Finite Group Databasebeta

← C2×#11733918 #13560121

Subgroups — C2×#11733918 #13560121

Order 1792.

2434 conjugacy classes of subgroups.

The subgroup lattice has 844 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C7×#390C211yesmaximal, characteristic, complemented
2C2×#89995C211yesmaximal, characteristic
3C2×#89994C211yesmaximal, characteristic, complemented
4C2×#89766C211yesmaximal, characteristic, complemented
5C2×#89756C211yesmaximal, characteristic, complemented
6C2×#89731C211yesmaximal, characteristic, complemented
7C2×#89731C211yesmaximal, characteristic, complemented
8C2×#89731C211yesmaximal, characteristic, complemented
9C2×#89721C211yesmaximal, characteristic, complemented
10C2×#89725C211yesmaximal, characteristic, complemented
11C2×#89724C211yesmaximal, characteristic, complemented
12C2×#89720C211yesmaximal, characteristic, complemented
13C2×#89733C211yesmaximal, characteristic, complemented
14C2×#89712C211yesmaximal, characteristic, complemented
15C2×#89705C211yesmaximal, characteristic, complemented
16#11733918C2116yesmaximal, direct product factor
17C23×C7×D4C2211yescharacteristic
18C23×C22⋊D7C2211yescharacteristic
19C23×C22⋊D7C2211yescharacteristic
20C22×C7×C4⋊C4C2211yescharacteristic
21C22×C7×C22⋊C4C2211yescharacteristic
22C22×C7×C22⋊C4C2211yescharacteristic
23C22×C7×C22⋊C4C2211yescharacteristic
24C22×C7×C22⋊C4C2211yescharacteristic
25C22×C42×C7C2211yescharacteristic
26C22×C22⋊Dic7C2211yescharacteristic
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
40C22×Dic7⋊C4C2211yescharacteristic
41C22×Dic7⋊C4C2211yescharacteristic
42C22×Dic7⋊C4C2211yescharacteristic
43C22×Dic7⋊C4C2211yescharacteristic
44C7×#390C2218yescomplemented
45#89995C2218yes—
46#89994C2218yescomplemented
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#89766C2218yescomplemented
56#89756C2218yescomplemented
57#89733C2218yescomplemented
58#89731C2218yescomplemented
59#89731C2218yescomplemented
60#89731C2218yescomplemented
61#89725C2218yescomplemented
62#89724C2218yescomplemented
63#89721C2218yescomplemented
64#89720C2218yescomplemented
65#89712C2218yescomplemented
66#89705C2218yescomplemented
67C2×#2829—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—42no—
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×Dic7C2311yescharacteristic
89C23×Dic7C2311yescharacteristic
90C23×Dic7C2311yescharacteristic
91C23×Dic7C2311yescharacteristic
92C23×Dic7C2311yescharacteristic
93C23×Dic7C2311yescharacteristic
94C23×Dic7C2311yescharacteristic
95C2×C7×C4⋊C4—42no—
96C2×C7×C4⋊C4C2314yes—
97C2×C7×C22⋊C4—42no—
98C2×C7×C22⋊C4—42no—
99C2×C7×C22⋊C4—42no—
100C2×C7×C22⋊C4—42no—
101C2×C7×C22⋊C4C2314yes—
102C2×C7×C22⋊C4C2314yes—
103C2×C7×C22⋊C4C2314yes—
104C2×C7×C22⋊C4C2314yes—
105C2×C42×C7—42no—
106C2×C42×C7C2314yes—
107C2×C22⋊Dic7—42no—
108C2×C22⋊Dic7—42no—
109C2×C22⋊Dic7—42no—
110C2×C22⋊Dic7—42no—
111C2×C22⋊Dic7—42no—
112C2×C22⋊Dic7—42no—
113C2×C22⋊Dic7C2314yes—
114C2×C22⋊Dic7C2314yes—
115C2×C22⋊Dic7C2314yes—
116C2×C22⋊Dic7C2314yes—
117C2×C22⋊Dic7C2314yes—
118C2×C22⋊Dic7C2314yes—
119C2×(C2×D7)⋊C4—24no—
120C2×(C2×D7)⋊C4—42no—
121C2×(C2×D7)⋊C4—42no—
122C2×(C2×D7)⋊C4—42no—
123C2×(C2×D7)⋊C4—42no—
124C2×(C2×D7)⋊C4C2314yes—
125C2×(C2×D7)⋊C4C2314yes—
126C2×(C2×D7)⋊C4C2314yes—
127C2×(C2×D7)⋊C4C2314yes—
128C2×(C2×D7)⋊C4C2314yes—
129C2×C4⋊Dic7—42no—
130C2×C4⋊Dic7—42no—
131C2×C4⋊Dic7C2314yes—
132C2×C4⋊Dic7C2314yes—
133C2×Dic7⋊C4—24no—
134C2×Dic7⋊C4—42no—
135C2×Dic7⋊C4—42no—
136C2×Dic7⋊C4—42no—
137C2×Dic7⋊C4—42no—
138C2×Dic7⋊C4C2314yes—
139C2×Dic7⋊C4C2314yes—
140C2×Dic7⋊C4C2314yes—
141C2×Dic7⋊C4C2314yes—
142C2×Dic7⋊C4C2314yes—
143C7⋊#95C2314yes—
144C7⋊#95C2314yes—
145C7⋊#95C2314yes—
146C7⋊#95C2314yes—
147C7⋊#95C2314yes—
148C7⋊#95C2314yes—
149C7⋊#95C2314yes—
150C7⋊#95C2314yes—
151#2829—716no—
152C2×#399—71no—
153C2×#398—71no—
154C2×#397—71no—
155C2×#397—71no—
156C2×#396—71no—
157C2×#396—71no—
158C2×#394—71no—
159C2×#394—71no—
160C2×#394—71no—
161C2×#394—71no—
162C2×#394—71no—
163C2×#392—71no—
164C2×#390D711yescharacteristic, complemented
165C2×#388—71no—
166C2×#387—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—22no—
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#4114yes—
211C22×C4×C7C2412yes—
212C22×C4×C7C2412yes—
213C22×C4×C7C2412yes—
214C22×C4×C7C2412yes—
215C22×C4×C7C2412yes—
216C2×C22⋊D7—44no—
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×Dic7C2412yes—
246C22×Dic7C2412yes—
247C22×Dic7C2412yes—
248C22×Dic7C2412yes—
249C22×Dic7C2412yes—
250C22×Dic7C2412yes—
251C22×Dic7C2412yes—
252C7×C4⋊C4—44no—
253C7×C22⋊C4—44no—
254C7×C22⋊C4—44no—
255C7×C22⋊C4—44no—
256C7×C22⋊C4—44no—
257C42×C7—44no—
258C22⋊Dic7—44no—
259C22⋊Dic7—44no—
260C22⋊Dic7—44no—
261C22⋊Dic7—44no—
262C22⋊Dic7—44no—
263C22⋊Dic7—44no—
264(C2×D7)⋊C4—28no—
265(C2×D7)⋊C4—44no—
266(C2×D7)⋊C4—44no—
267(C2×D7)⋊C4—44no—
268(C2×D7)⋊C4—44no—
269C4⋊Dic7—44no—
270C4⋊Dic7—44no—
271Dic7⋊C4—28no—
272Dic7⋊C4—44no—
273Dic7⋊C4—44no—
274Dic7⋊C4—44no—
275Dic7⋊C4—44no—
276C23×D4—71no—
277C23×D4—71no—
278C23×D4C2×D711yescharacteristic
279C22×C4⋊C4—71no—
280C22×C4⋊C4—71no—
281C22×C4⋊C4—71no—
282C22×C4⋊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⋊C4—71no—
298C22×C22⋊C4C2×D711yescharacteristic
299C22×C22⋊C4C2×D711yescharacteristic
300C22×C22⋊C4C2×D711yescharacteristic
301C22×C22⋊C4C2×D711yescharacteristic
302C22×C42C2×D711yescharacteristic
303#399—78no—
304#398—78no—
305#397—78no—
306#397—78no—
307#396—78no—
308#396—78no—
309#394—78no—
310#394—78no—
311#394—78no—
312#394—78no—
313#394—78no—
314#392—78no—
315#390C2×D718yescomplemented
316#388—78no—
317#387—78no—
318C2×#95—71no—
319C2×#95—71no—
320C2×#95—71no—
321C2×#95—71no—
322C2×#95—71no—
323C2×#95—71no—
324C2×#95—71no—
325C2×#95—71no—
326C23×C7—22no—
327C23×C7—22no—
328C23×C7—22no—
329C23×C7—22no—
330C23×C7—22no—
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—44no—
341C23×C7—44no—
342C23×C7—44no—
343C23×C7—44no—
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×C7C2×#4112yes—
355C23×C7H(5,𝔽2)12yes—
356C23×C7H(5,𝔽2)12yes—
357C23×C7H(5,𝔽2)12yes—
358C23×C7H(5,𝔽2)12yes—
359C23×C7H(5,𝔽2)12yes—
360C23×C72−1+412yes—
361C23×C7C2511yescharacteristic
362C22×D7—22no—
363C22×D7—22no—
364C22×D7—22no—
365C22×D7—22no—
366C22×D7—22no—
367C22×D7—22no—
368C22×D7—22no—
369C22×D7—44no—
370C22×D7—44no—
371C22×D7—44no—
372C22×D7—44no—
373C22×D7—44no—
374C22×D7—44no—
375C22×D7—44no—
376C7×D4—416no—
377C2×C4×C7—28no—
378C2×C4×C7—22no—
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—44no—
393C2×C4×C7—44no—
394C2×C4×C7—44no—
395C2×C4×C7—44no—
396C2×C4×C7C2×#4114yes—
397C22⋊D7—416no—
398C22⋊D7—416no—
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—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—44no—
421C2×Dic7—44no—
422C2×Dic7—44no—
423C2×Dic7—44no—
424C2×Dic7—44no—
425C2×Dic7—44no—
426C2×Dic7—44no—
427C25—71no—
428C25C22×D711yescharacteristic
429C25C22×D711yescharacteristic
430C22×D4—24no—
431C22×D4—42no—
432C22×D4—42no—
433C22×D4—74no—
434C22×D4—74no—
435C22×D4—282no—
436C22×D4—282no—
437C22×D4—282no—
438C22×D4—282no—
439C22×D4—282no—
440C22×D4—282no—
441C22×D4C22×D714yes—
442C23×C4—71no—
443C23×C4—71no—
444C23×C4—71no—
445C23×C4—71no—
446C23×C4—71no—
447C23×C4—71no—
448C23×C4—71no—
449C23×C4C22×D711yescharacteristic
450C23×C4C22×D711yescharacteristic
451C23×C4C22×D711yescharacteristic
452C23×C4C22×D711yescharacteristic
453C23×C4C22×D711yescharacteristic
454C2×C4⋊C4—42no—
455C2×C4⋊C4—74no—
456C2×C4⋊C4—74no—
457C2×C4⋊C4—74no—
458C2×C4⋊C4—74no—
459C2×C4⋊C4—74no—
460C2×C4⋊C4—74no—
461C2×C4⋊C4—74no—
462C2×C4⋊C4—144no—
463C2×C4⋊C4—282no—
464C2×C4⋊C4—282no—
465C2×C4⋊C4—282no—
466C2×C4⋊C4—282no—
467C2×C4⋊C4—282no—
468C2×C4⋊C4—282no—
469C2×C4⋊C4C22×D714yes—
470C2×C22⋊C4—42no—
471C2×C22⋊C4—42no—
472C2×C22⋊C4—42no—
473C2×C22⋊C4—42no—
474C2×C22⋊C4—74no—
475C2×C22⋊C4—74no—
476C2×C22⋊C4—74no—
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—144no—
486C2×C22⋊C4—282no—
487C2×C22⋊C4—282no—
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⋊C4C22×D714yes—
497C2×C22⋊C4C22×D714yes—
498C2×C22⋊C4C22×D714yes—
499C2×C22⋊C4C22×D714yes—
500C2×C42—42no—
501C2×C42C22×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—
510C22×C7—42no—
511C22×C7—42no—
512C22×C7—42no—
513C22×C7—42no—
514C22×C7—42no—
515C22×C7—42no—
516C22×C7—42no—
517C22×C7—42no—
518C22×C7—42no—
519C22×C7—42no—
520C22×C7—42no—
521C22×C7—42no—
522C22×C7—42no—
523C22×C7—42no—
524C22×C7—88no—
525C22×C7—88no—
526C22×C7#53814yes—
527C22×C7#54014yes—
528C22×C7#54214yes—
529C22×C7#56014yes—
530C22×C7#56014yes—
531C22×C7#56214yes—
532C22×C7#56214yes—
533C22×C7C22×#4111yescharacteristic
534C22×C7C2×H(5,𝔽2)11yescharacteristic
535C22×C7C2×H(5,𝔽2)11yescharacteristic
536C22×C7C2×H(5,𝔽2)11yescharacteristic
537C22×C7C2×H(5,𝔽2)11yescharacteristic
538C22×C7C2×H(5,𝔽2)11yescharacteristic
539C22×C7C2×2−1+411yescharacteristic
540C2×D7—42no—
541C2×D7—42no—
542C2×D7—42no—
543C2×D7—42no—
544C2×D7—42no—
545C2×D7—42no—
546C2×D7—42no—
547C2×D7—88no—
548C4×C7—24no—
549C4×C7—42no—
550C4×C7—42no—
551C4×C7—42no—
552C4×C7—42no—
553Dic7—42no—
554Dic7—42no—
555Dic7—42no—
556Dic7—42no—
557Dic7—42no—
558Dic7—42no—
559Dic7—42no—
560C24—22no—
561C24—22no—
562C24—22no—
563C24—22no—
564C24—22no—
565C24—22no—
566C24—22no—
567C24—22no—
568C24—22no—
569C24—22no—
570C24—22no—
571C24—22no—
572C24—22no—
573C24—22no—
574C24—72no—
575C24—142no—
576C24—142no—
577C24—142no—
578C24—142no—
579C24—142no—
580C24—142no—
581C24—142no—
582C24C23×D712yes—
583C24C23×D712yes—
584C24C23×D711yescharacteristic
585C2×D4—28no—
586C2×D4—44no—
587C2×D4—44no—
588C2×D4—416no—
589C2×D4—284no—
590C2×D4—284no—
591C2×D4—284no—
592C2×D4—284no—
593C2×D4—284no—
594C2×D4—284no—
595C2×D4—2816no—
596C2×D4—2816no—
597C22×C4—22no—
598C22×C4—22no—
599C22×C4—22no—
600C22×C4—22no—
601C22×C4—22no—
602C22×C4—22no—
603C22×C4—22no—
604C22×C4—22no—
605C22×C4—22no—
606C22×C4—22no—
607C22×C4—22no—
608C22×C4—22no—
609C22×C4—22no—
610C22×C4—22no—
611C22×C4—72no—
612C22×C4—72no—
613C22×C4—72no—
614C22×C4—72no—
615C22×C4—72no—
616C22×C4—72no—
617C22×C4—72no—
618C22×C4—142no—
619C22×C4—142no—
620C22×C4—142no—
621C22×C4—142no—
622C22×C4—142no—
623C22×C4—142no—
624C22×C4—142no—
625C22×C4—142no—
626C22×C4—142no—
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#115714yes—
640C22×C4C23×D712yes—
641C22×C4C23×D712yes—
642C22×C4C23×D712yes—
643C22×C4C23×D712yes—
644C22×C4C23×D712yes—
645C4⋊C4—44no—
646C4⋊C4—148no—
647C4⋊C4—284no—
648C4⋊C4—284no—
649C4⋊C4—284no—
650C4⋊C4—284no—
651C4⋊C4—284no—
652C4⋊C4—284no—
653C22⋊C4—44no—
654C22⋊C4—44no—
655C22⋊C4—44no—
656C22⋊C4—44no—
657C22⋊C4—148no—
658C22⋊C4—284no—
659C22⋊C4—284no—
660C22⋊C4—284no—
661C22⋊C4—284no—
662C22⋊C4—284no—
663C22⋊C4—284no—
664C22⋊C4—284no—
665C22⋊C4—284no—
666C22⋊C4—284no—
667C22⋊C4—284no—
668C42—44no—
669C2×C7—82no—
670C2×C7—82no—
671C2×C7#282918yescomplemented
672C2×C7C2×#53811yescharacteristic
673C2×C7C2×#54011yescharacteristic
674C2×C7C2×#54211yescharacteristic
675C2×C7C2×#56011yescharacteristic
676C2×C7C2×#56011yescharacteristic
677C2×C7C2×#56211yescharacteristic
678C2×C7C2×#56211yescharacteristic
679D7—82no—
680C23—22no—
681C23—22no—
682C23—22no—
683C23—22no—
684C23—22no—
685C23—22no—
686C23—22no—
687C23—22no—
688C23—22no—
689C23—22no—
690C23—22no—
691C23—22no—
692C23—22no—
693C23—22no—
694C23—44no—
695C23—44no—
696C23—44no—
697C23—44no—
698C23—44no—
699C23—44no—
700C23—44no—
701C23—44no—
702C23—44no—
703C23—44no—
704C23—44no—
705C23—44no—
706C23—44no—
707C23—44no—
708C23—142no—
709C23—142no—
710C23—142no—
711C23—142no—
712C23—142no—
713C23—142no—
714C23—142no—
715C23—284no—
716C23—284no—
717C23—284no—
718C23—284no—
719C23—284no—
720C23—284no—
721C23—284no—
722C23C2×#115712yes—
723C23#654812yes—
724C23#654812yes—
725C23#654812yes—
726C23#654812yes—
727C23#655312yes—
728C23#655412yes—
729C23C24×D711yescharacteristic
730D4—416no—
731D4—2816no—
732D4—2816no—
733C2×C4—28no—
734C2×C4—22no—
735C2×C4—22no—
736C2×C4—22no—
737C2×C4—22no—
738C2×C4—22no—
739C2×C4—22no—
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—44no—
749C2×C4—44no—
750C2×C4—44no—
751C2×C4—44no—
752C2×C4—142no—
753C2×C4—142no—
754C2×C4—142no—
755C2×C4—142no—
756C2×C4—142no—
757C2×C4—142no—
758C2×C4—142no—
759C2×C4—142no—
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—284no—
774C2×C4—284no—
775C2×C4—284no—
776C2×C4—284no—
777C2×C4—284no—
778C2×C4—284no—
779C2×C4—284no—
780C2×C4C2×#115714yes—
781C7C2×#282911yescharacteristic, complemented, Sylow
782C22—42no—
783C22—42no—
784C22—42no—
785C22—42no—
786C22—42no—
787C22—42no—
788C22—42no—
789C22—42no—
790C22—42no—
791C22—42no—
792C22—42no—
793C22—42no—
794C22—42no—
795C22—42no—
796C22—88no—
797C22—88no—
798C22—282no—
799C22—282no—
800C22—282no—
801C22—282no—
802C22—282no—
803C22—282no—
804C22—282no—
805C22—568no—
806C22#9018514yes—
807C22#9025214yes—
808C22#9025314yes—
809C22#9031114yes—
810C22#9031214yes—
811C22#9037514yes—
812C22#9041114yes—
813C22C22×#115711yescharacteristic
814C22C2×#654811yescharacteristic
815C22C2×#654811yescharacteristic
816C22C2×#654811yescharacteristic
817C22C2×#654811yescharacteristic
818C22C2×#655311yescharacteristic
819C22C2×#655411yescharacteristic
820C4—24no—
821C4—42no—
822C4—42no—
823C4—42no—
824C4—42no—
825C4—282no—
826C4—282no—
827C4—282no—
828C4—282no—
829C4—282no—
830C4—282no—
831C4—282no—
832C2—82no—
833C2—82no—
834C2—562no—
835C2#1173391818yesdirect product factor
836C2C2×#9018511yescharacteristic
837C2C2×#9025311yescharacteristic
838C2C2×#9025211yescharacteristic
839C2C2×#9031111yescharacteristic
840C2C2×#9031211yescharacteristic
841C2C2×#9037511yescharacteristic
842C2C2×#9041111yescharacteristic
subgroupG/H
centerC24C23×D7
commutator, cosocleC23×C7C25
FrattiniC23C24×D7
FittingC2×C7×#390C2
socleC24×C7C24
prime radicalC2×#89995C2
hypercenterC2×#390D7
hypocenterC7C2×#2829
LCSG ▷ C23×C7 ▷ C7
UCSC1 ◁ C24 ◁ C2×#390

Complements

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

NH ≅ G/Ntype
1. C2×C7×#390C2semidirect
3. C2×#89994C2semidirect
4. C2×#89766C2semidirect
5. C2×#89756C2semidirect
6. C2×#89731C2semidirect
7. C2×#89731C2semidirect
8. C2×#89731C2semidirect
9. C2×#89721C2semidirect
10. C2×#89725C2semidirect
11. C2×#89724C2semidirect
12. C2×#89720C2semidirect
13. C2×#89733C2semidirect
14. C2×#89712C2semidirect
15. C2×#89705C2semidirect
16. #11733918C2direct (N × H)
44. C7×#390C22semidirect
46. #89994C22semidirect
55. #89766C22semidirect
56. #89756C22semidirect
57. #89733C22semidirect
58. #89731C22semidirect
59. #89731C22semidirect
60. #89731C22semidirect
61. #89725C22semidirect
62. #89724C22semidirect
63. #89721C22semidirect
64. #89720C22semidirect
65. #89712C22semidirect
66. #89705C22semidirect
164. C2×#390D7semidirect
315. #390C2×D7semidirect
671. C2×C7#2829semidirect
781. C7C2×#2829semidirect
835. C2#11733918direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C7×#3902
C2×#899952
C2×#899942
C2×#897662
C2×#897562
C2×#897312
C2×#897212
C2×#897252
C2×#897242
C2×#897202
C2×#897332
C2×#897122
C2×#897052
#117339182
C2×#28297