Finite Group Databasebeta

← C2×#11734194 #13560141

Subgroups — C2×#11734194 #13560141

Order 1792.

2822 conjugacy classes of subgroups.

The subgroup lattice has 924 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C7×#392C211yesmaximal, characteristic, complemented
2C2×#89995C211yesmaximal, characteristic, complemented
3C2×#89995C211yesmaximal, characteristic, complemented
4C2×#89995C211yesmaximal, characteristic, complemented
5C2×#89994C211yesmaximal, characteristic, complemented
6C2×#89994C211yesmaximal, characteristic, complemented
7C2×#89993C211yesmaximal, characteristic, complemented
8C2×#89731C211yesmaximal, characteristic, complemented
9C2×#89725C211yesmaximal, characteristic, complemented
10C2×#89724C211yesmaximal, characteristic, complemented
11C2×#89733C211yesmaximal, characteristic, complemented
12C2×#89733C211yesmaximal, characteristic, complemented
13C2×#89723C211yesmaximal, characteristic, complemented
14#11734194C2116yesmaximal, direct product factor
15C2×#89432C211yesmaximal, characteristic, complemented
16C2×#89441C211yesmaximal, characteristic, complemented
17C23×C7×D4C2211yescharacteristic
18C23×C7×D4C2211yescharacteristic
19C23×C7×D4C2211yescharacteristic
20C23×C22⋊D7C2211yescharacteristic
21C23×C22⋊D7C2211yescharacteristic
22C23×C22⋊D7C2211yescharacteristic
23C22×C7×C22⋊C4C2211yescharacteristic
24C22×C7×C22⋊C4C2211yescharacteristic
25C22×C7×C22⋊C4C2211yescharacteristic
26C22×C22⋊Dic7C2211yescharacteristic
27C22×C22⋊Dic7C2211yescharacteristic
28C22×C22⋊Dic7C2211yescharacteristic
29C22×C22⋊Dic7C2211yescharacteristic
30C22×C22⋊Dic7C2211yescharacteristic
31C22×C22⋊Dic7C2211yescharacteristic
32C22×C22⋊Dic7C2211yescharacteristic
33C22×C22⋊Dic7C2211yescharacteristic
34C22×C22⋊Dic7C2211yescharacteristic
35C22×(C2×D7)⋊C4C2211yescharacteristic
36C22×(C2×D7)⋊C4C2211yescharacteristic
37C22×(C2×D7)⋊C4C2211yescharacteristic
38C22×(C2×D7)⋊C4C2211yescharacteristic
39C22×C4⋊Dic7C2211yescharacteristic
40C22×C4⋊Dic7C2211yescharacteristic
41C22×Dic7⋊C4C2211yescharacteristic
42C22×Dic7⋊C4C2211yescharacteristic
43C22×C4×Dic7C2211yescharacteristic
44C7×#392C2218yescomplemented
45C2×C7×#95C2211yescharacteristic
46#89995C2218yescomplemented
47#89995C2218yescomplemented
48#89995C2218yescomplemented
49#89994C2218yescomplemented
50#89994C2218yescomplemented
51#89993C2218yescomplemented
52C2×C7⋊#95C2211yescharacteristic
53C2×C7⋊#95C2211yescharacteristic
54C2×C7⋊#95C2211yescharacteristic
55C2×C7⋊#95C2211yescharacteristic
56C2×C7⋊#95C2211yescharacteristic
57C2×C7⋊#95C2211yescharacteristic
58C2×C7⋊#95C2211yescharacteristic
59#89733C2218yescomplemented
60#89733C2218yescomplemented
61#89731C2218yescomplemented
62#89725C2218yescomplemented
63#89724C2218yescomplemented
64#89723C2218yescomplemented
65#89441C2218yescomplemented
66#89432C2218yescomplemented
67C2×#2828—71nomaximal, Sylow
68C25×C7C2311yescharacteristic
69C25×C7C2311yescharacteristic
70C25×C7C2311yescharacteristic
71C24×D7C2311yescharacteristic
72C22×C7×D4—24no—
73C22×C7×D4—42no—
74C22×C7×D4—42no—
75C22×C7×D4—42no—
76C22×C7×D4—42no—
77C22×C7×D4—42no—
78C22×C7×D4—42no—
79C22×C7×D4—42no—
80C22×C7×D4—42no—
81C22×C7×D4C2314yes—
82C22×C7×D4C2314yes—
83C22×C7×D4C2314yes—
84C23×C4×C7C2311yescharacteristic
85C23×C4×C7C2311yescharacteristic
86C23×C4×C7C2311yescharacteristic
87C23×C4×C7C2311yescharacteristic
88C22×C22⋊D7—42no—
89C22×C22⋊D7—42no—
90C22×C22⋊D7—42no—
91C22×C22⋊D7—42no—
92C22×C22⋊D7—42no—
93C22×C22⋊D7—42no—
94C22×C22⋊D7—42no—
95C22×C22⋊D7—42no—
96C22×C22⋊D7—42no—
97C22×C22⋊D7C2314yes—
98C22×C22⋊D7C2314yes—
99C22×C22⋊D7C2314yes—
100C23×Dic7C2311yescharacteristic
101C23×Dic7C2311yescharacteristic
102C23×Dic7C2311yescharacteristic
103C23×Dic7C2311yescharacteristic
104C23×Dic7C2311yescharacteristic
105C23×Dic7C2311yescharacteristic
106C23×Dic7C2311yescharacteristic
107C2×C7×C22⋊C4—24no—
108C2×C7×C22⋊C4—42no—
109C2×C7×C22⋊C4—42no—
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⋊Dic7—42no—
119C2×C22⋊Dic7—42no—
120C2×C22⋊Dic7—42no—
121C2×C22⋊Dic7—42no—
122C2×C22⋊Dic7C2314yes—
123C2×C22⋊Dic7C2314yes—
124C2×C22⋊Dic7C2314yes—
125C2×C22⋊Dic7C2314yes—
126C2×C22⋊Dic7C2314yes—
127C2×C22⋊Dic7C2314yes—
128C2×C22⋊Dic7C2314yes—
129C2×C22⋊Dic7C2314yes—
130C2×C22⋊Dic7C2314yes—
131C2×(C2×D7)⋊C4—24no—
132C2×(C2×D7)⋊C4—42no—
133C2×(C2×D7)⋊C4—42no—
134C2×(C2×D7)⋊C4—42no—
135C2×(C2×D7)⋊C4C2314yes—
136C2×(C2×D7)⋊C4C2314yes—
137C2×(C2×D7)⋊C4C2314yes—
138C2×(C2×D7)⋊C4C2314yes—
139C2×C4⋊Dic7—42no—
140C2×C4⋊Dic7—42no—
141C2×C4⋊Dic7C2314yes—
142C2×C4⋊Dic7C2314yes—
143C2×Dic7⋊C4—42no—
144C2×Dic7⋊C4—42no—
145C2×Dic7⋊C4C2314yes—
146C2×Dic7⋊C4C2314yes—
147C2×C4×Dic7—42no—
148C2×C4×Dic7C2314yes—
149C7×#95C2314yes—
150C7⋊#95C2314yes—
151C7⋊#95C2314yes—
152C7⋊#95C2314yes—
153C7⋊#95C2314yes—
154C7⋊#95C2314yes—
155C7⋊#95C2314yes—
156C7⋊#95C2314yes—
157#2828—716no—
158C2×#400—71no—
159C2×#397—71no—
160C2×#397—71no—
161C2×#394—71no—
162C2×#394—71no—
163C2×#394—71no—
164C2×#394—71no—
165C2×#394—71no—
166C2×#392—71no—
167C2×#392—71no—
168C2×#392—71no—
169C2×#392D711yescharacteristic, complemented
170C2×#390—71no—
171C2×#388—71no—
172C2×#388—71no—
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×C7—22no—
182C24×C7—22no—
183C24×C7—22no—
184C24×C7—22no—
185C24×C7—22no—
186C24×C7—22no—
187C24×C7—22no—
188C24×C7—22no—
189C24×C7—22no—
190C24×C7—22no—
191C24×C7—22no—
192C24×C7—22no—
193C24×C7—22no—
194C24×C7C2412yes—
195C24×C7C2412yes—
196C24×C7C2412yes—
197C24×C7C2411yescharacteristic
198C23×D7—22no—
199C23×D7—22no—
200C23×D7—22no—
201C23×D7—22no—
202C23×D7—22no—
203C23×D7—22no—
204C23×D7—22no—
205C23×D7C2412yes—
206C2×C7×D4—28no—
207C2×C7×D4—44no—
208C2×C7×D4—44no—
209C2×C7×D4—44no—
210C2×C7×D4—44no—
211C2×C7×D4—44no—
212C2×C7×D4—44no—
213C2×C7×D4—44no—
214C2×C7×D4—44no—
215C2×C7×D4—416no—
216C2×C7×D4—416no—
217C2×C7×D4—416no—
218C22×C4×C7—22no—
219C22×C4×C7—22no—
220C22×C4×C7—22no—
221C22×C4×C7—22no—
222C22×C4×C7—22no—
223C22×C4×C7—22no—
224C22×C4×C7—22no—
225C22×C4×C7—22no—
226C22×C4×C7—22no—
227C22×C4×C7—22no—
228C22×C4×C7—22no—
229C22×C4×C7#4114yes—
230C22×C4×C7C2412yes—
231C22×C4×C7C2412yes—
232C22×C4×C7C2412yes—
233C22×C4×C7C2412yes—
234C2×C22⋊D7—44no—
235C2×C22⋊D7—44no—
236C2×C22⋊D7—44no—
237C2×C22⋊D7—44no—
238C2×C22⋊D7—44no—
239C2×C22⋊D7—44no—
240C2×C22⋊D7—44no—
241C2×C22⋊D7—44no—
242C2×C22⋊D7—44no—
243C2×C22⋊D7—416no—
244C2×C22⋊D7—416no—
245C2×C22⋊D7—416no—
246C22×Dic7—22no—
247C22×Dic7—22no—
248C22×Dic7—22no—
249C22×Dic7—22no—
250C22×Dic7—22no—
251C22×Dic7—22no—
252C22×Dic7—22no—
253C22×Dic7—22no—
254C22×Dic7—22no—
255C22×Dic7—22no—
256C22×Dic7—22no—
257C22×Dic7—22no—
258C22×Dic7—22no—
259C22×Dic7—22no—
260C22×Dic7—22no—
261C22×Dic7—22no—
262C22×Dic7—22no—
263C22×Dic7—22no—
264C22×Dic7—22no—
265C22×Dic7—22no—
266C22×Dic7—22no—
267C22×Dic7C2412yes—
268C22×Dic7C2412yes—
269C22×Dic7C2412yes—
270C22×Dic7C2412yes—
271C22×Dic7C2412yes—
272C22×Dic7C2412yes—
273C22×Dic7C2412yes—
274C7×C22⋊C4—28no—
275C7×C22⋊C4—44no—
276C7×C22⋊C4—44no—
277C22⋊Dic7—44no—
278C22⋊Dic7—44no—
279C22⋊Dic7—44no—
280C22⋊Dic7—44no—
281C22⋊Dic7—44no—
282C22⋊Dic7—44no—
283C22⋊Dic7—44no—
284C22⋊Dic7—44no—
285C22⋊Dic7—44no—
286(C2×D7)⋊C4—28no—
287(C2×D7)⋊C4—44no—
288(C2×D7)⋊C4—44no—
289(C2×D7)⋊C4—44no—
290C4⋊Dic7—44no—
291C4⋊Dic7—44no—
292Dic7⋊C4—44no—
293Dic7⋊C4—44no—
294C4×Dic7—44no—
295C23×D4—71no—
296C23×D4—71no—
297C23×D4—71no—
298C23×D4C2×D711yescharacteristic
299C23×D4C2×D711yescharacteristic
300C23×D4C2×D711yescharacteristic
301C22×C4⋊C4—71no—
302C22×C4⋊C4—71no—
303C22×C4⋊C4—71no—
304C22×C4⋊C4—71no—
305C22×C22⋊C4—71no—
306C22×C22⋊C4—71no—
307C22×C22⋊C4—71no—
308C22×C22⋊C4—71no—
309C22×C22⋊C4—71no—
310C22×C22⋊C4—71no—
311C22×C22⋊C4—71no—
312C22×C22⋊C4—71no—
313C22×C22⋊C4—71no—
314C22×C22⋊C4—71no—
315C22×C22⋊C4—71no—
316C22×C22⋊C4—71no—
317C22×C22⋊C4—71no—
318C22×C22⋊C4C2×D711yescharacteristic
319C22×C22⋊C4C2×D711yescharacteristic
320C22×C22⋊C4C2×D711yescharacteristic
321C22×C42—71no—
322#400—78no—
323#397—78no—
324#397—78no—
325#394—78no—
326#394—78no—
327#394—78no—
328#394—78no—
329#394—78no—
330#392—78no—
331#392—78no—
332#392—78no—
333#392C2×D718yescomplemented
334#390—78no—
335#388—78no—
336#388—78no—
337C2×#95—71no—
338C2×#95—71no—
339C2×#95—71no—
340C2×#95—71no—
341C2×#95—71no—
342C2×#95—71no—
343C2×#95—71no—
344C2×#95C2×D711yescharacteristic
345C23×C7—22no—
346C23×C7—22no—
347C23×C7—22no—
348C23×C7—22no—
349C23×C7—22no—
350C23×C7—22no—
351C23×C7—22no—
352C23×C7—22no—
353C23×C7—22no—
354C23×C7—22no—
355C23×C7—22no—
356C23×C7—22no—
357C23×C7—22no—
358C23×C7—22no—
359C23×C7—22no—
360C23×C7—22no—
361C23×C7—22no—
362C23×C7—22no—
363C23×C7—22no—
364C23×C7—22no—
365C23×C7—22no—
366C23×C7—44no—
367C23×C7—44no—
368C23×C7—44no—
369C23×C7—44no—
370C23×C7—44no—
371C23×C7—44no—
372C23×C7—44no—
373C23×C7—44no—
374C23×C7—44no—
375C23×C7—44no—
376C23×C7—44no—
377C23×C7—44no—
378C23×C7—44no—
379C23×C7—44no—
380C23×C7—44no—
381C23×C7—44no—
382C23×C7—44no—
383C23×C7—44no—
384C23×C7—44no—
385C23×C7—44no—
386C23×C7—44no—
387C23×C7C2×#4112yes—
388C23×C7H(5,𝔽2)12yes—
389C23×C7H(5,𝔽2)12yes—
390C23×C7H(5,𝔽2)12yes—
391C23×C7H(5,𝔽2)12yes—
392C23×C7H(5,𝔽2)12yes—
393C23×C7H(5,𝔽2)12yes—
394C23×C7C2511yescharacteristic
395C22×D7—22no—
396C22×D7—22no—
397C22×D7—22no—
398C22×D7—22no—
399C22×D7—22no—
400C22×D7—22no—
401C22×D7—22no—
402C22×D7—44no—
403C22×D7—44no—
404C22×D7—44no—
405C22×D7—44no—
406C22×D7—44no—
407C22×D7—44no—
408C22×D7—44no—
409C7×D4—416no—
410C7×D4—416no—
411C7×D4—416no—
412C2×C4×C7—28no—
413C2×C4×C7—22no—
414C2×C4×C7—22no—
415C2×C4×C7—22no—
416C2×C4×C7—22no—
417C2×C4×C7—22no—
418C2×C4×C7—22no—
419C2×C4×C7—22no—
420C2×C4×C7—22no—
421C2×C4×C7—22no—
422C2×C4×C7—22no—
423C2×C4×C7—22no—
424C2×C4×C7—44no—
425C2×C4×C7—44no—
426C2×C4×C7—44no—
427C2×C4×C7C2×#4114yes—
428C22⋊D7—416no—
429C22⋊D7—416no—
430C22⋊D7—416no—
431C2×Dic7—22no—
432C2×Dic7—22no—
433C2×Dic7—22no—
434C2×Dic7—22no—
435C2×Dic7—22no—
436C2×Dic7—22no—
437C2×Dic7—22no—
438C2×Dic7—22no—
439C2×Dic7—22no—
440C2×Dic7—22no—
441C2×Dic7—22no—
442C2×Dic7—22no—
443C2×Dic7—22no—
444C2×Dic7—22no—
445C2×Dic7—22no—
446C2×Dic7—22no—
447C2×Dic7—22no—
448C2×Dic7—22no—
449C2×Dic7—22no—
450C2×Dic7—22no—
451C2×Dic7—22no—
452C2×Dic7—44no—
453C2×Dic7—44no—
454C2×Dic7—44no—
455C2×Dic7—44no—
456C2×Dic7—44no—
457C2×Dic7—44no—
458C2×Dic7—44no—
459C25—71no—
460C25C22×D711yescharacteristic
461C25C22×D711yescharacteristic
462C25C22×D711yescharacteristic
463C22×D4—24no—
464C22×D4—42no—
465C22×D4—42no—
466C22×D4—42no—
467C22×D4—42no—
468C22×D4—42no—
469C22×D4—42no—
470C22×D4—42no—
471C22×D4—42no—
472C22×D4—74no—
473C22×D4—74no—
474C22×D4—74no—
475C22×D4—282no—
476C22×D4—282no—
477C22×D4—282no—
478C22×D4—282no—
479C22×D4—282no—
480C22×D4—282no—
481C22×D4—282no—
482C22×D4—282no—
483C22×D4—282no—
484C22×D4C22×D714yes—
485C22×D4C22×D714yes—
486C22×D4C22×D714yes—
487C23×C4—71no—
488C23×C4—71no—
489C23×C4—71no—
490C23×C4—71no—
491C23×C4—71no—
492C23×C4—71no—
493C23×C4—71no—
494C23×C4C22×D711yescharacteristic
495C23×C4C22×D711yescharacteristic
496C23×C4C22×D711yescharacteristic
497C23×C4C22×D711yescharacteristic
498C2×C4⋊C4—74no—
499C2×C4⋊C4—74no—
500C2×C4⋊C4—74no—
501C2×C4⋊C4—74no—
502C2×C4⋊C4—282no—
503C2×C4⋊C4—282no—
504C2×C4⋊C4—282no—
505C2×C4⋊C4—282no—
506C2×C22⋊C4—24no—
507C2×C22⋊C4—42no—
508C2×C22⋊C4—42no—
509C2×C22⋊C4—74no—
510C2×C22⋊C4—74no—
511C2×C22⋊C4—74no—
512C2×C22⋊C4—74no—
513C2×C22⋊C4—74no—
514C2×C22⋊C4—74no—
515C2×C22⋊C4—74no—
516C2×C22⋊C4—74no—
517C2×C22⋊C4—74no—
518C2×C22⋊C4—74no—
519C2×C22⋊C4—74no—
520C2×C22⋊C4—74no—
521C2×C22⋊C4—74no—
522C2×C22⋊C4—144no—
523C2×C22⋊C4—282no—
524C2×C22⋊C4—282no—
525C2×C22⋊C4—282no—
526C2×C22⋊C4—282no—
527C2×C22⋊C4—282no—
528C2×C22⋊C4—282no—
529C2×C22⋊C4—282no—
530C2×C22⋊C4—282no—
531C2×C22⋊C4—282no—
532C2×C22⋊C4—282no—
533C2×C22⋊C4—282no—
534C2×C22⋊C4—282no—
535C2×C22⋊C4C22×D714yes—
536C2×C22⋊C4C22×D714yes—
537C2×C22⋊C4C22×D714yes—
538C2×C42—74no—
539C2×C42—282no—
540#95—74no—
541#95—74no—
542#95—74no—
543#95—74no—
544#95—74no—
545#95—74no—
546#95—74no—
547#95C22×D714yes—
548C22×C7—42no—
549C22×C7—42no—
550C22×C7—42no—
551C22×C7—42no—
552C22×C7—42no—
553C22×C7—42no—
554C22×C7—42no—
555C22×C7—42no—
556C22×C7—42no—
557C22×C7—42no—
558C22×C7—42no—
559C22×C7—42no—
560C22×C7—42no—
561C22×C7—42no—
562C22×C7—42no—
563C22×C7—42no—
564C22×C7—42no—
565C22×C7—42no—
566C22×C7—42no—
567C22×C7—42no—
568C22×C7—42no—
569C22×C7—88no—
570C22×C7—88no—
571C22×C7—88no—
572C22×C7#53814yes—
573C22×C7#54014yes—
574C22×C7#54014yes—
575C22×C7#56014yes—
576C22×C7#56014yes—
577C22×C7#56014yes—
578C22×C7H(3,𝔽4)14yes—
579C22×C7C22×#4111yescharacteristic
580C22×C7C2×H(5,𝔽2)11yescharacteristic
581C22×C7C2×H(5,𝔽2)11yescharacteristic
582C22×C7C2×H(5,𝔽2)11yescharacteristic
583C22×C7C2×H(5,𝔽2)11yescharacteristic
584C22×C7C2×H(5,𝔽2)11yescharacteristic
585C22×C7C2×H(5,𝔽2)11yescharacteristic
586C2×D7—42no—
587C2×D7—42no—
588C2×D7—42no—
589C2×D7—42no—
590C2×D7—42no—
591C2×D7—42no—
592C2×D7—42no—
593C2×D7—88no—
594C4×C7—24no—
595C4×C7—42no—
596C4×C7—42no—
597C4×C7—42no—
598Dic7—42no—
599Dic7—42no—
600Dic7—42no—
601Dic7—42no—
602Dic7—42no—
603Dic7—42no—
604Dic7—42no—
605C24—22no—
606C24—22no—
607C24—22no—
608C24—22no—
609C24—22no—
610C24—22no—
611C24—22no—
612C24—22no—
613C24—22no—
614C24—22no—
615C24—22no—
616C24—22no—
617C24—22no—
618C24—22no—
619C24—22no—
620C24—22no—
621C24—22no—
622C24—22no—
623C24—22no—
624C24—22no—
625C24—22no—
626C24—72no—
627C24—142no—
628C24—142no—
629C24—142no—
630C24—142no—
631C24—142no—
632C24—142no—
633C24—142no—
634C24C23×D712yes—
635C24C23×D712yes—
636C24C23×D712yes—
637C24C23×D711yescharacteristic
638C2×D4—28no—
639C2×D4—44no—
640C2×D4—44no—
641C2×D4—44no—
642C2×D4—44no—
643C2×D4—44no—
644C2×D4—44no—
645C2×D4—44no—
646C2×D4—44no—
647C2×D4—416no—
648C2×D4—416no—
649C2×D4—416no—
650C2×D4—284no—
651C2×D4—284no—
652C2×D4—284no—
653C2×D4—284no—
654C2×D4—284no—
655C2×D4—284no—
656C2×D4—284no—
657C2×D4—284no—
658C2×D4—284no—
659C2×D4—2816no—
660C2×D4—2816no—
661C2×D4—2816no—
662C22×C4—22no—
663C22×C4—22no—
664C22×C4—22no—
665C22×C4—22no—
666C22×C4—22no—
667C22×C4—22no—
668C22×C4—22no—
669C22×C4—22no—
670C22×C4—22no—
671C22×C4—22no—
672C22×C4—22no—
673C22×C4—72no—
674C22×C4—72no—
675C22×C4—72no—
676C22×C4—72no—
677C22×C4—72no—
678C22×C4—72no—
679C22×C4—72no—
680C22×C4—142no—
681C22×C4—142no—
682C22×C4—142no—
683C22×C4—142no—
684C22×C4—142no—
685C22×C4—142no—
686C22×C4—142no—
687C22×C4—142no—
688C22×C4—142no—
689C22×C4—142no—
690C22×C4—142no—
691C22×C4—142no—
692C22×C4—142no—
693C22×C4—142no—
694C22×C4—142no—
695C22×C4—142no—
696C22×C4—142no—
697C22×C4—142no—
698C22×C4—142no—
699C22×C4—142no—
700C22×C4—142no—
701C22×C4#115914yes—
702C22×C4C23×D712yes—
703C22×C4C23×D712yes—
704C22×C4C23×D712yes—
705C22×C4C23×D712yes—
706C4⋊C4—284no—
707C4⋊C4—284no—
708C4⋊C4—284no—
709C4⋊C4—284no—
710C22⋊C4—28no—
711C22⋊C4—44no—
712C22⋊C4—44no—
713C22⋊C4—148no—
714C22⋊C4—284no—
715C22⋊C4—284no—
716C22⋊C4—284no—
717C22⋊C4—284no—
718C22⋊C4—284no—
719C22⋊C4—284no—
720C22⋊C4—284no—
721C22⋊C4—284no—
722C22⋊C4—284no—
723C22⋊C4—284no—
724C22⋊C4—284no—
725C22⋊C4—284no—
726C42—284no—
727C2×C7—82no—
728C2×C7—82no—
729C2×C7—82no—
730C2×C7#282818yescomplemented
731C2×C7C2×#53811yescharacteristic
732C2×C7C2×#54011yescharacteristic
733C2×C7C2×#54011yescharacteristic
734C2×C7C2×#56011yescharacteristic
735C2×C7C2×#56011yescharacteristic
736C2×C7C2×#56011yescharacteristic
737C2×C7C2×H(3,𝔽4)11yescharacteristic
738D7—82no—
739C23—22no—
740C23—22no—
741C23—22no—
742C23—22no—
743C23—22no—
744C23—22no—
745C23—22no—
746C23—22no—
747C23—22no—
748C23—22no—
749C23—22no—
750C23—22no—
751C23—22no—
752C23—22no—
753C23—22no—
754C23—22no—
755C23—22no—
756C23—22no—
757C23—22no—
758C23—22no—
759C23—22no—
760C23—44no—
761C23—44no—
762C23—44no—
763C23—44no—
764C23—44no—
765C23—44no—
766C23—44no—
767C23—44no—
768C23—44no—
769C23—44no—
770C23—44no—
771C23—44no—
772C23—44no—
773C23—44no—
774C23—44no—
775C23—44no—
776C23—44no—
777C23—44no—
778C23—44no—
779C23—44no—
780C23—44no—
781C23—142no—
782C23—142no—
783C23—142no—
784C23—142no—
785C23—142no—
786C23—142no—
787C23—142no—
788C23—284no—
789C23—284no—
790C23—284no—
791C23—284no—
792C23—284no—
793C23—284no—
794C23—284no—
795C23C2×#115912yes—
796C23#654812yes—
797C23#654812yes—
798C23#654812yes—
799C23#654812yes—
800C23#654812yes—
801C23#655312yes—
802C23C24×D711yescharacteristic
803D4—416no—
804D4—416no—
805D4—416no—
806D4—2816no—
807D4—2816no—
808D4—2816no—
809C2×C4—28no—
810C2×C4—22no—
811C2×C4—22no—
812C2×C4—22no—
813C2×C4—22no—
814C2×C4—22no—
815C2×C4—22no—
816C2×C4—22no—
817C2×C4—22no—
818C2×C4—22no—
819C2×C4—22no—
820C2×C4—22no—
821C2×C4—44no—
822C2×C4—44no—
823C2×C4—44no—
824C2×C4—142no—
825C2×C4—142no—
826C2×C4—142no—
827C2×C4—142no—
828C2×C4—142no—
829C2×C4—142no—
830C2×C4—142no—
831C2×C4—142no—
832C2×C4—142no—
833C2×C4—142no—
834C2×C4—142no—
835C2×C4—142no—
836C2×C4—142no—
837C2×C4—142no—
838C2×C4—142no—
839C2×C4—142no—
840C2×C4—142no—
841C2×C4—142no—
842C2×C4—142no—
843C2×C4—142no—
844C2×C4—142no—
845C2×C4—284no—
846C2×C4—284no—
847C2×C4—284no—
848C2×C4—284no—
849C2×C4—284no—
850C2×C4—284no—
851C2×C4—284no—
852C2×C4C2×#115914yes—
853C7C2×#282811yescharacteristic, complemented, Sylow
854C22—42no—
855C22—42no—
856C22—42no—
857C22—42no—
858C22—42no—
859C22—42no—
860C22—42no—
861C22—42no—
862C22—42no—
863C22—42no—
864C22—42no—
865C22—42no—
866C22—42no—
867C22—42no—
868C22—42no—
869C22—42no—
870C22—42no—
871C22—42no—
872C22—42no—
873C22—42no—
874C22—42no—
875C22—88no—
876C22—88no—
877C22—88no—
878C22—282no—
879C22—282no—
880C22—282no—
881C22—282no—
882C22—282no—
883C22—282no—
884C22—282no—
885C22—568no—
886C22#9028414yes—
887C22#9028514yes—
888C22#9028614yes—
889C22#9031014yes—
890C22#9031114yes—
891C22#9031114yes—
892C22#9041014yes—
893C22C22×#115911yescharacteristic
894C22C2×#654811yescharacteristic
895C22C2×#654811yescharacteristic
896C22C2×#654811yescharacteristic
897C22C2×#654811yescharacteristic
898C22C2×#654811yescharacteristic
899C22C2×#655311yescharacteristic
900C4—24no—
901C4—42no—
902C4—42no—
903C4—42no—
904C4—282no—
905C4—282no—
906C4—282no—
907C4—282no—
908C4—282no—
909C4—282no—
910C4—282no—
911C2—82no—
912C2—82no—
913C2—82no—
914C2—562no—
915C2#1173419418yesdirect product factor
916C2C2×#9028411yescharacteristic
917C2C2×#9028511yescharacteristic
918C2C2×#9028611yescharacteristic
919C2C2×#9031011yescharacteristic
920C2C2×#9031111yescharacteristic
921C2C2×#9031111yescharacteristic
922C2C2×#9041011yescharacteristic
subgroupG/H
centerC24C23×D7
commutator, cosocleC23×C7C25
FrattiniC23C24×D7
FittingC2×C7×#392C2
socleC24×C7C24
hypercenterC2×#392D7
hypocenterC7C2×#2828
LCSG ▷ C23×C7 ▷ C7
UCSC1 ◁ C24 ◁ C2×#392

Complements

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

NH ≅ G/Ntype
1. C2×C7×#392C2semidirect
2. C2×#89995C2semidirect
3. C2×#89995C2semidirect
4. C2×#89995C2semidirect
5. C2×#89994C2semidirect
6. C2×#89994C2semidirect
7. C2×#89993C2semidirect
8. C2×#89731C2semidirect
9. C2×#89725C2semidirect
10. C2×#89724C2semidirect
11. C2×#89733C2semidirect
12. C2×#89733C2semidirect
13. C2×#89723C2semidirect
14. #11734194C2direct (N × H)
15. C2×#89432C2semidirect
16. C2×#89441C2semidirect
44. C7×#392C22semidirect
46. #89995C22semidirect
47. #89995C22semidirect
48. #89995C22semidirect
49. #89994C22semidirect
50. #89994C22semidirect
51. #89993C22semidirect
59. #89733C22semidirect
60. #89733C22semidirect
61. #89731C22semidirect
62. #89725C22semidirect
63. #89724C22semidirect
64. #89723C22semidirect
65. #89441C22semidirect
66. #89432C22semidirect
169. C2×#392D7semidirect
333. #392C2×D7semidirect
730. C2×C7#2828semidirect
853. C7C2×#2828semidirect
915. C2#11734194direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C7×#3922
C2×#899952
C2×#899942
C2×#899932
C2×#897312
C2×#897252
C2×#897242
C2×#897332
C2×#897232
#117341942
C2×#894322
C2×#894412
C2×#28287