Finite Group Databasebeta

← C2×#11740963 #14232321

Subgroups — C2×#11740963 #14232321

Order 1792.

2094 conjugacy classes of subgroups.

The subgroup lattice has 748 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C7×#547C211yesmaximal, characteristic
2C2×#90232C211yesmaximal, characteristic, complemented
3#11740963C2116yesmaximal, direct product factor
4C2×#89863C211yesmaximal, characteristic, complemented
5C2×#89852C211yesmaximal, characteristic, complemented
6C2×#89814C211yesmaximal, characteristic, complemented
7C2×#89813C211yesmaximal, characteristic, complemented
8C2×#89807C211yesmaximal, characteristic, complemented
9C2×#89805C211yesmaximal, characteristic, complemented
10C2×#89783C211yesmaximal, characteristic, complemented
11C2×#89781C211yesmaximal, characteristic, complemented
12C2×#89790C211yesmaximal, characteristic, complemented
13C2×#89742C211yesmaximal, characteristic, complemented
14C2×#89743C211yesmaximal, characteristic, complemented
15C2×#89736C211yesmaximal, characteristic, complemented
16C22×#6381C211yesmaximal, characteristic, complemented
17C22×C7×#41—21no—
18C7×#547—24no—
19C7×#547C2218yes—
20C2×C7×C4⋊Q8C2211yescharacteristic
21C2×C7×#123—21no—
22C2×C7×#123—21no—
23C2×C7×C22⋊Q8—21no—
24C2×C7×#121C2211yescharacteristic
25C2×C7×#121C2211yescharacteristic
26C2×C4×C7×D4C2211yescharacteristic
27C2×C4×C7×D4C2211yescharacteristic
28C22×C7×C4⋊C4C2211yescharacteristic
29C22×C7×C4⋊C4C2211yescharacteristic
30C2×#6498—21no—
31C22×#1142C2211yescharacteristic
32C2×#6489C2211yescharacteristic
33C22×C4⋊Dic7C2211yescharacteristic
34C2×#6487C2211yescharacteristic
35C2×#6487C2211yescharacteristic
36C22×#1136C2211yescharacteristic
37C23×C7⋊C8C2211yescharacteristic
38#90232—24no—
39#90232C2218yescomplemented
40C2×#6452—21no—
41C2×#6442—21no—
42C2×#6440—21no—
43C2×#6433C2211yescharacteristic
44C2×C4×Dic14C2211yescharacteristic
45C2×#6406C2211yescharacteristic
46C2×#6406C2211yescharacteristic
47C2×#6406C2211yescharacteristic
48C2×C22⋊(C7⋊C8)C2211yescharacteristic
49C2×C22⋊(C7⋊C8)C2211yescharacteristic
50#89863C2218yescomplemented
51#89852C2218yescomplemented
52#89814C2218yescomplemented
53#89813C2218yescomplemented
54#89807C2218yescomplemented
55#89805C2218yescomplemented
56#89790C2218yescomplemented
57#89783C2218yescomplemented
58#89781C2218yescomplemented
59#89743C2218yescomplemented
60#89742C2218yescomplemented
61C2×#6384C2211yescharacteristic
62C2×#6384C2211yescharacteristic
63C2×#6384C2211yescharacteristic
64#89736C2218yescomplemented
65C2×#6382C2211yescharacteristic
66C2×#6382C2211yescharacteristic
67C2×#6382C2211yescharacteristic
68C2×#6381C2211yescharacteristic
69C2×#6381C2211yescharacteristic
70C2×#6381C2211yescharacteristic
71C2×#6381C2211yescharacteristic
72C2×#6381C2211yescharacteristic
73C2×#6381C2211yescharacteristic
74C2×#6381C2218yescomplemented
75C2×C4⋊(C7⋊C8)C2211yescharacteristic
76C2×#6377C2211yescharacteristic
77C2×#3343—71nomaximal, Sylow
78C2×C7×#41—28no—
79C2×C7×#41—48no—
80C22×C7×Q8—21no—
81C22×C7×D4—21no—
82C22×C7×D4—21no—
83C22×C7×D4D411yescharacteristic
84C22×C7×D4C2311yescharacteristic
85C23×C4×C7—21no—
86C23×C4×C7—21no—
87C23×C4×C7—21no—
88C23×C4×C7C2311yescharacteristic
89C23×C4×C7C2311yescharacteristic
90C23×Dic7—21no—
91C22×Dic14C2311yescharacteristic
92C7×C4⋊Q8—22no—
93C7×C4⋊Q8C2314yes—
94C7×#123—28no—
95C7×#123—28no—
96C7×C22⋊Q8—28no—
97C7×#121—22no—
98C7×#121—22no—
99C7×#121C2314yes—
100C7×#121C2314yes—
101C4×C7×D4—22no—
102C4×C7×D4D414yes—
103C4×C7×D4C2314yes—
104C4×C7×D4C2314yes—
105C2×C7×C4⋊C4—21no—
106C2×C7×C4⋊C4—21no—
107C2×C7×C4⋊C4—22no—
108C2×C7×C4⋊C4—22no—
109C2×C7×C4⋊C4—21no—
110C2×C7×C4⋊C4D411yescharacteristic
111C2×C7×C4⋊C4C2311yescharacteristic
112C2×C7×C4⋊C4C2311yescharacteristic
113C2×C7×C4⋊C4C2311yescharacteristic
114C2×C7×C4⋊C4C2314yes—
115C2×C7×C4⋊C4C2314yes—
116C2×C7×C22⋊C4—21no—
117C2×C7×C22⋊C4—21no—
118C2×C7×C22⋊C4—21no—
119C2×C7×C22⋊C4D411yescharacteristic
120C2×C7×C22⋊C4D411yescharacteristic
121C2×C42×C7C2311yescharacteristic
122C2×C22⋊Dic7—21no—
123C2×C22⋊Dic7—21no—
124C2×C22⋊Dic7—21no—
125#6498—28no—
126C2×#1142—24no—
127C2×#1142C2314yes—
128#6489—22no—
129#6489C2314yes—
130C2×C4⋊Dic7—21no—
131C2×C4⋊Dic7—22no—
132C2×C4⋊Dic7C2311yescharacteristic
133C2×C4⋊Dic7C2311yescharacteristic
134C2×C4⋊Dic7C2311yescharacteristic
135C2×C4⋊Dic7C2314yes—
136#6487—22no—
137#6487—22no—
138#6487C2314yes—
139#6487C2314yes—
140C2×Dic7⋊C4—21no—
141C2×Dic7⋊C4—21no—
142C2×Dic7⋊C4—21no—
143C2×Dic7⋊C4—21no—
144C2×Dic7⋊C4—21no—
145C2×C4×Dic7—21no—
146C2×C4×Dic7—21no—
147C2×#1136—24no—
148C2×#1136C2314yes—
149C22×C7⋊C8—24no—
150C22×C7⋊C8C2311yescharacteristic
151C22×C7⋊C8C2311yescharacteristic
152C22×C7⋊C8C2311yescharacteristic
153C22×C7⋊C8C2314yes—
154C22×C7⋊C8C2311yescharacteristic
155#6452—28no—
156#6442—28no—
157#6440—28no—
158#6433—22no—
159#6433C2314yes—
160C4×Dic14—22no—
161C4×Dic14C2314yes—
162#6406C2314yes—
163#6406C2314yes—
164#6406C2314yes—
165C22⋊(C7⋊C8)C2314yes—
166C22⋊(C7⋊C8)C2314yes—
167#6384C2314yes—
168#6384C2314yes—
169#6384C2314yes—
170#6382C2314yes—
171#6382C2314yes—
172#6382C2314yes—
173#6381C2314yes—
174#6381C2314yes—
175#6381C2314yes—
176#6381C2314yes—
177#6381C2314yes—
178#6381C2314yes—
179C4⋊(C7⋊C8)C2314yes—
180#6377C2314yes—
181C2×#552—71no—
182C2×#547D711yescharacteristic
183#3343—716no—
184C2×#501—71no—
185C2×#484—71no—
186C2×#482—71no—
187C2×#483—71no—
188C2×#480—71no—
189C2×#477—71no—
190C2×#478—71no—
191C2×#468—71no—
192C2×#465—71no—
193C2×#440—71no—
194C2×#435—71no—
195C2×#428—71no—
196C22×#107—71no—
197C24×C7—21no—
198C24×C7C2×D411yescharacteristic
199C24×C7C2×D411yescharacteristic
200C7×#41—432no—
201C2×C7×Q8—24no—
202C2×C7×Q8—44no—
203C2×C7×D4—24no—
204C2×C7×D4—24no—
205C2×C7×D4—24no—
206C2×C7×D4—21no—
207C2×C7×D4—22no—
208C2×C7×D4—22no—
209C2×C7×D4—44no—
210C2×C7×D4—44no—
211C2×C7×D4C2×D414yes—
212C2×C7×D4C2412yes—
213C22×C4×C7—22no—
214C22×C4×C7—22no—
215C22×C4×C7—22no—
216C22×C4×C7—22no—
217C22×C4×C7—21no—
218C22×C4×C7—21no—
219C22×C4×C7—21no—
220C22×C4×C7—24no—
221C22×C4×C7—24no—
222C22×C4×C7—24no—
223C22×C4×C7—44no—
224C22×C4×C7—44no—
225C22×C4×C7—44no—
226C22×C4×C7C2×D411yescharacteristic
227C22×C4×C7C2×D411yescharacteristic
228C22×C4×C7C2×D411yescharacteristic
229C22×C4×C7C2×D411yescharacteristic
230C22×C4×C7C2×D412yes—
231C22×C4×C7C2×D412yes—
232C22×C4×C7C2412yes—
233C22×C4×C7C2412yes—
234C22×C4×C7C2411yescharacteristic
235C22×Dic7—24no—
236C22×Dic7—21no—
237C22×Dic7—21no—
238C22×Dic7—21no—
239C22×Dic7—21no—
240C22×Dic7—44no—
241C2×Dic14—22no—
242C2×Dic14—22no—
243C2×Dic14—21no—
244C2×Dic14C2412yes—
245C7×C4⋊C4—21no—
246C7×C4⋊C4—21no—
247C7×C4⋊C4—21no—
248C7×C4⋊C4—24no—
249C7×C4⋊C4—24no—
250C7×C4⋊C4—24no—
251C7×C4⋊C4C2×D414yes—
252C7×C4⋊C4C2412yes—
253C7×C4⋊C4C2412yes—
254C7×C4⋊C4C2412yes—
255C7×C22⋊C4—24no—
256C7×C22⋊C4—24no—
257C7×C22⋊C4—24no—
258C7×C22⋊C4C2×D414yes—
259C7×C22⋊C4C2×D414yes—
260C42×C7C2×D412yes—
261C42×C7C2412yes—
262C22⋊Dic7—24no—
263C22⋊Dic7—24no—
264C22⋊Dic7—24no—
265#1142—28no—
266C4⋊Dic7—21no—
267C4⋊Dic7—21no—
268C4⋊Dic7—21no—
269C4⋊Dic7—24no—
270C4⋊Dic7C2412yes—
271C4⋊Dic7C2412yes—
272C4⋊Dic7C2412yes—
273Dic7⋊C4—24no—
274Dic7⋊C4—24no—
275Dic7⋊C4—24no—
276Dic7⋊C4—24no—
277Dic7⋊C4—24no—
278C4×Dic7—24no—
279C4×Dic7—24no—
280#1136—28no—
281C2×C7⋊C8—22no—
282C2×C7⋊C8—22no—
283C2×C7⋊C8—22no—
284C2×C7⋊C8—28no—
285C2×C7⋊C8#4114yescomplemented
286C2×C7⋊C8C2412yes—
287C2×C7⋊C8C2412yes—
288C2×C7⋊C8C2412yes—
289C2×C7⋊C8C2412yes—
290C22×#41—21no—
291C22×SD16—71no—
292C22×M16—71no—
293C23×C8—71no—
294#552—78no—
295#552—144no—
296#547—24no—
297#547C2×D718yes—
298C2×C4⋊Q8C2×D711yescharacteristic
299C2×#126—141no—
300C2×#125—71no—
301C2×#125—141no—
302C2×#123—21no—
303C2×#123—21no—
304C2×#123—141no—
305C2×C22⋊Q8—21no—
306C2×C22⋊Q8—71no—
307C2×C22⋊Q8—71no—
308C2×#121C2×D711yescharacteristic
309C2×#121C2×D711yescharacteristic
310C2×C4×Q8—71no—
311C2×C4×D4C2×D711yescharacteristic
312C2×C4×D4C2×D711yescharacteristic
313C2×#117—71no—
314C2×#117—141no—
315C22×C4⋊C4—71no—
316C22×C4⋊C4C2×D711yescharacteristic
317C22×C4⋊C4C2×D711yescharacteristic
318#501—78no—
319#484—78no—
320#483—78no—
321#482—78no—
322#480—78no—
323#478—78no—
324#477—78no—
325#468—78no—
326#465—78no—
327#440—78no—
328#435—78no—
329#428—78no—
330C2×#107—71no—
331C2×#107—71no—
332C2×#107—71no—
333C2×#107—71no—
334C2×#107—78no—
335C2×#107—71no—
336C2×#107—71no—
337C2×#106—71no—
338C2×#106—71no—
339C2×#106—71no—
340C2×C4⋊C8—71no—
341C2×#103—71no—
342C2×#103—71no—
343C2×#103—71no—
344C2×#102—71no—
345C2×#102—71no—
346C2×#102—71no—
347C2×C22⋊C8—71no—
348C2×C22⋊C8—71no—
349C2×#97—71no—
350C23×C7—22no—
351C23×C7—22no—
352C23×C7—22no—
353C23×C7—22no—
354C23×C7—22no—
355C23×C7—22no—
356C23×C7—42no—
357C23×C7—42no—
358C23×C7—42no—
359C23×C7AGL(1,ℤ/8)14yes—
360C23×C7C22×D412yes—
361C23×C7C22×D412yes—
362C23×C7C22×D411yescharacteristic
363C7×Q8—48no—
364C7×D4—28no—
365C7×D4—22no—
366C7×D4—22no—
367C7×D4—48no—
368C7×D4—48no—
369C7×D4—42no—
370C2×C4×C7—22no—
371C2×C4×C7—22no—
372C2×C4×C7—22no—
373C2×C4×C7—22no—
374C2×C4×C7—24no—
375C2×C4×C7—24no—
376C2×C4×C7—22no—
377C2×C4×C7—22no—
378C2×C4×C7—22no—
379C2×C4×C7—22no—
380C2×C4×C7—22no—
381C2×C4×C7—22no—
382C2×C4×C7—22no—
383C2×C4×C7—48no—
384C2×C4×C7—48no—
385C2×C4×C7—42no—
386C2×C4×C7—42no—
387C2×C4×C7—42no—
388C2×C4×C7—48no—
389C2×C4×C7C22×D412yes—
390C2×C4×C7C22×D412yes—
391C2×C4×C7C22×D412yes—
392C2×C4×C7C22×D412yes—
393C2×C4×C7C22×D411yescharacteristic
394C2×C4×C7C2×#4112yes—
395C2×C4×C72−1+412yes—
396C2×C4×C7C2511yescharacteristic
397C2×Dic7—22no—
398C2×Dic7—22no—
399C2×Dic7—22no—
400C2×Dic7—22no—
401C2×Dic7—42no—
402C2×Dic7—48no—
403C2×Dic7—42no—
404C2×Dic7—42no—
405C2×Dic7—42no—
406Dic14—22no—
407Dic14—22no—
408Dic14—42no—
409C7⋊C8—22no—
410C7⋊C8—22no—
411C7⋊C8—22no—
412C7⋊C8C2×#4114yescomplemented
413C2×#41—28no—
414C2×#41—48no—
415C22×Q8—21no—
416C22×Q8—71no—
417C22×D4—21no—
418C22×D4—21no—
419C22×D4C22⋊D711yescharacteristic
420C22×D4C22×D711yescharacteristic
421C23×C4—21no—
422C23×C4—21no—
423C23×C4—21no—
424C23×C4—141no—
425C23×C4C22×D711yescharacteristic
426C23×C4C22×D711yescharacteristic
427C2×SD16—74no—
428C2×SD16—144no—
429C2×M16—74no—
430C2×M16—144no—
431C22×C8—71no—
432C22×C8—71no—
433C22×C8—74no—
434C22×C8—71no—
435C22×C8—71no—
436C22×C8—144no—
437C4⋊Q8—22no—
438C4⋊Q8C22×D714yes—
439#126—148no—
440#125—74no—
441#125—148no—
442#125—142no—
443#123—28no—
444#123—28no—
445#123—148no—
446C22⋊Q8—28no—
447C22⋊Q8—74no—
448C22⋊Q8—74no—
449C22⋊Q8—142no—
450C22⋊Q8—142no—
451#121—22no—
452#121—22no—
453#121C22×D714yes—
454#121C22×D714yes—
455C4×Q8—74no—
456C4×Q8—142no—
457C4×D4—22no—
458C4×D4C22⋊D714yes—
459C4×D4C22×D714yes—
460C4×D4C22×D714yes—
461#117—74no—
462#117—142no—
463#117—148no—
464C2×C4⋊C4—21no—
465C2×C4⋊C4—21no—
466C2×C4⋊C4—22no—
467C2×C4⋊C4—22no—
468C2×C4⋊C4—21no—
469C2×C4⋊C4—71no—
470C2×C4⋊C4—71no—
471C2×C4⋊C4—74no—
472C2×C4⋊C4—71no—
473C2×C4⋊C4—141no—
474C2×C4⋊C4—142no—
475C2×C4⋊C4—141no—
476C2×C4⋊C4—141no—
477C2×C4⋊C4—141no—
478C2×C4⋊C4—141no—
479C2×C4⋊C4—141no—
480C2×C4⋊C4C22⋊D711yescharacteristic
481C2×C4⋊C4C22×D711yescharacteristic
482C2×C4⋊C4C22×D711yescharacteristic
483C2×C4⋊C4C22×D711yescharacteristic
484C2×C4⋊C4C22×D714yes—
485C2×C4⋊C4C22×D714yes—
486C2×C22⋊C4—21no—
487C2×C22⋊C4—21no—
488C2×C22⋊C4—21no—
489C2×C22⋊C4—141no—
490C2×C22⋊C4—141no—
491C2×C22⋊C4—141no—
492C2×C22⋊C4C22⋊D711yescharacteristic
493C2×C22⋊C4C22⋊D711yescharacteristic
494C2×C42—141no—
495C2×C42—141no—
496C2×C42C22×D711yescharacteristic
497#107—74no—
498#107—74no—
499#107—74no—
500#107—74no—
501#107—74no—
502#107—74no—
503#106—74no—
504#106—74no—
505#106—74no—
506C4⋊C8—74no—
507#103—74no—
508#103—74no—
509#103—74no—
510#102—74no—
511#102—74no—
512#102—74no—
513C22⋊C8—74no—
514C22⋊C8—74no—
515#97—74no—
516C22×C7—28no—
517C22×C7—22no—
518C22×C7—22no—
519C22×C7—22no—
520C22×C7—22no—
521C22×C7—22no—
522C22×C7—44no—
523C22×C7—42no—
524C22×C7—42no—
525C22×C7—42no—
526C22×C7—84no—
527C22×C7#54712yes—
528C22×C7C2×AGL(1,ℤ/8)14yes—
529C22×C7C2×AGL(1,ℤ/8)12yes—
530C22×C7#57812yes—
531C22×C7C23×D411yescharacteristic
532C4×C7—22no—
533C4×C7—22no—
534C4×C7—22no—
535C4×C7—22no—
536C4×C7—42no—
537C4×C7—42no—
538C4×C7—42no—
539C4×C7#54712yes—
540C4×C7C22×#4111yescharacteristic
541C4×C7C2×2−1+411yescharacteristic
542Dic7—42no—
543Dic7—42no—
544Dic7—42no—
545Dic7—42no—
546C24—21no—
547C24C2×C22⋊D711yescharacteristic
548C24C2×C22⋊D711yescharacteristic
549#41—432no—
550C2×Q8—24no—
551C2×Q8—44no—
552C2×Q8—72no—
553C2×Q8—141no—
554C2×Q8—142no—
555C2×Q8—142no—
556C2×D4—24no—
557C2×D4—24no—
558C2×D4—24no—
559C2×D4—22no—
560C2×D4—22no—
561C2×D4—21no—
562C2×D4—44no—
563C2×D4—44no—
564C2×D4C2×C22⋊D714yes—
565C2×D4C23×D712yes—
566C22×C4—22no—
567C22×C4—22no—
568C22×C4—22no—
569C22×C4—22no—
570C22×C4—24no—
571C22×C4—24no—
572C22×C4—21no—
573C22×C4—21no—
574C22×C4—21no—
575C22×C4—24no—
576C22×C4—44no—
577C22×C4—44no—
578C22×C4—44no—
579C22×C4—144no—
580C22×C4—141no—
581C22×C4—141no—
582C22×C4—141no—
583C22×C4—141no—
584C22×C4—284no—
585C22×C4C2×C22⋊D712yes—
586C22×C4C2×C22⋊D712yes—
587C22×C4C2×C22⋊D711yescharacteristic
588C22×C4C2×C22⋊D711yescharacteristic
589C22×C4C2×C22⋊D711yescharacteristic
590C22×C4C2×C22⋊D711yescharacteristic
591C22×C4C23×D712yes—
592C22×C4C23×D712yes—
593C22×C4C23×D711yescharacteristic
594SD16—148no—
595M16—148no—
596C2×C8—74no—
597C2×C8—72no—
598C2×C8—72no—
599C2×C8—72no—
600C2×C8—72no—
601C2×C8—148no—
602C2×C8—142no—
603C2×C8—142no—
604C2×C8—142no—
605C4⋊C4—21no—
606C4⋊C4—21no—
607C4⋊C4—21no—
608C4⋊C4—24no—
609C4⋊C4—24no—
610C4⋊C4—24no—
611C4⋊C4—72no—
612C4⋊C4—72no—
613C4⋊C4—72no—
614C4⋊C4—144no—
615C4⋊C4—144no—
616C4⋊C4—144no—
617C4⋊C4—144no—
618C4⋊C4—144no—
619C4⋊C4—141no—
620C4⋊C4—141no—
621C4⋊C4—144no—
622C4⋊C4—141no—
623C4⋊C4C2×C22⋊D714yes—
624C4⋊C4C23×D712yes—
625C4⋊C4C23×D712yes—
626C4⋊C4C23×D712yes—
627C22⋊C4—24no—
628C22⋊C4—24no—
629C22⋊C4—24no—
630C22⋊C4—144no—
631C22⋊C4—144no—
632C22⋊C4—144no—
633C22⋊C4C2×C22⋊D714yes—
634C22⋊C4C2×C22⋊D714yes—
635C42—144no—
636C42—144no—
637C42C2×C22⋊D712yes—
638C42C23×D712yes—
639C2×C7—24no—
640C2×C7—42no—
641C2×C7—82no—
642C2×C7#334314yescomplemented
643C2×C7C2×#54711yescharacteristic
644C2×C7C22×AGL(1,ℤ/8)11yescharacteristic
645C2×C7C2×#57811yescharacteristic
646C23—22no—
647C23—22no—
648C23—22no—
649C23—22no—
650C23—22no—
651C23—22no—
652C23—42no—
653C23—42no—
654C23—42no—
655C23#649514yes—
656C23C22×C22⋊D712yes—
657C23C22×C22⋊D712yes—
658C23C22×C22⋊D711yescharacteristic
659Q8—48no—
660Q8—142no—
661Q8—142no—
662Q8—282no—
663D4—28no—
664D4—22no—
665D4—22no—
666D4—48no—
667D4—48no—
668D4—42no—
669C2×C4—22no—
670C2×C4—22no—
671C2×C4—22no—
672C2×C4—22no—
673C2×C4—24no—
674C2×C4—24no—
675C2×C4—22no—
676C2×C4—22no—
677C2×C4—22no—
678C2×C4—22no—
679C2×C4—22no—
680C2×C4—22no—
681C2×C4—22no—
682C2×C4—48no—
683C2×C4—48no—
684C2×C4—42no—
685C2×C4—42no—
686C2×C4—42no—
687C2×C4—48no—
688C2×C4—142no—
689C2×C4—142no—
690C2×C4—142no—
691C2×C4—142no—
692C2×C4—288no—
693C2×C4—282no—
694C2×C4—282no—
695C2×C4—282no—
696C2×C4—282no—
697C2×C4D7×#4112yes—
698C2×C4#655412yes—
699C2×C4C22×C22⋊D712yes—
700C2×C4C22×C22⋊D712yes—
701C2×C4C22×C22⋊D712yes—
702C2×C4C22×C22⋊D712yes—
703C2×C4C22×C22⋊D711yescharacteristic
704C2×C4C24×D711yescharacteristic
705C8—74no—
706C8—142no—
707C8—142no—
708C8—142no—
709C7C2×#334311yescharacteristic, complemented, Sylow
710C22—28no—
711C22—22no—
712C22—22no—
713C22—22no—
714C22—22no—
715C22—22no—
716C22—44no—
717C22—42no—
718C22—42no—
719C22—42no—
720C22—84no—
721C22C2×#649514yes—
722C22C2×#649512yes—
723C22#9051512yes—
724C22#9052912yes—
725C22C23×C22⋊D711yescharacteristic
726C4—22no—
727C4—22no—
728C4—22no—
729C4—22no—
730C4—42no—
731C4—42no—
732C4—42no—
733C4—282no—
734C4—282no—
735C4—282no—
736C4—282no—
737C4#9051512yes—
738C4C2×D7×#4111yescharacteristic
739C4C2×#655411yescharacteristic
740C2—24no—
741C2—42no—
742C2—82no—
743C2#1174096314yesdirect product factor
744C2C22×#649511yescharacteristic
745C2C2×#9051511yescharacteristic
746C2C2×#9052911yescharacteristic
subgroupG/H
centerC23C22×C22⋊D7
commutator, cosocleC2×C4×C7C25
FrattiniC2×C4C24×D7
Fitting, prime radicalC2×C7×#547C2
socleC23×C7C22×D4
hypercenterC2×#547D7
hypocenterC7C2×#3343
LCSG ▷ C2×C4×C7 ▷ C2×C7 ▷ C7
UCSC1 ◁ C23 ◁ C2×C4×D4 ◁ C2×#547

Complements

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

NH ≅ G/Ntype
2. C2×#90232C2semidirect
3. #11740963C2direct (N × H)
4. C2×#89863C2semidirect
5. C2×#89852C2semidirect
6. C2×#89814C2semidirect
7. C2×#89813C2semidirect
8. C2×#89807C2semidirect
9. C2×#89805C2semidirect
10. C2×#89783C2semidirect
11. C2×#89781C2semidirect
12. C2×#89790C2semidirect
13. C2×#89742C2semidirect
14. C2×#89743C2semidirect
15. C2×#89736C2semidirect
16. C22×#6381C2semidirect
39. #90232C22semidirect
50. #89863C22semidirect
51. #89852C22semidirect
52. #89814C22semidirect
53. #89813C22semidirect
54. #89807C22semidirect
55. #89805C22semidirect
56. #89790C22semidirect
57. #89783C22semidirect
58. #89781C22semidirect
59. #89743C22semidirect
60. #89742C22semidirect
64. #89736C22semidirect
74. C2×#6381C22semidirect
285. C2×C7⋊C8#41semidirect
412. C7⋊C8C2×#41semidirect
642. C2×C7#3343semidirect
709. C7C2×#3343semidirect
743. C2#11740963direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C7×#5472
C2×#902322
#117409632
C2×#898632
C2×#898522
C2×#898142
C2×#898132
C2×#898072
C2×#898052
C2×#897832
C2×#897812
C2×#897902
C2×#897422
C2×#897432
C2×#897362
C22×#63812
C2×#33437