Finite Group Databasebeta

← C2×#11734608 #13559977

Subgroups — C2×#11734608 #13559977

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×#394C211yesmaximal, characteristic, complemented
2C2×#89995C211yesmaximal, characteristic
3C2×#89992C211yesmaximal, characteristic, complemented
4C2×#89765C211yesmaximal, characteristic, complemented
5C2×#89758C211yesmaximal, characteristic, complemented
6C2×#89731C211yesmaximal, characteristic, complemented
7C2×#89724C211yesmaximal, characteristic, complemented
8C2×#89733C211yesmaximal, characteristic, complemented
9C2×#89733C211yesmaximal, characteristic, complemented
10C2×#89719C211yesmaximal, characteristic, complemented
11C2×#89719C211yesmaximal, characteristic, complemented
12C2×#89730C211yesmaximal, characteristic, complemented
13C2×#89722C211yesmaximal, characteristic, complemented
14#11734608C2116yesmaximal, direct product factor
15C2×#89445C211yesmaximal, characteristic, complemented
16C2×#89431C211yesmaximal, characteristic, complemented
17C23×C7×D4C2211yescharacteristic
18C23×C22⋊D7C2211yescharacteristic
19C23×C22⋊D7C2211yescharacteristic
20C24×Dic7C2211yescharacteristic
21C23×Dic14C2211yescharacteristic
22C22×C7×C4⋊C4C2211yescharacteristic
23C22×C7×C22⋊C4C2211yescharacteristic
24C22×C7×C22⋊C4C2211yescharacteristic
25C22×C7×C22⋊C4C2211yescharacteristic
26C22×C7×C22⋊C4C2211yescharacteristic
27C22×C22⋊Dic7C2211yescharacteristic
28C22×C22⋊Dic7C2211yescharacteristic
29C22×C22⋊Dic7C2211yescharacteristic
30C22×C22⋊Dic7C2211yescharacteristic
31C22×C22⋊Dic7C2211yescharacteristic
32C22×(C2×D7)⋊C4C2211yescharacteristic
33C22×(C2×D7)⋊C4C2211yescharacteristic
34C22×(C2×D7)⋊C4C2211yescharacteristic
35C22×(C2×D7)⋊C4C2211yescharacteristic
36C22×(C2×D7)⋊C4C2211yescharacteristic
37C22×C4⋊Dic7C2211yescharacteristic
38C22×C4⋊Dic7C2211yescharacteristic
39C22×Dic7⋊C4C2211yescharacteristic
40C7×#394C2218yescomplemented
41C2×C7×#95C2211yescharacteristic
42#89995C2218yes—
43#89992C2218yescomplemented
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
55#89765C2218yescomplemented
56#89758C2218yescomplemented
57#89733C2218yescomplemented
58#89733C2218yescomplemented
59#89731C2218yescomplemented
60#89730C2218yescomplemented
61#89724C2218yescomplemented
62#89722C2218yescomplemented
63#89719C2218yescomplemented
64#89719C2218yescomplemented
65#89445C2218yescomplemented
66#89431C2218yescomplemented
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×C7C2311yescharacteristic
76C23×C4×C7C2311yescharacteristic
77C23×C4×C7C2311yescharacteristic
78C23×C4×C7C2311yescharacteristic
79C23×C4×C7C2311yescharacteristic
80C22×C22⋊D7—24no—
81C22×C22⋊D7—42no—
82C22×C22⋊D7—42no—
83C22×C22⋊D7—42no—
84C22×C22⋊D7—42no—
85C22×C22⋊D7—42no—
86C22×C22⋊D7C2314yes—
87C22×C22⋊D7C2314yes—
88C23×Dic7—42no—
89C23×Dic7—42no—
90C23×Dic7—42no—
91C23×Dic7C2311yescharacteristic
92C23×Dic7C2311yescharacteristic
93C23×Dic7C2311yescharacteristic
94C23×Dic7C2311yescharacteristic
95C23×Dic7C2311yescharacteristic
96C23×Dic7C2311yescharacteristic
97C23×Dic7C2311yescharacteristic
98C23×Dic7C2314yes—
99C22×Dic14—42no—
100C22×Dic14—42no—
101C22×Dic14—42no—
102C22×Dic14C2314yes—
103C2×C7×C4⋊C4—42no—
104C2×C7×C4⋊C4C2314yes—
105C2×C7×C22⋊C4—24no—
106C2×C7×C22⋊C4—42no—
107C2×C7×C22⋊C4—42no—
108C2×C7×C22⋊C4—42no—
109C2×C7×C22⋊C4C2314yes—
110C2×C7×C22⋊C4C2314yes—
111C2×C7×C22⋊C4C2314yes—
112C2×C7×C22⋊C4C2314yes—
113C2×C22⋊Dic7—42no—
114C2×C22⋊Dic7—42no—
115C2×C22⋊Dic7—42no—
116C2×C22⋊Dic7—42no—
117C2×C22⋊Dic7—42no—
118C2×C22⋊Dic7C2314yes—
119C2×C22⋊Dic7C2314yes—
120C2×C22⋊Dic7C2314yes—
121C2×C22⋊Dic7C2314yes—
122C2×C22⋊Dic7C2314yes—
123C2×(C2×D7)⋊C4—42no—
124C2×(C2×D7)⋊C4—42no—
125C2×(C2×D7)⋊C4—42no—
126C2×(C2×D7)⋊C4—42no—
127C2×(C2×D7)⋊C4—42no—
128C2×(C2×D7)⋊C4C2314yes—
129C2×(C2×D7)⋊C4C2314yes—
130C2×(C2×D7)⋊C4C2314yes—
131C2×(C2×D7)⋊C4C2314yes—
132C2×(C2×D7)⋊C4C2314yes—
133C2×C4⋊Dic7—42no—
134C2×C4⋊Dic7—42no—
135C2×C4⋊Dic7C2314yes—
136C2×C4⋊Dic7C2314yes—
137C2×Dic7⋊C4—42no—
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×#394D711yescharacteristic, complemented
160C2×#393—71no—
161C2×#393—71no—
162C2×#393—71no—
163C2×#392—71no—
164C2×#386—71no—
165C2×#386—71no—
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×C7C2412yes—
212C22×C4×C7C2412yes—
213C22×C4×C7C2412yes—
214C22×C4×C7C2412yes—
215C22×C4×C7C2412yes—
216C2×C22⋊D7—28no—
217C2×C22⋊D7—44no—
218C2×C22⋊D7—44no—
219C2×C22⋊D7—44no—
220C2×C22⋊D7—44no—
221C2×C22⋊D7—44no—
222C2×C22⋊D7—416no—
223C2×C22⋊D7—416no—
224C22×Dic7—22no—
225C22×Dic7—22no—
226C22×Dic7—22no—
227C22×Dic7—22no—
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—44no—
246C22×Dic7—44no—
247C22×Dic7—44no—
248C22×Dic7—416no—
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×C4⋊C4—44no—
261C7×C22⋊C4—28no—
262C7×C22⋊C4—44no—
263C7×C22⋊C4—44no—
264C7×C22⋊C4—44no—
265C22⋊Dic7—44no—
266C22⋊Dic7—44no—
267C22⋊Dic7—44no—
268C22⋊Dic7—44no—
269C22⋊Dic7—44no—
270(C2×D7)⋊C4—44no—
271(C2×D7)⋊C4—44no—
272(C2×D7)⋊C4—44no—
273(C2×D7)⋊C4—44no—
274(C2×D7)⋊C4—44no—
275C4⋊Dic7—44no—
276C4⋊Dic7—44no—
277Dic7⋊C4—44no—
278C23×Q8—71no—
279C23×D4—71no—
280C23×D4—71no—
281C23×D4C2×D711yescharacteristic
282C24×C4—71no—
283C22×C4⋊C4—71no—
284C22×C4⋊C4—71no—
285C22×C4⋊C4—71no—
286C22×C4⋊C4C2×D711yescharacteristic
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⋊C4C2×D711yescharacteristic
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#394C2×D718yescomplemented
309#393—78no—
310#393—78no—
311#393—78no—
312#392—78no—
313#386—78no—
314#386—78no—
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×#95—71no—
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—44no—
395C2×C4×C7—44no—
396C2×C4×C7—44no—
397C2×C4×C7—44no—
398C2×C4×C7—44no—
399C22⋊D7—416no—
400C22⋊D7—416no—
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—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—416no—
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—71no—
451C23×C4—71no—
452C23×C4—71no—
453C23×C4—71no—
454C23×C4—71no—
455C23×C4—71no—
456C23×C4—71no—
457C23×C4—74no—
458C23×C4—282no—
459C23×C4—282no—
460C23×C4—282no—
461C23×C4C22×D711yescharacteristic
462C23×C4C22×D711yescharacteristic
463C23×C4C22×D711yescharacteristic
464C23×C4C22×D711yescharacteristic
465C23×C4C22×D711yescharacteristic
466C2×C4⋊C4—42no—
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⋊C4C22×D714yes—
474C2×C22⋊C4—24no—
475C2×C22⋊C4—42no—
476C2×C22⋊C4—42no—
477C2×C22⋊C4—42no—
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—282no—
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⋊C4C22×D714yes—
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#95—74no—
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#115914yes—
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—72no—
621C22×C4—72no—
622C22×C4—72no—
623C22×C4—72no—
624C22×C4—72no—
625C22×C4—72no—
626C22×C4—72no—
627C22×C4—142no—
628C22×C4—142no—
629C22×C4—142no—
630C22×C4—142no—
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—284no—
649C22×C4—284no—
650C22×C4—284no—
651C22×C4—2816no—
652C22×C4C23×D712yes—
653C22×C4C23×D712yes—
654C22×C4C23×D712yes—
655C22×C4C23×D712yes—
656C22×C4C23×D712yes—
657C4⋊C4—44no—
658C4⋊C4—284no—
659C4⋊C4—284no—
660C4⋊C4—284no—
661C22⋊C4—28no—
662C22⋊C4—44no—
663C22⋊C4—44no—
664C22⋊C4—44no—
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—22no—
689C23—22no—
690C23—22no—
691C23—28no—
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×#115914yes—
728C23C2×#115912yes—
729C23#654812yes—
730C23#654812yes—
731C23#654812yes—
732C23#655312yes—
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—44no—
756C2×C4—44no—
757C2×C4—44no—
758C2×C4—44no—
759C2×C4—44no—
760C2×C4—142no—
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—2816no—
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—416no—
796C22—42no—
797C22—42no—
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#9028414yes—
815C22#9030814yes—
816C22#9031114yes—
817C22#9031214yes—
818C22#9035614yes—
819C22#9035814yes—
820C22#9037414yes—
821C22C22×#115911yescharacteristic
822C22C2×#654811yescharacteristic
823C22C2×#654811yescharacteristic
824C22C2×#654811yescharacteristic
825C22C2×#655311yescharacteristic
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#1173460818yesdirect product factor
844C2C2×#9028411yescharacteristic
845C2C2×#9030811yescharacteristic
846C2C2×#9031111yescharacteristic
847C2C2×#9031211yescharacteristic
848C2C2×#9035611yescharacteristic
849C2C2×#9035811yescharacteristic
850C2C2×#9037411yescharacteristic
subgroupG/H
centerC24C23×D7
commutator, cosocleC23×C7C25
FrattiniC23C24×D7
FittingC2×C7×#394C2
socleC24×C7C24
prime radicalC2×#89995C2
hypercenterC2×#394D7
hypocenterC7C2×#2824
LCSG ▷ C23×C7 ▷ C7
UCSC1 ◁ C24 ◁ C2×#394

Complements

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

NH ≅ G/Ntype
1. C2×C7×#394C2semidirect
3. C2×#89992C2semidirect
4. C2×#89765C2semidirect
5. C2×#89758C2semidirect
6. C2×#89731C2semidirect
7. C2×#89724C2semidirect
8. C2×#89733C2semidirect
9. C2×#89733C2semidirect
10. C2×#89719C2semidirect
11. C2×#89719C2semidirect
12. C2×#89730C2semidirect
13. C2×#89722C2semidirect
14. #11734608C2direct (N × H)
15. C2×#89445C2semidirect
16. C2×#89431C2semidirect
40. C7×#394C22semidirect
43. #89992C22semidirect
55. #89765C22semidirect
56. #89758C22semidirect
57. #89733C22semidirect
58. #89733C22semidirect
59. #89731C22semidirect
60. #89730C22semidirect
61. #89724C22semidirect
62. #89722C22semidirect
63. #89719C22semidirect
64. #89719C22semidirect
65. #89445C22semidirect
66. #89431C22semidirect
159. C2×#394D7semidirect
308. #394C2×D7semidirect
677. C2×C7#2824semidirect
789. C7C2×#2824semidirect
843. C2#11734608direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C7×#3942
C2×#899952
C2×#899922
C2×#897652
C2×#897582
C2×#897312
C2×#897242
C2×#897332
C2×#897192
C2×#897302
C2×#897222
#117346082
C2×#894452
C2×#894312
C2×#28247