Finite Group Databasebeta

← C2×#11738765 #14232217

Subgroups — C2×#11738765 #14232217

Order 1792.

2158 conjugacy classes of subgroups.

The subgroup lattice has 756 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#90302C211yesmaximal, characteristic
2C2×#90202C211yesmaximal, characteristic, complemented
3C2×C7×#481C211yesmaximal, characteristic, complemented
4C2×#89813C211yesmaximal, characteristic, complemented
5C22×#6382C211yesmaximal, characteristic, complemented
6#11738765C2116yesmaximal, direct product factor
7C2×#89626C211yesmaximal, characteristic, complemented
8C2×#89634C211yesmaximal, characteristic, complemented
9C2×D7×#106C211yesmaximal, characteristic, complemented
10C2×#89627C211yesmaximal, characteristic, complemented
11C2×#89549C211yesmaximal, characteristic, complemented
12C2×#89550C211yesmaximal, characteristic, complemented
13C2×#89533C211yesmaximal, characteristic, complemented
14C2×#89530C211yesmaximal, characteristic, complemented
15C2×(C22⋊D7)⋊C8C211yesmaximal, characteristic, complemented
16C2×#89493C211yesmaximal, characteristic, complemented
17C22×#1159—21no—
18C2×C7×#121C2211yescharacteristic
19C22×C7×C4⋊C4C2211yescharacteristic
20C2×#6501C2211yescharacteristic
21C2×#6498—21no—
22C2×D4×Dic7C2211yescharacteristic
23C22×#1142C2211yescharacteristic
24C2×C4×C22⋊D7—21no—
25C2×C4×C22⋊D7C2211yescharacteristic
26C22×C4⋊Dic7C2211yescharacteristic
27C2×#6487—21no—
28C2×#6487C2211yescharacteristic
29C23×C7⋊C8C2211yescharacteristic
30C22×C8×D7C2211yescharacteristic
31#90302—24no—
32#90302C2218yes—
33#90202—24no—
34#90202C2218yescomplemented
35C2×#6460C2211yescharacteristic
36C2×#6459—21no—
37C2×D7×C4⋊C4C2211yescharacteristic
38C2×D7×C4⋊C4C2211yescharacteristic
39C2×#6452—21no—
40C2×#6451C2211yescharacteristic
41C2×#6451C2211yescharacteristic
42C2×#6450C2211yescharacteristic
43C2×#6446—21no—
44C2×#6441—21no—
45C7×#481C2218yescomplemented
46C2×C7×#106C2211yescharacteristic
47C2×C7×#106C2211yescharacteristic
48C2×C7×#102C2211yescharacteristic
49C2×C7×#102C2211yescharacteristic
50C2×C7×C22⋊C8C2211yescharacteristic
51C2×#6406C2211yescharacteristic
52C2×(C2×D7)⋊C8C2211yescharacteristic
53C2×#6391C2211yescharacteristic
54C2×#6391C2211yescharacteristic
55C2×#6390C2211yescharacteristic
56C2×#6390C2211yescharacteristic
57C2×Dic7⋊C8C2211yescharacteristic
58C2×C8×Dic7C2211yescharacteristic
59#89813C2218yescomplemented
60C2×#6384C2211yescharacteristic
61C2×#6382C2211yescharacteristic
62C2×#6382C2211yescharacteristic
63C2×#6382C2211yescharacteristic
64C2×#6382C2211yescharacteristic
65C2×#6382C2211yescharacteristic
66C2×#6382C2218yescomplemented
67#89634C2218yescomplemented
68D7×#106C2218yescomplemented
69#89627C2218yescomplemented
70#89626C2218yescomplemented
71#89550C2218yescomplemented
72#89549C2218yescomplemented
73#89533C2218yescomplemented
74#89530C2218yescomplemented
75(C22⋊D7)⋊C8C2218yescomplemented
76#89493C2218yescomplemented
77C2×#3335—71nomaximal, Sylow
78C22×C7×D4—21no—
79C22×C7×D4C2311yescharacteristic
80C23×C4×C7—21no—
81C23×C4×C7C2311yescharacteristic
82C22×C22⋊D7—21no—
83C22×C22⋊D7D411yescharacteristic
84C23×Dic7—21no—
85C23×Dic7—21no—
86C2×#1159—28no—
87C2×#1159—48no—
88C22×C4×D7—21no—
89C22×C4×D7—21no—
90C22×C4×D7C2311yescharacteristic
91C22×Dic14—21no—
92C22×Dic14—21no—
93C22×Dic14C2311yescharacteristic
94C22×C7×C8C2311yescharacteristic
95C22×C7×C8C2311yescharacteristic
96C7×#121—22no—
97C7×#121C2314yes—
98C2×C7×C4⋊C4—21no—
99C2×C7×C4⋊C4—22no—
100C2×C7×C4⋊C4C2314yes—
101C2×C7×C4⋊C4C2311yescharacteristic
102C2×C7×C4⋊C4C2311yescharacteristic
103C2×C7×C4⋊C4C2311yescharacteristic
104C2×C7×C22⋊C4—21no—
105C2×C22⋊Dic7—21no—
106C2×C22⋊Dic7—21no—
107C2×C22⋊Dic7—21no—
108C2×C22⋊Dic7D411yescharacteristic
109#6501—22no—
110#6501C2314yes—
111#6498—28no—
112D4×Dic7—22no—
113D4×Dic7C2314yes—
114C2×#1142—24no—
115C2×#1142C2314yes—
116C4×C22⋊D7—28no—
117C4×C22⋊D7D414yes—
118C4×C22⋊D7C2314yes—
119C2×(C2×D7)⋊C4—21no—
120C2×(C2×D7)⋊C4D411yescharacteristic
121C2×C4⋊Dic7—21no—
122C2×C4⋊Dic7—22no—
123C2×C4⋊Dic7—21no—
124C2×C4⋊Dic7C2311yescharacteristic
125C2×C4⋊Dic7C2311yescharacteristic
126C2×C4⋊Dic7C2311yescharacteristic
127C2×C4⋊Dic7C2314yes—
128#6487—22no—
129#6487—28no—
130#6487C2314yes—
131C2×Dic7⋊C4—21no—
132C2×Dic7⋊C4—21no—
133C2×Dic7⋊C4—21no—
134C2×Dic7⋊C4—21no—
135C2×Dic7⋊C4—21no—
136C2×Dic7⋊C4—21no—
137C2×Dic7⋊C4D411yescharacteristic
138C2×C4×Dic7—21no—
139C2×C4×Dic7C2311yescharacteristic
140C22×C7⋊C8—24no—
141C22×C7⋊C8C2311yescharacteristic
142C22×C7⋊C8C2314yes—
143C22×C7⋊C8C2311yescharacteristic
144C2×C8×D7—24no—
145C2×C8×D7C2314yes—
146#6460—22no—
147#6460C2314yes—
148#6459—28no—
149D7×C4⋊C4—22no—
150D7×C4⋊C4—22no—
151D7×C4⋊C4C2314yes—
152D7×C4⋊C4C2314yes—
153#6452—28no—
154#6451—22no—
155#6451—22no—
156#6451C2314yes—
157#6451C2314yes—
158#6450—22no—
159#6450C2314yes—
160#6446—28no—
161#6441—28no—
162C7×#106C2314yes—
163C7×#106C2314yes—
164C7×#102C2314yes—
165C7×#102C2314yes—
166C7×C22⋊C8C2314yes—
167#6406C2314yes—
168(C2×D7)⋊C8C2314yes—
169#6391C2314yes—
170#6391C2314yes—
171#6390C2314yes—
172#6390C2314yes—
173Dic7⋊C8C2314yes—
174C8×Dic7C2314yes—
175#6384C2314yes—
176#6382C2314yes—
177#6382C2314yes—
178#6382C2314yes—
179#6382C2314yes—
180#6382C2314yes—
181C2×#554—71no—
182C2×#547—71no—
183#3335—716no—
184C2×#498—71no—
185C2×#481—71no—
186C2×#481D711yescharacteristic, complemented
187C2×#483—71no—
188C2×#483—71no—
189C2×#475—71no—
190C2×#476—71no—
191C2×#465—71no—
192C2×#465—71no—
193C2×C4×SD16—71no—
194C2×C8×D4—71no—
195C22×#106—71no—
196C22×#106—71no—
197C24×C7—21no—
198C24×C7C2×D411yescharacteristic
199C23×D7C2×D411yescharacteristic
200C2×C7×D4—24no—
201C2×C7×D4—21no—
202C2×C7×D4—22no—
203C2×C7×D4—22no—
204C2×C7×D4—44no—
205C2×C7×D4C2412yes—
206C22×C4×C7—22no—
207C22×C4×C7—22no—
208C22×C4×C7—21no—
209C22×C4×C7—21no—
210C22×C4×C7—21no—
211C22×C4×C7—24no—
212C22×C4×C7—82no—
213C22×C4×C7C2×D411yescharacteristic
214C22×C4×C7C2×D412yes—
215C22×C4×C7C2412yes—
216C22×C4×C7C2411yescharacteristic
217C2×C22⋊D7—24no—
218C2×C22⋊D7—44no—
219C2×C22⋊D7SD1618yescomplemented
220C2×C22⋊D7C2×D414yes—
221C22×Dic7—21no—
222C22×Dic7—21no—
223C22×Dic7—21no—
224C22×Dic7—21no—
225C22×Dic7—24no—
226C22×Dic7—24no—
227C22×Dic7—44no—
228C22×Dic7—44no—
229C22×Dic7C2×D411yescharacteristic
230C22×Dic7C2×D411yescharacteristic
231C22×Dic7C2×D411yescharacteristic
232#1159—432no—
233C2×C4×D7—22no—
234C2×C4×D7—22no—
235C2×C4×D7—24no—
236C2×C4×D7—24no—
237C2×C4×D7—44no—
238C2×C4×D7—82no—
239C2×C4×D7C2×D412yes—
240C2×C4×D7C2412yes—
241C2×Dic14—22no—
242C2×Dic14—22no—
243C2×Dic14—21no—
244C2×Dic14—24no—
245C2×Dic14—24no—
246C2×Dic14—44no—
247C2×Dic14—82no—
248C2×Dic14C2412yes—
249C2×C7×C8—22no—
250C2×C7×C8—22no—
251C2×C7×C8C2412yes—
252C2×C7×C8C2412yes—
253C7×C4⋊C4—21no—
254C7×C4⋊C4—21no—
255C7×C4⋊C4—21no—
256C7×C4⋊C4—24no—
257C7×C4⋊C4C2412yes—
258C7×C4⋊C4C2412yes—
259C7×C4⋊C4C2412yes—
260C7×C22⋊C4—24no—
261C22⋊Dic7—24no—
262C22⋊Dic7—24no—
263C22⋊Dic7—24no—
264C22⋊Dic7C2×D414yes—
265#1142—28no—
266(C2×D7)⋊C4—24no—
267(C2×D7)⋊C4C2×D414yes—
268C4⋊Dic7—24no—
269C4⋊Dic7—21no—
270C4⋊Dic7—21no—
271C4⋊Dic7—21no—
272C4⋊Dic7—24no—
273C4⋊Dic7C2412yes—
274C4⋊Dic7C2412yes—
275C4⋊Dic7C2412yes—
276Dic7⋊C4—24no—
277Dic7⋊C4—24no—
278Dic7⋊C4—24no—
279Dic7⋊C4—24no—
280Dic7⋊C4—24no—
281Dic7⋊C4—24no—
282Dic7⋊C4C2×D414yes—
283C4×Dic7—24no—
284C4×Dic7C2×D412yes—
285C4×Dic7C2412yes—
286C2×C7⋊C8—22no—
287C2×C7⋊C8—28no—
288C2×C7⋊C8#4114yescomplemented
289C2×C7⋊C8C2412yes—
290C2×C7⋊C8C2412yes—
291C8×D7—28no—
292C22×#41—141no—
293C22×SD16—71no—
294C23×C8—71no—
295C23×C8—71no—
296#554—78no—
297#554—144no—
298#547—78no—
299#547—144no—
300C2×C4⋊Q8—71no—
301C2×C4⋊Q8—71no—
302C2×#125—141no—
303C2×#123—141no—
304C2×#123—141no—
305C2×C22⋊Q8—71no—
306C2×C22⋊Q8—71no—
307C2×C22⋊Q8—141no—
308C2×C22⋊Q8—141no—
309C2×C22⋊Q8—141no—
310C2×#121—71no—
311C2×#121C2×D711yescharacteristic
312C2×C4×Q8—71no—
313C2×C4×D4—71no—
314C2×C4×D4—71no—
315C2×C4×D4—141no—
316C22×C4⋊C4—71no—
317C22×C4⋊C4—71no—
318C22×C4⋊C4—71no—
319C22×C4⋊C4C2×D711yescharacteristic
320#498—78no—
321#483—78no—
322#483—78no—
323#481—78no—
324#481C2×D718yescomplemented
325#476—78no—
326#475—78no—
327#465—78no—
328#465—78no—
329C4×SD16—78no—
330C8×D4—78no—
331C2×#106—71no—
332C2×#106—71no—
333C2×#106—71no—
334C2×#106—78no—
335C2×#106—71no—
336C2×#106—71no—
337C2×#106—71no—
338C2×#106—71no—
339C2×#106—78no—
340C2×#106C2×D711yescharacteristic
341C2×#106C2×D711yescharacteristic
342C2×C4⋊C8—71no—
343C2×#103—71no—
344C2×#103—71no—
345C2×#103—71no—
346C2×#102—71no—
347C2×#102C2×D711yescharacteristic
348C2×#102C2×D711yescharacteristic
349C2×C22⋊C8—71no—
350C2×C22⋊C8C2×D711yescharacteristic
351C2×C4×C8—71no—
352C23×C7—22no—
353C23×C7—22no—
354C23×C7—22no—
355C23×C7—42no—
356C23×C7—42no—
357C23×C7—42no—
358C23×C7C2×SD1614yes—
359C23×C7C22×D412yes—
360C23×C7C22×D411yescharacteristic
361C22×D7—22no—
362C22×D7—22no—
363C22×D7C2×SD1614yes—
364C22×D7C22×D412yes—
365C7×D4—22no—
366C7×D4—22no—
367C7×D4—48no—
368C7×D4—42no—
369C2×C4×C7—22no—
370C2×C4×C7—24no—
371C2×C4×C7—22no—
372C2×C4×C7—22no—
373C2×C4×C7—22no—
374C2×C4×C7—22no—
375C2×C4×C7—22no—
376C2×C4×C7—42no—
377C2×C4×C7—42no—
378C2×C4×C7—42no—
379C2×C4×C7—84no—
380C2×C4×C7C22×D412yes—
381C2×C4×C7C22×D411yescharacteristic
382C2×C4×C7C2×#4112yes—
383C2×C4×C72−1+412yes—
384C2×C4×C7C2511yescharacteristic
385C22⋊D7—48no—
386C22⋊D7C2×SD16116yescomplemented
387C2×Dic7—22no—
388C2×Dic7—22no—
389C2×Dic7—22no—
390C2×Dic7—22no—
391C2×Dic7—22no—
392C2×Dic7—22no—
393C2×Dic7—42no—
394C2×Dic7—42no—
395C2×Dic7—42no—
396C2×Dic7—48no—
397C2×Dic7—42no—
398C2×Dic7—48no—
399C2×Dic7C2×SD1614yes—
400C2×Dic7C22×D412yes—
401C2×Dic7C22×D412yes—
402C2×Dic7C22×D412yes—
403C4×D7—24no—
404C4×D7—22no—
405C4×D7—22no—
406C4×D7—48no—
407C4×D7—84no—
408Dic14—22no—
409Dic14—22no—
410Dic14—42no—
411Dic14—48no—
412Dic14—84no—
413C7×C8—22no—
414C7×C8—22no—
415C7⋊C8—22no—
416C7⋊C8C2×#4114yescomplemented
417C2×#41—148no—
418C2×#41—288no—
419C22×Q8—71no—
420C22×Q8—141no—
421C22×Q8—141no—
422C22×D4—21no—
423C22×D4—71no—
424C22×D4—141no—
425C22×D4C22×D711yescharacteristic
426C23×C4—21no—
427C23×C4—71no—
428C23×C4—141no—
429C23×C4—141no—
430C23×C4—141no—
431C23×C4—141no—
432C23×C4C22×D711yescharacteristic
433C2×SD16—74no—
434C2×SD16—144no—
435C22×C8—71no—
436C22×C8—71no—
437C22×C8—74no—
438C22×C8—74no—
439C22×C8—144no—
440C22×C8—144no—
441C22×C8C22×D711yescharacteristic
442C22×C8C22×D711yescharacteristic
443C4⋊Q8—74no—
444C4⋊Q8—74no—
445C4⋊Q8—142no—
446C4⋊Q8—142no—
447#125—148no—
448#123—148no—
449#123—148no—
450C22⋊Q8—74no—
451C22⋊Q8—74no—
452C22⋊Q8—148no—
453C22⋊Q8—148no—
454C22⋊Q8—148no—
455C22⋊Q8—142no—
456C22⋊Q8—142no—
457#121—22no—
458#121—74no—
459#121—142no—
460#121C22×D714yes—
461C4×Q8—74no—
462C4×Q8—142no—
463C4×D4—74no—
464C4×D4—74no—
465C4×D4—74no—
466C4×D4—142no—
467C4×D4—148no—
468C2×C4⋊C4—21no—
469C2×C4⋊C4—22no—
470C2×C4⋊C4—71no—
471C2×C4⋊C4—71no—
472C2×C4⋊C4—71no—
473C2×C4⋊C4—71no—
474C2×C4⋊C4—74no—
475C2×C4⋊C4—74no—
476C2×C4⋊C4—74no—
477C2×C4⋊C4—142no—
478C2×C4⋊C4—142no—
479C2×C4⋊C4—141no—
480C2×C4⋊C4—141no—
481C2×C4⋊C4—141no—
482C2×C4⋊C4—141no—
483C2×C4⋊C4—141no—
484C2×C4⋊C4—141no—
485C2×C4⋊C4—141no—
486C2×C4⋊C4—142no—
487C2×C4⋊C4—141no—
488C2×C4⋊C4C22×D711yescharacteristic
489C2×C4⋊C4C22×D711yescharacteristic
490C2×C4⋊C4C22×D711yescharacteristic
491C2×C4⋊C4C22×D714yes—
492C2×C22⋊C4—21no—
493C2×C22⋊C4—71no—
494C2×C22⋊C4—71no—
495C2×C22⋊C4—141no—
496C2×C22⋊C4—141no—
497C2×C22⋊C4—141no—
498C2×C22⋊C4—141no—
499C2×C42—71no—
500C2×C42—141no—
501#106—74no—
502#106—74no—
503#106—74no—
504#106—74no—
505#106—74no—
506#106—74no—
507#106—74no—
508#106C22×D714yes—
509#106C22×D714yes—
510C4⋊C8—74no—
511#103—74no—
512#103—74no—
513#103—74no—
514#102—74no—
515#102C22×D714yes—
516#102C22×D714yes—
517C22⋊C8—74no—
518C22⋊C8C22×D714yes—
519C4×C8—74no—
520C22×C7—28no—
521C22×C7—22no—
522C22×C7—22no—
523C22×C7—42no—
524C22×C7—42no—
525C22×C7—42no—
526C22×C7—84no—
527C22×C7#54712yes—
528C22×C7C22×SD1614yes—
529C22×C7C22×SD1612yes—
530C22×C7#57712yes—
531C22×C7C23×D411yescharacteristic
532C2×D7—28no—
533C2×D7—22no—
534C2×D7—22no—
535C2×D7C22×SD1614yes—
536C4×C7—22no—
537C4×C7—42no—
538C4×C7—42no—
539C4×C7—42no—
540C4×C7#54712yes—
541C4×C7C22×#4111yescharacteristic
542C4×C7C2×2−1+411yescharacteristic
543Dic7—22no—
544Dic7—22no—
545Dic7—42no—
546Dic7—42no—
547Dic7—42no—
548Dic7—42no—
549Dic7C22×SD1614yes—
550C24—21no—
551C24—71no—
552C24D4×D711yescharacteristic
553#41—2832no—
554C2×Q8—72no—
555C2×Q8—144no—
556C2×Q8—144no—
557C2×Q8—141no—
558C2×Q8—142no—
559C2×Q8—142no—
560C2×Q8—284no—
561C2×Q8—562no—
562C2×D4—24no—
563C2×D4—21no—
564C2×D4—22no—
565C2×D4—22no—
566C2×D4—44no—
567C2×D4—78no—
568C2×D4—74no—
569C2×D4—144no—
570C2×D4—284no—
571C2×D4C23×D712yes—
572C22×C4—22no—
573C22×C4—22no—
574C22×C4—21no—
575C22×C4—21no—
576C22×C4—21no—
577C22×C4—24no—
578C22×C4—71no—
579C22×C4—71no—
580C22×C4—71no—
581C22×C4—72no—
582C22×C4—72no—
583C22×C4—82no—
584C22×C4—144no—
585C22×C4—144no—
586C22×C4—144no—
587C22×C4—142no—
588C22×C4—142no—
589C22×C4—144no—
590C22×C4—141no—
591C22×C4—141no—
592C22×C4—141no—
593C22×C4—141no—
594C22×C4—284no—
595C22×C4—284no—
596C22×C4—284no—
597C22×C4—562no—
598C22×C4D4×D712yes—
599C22×C4D4×D711yescharacteristic
600C22×C4C23×D712yes—
601C22×C4C23×D711yescharacteristic
602SD16—148no—
603C2×C8—22no—
604C2×C8—22no—
605C2×C8—74no—
606C2×C8—72no—
607C2×C8—72no—
608C2×C8—148no—
609C2×C8—148no—
610C2×C8—142no—
611C2×C8C23×D712yes—
612C2×C8C23×D712yes—
613C4⋊C4—21no—
614C4⋊C4—24no—
615C4⋊C4—21no—
616C4⋊C4—21no—
617C4⋊C4—74no—
618C4⋊C4—72no—
619C4⋊C4—72no—
620C4⋊C4—72no—
621C4⋊C4—144no—
622C4⋊C4—144no—
623C4⋊C4—144no—
624C4⋊C4—144no—
625C4⋊C4—144no—
626C4⋊C4—144no—
627C4⋊C4—144no—
628C4⋊C4—141no—
629C4⋊C4—141no—
630C4⋊C4—144no—
631C4⋊C4—141no—
632C4⋊C4C23×D712yes—
633C4⋊C4C23×D712yes—
634C4⋊C4C23×D712yes—
635C22⋊C4—24no—
636C22⋊C4—74no—
637C22⋊C4—74no—
638C22⋊C4—144no—
639C22⋊C4—144no—
640C22⋊C4—144no—
641C22⋊C4—144no—
642C42—72no—
643C42—72no—
644C42—144no—
645C2×C7—24no—
646C2×C7—82no—
647C2×C7#333514yescomplemented
648C2×C7C2×#54711yescharacteristic
649C2×C7C23×SD1611yescharacteristic
650C2×C7C2×#57711yescharacteristic
651D7—24no—
652C23—22no—
653C23—22no—
654C23—22no—
655C23—42no—
656C23—42no—
657C23—42no—
658C23—74no—
659C23—72no—
660C23—142no—
661C23—142no—
662C23D7×SD1614yes—
663C23C2×D4×D712yes—
664C23C2×D4×D711yescharacteristic
665Q8—142no—
666Q8—142no—
667Q8—288no—
668Q8—282no—
669Q8—564no—
670D4—22no—
671D4—22no—
672D4—48no—
673D4—42no—
674D4—716no—
675D4—288no—
676C2×C4—22no—
677C2×C4—24no—
678C2×C4—22no—
679C2×C4—22no—
680C2×C4—22no—
681C2×C4—22no—
682C2×C4—22no—
683C2×C4—42no—
684C2×C4—42no—
685C2×C4—42no—
686C2×C4—74no—
687C2×C4—72no—
688C2×C4—72no—
689C2×C4—72no—
690C2×C4—84no—
691C2×C4—142no—
692C2×C4—142no—
693C2×C4—144no—
694C2×C4—142no—
695C2×C4—142no—
696C2×C4—142no—
697C2×C4—142no—
698C2×C4—142no—
699C2×C4—142no—
700C2×C4—288no—
701C2×C4—288no—
702C2×C4—282no—
703C2×C4—282no—
704C2×C4—288no—
705C2×C4—282no—
706C2×C4—282no—
707C2×C4—564no—
708C2×C4C2×D4×D712yes—
709C2×C4C2×D4×D711yescharacteristic
710C2×C4D7×#4112yes—
711C2×C4#655412yes—
712C2×C4C24×D711yescharacteristic
713C8—22no—
714C8—22no—
715C8—74no—
716C8—142no—
717C7C2×#333511yescharacteristic, complemented, Sylow
718C22—22no—
719C22—22no—
720C22—28no—
721C22—42no—
722C22—42no—
723C22—42no—
724C22—74no—
725C22—84no—
726C22—142no—
727C22—142no—
728C22—148no—
729C22#9034612yes—
730C22C2×D7×SD1614yes—
731C22C2×D7×SD1612yes—
732C22#9046612yes—
733C22C22×D4×D711yescharacteristic
734C4—22no—
735C4—42no—
736C4—42no—
737C4—42no—
738C4—74no—
739C4—142no—
740C4—142no—
741C4—282no—
742C4—282no—
743C4—282no—
744C4—282no—
745C4#9034612yes—
746C4C2×D7×#4111yescharacteristic
747C4C2×#655411yescharacteristic
748C2—24no—
749C2—82no—
750C2—144no—
751C2#1173876514yesdirect product factor
752C2C2×#9034611yescharacteristic
753C2C22×D7×SD1611yescharacteristic
754C2C2×#9046611yescharacteristic
subgroupG/H
centerC23C2×D4×D7
commutator, cosocleC2×C4×C7C25
FrattiniC2×C4C24×D7
FittingC2×C7×#481C2
socleC23×C7C22×D4
prime radicalC2×#90302C2
hypercenterC2×#481D7
hypocenterC7C2×#3335
LCSG ▷ C2×C4×C7 ▷ C2×C7 ▷ C7
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#481

Complements

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

NH ≅ G/Ntype
2. C2×#90202C2semidirect
3. C2×C7×#481C2semidirect
4. C2×#89813C2semidirect
5. C22×#6382C2semidirect
6. #11738765C2direct (N × H)
7. C2×#89626C2semidirect
8. C2×#89634C2semidirect
9. C2×D7×#106C2semidirect
10. C2×#89627C2semidirect
11. C2×#89549C2semidirect
12. C2×#89550C2semidirect
13. C2×#89533C2semidirect
14. C2×#89530C2semidirect
15. C2×(C22⋊D7)⋊C8C2semidirect
16. C2×#89493C2semidirect
34. #90202C22semidirect
45. C7×#481C22semidirect
59. #89813C22semidirect
66. C2×#6382C22semidirect
67. #89634C22semidirect
68. D7×#106C22semidirect
69. #89627C22semidirect
70. #89626C22semidirect
71. #89550C22semidirect
72. #89549C22semidirect
73. #89533C22semidirect
74. #89530C22semidirect
75. (C22⋊D7)⋊C8C22semidirect
76. #89493C22semidirect
186. C2×#481D7semidirect
219. C2×C22⋊D7SD16semidirect
288. C2×C7⋊C8#41semidirect
324. #481C2×D7semidirect
386. C22⋊D7C2×SD16semidirect
416. C7⋊C8C2×#41semidirect
647. C2×C7#3335semidirect
717. C7C2×#3335semidirect
751. C2#11738765direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#903022
C2×#902022
C2×C7×#4812
C2×#898132
C22×#63822
#117387652
C2×#896262
C2×#896342
C2×D7×#1062
C2×#896272
C2×#895492
C2×#895502
C2×#895332
C2×#895302
C2×(C22⋊D7)⋊C82
C2×#894932
C2×#33357