Finite Group Databasebeta

← C2×#11731853 #13521506

Subgroups — C2×#11731853 #13521506

Order 1792.

3222 conjugacy classes of subgroups.

The subgroup lattice has 808 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C4×C22⋊D7C211yesmaximal, characteristic
2C22×#6449C211yesmaximal, characteristic
3C2×C7×#385C211yesmaximal, characteristic, complemented
4C22×C7⋊#95C211yesmaximal, characteristic, complemented
5C2×#89765C211yesmaximal, characteristic, complemented
6C2×#89761C211yesmaximal, characteristic, complemented
7C2×#89756C211yesmaximal, characteristic, complemented
8C2×#89753C211yesmaximal, characteristic, complemented
9C2×#89730C211yesmaximal, characteristic
10C2×#89715C211yesmaximal, characteristic, complemented
11C2×#89714C211yesmaximal, characteristic, complemented
12#11731853C2116yesmaximal, direct product factor
13C2×#89447C211yesmaximal, characteristic, complemented
14C2×#89436C211yesmaximal, characteristic, complemented
15C2×#89432C211yesmaximal, characteristic, complemented
16C2×#89427C211yesmaximal, characteristic, complemented
17C24×C4×C7C2211yescharacteristic
18C23×C22⋊D7C2211yescharacteristic
19C24×Dic7C2211yescharacteristic
20C24×Dic7C2211yescharacteristic
21C23×C4×D7C2211yescharacteristic
22C22×C7×C4⋊C4C2211yescharacteristic
23C22×C7×C4⋊C4C2211yescharacteristic
24C22×C7×C22⋊C4C2211yescharacteristic
25C22×C7×C22⋊C4C2211yescharacteristic
26C22×C22⋊Dic7C2211yescharacteristic
27C2×C4×C22⋊D7—28no—
28C2×C4×C22⋊D7C2218yes—
29C22×(C2×D7)⋊C4C2211yescharacteristic
30C22×(C2×D7)⋊C4C2211yescharacteristic
31C22×(C2×D7)⋊C4C2211yescharacteristic
32C22×(C2×D7)⋊C4C2211yescharacteristic
33C22×(C2×D7)⋊C4C2211yescharacteristic
34C22×C4⋊Dic7C2211yescharacteristic
35C22×C4⋊Dic7C2211yescharacteristic
36C22×Dic7⋊C4C2211yescharacteristic
37C22×Dic7⋊C4C2211yescharacteristic
38C22×Dic7⋊C4C2211yescharacteristic
39C22×C4×Dic7C2211yescharacteristic
40C2×#6449—28no—
41C2×#6449C2218yes—
42C7×#385C2218yescomplemented
43C2×C7×#95C2211yescharacteristic
44C2×C7×#95C2211yescharacteristic
45C2×C7⋊#95C2211yescharacteristic
46C2×C7⋊#95C2211yescharacteristic
47C2×C7⋊#95C2211yescharacteristic
48C2×C7⋊#95C2211yescharacteristic
49C2×C7⋊#95C2211yescharacteristic
50C2×C7⋊#95C2211yescharacteristic
51C2×C7⋊#95C2211yescharacteristic
52C2×C7⋊#95C2211yescharacteristic
53C2×C7⋊#95C2211yescharacteristic
54C2×C7⋊#95C2211yescharacteristic
55C2×C7⋊#95C2211yescharacteristic
56C2×C7⋊#95C2211yescharacteristic
57C2×C7⋊#95C2218yescomplemented
58#89765C2218yescomplemented
59#89761C2218yescomplemented
60#89756C2218yescomplemented
61#89753C2218yescomplemented
62#89730C2218yes—
63#89715C2218yescomplemented
64#89714C2218yescomplemented
65#89447C2218yescomplemented
66#89436C2218yescomplemented
67#89432C2218yescomplemented
68#89427C2218yescomplemented
69C2×#2419—71nomaximal, Sylow
70C25×C7C2311yescharacteristic
71C24×D7C2311yescharacteristic
72C23×C4×C7—24no—
73C23×C4×C7—24no—
74C23×C4×C7—42no—
75C23×C4×C7C2311yescharacteristic
76C23×C4×C7C2311yescharacteristic
77C23×C4×C7C2311yescharacteristic
78C23×C4×C7C2311yescharacteristic
79C23×C4×C7C2311yescharacteristic
80C23×C4×C7C2314yes—
81C23×C4×C7C2311yescharacteristic
82C22×C22⋊D7—24no—
83C22×C22⋊D7—24no—
84C22×C22⋊D7D418yes—
85C22×C22⋊D7C2314yes—
86C23×Dic7—24no—
87C23×Dic7—24no—
88C23×Dic7—24no—
89C23×Dic7—24no—
90C23×Dic7—24no—
91C23×Dic7—42no—
92C23×Dic7C2314yes—
93C23×Dic7C2311yescharacteristic
94C23×Dic7C2311yescharacteristic
95C23×Dic7C2311yescharacteristic
96C23×Dic7C2311yescharacteristic
97C23×Dic7C2311yescharacteristic
98C23×Dic7C2314yes—
99C23×Dic7C2311yescharacteristic
100C23×Dic7C2311yescharacteristic
101C22×C4×D7—24no—
102C22×C4×D7—24no—
103C22×C4×D7—42no—
104C22×C4×D7C2314yes—
105C2×C7×C4⋊C4—24no—
106C2×C7×C4⋊C4—42no—
107C2×C7×C4⋊C4C2314yes—
108C2×C7×C4⋊C4C2314yes—
109C2×C7×C22⋊C4—24no—
110C2×C7×C22⋊C4—24no—
111C2×C7×C22⋊C4C2314yes—
112C2×C7×C22⋊C4C2314yes—
113C2×C22⋊Dic7—24no—
114C2×C22⋊Dic7C2314yes—
115C4×C22⋊D7—232no—
116C2×(C2×D7)⋊C4—24no—
117C2×(C2×D7)⋊C4—24no—
118C2×(C2×D7)⋊C4—24no—
119C2×(C2×D7)⋊C4—24no—
120C2×(C2×D7)⋊C4—42no—
121C2×(C2×D7)⋊C4C2314yes—
122C2×(C2×D7)⋊C4C2314yes—
123C2×(C2×D7)⋊C4C2314yes—
124C2×(C2×D7)⋊C4C2314yes—
125C2×(C2×D7)⋊C4C2314yes—
126C2×C4⋊Dic7—24no—
127C2×C4⋊Dic7—24no—
128C2×C4⋊Dic7C2314yes—
129C2×C4⋊Dic7C2314yes—
130C2×Dic7⋊C4—24no—
131C2×Dic7⋊C4—24no—
132C2×Dic7⋊C4—42no—
133C2×Dic7⋊C4C2314yes—
134C2×Dic7⋊C4C2314yes—
135C2×Dic7⋊C4C2314yes—
136C2×C4×Dic7—24no—
137C2×C4×Dic7C2314yes—
138#6449—232no—
139C7×#95C2314yes—
140C7×#95C2314yes—
141C7⋊#95C2314yes—
142C7⋊#95C2314yes—
143C7⋊#95C2314yes—
144C7⋊#95C2314yes—
145C7⋊#95C2314yes—
146C7⋊#95C2314yes—
147C7⋊#95C2314yes—
148C7⋊#95C2314yes—
149C7⋊#95C2314yes—
150C7⋊#95C2314yes—
151C7⋊#95C2314yes—
152C7⋊#95C2314yes—
153C22×#123—71no—
154C22×C4×D4—71no—
155#2419—716no—
156C2×#400—71no—
157C2×#398—71no—
158C2×#397—71no—
159C2×#397—71no—
160C2×#387—71no—
161C2×#387—71no—
162C2×#386—71no—
163C2×#385—71no—
164C2×#385D711yescharacteristic, complemented
165C2×#381—71no—
166C2×#381—71no—
167C2×#380—71no—
168C22×#95—71no—
169C24×C7—22no—
170C24×C7—22no—
171C24×C7—22no—
172C24×C7—22no—
173C24×C7C2×D414yes—
174C24×C7#4114yes—
175C24×C7#4114yes—
176C24×C7C2412yes—
177C24×C7C2411yescharacteristic
178C23×D7—22no—
179C23×D7—22no—
180C23×D7—22no—
181C23×D7—22no—
182C23×D7—22no—
183C23×D7—22no—
184C23×D7C2×D414yes—
185C23×D7C2412yes—
186C22×C4×C7—22no—
187C22×C4×C7—22no—
188C22×C4×C7—22no—
189C22×C4×C7—22no—
190C22×C4×C7—22no—
191C22×C4×C7—28no—
192C22×C4×C7—22no—
193C22×C4×C7—22no—
194C22×C4×C7—22no—
195C22×C4×C7—22no—
196C22×C4×C7—22no—
197C22×C4×C7—22no—
198C22×C4×C7—22no—
199C22×C4×C7—22no—
200C22×C4×C7—22no—
201C22×C4×C7—22no—
202C22×C4×C7—22no—
203C22×C4×C7—22no—
204C22×C4×C7—28no—
205C22×C4×C7—44no—
206C22×C4×C7—416no—
207C22×C4×C7#4114yes—
208C22×C4×C7C2412yes—
209C22×C4×C7C2412yes—
210C22×C4×C7C2412yes—
211C22×C4×C7C2412yes—
212C22×C4×C7C2412yes—
213C22×C4×C7C2412yes—
214C2×C22⋊D7—232no—
215C2×C22⋊D7—28no—
216C2×C22⋊D7—28no—
217C2×C22⋊D7C2×D4116yes—
218C22×Dic7—22no—
219C22×Dic7—22no—
220C22×Dic7—22no—
221C22×Dic7—22no—
222C22×Dic7—28no—
223C22×Dic7—22no—
224C22×Dic7—22no—
225C22×Dic7—22no—
226C22×Dic7—22no—
227C22×Dic7—22no—
228C22×Dic7—22no—
229C22×Dic7—28no—
230C22×Dic7—28no—
231C22×Dic7—22no—
232C22×Dic7—22no—
233C22×Dic7—28no—
234C22×Dic7—22no—
235C22×Dic7—22no—
236C22×Dic7—22no—
237C22×Dic7—22no—
238C22×Dic7—22no—
239C22×Dic7—22no—
240C22×Dic7—22no—
241C22×Dic7—28no—
242C22×Dic7—44no—
243C22×Dic7—416no—
244C22×Dic7—416no—
245C22×Dic7C2×D414yes—
246C22×Dic7#4114yes—
247C22×Dic7C2412yes—
248C22×Dic7C2412yes—
249C22×Dic7C2412yes—
250C22×Dic7C2412yes—
251C22×Dic7C2412yes—
252C22×Dic7C2412yes—
253C22×Dic7C2412yes—
254C2×C4×D7—28no—
255C2×C4×D7—28no—
256C2×C4×D7—44no—
257C2×C4×D7—416no—
258C7×C4⋊C4—28no—
259C7×C4⋊C4—44no—
260C7×C22⋊C4—28no—
261C7×C22⋊C4—28no—
262C22⋊Dic7—28no—
263(C2×D7)⋊C4—28no—
264(C2×D7)⋊C4—28no—
265(C2×D7)⋊C4—28no—
266(C2×D7)⋊C4—28no—
267(C2×D7)⋊C4—44no—
268C4⋊Dic7—28no—
269C4⋊Dic7—28no—
270Dic7⋊C4—28no—
271Dic7⋊C4—28no—
272Dic7⋊C4—44no—
273C4×Dic7—28no—
274C23×D4—71no—
275C24×C4—71no—
276C24×C4—71no—
277C24×C4—71no—
278C24×C4C2×D711yescharacteristic
279C2×#123—78no—
280C2×#123—148no—
281C2×C4×D4—78no—
282C2×C4×D4—148no—
283C22×C4⋊C4—71no—
284C22×C4⋊C4—71no—
285C22×C4⋊C4—71no—
286C22×C4⋊C4—71no—
287C22×C4⋊C4—71no—
288C22×C4⋊C4C2×D711yescharacteristic
289C22×C4⋊C4C2×D711yescharacteristic
290C22×C22⋊C4—71no—
291C22×C22⋊C4—71no—
292C22×C22⋊C4—71no—
293C22×C22⋊C4—71no—
294C22×C22⋊C4—71no—
295C22×C22⋊C4—71no—
296C22×C22⋊C4C2×D711yescharacteristic
297C22×C22⋊C4C2×D711yescharacteristic
298C22×C42—71no—
299#400—78no—
300#398—78no—
301#397—78no—
302#397—78no—
303#387—78no—
304#387—78no—
305#386—78no—
306#385—78no—
307#385C2×D718yescomplemented
308#381—78no—
309#381—78no—
310#380—78no—
311C2×#95—71no—
312C2×#95—71no—
313C2×#95—71no—
314C2×#95—71no—
315C2×#95—71no—
316C2×#95—71no—
317C2×#95—71no—
318C2×#95—71no—
319C2×#95—71no—
320C2×#95—71no—
321C2×#95—78no—
322C2×#95—71no—
323C2×#95—71no—
324C2×#95C2×D711yescharacteristic
325C2×#95C2×D711yescharacteristic
326C23×C7—28no—
327C23×C7—28no—
328C23×C7—28no—
329C23×C7—28no—
330C23×C7—28no—
331C23×C7—28no—
332C23×C7—22no—
333C23×C7—22no—
334C23×C7—22no—
335C23×C7—22no—
336C23×C7#123116yes—
337C23×C7C22×D414yes—
338C23×C7C22×D412yes—
339C23×C7C2×#4114yes—
340C23×C7C2×#4112yes—
341C23×C7C2×#4112yes—
342C23×C7C2×#4114yes—
343C23×C7C2×#4112yes—
344C23×C7C2×#4112yes—
345C23×C7H(5,𝔽2)12yes—
346C23×C72−1+412yes—
347C23×C7C2511yescharacteristic
348C22×D7—28no—
349C22×D7—28no—
350C22×D7—28no—
351C22×D7—22no—
352C22×D7—22no—
353C22×D7—22no—
354C22×D7—22no—
355C22×D7—22no—
356C22×D7—22no—
357C22×D7—44no—
358C22×D7—44no—
359C22×D7—44no—
360C22×D7—44no—
361C22×D7C22×D414yes—
362C2×C4×C7—28no—
363C2×C4×C7—22no—
364C2×C4×C7—22no—
365C2×C4×C7—22no—
366C2×C4×C7—22no—
367C2×C4×C7—22no—
368C2×C4×C7—22no—
369C2×C4×C7—22no—
370C2×C4×C7—22no—
371C2×C4×C7—22no—
372C2×C4×C7—22no—
373C2×C4×C7—22no—
374C2×C4×C7—22no—
375C2×C4×C7—22no—
376C2×C4×C7—22no—
377C2×C4×C7—22no—
378C2×C4×C7—22no—
379C2×C4×C7—22no—
380C2×C4×C7—416no—
381C2×C4×C7—44no—
382C2×C4×C7—44no—
383C2×C4×C7—44no—
384C2×C4×C7—44no—
385C2×C4×C7—44no—
386C2×C4×C7C2×#4114yes—
387C22⋊D7—232no—
388C2×Dic7—28no—
389C2×Dic7—28no—
390C2×Dic7—22no—
391C2×Dic7—22no—
392C2×Dic7—22no—
393C2×Dic7—22no—
394C2×Dic7—22no—
395C2×Dic7—22no—
396C2×Dic7—22no—
397C2×Dic7—22no—
398C2×Dic7—22no—
399C2×Dic7—22no—
400C2×Dic7—22no—
401C2×Dic7—22no—
402C2×Dic7—22no—
403C2×Dic7—22no—
404C2×Dic7—22no—
405C2×Dic7—22no—
406C2×Dic7—22no—
407C2×Dic7—22no—
408C2×Dic7—22no—
409C2×Dic7—416no—
410C2×Dic7—416no—
411C2×Dic7—44no—
412C2×Dic7—44no—
413C2×Dic7—44no—
414C2×Dic7—44no—
415C2×Dic7—44no—
416C2×Dic7C22×D414yes—
417C2×Dic7C2×#4114yes—
418C4×D7—416no—
419C25—71no—
420C25C22×D711yescharacteristic
421C22×D4—78no—
422C22×D4—74no—
423C22×D4—144no—
424C22×D4—144no—
425C23×C4—24no—
426C23×C4—24no—
427C23×C4—42no—
428C23×C4—71no—
429C23×C4—71no—
430C23×C4—74no—
431C23×C4—71no—
432C23×C4—71no—
433C23×C4—71no—
434C23×C4—71no—
435C23×C4—71no—
436C23×C4—74no—
437C23×C4—74no—
438C23×C4—144no—
439C23×C4—144no—
440C23×C4—144no—
441C23×C4—144no—
442C23×C4—144no—
443C23×C4—144no—
444C23×C4—144no—
445C23×C4—282no—
446C23×C4—282no—
447C23×C4C22×D711yescharacteristic
448C23×C4C22×D711yescharacteristic
449C23×C4C22×D711yescharacteristic
450C23×C4C22×D711yescharacteristic
451C23×C4C22×D711yescharacteristic
452C23×C4C22×D714yes—
453C23×C4C22×D711yescharacteristic
454#123—1432no—
455C4×D4—1432no—
456C2×C4⋊C4—24no—
457C2×C4⋊C4—42no—
458C2×C4⋊C4—74no—
459C2×C4⋊C4—74no—
460C2×C4⋊C4—74no—
461C2×C4⋊C4—74no—
462C2×C4⋊C4—74no—
463C2×C4⋊C4—144no—
464C2×C4⋊C4—144no—
465C2×C4⋊C4—144no—
466C2×C4⋊C4—144no—
467C2×C4⋊C4—282no—
468C2×C4⋊C4C22×D714yes—
469C2×C4⋊C4C22×D714yes—
470C2×C22⋊C4—24no—
471C2×C22⋊C4—24no—
472C2×C22⋊C4—74no—
473C2×C22⋊C4—74no—
474C2×C22⋊C4—74no—
475C2×C22⋊C4—74no—
476C2×C22⋊C4—74no—
477C2×C22⋊C4—74no—
478C2×C22⋊C4—144no—
479C2×C22⋊C4—144no—
480C2×C22⋊C4—144no—
481C2×C22⋊C4—144no—
482C2×C22⋊C4—144no—
483C2×C22⋊C4—282no—
484C2×C22⋊C4C22×D714yes—
485C2×C22⋊C4C22×D714yes—
486C2×C42—74no—
487C2×C42—144no—
488#95—74no—
489#95—74no—
490#95—74no—
491#95—74no—
492#95—74no—
493#95—74no—
494#95—74no—
495#95—74no—
496#95—74no—
497#95—74no—
498#95—74no—
499#95—74no—
500#95C22×D714yes—
501#95C22×D714yes—
502C22×C7—24no—
503C22×C7—232no—
504C22×C7—24no—
505C22×C7—24no—
506C22×C7—24no—
507C22×C7—24no—
508C22×C7—24no—
509C22×C7C2×#12318yes—
510C22×C7C2×#12314yes—
511C22×C7#52914yes—
512C22×C7#53914yes—
513C22×C7#54614yes—
514C22×C7#54714yes—
515C22×C7#55114yes—
516C22×C7#55214yes—
517C22×C7C23×D411yescharacteristic
518C22×C7C22×#4111yescharacteristic
519C22×C7C22×#4111yescharacteristic
520C22×C7C22×#4111yescharacteristic
521C22×C7C22×#4111yescharacteristic
522C22×C7C2×H(5,𝔽2)11yescharacteristic
523C22×C7C2×2−1+411yescharacteristic
524C2×D7—24no—
525C2×D7—24no—
526C2×D7—24no—
527C2×D7—42no—
528C2×D7—416no—
529C2×D7—42no—
530C2×D7—42no—
531C2×D7—42no—
532C4×C7—24no—
533C4×C7—42no—
534C4×C7—42no—
535C4×C7—42no—
536C4×C7—42no—
537C4×C7—42no—
538Dic7—24no—
539Dic7—24no—
540Dic7—42no—
541Dic7—42no—
542Dic7—42no—
543Dic7—42no—
544Dic7—42no—
545C24—22no—
546C24—22no—
547C24—22no—
548C24—22no—
549C24—74no—
550C24—72no—
551C24—142no—
552C24—142no—
553C24—142no—
554C24—142no—
555C24—142no—
556C24—142no—
557C24#115714yes—
558C24D4×D714yes—
559C24#116114yes—
560C24C23×D712yes—
561C24C23×D711yescharacteristic
562C2×D4—716no—
563C2×D4—1432no—
564C2×D4—148no—
565C2×D4—148no—
566C22×C4—22no—
567C22×C4—22no—
568C22×C4—22no—
569C22×C4—22no—
570C22×C4—22no—
571C22×C4—22no—
572C22×C4—22no—
573C22×C4—28no—
574C22×C4—22no—
575C22×C4—22no—
576C22×C4—22no—
577C22×C4—22no—
578C22×C4—22no—
579C22×C4—22no—
580C22×C4—22no—
581C22×C4—22no—
582C22×C4—22no—
583C22×C4—22no—
584C22×C4—28no—
585C22×C4—44no—
586C22×C4—416no—
587C22×C4—74no—
588C22×C4—74no—
589C22×C4—72no—
590C22×C4—72no—
591C22×C4—72no—
592C22×C4—72no—
593C22×C4—72no—
594C22×C4—72no—
595C22×C4—72no—
596C22×C4—148no—
597C22×C4—148no—
598C22×C4—142no—
599C22×C4—142no—
600C22×C4—142no—
601C22×C4—142no—
602C22×C4—148no—
603C22×C4—142no—
604C22×C4—142no—
605C22×C4—142no—
606C22×C4—142no—
607C22×C4—142no—
608C22×C4—142no—
609C22×C4—148no—
610C22×C4—142no—
611C22×C4—142no—
612C22×C4—142no—
613C22×C4—148no—
614C22×C4—148no—
615C22×C4—142no—
616C22×C4—142no—
617C22×C4—142no—
618C22×C4—142no—
619C22×C4—142no—
620C22×C4—142no—
621C22×C4—148no—
622C22×C4—284no—
623C22×C4—2816no—
624C22×C4—284no—
625C22×C4—2816no—
626C22×C4—2816no—
627C22×C4#115914yes—
628C22×C4C23×D712yes—
629C22×C4C23×D712yes—
630C22×C4C23×D712yes—
631C22×C4C23×D712yes—
632C22×C4C23×D712yes—
633C22×C4C23×D712yes—
634C4⋊C4—28no—
635C4⋊C4—44no—
636C4⋊C4—148no—
637C4⋊C4—148no—
638C4⋊C4—148no—
639C4⋊C4—148no—
640C4⋊C4—284no—
641C22⋊C4—28no—
642C22⋊C4—28no—
643C22⋊C4—148no—
644C22⋊C4—148no—
645C22⋊C4—148no—
646C22⋊C4—148no—
647C22⋊C4—148no—
648C22⋊C4—284no—
649C42—148no—
650C2×C7—28no—
651C2×C7#241918yescomplemented
652C2×C7C22×#12311yescharacteristic
653C2×C7C2×#52911yescharacteristic
654C2×C7C2×#53911yescharacteristic
655C2×C7C2×#54611yescharacteristic
656C2×C7C2×#54711yescharacteristic
657C2×C7C2×#55111yescharacteristic
658C2×C7C2×#55211yescharacteristic
659D7—44no—
660C23—28no—
661C23—28no—
662C23—28no—
663C23—28no—
664C23—28no—
665C23—28no—
666C23—22no—
667C23—22no—
668C23—22no—
669C23—22no—
670C23—74no—
671C23—148no—
672C23—148no—
673C23—148no—
674C23—142no—
675C23—142no—
676C23—142no—
677C23—142no—
678C23—142no—
679C23—142no—
680C23—284no—
681C23—284no—
682C23—284no—
683C23—284no—
684C23#6457116yes—
685C23C2×#115714yes—
686C23C2×#115712yes—
687C23C2×D4×D714yes—
688C23C2×D4×D712yes—
689C23C2×#115912yes—
690C23#654812yes—
691C23C2×#116114yes—
692C23C2×#116112yes—
693C23D7×#4112yes—
694C23#655412yes—
695C23C24×D711yescharacteristic
696D4—1432no—
697C2×C4—28no—
698C2×C4—22no—
699C2×C4—22no—
700C2×C4—22no—
701C2×C4—22no—
702C2×C4—22no—
703C2×C4—22no—
704C2×C4—22no—
705C2×C4—22no—
706C2×C4—22no—
707C2×C4—22no—
708C2×C4—22no—
709C2×C4—22no—
710C2×C4—22no—
711C2×C4—22no—
712C2×C4—22no—
713C2×C4—22no—
714C2×C4—22no—
715C2×C4—416no—
716C2×C4—44no—
717C2×C4—44no—
718C2×C4—44no—
719C2×C4—44no—
720C2×C4—44no—
721C2×C4—74no—
722C2×C4—74no—
723C2×C4—148no—
724C2×C4—148no—
725C2×C4—142no—
726C2×C4—142no—
727C2×C4—142no—
728C2×C4—142no—
729C2×C4—142no—
730C2×C4—142no—
731C2×C4—142no—
732C2×C4—142no—
733C2×C4—142no—
734C2×C4—142no—
735C2×C4—142no—
736C2×C4—142no—
737C2×C4—142no—
738C2×C4—142no—
739C2×C4—142no—
740C2×C4—142no—
741C2×C4—142no—
742C2×C4—142no—
743C2×C4—142no—
744C2×C4—2816no—
745C2×C4—2816no—
746C2×C4—2816no—
747C2×C4—284no—
748C2×C4—284no—
749C2×C4—284no—
750C2×C4—284no—
751C2×C4—284no—
752C2×C4C2×#115914yes—
753C7C2×#241911yescharacteristic, complemented, Sylow
754C22—24no—
755C22—24no—
756C22—24no—
757C22—24no—
758C22—24no—
759C22—24no—
760C22—232no—
761C22—144no—
762C22—144no—
763C22—144no—
764C22—282no—
765C22—282no—
766C22—282no—
767C22—282no—
768C22—2816no—
769C22C2×#645718yes—
770C22C2×#645714yes—
771C22#9022914yes—
772C22#9025514yes—
773C22#9028214yes—
774C22#9032814yes—
775C22#9033314yes—
776C22#9034614yes—
777C22C22×#115711yescharacteristic
778C22C22×D4×D711yescharacteristic
779C22C22×#115911yescharacteristic
780C22C2×#654811yescharacteristic
781C22C22×#116111yescharacteristic
782C22C2×D7×#4111yescharacteristic
783C22C2×#655411yescharacteristic
784C4—24no—
785C4—42no—
786C4—42no—
787C4—42no—
788C4—42no—
789C4—42no—
790C4—144no—
791C4—144no—
792C4—282no—
793C4—282no—
794C4—282no—
795C4—282no—
796C4—282no—
797C2—28no—
798C2—284no—
799C2#1173185318yesdirect product factor
800C2C22×#645711yescharacteristic
801C2C2×#9022911yescharacteristic
802C2C2×#9025511yescharacteristic
803C2C2×#9028211yescharacteristic
804C2C2×#9033311yescharacteristic
805C2C2×#9032811yescharacteristic
806C2C2×#9034611yescharacteristic
subgroupG/H
centerC24C23×D7
commutator, cosocleC23×C7C25
FrattiniC23C24×D7
FittingC2×C7×#385C2
socleC24×C7C24
prime radicalC23×C22⋊D7C22
hypercenterC2×#385D7
hypocenterC7C2×#2419
LCSG ▷ C23×C7 ▷ C7
UCSC1 ◁ C24 ◁ C2×#385

Complements

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

NH ≅ G/Ntype
3. C2×C7×#385C2semidirect
4. C22×C7⋊#95C2semidirect
5. C2×#89765C2semidirect
6. C2×#89761C2semidirect
7. C2×#89756C2semidirect
8. C2×#89753C2semidirect
10. C2×#89715C2semidirect
11. C2×#89714C2semidirect
12. #11731853C2direct (N × H)
13. C2×#89447C2semidirect
14. C2×#89436C2semidirect
15. C2×#89432C2semidirect
16. C2×#89427C2semidirect
42. C7×#385C22semidirect
57. C2×C7⋊#95C22semidirect
58. #89765C22semidirect
59. #89761C22semidirect
60. #89756C22semidirect
61. #89753C22semidirect
63. #89715C22semidirect
64. #89714C22semidirect
65. #89447C22semidirect
66. #89436C22semidirect
67. #89432C22semidirect
68. #89427C22semidirect
164. C2×#385D7semidirect
307. #385C2×D7semidirect
651. C2×C7#2419semidirect
753. C7C2×#2419semidirect
799. C2#11731853direct (N × H)

Maximal subgroups

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

subgroupindex
C22×C4×C22⋊D72
C22×#64492
C2×C7×#3852
C22×C7⋊#952
C2×#897652
C2×#897612
C2×#897562
C2×#897532
C2×#897302
C2×#897152
C2×#897142
#117318532
C2×#894472
C2×#894362
C2×#894322
C2×#894272
C2×#24197