Finite Group Databasebeta

← C2×#11734868 #13520157

Subgroups — C2×#11734868 #13520157

Order 1792.

3718 conjugacy classes of subgroups.

The subgroup lattice has 904 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#6457C211yesmaximal, characteristic, complemented
2C22×D7×C4⋊C4C211yesmaximal, characteristic, complemented
3C22×#6446C211yesmaximal, characteristic, complemented
4C22×#6447C211yesmaximal, characteristic
5C2×C7×#396C211yesmaximal, characteristic, complemented
6C2×#89766C211yesmaximal, characteristic, complemented
7C2×#89766C211yesmaximal, characteristic, complemented
8C2×#89759C211yesmaximal, characteristic, complemented
9C2×#89756C211yesmaximal, characteristic, complemented
10C2×#89731C211yesmaximal, characteristic, complemented
11C2×#89728C211yesmaximal, characteristic, complemented
12C2×#89720C211yesmaximal, characteristic, complemented
13C2×#89733C211yesmaximal, characteristic, complemented
14#11734868C2116yesmaximal, direct product factor
15C2×#89437C211yesmaximal, characteristic, complemented
16C2×#89429C211yesmaximal, characteristic, complemented
17C23×C22⋊D7C2211yescharacteristic
18C23×C22⋊D7C2211yescharacteristic
19C23×D28C2211yescharacteristic
20C23×C4×D7C2211yescharacteristic
21C23×C4×D7C2211yescharacteristic
22C23×C4×D7C2211yescharacteristic
23C22×C7×C4⋊C4C2211yescharacteristic
24C22×C7×C4⋊C4C2211yescharacteristic
25C22×C7×C4⋊C4C2211yescharacteristic
26C22×C7×C22⋊C4C2211yescharacteristic
27C22×C7×C22⋊C4C2211yescharacteristic
28C22×C7×C22⋊C4C2211yescharacteristic
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×(C2×D7)⋊C4C2211yescharacteristic
37C22×(C2×D7)⋊C4C2211yescharacteristic
38C22×C4⋊Dic7C2211yescharacteristic
39C22×C4⋊Dic7C2211yescharacteristic
40C22×C4⋊Dic7C2211yescharacteristic
41C22×Dic7⋊C4C2211yescharacteristic
42C22×Dic7⋊C4C2211yescharacteristic
43C22×Dic7⋊C4C2211yescharacteristic
44C22×Dic7⋊C4C2211yescharacteristic
45C22×Dic7⋊C4C2211yescharacteristic
46C2×#6457—28no—
47C2×#6457C2218yescomplemented
48C2×D7×C4⋊C4—28no—
49C2×D7×C4⋊C4C2218yescomplemented
50C2×#6447—28no—
51C2×#6447C2218yes—
52C2×#6446—28no—
53C2×#6446C2218yescomplemented
54C7×#396C2218yescomplemented
55C2×C7×#95C2211yescharacteristic
56C2×C7⋊#95C2211yescharacteristic
57C2×C7⋊#95C2211yescharacteristic
58C2×C7⋊#95C2211yescharacteristic
59C2×C7⋊#95C2211yescharacteristic
60C2×C7⋊#95C2211yescharacteristic
61#89766C2218yescomplemented
62#89766C2218yescomplemented
63#89759C2218yescomplemented
64#89756C2218yescomplemented
65#89733C2218yescomplemented
66#89731C2218yescomplemented
67#89728C2218yescomplemented
68#89720C2218yescomplemented
69#89437C2218yescomplemented
70#89429C2218yescomplemented
71C2×#2618—71nomaximal, Sylow
72C25×C7C2311yescharacteristic
73C24×D7C2311yescharacteristic
74C24×D7C2311yescharacteristic
75C23×C4×C7C2311yescharacteristic
76C23×C4×C7C2311yescharacteristic
77C23×C4×C7C2311yescharacteristic
78C23×C4×C7C2311yescharacteristic
79C23×C4×C7C2311yescharacteristic
80C23×C4×C7C2311yescharacteristic
81C22×C22⋊D7—24no—
82C22×C22⋊D7—24no—
83C22×C22⋊D7—24no—
84C22×C22⋊D7—24no—
85C22×C22⋊D7—42no—
86C22×C22⋊D7—42no—
87C22×C22⋊D7C2314yes—
88C22×C22⋊D7C2314yes—
89C23×Dic7C2311yescharacteristic
90C23×Dic7C2311yescharacteristic
91C23×Dic7C2311yescharacteristic
92C23×Dic7C2311yescharacteristic
93C23×Dic7C2311yescharacteristic
94C23×Dic7C2311yescharacteristic
95C22×D28—24no—
96C22×D28—24no—
97C22×D28—24no—
98C22×D28C2314yes—
99C22×C4×D7—24no—
100C22×C4×D7—24no—
101C22×C4×D7—24no—
102C22×C4×D7—42no—
103C22×C4×D7—42no—
104C22×C4×D7—42no—
105C22×C4×D7—42no—
106C22×C4×D7D418yes—
107C22×C4×D7D418yescomplemented
108C22×C4×D7C2314yes—
109C22×C4×D7C2314yes—
110C22×C4×D7C2314yes—
111C2×C7×C4⋊C4—24no—
112C2×C7×C4⋊C4—24no—
113C2×C7×C4⋊C4—42no—
114C2×C7×C4⋊C4C2314yes—
115C2×C7×C4⋊C4C2314yes—
116C2×C7×C4⋊C4C2314yes—
117C2×C7×C22⋊C4—24no—
118C2×C7×C22⋊C4—24no—
119C2×C7×C22⋊C4—42no—
120C2×C7×C22⋊C4C2314yes—
121C2×C7×C22⋊C4C2314yes—
122C2×C7×C22⋊C4C2314yes—
123C2×C22⋊Dic7—24no—
124C2×C22⋊Dic7—42no—
125C2×C22⋊Dic7C2314yes—
126C2×C22⋊Dic7C2314yes—
127C2×(C2×D7)⋊C4—24no—
128C2×(C2×D7)⋊C4—24no—
129C2×(C2×D7)⋊C4—24no—
130C2×(C2×D7)⋊C4—24no—
131C2×(C2×D7)⋊C4—24no—
132C2×(C2×D7)⋊C4—42no—
133C2×(C2×D7)⋊C4—42no—
134C2×(C2×D7)⋊C4C2314yes—
135C2×(C2×D7)⋊C4C2314yes—
136C2×(C2×D7)⋊C4C2314yes—
137C2×(C2×D7)⋊C4C2314yes—
138C2×(C2×D7)⋊C4C2314yes—
139C2×(C2×D7)⋊C4C2314yes—
140C2×(C2×D7)⋊C4C2314yes—
141C2×C4⋊Dic7—24no—
142C2×C4⋊Dic7—24no—
143C2×C4⋊Dic7—42no—
144C2×C4⋊Dic7C2314yes—
145C2×C4⋊Dic7C2314yes—
146C2×C4⋊Dic7C2314yes—
147C2×Dic7⋊C4—24no—
148C2×Dic7⋊C4—24no—
149C2×Dic7⋊C4—24no—
150C2×Dic7⋊C4—24no—
151C2×Dic7⋊C4—24no—
152C2×Dic7⋊C4C2314yes—
153C2×Dic7⋊C4C2314yes—
154C2×Dic7⋊C4C2314yes—
155C2×Dic7⋊C4C2314yes—
156C2×Dic7⋊C4C2314yes—
157#6457—232no—
158D7×C4⋊C4—232no—
159#6447—232no—
160#6446—232no—
161C7×#95C2314yes—
162C7⋊#95C2314yes—
163C7⋊#95C2314yes—
164C7⋊#95C2314yes—
165C7⋊#95C2314yes—
166C7⋊#95C2314yes—
167C22×#123—71no—
168C22×#123—71no—
169C22×#121—71no—
170C23×C4⋊C4—71no—
171#2618—716no—
172C2×#398—71no—
173C2×#398—71no—
174C2×#396—71no—
175C2×#396—71no—
176C2×#396—71no—
177C2×#396D711yescharacteristic, complemented
178C2×#394—71no—
179C2×#394—71no—
180C2×#386—71no—
181C2×#386—71no—
182C2×#380—71no—
183C24×C7—22no—
184C24×C7—22no—
185C24×C7—22no—
186C24×C7—22no—
187C24×C7—22no—
188C24×C7—22no—
189C24×C7—22no—
190C24×C7C2412yes—
191C24×C7C2411yescharacteristic
192C23×D7—22no—
193C23×D7—22no—
194C23×D7—22no—
195C23×D7—22no—
196C23×D7—22no—
197C23×D7—22no—
198C23×D7—22no—
199C23×D7—22no—
200C23×D7—22no—
201C23×D7—22no—
202C23×D7—22no—
203C23×D7C2×D414yes—
204C23×D7C2×D414yes—
205C23×D7#4114yes—
206C23×D7C2412yes—
207C23×D7C2412yes—
208C22×C4×C7—22no—
209C22×C4×C7—22no—
210C22×C4×C7—22no—
211C22×C4×C7—22no—
212C22×C4×C7—22no—
213C22×C4×C7—22no—
214C22×C4×C7—22no—
215C22×C4×C7—22no—
216C22×C4×C7—22no—
217C22×C4×C7—22no—
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×C7C2×D414yes—
225C22×C4×C7C2×D414yes—
226C22×C4×C7C2412yes—
227C22×C4×C7C2412yes—
228C22×C4×C7C2412yes—
229C22×C4×C7C2412yes—
230C22×C4×C7C2412yes—
231C22×C4×C7C2412yes—
232C2×C22⋊D7—28no—
233C2×C22⋊D7—28no—
234C2×C22⋊D7—28no—
235C2×C22⋊D7—28no—
236C2×C22⋊D7—44no—
237C2×C22⋊D7—44no—
238C2×C22⋊D7—416no—
239C2×C22⋊D7—416no—
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×Dic7—22no—
250C22×Dic7—22no—
251C22×Dic7—22no—
252C22×Dic7—22no—
253C22×Dic7—22no—
254C22×Dic7—22no—
255C22×Dic7—22no—
256C22×Dic7C2×D414yes—
257C22×Dic7C2×D414yes—
258C22×Dic7C2412yes—
259C22×Dic7C2412yes—
260C22×Dic7C2412yes—
261C22×Dic7C2412yes—
262C22×Dic7C2412yes—
263C22×Dic7C2412yes—
264C2×D28—28no—
265C2×D28—28no—
266C2×D28—28no—
267C2×D28—416no—
268C2×C4×D7—232no—
269C2×C4×D7—28no—
270C2×C4×D7—28no—
271C2×C4×D7—28no—
272C2×C4×D7—416no—
273C2×C4×D7—44no—
274C2×C4×D7—44no—
275C2×C4×D7—44no—
276C2×C4×D7—44no—
277C2×C4×D7—416no—
278C2×C4×D7C2×D4116yes—
279C2×C4×D7C2×D4116yescomplemented
280C7×C4⋊C4—28no—
281C7×C4⋊C4—28no—
282C7×C4⋊C4—44no—
283C7×C22⋊C4—28no—
284C7×C22⋊C4—28no—
285C7×C22⋊C4—44no—
286C22⋊Dic7—28no—
287C22⋊Dic7—44no—
288(C2×D7)⋊C4—28no—
289(C2×D7)⋊C4—28no—
290(C2×D7)⋊C4—28no—
291(C2×D7)⋊C4—28no—
292(C2×D7)⋊C4—28no—
293(C2×D7)⋊C4—44no—
294(C2×D7)⋊C4—44no—
295C4⋊Dic7—28no—
296C4⋊Dic7—28no—
297C4⋊Dic7—44no—
298Dic7⋊C4—28no—
299Dic7⋊C4—28no—
300Dic7⋊C4—28no—
301Dic7⋊C4—28no—
302Dic7⋊C4—28no—
303C23×D4—71no—
304C23×D4—71no—
305C23×D4—71no—
306C24×C4—71no—
307C24×C4—71no—
308C24×C4—71no—
309C2×#123—78no—
310C2×#123—78no—
311C2×#123—148no—
312C2×#123—148no—
313C2×#121—78no—
314C2×#121—148no—
315C22×C4⋊C4—71no—
316C22×C4⋊C4—71no—
317C22×C4⋊C4—71no—
318C22×C4⋊C4—71no—
319C22×C4⋊C4—71no—
320C22×C4⋊C4—71no—
321C22×C4⋊C4—71no—
322C22×C4⋊C4—71no—
323C22×C4⋊C4—78no—
324C22×C4⋊C4—148no—
325C22×C4⋊C4C2×D711yescharacteristic
326C22×C4⋊C4C2×D711yescharacteristic
327C22×C4⋊C4C2×D711yescharacteristic
328C22×C22⋊C4—71no—
329C22×C22⋊C4—71no—
330C22×C22⋊C4—71no—
331C22×C22⋊C4—71no—
332C22×C22⋊C4—71no—
333C22×C22⋊C4—71no—
334C22×C22⋊C4—71no—
335C22×C22⋊C4—71no—
336C22×C22⋊C4—71no—
337C22×C22⋊C4C2×D711yescharacteristic
338C22×C22⋊C4C2×D711yescharacteristic
339C22×C22⋊C4C2×D711yescharacteristic
340#398—78no—
341#398—78no—
342#396—78no—
343#396—78no—
344#396—78no—
345#396C2×D718yescomplemented
346#394—78no—
347#394—78no—
348#386—78no—
349#386—78no—
350#380—78no—
351C2×#95—71no—
352C2×#95—71no—
353C2×#95—71no—
354C2×#95—71no—
355C2×#95—71no—
356C2×#95C2×D711yescharacteristic
357C23×C7—22no—
358C23×C7—22no—
359C23×C7—22no—
360C23×C7—22no—
361C23×C7—22no—
362C23×C7—22no—
363C23×C7—22no—
364C23×C7—44no—
365C23×C7—44no—
366C23×C7—44no—
367C23×C7—44no—
368C23×C7—44no—
369C23×C7—44no—
370C23×C7—44no—
371C23×C7C22×D412yes—
372C23×C7C22×D412yes—
373C23×C7C2×#4112yes—
374C23×C7H(5,𝔽2)12yes—
375C23×C7H(5,𝔽2)12yes—
376C23×C72−1+412yes—
377C23×C72−1+412yes—
378C23×C7C2511yescharacteristic
379C22×D7—28no—
380C22×D7—28no—
381C22×D7—28no—
382C22×D7—28no—
383C22×D7—28no—
384C22×D7—28no—
385C22×D7—22no—
386C22×D7—22no—
387C22×D7—22no—
388C22×D7—22no—
389C22×D7—22no—
390C22×D7—22no—
391C22×D7—22no—
392C22×D7—22no—
393C22×D7—22no—
394C22×D7—22no—
395C22×D7—22no—
396C22×D7—44no—
397C22×D7—44no—
398C22×D7—44no—
399C22×D7—44no—
400C22×D7—44no—
401C22×D7—44no—
402C22×D7—44no—
403C22×D7#121116yes—
404C22×D7C22×D414yes—
405C22×D7C22×D414yes—
406C22×D7C2×#4114yes—
407C2×C4×C7—28no—
408C2×C4×C7—28no—
409C2×C4×C7—22no—
410C2×C4×C7—22no—
411C2×C4×C7—22no—
412C2×C4×C7—22no—
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—22no—
425C2×C4×C7—44no—
426C2×C4×C7—44no—
427C2×C4×C7—44no—
428C2×C4×C7—44no—
429C2×C4×C7C22×D414yes—
430C2×C4×C7C22×D414yes—
431C22⋊D7—416no—
432C22⋊D7—416no—
433C2×Dic7—28no—
434C2×Dic7—28no—
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—44no—
452C2×Dic7—44no—
453C2×Dic7—44no—
454C2×Dic7—44no—
455C2×Dic7C22×D414yes—
456C2×Dic7C22×D414yes—
457D28—416no—
458C4×D7—232no—
459C4×D7—416no—
460C4×D7—416no—
461C25—71no—
462C25—71no—
463C25C22×D711yescharacteristic
464C22×D4—74no—
465C22×D4—74no—
466C22×D4—74no—
467C22×D4—144no—
468C22×D4—144no—
469C22×D4—144no—
470C22×D4—144no—
471C22×D4—144no—
472C22×D4—144no—
473C22×D4—144no—
474C22×D4—282no—
475C22×D4—282no—
476C23×C4—71no—
477C23×C4—71no—
478C23×C4—78no—
479C23×C4—74no—
480C23×C4—78no—
481C23×C4—74no—
482C23×C4—71no—
483C23×C4—71no—
484C23×C4—71no—
485C23×C4—71no—
486C23×C4—74no—
487C23×C4—144no—
488C23×C4—144no—
489C23×C4—144no—
490C23×C4—282no—
491C23×C4—282no—
492C23×C4—282no—
493C23×C4—282no—
494C23×C4C22×D711yescharacteristic
495C23×C4C22×D711yescharacteristic
496C23×C4C22×D711yescharacteristic
497C23×C4C22×D711yescharacteristic
498C23×C4C22×D711yescharacteristic
499C23×C4C22×D711yescharacteristic
500#123—1432no—
501#123—1432no—
502#121—1432no—
503C2×C4⋊C4—24no—
504C2×C4⋊C4—24no—
505C2×C4⋊C4—42no—
506C2×C4⋊C4—74no—
507C2×C4⋊C4—74no—
508C2×C4⋊C4—74no—
509C2×C4⋊C4—74no—
510C2×C4⋊C4—74no—
511C2×C4⋊C4—74no—
512C2×C4⋊C4—74no—
513C2×C4⋊C4—74no—
514C2×C4⋊C4—1432no—
515C2×C4⋊C4—144no—
516C2×C4⋊C4—144no—
517C2×C4⋊C4—144no—
518C2×C4⋊C4—144no—
519C2×C4⋊C4—144no—
520C2×C4⋊C4—144no—
521C2×C4⋊C4—144no—
522C2×C4⋊C4—282no—
523C2×C4⋊C4C22×D714yes—
524C2×C4⋊C4C22×D714yes—
525C2×C4⋊C4C22×D714yes—
526C2×C22⋊C4—24no—
527C2×C22⋊C4—24no—
528C2×C22⋊C4—42no—
529C2×C22⋊C4—74no—
530C2×C22⋊C4—74no—
531C2×C22⋊C4—74no—
532C2×C22⋊C4—74no—
533C2×C22⋊C4—74no—
534C2×C22⋊C4—74no—
535C2×C22⋊C4—74no—
536C2×C22⋊C4—74no—
537C2×C22⋊C4—74no—
538C2×C22⋊C4—144no—
539C2×C22⋊C4—144no—
540C2×C22⋊C4—144no—
541C2×C22⋊C4—144no—
542C2×C22⋊C4—144no—
543C2×C22⋊C4—144no—
544C2×C22⋊C4—282no—
545C2×C22⋊C4—282no—
546C2×C22⋊C4—282no—
547C2×C22⋊C4C22×D714yes—
548C2×C22⋊C4C22×D714yes—
549C2×C22⋊C4C22×D714yes—
550#95—74no—
551#95—74no—
552#95—74no—
553#95—74no—
554#95—74no—
555#95C22×D714yes—
556C22×C7—42no—
557C22×C7—42no—
558C22×C7—42no—
559C22×C7—42no—
560C22×C7—42no—
561C22×C7—42no—
562C22×C7—42no—
563C22×C7—88no—
564C22×C7C2×#12114yes—
565C22×C7#53414yes—
566C22×C7#53614yes—
567C22×C7#53714yes—
568C22×C7#53714yes—
569C22×C7#53914yes—
570C22×C7#53914yes—
571C22×C7C23×D411yescharacteristic
572C22×C7C23×D411yescharacteristic
573C22×C7C22×#4111yescharacteristic
574C22×C7C2×H(5,𝔽2)11yescharacteristic
575C22×C7C2×H(5,𝔽2)11yescharacteristic
576C22×C7C2×2−1+411yescharacteristic
577C22×C7C2×2−1+411yescharacteristic
578C2×D7—232no—
579C2×D7—24no—
580C2×D7—24no—
581C2×D7—24no—
582C2×D7—24no—
583C2×D7—24no—
584C2×D7—24no—
585C2×D7—42no—
586C2×D7—42no—
587C2×D7—42no—
588C2×D7—42no—
589C2×D7—42no—
590C2×D7—42no—
591C2×D7—42no—
592C2×D7—88no—
593C2×D7C2×#12118yes—
594C4×C7—24no—
595C4×C7—24no—
596C4×C7—42no—
597C4×C7—42no—
598C4×C7—42no—
599C4×C7—42no—
600Dic7—24no—
601Dic7—24no—
602Dic7—42no—
603Dic7—42no—
604Dic7—42no—
605Dic7—42no—
606C24—22no—
607C24—22no—
608C24—22no—
609C24—22no—
610C24—22no—
611C24—22no—
612C24—22no—
613C24—74no—
614C24—74no—
615C24—74no—
616C24—72no—
617C24—72no—
618C24—142no—
619C24—142no—
620C24—142no—
621C24—142no—
622C24—142no—
623C24—142no—
624C24—142no—
625C24—142no—
626C24—142no—
627C24—142no—
628C24—142no—
629C24C23×D712yes—
630C24C23×D711yescharacteristic
631C2×D4—148no—
632C2×D4—148no—
633C2×D4—148no—
634C2×D4—148no—
635C2×D4—148no—
636C2×D4—148no—
637C2×D4—148no—
638C2×D4—2816no—
639C2×D4—284no—
640C2×D4—284no—
641C2×D4—2816no—
642C2×D4—2816no—
643C22×C4—22no—
644C22×C4—22no—
645C22×C4—22no—
646C22×C4—22no—
647C22×C4—22no—
648C22×C4—22no—
649C22×C4—22no—
650C22×C4—22no—
651C22×C4—22no—
652C22×C4—22no—
653C22×C4—22no—
654C22×C4—22no—
655C22×C4—22no—
656C22×C4—22no—
657C22×C4—22no—
658C22×C4—22no—
659C22×C4—74no—
660C22×C4—74no—
661C22×C4—72no—
662C22×C4—72no—
663C22×C4—716no—
664C22×C4—716no—
665C22×C4—72no—
666C22×C4—72no—
667C22×C4—72no—
668C22×C4—72no—
669C22×C4—148no—
670C22×C4—1432no—
671C22×C4—148no—
672C22×C4—148no—
673C22×C4—142no—
674C22×C4—142no—
675C22×C4—142no—
676C22×C4—142no—
677C22×C4—142no—
678C22×C4—142no—
679C22×C4—142no—
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—2816no—
690C22×C4—284no—
691C22×C4—284no—
692C22×C4—284no—
693C22×C4—284no—
694C22×C4—2816no—
695C22×C4D4×D714yes—
696C22×C4D4×D714yes—
697C22×C4C23×D712yes—
698C22×C4C23×D712yes—
699C22×C4C23×D712yes—
700C22×C4C23×D712yes—
701C22×C4C23×D712yes—
702C22×C4C23×D712yes—
703C4⋊C4—28no—
704C4⋊C4—28no—
705C4⋊C4—44no—
706C4⋊C4—148no—
707C4⋊C4—148no—
708C4⋊C4—148no—
709C4⋊C4—148no—
710C4⋊C4—148no—
711C4⋊C4—148no—
712C4⋊C4—148no—
713C4⋊C4—284no—
714C22⋊C4—28no—
715C22⋊C4—28no—
716C22⋊C4—44no—
717C22⋊C4—148no—
718C22⋊C4—148no—
719C22⋊C4—148no—
720C22⋊C4—148no—
721C22⋊C4—148no—
722C22⋊C4—148no—
723C22⋊C4—284no—
724C22⋊C4—284no—
725C22⋊C4—284no—
726C2×C7—82no—
727C2×C7#261818yescomplemented
728C2×C7C22×#12111yescharacteristic
729C2×C7C2×#53411yescharacteristic
730C2×C7C2×#53611yescharacteristic
731C2×C7C2×#53711yescharacteristic
732C2×C7C2×#53711yescharacteristic
733C2×C7C2×#53911yescharacteristic
734C2×C7C2×#53911yescharacteristic
735D7—28no—
736D7—82no—
737C23—22no—
738C23—22no—
739C23—22no—
740C23—22no—
741C23—22no—
742C23—22no—
743C23—22no—
744C23—44no—
745C23—44no—
746C23—44no—
747C23—44no—
748C23—44no—
749C23—44no—
750C23—44no—
751C23—716no—
752C23—74no—
753C23—74no—
754C23—74no—
755C23—148no—
756C23—148no—
757C23—148no—
758C23—148no—
759C23—148no—
760C23—148no—
761C23—142no—
762C23—142no—
763C23—142no—
764C23—142no—
765C23—142no—
766C23—142no—
767C23—142no—
768C23—142no—
769C23—142no—
770C23—142no—
771C23—142no—
772C23—284no—
773C23—284no—
774C23—284no—
775C23—284no—
776C23—284no—
777C23—284no—
778C23—284no—
779C23C2×D4×D712yes—
780C23C2×D4×D712yes—
781C23#654812yes—
782C23#655112yes—
783C23D7×#4112yes—
784C23#655312yes—
785C23#655412yes—
786C23C24×D711yescharacteristic
787D4—2816no—
788D4—2816no—
789D4—2816no—
790C2×C4—28no—
791C2×C4—28no—
792C2×C4—22no—
793C2×C4—22no—
794C2×C4—22no—
795C2×C4—22no—
796C2×C4—22no—
797C2×C4—22no—
798C2×C4—22no—
799C2×C4—22no—
800C2×C4—22no—
801C2×C4—22no—
802C2×C4—22no—
803C2×C4—22no—
804C2×C4—22no—
805C2×C4—22no—
806C2×C4—22no—
807C2×C4—22no—
808C2×C4—44no—
809C2×C4—44no—
810C2×C4—44no—
811C2×C4—44no—
812C2×C4—74no—
813C2×C4—74no—
814C2×C4—1432no—
815C2×C4—148no—
816C2×C4—148no—
817C2×C4—142no—
818C2×C4—142no—
819C2×C4—142no—
820C2×C4—142no—
821C2×C4—142no—
822C2×C4—142no—
823C2×C4—142no—
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—2816no—
834C2×C4—2816no—
835C2×C4—284no—
836C2×C4—284no—
837C2×C4—284no—
838C2×C4—284no—
839C2×C4C2×D4×D714yes—
840C2×C4C2×D4×D714yes—
841C7C2×#261811yescharacteristic, complemented, Sylow
842C22—42no—
843C22—42no—
844C22—42no—
845C22—42no—
846C22—42no—
847C22—42no—
848C22—42no—
849C22—78no—
850C22—88no—
851C22—144no—
852C22—144no—
853C22—144no—
854C22—144no—
855C22—144no—
856C22—1432no—
857C22—144no—
858C22—282no—
859C22—282no—
860C22—282no—
861C22—282no—
862C22—282no—
863C22—282no—
864C22—282no—
865C22—568no—
866C22D7×#12114yes—
867C22#9029614yes—
868C22#9029914yes—
869C22#9031914yes—
870C22#9032014yes—
871C22#9032914yes—
872C22#9039814yes—
873C22C22×D4×D711yescharacteristic
874C22C22×D4×D711yescharacteristic
875C22C2×#654811yescharacteristic
876C22C2×#655111yescharacteristic
877C22C2×D7×#4111yescharacteristic
878C22C2×#655311yescharacteristic
879C22C2×#655411yescharacteristic
880C4—24no—
881C4—24no—
882C4—42no—
883C4—42no—
884C4—42no—
885C4—42no—
886C4—144no—
887C4—144no—
888C4—282no—
889C4—282no—
890C4—282no—
891C4—282no—
892C2—82no—
893C2—148no—
894C2—562no—
895C2#1173486818yesdirect product factor
896C2C2×D7×#12111yescharacteristic
897C2C2×#9029611yescharacteristic
898C2C2×#9029911yescharacteristic
899C2C2×#9031911yescharacteristic
900C2C2×#9032011yescharacteristic
901C2C2×#9032911yescharacteristic
902C2C2×#9039811yescharacteristic
subgroupG/H
centerC24C23×D7
commutator, cosocleC23×C7C25
FrattiniC23C24×D7
FittingC2×C7×#396C2
socleC24×C7C24
prime radicalC22×#6447C2
hypercenterC2×#396D7
hypocenterC7C2×#2618
LCSG ▷ C23×C7 ▷ C7
UCSC1 ◁ C24 ◁ C2×#396

Complements

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

NH ≅ G/Ntype
1. C22×#6457C2semidirect
2. C22×D7×C4⋊C4C2semidirect
3. C22×#6446C2semidirect
5. C2×C7×#396C2semidirect
6. C2×#89766C2semidirect
7. C2×#89766C2semidirect
8. C2×#89759C2semidirect
9. C2×#89756C2semidirect
10. C2×#89731C2semidirect
11. C2×#89728C2semidirect
12. C2×#89720C2semidirect
13. C2×#89733C2semidirect
14. #11734868C2direct (N × H)
15. C2×#89437C2semidirect
16. C2×#89429C2semidirect
47. C2×#6457C22semidirect
49. C2×D7×C4⋊C4C22semidirect
53. C2×#6446C22semidirect
54. C7×#396C22semidirect
61. #89766C22semidirect
62. #89766C22semidirect
63. #89759C22semidirect
64. #89756C22semidirect
65. #89733C22semidirect
66. #89731C22semidirect
67. #89728C22semidirect
68. #89720C22semidirect
69. #89437C22semidirect
70. #89429C22semidirect
107. C22×C4×D7D4semidirect
177. C2×#396D7semidirect
279. C2×C4×D7C2×D4semidirect
345. #396C2×D7semidirect
727. C2×C7#2618semidirect
841. C7C2×#2618semidirect
895. C2#11734868direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#64572
C22×D7×C4⋊C42
C22×#64462
C22×#64472
C2×C7×#3962
C2×#897662
C2×#897592
C2×#897562
C2×#897312
C2×#897282
C2×#897202
C2×#897332
#117348682
C2×#894372
C2×#894292
C2×#26187