Q8—22no—
599C2×Q8—72no—
600C2×Q8—144no—
601C2×Q8—144no—
602C2×Q8—141no—
603C2×Q8—148no—
604C2×Q8—142no—
605C2×Q8—142no—
606C2×Q8—284no—
607C2×Q8—284no—
608C2×Q8—284no—
609C2×Q8—288no—
610C2×Q8#115714yescomplemented
611C2×Q8C23×D712yes—
612C2×D4—24no—
613C2×D4—22no—
614C2×D4—21no—
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—142no—
624C2×D4—141no—
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—24no—
637C22×C4—44no—
638C22×C4—44no—
639C22×C4—71no—
640C22×C4—71no—
641C22×C4—71no—
642C22×C4—72no—
643C22×C4—72no—
644C22×C4—144no—
645C22×C4—144no—
646C22×C4—144no—
647C22×C4—142no—
648C22×C4—142no—
649C22×C4—141no—
650C22×C4—141no—
651C22×C4—141no—
652C22×C4—284no—
653C22×C4—284no—
654C22×C4—284no—
655C22×C4D4×D712yes—
656C22×C4D4×D711yescharacteristic
657C22×C4C23×D712yes—
658C22×C4C23×D711yescharacteristic
659SD16—148no—
660SD16—284no—
661D8—284no—
662M16—44no—
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—21no—
674C4⋊C4—24no—
675C4⋊C4—74no—
676C4⋊C4—72no—
677C4⋊C4—72no—
678C4⋊C4—144no—
679C4⋊C4—144no—
680C4⋊C4—144no—
681C4⋊C4—144no—
682C4⋊C4—141no—
683C4⋊C4—141no—
684C4⋊C4C23×D712yes—
685C4⋊C4C23×D712yes—
686C22⋊C4—74no—
687C22⋊C4—74no—
688C22⋊C4—144no—
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—42no—
699C2×C7—82no—
700C2×C7#330814yescomplemented
701C2×C7C2×#54611yescharacteristic
702C2×C7C22×AGL(1,ℤ/8)11yescharacteristic
703C2×C7C2×#57811yescharacteristic
704D7—24no—
705D7—82no—
706C23—22no—
707C23—22no—
708C23—22no—
709C23—22no—
710C23—42no—
711C23—42no—
712C23—42no—
713C23—74no—
714C23—72no—
715C23—142no—
716C23—142no—
717C23—142no—
718C23—282no—
719C23—282no—
720C23—282no—
721C23C2×D4×D712yes—
722C23C2×D4×D711yescharacteristic
723Q8—24no—
724Q8—22no—
725Q8—142no—
726Q8—142no—
727Q8—288no—
728Q8—288no—
729Q8—282no—
730Q8C2×#115714yescomplemented
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—48no—
752C2×C4—42no—
753C2×C4—42no—
754C2×C4—72no—
755C2×C4—72no—
756C2×C4—72no—
757C2×C4—142no—
758C2×C4—142no—
759C2×C4—142no—
760C2×C4—144no—
761C2×C4—142no—
762C2×C4—142no—
763C2×C4—142no—
764C2×C4—142no—
765C2×C4—142no—
766C2×C4—288no—
767C2×C4—288no—
768C2×C4—288no—
769C2×C4—282no—
770C2×C4—282no—
771C2×C4—282no—
772C2×C4C2×#115712yes—
773C2×C4C2×D4×D712yes—
774C2×C4C2×D4×D711yescharacteristic
775C2×C4#654812yes—
776C2×C4C24×D711yescharacteristic
777C8—22no—
778C8—22no—
779C8—142no—
780C8—142no—
781C7C2×#330811yescharacteristic, complemented, Sylow
782C22—22no—
783C22—22no—
784C22—22no—
785C22—44no—
786C22—42no—
787C22—42no—
788C22—42no—
789C22—74no—
790C22—84no—
791C22—142no—
792C22—148no—
793C22—142no—
794C22—282no—
795C22—282no—
796C22—282no—
797C22—564no—
798C22#9018112yes—
799C22D7×AGL(1,ℤ/8)12yes—
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#9018112yes—
813C4C22×#115711yescharacteristic
814C4C2×#654811yescharacteristic
815C2—42no—
816C2—82no—
817C2—144no—
818C2—562no—
819C2#1173634114yesdirect product factor
820C2C2×#9018111yescharacteristic
821C2C2×D7×AGL(1,ℤ/8)11yescharacteristic
822C2C2×#9047011yescharacteristic
subgroupG/H
centerC23C2×D4×D7
commutator, cosocleC2×C4×C7C25
FrattiniC2×C4C24×D7
FittingC2×C7×#417C2
socleC23×C7C22×D4
hypercenterC2×#417D7
hypocenterC7C2×#3308
LCSG ▷ C2×C4×C7 ▷ C2×C7 ▷ C7
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#417

Complements

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

NH ≅ G/Ntype
1. C2×#90522C2semidirect
2. C2×#90198C2semidirect
3. C2×C7×#417C2semidirect
4. C2×#90010C2semidirect
5. C2×#89906C2semidirect
6. C2×#89899C2semidirect
7. C2×#89742C2semidirect
8. #11736341C2direct (N × H)
9. C2×#89578C2semidirect
10. C2×D7×#103C2semidirect
11. C2×#89566C2semidirect
12. C2×#89589C2semidirect
13. C2×#89559C2semidirect
14. C2×#89546C2semidirect
15. C2×#89547C2semidirect
16. C2×#89537C2semidirect
23. #90522C22semidirect
41. #90198C22semidirect
47. C7×#417C22semidirect
52. #90010C22semidirect
56. #89906C22semidirect
57. #89899C22semidirect
64. #89742C22semidirect
69. #89589C22semidirect
70. #89578C22semidirect
71. D7×#103C22semidirect
72. #89566C22semidirect
73. #89559C22semidirect
74. #89547C22semidirect
75. #89546C22semidirect
76. #89537C22semidirect
201. C2×#417D7semidirect
212. C2×C7×Q8#41semidirect
357. #417C2×D7semidirect
391. C7×Q8C2×#41semidirect
610. C2×Q8#1157semidirect
700. C2×C7#3308semidirect
730. Q8C2×#1157semidirect
781. C7C2×#3308semidirect
819. C2#11736341direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#905222
C2×#901982
C2×C7×#4172
C2×#900102
C2×#899062
C2×#898992
C2×#897422
#117363412
C2×#895782
C2×D7×#1032
C2×#895662
C2×#895892
C2×#895592
C2×#895462
C2×#895472
C2×#895372
C2×#33087