Finite Group Databasebeta

← C2×#11732378 #13559974

Subgroups — C2×#11732378 #13559974

Order 1792.

2606 conjugacy classes of subgroups.

The subgroup lattice has 852 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C7×#386C211yesmaximal, characteristic, complemented
2C2×#89995C211yesmaximal, characteristic
3C2×#89994C211yesmaximal, characteristic, complemented
4C2×#89985C211yesmaximal, characteristic, complemented
5C2×#89982C211yesmaximal, characteristic, complemented
6C2×#89731C211yesmaximal, characteristic, complemented
7C2×#89731C211yesmaximal, characteristic, complemented
8C2×#89725C211yesmaximal, characteristic, complemented
9C2×#89733C211yesmaximal, characteristic, complemented
10C2×#89719C211yesmaximal, characteristic, complemented
11C2×#89719C211yesmaximal, characteristic, complemented
12#11732378C2116yesmaximal, direct product factor
13C2×#89447C211yesmaximal, characteristic, complemented
14C2×#89445C211yesmaximal, characteristic, complemented
15C2×#89432C211yesmaximal, characteristic, complemented
16C2×#89430C211yesmaximal, characteristic, complemented
17C23×C7×D4C2211yescharacteristic
18C24×C4×C7C2211yescharacteristic
19C23×C22⋊D7C2211yescharacteristic
20C23×C22⋊D7C2211yescharacteristic
21C23×Dic14C2211yescharacteristic
22C22×C7×C22⋊C4C2211yescharacteristic
23C22×C7×C22⋊C4C2211yescharacteristic
24C22×C7×C22⋊C4C2211yescharacteristic
25C22×C22⋊Dic7C2211yescharacteristic
26C22×C22⋊Dic7C2211yescharacteristic
27C22×C22⋊Dic7C2211yescharacteristic
28C22×C22⋊Dic7C2211yescharacteristic
29C22×C22⋊Dic7C2211yescharacteristic
30C22×C22⋊Dic7C2211yescharacteristic
31C22×(C2×D7)⋊C4C2211yescharacteristic
32C22×(C2×D7)⋊C4C2211yescharacteristic
33C22×(C2×D7)⋊C4C2211yescharacteristic
34C22×(C2×D7)⋊C4C2211yescharacteristic
35C22×(C2×D7)⋊C4C2211yescharacteristic
36C22×C4⋊Dic7C2211yescharacteristic
37C22×Dic7⋊C4C2211yescharacteristic
38C22×Dic7⋊C4C2211yescharacteristic
39C22×Dic7⋊C4C2211yescharacteristic
40C7×#386C2218yescomplemented
41C2×C7×#95C2211yescharacteristic
42C2×C7×#95C2211yescharacteristic
43#89995C2218yes—
44#89994C2218yescomplemented
45#89985C2218yescomplemented
46#89982C2218yescomplemented
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
57#89733C2218yescomplemented
58#89731C2218yescomplemented
59#89731C2218yescomplemented
60#89725C2218yescomplemented
61#89719C2218yescomplemented
62#89719C2218yescomplemented
63#89447C2218yescomplemented
64#89445C2218yescomplemented
65#89432C2218yescomplemented
66#89430C2218yescomplemented
67C2×#2824—71nomaximal, Sylow
68C25×C7C2311yescharacteristic
69C25×C7C2311yescharacteristic
70C24×D7C2311yescharacteristic
71C22×C7×D4—24no—
72C22×C7×D4—42no—
73C22×C7×D4—42no—
74C22×C7×D4C2314yes—
75C23×C4×C7—42no—
76C23×C4×C7—42no—
77C23×C4×C7—42no—
78C23×C4×C7C2311yescharacteristic
79C23×C4×C7C2311yescharacteristic
80C23×C4×C7C2311yescharacteristic
81C23×C4×C7C2311yescharacteristic
82C23×C4×C7C2311yescharacteristic
83C23×C4×C7C2314yes—
84C22×C22⋊D7—24no—
85C22×C22⋊D7—42no—
86C22×C22⋊D7—42no—
87C22×C22⋊D7—42no—
88C22×C22⋊D7—42no—
89C22×C22⋊D7—42no—
90C22×C22⋊D7C2314yes—
91C22×C22⋊D7C2314yes—
92C23×Dic7C2311yescharacteristic
93C23×Dic7C2311yescharacteristic
94C23×Dic7C2311yescharacteristic
95C23×Dic7C2311yescharacteristic
96C23×Dic7C2311yescharacteristic
97C23×Dic7C2311yescharacteristic
98C23×Dic7C2311yescharacteristic
99C22×Dic14—42no—
100C22×Dic14—42no—
101C22×Dic14—42no—
102C22×Dic14C2314yes—
103C2×C7×C22⋊C4—42no—
104C2×C7×C22⋊C4—42no—
105C2×C7×C22⋊C4—42no—
106C2×C7×C22⋊C4C2314yes—
107C2×C7×C22⋊C4C2314yes—
108C2×C7×C22⋊C4C2314yes—
109C2×C22⋊Dic7—24no—
110C2×C22⋊Dic7—42no—
111C2×C22⋊Dic7—42no—
112C2×C22⋊Dic7—42no—
113C2×C22⋊Dic7—42no—
114C2×C22⋊Dic7—42no—
115C2×C22⋊Dic7C2314yes—
116C2×C22⋊Dic7C2314yes—
117C2×C22⋊Dic7C2314yes—
118C2×C22⋊Dic7C2314yes—
119C2×C22⋊Dic7C2314yes—
120C2×C22⋊Dic7C2314yes—
121C2×(C2×D7)⋊C4—42no—
122C2×(C2×D7)⋊C4—42no—
123C2×(C2×D7)⋊C4—42no—
124C2×(C2×D7)⋊C4—42no—
125C2×(C2×D7)⋊C4—42no—
126C2×(C2×D7)⋊C4C2314yes—
127C2×(C2×D7)⋊C4C2314yes—
128C2×(C2×D7)⋊C4C2314yes—
129C2×(C2×D7)⋊C4C2314yes—
130C2×(C2×D7)⋊C4C2314yes—
131C2×C4⋊Dic7—42no—
132C2×C4⋊Dic7C2314yes—
133C2×Dic7⋊C4—42no—
134C2×Dic7⋊C4—42no—
135C2×Dic7⋊C4—42no—
136C2×Dic7⋊C4C2314yes—
137C2×Dic7⋊C4C2314yes—
138C2×Dic7⋊C4C2314yes—
139C7×#95C2314yes—
140C7×#95C2314yes—
141C7⋊#95C2314yes—
142C7⋊#95C2314yes—
143C7⋊#95C2314yes—
144C7⋊#95C2314yes—
145C7⋊#95C2314yes—
146C7⋊#95C2314yes—
147C7⋊#95C2314yes—
148C7⋊#95C2314yes—
149C7⋊#95C2314yes—
150C7⋊#95C2314yes—
151#2824—716no—
152C2×#400—71no—
153C2×#400—71no—
154C2×#397—71no—
155C2×#397—71no—
156C2×#394—71no—
157C2×#394—71no—
158C2×#394—71no—
159C2×#394—71no—
160C2×#393—71no—
161C2×#393—71no—
162C2×#393—71no—
163C2×#392—71no—
164C2×#386—71no—
165C2×#386D711yescharacteristic, complemented
166C2×#385—71no—
167C24×C7—22no—
168C24×C7—22no—
169C24×C7—22no—
170C24×C7—22no—
171C24×C7—22no—
172C24×C7—22no—
173C24×C7—22no—
174C24×C7—22no—
175C24×C7—22no—
176C24×C7—22no—
177C24×C7—22no—
178C24×C7—22no—
179C24×C7—22no—
180C24×C7#4114yes—
181C24×C7C2412yes—
182C24×C7C2412yes—
183C24×C7C2411yescharacteristic
184C23×D7—22no—
185C23×D7—22no—
186C23×D7—22no—
187C23×D7—22no—
188C23×D7—22no—
189C23×D7—22no—
190C23×D7—22no—
191C23×D7C2412yes—
192C2×C7×D4—28no—
193C2×C7×D4—44no—
194C2×C7×D4—44no—
195C2×C7×D4—416no—
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—22no—
205C22×C4×C7—22no—
206C22×C4×C7—22no—
207C22×C4×C7—22no—
208C22×C4×C7—22no—
209C22×C4×C7—22no—
210C22×C4×C7—22no—
211C22×C4×C7—44no—
212C22×C4×C7—44no—
213C22×C4×C7—44no—
214C22×C4×C7—416no—
215C22×C4×C7C2412yes—
216C22×C4×C7C2412yes—
217C22×C4×C7C2412yes—
218C22×C4×C7C2412yes—
219C22×C4×C7C2412yes—
220C2×C22⋊D7—28no—
221C2×C22⋊D7—44no—
222C2×C22⋊D7—44no—
223C2×C22⋊D7—44no—
224C2×C22⋊D7—44no—
225C2×C22⋊D7—44no—
226C2×C22⋊D7—416no—
227C2×C22⋊D7—416no—
228C22×Dic7—22no—
229C22×Dic7—22no—
230C22×Dic7—22no—
231C22×Dic7—22no—
232C22×Dic7—22no—
233C22×Dic7—22no—
234C22×Dic7—22no—
235C22×Dic7—22no—
236C22×Dic7—22no—
237C22×Dic7—22no—
238C22×Dic7—22no—
239C22×Dic7—22no—
240C22×Dic7—22no—
241C22×Dic7—22no—
242C22×Dic7—22no—
243C22×Dic7—22no—
244C22×Dic7—22no—
245C22×Dic7—22no—
246C22×Dic7—22no—
247C22×Dic7—22no—
248C22×Dic7—22no—
249C22×Dic7C2412yes—
250C22×Dic7C2412yes—
251C22×Dic7C2412yes—
252C22×Dic7C2412yes—
253C22×Dic7C2412yes—
254C22×Dic7C2412yes—
255C22×Dic7C2412yes—
256C2×Dic14—44no—
257C2×Dic14—44no—
258C2×Dic14—44no—
259C2×Dic14—416no—
260C7×C22⋊C4—44no—
261C7×C22⋊C4—44no—
262C7×C22⋊C4—44no—
263C22⋊Dic7—28no—
264C22⋊Dic7—44no—
265C22⋊Dic7—44no—
266C22⋊Dic7—44no—
267C22⋊Dic7—44no—
268C22⋊Dic7—44no—
269(C2×D7)⋊C4—44no—
270(C2×D7)⋊C4—44no—
271(C2×D7)⋊C4—44no—
272(C2×D7)⋊C4—44no—
273(C2×D7)⋊C4—44no—
274C4⋊Dic7—44no—
275Dic7⋊C4—44no—
276Dic7⋊C4—44no—
277Dic7⋊C4—44no—
278C23×Q8—71no—
279C23×D4—71no—
280C23×D4—71no—
281C23×D4C2×D711yescharacteristic
282C24×C4C2×D711yescharacteristic
283C22×C4⋊C4—71no—
284C22×C4⋊C4—71no—
285C22×C4⋊C4—71no—
286C22×C4⋊C4—71no—
287C22×C22⋊C4—71no—
288C22×C22⋊C4—71no—
289C22×C22⋊C4—71no—
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⋊C4—71no—
297C22×C22⋊C4—71no—
298C22×C22⋊C4C2×D711yescharacteristic
299C22×C22⋊C4C2×D711yescharacteristic
300C22×C22⋊C4C2×D711yescharacteristic
301#400—78no—
302#400—78no—
303#397—78no—
304#397—78no—
305#394—78no—
306#394—78no—
307#394—78no—
308#394—78no—
309#393—78no—
310#393—78no—
311#393—78no—
312#392—78no—
313#386—78no—
314#386C2×D718yescomplemented
315#385—78no—
316C2×#95—71no—
317C2×#95—71no—
318C2×#95—71no—
319C2×#95—71no—
320C2×#95—71no—
321C2×#95—71no—
322C2×#95—71no—
323C2×#95—71no—
324C2×#95—71no—
325C2×#95—71no—
326C2×#95C2×D711yescharacteristic
327C2×#95C2×D711yescharacteristic
328C23×C7—28no—
329C23×C7—28no—
330C23×C7—28no—
331C23×C7—22no—
332C23×C7—22no—
333C23×C7—22no—
334C23×C7—22no—
335C23×C7—22no—
336C23×C7—22no—
337C23×C7—22no—
338C23×C7—22no—
339C23×C7—22no—
340C23×C7—22no—
341C23×C7—22no—
342C23×C7—22no—
343C23×C7—22no—
344C23×C7—44no—
345C23×C7—44no—
346C23×C7—44no—
347C23×C7—44no—
348C23×C7—44no—
349C23×C7—44no—
350C23×C7—44no—
351C23×C7—44no—
352C23×C7—44no—
353C23×C7—44no—
354C23×C7—44no—
355C23×C7C2×#4114yes—
356C23×C7C2×#4112yes—
357C23×C7H(5,𝔽2)12yes—
358C23×C7H(5,𝔽2)12yes—
359C23×C7H(5,𝔽2)12yes—
360C23×C7H(5,𝔽2)12yes—
361C23×C7H(5,𝔽2)12yes—
362C23×C72−1+412yes—
363C23×C7C2511yescharacteristic
364C22×D7—22no—
365C22×D7—22no—
366C22×D7—22no—
367C22×D7—22no—
368C22×D7—22no—
369C22×D7—22no—
370C22×D7—22no—
371C22×D7—44no—
372C22×D7—44no—
373C22×D7—44no—
374C22×D7—44no—
375C22×D7—44no—
376C22×D7—44no—
377C22×D7—44no—
378C7×D4—416no—
379C2×C4×C7—22no—
380C2×C4×C7—22no—
381C2×C4×C7—22no—
382C2×C4×C7—22no—
383C2×C4×C7—22no—
384C2×C4×C7—22no—
385C2×C4×C7—22no—
386C2×C4×C7—22no—
387C2×C4×C7—22no—
388C2×C4×C7—22no—
389C2×C4×C7—22no—
390C2×C4×C7—22no—
391C2×C4×C7—22no—
392C2×C4×C7—22no—
393C2×C4×C7—22no—
394C2×C4×C7—416no—
395C2×C4×C7—44no—
396C2×C4×C7—44no—
397C2×C4×C7—44no—
398C2×C4×C7—44no—
399C2×C4×C7—44no—
400C22⋊D7—416no—
401C22⋊D7—416no—
402C2×Dic7—22no—
403C2×Dic7—22no—
404C2×Dic7—22no—
405C2×Dic7—22no—
406C2×Dic7—22no—
407C2×Dic7—22no—
408C2×Dic7—22no—
409C2×Dic7—22no—
410C2×Dic7—22no—
411C2×Dic7—22no—
412C2×Dic7—22no—
413C2×Dic7—22no—
414C2×Dic7—22no—
415C2×Dic7—22no—
416C2×Dic7—22no—
417C2×Dic7—22no—
418C2×Dic7—22no—
419C2×Dic7—22no—
420C2×Dic7—22no—
421C2×Dic7—22no—
422C2×Dic7—22no—
423C2×Dic7—44no—
424C2×Dic7—44no—
425C2×Dic7—44no—
426C2×Dic7—44no—
427C2×Dic7—44no—
428C2×Dic7—44no—
429C2×Dic7—44no—
430Dic14—416no—
431C25—71no—
432C25C22×D711yescharacteristic
433C25C22×D711yescharacteristic
434C22×Q8—74no—
435C22×Q8—282no—
436C22×Q8—282no—
437C22×Q8—282no—
438C22×D4—24no—
439C22×D4—42no—
440C22×D4—42no—
441C22×D4—74no—
442C22×D4—74no—
443C22×D4—144no—
444C22×D4—282no—
445C22×D4—282no—
446C22×D4—282no—
447C22×D4—282no—
448C22×D4—282no—
449C22×D4C22×D714yes—
450C23×C4—42no—
451C23×C4—42no—
452C23×C4—42no—
453C23×C4—71no—
454C23×C4—71no—
455C23×C4—71no—
456C23×C4—71no—
457C23×C4—71no—
458C23×C4—71no—
459C23×C4—71no—
460C23×C4C22×D711yescharacteristic
461C23×C4C22×D711yescharacteristic
462C23×C4C22×D711yescharacteristic
463C23×C4C22×D711yescharacteristic
464C23×C4C22×D711yescharacteristic
465C23×C4C22×D714yes—
466C2×C4⋊C4—74no—
467C2×C4⋊C4—74no—
468C2×C4⋊C4—74no—
469C2×C4⋊C4—74no—
470C2×C4⋊C4—282no—
471C2×C4⋊C4—282no—
472C2×C4⋊C4—282no—
473C2×C4⋊C4—282no—
474C2×C22⋊C4—42no—
475C2×C22⋊C4—42no—
476C2×C22⋊C4—42no—
477C2×C22⋊C4—74no—
478C2×C22⋊C4—74no—
479C2×C22⋊C4—74no—
480C2×C22⋊C4—74no—
481C2×C22⋊C4—74no—
482C2×C22⋊C4—74no—
483C2×C22⋊C4—74no—
484C2×C22⋊C4—74no—
485C2×C22⋊C4—74no—
486C2×C22⋊C4—74no—
487C2×C22⋊C4—74no—
488C2×C22⋊C4—144no—
489C2×C22⋊C4—282no—
490C2×C22⋊C4—282no—
491C2×C22⋊C4—282no—
492C2×C22⋊C4—282no—
493C2×C22⋊C4—282no—
494C2×C22⋊C4—282no—
495C2×C22⋊C4—282no—
496C2×C22⋊C4—282no—
497C2×C22⋊C4—282no—
498C2×C22⋊C4—282no—
499C2×C22⋊C4C22×D714yes—
500C2×C22⋊C4C22×D714yes—
501C2×C22⋊C4C22×D714yes—
502#95—74no—
503#95—74no—
504#95—74no—
505#95—74no—
506#95—74no—
507#95—74no—
508#95—74no—
509#95—74no—
510#95—74no—
511#95—74no—
512#95C22×D714yes—
513#95C22×D714yes—
514C22×C7—24no—
515C22×C7—24no—
516C22×C7—24no—
517C22×C7—416no—
518C22×C7—42no—
519C22×C7—42no—
520C22×C7—42no—
521C22×C7—42no—
522C22×C7—42no—
523C22×C7—42no—
524C22×C7—42no—
525C22×C7—42no—
526C22×C7—42no—
527C22×C7—42no—
528C22×C7—42no—
529C22×C7—88no—
530C22×C7#53814yes—
531C22×C7#53814yes—
532C22×C7#53914yes—
533C22×C7#56014yes—
534C22×C7H(3,𝔽4)14yes—
535C22×C7#56214yes—
536C22×C7#56214yes—
537C22×C7C22×#4111yescharacteristic
538C22×C7C2×H(5,𝔽2)11yescharacteristic
539C22×C7C2×H(5,𝔽2)11yescharacteristic
540C22×C7C2×H(5,𝔽2)11yescharacteristic
541C22×C7C2×H(5,𝔽2)11yescharacteristic
542C22×C7C2×H(5,𝔽2)11yescharacteristic
543C22×C7C2×2−1+411yescharacteristic
544C2×D7—42no—
545C2×D7—42no—
546C2×D7—42no—
547C2×D7—42no—
548C2×D7—42no—
549C2×D7—42no—
550C2×D7—42no—
551C2×D7—88no—
552C4×C7—42no—
553C4×C7—42no—
554C4×C7—42no—
555C4×C7—42no—
556C4×C7—42no—
557Dic7—42no—
558Dic7—42no—
559Dic7—42no—
560Dic7—42no—
561Dic7—42no—
562Dic7—42no—
563Dic7—42no—
564C24—22no—
565C24—22no—
566C24—22no—
567C24—22no—
568C24—22no—
569C24—22no—
570C24—22no—
571C24—22no—
572C24—22no—
573C24—22no—
574C24—22no—
575C24—22no—
576C24—22no—
577C24—72no—
578C24—142no—
579C24—142no—
580C24—142no—
581C24—142no—
582C24—142no—
583C24—142no—
584C24—142no—
585C24#115714yes—
586C24C23×D712yes—
587C24C23×D712yes—
588C24C23×D711yescharacteristic
589C2×Q8—284no—
590C2×Q8—284no—
591C2×Q8—284no—
592C2×Q8—2816no—
593C2×D4—28no—
594C2×D4—44no—
595C2×D4—44no—
596C2×D4—416no—
597C2×D4—148no—
598C2×D4—284no—
599C2×D4—284no—
600C2×D4—284no—
601C2×D4—284no—
602C2×D4—284no—
603C2×D4—2816no—
604C2×D4—2816no—
605C22×C4—22no—
606C22×C4—22no—
607C22×C4—22no—
608C22×C4—22no—
609C22×C4—22no—
610C22×C4—22no—
611C22×C4—22no—
612C22×C4—22no—
613C22×C4—22no—
614C22×C4—22no—
615C22×C4—22no—
616C22×C4—22no—
617C22×C4—22no—
618C22×C4—22no—
619C22×C4—22no—
620C22×C4—44no—
621C22×C4—44no—
622C22×C4—44no—
623C22×C4—416no—
624C22×C4—72no—
625C22×C4—72no—
626C22×C4—72no—
627C22×C4—72no—
628C22×C4—72no—
629C22×C4—72no—
630C22×C4—72no—
631C22×C4—142no—
632C22×C4—142no—
633C22×C4—142no—
634C22×C4—142no—
635C22×C4—142no—
636C22×C4—142no—
637C22×C4—142no—
638C22×C4—142no—
639C22×C4—142no—
640C22×C4—142no—
641C22×C4—142no—
642C22×C4—142no—
643C22×C4—142no—
644C22×C4—142no—
645C22×C4—142no—
646C22×C4—142no—
647C22×C4—142no—
648C22×C4—142no—
649C22×C4—142no—
650C22×C4—142no—
651C22×C4—142no—
652C22×C4C23×D712yes—
653C22×C4C23×D712yes—
654C22×C4C23×D712yes—
655C22×C4C23×D712yes—
656C22×C4C23×D712yes—
657C4⋊C4—284no—
658C4⋊C4—284no—
659C4⋊C4—284no—
660C4⋊C4—284no—
661C22⋊C4—44no—
662C22⋊C4—44no—
663C22⋊C4—44no—
664C22⋊C4—148no—
665C22⋊C4—284no—
666C22⋊C4—284no—
667C22⋊C4—284no—
668C22⋊C4—284no—
669C22⋊C4—284no—
670C22⋊C4—284no—
671C22⋊C4—284no—
672C22⋊C4—284no—
673C22⋊C4—284no—
674C22⋊C4—284no—
675C2×C7—44no—
676C2×C7—82no—
677C2×C7#282418yescomplemented
678C2×C7C2×#53811yescharacteristic
679C2×C7C2×#53811yescharacteristic
680C2×C7C2×#53911yescharacteristic
681C2×C7C2×#56011yescharacteristic
682C2×C7C2×H(3,𝔽4)11yescharacteristic
683C2×C7C2×#56211yescharacteristic
684C2×C7C2×#56211yescharacteristic
685D7—82no—
686C23—28no—
687C23—28no—
688C23—28no—
689C23—22no—
690C23—22no—
691C23—22no—
692C23—22no—
693C23—22no—
694C23—22no—
695C23—22no—
696C23—22no—
697C23—22no—
698C23—22no—
699C23—22no—
700C23—22no—
701C23—22no—
702C23—44no—
703C23—44no—
704C23—44no—
705C23—44no—
706C23—44no—
707C23—44no—
708C23—44no—
709C23—44no—
710C23—44no—
711C23—44no—
712C23—44no—
713C23—142no—
714C23—142no—
715C23—142no—
716C23—142no—
717C23—142no—
718C23—142no—
719C23—142no—
720C23—284no—
721C23—284no—
722C23—284no—
723C23—284no—
724C23—284no—
725C23—284no—
726C23—284no—
727C23C2×#115714yes—
728C23C2×#115712yes—
729C23#654812yes—
730C23#654812yes—
731C23#654812yes—
732C23#654812yes—
733C23#655312yes—
734C23#655412yes—
735C23C24×D711yescharacteristic
736Q8—2816no—
737D4—416no—
738D4—2816no—
739D4—2816no—
740C2×C4—22no—
741C2×C4—22no—
742C2×C4—22no—
743C2×C4—22no—
744C2×C4—22no—
745C2×C4—22no—
746C2×C4—22no—
747C2×C4—22no—
748C2×C4—22no—
749C2×C4—22no—
750C2×C4—22no—
751C2×C4—22no—
752C2×C4—22no—
753C2×C4—22no—
754C2×C4—22no—
755C2×C4—416no—
756C2×C4—44no—
757C2×C4—44no—
758C2×C4—44no—
759C2×C4—44no—
760C2×C4—44no—
761C2×C4—142no—
762C2×C4—142no—
763C2×C4—142no—
764C2×C4—142no—
765C2×C4—142no—
766C2×C4—142no—
767C2×C4—142no—
768C2×C4—142no—
769C2×C4—142no—
770C2×C4—142no—
771C2×C4—142no—
772C2×C4—142no—
773C2×C4—142no—
774C2×C4—142no—
775C2×C4—142no—
776C2×C4—142no—
777C2×C4—142no—
778C2×C4—142no—
779C2×C4—142no—
780C2×C4—142no—
781C2×C4—142no—
782C2×C4—284no—
783C2×C4—284no—
784C2×C4—284no—
785C2×C4—284no—
786C2×C4—284no—
787C2×C4—284no—
788C2×C4—284no—
789C7C2×#282411yescharacteristic, complemented, Sylow
790C22—24no—
791C22—24no—
792C22—24no—
793C22—42no—
794C22—42no—
795C22—42no—
796C22—42no—
797C22—416no—
798C22—42no—
799C22—42no—
800C22—42no—
801C22—42no—
802C22—42no—
803C22—42no—
804C22—42no—
805C22—88no—
806C22—282no—
807C22—282no—
808C22—282no—
809C22—282no—
810C22—282no—
811C22—282no—
812C22—282no—
813C22—568no—
814C22#9018514yes—
815C22#9025114yes—
816C22#9025514yes—
817C22#9028514yes—
818C22#9031114yes—
819C22#9031214yes—
820C22#9035814yes—
821C22C22×#115711yescharacteristic
822C22C2×#654811yescharacteristic
823C22C2×#654811yescharacteristic
824C22C2×#654811yescharacteristic
825C22C2×#654811yescharacteristic
826C22C2×#655311yescharacteristic
827C22C2×#655411yescharacteristic
828C4—42no—
829C4—42no—
830C4—42no—
831C4—42no—
832C4—42no—
833C4—282no—
834C4—282no—
835C4—282no—
836C4—282no—
837C4—282no—
838C4—282no—
839C4—282no—
840C2—44no—
841C2—82no—
842C2—562no—
843C2#1173237818yesdirect product factor
844C2C2×#9018511yescharacteristic
845C2C2×#9025511yescharacteristic
846C2C2×#9025111yescharacteristic
847C2C2×#9028511yescharacteristic
848C2C2×#9031111yescharacteristic
849C2C2×#9031211yescharacteristic
850C2C2×#9035811yescharacteristic
subgroupG/H
centerC24C23×D7
commutator, cosocleC23×C7C25
FrattiniC23C24×D7
FittingC2×C7×#386C2
socleC24×C7C24
prime radicalC2×#89995C2
hypercenterC2×#386D7
hypocenterC7C2×#2824
LCSG ▷ C23×C7 ▷ C7
UCSC1 ◁ C24 ◁ C2×#386

Complements

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

NH ≅ G/Ntype
1. C2×C7×#386C2semidirect
3. C2×#89994C2semidirect
4. C2×#89985C2semidirect
5. C2×#89982C2semidirect
6. C2×#89731C2semidirect
7. C2×#89731C2semidirect
8. C2×#89725C2semidirect
9. C2×#89733C2semidirect
10. C2×#89719C2semidirect
11. C2×#89719C2semidirect
12. #11732378C2direct (N × H)
13. C2×#89447C2semidirect
14. C2×#89445C2semidirect
15. C2×#89432C2semidirect
16. C2×#89430C2semidirect
40. C7×#386C22semidirect
44. #89994C22semidirect
45. #89985C22semidirect
46. #89982C22semidirect
57. #89733C22semidirect
58. #89731C22semidirect
59. #89731C22semidirect
60. #89725C22semidirect
61. #89719C22semidirect
62. #89719C22semidirect
63. #89447C22semidirect
64. #89445C22semidirect
65. #89432C22semidirect
66. #89430C22semidirect
165. C2×#386D7semidirect
314. #386C2×D7semidirect
677. C2×C7#2824semidirect
789. C7C2×#2824semidirect
843. C2#11732378direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C7×#3862
C2×#899952
C2×#899942
C2×#899852
C2×#899822
C2×#897312
C2×#897252
C2×#897332
C2×#897192
#117323782
C2×#894472
C2×#894452
C2×#894322
C2×#894302
C2×#28247